```{r} suppressMessages({ library(hdm) library(AER) data("AJR") }) ``` The original paper: D. Acemoglu, S. Johnson, J. A. Robinson (2001). "Colonial origins of comparative development: an empirical investigation." American Economic Review, 91, 1369–1401. # Model $$\begin{equation} \log (\text{GDP}_i) = \alpha\cdot \text{PropertyRights}_i+X_i'\beta+U_i. \end{equation}$$ * `GDP` = GDP per capita. * Property Rights: Institutions, protection from expropriation (the `Exprop` variable). * Endogeneity: Simultaneity between the output and institutions. * IV: Mortality of early settlers (`logMort`). First stage: $$\begin{equation} \text{PropertyRights}_i = \pi_1\cdot \text{logMortality}_i+X_i'\Pi_2+V_i \end{equation}$$ Potential controls in $X_i$: * `Latitude` * `Latitude2` (latitude squared) * `Africa` * `Asia` * `Namer` (North America) * `Samer` (South America) * `Neo` (Neo-Europes) # 2SLS estimation with all controls: ```{r} TSLS<-ivreg(log(GDP)~Exprop+Latitude+Latitude2+Africa+Asia+Namer+Samer+Neo | logMort+Latitude+Latitude2+Africa+Asia+Namer+Samer+Neo,data=AJR) coeftest(TSLS,vcov. = vcovHC(TSLS,type="HC0")) ``` * We use `vcovHC` to correct for heteroskedasticity. * Insignificant estimate on the main variable `Exprop`. First stage: ```{r} FS<-lm(Exprop~logMort+Latitude+Latitude2+Africa+Asia+Namer+Samer+Neo,data=AJR) coeftest(FS,vcov. = vcovHC(FS,type="HC0")) ``` * Insignificant IV in the first stage. # Lasso-based approach We generate the vector/matrices for the dep. variable, main regressor, IV, potential controls ```{r} Y<-log(AJR$GDP) X<-model.matrix(Exprop~Latitude+Latitude2+Africa+Asia+Namer+Samer+Neo,data=AJR)[,-1] Z<-AJR$logMort D<-AJR$Exprop ``` Lasso implementation: * `y` = dep. var * `d` = the main regressor of interest * `z` = IVs * `x` = controls * `select.X=` for controls selection * `select.Z=` for IVs selection ```{r} rTSLS<-rlassoIV(y=Y,x=X,d=D,z=Z,select.X = TRUE,select.Z = FALSE) summary(rTSLS) ``` * Significant estimates * Marginal effect: 10% increase in GDP due to property rights # Step by step with Lasso selection (Many controls, few IVs) ### Step 1: Controls and $D$ ```{r} model.D<-rlasso(D~X) model.D$index ``` * Only `Neo` is selected Residuals: ```{r} Dtilde<-model.D$residuals ``` * The residuals in the `rlasso()` output are post-lasso! * `rlasso()` has the option for post-Lasso: `post=TRUE` (default) or `post=FALSE`. ```{r} coef(model.D) ``` ### Step 2: Controls and $Y$ ```{r} model.Y<-rlasso(Y~X) Ytilde<-model.Y$residuals model.Y$index ``` * Selected controls for $Y$: - `Latitude2` - `Africa` - `Samer` - `Neo` ### Step 3: Controls and $Z$ ```{r} model.Z<-rlasso(Z~X) Ztilde<-model.Z$residuals model.Z$index ``` * Selected controls for $Z$: - `Africa` - `Neo` ### Step 4: IV estimation using the residuals Run without the intercept: all variables are in the residual form: ```{r} rTSLStilde<-ivreg(Ytilde ~ -1 +Dtilde | Ztilde) coeftest(rTSLStilde,vcov.=vcovHC(rTSLStilde,type="HC0")) ``` --- 