## Exercise Chapter 3
## Problem 3
## Background
install.packages(“AER”)
suppressMessages(library(“AER”))
## attach the data-set Journals to the current R-session
data(“Journals”, package = “AER”)
## ?Journals # Check the help file # 一组数据，美国图书馆经济期刊的订阅量
## Select variable “subs” and “price”
journals <- Journals[, c(“subs”, “price”)] # sub为订阅量，price为订阅价格；方括号为select；逗号前是行，逗号后是列，这里选中列## Define variable ‘journals-price per citation’journals$citeprice <- Journals$price/Journals$citations # 定义列；$用来引用Journals中的数据## Define variable ‘journals-age’journals$age <- 2020 – Journals$foundingyear # 定义列；foundingyear为期刊成立年份## Check variable name in ‘journals’names(journals)## [1] “subs””price” “citeprice” “age”## Estimate the coefficients beta_1 and beta_2 of the linear regression model: log(Y) = beta_1 + beta_2*log(X) + eps## log(Y) = log(subs) and log(X) = log(citeprice)## Problem 3a 画residuals – fitted value图看是否有heteroscedastic error-term variances(异方差)## Solutionjour_lm <- lm(log(subs) ~ log(citeprice), data = journals) # lm 用于拟合线性模型，格式 lm(Y~X1+…+Xk, data), Y~X1+…+Xk 为通过X预测Y，其中+用于分隔预测变量## Diagnostic plot residuals against fitted values## plot(y = resid(jour_lm), x = fitted(jour_lm)) # 朴素画法## Or 高级画法plot(jour_lm, which = 1) # which是图的类型## 图中点的分布明显左边更高，右边更低，说明不均匀，有different variance in the error term，所以说是heteroscedastic## Problem 3b Estimate the standard error of the OLS estimator beta_hat_2## Solution## HC robust variance estimationlibrary(“sandwich”) ## Robust estimation of the variance of hatbetaVar_hat_beta_HC3 <- sandwich::vcovHC(jour_lm, type = “HC3”) # sandwich::vcovHC为Heteroscedasticity-Consistent Covariance Matrix Estimation；HC3最常用，作业都用了HC3# type为estimation type## Robust standard error of hatbeta_2sqrt(diag(Var_hat_beta_HC3)[2]) # sqrt开方；diag(x)用x中元素作为主对角元素创造对角矩阵；方括号选出2代表2. variance component## log(citeprice) ## 0.03447364 ## Comparison with the classic standard error estimationsqrt(diag(vcov(jour_lm))[2]) # Calculate Variance-Covariance Matrix for a Fitted Model Object## log(citeprice) ## 0.0356132
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