wooldridge-vignette
+Justin M Shea
+ +-
+
- Introduction +
- Chapter 2: The Simple Regression Model +
- Chapter 3: Multiple Regression Analysis: Estimation +
- Chapter 4: Multiple Regression Analysis: Inference +
- Chapter 5: Multiple Regression Analysis: OLS Asymptotics +
- Chapter 6: Multiple Regression: Further Issues +
- Chapter 7: Multiple Regression Analysis with Qualitative Information +
- Chapter 8: Heteroskedasticity +
- Chapter 9: More on Specification and Data Issues +
- Chapter 10: Basic Regression Analysis with Time Series Data +
- Chapter 11: Further Issues in Using OLS with with Time Series Data +
- Chapter 12: Serial Correlation and Heteroskedasticiy in Time Series Regressions +
- Chapter 13: Pooling Cross Sections across Time: Simple Panel Data Methods +
- Chapter 14: Advanced Panel Data Methods +
- Chapter 15: Instrumental Variables Estimation and Two Stage Least Squares +
- Chapter 16: Simultaneous Equations Models +
- Chapter 17: Limited Dependent Variable Models and Sample Selection Corrections +
- Chapter 18: Advanced Time Series Topics +
Introduction
+This vignette contains examples of using R with “Introductory Econometrics: A Modern Approach” by Jeffrey M. Wooldridge. Each example illustrates how to load data, run econometric models, and view the results with R.
+While the course companion site also provides publicly available data sets for E-views, Excel, MiniTab, and Stata commercial software products, R is an open source option. Furthermore, taking the step to use R while building a foundation in Econometrics, offers the curious Student a gateway to accessing advanced topics available in the greater package ecosystem.
+First, load the wooldridge package to access data in the manner specified in each example.
library(wooldridge)Chapter 2: The Simple Regression Model
+Example 2.10: A Log Wage Equation
\[\widehat{log(wage)} = \beta_0 + \beta_1educ\]
+First, load the wage1 data.
data(wage1)Next, estimate a linear relationship between the log of wage and education.
+log_wage_model <- lm(lwage ~ educ, data = wage1)Finally, print the coefficients and \(R^2\).
+stargazer(log_wage_model, single.row = TRUE, header = FALSE)Chapter 3: Multiple Regression Analysis: Estimation
+Example 3.2: Hourly Wage Equation
\[\widehat{log(wage)} = \beta_0 + \beta_1educ + \beta_3exper + \beta_4tenure\]
+Estimate the model regressing education, experience, and tenure against log(wage).
+hourly_wage_model <- lm(lwage ~ educ + exper + tenure, data = wage1)Again, print the estimated model coefficients:
+stargazer(hourly_wage_model, single.row = TRUE, header = FALSE)Chapter 4: Multiple Regression Analysis: Inference
+Example 4.7 Effect of Job Training on Firm Scrap Rates
First, load the jtrain data set.
data("jtrain")Next, create a logical index identifying which observations occur in 1987 and are non-union.
+index <- jtrain$year == 1987 & jtrain$union == 0Next, subset the jtrain data by the new index. This returns a data.frame of jtrain data of non-union firms for the year 1987.
jtrain_1987_nonunion <- jtrain[index,]Now create the linear model regressing hrsemp(total hours training/total employees trained), the log of annual sales, and the log of the number of the employees, against the log of the scrape rate.
+\[lscrap = \alpha + \beta_1 hrsemp + \beta_2 lsales + \beta_3 lemploy\]
+linear_model <- lm(lscrap ~ hrsemp + lsales + lemploy, data = jtrain_1987_nonunion)Finally, print the complete summary statistic diagnostics of the model.
+stargazer(linear_model, single.row = TRUE, header = FALSE)Chapter 5: Multiple Regression Analysis: OLS Asymptotics
+Example 5.3: Economic Model of Crime
\[narr86 = \beta_0 + \beta_1pcnv + \beta_2avgsen + \beta_3tottime + \beta_4ptime86 + \beta_5qemp86 + \mu\]
+\(narr86:\) number of times arrested, 1986.
+\(pcnv:\) proportion of prior arrests leading to convictions.
+\(avgsen:\) average sentence served, length in months.
+\(tottime:\) time in prison since reaching the age of 18, length in months.
+\(ptime86:\) months in prison during 1986
+\(qemp86:\) quarters employed, 1986
+Load the crime1 data set containing arrests during the year 1986 and other information on 2,725 men born in either 1960 or 1961 in California.
data(crime1)restricted_model <- lm(narr86 ~ pcnv + ptime86 + qemp86, data = crime1)We obtain the residuals \(\tilde{\mu}\) from this regression, 2,725 of them.
+restricted_model_u <- restricted_model$residualsNext, we run the regression of:
+\[\tilde{\mu} = \beta_1pcnv + \beta_2avgsen + \beta_3tottime + \beta_4ptime86 + \beta_5qemp86\]
+LM_u_model <- lm(restricted_model_u ~ pcnv + ptime86 + qemp86 + avgsen + tottime,
+ data = crime1)
+
+summary(LM_u_model)$r.square## [1] 0.001493846\[LM = 2,725(0.0015)\]
+LM_test <- nobs(LM_u_model) * 0.0015
+LM_test## [1] 4.0875qchisq(1 - 0.10, 2)## [1] 4.60517The p-value is: \[P(X^2_{2} > 4.09) \approx 0.129\] so we would reject the \(H_0\) at the 15% level.
+1-pchisq(LM_test, 2)## [1] 0.129542Chapter 6: Multiple Regression: Further Issues
+Example 6.1: Effects of Pollution on Housing Prices, standardized.
\[price = \beta_0 + \beta_1nox + \beta_2crime + \beta_3rooms + \beta_4dist + \beta_5stratio + \mu\]
+\(price\): median housing price.
+\(nox\): Nitrous Oxide concentration; parts per million.
+\(crime\): number of reported crimes per capita.
+\(rooms\): average number of rooms in houses in the community.
+\(dist\): weighted distance of the community to 5 employment centers.
+\(stratio\): average student-teacher ratio of schools in the community.
+\[\widehat{zprice} = \beta_1znox + \beta_2zcrime + \beta_3zrooms + \beta_4zdist + \beta_5zstratio\] First, load the hrpice2 data.
data(hrpice2)Next, estimate the coefficient with the usual lm regression model but this time, standardized coefficients by wrapping each variable with R’s scale function:
housing_standard <- lm(scale(price) ~ 0 + scale(nox) + scale(crime) + scale(rooms) +
+ scale(dist) + scale(stratio), data = hprice2)stargazer(housing_standard, single.row = TRUE, header = FALSE)Example 6.2: Effects of Pollution on Housing Prices, Quadratic Interactive Term
We modify the housing model, adding a quadratic term in rooms:
+\[log(price) = \beta_0 + \beta_1log(nox) + \beta_2log(dist) + \beta_3rooms + \beta_4rooms^2 + \beta_5stratio + \mu\]
+housing_interactive <- lm(lprice ~ lnox + log(dist) + rooms+I(rooms^2) + stratio, data = hprice2)Lets compare the results with the model from example 6.1.
stargazer(housing_standard, housing_interactive, single.row = TRUE, header = FALSE)Chapter 7: Multiple Regression Analysis with Qualitative Information
+Example 7.4: Housing Price Regression, Qualitative Binary variable
This time we use the hrpice1 data.
data(hrpice1)Having just worked with hrpice2, it may be helpful to view the documentation on this data set and read the variable names.
?hprice1\[\widehat{log(price)} = \beta_0 + \beta_1log(lotsize) + \beta_2log(sqrft) + \beta_3bdrms + \beta_4colonial \]
+Estimate the coefficients of the above linear model on the hprice data set.
housing_qualitative <- lm(lprice ~ llotsize + lsqrft + bdrms + colonial, data = hprice1)stargazer(housing_qualitative, single.row = TRUE, header = FALSE)Chapter 8: Heteroskedasticity
+Example 8.9: Determinants of Personal Computer Ownership
\[\widehat{PC} = \beta_0 + \beta_1hsGPA + \beta_2ACT + \beta_3parcoll + \beta_4colonial \]
+Create a new variable combining thefathcoll and mothcoll, into parcoll. This new column indicates if either parent went to college.
data("gpa1")
+gpa1$parcoll <- as.integer(gpa1$fathcoll==1 | gpa1$mothcoll)GPA_OLS <- lm(PC ~ hsGPA + ACT + parcoll, data = gpa1)First, calculate the weights and then pass them to the same linear model.
+weights <- GPA_OLS$fitted.values * (1-GPA_OLS$fitted.values)
+
+GPA_WLS <- lm(PC ~ hsGPA + ACT + parcoll, data = gpa1, weights = 1/weights)Compare the OLS and WLS model in the table below:
+stargazer(GPA_OLS, GPA_WLS, single.row = TRUE, header = FALSE)Chapter 9: More on Specification and Data Issues
+Example 9.8: R&D Intensity and Firm Size
\[rdintens = \beta_0 + \beta_1sales + \beta_2profmarg + \mu\]
+Load the data, run the model, and apply the summary diagnostics function to the model.
data(rdchem)
+
+all_rdchem <- lm(rdintens ~ sales + profmarg, data = rdchem)Notice the outlier on the far right of the plot.
+plot_title <- "FIGURE 9.1: Scatterplot of R&D intensity against firm sales"
+x_axis <- "firm sales (in millions of dollars)"
+y_axis <- "R&D as a percentage of sales"
+
+plot(rdintens ~ sales, pch = 21, bg = "lightblue", data = rdchem, main = plot_title,
+ xlab = x_axis, ylab = y_axis)
smallest_rdchem <- lm(rdintens ~ sales + profmarg, data = rdchem,
+ subset = (sales < max(sales)))The table below compares the results of both models side by side. By removing the outlier firm, \(sales\) become a more significant determination of R&D expenditures.
+stargazer(all_rdchem, smallest_rdchem, single.row = TRUE, header = FALSE)Chapter 10: Basic Regression Analysis with Time Series Data
+Example 10.2: Effects of Inflation and Deficits on Interest Rates
\[\widehat{i3} = \beta_0 + \beta_1inf_t + \beta_2def_t\]
+data("intdef")
+
+tbill_model <- lm(i3 ~ inf + def, data = intdef)stargazer(tbill_model, single.row = TRUE, header = FALSE)Example 10.11: Seasonal Effects of Antidumping Filings
In Example 10.5, we used monthly data (in the file BARIUM) that have not been seasonally adjusted.
data("barium")
+barium_imports <- lm(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 +
+ afdec6, data = barium)barium_seasonal <- lm(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 +
+ afdec6 + feb + mar + apr + may + jun + jul + aug + sep + oct + nov + dec,
+ data = barium)
+
+barium_anova <- anova(barium_imports, barium_seasonal)stargazer(barium_imports, barium_seasonal, single.row = TRUE, header = FALSE)stargazer(barium_anova, single.row = TRUE, header = FALSE)Chapter 11: Further Issues in Using OLS with with Time Series Data
+Example 11.7: Wages and Productivity
\[\widehat{log(hrwage_t)} = \beta_0 + \beta_1log(outphr_t) + \beta_2t + \mu_t\]
+data("earns")
+
+wage_time <- lm(lhrwage ~ loutphr + t, data = earns)wage_diff <- lm(diff(lhrwage) ~ diff(loutphr), data = earns)stargazer(wage_time, wage_diff, single.row = TRUE, header = FALSE)Chapter 12: Serial Correlation and Heteroskedasticiy in Time Series Regressions
+Example 12.4: Prais-Winsten Estimation in the Event Study
data("barium")
+barium_model <- lm(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 + afdec6,
+ data = barium)
+# Load the `prais` package, use the `prais.winsten` function to estimate.
+library(prais)
+barium_prais_winsten <- prais.winsten(lchnimp ~ lchempi + lgas + lrtwex + befile6 +
+ affile6 + afdec6, data = barium)barium_model##
+## Call:
+## lm(formula = lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 +
+## afdec6, data = barium)
+##
+## Coefficients:
+## (Intercept) lchempi lgas lrtwex befile6
+## -17.80300 3.11719 0.19635 0.98302 0.05957
+## affile6 afdec6
+## -0.03241 -0.56524barium_prais_winsten## [[1]]
+##
+## Call:
+## lm(formula = fo)
+##
+## Residuals:
+## Min 1Q Median 3Q Max
+## -2.01146 -0.39152 0.06758 0.35063 1.35021
+##
+## Coefficients:
+## Estimate Std. Error t value Pr(>|t|)
+## Intercept -37.07771 22.77830 -1.628 0.1061
+## lchempi 2.94095 0.63284 4.647 8.46e-06 ***
+## lgas 1.04638 0.97734 1.071 0.2864
+## lrtwex 1.13279 0.50666 2.236 0.0272 *
+## befile6 -0.01648 0.31938 -0.052 0.9589
+## affile6 -0.03316 0.32181 -0.103 0.9181
+## afdec6 -0.57681 0.34199 -1.687 0.0942 .
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+##
+## Residual standard error: 0.5733 on 124 degrees of freedom
+## Multiple R-squared: 0.9841, Adjusted R-squared: 0.9832
+## F-statistic: 1096 on 7 and 124 DF, p-value: < 2.2e-16
+##
+##
+## [[2]]
+## Rho Rho.t.statistic Iterations
+## 0.2932171 3.483363 8Example 12.8: Heteroskedasticity and the Efficient Markets Hypothesis
\[return_t = \beta_0 + \beta_1return_{t-1} + \mu_t\]
+data("nyse")
+
+return_AR1 <-lm(return ~ return_1, data = nyse)\[\hat{\mu^2_t} = \beta_0 + \beta_1return_{t-1} + residual_t\]
+return_mu <- residuals(return_AR1)
+
+mu2_hat_model <- lm(return_mu^2 ~ return_1, data = return_AR1$model)stargazer(return_AR1, mu2_hat_model, single.row = TRUE, header = FALSE)Example 12.9: ARCH in Stock Returns
\[\hat{\mu^2_t} = \beta_0 + \hat{\mu^2_{t-1}} + residual_t\]
+We still have return_mu in the working environment so we can use it to create \(\hat{\mu^2_t}\), (mu2_hat) and \(\hat{\mu^2_{t-1}}\) (mu2_hat_1). Notice the use R’s matrix subset operations to perform the lag operation. We drop the first observation of mu2_hat and squared the results. Next, we remove the last observation of mu2_hat_1 using the subtraction operator combined with a call to the NROW function on return_mu. Now, both contain \(688\) observations and we can run a standard linear model.
mu2_hat <- return_mu[-1]^2
+
+mu2_hat_1 <- return_mu[-NROW(return_mu)]^2
+
+arch_model <- lm(mu2_hat ~ mu2_hat_1)stargazer(arch_model, single.row = TRUE, header = FALSE)Chapter 13: Pooling Cross Sections across Time: Simple Panel Data Methods
+Example 13.7: Effect of Drunk Driving Laws on Traffic Fatalities
\[\widehat{\Delta{dthrte}} = \beta_0 + \Delta{open} + \Delta{admin}\]
+data("traffic1")
+
+DD_model <- lm(cdthrte ~ copen + cadmn, data = traffic1)stargazer(DD_model, single.row = TRUE, header = FALSE)Chapter 14: Advanced Panel Data Methods
+Example 14.1: Effect of Job Training on Firm Scrap Rates
In this section, we will estimate a linear panel modeg using the plm function in the plm: Linear Models for Panel Data package.
library(plm)
+
+data("jtrain")
+
+scrap_panel <- plm(lscrap ~ d88 + d89 + grant + grant_1, data = jtrain, index = c("fcode",
+ "year"), model = "within", effect = "individual")stargazer(scrap_panel, single.row = TRUE, header = FALSE)Chapter 15: Instrumental Variables Estimation and Two Stage Least Squares
+Example 15.1: Estimating the Return to Education for Married Women
\[log(wage) = \beta_0 + \beta_1educ + \mu\]
+data("mroz")
+wage_educ_model <- lm(lwage ~ educ, data = mroz)\[\widehat{educ} = \beta_0 + \beta_1fatheduc\]
+We run the typical linear model, but notice the use of the subset argument. inlf is a binary variable in which a value of 1 means they are “In the Labor Force”. By sub-setting the mroz data.frame by observations in which inlf==1, only working women will be in the sample.
fatheduc_model <- lm(educ ~ fatheduc, data = mroz, subset = (inlf==1))In this section, we will perform an Instrumental-Variable Regression, using the ivreg function in the AER (Applied Econometrics with R) package.
library("AER")
+wage_educ_IV <- ivreg(lwage ~ educ | fatheduc, data = mroz)stargazer(wage_educ_model, fatheduc_model, wage_educ_IV, single.row = TRUE,
+ header = FALSE)Example 15.2: Estimating the Return to Education for Men
\[\widehat{educ} = \beta_0 + sibs\]
+data("wage2")
+
+educ_sibs_model <- lm(educ ~ sibs, data = wage2)\[\widehat{log(wage)} = \beta_0 + educ\]
+In this section, we will perform an Instrumental-Variable Regression, using the ivreg function in the AER (Applied Econometrics with R) package.
library("AER")
+
+educ_sibs_IV <- ivreg(lwage ~ educ | sibs, data = wage2)stargazer(educ_sibs_model, educ_sibs_IV, wage_educ_IV, single.row = TRUE, header = FALSE)Example 15.5: Return to Education for Working Women
\[\widehat{log(wage)} = \beta_0 + \beta_1educ + \beta_2exper + \beta_3exper^2\]
+data("mroz")
+wage_educ_exper_IV <- ivreg(lwage ~ educ + exper + expersq | exper + expersq +
+ motheduc + fatheduc, data = mroz)Chapter 16: Simultaneous Equations Models
+Example 16.4: INFLATION AND OPENNESS
\[inf = \beta_{10} + \alpha_1open + \beta_{11}log(pcinc) + \mu_1\] \[open = \beta_{20} + \alpha_2inf + \beta_{21}log(pcinc) + \beta_{22}log(land) + \mu_2\]
+Example 16.6: INFLATION AND OPENNESS
\[\widehat{open} = \beta_0 + \beta_{1}log(pcinc) + \beta_{2}log(land)\]
+data("openness")
+
+open_model <-lm(open ~ lpcinc + lland, data = openness)\[\widehat{inf} = \beta_0 + \beta_{1}open + \beta_{2}log(pcinc)\]
+library(AER)
+
+inflation_IV <- ivreg(inf ~ open + lpcinc | lpcinc + lland, data = openness)stargazer(open_model, inflation_IV, single.row = TRUE, header = FALSE)Chapter 17: Limited Dependent Variable Models and Sample Selection Corrections
+Example 17.3: POISSON REGRESSION FOR NUMBER OF ARRESTS
data("crime1")
+
+formula <- (narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + inc86 + black +
+ hispan + born60)
+
+econ_crime_model <- lm(formula, data = crime1)
+
+econ_crim_poisson <- glm(formula, data = crime1, family = poisson)stargazer(econ_crime_model, econ_crim_poisson, single.row = TRUE, header = FALSE)Chapter 18: Advanced Time Series Topics
+Example 18.8: FORECASTING THE U.S. UNEMPLOYMENT RATE
\[\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1}\]
+\[\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1} + \beta_2inf_{t-1}\]
+data("phillips")
+
+unem_AR1 <- lm(unem ~ unem_1, data = phillips, subset = (year <= 1996))
+
+unem_inf_VAR1 <- lm(unem ~ unem_1 + inf_1, data = phillips, subset = (year <= 1996))