[SOLVED] CS round(var(beta_hat_2), 5)

round(var(beta_hat_2), 5)
library(scales)
curve(expr = dnorm(x, mean = beta_true_2,
sd=sqrt(var_true_beta_2)),
xlab=,ylab=, col=gray(.2), lwd=3, lty=1,
xlim=c(2,4), ylim=c(0,3),main=paste0(n=,n))
lines(density(beta_hat_2, bw = bw.SJ(beta_hat_2)),
col=alpha(blue,.5), lwd=3)
legend(topleft, lty=c(1,1), lwd=c(3,3),
col=c(gray(.2), alpha(blue,.5)), bty=n, legend=
c(expression(
Theoretical (Asymptotic) Gaussian Density of~hat(beta)[2]),
expression(
Empirical Density Estimation based on MC realizations from~
hat(beta)[2])))
suppressMessages(library(car))
library(sandwich)
## Generate data
MC_data <- myDataGenerator(n= 100,beta = beta_true)lm_obj <- lm(Y ~ X_2 + X_3, data = MC_data)vcovHC3_mat <- sandwich::vcovHC(lm_obj, type=”HC3″)lm_obj <- lm(Y ~ X_2 + X_3, data = MC_data)vcovHC3_mat <- sandwich::vcovHC(lm_obj, type=”HC3″)car::linearHypothesis(model = lm_obj,hypothesis.matrix = c(“X_2=3”, “X_3=5”),vcov=vcovHC3_mat)R <- rbind(c(0,1,0),c(0,0,1))car::linearHypothesis(model = lm_obj,hypothesis.matrix = R,rhs = c(3,5),vcov=vcovHC3_mat)suppressMessages(library(“car”)) # for linearHyothesis()# ?linearHypothesislibrary(“sandwich”)## Generate dataMC_data <- myDataGenerator(n= 100,beta = beta_true)## Estimate the linear regression model parameterslm_obj <- lm(Y ~ X_2 + X_3, data = MC_data)vcovHC3_mat <- sandwich::vcovHC(lm_obj, type=”HC3″)## Option 1:car::linearHypothesis(model = lm_obj,hypothesis.matrix = c(“X_2=3”, “X_3=5”),vcov=vcovHC3_mat)R <- rbind(c(0,1,0),c(0,0,1))car::linearHypothesis(model = lm_obj,hypothesis.matrix = R,rhs = c(3,5),vcov=vcovHC3_mat)suppressMessages(library(“car”)) # for linearHyothesis()library(“sandwich”)## Generate dataMC_data <- myDataGenerator(n= 100,beta = beta_true)lm_obj <- lm(Y ~ X_2 + X_3, data = MC_data)vcovHC3_mat <- sandwich::vcovHC(lm_obj, type=”HC3″)car::linearHypothesis(model = lm_obj,hypothesis.matrix = “X_3=5”,vcov=vcovHC3_mat)install.packages(“sandwich”)install.packages(“lmtest”)install.packages(“car”)install.packages(“AER”)install.packages(“car”)install.packages(“car”)install.packages(“AER”)install.packages(“lmtest”)install.packages(“sandwich”)library(“lmtest”) # for coeftest()library(“MASS”) # for Boston housing datadata(“Boston”)# ?Boston; names(Boston)# focusing here on a small sample case (n=20):Boston_small <- Boston[1:20,]lm_obj <- lm(medv ~ ptratio + lstat + nox + crim, data = Boston_small)round(coeftest(lm_obj), 2)library(“car”)linearHypothesis(lm_obj, c(“lstat=0”, “nox=0”))install.packages(“car”)install.packages(“car”)library(“car”)linearHypothesis(lm_obj, c(“lstat=0”, “nox=0”))## Below I use the same data that was used to produce the## results in Table 6.1 of our script. However, you## can produce new data by setting another seed-valuetheta_true <- 0.2# unknown true theta valuen<-5 # sample size## Use a common Random Number Generator:RNGkind(sample.kind = “Rounding”)## Warning in RNGkind(sample.kind = “Rounding”): non-uniform ‘Rounding’ sampler usedset.seed(1)# simulate data: n many (unfair) coin tossesx <- sample(x = c(0,1),size =n,replace = TRUE,prob = c(1-theta_true, theta_true))## number of heads (i.e., the number of “1”s in x)h <- sum(x)## First derivative of the log-likelihood functionLp_fct <- function(theta, h = h, n = n){(h/theta) – (n – h)/(1 – theta)}## Second derivative of the log-likelihood functionLpp_fct <- function(theta, h = h, n = n){- (h/theta^2) – (n – h)/(1 – theta)^2}t <- 1e-10 # convergence criterioncheck <- TRUE # for stopping the while-loopi <- 0 # count iterationstheta <- 0.4 # starting valueLp<- Lp_fct( theta, h=h, n=n)Lpp <- Lpp_fct(theta, h=h, n=n)while(check){i <- i + 1##theta_new <- theta[i] – (Lp_fct(theta[i], h=h, n=n) / Lpp_fct(theta[i], h=h, n=n))Lp_new <- Lp_fct( theta_new, h = h, n = n)Lpp_new <- Lpp_fct(theta_new, h = h, n = n)##theta <- c(theta, theta_new)Lp <- c(Lp, Lp_new)Lpp <- c(Lpp, Lpp_new)##if(abs(Lp_fct(theta_new, h=h, n=n)) < t ){check <- FALSE}}cbind(theta, Lp, Lp/Lpp)?RNGkind()?samplexset.seed(1)# ?sample# simulate data: n many (unfair) coin tossesx <- sample(x = c(0,1),size = n,replace = TRUE,prob = c(1-theta_true, theta_true))xh <- sum(x)htlibrary(“AER”)data(“CigarettesSW”)summary(CigarettesSW)pchisq(cig_OR_test[2, 5], df = 1, lower.tail = FALSE)library(“AER”)data(“CigarettesSW”)summary(CigarettesSW)#> stateyear cpipopulation packsincome
#> AL : 2 1985:48 Min. :1.076 Min. :478447 Min. : 49.27 Min. :6887097
#> AR : 2 1995:48 1st Qu.:1.076 1st Qu.: 1622606 1st Qu.: 92.45 1st Qu.: 25520384
#> AZ : 2 Median :1.300 Median : 3697472 Median :110.16 Median : 61661644
#> CA : 2 Mean :1.300 Mean : 5168866 Mean :109.18 Mean : 99878736
#> CO : 2 3rd Qu.:1.524 3rd Qu.: 5901500 3rd Qu.:123.52 3rd Qu.:127313964
#> CT : 2 Max. :1.524 Max. :31493524 Max. :197.99 Max. :771470144
#> (Other):84
#> taxprice taxs
#> Min. :18.00 Min. : 84.97 Min. : 21.27
#> 1st Qu.:31.00 1st Qu.:102.71 1st Qu.: 34.77
#> Median :37.00 Median :137.72 Median : 41.05
#> Mean :42.68 Mean :143.45 Mean : 48.33
#> 3rd Qu.:50.88 3rd Qu.:176.15 3rd Qu.: 59.48
#> Max. :99.00 Max. :240.85 Max. :112.63
# P168
##
# compute real per capita prices
CigarettesSW$rprice <- with(CigarettesSW, price / cpi)#compute the sales taxCigarettesSW$salestax <- with(CigarettesSW, (taxs – tax) / cpi)# check the correlation between sales tax and pricecor(CigarettesSW$salestax, CigarettesSW$price)# generate a subset for the year 1995c1995 <- subset(CigarettesSW, year == “1995”)## ————————————————————————————————# perform the first stage regressioncig_s1 <- lm(log(rprice) ~ salestax, data = c1995)coeftest(cig_s1, vcov = vcovHC, type = “HC1”)## ————————————————————————————————# inspect the R^2 of the first stage regressionsummary(cig_s1)$r.squared## ————————————————————————————————# store the predicted valueslcigp_pred <- cig_s1$fitted.values## ————————————————————————————————# run the stage 2 regressioncig_s2 <- lm(log(c1995$packs) ~ lcigp_pred)coeftest(cig_s2, vcov = vcovHC)## ————————————————————————————————# perform TSLS using ‘ivreg()’cig_ivreg <- ivreg(log(packs) ~ log(rprice) | salestax,data = c1995)coeftest(cig_ivreg, vcov = vcovHC, type = “HC1”)## ————————————————————————————————# add real income to the dataset (cpi: consumer price index)CigarettesSW$rincome <- with(CigarettesSW,income / population / cpi)c1995 <- subset(CigarettesSW, year == “1995”)## ————————————————————————————————# estimate the modelcig_ivreg2 <- ivreg(log(packs) ~ log(rprice) +log(rincome) | log(rincome) +salestax, data = c1995)coeftest(cig_ivreg2, vcov = vcovHC, type = “HC1”)## ————————————————————————————————# add cigtax to the data setCigarettesSW$cigtax <- with(CigarettesSW, tax/cpi)c1995 <- subset(CigarettesSW, year == “1995”)## ————————————————————————————————# estimate the modelcig_ivreg3 <- ivreg(log(packs) ~ log(rprice) + log(rincome) |log(rincome) + salestax + cigtax,data = c1995)coeftest(cig_ivreg3, vcov = vcovHC, type = “HC1”)## ————————————————————————————————# subset data for year 1985c1985 <- subset(CigarettesSW, year == “1985”)# define differences in variablespacksdiff <- log(c1995$packs) – log(c1985$packs)pricediff <- log(c1995$price/c1995$cpi) – log(c1985$price/c1985$cpi)incomediff <- log(c1995$income/c1995$population/c1995$cpi) -log(c1985$income/c1985$population/c1985$cpi)salestaxdiff <- (c1995$taxs – c1995$tax)/c1995$cpi – (c1985$taxs – c1985$tax)/c1985$cpicigtaxdiff <- c1995$tax/c1995$cpi – c1985$tax/c1985$cpi## ————————————————————————————————# estimate the three modelscig_ivreg_diff1 <- ivreg(packsdiff ~ pricediff +incomediff | incomediff +salestaxdiff)cig_ivreg_diff2 <- ivreg(packsdiff ~ pricediff +incomediff | incomediff +cigtaxdiff)cig_ivreg_diff3 <- ivreg(packsdiff ~ pricediff +incomediff | incomediff +salestaxdiff + cigtaxdiff)## ————————————————————————————————# robust coefficient summary for 1.coeftest(cig_ivreg_diff1, vcov = vcovHC, type = “HC1”)# robust coefficient summary for 2.coeftest(cig_ivreg_diff2, vcov = vcovHC, type = “HC1”)# robust coefficient summary for 3.coeftest(cig_ivreg_diff3, vcov = vcovHC, type = “HC1”)## —- eval = FALSE, echo=TRUE——————————————————————–## # gather robust standard errors in a list## rob_se <- list(sqrt(diag(vcovHC(cig_ivreg_diff1, type = “HC1”))),##sqrt(diag(vcovHC(cig_ivreg_diff2, type = “HC1”))),##sqrt(diag(vcovHC(cig_ivreg_diff3, type = “HC1”))))#### # generate table## stargazer(cig_ivreg_diff1, cig_ivreg_diff2, cig_ivreg_diff3,## header = FALSE,## type = “latex”,## omit.table.layout = “n”,## digits = 3,## column.labels = c(“IV: salestax”, “IV: cigtax”,## “IVs: salestax, cigtax”),## dep.var.labels.include = FALSE,## dep.var.caption =## “Dependent Variable: 1985-1995 Difference in Log per Pack Price”,## se = rob_se)## ————————————————————————————————# first-stage regressionsmod_relevance1 <- lm(pricediff ~ salestaxdiff + incomediff)mod_relevance2 <- lm(pricediff ~ cigtaxdiff + incomediff)mod_relevance3 <- lm(pricediff ~ incomediff + salestaxdiff +cigtaxdiff)## ————————————————————————————————# check instrument relevance for model (1)linearHypothesis(mod_relevance1,”salestaxdiff = 0″,vcov = vcovHC, type = “HC1″)## ————————————————————————————————# check instrument relevance for model (2)linearHypothesis(mod_relevance2,”cigtaxdiff = 0”,vcov = vcovHC, type = “HC1”)## ————————————————————————————————# check instrument relevance for model (3)linearHypothesis(mod_relevance3,c(“salestaxdiff = 0”, “cigtaxdiff = 0”),vcov = vcovHC, type = “HC1”)## ————————————————————————————————# compute the J-statisticcig_iv_OR <- lm(residuals(cig_ivreg_diff3) ~ incomediff +salestaxdiff + cigtaxdiff)cig_OR_test <- linearHypothesis(cig_iv_OR,c(“salestaxdiff = 0″,”cigtaxdiff = 0”),test = “Chisq”)cig_OR_test## ————————————————————————————————# the p-value reported by linearHypothesis() is wrong# because the degrees of freedom are set to 2.# This differs from the degree of overidentification (m (K 1) = 2 (2 1) = 1)# so the J -statistic is 21 distributed instead of following a 2 distribution# as assumed defaultly by linearHypothesis().# compute correct p-value for J-statisticpchisq(cig_OR_test[2, 5], df = 1, lower.tail = FALSE)library(“sandwich”)library(“lmtest”)library(“car”)library(“AER”)data(“Affairs”)lm_obj <- lm(affairs ~ age + yearsmarried + religiousness + rating, data = Affairs)Var_beta_hat_robust <- sandwich::vcovHC(lm_fit, type=”HC3″)Var_beta_hat_robust <- sandwich::vcovHC(lm_obj, type=”HC3″)Var_beta_hat_robustvcovHC3 <- sandwich::vcovHC(lm_obj, type=”HC3″)vcovHC3 <- sandwich::vcovHC(lm_obj, type=”HC3″)car::linearHypothesis(model = lm_obj,hypothesis.matrix = c(“age=o”, “yearsmarried=0″),vcov=vcovHC3)vcovHC3 <- sandwich::vcovHC(lm_obj, type=”HC3”)car::linearHypothesis(model = lm_obj,hypothesis.matrix = c(“age=0”, “yearsmarried=0”),vcov=vcovHC3)car::linearHypothesis(model = lm_obj,hypothesis.matrix = c(“age+yearsmarried=0”),vcov=vcovHC3)n<-100X_2<-runif(n, 1, 4)V<-rnorm(n)X_3<-2 * X_2 + Veps<-rnorm(n, sd=sqrt(2/3))rep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3, data = MC_data)beta_hat_2[r] <- coef(lm_obj)[2]}rep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}c(2,3,4)beta <- c(2,3,4)X <- c(X_2, X_3)Y <- beta %*% X + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}beta <- c(2,3,4)X <- c(X_2, X_3)Y <- beta %*% X + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}n<-100X_2<-runif(n, 1, 4)V<-rnorm(n)X_3<-2 * X_2 + Veps<-rnorm(n, sd=sqrt(2/3))## a.beta <- c(2,3,4)X <- c(X_2, X_3)Y <- beta %*% X + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}## a.beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}beta_true_2round(mean(beta_hat_2), 3)beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)round(var(beta_hat_2), 5)beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)n<-100X_2<-runif(n, 1, 4)V<-rnorm(n)X_3<-2 * X_2 + Veps<-rnorm(n, sd=sqrt(2/3))## a.beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)myDataGenerator <- function(n, beta, X=NULL, sigma=3){if (is.null(X)){X <- cbind(rep(1,n)),runif(n,2,10),runif(n,12,22)}}for(r in 1:rep){MC_data_2 <- myDataGenerator(n=n,beta=beta_true,X=X_cond)lm_obj_2<- lm(Y ~ X_2, data = MC_data_2)beta_hat_2[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)for(r in 1:rep){lm_obj<- lm(Y ~ X_2)beta_hat_2[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)round(mean(beta_hat_2_b), 5)Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]beta_hat_2_b[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)round(mean(beta_hat_2_b), 5)beta_hat_2_b[r] <- coef(lm_obj)[2]Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2 <- rep(NA, times=rep)beta_hat_2_b <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2[r] <- coef(lm_obj)[2]beta_hat_2_b[r] <- coef(lm_obj)[2]}round(var(beta_hat_2), 5)round(mean(beta_hat_2_b), 5)Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2_b <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2_b[r] <- coef(lm_obj)[2]}round(mean(beta_hat_2_b), 5)Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2_b <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 )beta_hat_2_b[r] <- coef(lm_obj)[2]}round(mean(beta_hat_2_b), 5)beta_1 <- 2beta_2 <- 3beta_3 <- 4Y <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2_b <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 + X_3)beta_hat_2_b[r] <- coef(lm_obj)[2]}round(mean(beta_hat_2_b), 5)## bY <- beta_1 + beta_2*X_2 + beta_3*X_3 + epsrep<- 500beta_hat_2_b <- rep(NA, times=rep)for(r in 1:rep){lm_obj<- lm(Y ~ X_2 )beta_hat_2_b[r] <- coef(lm_obj)[2]}round(mean(beta_hat_2_b), 5)