class: center, middle, inverse, title-slide # <font class = "title-panel"> PPOL561 | Accelerated Statistics for Public Policy II</font> <font size=6, face="bold"> Week 5 </font> <br> <br> <font size=100, face="bold"> Panel Data<br>&<br>Difference-in-Difference </font> ### <font class = "title-footer">  Prof. Eric Dunford  ◆  Georgetown University  ◆  McCourt School of Public Policy  ◆  <a href="mailto:eric.dunford@georgetown.edu" class="email">eric.dunford@georgetown.edu</a></font> --- layout: true <div class="slide-footer"><span> PPOL561 | Accelerated Statistics for Public Policy II &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; Week 5 <!-- Week of the Footer Here --> &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; Panel Data & DID <!-- Title of the lecture here --> </span></div> --- class: outline # Outline for Today ![:space 10 ] - Discuss **Panel Data** ![:space 5 ] - Delve into **Difference-in-Difference** models --- class: newsection # Panel Data --- ## The problem `$$y_{it} = \beta_0 + \beta_1 x_{it} + \epsilon_{it}$$` OLS assumes `\(cor(x,\epsilon) = 0\)`, when violated we get biased results. This is known as **omitted variable bias** because some factor correlated with `\(y\)` and `\(x\)` is unaccounted for and distorting our estimates. It can be difficult to account for _all_ potential confounders, especially when concepts are difficult or impossible to measure. --- ## The problem `$$crime_{it} = \beta_0 + \beta_1 police_{it} + \epsilon_{it}$$` OLS assumes `\(cor(x,\epsilon) = 0\)`, when violated we get biased results. This is known as **omitted variable bias** because some factor correlated with `\(y\)` and `\(x\)` is unaccounted for and distorting our estimates. It can be difficult to account for _all_ potential confounders, especially when concepts are difficult or impossible to measure. - history of segregation in a city ( `\(hs\)` ) - culture ( `\(cl\)` ) - quality of life ( `\(ql\)` ) - ... `$$crime_{it} = \beta_0 + \beta_1 police_{it} + ( hs_i + cl_i + ql_i + \dots + \nu_{it} )$$` --- ## The problem We might never be able to measure everything that makes a place or time what it is, but we _can_ control for them. We do this by putting in a **dummy variable** that soaks up all the unique features of a specific **unit** (e.g. a state, a time period, a dyad, a country, etc.). -- .center[ <table> <thead> <tr> <th style="text-align:center;"> i </th> <th style="text-align:center;"> t </th> <th style="text-align:center;"> history </th> <th style="text-align:center;"> culture </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 1.0 </td> <td style="text-align:center;"> 3.4 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 1.0 </td> <td style="text-align:center;"> 3.4 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 1.0 </td> <td style="text-align:center;"> 3.4 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 4.0 </td> <td style="text-align:center;"> 10.2 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 4.0 </td> <td style="text-align:center;"> 10.2 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 4.0 </td> <td style="text-align:center;"> 10.2 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 2.3 </td> <td style="text-align:center;"> 9.8 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 2.3 </td> <td style="text-align:center;"> 9.8 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 2.3 </td> <td style="text-align:center;"> 9.8 </td> </tr> </tbody> </table> ] --- ## The problem We might never be able to measure everything that makes a place or time what it is, but we _can_ control for them. We do this by putting in a **dummy variable** that soaks up all the unique features of a specific **unit** (e.g. a state, a time period, a dyad, a country, etc.). .center[ <table> <thead> <tr> <th style="text-align:center;"> i </th> <th style="text-align:center;"> t </th> <th style="text-align:center;"> city1 </th> <th style="text-align:center;"> city2 </th> <th style="text-align:center;"> city3 </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> <td style="text-align:center;"> 0 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 0 </td> <td style="text-align:center;"> 1 </td> </tr> </tbody> </table> ] --- ## The problem We might never be able to measure everything that makes a place or time what it is, but we _can_ control for them. We do this by putting in a **dummy variable** that soaks up all the unique features of a specific **unit** (e.g. a state, a time period, a dyad, a country, etc.). `$$crime_{it} = \beta_1 police_{it} + \\\alpha_1{city_1} + \alpha_2{city_2} + \dots + \alpha_i{city_i} + \nu_{it}$$` <br> `$$crime_{1t} = \beta_1 police_{1t} +\\ \alpha_1(1) + \alpha_2(0) + \dots + \alpha_i(0) + \nu_{1t}$$` --- ## The problem We might never be able to measure everything that makes a place or time what it is, but we _can_ control for them. We do this by putting in a **dummy variable** that soaks up all the unique features of a specific **unit** (e.g. a state, a time period, a dyad, a country, etc.). `$$crime_{1t} = \alpha_1 + \beta_1 police_{1t} + \nu_{1t}$$` `$$crime_{2t} = \alpha_2 + \beta_1 police_{2t} + \nu_{2t}$$` `$$\vdots$$` `$$crime_{it} = \alpha_i + \beta_1 police_{it} + \nu_{it}$$` --- ## Let's simulate to see it in practice ```r set.seed(1234) # set seed to replicate N_cities = 50 # No. of Fake cities city = paste0("city",1:N_cities) # City name ID city_effect = rnorm(N_cities, # Baseline mean for mean = 20,sd = 5) # each city year = 1990:2000 # Fake year range D = expand.grid(city=city,year=year) # Combine city-years D = left_join(D,tibble(city,city_effect)) # merge data D ``` ``` ## city year city_effect ## 1 city1 1990 13.964671 ## 2 city2 1990 21.387146 ## 3 city3 1990 25.422206 ## 4 city4 1990 8.271511 ## 5 city5 1990 22.145623 ## 6 city6 1990 22.530279 ## 7 city7 1990 17.126300 ## 8 city8 1990 17.266841 ## 9 city9 1990 17.177740 ## 10 city10 1990 15.549811 ## 11 city11 1990 17.614037 ## 12 city12 1990 15.008068 ## 13 city13 1990 16.118731 ## 14 city14 1990 20.322294 ## 15 city15 1990 24.797470 ## 16 city16 1990 19.448573 ## 17 city17 1990 17.444952 ## 18 city18 1990 15.444023 ## 19 city19 1990 15.814142 ## 20 city20 1990 32.079176 ## 21 city21 1990 20.670441 ## 22 city22 1990 17.546571 ## 23 city23 1990 17.797261 ## 24 city24 1990 22.297947 ## 25 city25 1990 16.531399 ## 26 city26 1990 12.758975 ## 27 city27 1990 22.873779 ## 28 city28 1990 14.881721 ## 29 city29 1990 19.924308 ## 30 city30 1990 15.320257 ## 31 city31 1990 25.511488 ## 32 city32 1990 17.622035 ## 33 city33 1990 16.452800 ## 34 city34 1990 17.493710 ## 35 city35 1990 11.854533 ## 36 city36 1990 14.161904 ## 37 city37 1990 9.099802 ## 38 city38 1990 13.295034 ## 39 city39 1990 18.528531 ## 40 city40 1990 17.670512 ## 41 city41 1990 27.247481 ## 42 city42 1990 14.656786 ## 43 city43 1990 15.723177 ## 44 city44 1990 18.596885 ## 45 city45 1990 15.028300 ## 46 city46 1990 15.157428 ## 47 city47 1990 14.463409 ## 48 city48 1990 13.740071 ## 49 city49 1990 17.380859 ## 50 city50 1990 17.515750 ## 51 city1 1991 13.964671 ## 52 city2 1991 21.387146 ## 53 city3 1991 25.422206 ## 54 city4 1991 8.271511 ## 55 city5 1991 22.145623 ## 56 city6 1991 22.530279 ## 57 city7 1991 17.126300 ## 58 city8 1991 17.266841 ## 59 city9 1991 17.177740 ## 60 city10 1991 15.549811 ## 61 city11 1991 17.614037 ## 62 city12 1991 15.008068 ## 63 city13 1991 16.118731 ## 64 city14 1991 20.322294 ## 65 city15 1991 24.797470 ## 66 city16 1991 19.448573 ## 67 city17 1991 17.444952 ## 68 city18 1991 15.444023 ## 69 city19 1991 15.814142 ## 70 city20 1991 32.079176 ## 71 city21 1991 20.670441 ## 72 city22 1991 17.546571 ## 73 city23 1991 17.797261 ## 74 city24 1991 22.297947 ## 75 city25 1991 16.531399 ## 76 city26 1991 12.758975 ## 77 city27 1991 22.873779 ## 78 city28 1991 14.881721 ## 79 city29 1991 19.924308 ## 80 city30 1991 15.320257 ## 81 city31 1991 25.511488 ## 82 city32 1991 17.622035 ## 83 city33 1991 16.452800 ## 84 city34 1991 17.493710 ## 85 city35 1991 11.854533 ## 86 city36 1991 14.161904 ## 87 city37 1991 9.099802 ## 88 city38 1991 13.295034 ## 89 city39 1991 18.528531 ## 90 city40 1991 17.670512 ## 91 city41 1991 27.247481 ## 92 city42 1991 14.656786 ## 93 city43 1991 15.723177 ## 94 city44 1991 18.596885 ## 95 city45 1991 15.028300 ## 96 city46 1991 15.157428 ## 97 city47 1991 14.463409 ## 98 city48 1991 13.740071 ## 99 city49 1991 17.380859 ## 100 city50 1991 17.515750 ## 101 city1 1992 13.964671 ## 102 city2 1992 21.387146 ## 103 city3 1992 25.422206 ## 104 city4 1992 8.271511 ## 105 city5 1992 22.145623 ## 106 city6 1992 22.530279 ## 107 city7 1992 17.126300 ## 108 city8 1992 17.266841 ## 109 city9 1992 17.177740 ## 110 city10 1992 15.549811 ## 111 city11 1992 17.614037 ## 112 city12 1992 15.008068 ## 113 city13 1992 16.118731 ## 114 city14 1992 20.322294 ## 115 city15 1992 24.797470 ## 116 city16 1992 19.448573 ## 117 city17 1992 17.444952 ## 118 city18 1992 15.444023 ## 119 city19 1992 15.814142 ## 120 city20 1992 32.079176 ## 121 city21 1992 20.670441 ## 122 city22 1992 17.546571 ## 123 city23 1992 17.797261 ## 124 city24 1992 22.297947 ## 125 city25 1992 16.531399 ## 126 city26 1992 12.758975 ## 127 city27 1992 22.873779 ## 128 city28 1992 14.881721 ## 129 city29 1992 19.924308 ## 130 city30 1992 15.320257 ## 131 city31 1992 25.511488 ## 132 city32 1992 17.622035 ## 133 city33 1992 16.452800 ## 134 city34 1992 17.493710 ## 135 city35 1992 11.854533 ## 136 city36 1992 14.161904 ## 137 city37 1992 9.099802 ## 138 city38 1992 13.295034 ## 139 city39 1992 18.528531 ## 140 city40 1992 17.670512 ## 141 city41 1992 27.247481 ## 142 city42 1992 14.656786 ## 143 city43 1992 15.723177 ## 144 city44 1992 18.596885 ## 145 city45 1992 15.028300 ## 146 city46 1992 15.157428 ## 147 city47 1992 14.463409 ## 148 city48 1992 13.740071 ## 149 city49 1992 17.380859 ## 150 city50 1992 17.515750 ## 151 city1 1993 13.964671 ## 152 city2 1993 21.387146 ## 153 city3 1993 25.422206 ## 154 city4 1993 8.271511 ## 155 city5 1993 22.145623 ## 156 city6 1993 22.530279 ## 157 city7 1993 17.126300 ## 158 city8 1993 17.266841 ## 159 city9 1993 17.177740 ## 160 city10 1993 15.549811 ## 161 city11 1993 17.614037 ## 162 city12 1993 15.008068 ## 163 city13 1993 16.118731 ## 164 city14 1993 20.322294 ## 165 city15 1993 24.797470 ## 166 city16 1993 19.448573 ## 167 city17 1993 17.444952 ## 168 city18 1993 15.444023 ## 169 city19 1993 15.814142 ## 170 city20 1993 32.079176 ## 171 city21 1993 20.670441 ## 172 city22 1993 17.546571 ## 173 city23 1993 17.797261 ## 174 city24 1993 22.297947 ## 175 city25 1993 16.531399 ## 176 city26 1993 12.758975 ## 177 city27 1993 22.873779 ## 178 city28 1993 14.881721 ## 179 city29 1993 19.924308 ## 180 city30 1993 15.320257 ## 181 city31 1993 25.511488 ## 182 city32 1993 17.622035 ## 183 city33 1993 16.452800 ## 184 city34 1993 17.493710 ## 185 city35 1993 11.854533 ## 186 city36 1993 14.161904 ## 187 city37 1993 9.099802 ## 188 city38 1993 13.295034 ## 189 city39 1993 18.528531 ## 190 city40 1993 17.670512 ## 191 city41 1993 27.247481 ## 192 city42 1993 14.656786 ## 193 city43 1993 15.723177 ## 194 city44 1993 18.596885 ## 195 city45 1993 15.028300 ## 196 city46 1993 15.157428 ## 197 city47 1993 14.463409 ## 198 city48 1993 13.740071 ## 199 city49 1993 17.380859 ## 200 city50 1993 17.515750 ## 201 city1 1994 13.964671 ## 202 city2 1994 21.387146 ## 203 city3 1994 25.422206 ## 204 city4 1994 8.271511 ## 205 city5 1994 22.145623 ## 206 city6 1994 22.530279 ## 207 city7 1994 17.126300 ## 208 city8 1994 17.266841 ## 209 city9 1994 17.177740 ## 210 city10 1994 15.549811 ## 211 city11 1994 17.614037 ## 212 city12 1994 15.008068 ## 213 city13 1994 16.118731 ## 214 city14 1994 20.322294 ## 215 city15 1994 24.797470 ## 216 city16 1994 19.448573 ## 217 city17 1994 17.444952 ## 218 city18 1994 15.444023 ## 219 city19 1994 15.814142 ## 220 city20 1994 32.079176 ## 221 city21 1994 20.670441 ## 222 city22 1994 17.546571 ## 223 city23 1994 17.797261 ## 224 city24 1994 22.297947 ## 225 city25 1994 16.531399 ## 226 city26 1994 12.758975 ## 227 city27 1994 22.873779 ## 228 city28 1994 14.881721 ## 229 city29 1994 19.924308 ## 230 city30 1994 15.320257 ## 231 city31 1994 25.511488 ## 232 city32 1994 17.622035 ## 233 city33 1994 16.452800 ## 234 city34 1994 17.493710 ## 235 city35 1994 11.854533 ## 236 city36 1994 14.161904 ## 237 city37 1994 9.099802 ## 238 city38 1994 13.295034 ## 239 city39 1994 18.528531 ## 240 city40 1994 17.670512 ## 241 city41 1994 27.247481 ## 242 city42 1994 14.656786 ## 243 city43 1994 15.723177 ## 244 city44 1994 18.596885 ## 245 city45 1994 15.028300 ## 246 city46 1994 15.157428 ## 247 city47 1994 14.463409 ## 248 city48 1994 13.740071 ## 249 city49 1994 17.380859 ## 250 city50 1994 17.515750 ## 251 city1 1995 13.964671 ## 252 city2 1995 21.387146 ## 253 city3 1995 25.422206 ## 254 city4 1995 8.271511 ## 255 city5 1995 22.145623 ## 256 city6 1995 22.530279 ## 257 city7 1995 17.126300 ## 258 city8 1995 17.266841 ## 259 city9 1995 17.177740 ## 260 city10 1995 15.549811 ## 261 city11 1995 17.614037 ## 262 city12 1995 15.008068 ## 263 city13 1995 16.118731 ## 264 city14 1995 20.322294 ## 265 city15 1995 24.797470 ## 266 city16 1995 19.448573 ## 267 city17 1995 17.444952 ## 268 city18 1995 15.444023 ## 269 city19 1995 15.814142 ## 270 city20 1995 32.079176 ## 271 city21 1995 20.670441 ## 272 city22 1995 17.546571 ## 273 city23 1995 17.797261 ## 274 city24 1995 22.297947 ## 275 city25 1995 16.531399 ## 276 city26 1995 12.758975 ## 277 city27 1995 22.873779 ## 278 city28 1995 14.881721 ## 279 city29 1995 19.924308 ## 280 city30 1995 15.320257 ## 281 city31 1995 25.511488 ## 282 city32 1995 17.622035 ## 283 city33 1995 16.452800 ## 284 city34 1995 17.493710 ## 285 city35 1995 11.854533 ## 286 city36 1995 14.161904 ## 287 city37 1995 9.099802 ## 288 city38 1995 13.295034 ## 289 city39 1995 18.528531 ## 290 city40 1995 17.670512 ## 291 city41 1995 27.247481 ## 292 city42 1995 14.656786 ## 293 city43 1995 15.723177 ## 294 city44 1995 18.596885 ## 295 city45 1995 15.028300 ## 296 city46 1995 15.157428 ## 297 city47 1995 14.463409 ## 298 city48 1995 13.740071 ## 299 city49 1995 17.380859 ## 300 city50 1995 17.515750 ## 301 city1 1996 13.964671 ## 302 city2 1996 21.387146 ## 303 city3 1996 25.422206 ## 304 city4 1996 8.271511 ## 305 city5 1996 22.145623 ## 306 city6 1996 22.530279 ## 307 city7 1996 17.126300 ## 308 city8 1996 17.266841 ## 309 city9 1996 17.177740 ## 310 city10 1996 15.549811 ## 311 city11 1996 17.614037 ## 312 city12 1996 15.008068 ## 313 city13 1996 16.118731 ## 314 city14 1996 20.322294 ## 315 city15 1996 24.797470 ## 316 city16 1996 19.448573 ## 317 city17 1996 17.444952 ## 318 city18 1996 15.444023 ## 319 city19 1996 15.814142 ## 320 city20 1996 32.079176 ## 321 city21 1996 20.670441 ## 322 city22 1996 17.546571 ## 323 city23 1996 17.797261 ## 324 city24 1996 22.297947 ## 325 city25 1996 16.531399 ## 326 city26 1996 12.758975 ## 327 city27 1996 22.873779 ## 328 city28 1996 14.881721 ## 329 city29 1996 19.924308 ## 330 city30 1996 15.320257 ## 331 city31 1996 25.511488 ## 332 city32 1996 17.622035 ## 333 city33 1996 16.452800 ## 334 city34 1996 17.493710 ## 335 city35 1996 11.854533 ## 336 city36 1996 14.161904 ## 337 city37 1996 9.099802 ## 338 city38 1996 13.295034 ## 339 city39 1996 18.528531 ## 340 city40 1996 17.670512 ## 341 city41 1996 27.247481 ## 342 city42 1996 14.656786 ## 343 city43 1996 15.723177 ## 344 city44 1996 18.596885 ## 345 city45 1996 15.028300 ## 346 city46 1996 15.157428 ## 347 city47 1996 14.463409 ## 348 city48 1996 13.740071 ## 349 city49 1996 17.380859 ## 350 city50 1996 17.515750 ## 351 city1 1997 13.964671 ## 352 city2 1997 21.387146 ## 353 city3 1997 25.422206 ## 354 city4 1997 8.271511 ## 355 city5 1997 22.145623 ## 356 city6 1997 22.530279 ## 357 city7 1997 17.126300 ## 358 city8 1997 17.266841 ## 359 city9 1997 17.177740 ## 360 city10 1997 15.549811 ## 361 city11 1997 17.614037 ## 362 city12 1997 15.008068 ## 363 city13 1997 16.118731 ## 364 city14 1997 20.322294 ## 365 city15 1997 24.797470 ## 366 city16 1997 19.448573 ## 367 city17 1997 17.444952 ## 368 city18 1997 15.444023 ## 369 city19 1997 15.814142 ## 370 city20 1997 32.079176 ## 371 city21 1997 20.670441 ## 372 city22 1997 17.546571 ## 373 city23 1997 17.797261 ## 374 city24 1997 22.297947 ## 375 city25 1997 16.531399 ## 376 city26 1997 12.758975 ## 377 city27 1997 22.873779 ## 378 city28 1997 14.881721 ## 379 city29 1997 19.924308 ## 380 city30 1997 15.320257 ## 381 city31 1997 25.511488 ## 382 city32 1997 17.622035 ## 383 city33 1997 16.452800 ## 384 city34 1997 17.493710 ## 385 city35 1997 11.854533 ## 386 city36 1997 14.161904 ## 387 city37 1997 9.099802 ## 388 city38 1997 13.295034 ## 389 city39 1997 18.528531 ## 390 city40 1997 17.670512 ## 391 city41 1997 27.247481 ## 392 city42 1997 14.656786 ## 393 city43 1997 15.723177 ## 394 city44 1997 18.596885 ## 395 city45 1997 15.028300 ## 396 city46 1997 15.157428 ## 397 city47 1997 14.463409 ## 398 city48 1997 13.740071 ## 399 city49 1997 17.380859 ## 400 city50 1997 17.515750 ## 401 city1 1998 13.964671 ## 402 city2 1998 21.387146 ## 403 city3 1998 25.422206 ## 404 city4 1998 8.271511 ## 405 city5 1998 22.145623 ## 406 city6 1998 22.530279 ## 407 city7 1998 17.126300 ## 408 city8 1998 17.266841 ## 409 city9 1998 17.177740 ## 410 city10 1998 15.549811 ## 411 city11 1998 17.614037 ## 412 city12 1998 15.008068 ## 413 city13 1998 16.118731 ## 414 city14 1998 20.322294 ## 415 city15 1998 24.797470 ## 416 city16 1998 19.448573 ## 417 city17 1998 17.444952 ## 418 city18 1998 15.444023 ## 419 city19 1998 15.814142 ## 420 city20 1998 32.079176 ## 421 city21 1998 20.670441 ## 422 city22 1998 17.546571 ## 423 city23 1998 17.797261 ## 424 city24 1998 22.297947 ## 425 city25 1998 16.531399 ## 426 city26 1998 12.758975 ## 427 city27 1998 22.873779 ## 428 city28 1998 14.881721 ## 429 city29 1998 19.924308 ## 430 city30 1998 15.320257 ## 431 city31 1998 25.511488 ## 432 city32 1998 17.622035 ## 433 city33 1998 16.452800 ## 434 city34 1998 17.493710 ## 435 city35 1998 11.854533 ## 436 city36 1998 14.161904 ## 437 city37 1998 9.099802 ## 438 city38 1998 13.295034 ## 439 city39 1998 18.528531 ## 440 city40 1998 17.670512 ## 441 city41 1998 27.247481 ## 442 city42 1998 14.656786 ## 443 city43 1998 15.723177 ## 444 city44 1998 18.596885 ## 445 city45 1998 15.028300 ## 446 city46 1998 15.157428 ## 447 city47 1998 14.463409 ## 448 city48 1998 13.740071 ## 449 city49 1998 17.380859 ## 450 city50 1998 17.515750 ## 451 city1 1999 13.964671 ## 452 city2 1999 21.387146 ## 453 city3 1999 25.422206 ## 454 city4 1999 8.271511 ## 455 city5 1999 22.145623 ## 456 city6 1999 22.530279 ## 457 city7 1999 17.126300 ## 458 city8 1999 17.266841 ## 459 city9 1999 17.177740 ## 460 city10 1999 15.549811 ## 461 city11 1999 17.614037 ## 462 city12 1999 15.008068 ## 463 city13 1999 16.118731 ## 464 city14 1999 20.322294 ## 465 city15 1999 24.797470 ## 466 city16 1999 19.448573 ## 467 city17 1999 17.444952 ## 468 city18 1999 15.444023 ## 469 city19 1999 15.814142 ## 470 city20 1999 32.079176 ## 471 city21 1999 20.670441 ## 472 city22 1999 17.546571 ## 473 city23 1999 17.797261 ## 474 city24 1999 22.297947 ## 475 city25 1999 16.531399 ## 476 city26 1999 12.758975 ## 477 city27 1999 22.873779 ## 478 city28 1999 14.881721 ## 479 city29 1999 19.924308 ## 480 city30 1999 15.320257 ## 481 city31 1999 25.511488 ## 482 city32 1999 17.622035 ## 483 city33 1999 16.452800 ## 484 city34 1999 17.493710 ## 485 city35 1999 11.854533 ## 486 city36 1999 14.161904 ## 487 city37 1999 9.099802 ## 488 city38 1999 13.295034 ## 489 city39 1999 18.528531 ## 490 city40 1999 17.670512 ## 491 city41 1999 27.247481 ## 492 city42 1999 14.656786 ## 493 city43 1999 15.723177 ## 494 city44 1999 18.596885 ## 495 city45 1999 15.028300 ## 496 city46 1999 15.157428 ## 497 city47 1999 14.463409 ## 498 city48 1999 13.740071 ## 499 city49 1999 17.380859 ## 500 city50 1999 17.515750 ## 501 city1 2000 13.964671 ## 502 city2 2000 21.387146 ## 503 city3 2000 25.422206 ## 504 city4 2000 8.271511 ## 505 city5 2000 22.145623 ## 506 city6 2000 22.530279 ## 507 city7 2000 17.126300 ## 508 city8 2000 17.266841 ## 509 city9 2000 17.177740 ## 510 city10 2000 15.549811 ## 511 city11 2000 17.614037 ## 512 city12 2000 15.008068 ## 513 city13 2000 16.118731 ## 514 city14 2000 20.322294 ## 515 city15 2000 24.797470 ## 516 city16 2000 19.448573 ## 517 city17 2000 17.444952 ## 518 city18 2000 15.444023 ## 519 city19 2000 15.814142 ## 520 city20 2000 32.079176 ## 521 city21 2000 20.670441 ## 522 city22 2000 17.546571 ## 523 city23 2000 17.797261 ## 524 city24 2000 22.297947 ## 525 city25 2000 16.531399 ## 526 city26 2000 12.758975 ## 527 city27 2000 22.873779 ## 528 city28 2000 14.881721 ## 529 city29 2000 19.924308 ## 530 city30 2000 15.320257 ## 531 city31 2000 25.511488 ## 532 city32 2000 17.622035 ## 533 city33 2000 16.452800 ## 534 city34 2000 17.493710 ## 535 city35 2000 11.854533 ## 536 city36 2000 14.161904 ## 537 city37 2000 9.099802 ## 538 city38 2000 13.295034 ## 539 city39 2000 18.528531 ## 540 city40 2000 17.670512 ## 541 city41 2000 27.247481 ## 542 city42 2000 14.656786 ## 543 city43 2000 15.723177 ## 544 city44 2000 18.596885 ## 545 city45 2000 15.028300 ## 546 city46 2000 15.157428 ## 547 city47 2000 14.463409 ## 548 city48 2000 13.740071 ## 549 city49 2000 17.380859 ## 550 city50 2000 17.515750 ``` --- ## Let's simulate to see it in practice ```r set.seed(1234) # set seed to replicate N_cities = 50 # No. of Fake cities city = paste0("city",1:N_cities) # City name ID city_effect = rnorm(N_cities, # Baseline mean for mean = 20,sd = 5) # each city year = 1990:2000 # Fake year range D = expand.grid(city=city,year=year) # Combine city-years D = left_join(D,tibble(city,city_effect)) # merge data *D %>% arrange(city) ``` ``` ## city year city_effect ## 1 city1 1990 13.964671 ## 2 city1 1991 13.964671 ## 3 city1 1992 13.964671 ## 4 city1 1993 13.964671 ## 5 city1 1994 13.964671 ## 6 city1 1995 13.964671 ## 7 city1 1996 13.964671 ## 8 city1 1997 13.964671 ## 9 city1 1998 13.964671 ## 10 city1 1999 13.964671 ## 11 city1 2000 13.964671 ## 12 city10 1990 15.549811 ## 13 city10 1991 15.549811 ## 14 city10 1992 15.549811 ## 15 city10 1993 15.549811 ## 16 city10 1994 15.549811 ## 17 city10 1995 15.549811 ## 18 city10 1996 15.549811 ## 19 city10 1997 15.549811 ## 20 city10 1998 15.549811 ## 21 city10 1999 15.549811 ## 22 city10 2000 15.549811 ## 23 city11 1990 17.614037 ## 24 city11 1991 17.614037 ## 25 city11 1992 17.614037 ## 26 city11 1993 17.614037 ## 27 city11 1994 17.614037 ## 28 city11 1995 17.614037 ## 29 city11 1996 17.614037 ## 30 city11 1997 17.614037 ## 31 city11 1998 17.614037 ## 32 city11 1999 17.614037 ## 33 city11 2000 17.614037 ## 34 city12 1990 15.008068 ## 35 city12 1991 15.008068 ## 36 city12 1992 15.008068 ## 37 city12 1993 15.008068 ## 38 city12 1994 15.008068 ## 39 city12 1995 15.008068 ## 40 city12 1996 15.008068 ## 41 city12 1997 15.008068 ## 42 city12 1998 15.008068 ## 43 city12 1999 15.008068 ## 44 city12 2000 15.008068 ## 45 city13 1990 16.118731 ## 46 city13 1991 16.118731 ## 47 city13 1992 16.118731 ## 48 city13 1993 16.118731 ## 49 city13 1994 16.118731 ## 50 city13 1995 16.118731 ## 51 city13 1996 16.118731 ## 52 city13 1997 16.118731 ## 53 city13 1998 16.118731 ## 54 city13 1999 16.118731 ## 55 city13 2000 16.118731 ## 56 city14 1990 20.322294 ## 57 city14 1991 20.322294 ## 58 city14 1992 20.322294 ## 59 city14 1993 20.322294 ## 60 city14 1994 20.322294 ## 61 city14 1995 20.322294 ## 62 city14 1996 20.322294 ## 63 city14 1997 20.322294 ## 64 city14 1998 20.322294 ## 65 city14 1999 20.322294 ## 66 city14 2000 20.322294 ## 67 city15 1990 24.797470 ## 68 city15 1991 24.797470 ## 69 city15 1992 24.797470 ## 70 city15 1993 24.797470 ## 71 city15 1994 24.797470 ## 72 city15 1995 24.797470 ## 73 city15 1996 24.797470 ## 74 city15 1997 24.797470 ## 75 city15 1998 24.797470 ## 76 city15 1999 24.797470 ## 77 city15 2000 24.797470 ## 78 city16 1990 19.448573 ## 79 city16 1991 19.448573 ## 80 city16 1992 19.448573 ## 81 city16 1993 19.448573 ## 82 city16 1994 19.448573 ## 83 city16 1995 19.448573 ## 84 city16 1996 19.448573 ## 85 city16 1997 19.448573 ## 86 city16 1998 19.448573 ## 87 city16 1999 19.448573 ## 88 city16 2000 19.448573 ## 89 city17 1990 17.444952 ## 90 city17 1991 17.444952 ## 91 city17 1992 17.444952 ## 92 city17 1993 17.444952 ## 93 city17 1994 17.444952 ## 94 city17 1995 17.444952 ## 95 city17 1996 17.444952 ## 96 city17 1997 17.444952 ## 97 city17 1998 17.444952 ## 98 city17 1999 17.444952 ## 99 city17 2000 17.444952 ## 100 city18 1990 15.444023 ## 101 city18 1991 15.444023 ## 102 city18 1992 15.444023 ## 103 city18 1993 15.444023 ## 104 city18 1994 15.444023 ## 105 city18 1995 15.444023 ## 106 city18 1996 15.444023 ## 107 city18 1997 15.444023 ## 108 city18 1998 15.444023 ## 109 city18 1999 15.444023 ## 110 city18 2000 15.444023 ## 111 city19 1990 15.814142 ## 112 city19 1991 15.814142 ## 113 city19 1992 15.814142 ## 114 city19 1993 15.814142 ## 115 city19 1994 15.814142 ## 116 city19 1995 15.814142 ## 117 city19 1996 15.814142 ## 118 city19 1997 15.814142 ## 119 city19 1998 15.814142 ## 120 city19 1999 15.814142 ## 121 city19 2000 15.814142 ## 122 city2 1990 21.387146 ## 123 city2 1991 21.387146 ## 124 city2 1992 21.387146 ## 125 city2 1993 21.387146 ## 126 city2 1994 21.387146 ## 127 city2 1995 21.387146 ## 128 city2 1996 21.387146 ## 129 city2 1997 21.387146 ## 130 city2 1998 21.387146 ## 131 city2 1999 21.387146 ## 132 city2 2000 21.387146 ## 133 city20 1990 32.079176 ## 134 city20 1991 32.079176 ## 135 city20 1992 32.079176 ## 136 city20 1993 32.079176 ## 137 city20 1994 32.079176 ## 138 city20 1995 32.079176 ## 139 city20 1996 32.079176 ## 140 city20 1997 32.079176 ## 141 city20 1998 32.079176 ## 142 city20 1999 32.079176 ## 143 city20 2000 32.079176 ## 144 city21 1990 20.670441 ## 145 city21 1991 20.670441 ## 146 city21 1992 20.670441 ## 147 city21 1993 20.670441 ## 148 city21 1994 20.670441 ## 149 city21 1995 20.670441 ## 150 city21 1996 20.670441 ## 151 city21 1997 20.670441 ## 152 city21 1998 20.670441 ## 153 city21 1999 20.670441 ## 154 city21 2000 20.670441 ## 155 city22 1990 17.546571 ## 156 city22 1991 17.546571 ## 157 city22 1992 17.546571 ## 158 city22 1993 17.546571 ## 159 city22 1994 17.546571 ## 160 city22 1995 17.546571 ## 161 city22 1996 17.546571 ## 162 city22 1997 17.546571 ## 163 city22 1998 17.546571 ## 164 city22 1999 17.546571 ## 165 city22 2000 17.546571 ## 166 city23 1990 17.797261 ## 167 city23 1991 17.797261 ## 168 city23 1992 17.797261 ## 169 city23 1993 17.797261 ## 170 city23 1994 17.797261 ## 171 city23 1995 17.797261 ## 172 city23 1996 17.797261 ## 173 city23 1997 17.797261 ## 174 city23 1998 17.797261 ## 175 city23 1999 17.797261 ## 176 city23 2000 17.797261 ## 177 city24 1990 22.297947 ## 178 city24 1991 22.297947 ## 179 city24 1992 22.297947 ## 180 city24 1993 22.297947 ## 181 city24 1994 22.297947 ## 182 city24 1995 22.297947 ## 183 city24 1996 22.297947 ## 184 city24 1997 22.297947 ## 185 city24 1998 22.297947 ## 186 city24 1999 22.297947 ## 187 city24 2000 22.297947 ## 188 city25 1990 16.531399 ## 189 city25 1991 16.531399 ## 190 city25 1992 16.531399 ## 191 city25 1993 16.531399 ## 192 city25 1994 16.531399 ## 193 city25 1995 16.531399 ## 194 city25 1996 16.531399 ## 195 city25 1997 16.531399 ## 196 city25 1998 16.531399 ## 197 city25 1999 16.531399 ## 198 city25 2000 16.531399 ## 199 city26 1990 12.758975 ## 200 city26 1991 12.758975 ## 201 city26 1992 12.758975 ## 202 city26 1993 12.758975 ## 203 city26 1994 12.758975 ## 204 city26 1995 12.758975 ## 205 city26 1996 12.758975 ## 206 city26 1997 12.758975 ## 207 city26 1998 12.758975 ## 208 city26 1999 12.758975 ## 209 city26 2000 12.758975 ## 210 city27 1990 22.873779 ## 211 city27 1991 22.873779 ## 212 city27 1992 22.873779 ## 213 city27 1993 22.873779 ## 214 city27 1994 22.873779 ## 215 city27 1995 22.873779 ## 216 city27 1996 22.873779 ## 217 city27 1997 22.873779 ## 218 city27 1998 22.873779 ## 219 city27 1999 22.873779 ## 220 city27 2000 22.873779 ## 221 city28 1990 14.881721 ## 222 city28 1991 14.881721 ## 223 city28 1992 14.881721 ## 224 city28 1993 14.881721 ## 225 city28 1994 14.881721 ## 226 city28 1995 14.881721 ## 227 city28 1996 14.881721 ## 228 city28 1997 14.881721 ## 229 city28 1998 14.881721 ## 230 city28 1999 14.881721 ## 231 city28 2000 14.881721 ## 232 city29 1990 19.924308 ## 233 city29 1991 19.924308 ## 234 city29 1992 19.924308 ## 235 city29 1993 19.924308 ## 236 city29 1994 19.924308 ## 237 city29 1995 19.924308 ## 238 city29 1996 19.924308 ## 239 city29 1997 19.924308 ## 240 city29 1998 19.924308 ## 241 city29 1999 19.924308 ## 242 city29 2000 19.924308 ## 243 city3 1990 25.422206 ## 244 city3 1991 25.422206 ## 245 city3 1992 25.422206 ## 246 city3 1993 25.422206 ## 247 city3 1994 25.422206 ## 248 city3 1995 25.422206 ## 249 city3 1996 25.422206 ## 250 city3 1997 25.422206 ## 251 city3 1998 25.422206 ## 252 city3 1999 25.422206 ## 253 city3 2000 25.422206 ## 254 city30 1990 15.320257 ## 255 city30 1991 15.320257 ## 256 city30 1992 15.320257 ## 257 city30 1993 15.320257 ## 258 city30 1994 15.320257 ## 259 city30 1995 15.320257 ## 260 city30 1996 15.320257 ## 261 city30 1997 15.320257 ## 262 city30 1998 15.320257 ## 263 city30 1999 15.320257 ## 264 city30 2000 15.320257 ## 265 city31 1990 25.511488 ## 266 city31 1991 25.511488 ## 267 city31 1992 25.511488 ## 268 city31 1993 25.511488 ## 269 city31 1994 25.511488 ## 270 city31 1995 25.511488 ## 271 city31 1996 25.511488 ## 272 city31 1997 25.511488 ## 273 city31 1998 25.511488 ## 274 city31 1999 25.511488 ## 275 city31 2000 25.511488 ## 276 city32 1990 17.622035 ## 277 city32 1991 17.622035 ## 278 city32 1992 17.622035 ## 279 city32 1993 17.622035 ## 280 city32 1994 17.622035 ## 281 city32 1995 17.622035 ## 282 city32 1996 17.622035 ## 283 city32 1997 17.622035 ## 284 city32 1998 17.622035 ## 285 city32 1999 17.622035 ## 286 city32 2000 17.622035 ## 287 city33 1990 16.452800 ## 288 city33 1991 16.452800 ## 289 city33 1992 16.452800 ## 290 city33 1993 16.452800 ## 291 city33 1994 16.452800 ## 292 city33 1995 16.452800 ## 293 city33 1996 16.452800 ## 294 city33 1997 16.452800 ## 295 city33 1998 16.452800 ## 296 city33 1999 16.452800 ## 297 city33 2000 16.452800 ## 298 city34 1990 17.493710 ## 299 city34 1991 17.493710 ## 300 city34 1992 17.493710 ## 301 city34 1993 17.493710 ## 302 city34 1994 17.493710 ## 303 city34 1995 17.493710 ## 304 city34 1996 17.493710 ## 305 city34 1997 17.493710 ## 306 city34 1998 17.493710 ## 307 city34 1999 17.493710 ## 308 city34 2000 17.493710 ## 309 city35 1990 11.854533 ## 310 city35 1991 11.854533 ## 311 city35 1992 11.854533 ## 312 city35 1993 11.854533 ## 313 city35 1994 11.854533 ## 314 city35 1995 11.854533 ## 315 city35 1996 11.854533 ## 316 city35 1997 11.854533 ## 317 city35 1998 11.854533 ## 318 city35 1999 11.854533 ## 319 city35 2000 11.854533 ## 320 city36 1990 14.161904 ## 321 city36 1991 14.161904 ## 322 city36 1992 14.161904 ## 323 city36 1993 14.161904 ## 324 city36 1994 14.161904 ## 325 city36 1995 14.161904 ## 326 city36 1996 14.161904 ## 327 city36 1997 14.161904 ## 328 city36 1998 14.161904 ## 329 city36 1999 14.161904 ## 330 city36 2000 14.161904 ## 331 city37 1990 9.099802 ## 332 city37 1991 9.099802 ## 333 city37 1992 9.099802 ## 334 city37 1993 9.099802 ## 335 city37 1994 9.099802 ## 336 city37 1995 9.099802 ## 337 city37 1996 9.099802 ## 338 city37 1997 9.099802 ## 339 city37 1998 9.099802 ## 340 city37 1999 9.099802 ## 341 city37 2000 9.099802 ## 342 city38 1990 13.295034 ## 343 city38 1991 13.295034 ## 344 city38 1992 13.295034 ## 345 city38 1993 13.295034 ## 346 city38 1994 13.295034 ## 347 city38 1995 13.295034 ## 348 city38 1996 13.295034 ## 349 city38 1997 13.295034 ## 350 city38 1998 13.295034 ## 351 city38 1999 13.295034 ## 352 city38 2000 13.295034 ## 353 city39 1990 18.528531 ## 354 city39 1991 18.528531 ## 355 city39 1992 18.528531 ## 356 city39 1993 18.528531 ## 357 city39 1994 18.528531 ## 358 city39 1995 18.528531 ## 359 city39 1996 18.528531 ## 360 city39 1997 18.528531 ## 361 city39 1998 18.528531 ## 362 city39 1999 18.528531 ## 363 city39 2000 18.528531 ## 364 city4 1990 8.271511 ## 365 city4 1991 8.271511 ## 366 city4 1992 8.271511 ## 367 city4 1993 8.271511 ## 368 city4 1994 8.271511 ## 369 city4 1995 8.271511 ## 370 city4 1996 8.271511 ## 371 city4 1997 8.271511 ## 372 city4 1998 8.271511 ## 373 city4 1999 8.271511 ## 374 city4 2000 8.271511 ## 375 city40 1990 17.670512 ## 376 city40 1991 17.670512 ## 377 city40 1992 17.670512 ## 378 city40 1993 17.670512 ## 379 city40 1994 17.670512 ## 380 city40 1995 17.670512 ## 381 city40 1996 17.670512 ## 382 city40 1997 17.670512 ## 383 city40 1998 17.670512 ## 384 city40 1999 17.670512 ## 385 city40 2000 17.670512 ## 386 city41 1990 27.247481 ## 387 city41 1991 27.247481 ## 388 city41 1992 27.247481 ## 389 city41 1993 27.247481 ## 390 city41 1994 27.247481 ## 391 city41 1995 27.247481 ## 392 city41 1996 27.247481 ## 393 city41 1997 27.247481 ## 394 city41 1998 27.247481 ## 395 city41 1999 27.247481 ## 396 city41 2000 27.247481 ## 397 city42 1990 14.656786 ## 398 city42 1991 14.656786 ## 399 city42 1992 14.656786 ## 400 city42 1993 14.656786 ## 401 city42 1994 14.656786 ## 402 city42 1995 14.656786 ## 403 city42 1996 14.656786 ## 404 city42 1997 14.656786 ## 405 city42 1998 14.656786 ## 406 city42 1999 14.656786 ## 407 city42 2000 14.656786 ## 408 city43 1990 15.723177 ## 409 city43 1991 15.723177 ## 410 city43 1992 15.723177 ## 411 city43 1993 15.723177 ## 412 city43 1994 15.723177 ## 413 city43 1995 15.723177 ## 414 city43 1996 15.723177 ## 415 city43 1997 15.723177 ## 416 city43 1998 15.723177 ## 417 city43 1999 15.723177 ## 418 city43 2000 15.723177 ## 419 city44 1990 18.596885 ## 420 city44 1991 18.596885 ## 421 city44 1992 18.596885 ## 422 city44 1993 18.596885 ## 423 city44 1994 18.596885 ## 424 city44 1995 18.596885 ## 425 city44 1996 18.596885 ## 426 city44 1997 18.596885 ## 427 city44 1998 18.596885 ## 428 city44 1999 18.596885 ## 429 city44 2000 18.596885 ## 430 city45 1990 15.028300 ## 431 city45 1991 15.028300 ## 432 city45 1992 15.028300 ## 433 city45 1993 15.028300 ## 434 city45 1994 15.028300 ## 435 city45 1995 15.028300 ## 436 city45 1996 15.028300 ## 437 city45 1997 15.028300 ## 438 city45 1998 15.028300 ## 439 city45 1999 15.028300 ## 440 city45 2000 15.028300 ## 441 city46 1990 15.157428 ## 442 city46 1991 15.157428 ## 443 city46 1992 15.157428 ## 444 city46 1993 15.157428 ## 445 city46 1994 15.157428 ## 446 city46 1995 15.157428 ## 447 city46 1996 15.157428 ## 448 city46 1997 15.157428 ## 449 city46 1998 15.157428 ## 450 city46 1999 15.157428 ## 451 city46 2000 15.157428 ## 452 city47 1990 14.463409 ## 453 city47 1991 14.463409 ## 454 city47 1992 14.463409 ## 455 city47 1993 14.463409 ## 456 city47 1994 14.463409 ## 457 city47 1995 14.463409 ## 458 city47 1996 14.463409 ## 459 city47 1997 14.463409 ## 460 city47 1998 14.463409 ## 461 city47 1999 14.463409 ## 462 city47 2000 14.463409 ## 463 city48 1990 13.740071 ## 464 city48 1991 13.740071 ## 465 city48 1992 13.740071 ## 466 city48 1993 13.740071 ## 467 city48 1994 13.740071 ## 468 city48 1995 13.740071 ## 469 city48 1996 13.740071 ## 470 city48 1997 13.740071 ## 471 city48 1998 13.740071 ## 472 city48 1999 13.740071 ## 473 city48 2000 13.740071 ## 474 city49 1990 17.380859 ## 475 city49 1991 17.380859 ## 476 city49 1992 17.380859 ## 477 city49 1993 17.380859 ## 478 city49 1994 17.380859 ## 479 city49 1995 17.380859 ## 480 city49 1996 17.380859 ## 481 city49 1997 17.380859 ## 482 city49 1998 17.380859 ## 483 city49 1999 17.380859 ## 484 city49 2000 17.380859 ## 485 city5 1990 22.145623 ## 486 city5 1991 22.145623 ## 487 city5 1992 22.145623 ## 488 city5 1993 22.145623 ## 489 city5 1994 22.145623 ## 490 city5 1995 22.145623 ## 491 city5 1996 22.145623 ## 492 city5 1997 22.145623 ## 493 city5 1998 22.145623 ## 494 city5 1999 22.145623 ## 495 city5 2000 22.145623 ## 496 city50 1990 17.515750 ## 497 city50 1991 17.515750 ## 498 city50 1992 17.515750 ## 499 city50 1993 17.515750 ## 500 city50 1994 17.515750 ## 501 city50 1995 17.515750 ## 502 city50 1996 17.515750 ## 503 city50 1997 17.515750 ## 504 city50 1998 17.515750 ## 505 city50 1999 17.515750 ## 506 city50 2000 17.515750 ## 507 city6 1990 22.530279 ## 508 city6 1991 22.530279 ## 509 city6 1992 22.530279 ## 510 city6 1993 22.530279 ## 511 city6 1994 22.530279 ## 512 city6 1995 22.530279 ## 513 city6 1996 22.530279 ## 514 city6 1997 22.530279 ## 515 city6 1998 22.530279 ## 516 city6 1999 22.530279 ## 517 city6 2000 22.530279 ## 518 city7 1990 17.126300 ## 519 city7 1991 17.126300 ## 520 city7 1992 17.126300 ## 521 city7 1993 17.126300 ## 522 city7 1994 17.126300 ## 523 city7 1995 17.126300 ## 524 city7 1996 17.126300 ## 525 city7 1997 17.126300 ## 526 city7 1998 17.126300 ## 527 city7 1999 17.126300 ## 528 city7 2000 17.126300 ## 529 city8 1990 17.266841 ## 530 city8 1991 17.266841 ## 531 city8 1992 17.266841 ## 532 city8 1993 17.266841 ## 533 city8 1994 17.266841 ## 534 city8 1995 17.266841 ## 535 city8 1996 17.266841 ## 536 city8 1997 17.266841 ## 537 city8 1998 17.266841 ## 538 city8 1999 17.266841 ## 539 city8 2000 17.266841 ## 540 city9 1990 17.177740 ## 541 city9 1991 17.177740 ## 542 city9 1992 17.177740 ## 543 city9 1993 17.177740 ## 544 city9 1994 17.177740 ## 545 city9 1995 17.177740 ## 546 city9 1996 17.177740 ## 547 city9 1997 17.177740 ## 548 city9 1998 17.177740 ## 549 city9 1999 17.177740 ## 550 city9 2000 17.177740 ``` --- ## Let's simulate to see it in practice ```r N = nrow(D) # N obs (city-year) x = rnorm(N,mean=D$city_effect) # mean of x conditional on city error = rnorm(N,mean=D$city_effect,sd=3) # mean of y conditional # on city true_effect <- -.5 # population effect y = 1 + true_effect*x + error # true model D$crime <- y; D$police <- x # create variables head(D) ``` ``` ## city year city_effect crime police ## 1 city1 1990 13.964671 9.825787 12.158640 ## 2 city2 1990 21.387146 13.822031 20.805070 ## 3 city3 1990 25.422206 9.192298 24.313316 ## 4 city4 1990 8.271511 7.997333 7.256549 ## 5 city5 1990 22.145623 12.189742 21.983314 ## 6 city6 1990 22.530279 11.439846 23.093335 ``` --- ```r ggplot(D,aes(police,crime)) + geom_point(alpha=.4,size=4) + geom_smooth(method="lm",se=F) + theme(legend.position = "none") ``` <img src="week05-panel_data_and_did-ppol561_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" /> --- ```r *ggplot(D,aes(police,crime,color=factor(city))) + geom_point(alpha=.4,size=4) + geom_smooth(method="lm",se=F) + theme(legend.position = "none") ``` <img src="week05-panel_data_and_did-ppol561_files/figure-html/unnamed-chunk-7-1.png" style="display: block; margin: auto;" /> --- ```r # Remove city specific effects *D$police_star <- resid(lm(police ~ factor(city),data=D)) *D$crime_star <- resid(lm(crime ~ factor(city),data=D)) ggplot(D,aes(police_star,crime_star)) + geom_point(alpha=.4,size=4) + geom_smooth(method="lm",se=F) + theme(legend.position = "none") ``` <img src="week05-panel_data_and_did-ppol561_files/figure-html/unnamed-chunk-8-1.png" style="display: block; margin: auto;" /> --- **true effect** of police on crime `\(= -.5\)` ```r broom::tidy(lm(crime~police,data=D)) ``` ``` ## # A tibble: 2 x 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 2.38 0.526 4.53 7.10e- 6 ## 2 police 0.415 0.0287 14.5 2.17e-40 ``` -- ```r broom::tidy(lm(crime~police + factor(city),data=D)) ``` ``` ## # A tibble: 51 x 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 15.1 1.89 7.95 1.24e-14 ## 2 police -0.629 0.125 -5.04 6.54e- 7 ## 3 factor(city)city10 3.07 1.25 2.46 1.41e- 2 ## 4 factor(city)city11 7.18 1.32 5.44 8.35e- 8 ## 5 factor(city)city12 3.01 1.23 2.45 1.46e- 2 ## 6 factor(city)city13 3.39 1.26 2.70 7.15e- 3 ## 7 factor(city)city14 8.09 1.46 5.54 4.82e- 8 ## 8 factor(city)city15 13.9 1.85 7.53 2.35e-13 ## 9 factor(city)city16 7.49 1.45 5.16 3.60e- 7 ## 10 factor(city)city17 4.74 1.28 3.69 2.47e- 4 ## # … with 41 more rows ``` --- ## Do the coefficients for the fixed effects themselves tell us anything? -- <br><br> **Not really** - Recall that the intercept is meaningless when the independent variables cannot take on the value of `\(0\)`. (What does it mean to have 0 police in a city? State of nature?). - Fixed effects are treated as controls in the literature. The coefficients for the fixed effects are not reported explicitly (but usually denoted in the table reporting the results). --- ## Two approaches - **Least Squares Dummy Variables** &rarr; add a dummy for each unit (this is what we just did) -- - **De-meaning** &rarr; center `\(x\)` and `\(y\)` around their group mean + Recall from the simulation that `\(x\)` and `\(y\)` are centered around city-specific means? That, is each city has a different baseline for both `\(x\)` and `\(y\)`. + We want to remove this city-specific baselines. + We can by group mean centering -- `$$\tilde{y_t} = y_{it} - \bar{y}_{i}$$` `$$\tilde{x_t} = x_{it} - \bar{x}_{i}$$` `$$\tilde{\nu_t} = \nu_{it} - \bar{\nu}_{i}$$` $$ \tilde{y_t} = \beta_1\tilde{x_t} + \tilde{\nu}_t $$ --- ### The logic `$$y_{it} = \beta_0 + \beta_1 x_{it} + \epsilon_{it}$$` -- ![:space 3] `$$y_{it} = \beta_1 x_{it} + (\alpha_i + \nu_{it})$$` -- ![:space 3] `$$\bar{y}_i = \beta_1 \bar{x}_i + \alpha_i + \bar{\nu}_i$$` -- ![:space 3] ** `$$y_{it} -\bar{y}_i = \beta_1 (x_{it} - \bar{x}_i) + \alpha_i - \alpha_i + (\nu_{it} - \bar{\nu}_i)$$` ** ![:space 3] ** `$$\tilde{y}_t = \beta_1 \tilde{x}_t + \tilde{\nu}_t$$` ** --- .center[ <table> <thead> <tr> <th style="text-align:center;"> city </th> <th style="text-align:center;"> year </th> <th style="text-align:center;"> crime </th> <th style="text-align:center;"> city_mean </th> <th style="text-align:center;"> crime_group_mean_centered </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 9.83 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 9.83 - 6.56 = 3.27 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 13.82 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 13.82 - 11.87 = 1.95 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 9.19 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 9.19 - 11.98 = -2.79 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.00 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 8 - 6.53 = 1.47 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 12.19 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 12.19 - 11.73 = 0.46 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 11.44 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 11.44 - 12.41 = -0.97 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 12.06 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 12.06 - 9.75 = 2.31 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 14.46 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 14.46 - 9.03 = 5.43 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 5.34 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 5.34 - 9.46 = -4.12 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 12.39 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 12.39 - 8.19 = 4.2 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.58 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 7.58 - 11.13 = -3.55 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.63 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 7.63 - 8.61 = -0.98 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 10.52 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 10.52 - 8.37 = 2.15 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 11.90 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 11.9 - 10.57 = 1.33 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 9.01 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 9.01 - 13.46 = -4.45 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.32 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 8.32 - 10.04 = -1.72 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 14.91 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 14.91 - 9.21 = 5.7 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.56 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 8.56 - 7.47 = 1.09 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 5.73 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 5.73 - 8.42 = -2.69 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 14.90 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 14.9 - 16.97 = -2.07 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 14.50 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 14.5 - 10.15 = 4.35 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 11.04 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 11.04 - 9.06 = 1.98 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.39 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 7.39 - 9.45 = -2.06 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 11.84 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 11.84 - 12.04 = -0.2 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 10.02 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 10.02 - 8.64 = 1.38 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 12.62 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 12.62 - 9.08 = 3.54 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 10.49 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 10.49 - 11.91 = -1.42 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.66 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 7.66 - 8.03 = -0.37 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 13.82 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 13.82 - 10.43 = 3.39 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.44 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 7.44 - 6.46 = 0.98 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 18.23 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 18.23 - 15.92 = 2.31 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 13.03 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 13.03 - 10.01 = 3.02 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 4.94 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 4.94 - 9.24 = -4.3 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 11.11 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 11.11 - 9.33 = 1.78 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 2.24 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 2.24 - 7.12 = -4.88 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 3.34 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 3.34 - 8.16 = -4.82 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 5.49 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 5.49 - 6.83 = -1.34 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.02 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 8.02 - 6.54 = 1.48 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 10.26 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 10.26 - 10.66 = -0.4 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 14.23 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 14.23 - 10.23 = 4 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 15.54 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 15.54 - 14.62 = 0.92 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 6.18 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 6.18 - 8.31 = -2.13 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 8.37 - 9.72 = -1.35 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.25 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 8.25 - 10.98 = -2.73 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.56 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 8.56 - 7.68 = 0.88 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 4.96 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 4.96 - 8.89 = -3.93 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.45 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 8.45 - 10.78 = -2.33 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.74 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 7.74 - 7.5 = 0.24 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 7.10 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 7.1 - 8.63 = -1.53 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1990 </td> <td style="text-align:center;"> 8.82 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 8.82 - 9.33 = -0.51 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 5.83 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 5.83 - 6.56 = -0.73 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.00 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 10 - 11.87 = -1.87 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 13.06 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 13.06 - 11.98 = 1.08 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.86 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 6.86 - 6.53 = 0.33 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 11.87 - 11.73 = 0.14 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 12.75 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 12.75 - 12.41 = 0.34 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 12.92 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 12.92 - 9.75 = 3.17 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 8.69 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 8.69 - 9.03 = -0.34 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 9.10 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 9.1 - 9.46 = -0.36 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.33 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 10.33 - 8.19 = 2.14 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.13 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 6.13 - 11.13 = -5 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.46 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 10.46 - 8.61 = 1.85 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 8.01 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 8.01 - 8.37 = -0.36 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.32 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 7.32 - 10.57 = -3.25 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 8.08 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 8.08 - 13.46 = -5.38 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 8.16 - 10.04 = -1.88 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 6.83 - 9.21 = -2.38 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 5.10 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 5.1 - 7.47 = -2.37 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 13.45 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 13.45 - 8.42 = 5.03 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 13.42 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 13.42 - 16.97 = -3.55 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 14.42 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 14.42 - 10.15 = 4.27 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 11.80 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 11.8 - 9.06 = 2.74 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.22 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 6.22 - 9.45 = -3.23 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 9.94 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 9.94 - 12.04 = -2.1 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 7.12 - 8.64 = -1.52 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.91 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 7.91 - 9.08 = -1.17 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 11.71 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 11.71 - 11.91 = -0.2 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 11.68 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 11.68 - 8.03 = 3.65 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.40 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 10.4 - 10.43 = -0.03 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 2.05 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 2.05 - 6.46 = -4.41 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 12.96 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 12.96 - 15.92 = -2.96 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 4.13 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 4.13 - 10.01 = -5.88 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 12.63 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 12.63 - 9.24 = 3.39 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.17 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 7.17 - 9.33 = -2.16 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 4.41 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 4.41 - 7.12 = -2.71 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.49 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 6.49 - 8.16 = -1.67 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.46 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 7.46 - 6.83 = 0.63 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 2.87 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 2.87 - 6.54 = -3.67 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 10.57 - 10.66 = -0.09 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 7.23 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 7.23 - 10.23 = -3 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 14.77 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 14.77 - 14.62 = 0.15 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 9.67 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 9.67 - 8.31 = 1.36 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 10.25 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 10.25 - 9.72 = 0.53 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 14.86 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 14.86 - 10.98 = 3.88 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 8.64 - 7.68 = 0.96 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.28 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 6.28 - 8.89 = -2.61 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 13.86 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 13.86 - 10.78 = 3.08 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 6.82 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 6.82 - 7.5 = -0.68 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 11.86 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 11.86 - 8.63 = 3.23 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1991 </td> <td style="text-align:center;"> 12.38 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 12.38 - 9.33 = 3.05 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 9.54 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 9.54 - 6.56 = 2.98 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 15.92 - 11.87 = 4.05 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.26 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 12.26 - 11.98 = 0.28 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 1.88 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 1.88 - 6.53 = -4.65 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 10.93 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 10.93 - 11.73 = -0.8 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 9.94 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 9.94 - 12.41 = -2.47 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 10.66 - 9.75 = 0.91 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 7.36 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 7.36 - 9.03 = -1.67 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.07 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 12.07 - 9.46 = 2.61 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 5.48 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 5.48 - 8.19 = -2.71 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 15.50 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 15.5 - 11.13 = 4.37 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.98 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 12.98 - 8.61 = 4.37 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 7.92 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 7.92 - 8.37 = -0.45 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 11.67 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 11.67 - 10.57 = 1.1 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.07 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 12.07 - 13.46 = -1.39 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 6.79 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 6.79 - 10.04 = -3.25 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 0.90 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 0.9 - 9.21 = -8.31 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.68 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 8.68 - 7.47 = 1.21 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.96 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 8.96 - 8.42 = 0.54 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 21.23 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 21.23 - 16.97 = 4.26 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 4.50 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 4.5 - 10.15 = -5.65 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 7.77 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 7.77 - 9.06 = -1.29 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.71 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 12.71 - 9.45 = 3.26 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 14.09 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 14.09 - 12.04 = 2.05 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.93 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 8.93 - 8.64 = 0.29 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 5.94 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 5.94 - 9.08 = -3.14 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 13.60 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 13.6 - 11.91 = 1.69 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 6.21 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 6.21 - 8.03 = -1.82 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 11.19 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 11.19 - 10.43 = 0.76 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 6.94 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 6.94 - 6.46 = 0.48 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 18.69 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 18.69 - 15.92 = 2.77 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 13.04 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 13.04 - 10.01 = 3.03 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 12.75 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 12.75 - 9.24 = 3.51 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.44 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 8.44 - 9.33 = -0.89 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 5.56 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 5.56 - 7.12 = -1.56 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 6.04 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 6.04 - 8.16 = -2.12 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 9.09 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 9.09 - 6.83 = 2.26 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 7.00 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 7 - 6.54 = 0.46 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 10.21 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 10.21 - 10.66 = -0.45 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 11.08 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 11.08 - 10.23 = 0.85 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 16.93 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 16.93 - 14.62 = 2.31 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.95 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 8.95 - 8.31 = 0.64 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 16.29 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 16.29 - 9.72 = 6.57 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 7.27 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 7.27 - 10.98 = -3.71 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 3.15 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 3.15 - 7.68 = -4.53 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.46 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 8.46 - 8.89 = -0.43 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 13.22 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 13.22 - 10.78 = 2.44 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 8.51 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 8.51 - 7.5 = 1.01 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 9.94 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 9.94 - 8.63 = 1.31 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1992 </td> <td style="text-align:center;"> 13.39 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 13.39 - 9.33 = 4.06 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 7.44 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 7.44 - 6.56 = 0.88 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 11.66 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 11.66 - 11.87 = -0.21 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 17.24 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 17.24 - 11.98 = 5.26 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 5.07 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 5.07 - 6.53 = -1.46 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 9.66 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 9.66 - 11.73 = -2.07 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 13.07 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 13.07 - 12.41 = 0.66 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 5.37 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 5.37 - 9.75 = -4.38 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 4.70 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 4.7 - 9.03 = -4.33 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 9.20 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 9.2 - 9.46 = -0.26 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.03 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 6.03 - 8.19 = -2.16 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 11.34 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 11.34 - 11.13 = 0.21 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.26 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 8.26 - 8.61 = -0.35 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.01 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 6.01 - 8.37 = -2.36 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 16.83 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 16.83 - 10.57 = 6.26 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 13.28 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 13.28 - 13.46 = -0.18 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 14.78 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 14.78 - 10.04 = 4.74 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 9.46 - 9.21 = 0.25 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.04 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 8.04 - 7.47 = 0.57 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 10.18 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 10.18 - 8.42 = 1.76 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 19.81 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 19.81 - 16.97 = 2.84 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 19.00 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 19 - 10.15 = 8.85 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.34 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 6.34 - 9.06 = -2.72 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.21 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 8.21 - 9.45 = -1.24 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 14.80 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 14.8 - 12.04 = 2.76 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 10.15 - 8.64 = 1.51 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 7.15 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 7.15 - 9.08 = -1.93 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 7.07 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 7.07 - 11.91 = -4.84 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 7.27 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 7.27 - 8.03 = -0.76 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 10.75 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 10.75 - 10.43 = 0.32 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.32 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 8.32 - 6.46 = 1.86 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 18.75 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 18.75 - 15.92 = 2.83 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.56 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 8.56 - 10.01 = -1.45 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 4.97 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 4.97 - 9.24 = -4.27 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 11.18 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 11.18 - 9.33 = 1.85 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.43 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 6.43 - 7.12 = -0.69 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.01 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 8.01 - 8.16 = -0.15 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 9.07 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 9.07 - 6.83 = 2.24 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> -0.95 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> -0.95 - 6.54 = -7.49 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.59 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 8.59 - 10.66 = -2.07 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 9.08 - 10.23 = -1.15 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 16.41 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 16.41 - 14.62 = 1.79 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 7.34 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 7.34 - 8.31 = -0.97 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.40 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 6.4 - 9.72 = -3.32 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 11.06 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 11.06 - 10.98 = 0.08 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.21 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 8.21 - 7.68 = 0.53 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 8.78 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 8.78 - 8.89 = -0.11 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 11.02 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 11.02 - 10.78 = 0.24 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 6.04 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 6.04 - 7.5 = -1.46 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 5.81 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 5.81 - 8.63 = -2.82 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1993 </td> <td style="text-align:center;"> 5.78 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 5.78 - 9.33 = -3.55 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 4.69 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 4.69 - 6.56 = -1.87 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.00 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 7 - 11.87 = -4.87 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 13.34 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 13.34 - 11.98 = 1.36 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 10.24 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 10.24 - 6.53 = 3.71 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 12.34 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 12.34 - 11.73 = 0.61 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 14.78 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 14.78 - 12.41 = 2.37 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 5.52 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 5.52 - 9.75 = -4.23 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.58 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 9.58 - 9.03 = 0.55 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.16 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 11.16 - 9.46 = 1.7 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.51 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 7.51 - 8.19 = -0.68 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.67 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 11.67 - 11.13 = 0.54 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 10.76 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 10.76 - 8.61 = 2.15 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.08 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 7.08 - 8.37 = -1.29 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.73 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 9.73 - 10.57 = -0.84 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 20.30 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 20.3 - 13.46 = 6.84 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 10.48 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 10.48 - 10.04 = 0.44 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.86 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 9.86 - 9.21 = 0.65 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.15 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 9.15 - 7.47 = 1.68 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.01 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 7.01 - 8.42 = -1.41 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 13.93 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 13.93 - 16.97 = -3.04 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.08 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 8.08 - 10.15 = -2.07 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.60 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 11.6 - 9.06 = 2.54 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 6.61 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 6.61 - 9.45 = -2.84 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 13.68 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 13.68 - 12.04 = 1.64 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 12.46 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 12.46 - 8.64 = 3.82 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.18 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 11.18 - 9.08 = 2.1 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.62 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 11.62 - 11.91 = -0.29 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 6.33 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 6.33 - 8.03 = -1.7 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.73 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 7.73 - 10.43 = -2.7 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.44 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 8.44 - 6.46 = 1.98 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 13.56 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 13.56 - 15.92 = -2.36 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 10.04 - 10.01 = 0.03 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 7.76 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 7.76 - 9.24 = -1.48 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.23 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 11.23 - 9.33 = 1.9 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.48 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 9.48 - 7.12 = 2.36 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.15 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 11.15 - 8.16 = 2.99 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 12.72 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 12.72 - 6.83 = 5.89 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.36 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 8.36 - 6.54 = 1.82 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.31 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 9.31 - 10.66 = -1.35 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.54 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 9.54 - 10.23 = -0.69 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 9.25 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 9.25 - 14.62 = -5.37 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 8.63 - 8.31 = 0.32 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.47 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 8.47 - 9.72 = -1.25 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 11.83 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 11.83 - 10.98 = 0.85 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 6.88 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 6.88 - 7.68 = -0.8 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 3.53 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 3.53 - 8.89 = -5.36 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 8.93 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 8.93 - 10.78 = -1.85 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 3.99 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 3.99 - 7.5 = -3.51 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 12.20 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 12.2 - 8.63 = 3.57 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1994 </td> <td style="text-align:center;"> 4.11 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 4.11 - 9.33 = -5.22 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.85 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 7.85 - 6.56 = 1.29 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 13.54 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 13.54 - 11.87 = 1.67 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 9.24 - 11.98 = -2.74 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 8.83 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 8.83 - 6.53 = 2.3 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.40 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 9.4 - 11.73 = -2.33 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 11.07 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 11.07 - 12.41 = -1.34 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 10.31 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 10.31 - 9.75 = 0.56 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.81 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 7.81 - 9.03 = -1.22 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 6.70 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 6.7 - 9.46 = -2.76 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.62 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 9.62 - 8.19 = 1.43 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 7.5 - 11.13 = -3.63 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.80 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 9.8 - 8.61 = 1.19 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.76 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 7.76 - 8.37 = -0.61 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 8.31 - 10.57 = -2.26 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 13.36 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 13.36 - 13.46 = -0.1 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.06 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 12.06 - 10.04 = 2.02 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 10.52 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 10.52 - 9.21 = 1.31 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.77 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 7.77 - 7.47 = 0.3 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 3.34 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 3.34 - 8.42 = -5.08 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 21.72 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 21.72 - 16.97 = 4.75 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 11.14 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 11.14 - 10.15 = 0.99 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.17 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 7.17 - 9.06 = -1.89 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.55 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 9.55 - 9.45 = 0.1 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 13.72 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 13.72 - 12.04 = 1.68 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 4.70 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 4.7 - 8.64 = -3.94 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.89 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 9.89 - 9.08 = 0.81 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.64 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 12.64 - 11.91 = 0.73 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.53 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 12.53 - 8.03 = 4.5 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 13.36 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 13.36 - 10.43 = 2.93 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.37 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 7.37 - 6.46 = 0.91 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.14 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 12.14 - 15.92 = -3.78 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 6.38 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 6.38 - 10.01 = -3.63 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 8.40 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 8.4 - 9.24 = -0.84 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.30 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 12.3 - 9.33 = 2.97 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.35 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 12.35 - 7.12 = 5.23 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 11.43 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 11.43 - 8.16 = 3.27 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 0.20 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 0.2 - 6.83 = -6.63 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 9.30 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 9.3 - 6.54 = 2.76 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 13.48 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 13.48 - 10.66 = 2.82 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.10 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 12.1 - 10.23 = 1.87 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.09 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 12.09 - 14.62 = -2.53 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 11.36 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 11.36 - 8.31 = 3.05 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 10.57 - 9.72 = 0.85 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 11.71 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 11.71 - 10.98 = 0.73 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 7.32 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 7.32 - 7.68 = -0.36 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 10.53 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 10.53 - 8.89 = 1.64 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 8.95 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 8.95 - 10.78 = -1.83 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 8.84 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 8.84 - 7.5 = 1.34 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 14.39 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 14.39 - 8.63 = 5.76 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1995 </td> <td style="text-align:center;"> 12.29 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 12.29 - 9.33 = 2.96 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 0.52 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 0.52 - 6.56 = -6.04 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.13 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 10.13 - 11.87 = -1.74 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.64 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 9.64 - 11.98 = -2.34 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.02 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 7.02 - 6.53 = 0.49 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 11.54 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 11.54 - 11.73 = -0.19 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 14.70 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 14.7 - 12.41 = 2.29 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.02 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 10.02 - 9.75 = 0.27 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.14 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 10.14 - 9.03 = 1.11 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.39 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 9.39 - 9.46 = -0.07 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 6.72 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 6.72 - 8.19 = -1.47 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.94 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 9.94 - 11.13 = -1.19 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 4.22 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 4.22 - 8.61 = -4.39 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 11.08 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 11.08 - 8.37 = 2.71 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.05 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 10.05 - 10.57 = -0.52 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 11.42 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 11.42 - 13.46 = -2.04 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 9.03 - 10.04 = -1.01 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 15.99 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 15.99 - 9.21 = 6.78 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 3.29 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 3.29 - 7.47 = -4.18 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.88 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 7.88 - 8.42 = -0.54 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 16.23 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 16.23 - 16.97 = -0.74 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.03 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 10.03 - 10.15 = -0.12 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.29 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 9.29 - 9.06 = 0.23 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.93 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 10.93 - 9.45 = 1.48 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 12.84 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 12.84 - 12.04 = 0.8 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.66 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 7.66 - 8.64 = -0.98 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.02 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 9.02 - 9.08 = -0.06 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 13.11 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 13.11 - 11.91 = 1.2 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 10.84 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 10.84 - 8.03 = 2.81 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 6.73 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 6.73 - 10.43 = -3.7 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 6.52 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 6.52 - 6.46 = 0.06 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 14.10 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 14.1 - 15.92 = -1.82 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 14.01 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 14.01 - 10.01 = 4 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.93 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 7.93 - 9.24 = -1.31 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 5.92 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 5.92 - 9.33 = -3.41 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 8.82 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 8.82 - 7.12 = 1.7 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 8.87 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 8.87 - 8.16 = 0.71 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 1.38 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 1.38 - 6.83 = -5.45 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 13.63 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 13.63 - 6.54 = 7.09 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 15.51 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 15.51 - 10.66 = 4.85 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 5.57 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 5.57 - 10.23 = -4.66 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 20.29 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 20.29 - 14.62 = 5.67 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 4.84 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 4.84 - 8.31 = -3.47 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.56 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 9.56 - 9.72 = -0.16 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 6.32 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 6.32 - 10.98 = -4.66 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 7.12 - 7.68 = -0.56 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 7.14 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 7.14 - 8.89 = -1.75 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 8.97 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 8.97 - 10.78 = -1.81 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 4.23 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 4.23 - 7.5 = -3.27 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 1.41 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 1.41 - 8.63 = -7.22 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1996 </td> <td style="text-align:center;"> 9.93 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 9.93 - 9.33 = 0.6 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 6.36 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 6.36 - 6.56 = -0.2 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 12.31 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 12.31 - 11.87 = 0.44 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 11.38 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 11.38 - 11.98 = -0.6 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.96 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 7.96 - 6.53 = 1.43 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 11.95 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 11.95 - 11.73 = 0.22 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 14.00 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 14 - 12.41 = 1.59 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 5.85 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 5.85 - 9.75 = -3.9 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.56 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 9.56 - 9.03 = 0.53 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 10.88 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 10.88 - 9.46 = 1.42 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 8.54 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 8.54 - 8.19 = 0.35 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 15.47 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 15.47 - 11.13 = 4.34 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 2.76 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 2.76 - 8.61 = -5.85 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 11.68 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 11.68 - 8.37 = 3.31 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 12.28 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 12.28 - 10.57 = 1.71 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 16.38 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 16.38 - 13.46 = 2.92 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 10.69 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 10.69 - 10.04 = 0.65 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 0.94 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 0.94 - 9.21 = -8.27 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 10.28 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 10.28 - 7.47 = 2.81 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.97 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 7.97 - 8.42 = -0.45 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 14.00 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 14 - 16.97 = -2.97 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.98 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 9.98 - 10.15 = -0.17 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 9.75 - 9.06 = 0.69 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 17.31 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 17.31 - 9.45 = 7.86 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 12.63 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 12.63 - 12.04 = 0.59 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 6.00 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 6 - 8.64 = -2.64 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 13.03 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 13.03 - 9.08 = 3.95 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 10.33 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 10.33 - 11.91 = -1.58 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 5.89 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 5.89 - 8.03 = -2.14 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.85 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 7.85 - 10.43 = -2.58 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 6.27 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 6.27 - 6.46 = -0.19 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 20.17 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 20.17 - 15.92 = 4.25 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 13.49 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 13.49 - 10.01 = 3.48 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 11.84 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 11.84 - 9.24 = 2.6 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 10.56 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 10.56 - 9.33 = 1.23 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 8.08 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 8.08 - 7.12 = 0.96 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.05 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 9.05 - 8.16 = 0.89 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 5.38 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 5.38 - 6.83 = -1.45 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.75 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 7.75 - 6.54 = 1.21 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 13.76 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 13.76 - 10.66 = 3.1 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 9.33 - 10.23 = -0.9 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 15.15 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 15.15 - 14.62 = 0.53 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 5.70 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 5.7 - 8.31 = -2.61 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 13.53 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 13.53 - 9.72 = 3.81 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 14.95 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 14.95 - 10.98 = 3.97 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 3.72 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 3.72 - 7.68 = -3.96 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.23 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 7.23 - 8.89 = -1.66 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 9.75 - 10.78 = -1.03 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 9.52 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 9.52 - 7.5 = 2.02 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 11.81 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 11.81 - 8.63 = 3.18 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1997 </td> <td style="text-align:center;"> 7.39 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 7.39 - 9.33 = -1.94 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 4.19 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 4.19 - 6.56 = -2.37 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 11.89 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 11.89 - 11.87 = 0.02 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 8.41 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 8.41 - 11.98 = -3.57 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.25 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 7.25 - 6.53 = 0.72 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.80 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 13.8 - 11.73 = 2.07 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 6.87 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 6.87 - 12.41 = -5.54 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.12 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 13.12 - 9.75 = 3.37 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.56 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 9.56 - 9.03 = 0.53 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.64 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 7.64 - 9.46 = -1.82 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 9.21 - 8.19 = 1.02 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.60 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 13.6 - 11.13 = 2.47 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.60 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 13.6 - 8.61 = 4.99 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 5.34 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 5.34 - 8.37 = -3.03 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.50 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 9.5 - 10.57 = -1.07 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 14.49 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 14.49 - 13.46 = 1.03 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 11.45 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 11.45 - 10.04 = 1.41 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.36 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 9.36 - 9.21 = 0.15 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 2.33 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 2.33 - 7.47 = -5.14 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 8.52 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 8.52 - 8.42 = 0.1 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.64 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 13.64 - 16.97 = -3.33 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 10.73 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 10.73 - 10.15 = 0.58 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 6.82 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 6.82 - 9.06 = -2.24 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.41 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 9.41 - 9.45 = -0.04 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 10.21 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 10.21 - 12.04 = -1.83 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 8.06 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 8.06 - 8.64 = -0.58 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 5.97 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 5.97 - 9.08 = -3.11 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 16.67 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 16.67 - 11.91 = 4.76 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 10.06 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 10.06 - 8.03 = 2.03 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 9.72 - 10.43 = -0.71 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 5.56 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 5.56 - 6.46 = -0.9 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 17.27 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 17.27 - 15.92 = 1.35 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 4.90 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 4.9 - 10.01 = -5.11 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 6.52 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 6.52 - 9.24 = -2.72 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.21 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 7.21 - 9.33 = -2.12 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 3.89 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 3.89 - 7.12 = -3.23 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 3.77 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 3.77 - 8.16 = -4.39 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 10.78 - 6.83 = 3.95 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.75 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 7.75 - 6.54 = 1.21 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.78 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 7.78 - 10.66 = -2.88 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 11.01 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 11.01 - 10.23 = 0.78 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 14.80 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 14.8 - 14.62 = 0.18 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 5.38 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 5.38 - 8.31 = -2.93 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 6.06 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 6.06 - 9.72 = -3.66 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 12.78 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 12.78 - 10.98 = 1.8 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 14.92 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 14.92 - 7.68 = 7.24 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 13.35 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 13.35 - 8.89 = 4.46 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 9.63 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 9.63 - 10.78 = -1.15 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 7.58 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 7.58 - 7.5 = 0.08 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 4.15 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 4.15 - 8.63 = -4.48 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1998 </td> <td style="text-align:center;"> 6.70 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 6.7 - 9.33 = -2.63 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 6.84 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 6.84 - 6.56 = 0.28 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.78 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 13.78 - 11.87 = 1.91 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.53 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 13.53 - 11.98 = 1.55 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 5.37 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 5.37 - 6.53 = -1.16 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 16.70 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 16.7 - 11.73 = 4.97 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.55 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 13.55 - 12.41 = 1.14 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.49 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 9.49 - 9.75 = -0.26 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.10 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 8.1 - 9.03 = -0.93 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.70 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 9.7 - 9.46 = 0.24 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 6.34 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 6.34 - 8.19 = -1.85 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 14.44 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 14.44 - 11.13 = 3.31 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.06 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 8.06 - 8.61 = -0.55 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 7.48 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 7.48 - 8.37 = -0.89 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.02 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 8.02 - 10.57 = -2.55 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 16.39 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 16.39 - 13.46 = 2.93 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 7.33 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 7.33 - 10.04 = -2.71 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.67 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 9.67 - 9.21 = 0.46 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.41 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 9.41 - 7.47 = 1.94 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 8.37 - 8.42 = -0.05 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 17.14 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 17.14 - 16.97 = 0.17 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 6.65 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 6.65 - 10.15 = -3.5 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.55 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 8.55 - 9.06 = -0.51 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 4.14 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 4.14 - 9.45 = -5.31 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.62 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 9.62 - 12.04 = -2.42 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.05 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 13.05 - 8.64 = 4.41 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.56 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 8.56 - 9.08 = -0.52 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 12.87 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 12.87 - 11.91 = 0.96 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 5.53 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 5.53 - 8.03 = -2.5 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.31 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 9.31 - 10.43 = -1.12 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 5.51 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 5.51 - 6.46 = -0.95 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.82 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 13.82 - 15.92 = -2.1 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 11.75 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 11.75 - 10.01 = 1.74 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 10.26 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 10.26 - 9.24 = 1.02 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 7.08 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 7.08 - 9.33 = -2.25 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 8.37 - 7.12 = 1.25 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.84 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 9.84 - 8.16 = 1.68 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.22 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 8.22 - 6.83 = 1.39 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 6.07 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 6.07 - 6.54 = -0.47 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 6.93 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 6.93 - 10.66 = -3.73 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.41 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 9.41 - 10.23 = -0.82 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 15.31 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 15.31 - 14.62 = 0.69 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 12.35 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 12.35 - 8.31 = 4.04 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.98 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 8.98 - 9.72 = -0.74 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 11.59 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 11.59 - 10.98 = 0.61 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 8.55 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 8.55 - 7.68 = 0.87 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 15.61 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 15.61 - 8.89 = 6.72 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 13.17 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 13.17 - 10.78 = 2.39 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 7.08 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 7.08 - 7.5 = -0.42 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.01 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 9.01 - 8.63 = 0.38 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 1999 </td> <td style="text-align:center;"> 9.37 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 9.37 - 9.33 = 0.04 </td> </tr> <tr> <td style="text-align:center;"> city1 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.02 </td> <td style="text-align:center;"> 6.56 </td> <td style="text-align:center;"> 9.02 - 6.56 = 2.46 </td> </tr> <tr> <td style="text-align:center;"> city2 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.56 </td> <td style="text-align:center;"> 11.87 </td> <td style="text-align:center;"> 10.56 - 11.87 = -1.31 </td> </tr> <tr> <td style="text-align:center;"> city3 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 14.52 </td> <td style="text-align:center;"> 11.98 </td> <td style="text-align:center;"> 14.52 - 11.98 = 2.54 </td> </tr> <tr> <td style="text-align:center;"> city4 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 3.39 </td> <td style="text-align:center;"> 6.53 </td> <td style="text-align:center;"> 3.39 - 6.53 = -3.14 </td> </tr> <tr> <td style="text-align:center;"> city5 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 8.70 </td> <td style="text-align:center;"> 11.73 </td> <td style="text-align:center;"> 8.7 - 11.73 = -3.03 </td> </tr> <tr> <td style="text-align:center;"> city6 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 14.38 </td> <td style="text-align:center;"> 12.41 </td> <td style="text-align:center;"> 14.38 - 12.41 = 1.97 </td> </tr> <tr> <td style="text-align:center;"> city7 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.94 </td> <td style="text-align:center;"> 9.75 </td> <td style="text-align:center;"> 11.94 - 9.75 = 2.19 </td> </tr> <tr> <td style="text-align:center;"> city8 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.36 </td> <td style="text-align:center;"> 9.03 </td> <td style="text-align:center;"> 9.36 - 9.03 = 0.33 </td> </tr> <tr> <td style="text-align:center;"> city9 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 12.93 </td> <td style="text-align:center;"> 9.46 </td> <td style="text-align:center;"> 12.93 - 9.46 = 3.47 </td> </tr> <tr> <td style="text-align:center;"> city10 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 7.89 </td> <td style="text-align:center;"> 8.19 </td> <td style="text-align:center;"> 7.89 - 8.19 = -0.3 </td> </tr> <tr> <td style="text-align:center;"> city11 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.31 </td> <td style="text-align:center;"> 11.13 </td> <td style="text-align:center;"> 9.31 - 11.13 = -1.82 </td> </tr> <tr> <td style="text-align:center;"> city12 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 6.18 </td> <td style="text-align:center;"> 8.61 </td> <td style="text-align:center;"> 6.18 - 8.61 = -2.43 </td> </tr> <tr> <td style="text-align:center;"> city13 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.14 </td> <td style="text-align:center;"> 8.37 </td> <td style="text-align:center;"> 9.14 - 8.37 = 0.77 </td> </tr> <tr> <td style="text-align:center;"> city14 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.70 </td> <td style="text-align:center;"> 10.57 </td> <td style="text-align:center;"> 10.7 - 10.57 = 0.13 </td> </tr> <tr> <td style="text-align:center;"> city15 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 13.24 </td> <td style="text-align:center;"> 13.46 </td> <td style="text-align:center;"> 13.24 - 13.46 = -0.22 </td> </tr> <tr> <td style="text-align:center;"> city16 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.36 </td> <td style="text-align:center;"> 10.04 </td> <td style="text-align:center;"> 11.36 - 10.04 = 1.32 </td> </tr> <tr> <td style="text-align:center;"> city17 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 12.87 </td> <td style="text-align:center;"> 9.21 </td> <td style="text-align:center;"> 12.87 - 9.21 = 3.66 </td> </tr> <tr> <td style="text-align:center;"> city18 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.56 </td> <td style="text-align:center;"> 7.47 </td> <td style="text-align:center;"> 9.56 - 7.47 = 2.09 </td> </tr> <tr> <td style="text-align:center;"> city19 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.22 </td> <td style="text-align:center;"> 8.42 </td> <td style="text-align:center;"> 11.22 - 8.42 = 2.8 </td> </tr> <tr> <td style="text-align:center;"> city20 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 20.69 </td> <td style="text-align:center;"> 16.97 </td> <td style="text-align:center;"> 20.69 - 16.97 = 3.72 </td> </tr> <tr> <td style="text-align:center;"> city21 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 2.66 </td> <td style="text-align:center;"> 10.15 </td> <td style="text-align:center;"> 2.66 - 10.15 = -7.49 </td> </tr> <tr> <td style="text-align:center;"> city22 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.57 </td> <td style="text-align:center;"> 9.06 </td> <td style="text-align:center;"> 9.57 - 9.06 = 0.51 </td> </tr> <tr> <td style="text-align:center;"> city23 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.46 </td> <td style="text-align:center;"> 9.45 </td> <td style="text-align:center;"> 11.46 - 9.45 = 2.01 </td> </tr> <tr> <td style="text-align:center;"> city24 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 9.11 </td> <td style="text-align:center;"> 12.04 </td> <td style="text-align:center;"> 9.11 - 12.04 = -2.93 </td> </tr> <tr> <td style="text-align:center;"> city25 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 6.85 </td> <td style="text-align:center;"> 8.64 </td> <td style="text-align:center;"> 6.85 - 8.64 = -1.79 </td> </tr> <tr> <td style="text-align:center;"> city26 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 8.59 </td> <td style="text-align:center;"> 9.08 </td> <td style="text-align:center;"> 8.59 - 9.08 = -0.49 </td> </tr> <tr> <td style="text-align:center;"> city27 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.89 </td> <td style="text-align:center;"> 11.91 </td> <td style="text-align:center;"> 10.89 - 11.91 = -1.02 </td> </tr> <tr> <td style="text-align:center;"> city28 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 4.33 </td> <td style="text-align:center;"> 8.03 </td> <td style="text-align:center;"> 4.33 - 8.03 = -3.7 </td> </tr> <tr> <td style="text-align:center;"> city29 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 13.89 </td> <td style="text-align:center;"> 10.43 </td> <td style="text-align:center;"> 13.89 - 10.43 = 3.46 </td> </tr> <tr> <td style="text-align:center;"> city30 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 6.64 </td> <td style="text-align:center;"> 6.46 </td> <td style="text-align:center;"> 6.64 - 6.46 = 0.18 </td> </tr> <tr> <td style="text-align:center;"> city31 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 15.40 </td> <td style="text-align:center;"> 15.92 </td> <td style="text-align:center;"> 15.4 - 15.92 = -0.52 </td> </tr> <tr> <td style="text-align:center;"> city32 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.81 </td> <td style="text-align:center;"> 10.01 </td> <td style="text-align:center;"> 10.81 - 10.01 = 0.8 </td> </tr> <tr> <td style="text-align:center;"> city33 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 13.61 </td> <td style="text-align:center;"> 9.24 </td> <td style="text-align:center;"> 13.61 - 9.24 = 4.37 </td> </tr> <tr> <td style="text-align:center;"> city34 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.39 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 10.39 - 9.33 = 1.06 </td> </tr> <tr> <td style="text-align:center;"> city35 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 8.66 </td> <td style="text-align:center;"> 7.12 </td> <td style="text-align:center;"> 8.66 - 7.12 = 1.54 </td> </tr> <tr> <td style="text-align:center;"> city36 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.80 </td> <td style="text-align:center;"> 8.16 </td> <td style="text-align:center;"> 11.8 - 8.16 = 3.64 </td> </tr> <tr> <td style="text-align:center;"> city37 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 5.34 </td> <td style="text-align:center;"> 6.83 </td> <td style="text-align:center;"> 5.34 - 6.83 = -1.49 </td> </tr> <tr> <td style="text-align:center;"> city38 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 2.10 </td> <td style="text-align:center;"> 6.54 </td> <td style="text-align:center;"> 2.1 - 6.54 = -4.44 </td> </tr> <tr> <td style="text-align:center;"> city39 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.81 </td> <td style="text-align:center;"> 10.66 </td> <td style="text-align:center;"> 10.81 - 10.66 = 0.15 </td> </tr> <tr> <td style="text-align:center;"> city40 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 14.00 </td> <td style="text-align:center;"> 10.23 </td> <td style="text-align:center;"> 14 - 10.23 = 3.77 </td> </tr> <tr> <td style="text-align:center;"> city41 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.33 </td> <td style="text-align:center;"> 14.62 </td> <td style="text-align:center;"> 10.33 - 14.62 = -4.29 </td> </tr> <tr> <td style="text-align:center;"> city42 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 8.31 </td> <td style="text-align:center;"> 10.98 - 8.31 = 2.67 </td> </tr> <tr> <td style="text-align:center;"> city43 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 8.47 </td> <td style="text-align:center;"> 9.72 </td> <td style="text-align:center;"> 8.47 - 9.72 = -1.25 </td> </tr> <tr> <td style="text-align:center;"> city44 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 10.13 </td> <td style="text-align:center;"> 10.98 </td> <td style="text-align:center;"> 10.13 - 10.98 = -0.85 </td> </tr> <tr> <td style="text-align:center;"> city45 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 7.44 </td> <td style="text-align:center;"> 7.68 </td> <td style="text-align:center;"> 7.44 - 7.68 = -0.24 </td> </tr> <tr> <td style="text-align:center;"> city46 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 11.94 </td> <td style="text-align:center;"> 8.89 </td> <td style="text-align:center;"> 11.94 - 8.89 = 3.05 </td> </tr> <tr> <td style="text-align:center;"> city47 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 12.65 </td> <td style="text-align:center;"> 10.78 </td> <td style="text-align:center;"> 12.65 - 10.78 = 1.87 </td> </tr> <tr> <td style="text-align:center;"> city48 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 12.17 </td> <td style="text-align:center;"> 7.50 </td> <td style="text-align:center;"> 12.17 - 7.5 = 4.67 </td> </tr> <tr> <td style="text-align:center;"> city49 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 7.21 </td> <td style="text-align:center;"> 8.63 </td> <td style="text-align:center;"> 7.21 - 8.63 = -1.42 </td> </tr> <tr> <td style="text-align:center;"> city50 </td> <td style="text-align:center;"> 2000 </td> <td style="text-align:center;"> 12.51 </td> <td style="text-align:center;"> 9.33 </td> <td style="text-align:center;"> 12.51 - 9.33 = 3.18 </td> </tr> </tbody> </table> ] --- <br> .center[<img src="Figures/demeaned-fe-animation.gif">] --- ```r # Manually de-mean by transforming data D <- D %>% group_by(city) %>% mutate(crime_demeaned = crime - mean(crime), police_demeaned = police - mean(police)) %>% ungroup mod = lm(crime_demeaned~police_demeaned,data = D) round(mod$coefficients,3) ``` ``` ## (Intercept) police_demeaned ## 0.000 -0.629 ``` -- ```r # Use a package to do it... plm::plm(crime~police,data=D,index="city") ``` ``` ## ## Model Formula: crime ~ police ## ## Coefficients: ## police ## -0.62945 ``` --- ## Two-way fixed effects A two-way fixed effect model accounts for both **unit** and **time** specific errors. - **unit**: e.g. baseline differences between cities + DC and Chicago are different for a whole number of reasons. - **time**: e.g. baseline differences between years + 1999 and 2009 are different for a whole number of reasons. <br> > Since we can't possibly control for everything, we use fixed effects to remove the between year and between city differences. What is left is all the variation that is not explained by that time or location. --- ## Two-way fixed effects (LSDV) <br> `$$crime_{it} = \beta_1 police_{it} + \\\alpha_1{city_1} + \alpha_2{city_2} + \dots + \alpha_i{city_i} +\\ + \tau_1 year_1 + \tau_2 year_2 + \dots + \tau_t year_t + \nu_{it}$$` <br> `$$crime_{11} = \beta_1 police_{11} + \\\alpha_1(1) + \alpha_2(0) + \dots + \alpha_i(0) +\\ + \tau_1 (1) + \tau_2 (0) + \dots + \tau_t (0) + \nu_{11}$$` --- ## Two-way fixed effects (LSDV) `$$crime_{11} = (\alpha_1 + \tau_1) + \beta_1 police_{11} + \nu_{11}$$` `$$crime_{12} = (\alpha_1 + \tau_2) + \beta_1 police_{12} + \nu_{12}$$` `$$\vdots$$` `$$crime_{1t} = (\alpha_1 + \tau_t) + \beta_1 police_{1t} + \nu_{1t}$$` -- <br> Generalized form <strong> `$$y_{it} = \alpha_i + \tau_t + \beta_1 x_{it} + \nu_{it}$$` </strong> --- ## Two-way fixed effects (de-mean) ![:space 5] `$$y_i = \beta_0 +\beta_1 x_{it} + \epsilon_{it}$$` `$$y_i = \beta_1 x_{it} + (\alpha_i + \tau_t + \nu_{it})$$` -- ![:space 5] `$$y_{it} -\bar{y}_i - \bar{y}_t + \bar{y} = \\ \beta_1 (x_{it} - \bar{x}_i - \bar{x}_t + \bar{x}) +\\ \alpha_i - \alpha_i + \tau_t - \tau_t + \\(\nu_{it} - \bar{\nu}_i - \bar{\nu}_t + \bar{\nu})$$` `$$\tilde{y} = \beta_1 \tilde{x} + \tilde{\nu}$$` --- ## Two-way fixed effects (de-mean) ![:space 5] .center[ | | `\(y_{t=1}\)` | `\(y_{t=2}\)` | `\(\dots\)` | `\(y_{t}\)` |----| ---- | -----| -----| | `\(y_{i=1}\)` | `\(y_{11}\)` | `\(y_{12}\)` | `\(\dots\)` | `\(y_{1t}\)` | | `\(y_{i=2}\)` | `\(y_{21}\)` | `\(y_{22}\)` | `\(\dots\)` | `\(y_{2t}\)` | | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)`| | `\(y_{i}\)` | `\(y_{i1}\)` | `\(y_{i2}\)` | `\(\dots\)` | `\(y_{it}\)` | ] --- ## Two-way fixed effects (de-mean) ![:space 5] .center[ | | `\(y_{t=1}\)` | `\(y_{t=2}\)` | `\(\dots\)` | `\(y_{t}\)` | |----| ---- | -----| -----| ----| | `\(y_{i=1}\)` | `\(y_{11}\)` | `\(y_{12}\)` | `\(\dots\)` | `\(y_{1t}\)` | `\(\bar{y}_{i=1}\)` | `\(y_{i=2}\)` | `\(y_{21}\)` | `\(y_{22}\)` | `\(\dots\)` | `\(y_{2t}\)` | `\(\bar{y}_{i=1}\)` | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)` | `\(\vdots\)`| `\(\vdots\)` | `\(y_{i}\)` | `\(y_{i1}\)` | `\(y_{i2}\)` | `\(\dots\)` | `\(y_{it}\)` | `\(\bar{y}_{i=i}\)` | | `\(\bar{y}_{t=1}\)` | `\(\bar{y}_{t=2}\)` | `\(\dots\)` | `\(\bar{y}_{t=t}\)` | ** `\(\bar{y}\)` ** | ] ![:space 5] `$$\bar{y_t} = \frac{\sum^T_{t=1} y_{it}}{T} ~~~ \bar{y_i} = \frac{\sum^P_{i=1} y_{it}}{P} ~~~ \bar{y} = \frac{\sum^T_{t=1} \sum^P_{i=1} y_{it}}{PT}$$` --- ## Two-way fixed effects (hybrid) <br> `$$y_i = \beta_1 x_{it} + (\alpha_i + \tau_t + \nu_{it})$$` <br> `$$(y_{it} - \bar{y}_i) = \beta_1 (x_{it} - \bar{x}_i) + \alpha_i - \alpha_i + \tau_t + (\nu_{it} - \bar{\nu}_i)$$` <br> `$$\tilde{y_t} = \tau_t + \beta_1 \tilde{x}_t + \tilde{\nu_t}$$` --- ## Example: Trade and Alliances `$$\text{Bilateral Trade}_{it} = \beta_0 + \beta_1 Alliance_{it} + \alpha_i + \epsilon_{it}$$` .center[<img src="Figures/bilateral-trade.png">] --- ## Example: Trade and Alliances `$$\text{Bilateral Trade}_{it} = \beta_0 + \beta_1 Alliance_{it} + \alpha_i + \epsilon_{it}$$` - Does international trade flow more heavily between countries that are allies, _OR_ do economic factors alone determine trade? - `\(i\)` = dyad + A dyad is a unit that consists of two elements + e.g. node ties in a network, married couple, doctor-patient .center[ | | | |-----------|-----------| | `\(state_A\)` | `\(state_B\)` | | `\(state_B\)` | `\(state_A\)` | ] - `\(t\)` = year --- ## Example: Trade and Alliances .center[<img src="Figures/bilateral-trade-table.png" width=700>] --- ## Limitations <br> - No fix for **autocorrelation** <br> - **Lose between unit variation** (may hold most of the story!) <br> - **Incidental parameter problem** --- class:newsection ### <font size=25>Difference-in-Difference</font> --- ## The problem We want to know the effect of some policy in a state. Policy is implemented in some states (treated), but not others (control). -- The idea is to compare the outcome for states where the policy was implemented to the states where it was not. `$$y_{it} = \beta_0 + \beta_1 policy_{it} + \epsilon_{it}$$` -- <br> Consider the "stand your ground" law on the resulting state homicide rate. `$$homicide_{it} = \beta_0 + \beta_1 SYG_{it} + \epsilon_{it}$$` -- Say `\(\beta_1 > 0\)`, is that enough to conclude the law resulted in an increase in the number of homicides in the state? -- **Probably not**. Homicide rates could rise and fall for a bunch of reasons that have nothing to do with the policy. --- ## A solution - To get around this, we can compare states that passed the policy (treated) to those that did not (control). -- - Need to account for what life was like _before_ and _after_ the policy took effect in both groups. We can do this by taking the difference between the number of homicides in the treated and control states both before and after the policy took effect. `$$\Delta homicides^T = (State^{T}_{after} - State^{T}_{before})\\\Delta homicides^C =(State^{C}_{after} - State^{C}_{before})$$` -- - Then take the difference of those differences `$$(State^{T}_{after} - State^{T}_{before}) - (State^{C}_{after} - State^{C}_{before})\\\Delta homidices^T - \Delta homidices^C$$` --- ### OLS to estimate diff-in-diff model `$$y_{it} = \beta_0 + \beta_1 treated_{it} + \beta_2 after_{it} + \beta_3 (treated_{it}\times after_{it}) + \epsilon_{it}$$` where - `\(after\)` is 1 if post-treatment observation (i.e. after the policy went into effect) - `\(treated\)` is 1 if unit `\(i\)` is in treatment group (i.e. enacted the policy) <br> <br> -- .center[ | | **Control** | **Treatment** | |------|-------|-------| | **Before** | `\(\beta_0\)` | `\(\beta_0 + \beta_1\)` | | **After** | `\(\beta_0 + \beta_2\)` | `\(\beta_0 + \beta_1 + \beta_2 +\)` ** `\(\beta_3\)` ** | ] --- <br> .center[<img src="Figures/diff-in-diff-animation.gif">] --- <br> .center[ .left-column[<img src="Figures/did_no_treatment.png" width=250>] .right-column[<img src="Figures/did_treatment.png" width=250>] ] --- `$$homicide_{it} = \beta_0 + \beta_1 SYG_{it} + \beta_2 after_{it} +\\\beta_3 (SYG_{it}\times after_{it}) + \epsilon_{it}$$` .center[ | | | |----|-----| | `\(\beta_0\)` | mean level of homicide in control states | | `\(\beta_0 + \beta_1\)` | mean level of homicide in the treatment states | | `\(\beta_2\)` | national trends that impacted both groups | |** `\(\beta_3\)` ** | **the effect of the policy (treatment effect)** | ] -- <br> - `\(\beta_1\)` is the preexisting differences in the treated and untreated states. Analogous to a unit fixed effect (but only accounts for the treated and control groups). - `\(\beta_2\)` is denotes the change over time, Analogous to a time fixed effect (but only accounts for the pre-treatment and post-treatment groups). --- ### Parallel Trends Assumption The **_parallel trends assumption_** assumes that, in absence of treatment, the unobserved differences between treatment and control groups are the same overtime. `$$E[Y(0)_{t+1} - Y(0)_{t} | T = 1] = E[Y(0)_{t+1} - Y(0)_{t} | T = 0]$$` If violated, estimates of the causal effect will be biased. <img src="week05-panel_data_and_did-ppol561_files/figure-html/unnamed-chunk-14-1.png" style="display: block; margin: auto;" /> --- ### No Pretreatment Effect Assumption ![:space 2] The **_no pretreatment effect assumption_** assumes that there is no treatment effect in the period before the treatment is administered. ![:space 2] `$$E[Y(1)_{t} | T = 1] - E[Y(0)_{t} | T = 1] = 0$$` ![:space 2] This assumption is violated when soon-to-be treated units **_anticipate_** the treatment. ![:space 2] For example, say before an EPA policy goes into effect, companies that will be affected by the policy already begin to change their practices before the policy is enacted. --- ## Example: Mariel Boatlift ![:space 5] - How do inflows of immigrants affect the wages and employment of natives in local labor markets? - Card (1990) uses the Mariel Boatlift of 1980 as a natural experiment to measure the effect of a sudden influx of immigrants on unemployment among less-skilled natives. - The Mariel Boatlift increased the Miami labor force by 7% - Individual-level data on unemployment from the Current Population Survey (CPS) for Miami and four comparison cities (Atlanta, Los Angeles, Houston and Tampa-St. Petersburg) --- ## Example: Mariel Boatlift ![:space 5] .center[<img src = "Figures/mariel-boatlift-table.png">] --- ## Example: Mariel Boatlift ![:space 10] - What is the DID assumption here? ![:space 5] - Only the boatlift changed the trend of employment rates in treated and control cities. ![:space 5] - We must assume other economic factors that affect employment didn’t also change during this time period (parallel trends assumption). --- ## Diff-in-diff using panel model The basic difference-in-difference model is `$$y_{it} = \beta_0 + \beta_1 treated_{it} + \beta_2 after_{it} + \beta_3 (treated_{it}\times after_{it}) + \epsilon_{it}$$` -- We can generalize this with a two-way fixed effects model: `$$y_{it} = \alpha_i + \tau_t + \beta_3 (treated_{it}\times after_{it}) + \epsilon_{it}$$` where fixed effects capture - ** `\(\alpha_i\)` **: more focused differences between units that were treated/not treated - ** `\(\tau_t\)` **: more nuanced pre/post period definitions definitions -- It is easy to add co-variates that vary within-unit to the two-way fixed effects model. `$$y_{it} = \alpha_i + \tau_t + \beta_3 (treated_{it}\times after_{it}) + \beta_4 x_{it} + \epsilon_{it}$$`