Load libraries
library(haven)
library(AER)
library(stargazer)
library(readr)
library(gmm)Wage equation estimated by OLS
df <- read_dta("Data/schooling.dta")
df$exp76sq <- df$exp76**2
summary(OLS1 <- lm(lwage76 ~ ed76 + exp76 + exp76sq + black + smsa76 + south76, data=df))##
## Call:
## lm(formula = lwage76 ~ ed76 + exp76 + exp76sq + black + smsa76 +
## south76, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.59297 -0.22315 0.01893 0.24223 1.33190
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.7336643 0.0676026 70.022 < 2e-16 ***
## ed76 0.0740090 0.0035054 21.113 < 2e-16 ***
## exp76 0.0835958 0.0066478 12.575 < 2e-16 ***
## exp76sq -0.0022409 0.0003178 -7.050 2.21e-12 ***
## black -0.1896315 0.0176266 -10.758 < 2e-16 ***
## smsa76 0.1614230 0.0155733 10.365 < 2e-16 ***
## south76 -0.1248615 0.0151182 -8.259 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3742 on 3003 degrees of freedom
## Multiple R-squared: 0.2905, Adjusted R-squared: 0.2891
## F-statistic: 204.9 on 6 and 3003 DF, p-value: < 2.2e-16Reduced form for schooling, estimated by OLS
df$age76sq <- df$age76**2
summary(OLS2 <- lm(ed76 ~ age76 + age76sq + black + smsa76 + south76 + nearc4, data=df))##
## Call:
## lm(formula = ed76 ~ age76 + age76sq + black + smsa76 + south76 +
## nearc4, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.511 -1.722 -0.296 1.876 7.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.869524 4.298357 -0.435 0.663638
## age76 1.061441 0.301398 3.522 0.000435 ***
## age76sq -0.018760 0.005231 -3.586 0.000341 ***
## black -1.468367 0.115443 -12.719 < 2e-16 ***
## smsa76 0.835403 0.109252 7.647 2.76e-14 ***
## south76 -0.459700 0.102434 -4.488 7.47e-06 ***
## nearc4 0.347105 0.106997 3.244 0.001191 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.516 on 3003 degrees of freedom
## Multiple R-squared: 0.1185, Adjusted R-squared: 0.1168
## F-statistic: 67.29 on 6 and 3003 DF, p-value: < 2.2e-16Wage equation estimated by IV
summary(IV1 <- ivreg(lwage76 ~ ed76 + exp76 + exp76sq + black + smsa76 + south76 | age76 + age76sq + nearc4 + black + smsa76 + south76, data=df))##
## Call:
## ivreg(formula = lwage76 ~ ed76 + exp76 + exp76sq + black + smsa76 +
## south76 | age76 + age76sq + nearc4 + black + smsa76 + south76,
## data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.82400 -0.25248 0.02286 0.26349 1.31561
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.0656674 0.6084961 6.682 2.81e-11 ***
## ed76 0.1329473 0.0513794 2.588 0.009712 **
## exp76 0.0559614 0.0259944 2.153 0.031412 *
## exp76sq -0.0007957 0.0013403 -0.594 0.552797
## black -0.1031403 0.0773729 -1.333 0.182624
## smsa76 0.1079848 0.0497399 2.171 0.030010 *
## south76 -0.0981752 0.0287645 -3.413 0.000651 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4032 on 3003 degrees of freedom
## Multiple R-Squared: 0.1764, Adjusted R-squared: 0.1747
## Wald test: 148.1 on 6 and 3003 DF, p-value: < 2.2e-16OLS results explaining GDP per capita
df <- read_dta("Data/institutions.dta")
OLS3 <- lm(loggdp ~ qi + latitude, data=df)
OLS4 <- lm(loggdp ~ qi + latitude + africa + asia + malfal94, data=df)
stargazer(OLS3, OLS4, no.space=TRUE, type="text",
keep.stat=c("n", "rsq" ), title = "Table 5.4 OLS results explaining GDP per capita")##
## Table 5.4 OLS results explaining GDP per capita
## =========================================
## Dependent variable:
## ----------------------------
## loggdp
## (1) (2)
## -----------------------------------------
## qi 0.468*** 0.364***
## (0.064) (0.056)
## latitude 1.577** 0.234
## (0.710) (0.625)
## africa -0.414*
## (0.226)
## asia -0.457**
## (0.221)
## malfal94 -0.788***
## (0.278)
## Constant 4.728*** 6.178***
## (0.397) (0.404)
## -----------------------------------------
## Observations 64 62
## R2 0.574 0.740
## =========================================
## Note: *p<0.1; **p<0.05; ***p<0.01Table 5.5 OLS results reduced form (QI explained from exogenous variables
OLS5a <- lm(qi ~ logem4 + latitude, data=df)
OLS5b <- lm(qi ~ logem4 + euro1900 + latitude, data=df)
OLS6a <- lm(qi ~ logem4 + latitude + africa + asia + malfal94, data=df)
OLS6b <- lm(qi ~ logem4 + euro1900 + latitude + africa + asia + malfal94, data=df)
stargazer(OLS5a, OLS5b, OLS6a, OLS6b, no.space=TRUE, type="text",
keep.stat=c("n", "rsq"),
title = "Table 5.5 OLS results reduced form (QI explained from exogenous variables)")##
## Table 5.5 OLS results reduced form (QI explained from exogenous variables)
## =================================================
## Dependent variable:
## ------------------------------------
## qi
## (1) (2) (3) (4)
## -------------------------------------------------
## logem4 -0.510*** -0.368** -0.328 -0.031
## (0.141) (0.149) (0.199) (0.187)
## euro1900 0.021** 0.044***
## (0.008) (0.010)
## latitude 2.002 0.200 1.888 -1.654
## (1.337) (1.495) (1.457) (1.515)
## africa 0.135 1.272**
## (0.527) (0.531)
## asia 0.487 1.989***
## (0.519) (0.572)
## malfal94 -0.774 -1.241**
## (0.695) (0.617)
## Constant 8.529*** 7.853*** 7.872*** 5.861***
## (0.812) (0.831) (0.963) (0.962)
## -------------------------------------------------
## Observations 64 63 62 62
## R2 0.296 0.367 0.322 0.493
## =================================================
## Note: *p<0.1; **p<0.05; ***p<0.01IV results explaining GDP per capita
IV2a = ivreg(loggdp ~ qi + latitude | latitude + logem4, data=df)
IV2b = ivreg(loggdp ~ qi + latitude | latitude + logem4 + euro1900, data=df)
IV3a = ivreg(loggdp ~ qi + latitude + africa + asia + malfal94 | latitude + africa + asia + malfal94 + logem4, data=df)
IV3b = ivreg(loggdp ~ qi + latitude + africa + asia + malfal94 | latitude + africa + asia + malfal94 + logem4 + euro1900, data=df)
stargazer(IV2a, IV2b,IV3a, IV3b, no.space=TRUE, type="text",
title = "Table 5.6 IV results explaining GDP per capita)")##
## Table 5.6 IV results explaining GDP per capita)
## ===================================================================================
## Dependent variable:
## ---------------------------------------------------------------
## loggdp
## (1) (2) (3) (4)
## -----------------------------------------------------------------------------------
## qi 0.996*** 0.946*** 0.893** 0.548***
## (0.222) (0.173) (0.420) (0.115)
## latitude -0.647 -0.597 -1.070 -0.220
## (1.335) (1.186) (1.425) (0.723)
## africa -0.445 -0.425*
## (0.365) (0.247)
## asia -0.825* -0.585**
## (0.455) (0.250)
## malfal94 -0.106 -0.550*
## (0.691) (0.328)
## Constant 1.692 1.995* 2.772 4.991***
## (1.293) (1.018) (2.717) (0.764)
## -----------------------------------------------------------------------------------
## Observations 64 63 62 62
## R2 0.102 0.174 0.329 0.690
## Adjusted R2 0.073 0.147 0.270 0.663
## Residual Std. Error 1.005 (df = 61) 0.958 (df = 60) 0.883 (df = 56) 0.600 (df = 56)
## ===================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01GMM estimation results consumption-based asset pricing model
moment <- function(parm,x=NULL) {
n.col = ncol(x)
sdf = parm[1]*x[,1]^(-parm[2])
d1 = sdf*x[,2] - 1
d2 = as.matrix(rep(sdf,(n.col-2))*x[,3:n.col])
return(cbind(d1,d2))
}
df = read_csv("Data/pricing.csv")df = df[,-1]
df.matrix = as.matrix(df)
n.col = ncol(df.matrix)
exRet = apply(df.matrix[,2:(n.col-1)],2,
function(x,y){x-y},
df.matrix[,"RF"])
matrices = cbind(df.matrix[,"CONS"], 1+df.matrix[,"RF"],
exRet)
colnames(matrices)[1] = "CONS"
colnames(matrices)[2] = "RF"
start.vals = c(1,5)
names(start.vals) = c("delta","gamma")
summary(IterGMM <- gmm(g=moment, x=matrices, t0=start.vals, type="iterative", vcov="iid", optfct="optim"))##
## Call:
## gmm(g = moment, x = matrices, t0 = start.vals, type = "iterative",
## vcov = "iid", optfct = "optim")
##
##
## Method: iterative
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## delta 8.2736e-01 1.1616e-01 7.1228e+00 1.0578e-12
## gamma 5.7395e+01 3.4221e+01 1.6772e+00 9.3504e-02
##
## J-Test: degrees of freedom is 9
## J-test P-value
## Test E(g)=0: 5.76329 0.76336
##
## Initial values of the coefficients
## delta gamma
## 0.699629 91.404383
##
## #############
## Information related to the numerical optimization
## Convergence code = 0
## Function eval. = 63
## Gradian eval. = NAsummary(OneStepGMM <- gmm(g=moment, x=matrices, t0=coef(IterGMM), type="cue", vcov="iid", optfct="optim"))##
## Call:
## gmm(g = moment, x = matrices, t0 = coef(IterGMM), type = "cue",
## vcov = "iid", optfct = "optim")
##
##
## Method: cue
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## delta 6.9741e-01 1.1886e-01 5.8676e+00 4.4212e-09
## gamma 9.6193e+01 3.1617e+01 3.0425e+00 2.3466e-03
##
## J-Test: degrees of freedom is 9
## J-test P-value
## Test E(g)=0: 5.14334 0.82164
##
## Initial values of the coefficients
## delta gamma
## 0.8273564 57.3947461
##
## #############
## Information related to the numerical optimization
## Convergence code = 0
## Function eval. = 99
## Gradian eval. = NA