wooldridge-vignette

Introduction

This vignette contains examples from every chapter of Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge. Each example illustrates how to load data, build econometric models, and compute estimates with R.

Economics students new to both econometrics and R may find the introduction to both a bit challenging. In particular, the process of loading and preparing data prior to building one’s first econometric model can present challenges. The wooldridge data package aims to lighten this task. It contains 105 data sets from Introductory Econometrics: A Modern Approach, and will load any set by typing its name into the data() function.

While the course companion site also provides publicly available data sets for Eviews, Excel, MiniTab, and Stata commercial software, R is the open source option. Furthermore, using R while building a foundation in econometrics, can become the first step in a student’s longer journey toward using the most innovative new methods in statistical computing for handling larger, more modern data sets.

In addition, please visit the Appendix for sources on using R for econometrics. For example, an excellent reference is “Using R for Introductory Econometrics” by Florian Hess, written to compliment Introductory Econometrics: A Modern Approach. The full text can be viewed on the book website.

Now, load the wooldridge package and lets get started.

library(wooldridge)

Chapter 2: The Simple Regression Model

Example 2.10: A Log Wage Equation

\[\widehat{log(wage)} = \beta_0 + \beta_1educ\]

Load the wage1 data.

data(wage1)

Estimate a linear relationship between the log of wage and education.

log_wage_model <- lm(lwage ~ educ, data = wage1)

Print the results. I’m using the stargazer package to print the model results in a clean and easy to read format. See the bibliography for more information.

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)

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

Load the jtrain data set and if you are using R Studio, View the data set.

data("jtrain")

View(jtrain)

Create a logical index, identifying which observations occur in 1987 and are non-union.

index <- jtrain$year == 1987 & jtrain$union == 0

Next, 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 lsales(log of annual sales), and lemploy(the log of the number of the employees), against lscrap(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.

data(crime1)

Estimate the model.

restricted_model <- lm(narr86 ~ pcnv + ptime86 + qemp86, data = crime1)

Create a new variable restricted_model_u containing the residuals \(\tilde{\mu}\) from the above regression.

restricted_model_u <- restricted_model$residuals

Next, regress pcnv, ptime86, qemp86, avgsen, and tottime, against the residuals \(\tilde{\mu}\) saved in restricted_model_u.

\[\tilde{\mu} = \beta_1pcnv + \beta_2avgsen + \beta_3tottime + \beta_4ptime86 + \beta_5qemp86\]

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] 4.0875

qchisq(1 - 0.10, 2)

## [1] 4.60517

The p-value is: \[P(X^2_{2} > 4.09) \approx 0.129\]

1-pchisq(LM_test, 2)

## [1] 0.129542

Chapter 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.

\[\widehat{zprice} = \beta_1znox + \beta_2zcrime + \beta_3zrooms + \beta_4zdist + \beta_5zstratio\]

Load the hrpice2 data.

data(hrpice2)

## Warning in data(hrpice2): data set 'hrpice2' not found

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

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)

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, use the hrpice1 data.

data(hrpice1)

If you recently 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

\[\widehat{PC} = \beta_0 + \beta_1hsGPA + \beta_2ACT + \beta_3parcoll + \beta_4colonial \]

Load gpa1 and create a new variable combining the fathcoll 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)

Calculate the weights and then pass them to the weights argument.

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 and estimate the model.

data(rdchem)
 
all_rdchem <- lm(rdintens ~ sales + profmarg, data = rdchem)

Plotting the data reveals the outlier on the far right of the plot, which will skew the results of our model.

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 = "lightgrey", data = rdchem, main = plot_title, 
    xlab = x_axis, ylab = y_axis)

So, we can estimate the model without that data point to gain a better understanding of how sales and profmarg describe rdintens for most firms. We can use the subset argument of the linear model function to indicate that we only want to estimate the model using data that is less than the highest sales.

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

data("barium")
barium_imports <- lm(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 + 
    afdec6, data = barium)

Estimate a new model, barium_seasonal which accounts for seasonality by adding dummy variables contained in the data. Compute the anova between the two models.

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     -0.56524

barium_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          8

Example 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 estimate 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 from the plm: Linear Models for Panel Data package. See the bibliography for more information.

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. See the bibliography for more information.

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)

\[\widehat{log(wage)} = \beta_0 + educ\]

Again, estimate the model 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

\[\widehat{log(wage)} = \beta_0 + \beta_1educ + \beta_2exper + \beta_3exper^2\]

Use the ivreg function in the AER (Applied Econometrics with R) package to estimate.

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)

\[\widehat{inf} = \beta_0 + \beta_{1}open + \beta_{2}log(pcinc)\]

Use the ivreg function in the AER (Applied Econometrics with R) package to estimate.

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")

Sometimes, when estimating a model with many variables, defining a model object containing the formula makes for much cleaner code.

formula <- (narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + inc86 + black + 
    hispan + born60)

Then, pass the formula object into the lm function, and define the data argument as usual.

econ_crime_model <- lm(formula, data = crime1)

To estimate the poisson regression, use the general linear model function glm and define the family argument as poisson.

econ_crim_poisson <- glm(formula, data = crime1, family = poisson)

Use the stargazer package to easily compare diagnostic tables of both models.

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

data("phillips")

\[\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1}\]

Estimate the linear model in the usual way and note the use of the subset argument to define data equal to and before the year 1996.

unem_AR1 <- lm(unem ~ unem_1, data = phillips, subset = (year <= 1996))

\[\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1} + \beta_2inf_{t-1}\]

unem_inf_VAR1 <- lm(unem ~ unem_1 + inf_1, data = phillips, subset = (year <= 1996))

Bibliography

Yves Croissant, Giovanni Millo (2008). Panel Data Econometrics in R: The plm Package. Journal of Statistical Software 27(2). URL www.jstatsoft.org/v27/i02/.

Marek Hlavac (2015). stargazer: Well-Formatted Regression and Summary Statistics Tables. R package version 5.2. https://CRAN.R-project.org/package=stargazer

Christian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL https://CRAN.R-project.org/package=AER

Franz Mohr (2015). prais: Prais-Winsten Estimation Procedure for AR(1) Serial Correlation. R package version 0.1.1. https://CRAN.R-project.org/package=prais

R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

Hadley Wickham and Winston Chang (2016). devtools: Tools to Make Developing R Packages Easier. R package version 1.12.0. https://CRAN.R-project.org/package=devtools

Hadley Wickham. testthat: Get Started with Testing. R package version 1.0.2. https://CRAN.R-project.org/package=testthat

Jeffrey M. Wooldridge (2013). Introductory Econometrics: A Modern Approach. Mason, Ohio :South-Western Cengage Learning.

Yihui Xie (2017). knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.16. https://CRAN.R-project.org/package=knitr

Appendix

Econometrics in R

This 50 pg. document is posted on the Comprehensive R Archive Network site and contains useful econometric recipes as well as general information about R.

Farnsworth, Grant. Econometrics in R. 2008, Evanston, IL. url: https://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf

Using R for Introductory Econometrics

This excerpt from the books excellent website:

This book introduces the popular, powerful and free programming language and software package R with a focus on the implementation of standard tools and methods used in econometrics. Unlike other books on similar topics, it does not attempt to provide a self-contained discussion of econometric models and methods. Instead, it builds on the excellent and popular textbook “Introductory Econometrics” by Jeffrey M. Wooldridge.

Hess, Florian. Using R for Introductory Econometrics. ISBN: 978-1-523-28513-6, CreateSpace Independent Publishing Platform, 2016, Dusseldorf, Germany. url: https://urfie.net.