Nunn and Wantchekon Data,
library("dplyr")
library("broom")
library("plm")
library("lmtest")
library("multiwayvcov")
library("rio")
nunn <- import("data/Nunn_Wantchekon_AER_2011.dta")OLS Model
f <- trust_neighbors ~
ln_export_pop +
# controls
# individual level
age + age2 + male + urban_dum + education +
occupation + religion + living_conditions +
# district-level
district_ethnic_frac + frac_ethnicity_in_district +
# country-level
isocode
mod_nunn_ols <-
lm(f, data = nunn)
tidy(mod_nunn_ols) %>%
filter(term == "ln_export_pop")## term estimate std.error statistic p.value
## 1 ln_export_pop -0.8295741 0.06364998 -13.03338 1.192828e-38Standard errors clustered by district
coeftest(mod_nunn_ols, vcov. = function(x) cluster.vcov(x, ~ district)) %>%
tidy() %>%
filter(term == "ln_export_pop")## term estimate std.error statistic p.value
## 1 ln_export_pop -0.8295741 0.1105116 -7.506668 6.354142e-14Standard errors clustered by ethnicity,
coeftest(mod_nunn_ols, vcov. = function(x) cluster.vcov(x, ~ ethnicity)) %>%
tidy() %>%
filter(term == "ln_export_pop")## term estimate std.error statistic p.value
## 1 ln_export_pop -0.8295741 0.2016958 -4.112996 3.923305e-05An alternative way to calculate cluster robust standard errors is the clustered-bootstrap. Instead of resampling individual observations, we resample clusters. See Assignment 3
ethnicities <- select(nunn, ethnicity) %>% unique()
iter <- 1024
bs_samples <- list()
for (i in seq_len(iter)) {
# Resample ethnic groups
ethnic_sample <- sample_frac(ethnicities, 1, replace = TRUE)
# Merge with Nunn data to get a new dataset
newdata <- left_join(ethnic_sample, nunn, by = "ethnicity")
bs_samples[[i]] <- tidy(lm(f, data = newdata))
}
bs_samples <- bind_rows(bs_samples)
bs_samples %>% filter(term == "ln_export_pop") %>%
ungroup() %>%
summarize(conf.low = quantile(estimate, 0.025),
conf.high = quantile(estimate, 0.975),
se = sd(estimate))## Source: local data frame [1 x 3]
##
## conf.low conf.high se
## (dbl) (dbl) (dbl)
## 1 -1.332344 -0.1219693 0.2941223Example from Michael Ross, “Is Democracy Good for the Poor?”
library("rio")
ross <- import("data/ross-democracy.dta")In ross, the unit of observation is country (id), year (year).
The R package plm contains many functions for panel data.
library("plm")OLS ignoring fixed effects
mod_lm <- lm(log(kidmort_unicef) ~ democracy + log(GDPcur), data = ross)
summary(mod_lm)##
## Call:
## lm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur), data = ross)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4590 -0.5476 0.0945 0.5013 2.2643
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.76405 0.34491 28.31 <2e-16 ***
## democracy -0.95525 0.06978 -13.69 <2e-16 ***
## log(GDPcur) -0.22828 0.01548 -14.75 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7948 on 646 degrees of freedom
## (5773 observations deleted due to missingness)
## Multiple R-squared: 0.5044, Adjusted R-squared: 0.5029
## F-statistic: 328.7 on 2 and 646 DF, p-value: < 2.2e-16or using plm,
mod_pooled <- plm(log(kidmort_unicef) ~ democracy + log(GDPcur),
index = c("id", "year"),
data = ross,
model = "pooling")## series _merge is constant and has been removedsummary(mod_pooled)## Oneway (individual) effect Pooling Model
##
## Call:
## plm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur),
## data = ross, model = "pooling", index = c("id", "year"))
##
## Unbalanced Panel: n=166, T=1-7, N=649
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -2.4600 -0.5480 0.0945 0.5010 2.2600
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 9.764048 0.344910 28.309 < 2.2e-16 ***
## democracy -0.955248 0.069779 -13.690 < 2.2e-16 ***
## log(GDPcur) -0.228280 0.015481 -14.746 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 823.38
## Residual Sum of Squares: 408.07
## R-Squared: 0.5044
## Adj. R-Squared: 0.50206
## F-statistic: 328.73 on 2 and 646 DF, p-value: < 2.22e-16Fixed effects model using the “within” (de-meaned) estimator,
mod_fe <- plm(log(kidmort_unicef) ~ democracy + log(GDPcur),
index = c("id", "year"),
data = ross,
model = "within")## series _merge is constant and has been removedsummary(mod_fe)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur),
## data = ross, model = "within", index = c("id", "year"))
##
## Unbalanced Panel: n=166, T=1-7, N=649
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.70500 -0.11700 0.00628 0.12200 0.75700
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## democracy -0.143233 0.033500 -4.2756 2.299e-05 ***
## log(GDPcur) -0.375203 0.011328 -33.1226 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 81.711
## Residual Sum of Squares: 23.012
## R-Squared: 0.71838
## Adj. R-Squared: 0.53242
## F-statistic: 613.481 on 2 and 481 DF, p-value: < 2.22e-16Fixed effects model using the least-squares dummy variable (LSDV) estimator,
mod_fe_lsdv <- lm(log(kidmort_unicef) ~ democracy + log(GDPcur) + id,
data = ross)
summary(mod_fe_lsdv)##
## Call:
## lm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur) +
## id, data = ross)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70488 -0.11661 0.00628 0.12222 0.75745
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.76449 0.26597 51.751 < 2e-16 ***
## democracy -0.14323 0.03350 -4.276 2.30e-05 ***
## log(GDPcur) -0.37520 0.01133 -33.123 < 2e-16 ***
## idAGO 0.29972 0.16768 1.787 0.074489 .
## idALB -1.93096 0.19014 -10.155 < 2e-16 ***
## idARE -1.87629 0.17021 -11.024 < 2e-16 ***
## idARG -0.58802 0.16075 -3.658 0.000282 ***
## idARM -1.45969 0.19015 -7.676 9.20e-14 ***
## idAUS -1.51025 0.16394 -9.212 < 2e-16 ***
## idAUT -1.57413 0.16198 -9.718 < 2e-16 ***
## idAZE -0.74134 0.18976 -3.907 0.000107 ***
## idBDI -0.80359 0.14710 -5.463 7.53e-08 ***
## idBEL -1.45105 0.16284 -8.911 < 2e-16 ***
## idBEN -0.60805 0.14708 -4.134 4.20e-05 ***
## idBFA -0.43394 0.13726 -3.162 0.001669 **
## idBGD 0.36327 0.14933 2.433 0.015354 *
## idBGR -1.87071 0.16968 -11.025 < 2e-16 ***
## idBHR -2.36871 0.16728 -14.160 < 2e-16 ***
## idBHS -2.16000 0.17030 -12.683 < 2e-16 ***
## idBIH -2.81045 0.24454 -11.493 < 2e-16 ***
## idBLR -1.68806 0.19171 -8.805 < 2e-16 ***
## idBLZ -2.27677 0.19358 -11.761 < 2e-16 ***
## idBOL -0.50254 0.15554 -3.231 0.001318 **
## idBRA 0.47071 0.14560 3.233 0.001309 **
## idBRB -2.68611 0.15897 -16.897 < 2e-16 ***
## idBRN -3.14176 0.18963 -16.568 < 2e-16 ***
## idBTN -1.39583 0.16881 -8.269 1.33e-15 ***
## idBWA -1.50061 0.14683 -10.220 < 2e-16 ***
## idCAF -0.86421 0.14741 -5.863 8.47e-09 ***
## idCAN -1.25176 0.16574 -7.553 2.16e-13 ***
## idCHE -1.78091 0.16282 -10.938 < 2e-16 ***
## idCHL -1.19469 0.15846 -7.539 2.37e-13 ***
## idCHN 0.31609 0.14685 2.152 0.031864 *
## idCIV -0.15998 0.13742 -1.164 0.244932
## idCMR -0.30219 0.13730 -2.201 0.028218 *
## idCOG -1.02032 0.15500 -6.583 1.21e-10 ***
## idCOL -0.64567 0.15993 -4.037 6.29e-05 ***
## idCOM -1.76528 0.15768 -11.196 < 2e-16 ***
## idCPV -2.25096 0.19132 -11.765 < 2e-16 ***
## idCRI -1.98452 0.15811 -12.552 < 2e-16 ***
## idCYP -2.56222 0.24680 -10.382 < 2e-16 ***
## idCZE -2.19942 0.19424 -11.323 < 2e-16 ***
## idDEU -0.77917 0.18358 -4.244 2.63e-05 ***
## idDJI -1.16381 0.19015 -6.121 1.94e-09 ***
## idDNK -1.89376 0.16167 -11.714 < 2e-16 ***
## idDOM -0.83551 0.15816 -5.283 1.93e-07 ***
## idDZA -0.10341 0.15748 -0.657 0.511719
## idECU -0.77659 0.15695 -4.948 1.04e-06 ***
## idEGY 0.16910 0.13948 1.212 0.225979
## idERI -1.32232 0.24494 -5.398 1.06e-07 ***
## idESP -1.23692 0.16394 -7.545 2.28e-13 ***
## idEST -2.52895 0.19032 -13.288 < 2e-16 ***
## idETH 0.01159 0.16759 0.069 0.944875
## idFIN -2.25573 0.16112 -14.000 < 2e-16 ***
## idFJI -2.39516 0.15490 -15.462 < 2e-16 ***
## idFRA -0.93858 0.16871 -5.563 4.40e-08 ***
## idGAB -0.82089 0.15495 -5.298 1.79e-07 ***
## idGBR -0.99303 0.16779 -5.918 6.19e-09 ***
## idGEO -1.57140 0.18969 -8.284 1.19e-15 ***
## idGHA -0.43224 0.13751 -3.143 0.001773 **
## idGIN -0.20806 0.18950 -1.098 0.272793
## idGMB -1.28532 0.14897 -8.628 < 2e-16 ***
## idGNB -1.06477 0.16915 -6.295 6.93e-10 ***
## idGNQ -1.43062 0.17017 -8.407 4.80e-16 ***
## idGRC -1.49643 0.15965 -9.373 < 2e-16 ***
## idGTM -0.49309 0.15823 -3.116 0.001940 **
## idGUY -1.74421 0.15599 -11.182 < 2e-16 ***
## idHND -1.19084 0.15555 -7.656 1.06e-13 ***
## idHRV -2.34691 0.24743 -9.485 < 2e-16 ***
## idHTI -0.66113 0.15497 -4.266 2.39e-05 ***
## idHUN -1.73688 0.15724 -11.046 < 2e-16 ***
## idIDN 0.28404 0.14642 1.940 0.052974 .
## idIND 1.11405 0.14709 7.574 1.87e-13 ***
## idIRL -2.15107 0.15946 -13.489 < 2e-16 ***
## idIRN 0.28185 0.15322 1.839 0.066465 .
## idIRQ -0.45400 0.14313 -3.172 0.001611 **
## idISL -3.45055 0.15811 -21.823 < 2e-16 ***
## idISR -1.93961 0.15972 -12.144 < 2e-16 ***
## idITA -0.87556 0.16758 -5.225 2.60e-07 ***
## idJAM -2.01583 0.15811 -12.749 < 2e-16 ***
## idJOR -1.52897 0.15472 -9.882 < 2e-16 ***
## idJPN -0.87803 0.17179 -5.111 4.63e-07 ***
## idKAZ -0.56038 0.19181 -2.922 0.003647 **
## idKEN -0.62442 0.13734 -4.547 6.90e-06 ***
## idKGZ -1.07441 0.19224 -5.589 3.84e-08 ***
## idKHM -1.00030 0.18942 -5.281 1.95e-07 ***
## idKOR -1.50939 0.16056 -9.401 < 2e-16 ***
## idKWT -1.73330 0.15627 -11.092 < 2e-16 ***
## idLAO -0.91414 0.18950 -4.824 1.89e-06 ***
## idLBN -1.77283 0.18979 -9.341 < 2e-16 ***
## idLBR -0.60229 0.16737 -3.598 0.000353 ***
## idLBY -0.39755 0.19051 -2.087 0.037440 *
## idLKA -1.59779 0.15674 -10.194 < 2e-16 ***
## idLSO -1.42163 0.15578 -9.126 < 2e-16 ***
## idLTU -2.44657 0.19065 -12.833 < 2e-16 ***
## idLUX -2.66293 0.15820 -16.832 < 2e-16 ***
## idLVA -2.07983 0.19052 -10.917 < 2e-16 ***
## idMAR -0.26728 0.15645 -1.708 0.088213 .
## idMDA -1.73769 0.18980 -9.155 < 2e-16 ***
## idMDG -0.52272 0.13717 -3.811 0.000157 ***
## idMDV -1.89169 0.16965 -11.151 < 2e-16 ***
## idMEX 0.03179 0.14450 0.220 0.825959
## idMKD -1.83352 0.19022 -9.639 < 2e-16 ***
## idMLI -0.18946 0.14143 -1.340 0.180993
## idMLT -2.94978 0.15861 -18.597 < 2e-16 ***
## idMNG -1.39970 0.24724 -5.661 2.59e-08 ***
## idMOZ -0.14348 0.15474 -0.927 0.354292
## idMRT -0.87608 0.14727 -5.949 5.21e-09 ***
## idMUS -2.13080 0.15854 -13.440 < 2e-16 ***
## idMWI -0.46359 0.13767 -3.367 0.000820 ***
## idMYS -1.42262 0.15735 -9.041 < 2e-16 ***
## idNAM -1.24571 0.19225 -6.480 2.28e-10 ***
## idNER -0.13818 0.13728 -1.007 0.314658
## idNGA 0.54947 0.13978 3.931 9.70e-05 ***
## idNIC -1.29524 0.15573 -8.317 9.34e-16 ***
## idNLD -1.68155 0.16392 -10.258 < 2e-16 ***
## idNOR -2.03067 0.16128 -12.591 < 2e-16 ***
## idNPL -0.48249 0.13718 -3.517 0.000478 ***
## idNZL -2.11473 0.15957 -13.252 < 2e-16 ***
## idOMN -1.45828 0.15483 -9.418 < 2e-16 ***
## idPAK 0.22444 0.13974 1.606 0.108913
## idPAN -1.69591 0.15556 -10.902 < 2e-16 ***
## idPER -0.17974 0.15693 -1.145 0.252619
## idPHL -0.46866 0.13966 -3.356 0.000854 ***
## idPNG -0.76393 0.17024 -4.487 9.03e-06 ***
## idPOL -1.34580 0.19556 -6.882 1.85e-11 ***
## idPRT -1.42357 0.15901 -8.952 < 2e-16 ***
## idPRY -1.63831 0.15478 -10.585 < 2e-16 ***
## idQAT -2.02817 0.16777 -12.089 < 2e-16 ***
## idROM -1.15010 0.19401 -5.928 5.86e-09 ***
## idRUS -0.56400 0.19873 -2.838 0.004732 **
## idRWA -0.81370 0.13754 -5.916 6.27e-09 ***
## idSAU -0.22774 0.15929 -1.430 0.153446
## idSDN -0.37745 0.13757 -2.744 0.006300 **
## idSEN -0.35543 0.14134 -2.515 0.012238 *
## idSGP -2.55797 0.15648 -16.346 < 2e-16 ***
## idSLB -2.77937 0.17338 -16.030 < 2e-16 ***
## idSLE -0.29615 0.13772 -2.150 0.032022 *
## idSLV -0.97711 0.15557 -6.281 7.54e-10 ***
## idSOM -0.71914 0.16738 -4.296 2.10e-05 ***
## idSUR -2.33771 0.16846 -13.877 < 2e-16 ***
## idSVK -2.26083 0.19127 -11.820 < 2e-16 ***
## idSVN -2.80025 0.24743 -11.318 < 2e-16 ***
## idSWE -2.00927 0.16312 -12.318 < 2e-16 ***
## idSWZ -1.38623 0.14759 -9.392 < 2e-16 ***
## idSYR -1.08342 0.15546 -6.969 1.06e-11 ***
## idTCD -0.57830 0.14684 -3.938 9.42e-05 ***
## idTGO -0.92146 0.14703 -6.267 8.18e-10 ***
## idTHA -0.53458 0.15865 -3.370 0.000813 ***
## idTJK -0.71920 0.18950 -3.795 0.000166 ***
## idTKM -0.73211 0.18995 -3.854 0.000132 ***
## idTTO -1.93327 0.15810 -12.228 < 2e-16 ***
## idTUN -0.87748 0.15537 -5.648 2.78e-08 ***
## idTUR 0.45356 0.14784 3.068 0.002277 **
## idTZA -0.36919 0.18968 -1.946 0.052191 .
## idUGA -0.42881 0.14688 -2.919 0.003672 **
## idUKR -1.20553 0.19359 -6.227 1.04e-09 ***
## idURY -1.58840 0.15694 -10.121 < 2e-16 ***
## idUSA -0.18851 0.17592 -1.072 0.284451
## idUZB -1.00789 0.24525 -4.110 4.66e-05 ***
## idVEN -0.83171 0.16056 -5.180 3.27e-07 ***
## idVNM -1.09243 0.16842 -6.486 2.19e-10 ***
## idYEM -0.52843 0.18965 -2.786 0.005542 **
## idYUG -1.91139 0.24542 -7.788 4.21e-14 ***
## idZAF 0.01047 0.15229 0.069 0.945217
## idZAR 0.15894 0.14204 1.119 0.263718
## idZMB -0.46610 0.13718 -3.398 0.000736 ***
## idZWE -0.76736 0.13737 -5.586 3.89e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2187 on 481 degrees of freedom
## (5773 observations deleted due to missingness)
## Multiple R-squared: 0.9721, Adjusted R-squared: 0.9623
## F-statistic: 100.2 on 167 and 481 DF, p-value: < 2.2e-16Note that the coefficients on democracy are the same,
coef(mod_fe)['democracy']## democracy
## -0.1432331coef(mod_fe_lsdv)['democracy']## democracy
## -0.1432331Two-way fixed effects model using the within estimator,
mod_fe2 <- plm(log(kidmort_unicef) ~ democracy + log(GDPcur),
index = c("id", "year"),
data = ross,
effect = "twoway",
model = "within")## series _merge is constant and has been removedsummary(mod_fe2)## Twoways effects Within Model
##
## Call:
## plm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur),
## data = ross, effect = "twoway", model = "within", index = c("id",
## "year"))
##
## Unbalanced Panel: n=166, T=1-7, N=649
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.6250 -0.0838 0.0000 0.0836 0.6570
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## democracy -0.022272 0.029509 -0.7548 0.4508
## log(GDPcur) -0.239382 0.022343 -10.7138 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 19.279
## Residual Sum of Squares: 15.519
## R-Squared: 0.19504
## Adj. R-Squared: 0.14245
## F-statistic: 57.4248 on 2 and 474 DF, p-value: < 2.22e-16Random effects model,
mod_re <- plm(log(kidmort_unicef) ~ democracy + log(GDPcur),
index = c("id", "year"),
data = ross,
model = "random")## series _merge is constant and has been removedsummary(mod_re)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = log(kidmort_unicef) ~ democracy + log(GDPcur),
## data = ross, model = "random", index = c("id", "year"))
##
## Unbalanced Panel: n=166, T=1-7, N=649
##
## Effects:
## var std.dev share
## idiosyncratic 0.04784 0.21873 0.084
## individual 0.52109 0.72186 0.916
## theta :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.7100 0.8502 0.8502 0.8523 0.8772 0.8862
##
## Residuals :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.7710 -0.1370 0.0254 0.0138 0.1740 0.7790
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 12.298990 0.255875 48.0665 < 2.2e-16 ***
## democracy -0.194212 0.034184 -5.6814 2.021e-08 ***
## log(GDPcur) -0.360262 0.011061 -32.5712 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 99.259
## Residual Sum of Squares: 33.828
## R-Squared: 0.66418
## Adj. R-Squared: 0.66111
## F-statistic: 624.753 on 2 and 646 DF, p-value: < 2.22e-16