ecob_2
Matan Kolerman & Dor Goldenberg
May 1, 2019
Q1
1
describing data
The data includes for each person: years of schooling, cohort, region, log of his wage, and data about his region: average num of schools, if the program was intense in his reagion, number of children that went to school in 71.
path <- "C:/Users/dorgo/Documents/R/Indo_Schooling.dta"
data1<-read_dta(path)
data1$after<-data1$birth_year>62 #adding before/after info to data
regions<-unique(data1[c("birth_region", "num_schools", "program_intensity", "children71")])The size of each cohort is:
data1 %>%
count(birth_year) %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"), full_width = F) | birth_year | n |
|---|---|
| 50 | 2003 |
| 51 | 1455 |
| 52 | 1920 |
| 53 | 2118 |
| 54 | 2102 |
| 55 | 2576 |
| 56 | 2140 |
| 57 | 2369 |
| 58 | 2604 |
| 59 | 2616 |
| 60 | 3536 |
| 61 | 2388 |
| 62 | 2875 |
| 68 | 3114 |
| 69 | 3072 |
| 70 | 3473 |
| 71 | 2529 |
| 72 | 2734 |
The size of each birth region is:
data1 %>%
count(birth_region)%>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)| birth_region | n |
|---|---|
| 1101 | 109 |
| 1102 | 52 |
| 1103 | 110 |
| 1104 | 41 |
| 1105 | 87 |
| 1106 | 96 |
| 1107 | 150 |
| 1108 | 130 |
| 1171 | 122 |
| 1172 | 52 |
| 1201 | 61 |
| 1202 | 165 |
| 1203 | 83 |
| 1204 | 256 |
| 1205 | 153 |
| 1206 | 248 |
| 1207 | 271 |
| 1208 | 71 |
| 1209 | 72 |
| 1210 | 280 |
| 1211 | 211 |
| 1271 | 112 |
| 1272 | 110 |
| 1273 | 187 |
| 1274 | 130 |
| 1275 | 612 |
| 1276 | 135 |
| 1301 | 131 |
| 1302 | 120 |
| 1303 | 61 |
| 1304 | 127 |
| 1305 | 173 |
| 1306 | 115 |
| 1307 | 136 |
| 1308 | 74 |
| 1371 | 342 |
| 1372 | 54 |
| 1373 | 99 |
| 1374 | 56 |
| 1375 | 120 |
| 1376 | 93 |
| 1401 | 70 |
| 1402 | 51 |
| 1403 | 213 |
| 1404 | 90 |
| 1405 | 176 |
| 1471 | 104 |
| 1472 | 35 |
| 1501 | 96 |
| 1502 | 62 |
| 1503 | 71 |
| 1504 | 69 |
| 1505 | 40 |
| 1571 | 114 |
| 1601 | 85 |
| 1602 | 96 |
| 1603 | 108 |
| 1604 | 112 |
| 1605 | 74 |
| 1606 | 65 |
| 1607 | 200 |
| 1608 | 126 |
| 1671 | 296 |
| 1672 | 127 |
| 1701 | 97 |
| 1702 | 69 |
| 1703 | 24 |
| 1771 | 59 |
| 1801 | 128 |
| 1802 | 87 |
| 1803 | 56 |
| 1804 | 27 |
| 1871 | 152 |
| 3171 | 821 |
| 3172 | 863 |
| 3173 | 786 |
| 3174 | 808 |
| 3175 | 430 |
| 3201 | 161 |
| 3202 | 125 |
| 3203 | 319 |
| 3204 | 276 |
| 3205 | 234 |
| 3206 | 372 |
| 3207 | 291 |
| 3208 | 261 |
| 3209 | 242 |
| 3210 | 198 |
| 3211 | 351 |
| 3212 | 187 |
| 3213 | 205 |
| 3214 | 234 |
| 3215 | 238 |
| 3216 | 135 |
| 3217 | 221 |
| 3218 | 104 |
| 3219 | 194 |
| 3220 | 247 |
| 3271 | 197 |
| 3272 | 139 |
| 3273 | 406 |
| 3274 | 161 |
| 3275 | 99 |
| 3301 | 299 |
| 3302 | 374 |
| 3303 | 186 |
| 3304 | 165 |
| 3305 | 362 |
| 3306 | 337 |
| 3307 | 187 |
| 3308 | 278 |
| 3309 | 234 |
| 3310 | 390 |
| 3311 | 182 |
| 3312 | 320 |
| 3313 | 173 |
| 3314 | 190 |
| 3315 | 188 |
| 3316 | 142 |
| 3317 | 148 |
| 3318 | 295 |
| 3319 | 283 |
| 3320 | 253 |
| 3321 | 196 |
| 3322 | 286 |
| 3323 | 146 |
| 3324 | 217 |
| 3325 | 210 |
| 3326 | 252 |
| 3327 | 236 |
| 3328 | 267 |
| 3329 | 286 |
| 3371 | 203 |
| 3372 | 324 |
| 3373 | 142 |
| 3374 | 386 |
| 3375 | 155 |
| 3376 | 196 |
| 3401 | 126 |
| 3402 | 243 |
| 3403 | 186 |
| 3404 | 261 |
| 3471 | 300 |
| 3501 | 157 |
| 3502 | 222 |
| 3503 | 134 |
| 3504 | 230 |
| 3505 | 220 |
| 3506 | 349 |
| 3507 | 363 |
| 3508 | 213 |
| 3509 | 298 |
| 3510 | 321 |
| 3511 | 123 |
| 3512 | 128 |
| 3513 | 216 |
| 3514 | 242 |
| 3515 | 273 |
| 3516 | 272 |
| 3517 | 301 |
| 3518 | 250 |
| 3519 | 236 |
| 3520 | 184 |
| 3521 | 185 |
| 3522 | 149 |
| 3523 | 149 |
| 3524 | 194 |
| 3525 | 165 |
| 3526 | 122 |
| 3527 | 103 |
| 3528 | 89 |
| 3529 | 131 |
| 3571 | 176 |
| 3572 | 110 |
| 3573 | 185 |
| 3574 | 145 |
| 3575 | 130 |
| 3576 | 140 |
| 3577 | 131 |
| 3578 | 463 |
| 5101 | 94 |
| 5102 | 198 |
| 5103 | 185 |
| 5104 | 210 |
| 5105 | 117 |
| 5106 | 117 |
| 5107 | 100 |
| 5108 | 183 |
| 5171 | 135 |
| 5201 | 116 |
| 5202 | 117 |
| 5203 | 144 |
| 5204 | 73 |
| 5205 | 69 |
| 5206 | 166 |
| 5271 | 102 |
| 5301 | 45 |
| 5302 | 38 |
| 5303 | 108 |
| 5304 | 58 |
| 5305 | 51 |
| 5306 | 76 |
| 5307 | 85 |
| 5308 | 110 |
| 5309 | 45 |
| 5310 | 102 |
| 5311 | 69 |
| 5312 | 74 |
| 6101 | 101 |
| 6102 | 168 |
| 6103 | 75 |
| 6104 | 59 |
| 6105 | 66 |
| 6106 | 62 |
| 6171 | 148 |
| 6201 | 56 |
| 6202 | 54 |
| 6203 | 68 |
| 6204 | 77 |
| 6205 | 42 |
| 6271 | 28 |
| 6301 | 45 |
| 6302 | 72 |
| 6303 | 78 |
| 6304 | 36 |
| 6305 | 64 |
| 6306 | 98 |
| 6307 | 85 |
| 6308 | 71 |
| 6309 | 78 |
| 6371 | 171 |
| 6401 | 38 |
| 6402 | 101 |
| 6403 | 71 |
| 6404 | 85 |
| 6471 | 118 |
| 6472 | 82 |
| 7101 | 142 |
| 7102 | 67 |
| 7103 | 241 |
| 7104 | 183 |
| 7171 | 132 |
| 7172 | 165 |
| 7173 | 38 |
| 7201 | 73 |
| 7202 | 115 |
| 7203 | 152 |
| 7204 | 114 |
| 7301 | 57 |
| 7302 | 93 |
| 7303 | 39 |
| 7304 | 85 |
| 7305 | 62 |
| 7306 | 109 |
| 7307 | 73 |
| 7308 | 76 |
| 7309 | 82 |
| 7310 | 66 |
| 7311 | 132 |
| 7312 | 84 |
| 7313 | 64 |
| 7314 | 84 |
| 7315 | 63 |
| 7316 | 62 |
| 7317 | 93 |
| 7318 | 144 |
| 7319 | 85 |
| 7320 | 62 |
| 7321 | 31 |
| 7371 | 360 |
| 7372 | 81 |
| 7401 | 142 |
| 7402 | 77 |
| 7403 | 74 |
| 7404 | 30 |
| 8101 | 111 |
| 8102 | 131 |
| 8103 | 117 |
| 8104 | 68 |
| 8171 | 164 |
| 8201 | 53 |
| 8202 | 39 |
| 8203 | 82 |
| 8204 | 35 |
| 8205 | 36 |
| 8206 | 50 |
| 8207 | 43 |
| 8208 | 78 |
| 8209 | 93 |
| 8271 | 14 |
Summary of the data:
summary(data1)%>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover")) | education | birth_year | birth_region |
| num_schools | program_intensity | children71 | after | |
|---|---|---|---|---|---|---|---|---|
| Min. : 0.000 | Min. :50.00 | Min. :1101 | Min. : 9.21 | Min. :0.5908 | Min. :0.0000 | Min. : 3796 | Mode :logical | |
| 1st Qu.: 6.000 | 1st Qu.:55.00 | 1st Qu.:3173 | 1st Qu.:11.74 | 1st Qu.:1.3171 | 1st Qu.:0.0000 | 1st Qu.: 63580 | FALSE:30702 | |
| Median : 9.000 | Median :60.00 | Median :3319 | Median :12.18 | Median :1.7603 | Median :0.0000 | Median :159434 | TRUE :14922 | |
| Mean : 9.347 | Mean :60.96 | Mean :3670 | Mean :12.12 | Mean :2.0262 | Mean :0.4156 | Mean :162622 | NA | |
| 3rd Qu.:12.000 | 3rd Qu.:69.00 | 3rd Qu.:3573 | 3rd Qu.:12.58 | 3rd Qu.:2.3986 | 3rd Qu.:1.0000 | 3rd Qu.:221623 | NA | |
| Max. :19.000 | Max. :72.00 | Max. :8271 | Max. :16.15 | Max. :8.5983 | Max. :1.0000 | Max. :542835 | NA |
The average education level in the sample is 9.3471857
Number of schools in each region is:
regions[c("birth_region", "num_schools")]%>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"),full_width = F)| birth_region | num_schools |
|---|---|
| 1101 | 2.7295361 |
| 1102 | 2.6737239 |
| 1103 | 2.3670490 |
| 1104 | 2.0621350 |
| 1105 | 2.4550869 |
| 1106 | 2.3862851 |
| 1107 | 2.6452501 |
| 1108 | 2.4007659 |
| 1171 | 4.2678442 |
| 1172 | 5.0011368 |
| 1201 | 2.8798370 |
| 1202 | 2.1565940 |
| 1203 | 6.3137689 |
| 1204 | 1.6434790 |
| 1205 | 2.5201330 |
| 1206 | 2.3662519 |
| 1207 | 2.3666439 |
| 1208 | 2.7791309 |
| 1209 | 2.8007390 |
| 1210 | 1.7145150 |
| 1211 | 1.6756830 |
| 1271 | 4.8361540 |
| 1272 | 3.3309050 |
| 1273 | 2.7290239 |
| 1274 | 7.7355838 |
| 1275 | 1.1905100 |
| 1276 | 5.1110229 |
| 1301 | 1.5348140 |
| 1302 | 1.4699860 |
| 1303 | 1.7952110 |
| 1304 | 1.3995460 |
| 1305 | 1.3971270 |
| 1306 | 1.4346910 |
| 1307 | 1.8653700 |
| 1308 | 0.7795604 |
| 1371 | 1.1695690 |
| 1372 | 2.3205221 |
| 1373 | 4.2149630 |
| 1374 | 2.4052920 |
| 1375 | 1.3021600 |
| 1376 | 1.3560090 |
| 1401 | 2.3033280 |
| 1402 | 2.6923530 |
| 1403 | 2.1274519 |
| 1404 | 2.2996349 |
| 1405 | 1.8801950 |
| 1471 | 1.2654840 |
| 1472 | 2.1274519 |
| 1501 | 2.5409589 |
| 1502 | 3.4376070 |
| 1503 | 3.5463350 |
| 1504 | 2.3805931 |
| 1505 | 3.7855811 |
| 1571 | 1.8936890 |
| 1601 | 2.2052779 |
| 1602 | 1.9399470 |
| 1603 | 1.9793310 |
| 1604 | 1.7560660 |
| 1605 | 2.3951440 |
| 1606 | 2.0425949 |
| 1607 | 1.8233089 |
| 1608 | 2.0670049 |
| 1671 | 1.1948800 |
| 1672 | 1.6418860 |
| 1701 | 2.2461729 |
| 1702 | 2.4714079 |
| 1703 | 2.6943281 |
| 1771 | 2.8562009 |
| 1801 | 2.5934949 |
| 1802 | 2.4646139 |
| 1803 | 3.0068729 |
| 1804 | 3.0068729 |
| 1871 | 2.8613350 |
| 3171 | 1.0884160 |
| 3172 | 1.0172660 |
| 3173 | 1.0067750 |
| 3174 | 1.1077690 |
| 3175 | 1.0343610 |
| 3201 | 2.1341860 |
| 3202 | 3.0801890 |
| 3203 | 1.5842730 |
| 3204 | 2.1243589 |
| 3205 | 1.7952410 |
| 3206 | 1.4221630 |
| 3207 | 1.7423950 |
| 3208 | 1.3101290 |
| 3209 | 1.3752080 |
| 3210 | 1.5409280 |
| 3211 | 1.6889070 |
| 3212 | 1.7470860 |
| 3213 | 1.7089300 |
| 3214 | 3.0490570 |
| 3215 | 2.0846210 |
| 3216 | 2.3832610 |
| 3217 | 1.8563091 |
| 3218 | 2.2266030 |
| 3219 | 1.6635849 |
| 3220 | 2.0320580 |
| 3271 | 2.5647359 |
| 3272 | 3.7019899 |
| 3273 | 0.6890698 |
| 3274 | 2.4293089 |
| 3275 | 1.6635849 |
| 3301 | 2.1549530 |
| 3302 | 1.2609030 |
| 3303 | 1.9701350 |
| 3304 | 2.1974881 |
| 3305 | 1.7169050 |
| 3306 | 1.5067199 |
| 3307 | 1.9186161 |
| 3308 | 1.6306280 |
| 3309 | 1.6773560 |
| 3310 | 1.1128130 |
| 3311 | 1.5905020 |
| 3312 | 1.5373360 |
| 3313 | 1.6841180 |
| 3314 | 1.7702270 |
| 3315 | 1.7602950 |
| 3316 | 2.1317220 |
| 3317 | 2.8792040 |
| 3318 | 2.1859889 |
| 3319 | 2.3458500 |
| 3320 | 2.5842540 |
| 3321 | 1.9162300 |
| 3322 | 1.5911850 |
| 3323 | 1.9042790 |
| 3324 | 1.7280720 |
| 3325 | 2.7725649 |
| 3326 | 1.8434210 |
| 3327 | 2.0638101 |
| 3328 | 1.3900610 |
| 3329 | 2.5278530 |
| 3371 | 2.2286930 |
| 3372 | 1.3171149 |
| 3373 | 2.9230270 |
| 3374 | 1.3237309 |
| 3375 | 3.1954820 |
| 3376 | 2.7156489 |
| 3401 | 1.4292470 |
| 3402 | 1.4927810 |
| 3403 | 1.1108890 |
| 3404 | 1.3131150 |
| 3471 | 1.9011170 |
| 3501 | 1.0978611 |
| 3502 | 1.8671300 |
| 3503 | 1.2078190 |
| 3504 | 1.1902070 |
| 3505 | 0.8884923 |
| 3506 | 1.0577960 |
| 3507 | 1.7812400 |
| 3508 | 1.9329630 |
| 3509 | 1.9194790 |
| 3510 | 1.4854010 |
| 3511 | 2.9950581 |
| 3512 | 3.5144720 |
| 3513 | 2.7770450 |
| 3514 | 1.3776720 |
| 3515 | 1.2027540 |
| 3516 | 1.4826070 |
| 3517 | 1.4451070 |
| 3518 | 1.6200269 |
| 3519 | 1.3576649 |
| 3520 | 1.2807170 |
| 3521 | 1.6804140 |
| 3522 | 1.8170160 |
| 3523 | 2.2335050 |
| 3524 | 1.9502480 |
| 3525 | 1.7752399 |
| 3526 | 2.7881260 |
| 3527 | 3.4313951 |
| 3528 | 2.6238761 |
| 3529 | 3.7579989 |
| 3571 | 1.3503670 |
| 3572 | 2.7800300 |
| 3573 | 0.9724348 |
| 3574 | 4.1374002 |
| 3575 | 4.4542098 |
| 3576 | 1.8904819 |
| 3577 | 1.3537910 |
| 3578 | 1.0447520 |
| 5101 | 6.2169509 |
| 5102 | 3.8386741 |
| 5103 | 1.9794390 |
| 5104 | 2.4221449 |
| 5105 | 2.2933781 |
| 5106 | 2.7326550 |
| 5107 | 2.5184560 |
| 5108 | 5.0397038 |
| 5171 | 6.2169509 |
| 5201 | 2.6824999 |
| 5202 | 2.5176351 |
| 5203 | 2.1165099 |
| 5204 | 2.4011450 |
| 5205 | 3.8011401 |
| 5206 | 2.4745700 |
| 5271 | 2.6824999 |
| 5301 | 1.5901910 |
| 5302 | 2.1041999 |
| 5303 | 1.4917210 |
| 5304 | 1.0987900 |
| 5305 | 1.2669050 |
| 5306 | 1.3587980 |
| 5307 | 1.3002290 |
| 5308 | 1.3847899 |
| 5309 | 1.0491490 |
| 5310 | 1.2710381 |
| 5311 | 1.7286550 |
| 5312 | 1.3011520 |
| 6101 | 3.0580201 |
| 6102 | 3.5343959 |
| 6103 | 4.2833261 |
| 6104 | 3.7351811 |
| 6105 | 4.0835981 |
| 6106 | 4.8514628 |
| 6171 | 3.5148201 |
| 6201 | 5.9337578 |
| 6202 | 1.2420820 |
| 6203 | 3.1296151 |
| 6204 | 3.9591200 |
| 6205 | 2.9761910 |
| 6271 | 5.8611360 |
| 6301 | 2.5307620 |
| 6302 | 3.4769270 |
| 6303 | 3.1039579 |
| 6304 | 2.9740570 |
| 6305 | 3.7328010 |
| 6306 | 2.6002550 |
| 6307 | 1.4256949 |
| 6308 | 3.0846801 |
| 6309 | 2.7469950 |
| 6371 | 2.7410600 |
| 6401 | 4.5569620 |
| 6402 | 2.7785671 |
| 6403 | 8.2856102 |
| 6404 | 3.1951880 |
| 6471 | 2.0191040 |
| 6472 | 2.5428770 |
| 7101 | 1.1304560 |
| 7102 | 2.7679579 |
| 7103 | 1.0272530 |
| 7104 | 1.8386230 |
| 7171 | 3.8657529 |
| 7172 | 2.3266089 |
| 7173 | 1.0272530 |
| 7201 | 2.6525199 |
| 7202 | 2.3825841 |
| 7203 | 2.3786600 |
| 7204 | 3.0813611 |
| 7301 | 2.2497699 |
| 7302 | 1.4332870 |
| 7303 | 1.7116520 |
| 7304 | 1.1004590 |
| 7305 | 1.5964080 |
| 7306 | 0.9575184 |
| 7307 | 1.4452670 |
| 7308 | 0.5908243 |
| 7309 | 2.9157190 |
| 7310 | 1.0450490 |
| 7311 | 5.9082479 |
| 7312 | 1.3693269 |
| 7313 | 1.4170830 |
| 7314 | 1.4583380 |
| 7315 | 1.2177920 |
| 7316 | 1.3776170 |
| 7317 | 1.6752900 |
| 7318 | 1.2380700 |
| 7319 | 1.4001040 |
| 7320 | 1.8684980 |
| 7321 | 2.4706609 |
| 7371 | 1.1563500 |
| 7372 | 1.7667850 |
| 7401 | 2.1162281 |
| 7402 | 3.2918561 |
| 7403 | 2.3998170 |
| 7404 | 3.3388979 |
| 8101 | 1.1649840 |
| 8102 | 1.3271520 |
| 8103 | 8.5982695 |
| 8104 | 8.5982695 |
| 8171 | 2.1352310 |
| 8201 | 1.5582010 |
| 8202 | 1.1430660 |
| 8203 | 2.7032320 |
| 8204 | 1.3381300 |
| 8205 | 3.0836079 |
| 8206 | 1.7664779 |
| 8207 | 2.7515249 |
| 8208 | 2.2697790 |
| 8209 | 2.3986039 |
| 8271 | 2.7032320 |
2
a
beta1 is the effect of one more school year on the log wage of a individual in the time of the test.
b
The assumptions that should hold: 1. E(schools_year*epsilon)=0 2. iid of the observations
c
Assumption 1 is probably not holding, for example, schools are coordinated with parents’ wages.
lm_model<-lm(log_wage~ education, data=data1)
lm_model$coefficients## (Intercept) education
## 11.40289321 0.077033063
Number of schools in regions with low intensity is:
## [1] 1.884218Number of schools in regions with high intensity is:
mean(int1$X1.num_schools)## [1] 2.818086b
int_levels<- split(data1, data1$program_intensity)
low_int<-as.data.frame(int_levels[1])
mean(low_int$X0.education)## [1] 9.856125high_int<-as.data.frame(int_levels[2])
mean(high_int$X1.education)## [1] 8.631579summary(lm(education ~ program_intensity,data1))##
## Call:
## lm(formula = education ~ program_intensity, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.8561 -3.6316 0.3684 2.1439 10.3684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.85612 0.02434 404.88 <2e-16 ***
## program_intensity -1.22455 0.03776 -32.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.975 on 45622 degrees of freedom
## Multiple R-squared: 0.02253, Adjusted R-squared: 0.02251
## F-statistic: 1052 on 1 and 45622 DF, p-value: < 2.2e-16The difference cannot indicate causal effect of schools construction on years of education because the option of reverse causlity, i.e. in regions with more years of education more schools were build.
c
summary(lm(education ~ after, data1))##
## Call:
## lm(formula = education ~ after, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.6128 -3.2181 -0.2181 2.7819 9.7819
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.21810 0.02292 402.172 <2e-16 ***
## afterTRUE 0.39469 0.04008 9.848 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.016 on 45622 degrees of freedom
## Multiple R-squared: 0.002121, Adjusted R-squared: 0.002099
## F-statistic: 96.98 on 1 and 45622 DF, p-value: < 2.2e-16The difference cannot indicate causal effect - like in the prievios question there may be reverse causlity, i.e. the program was intense in regions with more(less) education years.
d
before_after<- split(data1, data1$after)
after_group<-as.data.frame(before_after[2])
coeff <- lm(TRUE.education ~ TRUE.program_intensity, after_group)%>%
summary() %>% coef()
after_diff<-coeff[2,1]
after_diff## [1] -1.18051In this section we calcuted the diffrence just in the areas with high intensity, so the reverse causlity is reject, despite this, we cannot indicate causal effect, because there is option that the effect is result of time trend.
e
before_group<-as.data.frame(before_after[1])
coeff <- lm(FALSE.education ~ FALSE.program_intensity, before_group)%>%
summary() %>% coef()
before_diff<-coeff[2,1]
before_diff## [1] -1.256866f
coeff <- lm(X0.education ~ X0.after, low_int)%>%
summary() %>% coef()
low_int_diff<-coeff[2,1]
low_int_diff## [1] 0.3856688coeff <- lm(X1.education ~ X1.after, high_int)%>%
summary() %>% coef()
high_int_diff<-coeff[2,1]
high_int_diff## [1] 0.4620243diff_in_diff_int<-high_int_diff-low_int_diff
diff_in_diff_b_a<-after_diff-before_diff
diff_in_diff_b_a-diff_in_diff_int## [1] -6.518119e-13diff_in_diff_int## [1] 0.07635548diff_in_diff_b_a## [1] 0.07635548Under some assumptions (that we will note in the next answer) this diffrences indicate the causal effect. the sign make sense becuase we assume that the effect of the program will be positive as the sign indicates it is.
h
The main assumption is:
common trends - that without the program the differences in years of education in the two groups will be the same.
i+j
summary(lm(education~ program_intensity + after + program_intensity*after, data=data1))##
## Call:
## lm(formula = education ~ program_intensity + after + program_intensity *
## after, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.1184 -3.4759 0.5241 2.2673 10.5241
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.73272 0.02948 330.099 < 2e-16 ***
## program_intensity -1.25687 0.04608 -27.277 < 2e-16 ***
## afterTRUE 0.38567 0.05212 7.399 1.39e-13 ***
## program_intensity:afterTRUE 0.07636 0.08023 0.952 0.341
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.97 on 45620 degrees of freedom
## Multiple R-squared: 0.02493, Adjusted R-squared: 0.02487
## F-statistic: 388.8 on 3 and 45620 DF, p-value: < 2.2e-16The differences is not significantly diffrent from 0, we can add control varibales or estimate with fixed effect regression.
4
a
summary(lm(log_wage~ program_intensity + after + program_intensity*after, data=data1))##
## Call:
## lm(formula = log_wage ~ program_intensity + after + program_intensity *
## after, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0687 -0.3606 0.0569 0.4001 4.2786
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.278991 0.004882 2515.116 <2e-16 ***
## program_intensity -0.136504 0.007630 -17.891 <2e-16 ***
## afterTRUE -0.304179 0.008631 -35.243 <2e-16 ***
## program_intensity:afterTRUE 0.001172 0.013285 0.088 0.93
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6574 on 45620 degrees of freedom
## Multiple R-squared: 0.05498, Adjusted R-squared: 0.05492
## F-statistic: 884.8 on 3 and 45620 DF, p-value: < 2.2e-16The intersting variable is the interaction variable, i.e. program_intensity*after. #### b
summary(lm(education~ program_intensity + after + program_intensity*after, data=data1))##
## Call:
## lm(formula = education ~ program_intensity + after + program_intensity *
## after, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.1184 -3.4759 0.5241 2.2673 10.5241
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.73272 0.02948 330.099 < 2e-16 ***
## program_intensity -1.25687 0.04608 -27.277 < 2e-16 ***
## afterTRUE 0.38567 0.05212 7.399 1.39e-13 ***
## program_intensity:afterTRUE 0.07636 0.08023 0.952 0.341
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.97 on 45620 degrees of freedom
## Multiple R-squared: 0.02493, Adjusted R-squared: 0.02487
## F-statistic: 388.8 on 3 and 45620 DF, p-value: < 2.2e-16c
data1$schols_after<-data1$num_schools*data1$after
fe_model<-plm(education~ num_schools + after + schols_after
,data = data1,model = "within", index = c("birth_region" ))
summary(fe_model)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = education ~ num_schools + after + schols_after,
## data = data1, model = "within", index = c("birth_region"))
##
## Unbalanced Panel: n = 290, T = 14-863, N = 45624
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -12.15798 -2.63126 0.36874 2.58778 11.58098
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## afterTRUE 0.295037 0.079177 3.7263 0.0001946 ***
## schols_after 0.067900 0.034098 1.9913 0.0464558 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 638620
## Residual Sum of Squares: 636710
## R-Squared: 0.0029785
## Adj. R-Squared: -0.0034217
## F-statistic: 67.7116 on 2 and 45332 DF, p-value: < 2.22e-16fe_model_clus<-fe_model
fe_model_clus%<>%coeftest(vcov=vcovHC(fe_model,type="HC1",cluster="group"))
fe_model_clus##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## afterTRUE 0.295037 0.120519 2.4481 0.01437 *
## schols_after 0.067900 0.041419 1.6393 0.10115
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The difference is that we allow for diffrent fixed effect in every region, we get more significant results, without clutering we get significe of 5%, and with clustring we get almost 10%.
d
dumm_year1<-dummy(data1$birth_year, sep = ".scools.")
dumm_year2<-dummy(data1$birth_year, sep = ".c71.")
dumm_year3<-dummy(data1$birth_year, sep=".")
first_inter<-(data1$num_schools)*dumm_year1
sec_inter<-(data1$children71)*dumm_year2
dumm_year1<-as.data.frame(dumm_year1)
b50<-dumm_year1$birth_year.scools.50
birth_region<-data1$birth_region
new_data<-cbind(data1,first_inter, sec_inter , dumm_year3)
model1<-plm(education~ first_inter+ sec_inter + dumm_year3 + num_schools + children71,data = new_data, model = "within", index = c("birth_region"))
summary(model1)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = education ~ first_inter + sec_inter + dumm_year3 +
## num_schools + children71, data = new_data, model = "within",
## index = c("birth_region"))
##
## Unbalanced Panel: n = 290, T = 14-863, N = 45624
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -12.18439 -2.66707 0.27045 2.54882 11.95078
##
## Coefficients: (3 dropped because of singularities)
## Estimate
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.50 -2.4350e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.51 -2.8615e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.52 -2.3187e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.53 -1.2166e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.54 -2.2176e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.55 -1.1929e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.56 -2.9329e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.57 -1.9670e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.58 -2.1750e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.59 -2.7758e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.60 -8.1495e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.61 -1.2765e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.62 -2.3863e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.68 2.5139e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.69 -5.3796e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.70 3.5967e-03
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.71 -4.5069e-02
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.50 -2.5460e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.51 -5.1982e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.52 -4.0203e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.53 -4.4413e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.54 -2.8453e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.55 -4.0534e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.56 -4.2513e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.57 -2.8096e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.58 -5.0351e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.59 -4.7916e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.60 -2.7987e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.61 -4.6337e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.62 -3.4431e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.68 -1.2624e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.69 -1.5904e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.70 -1.7440e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.71 -1.5863e-06
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.50 4.0391e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.51 1.3251e+00
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.52 7.6005e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.53 8.3522e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.54 8.5583e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.55 2.7077e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.56 1.0614e+00
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.57 6.3223e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.58 9.7913e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.59 1.2362e+00
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.60 1.8237e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.61 1.1585e+00
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.62 1.4090e+00
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.68 7.4368e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.69 7.6188e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.70 2.4310e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.71 5.4013e-01
## Std. Error
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.50 1.1284e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.51 1.1754e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.52 1.1197e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.53 1.0718e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.54 1.0698e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.55 1.0544e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.56 1.0759e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.57 1.0553e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.58 1.0094e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.59 9.9750e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.60 9.5864e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.61 1.1269e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.62 1.0036e-01
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.68 9.4736e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.69 9.8607e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.70 9.3857e-02
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.71 1.0089e-01
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.50 1.0945e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.51 1.1985e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.52 1.0945e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.53 1.0835e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.54 1.0808e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.55 1.0275e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.56 1.0894e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.57 1.0633e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.58 1.0242e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.59 1.0319e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.60 9.6296e-07
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.61 1.0661e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.62 1.0228e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.68 1.0051e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.69 1.0096e-06
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.70 9.7628e-07
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.71 1.0456e-06
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.50 3.6274e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.51 3.8705e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.52 3.6216e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.53 3.5344e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.54 3.5044e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.55 3.4072e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.56 3.5343e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.57 3.4464e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.58 3.3125e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.59 3.3249e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.60 3.1570e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.61 3.5712e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.62 3.2771e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.68 3.2329e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.69 3.3086e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.70 3.2013e-01
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.71 3.4066e-01
## t-value
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.50 -2.1578
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.51 -2.4346
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.52 -2.0709
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.53 -1.1350
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.54 -2.0729
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.55 -1.1314
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.56 -2.7260
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.57 -1.8640
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.58 -2.1548
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.59 -2.7828
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.60 -0.8501
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.61 -1.1328
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.62 -2.3778
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.68 0.2654
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.69 -0.5456
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.70 0.0383
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.71 -0.4467
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.50 -2.3262
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.51 -4.3374
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.52 -3.6731
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.53 -4.0989
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.54 -2.6325
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.55 -3.9450
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.56 -3.9022
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.57 -2.6422
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.58 -4.9163
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.59 -4.6435
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.60 -2.9063
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.61 -4.3464
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.62 -3.3664
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.68 -1.2560
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.69 -1.5754
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.70 -1.7864
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.71 -1.5172
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.50 1.1135
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.51 3.4237
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.52 2.0987
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.53 2.3631
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.54 2.4422
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.55 0.7947
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.56 3.0032
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.57 1.8345
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.58 2.9558
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.59 3.7180
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.60 0.5777
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.61 3.2441
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.62 4.2996
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.68 2.3003
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.69 2.3027
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.70 0.7594
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.71 1.5855
## Pr(>|t|)
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.50 0.0309474 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.51 0.0149131 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.52 0.0383708 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.53 0.2563741
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.54 0.0381917 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.55 0.2578829
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.56 0.0064131 **
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.57 0.0623279 .
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.58 0.0311828 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.59 0.0053915 **
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.60 0.3952713
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.61 0.2573245
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.62 0.0174194 *
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.68 0.7907383
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.69 0.5853707
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.70 0.9694320
## first_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.scools.71 0.6550917
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.50 0.0200147 *
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.51 1.445e-05 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.52 0.0002399 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.53 4.158e-05 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.54 0.0084780 **
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.55 7.993e-05 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.56 9.544e-05 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.57 0.0082386 **
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.58 8.852e-07 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.59 3.435e-06 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.60 0.0036587 **
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.61 1.387e-05 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.62 0.0007621 ***
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.68 0.2091103
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.69 0.1151826
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.70 0.0740470 .
## sec_interC:/Users/dorgo/Documents/R/ecob_2_2.Rmd.c71.71 0.1292217
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.50 0.2654986
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.51 0.0006184 ***
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.52 0.0358521 *
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.53 0.0181264 *
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.54 0.0146029 *
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.55 0.4267816
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.56 0.0026728 **
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.57 0.0665874 .
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.58 0.0031198 **
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.59 0.0002010 ***
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.60 0.5634869
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.61 0.0011790 **
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.62 1.715e-05 ***
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.68 0.0214332 *
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.69 0.0212989 *
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.70 0.4476353
## dumm_year3C:/Users/dorgo/Documents/R/ecob_2_2.Rmd.71 0.1128519
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 638620
## Residual Sum of Squares: 632480
## R-Squared: 0.0096011
## Adj. R-Squared: 0.0021649
## F-statistic: 8.60751 on 51 and 45283 DF, p-value: < 2.22e-16e
coeff1<-as.data.frame(model1$coefficients)
coeff1<-as.data.frame(t(coeff1))
coeff1 %<>% select( starts_with("first"))
coeff1<-as.data.frame(t(coeff1))
row_n<-row.names(coeff1)
row_n<-gsub("first_interbirth_year.scools.", "", row_n)
graph<-cbind(coeff1, row_n)
colnames(graph) <- c("X", "Y")
ggplot(data=graph) +
geom_point(aes(x=Y, y=X))
The results are as we exept: we see a significant positive difference in the interctions variable between the birth years of those who enjoy the program and those who don’t enjoy it. for the missing cohorts, we exepct that the intarctions dummies will be between the dummies of the cohorts who didn’t enjoy the program and the cohorts who enjoy it.
f
Because all the cohorts before 62 didn’t enjoy the program we don’t need interactions varibales for each of them, we can use one interaction variable for all of them (before).
g
Long period between the control and treatment group - because of the long period (6 year), maybe there was another thing that happened in those years and was corrlated with regions that get intense treatment and biased the results.
Maybe the effect is a result of externalities of the program and not of the schools that were built.
Q2
1
First, we will define parameters. We already have to address two issues:
Set seed - the “set seed” function works differently in R and stata, and there is no reasonable way to imitate stata’s function
We are treating X as deterministic, hence we are generating it only once.
Next, we will define function whose purpose is to create the monte carlo procedure as defined in the problem set. Afterward we will apply it, and then we will refer to the specific questions.
monte_carlo <- function(reg = "reg_2",beta = 1,sample = "none"){
u_i <- rnorm(50,0,0.25)
Ti_i <- rbinom(50,1,0.5)
Y_i <- alpha + beta*x_i + gamma*Ti_i + u_i
data <- cbind(Y_i,x_i,Ti_i) %>% as.data.frame()
if(sample == "none"){
if(reg == "reg_1"){
lm(Y_i~x_i+Ti_i,data = data)
} else {
lm(Y_i~Ti_i,data = data)
}
}
else{
if(sample == "general"){
temp_sample <- sample(c(1:50), replace = FALSE, size = 12)
data <- data[-temp_sample,]
lm(Y_i~Ti_i,data = data)
}
else{
if(sample == "low"){
control <- subset(data,Ti_i == 0)
data %<>% subset(!(Ti_i==0 & data$Y_i<quantile(control$Y_i,
probs = 0.25)))
lm(Y_i~Ti_i,data = data)
}
else{
if(sample == "defiers"){
control <- subset(data,Ti_i == 0)
threshold <- quantile(control$Y_i,probs = 0.25)+0.25
sub_group <- data[data$Y_i<threshold & data$Ti_i == 1,]
a <- sample_n(sub_group,0.5*nrow(sub_group))
b <- data[row.names(a),]
b$Y_i <- b$Y_i-0.25
data[row.names(a),] <- b
lm(Y_i~Ti_i,data = data)
}
}}}}full_reg <- lapply(1:200,monte_carlo, reg = "reg_1",
sample = "none")
unfull_reg <- lapply(1:200,monte_carlo,
sample = "none")
random_sam <- lapply(1:200,monte_carlo, beta = 0,
sample = "general")
censored <- lapply(1:200,monte_carlo, beta = 0,
sample = "low")
def_sample <- lapply(1:200,monte_carlo, beta = 0,
sample = "defiers")extracting <- function(reg, col = 3){
a <- lapply(reg, function(x)
summary(x)[["coefficients"]][, "t value"]) %>%
as.data.frame() %>% t() %>% as.data.frame()
reg %<>% lapply(function(x) coef(x)) %>%
as.data.frame() %>% t() %>% as.data.frame()
reg %<>% cbind(a)
rownames(reg) <- 1:nrow(reg)
reg <- reg[,-col]
}
RMSE <- function(outcome,gamma){
average_gamma <- outcome[["Ti_i"]] %>% mean()
bias <- average_gamma-gamma
variance <- sqrt(sum((outcome[["Ti_i"]]-average_gamma)^2)/
nrow(outcome))
RMSE <- sqrt((sum((bias^2) +
((outcome[["Ti_i"]]-average_gamma)^2)))/
nrow(outcome))
a <- cbind(RMSE,variance,bias,average_gamma)
return(a)
}
full_reg <- extracting(full_reg, col = 4)
unfull_reg <- extracting(unfull_reg)
censored <- extracting(censored)
def_sample <- extracting(def_sample)
random_sam <- extracting(random_sam)a)
We expect the two estimator to be consistent, since the treated are randomly selected and X is not correlated with the treatment. The difference we will be in the variance - we expect the variance of (ii) to be higher and consequently the rejection ratio to be lower.
b)
The number of rejection in regression (i) and (ii) are:
(sum(full_reg$Ti_i.1>1.96)/nrow(full_reg)) %>% percent()## [1] "94.0%"(sum(unfull_reg$Ti_i.1>1.96)/nrow(unfull_reg)) %>% percent()## [1] "79.0%"The RMSE, bias, variance and gamma of (i) and (ii) are given in the following tables, respectively:
full_reg_RMSE <- RMSE(full_reg,gamma = 0.25)
unfull_reg_RMSE <- RMSE(unfull_reg,gamma = 0.25)
full_reg_RMSE%>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"))| RMSE | variance | bias | average_gamma |
|---|---|---|---|
| 0.0695974 | 0.0695905 | 0.0009833 | 0.2509833 |
unfull_reg_RMSE%>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"))| RMSE | variance | bias | average_gamma |
|---|---|---|---|
| 0.0928201 | 0.0926893 | 0.0049265 | 0.2549265 |
As we can see the variance of (ii) is higher and the rejected ratio is lower.
2
a)
Now we will see that if we don’t see random individuals the estimator will not be biased. We expect the variance to be higher and the rejection ratio to be lower, since the sample is smaller and more exposed to variance. Next we see the rejection ratio and the RMSE of this situation:
(sum(random_sam$Ti_i.1>1.96)/nrow(random_sam)) %>% percent()## [1] "86.0%"random_sam_RMSE <- RMSE(random_sam,gamma = 0.25)
random_sam_RMSE %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"))| RMSE | variance | bias | average_gamma |
|---|---|---|---|
| 0.0830386 | 0.0830071 | -0.0022881 | 0.2477119 |
b)
We expect the estimator to be biased downwards, since the bottom quartile does not appear in the data and the income of the control group appears to be higher than it truly is. Hence, the effect of the treatment appears to be lower than the real effect.
#(sum(censored$Ti_i.1>1.96)/nrow(censored)) %>% percent()
censored_RMSE <- RMSE(censored,gamma = 0.25)
censored_RMSE %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"))| RMSE | variance | bias | average_gamma |
|---|---|---|---|
| 0.1335273 | 0.078478 | -0.1080311 | 0.1419689 |
We see that the estimator is, indeed, biased downwards.
3
a)
The question is ambiguous, but we understand the question as if the researchers do not see the individuals who dropped from the program. Therefore we expect the estimator to be biased downwards. We attribute the low income individuals to the program although they did not participate in it:
#(sum(def_sample$Ti_i.1>1.96)/nrow(def_sample)) %>% percent()
def_sample_RMSE <- RMSE(def_sample,gamma = 0.25)
def_sample_RMSE %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover"))| RMSE | variance | bias | average_gamma |
|---|---|---|---|
| 0.0907585 | 0.0850131 | -0.0317783 | 0.2182217 |
b)
The meaning of the coefficient is vague. It composed of the effect of the treatment, but it’s lessen by the counter-effect of lowering the income of the assigned mistakenly.
Q3
1
SUTVA may be violated because of the externalities: The people who were assigned to the treatment - the treatment group - influence the people who weren’t - the control group. The channel in which the influence flows is the labor market; Under diminishing RTS the labor market cannot absorb all of the job-seekers and a job-seeker who find a job diminishes the odds for another job-seeker to find a job. A job program will mostly (and in the extreme cases - exclusively) cause a “rat race” - a situation in which the program helps the enrollees to find a stable job on the expanse of those who weren’t in the program. If it’s correct - SUTVA fails. Tha bias that will take place will make the effect of the program look bigger than it really is; the real effect may be neglegible, because we are accounting for the externalities - not the program.
2
The randomization procedure is divided into two parts
- First, they randomize the share of entitled to participate in the program in each ditrict. Each district randomly gets share of 0%, 25%,50%, 75% or 100% of entitled.
- In each specific district the individuals who get the entitlment randomly selected. The participation is not mandatory. The researchers claim that each district labor market is distnict from other districts (except for one). The point in this experimental design is to deal with the claims about the externalities - in this experiment they randomize the externalities via the first stage, and then they can measure it.
3
In equation (6) we have coeffeicients on each level of assigning and interaction on assigned and not assigned on each level. That way we can compare between different level of assigning among the not treated and then one can get the influence of the treatment upon the control, which is the externality. The interpetation of the coeffiecients is different between the interaction coeffiecients and the indication coeffiecients - the interaction coeffiecients measures the effect of the treatment on the treated. The indication coeffiecients measures the effect of the treatment on the untreated - the externalities. The hypothesis is that the coeffecient is zero (in (6) each of them, in (7) all of them combined). The meaning of the hypothesis is that there is no externalities.
4
The data includes three different sources.
- Data from ANPE- the french beauro of employment - the data includes for every unemployed his age, postal address etc, number of month of unemployment and so on.
- Data from the counseling firms - the data let the researchers knowledge about the participants in the program.
- Follow-up surveys - the surveys conducted several times, and the most important one took place 8 month after the job-seeker found a job. The surveys helped the researchers to get a real data of current employment.
5
The only group in which we can clearly see externalities is men in districts with 25% of assigned job-seekers. We cannot see other externalities, and moreover, we don’t see difference between the 25%, 50% and 75% districts. Since it seems that the test is too weak in equation (7) the researchers change the test for externalities so that it will test the non-treated districts (with 0% assigned) against the treated (with 25%, 50% and 75% assigned). In this test the externalities become clear.
6
\(\kappa\) represents the percentage of eligible individuals with abilities on the same fields; For example, 30% of the economists are under 30 etc.
\(\sigma\) represents the percentage of job-seekers who were assigned to the program among those who were eligible.
\(\pi\) represents the percentage of workers who were assigned to the program among all the eligible job-seekers on specific field.
Generally, we expect that higher \(\pi\) will yield higher externalities, because the impact of filled vacancy is applied directly on competitors. Since we are assuming that \(\sigma\) is random, all the changes in \(\pi\) channels through \(\kappa\). Hence we see in the figure that the externalities rises with \(\kappa\) and \(\sigma\).