Introduction

This vignette contains examples from every chapter of Introductory Econometrics: A Modern Approach, 6e by Jeffrey M. Wooldridge. Each example illustrates how to load data, build econometric models, and compute estimates with R.

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 111 data sets from Introductory Econometrics: A Modern Approach, 6e, which can be loaded with a simple call to the data() function.

While the course companion site 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 econometric modeling introduces one to software tools capable of scaling with the demands of modern methods in statistical computing.

In addition, the Appendix cites additional sources about using R for econometrics.

Now, install and load the wooldridge package and lets get started.

install.packages("wooldridge")

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 and check out the documentation.

data("wage1")
?wage1

These are data from the 1976 Current Population Survey, collected by Henry Farber when he and Wooldridge were colleagues at MIT in 1988.

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.

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). The wage1 data should still be in your working environment.

hourly_wage_model <- lm(lwage ~ educ + exper + tenure, data = wage1)

Print the estimated model coefficients:

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")

From H. Holzer, R. Block, M. Cheatham, and J. Knott (1993), Are Training Subsidies Effective? The Michigan Experience, Industrial and Labor Relations Review 46, 625-636. The authors kindly provided the 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.

Chapter 5: Multiple Regression Analysis: OLS Asymptotics

Example 5.3: Economic Model of Crime

From J. Grogger (1991), Certainty vs. Severity of Punishment, Economic Inquiry 29, 297-309. Professor Grogger kindly provided a subset of the data he used in his article.

\[narr86 = \beta_0 + \beta_1pcnv + \beta_2avgsen + \beta_3tottime + \beta_4ptime86 + \beta_5qemp86 + \mu\]

\(narr86:\) 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")
?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 hprice2 data and view the documentation.

data("hprice2")
?hprice2

Data from Hedonic Housing Prices and the Demand for Clean Air, by Harrison, D. and D.L.Rubinfeld, Journal of Environmental Economics and Management 5, 81-102. Diego Garcia, a former Ph.D. student in economics at MIT, kindly provided these data, which he obtained from the book Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, by D.A. Belsey, E. Kuh, and R. Welsch, 1990. New York: Wiley.

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)

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.

Chapter 7: Multiple Regression Analysis with Qualitative Information

Example 7.4: Housing Price Regression, Qualitative Binary variable

This time, use the hrprice1 data.

data("hprice1")

Data collected from the real estate pages of the Boston Globe during 1990. These are homes that sold in the Boston, MA area.

If you recently worked with hprice2, 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)

Chapter 8: Heteroskedasticity

Example 8.9: Determinants of Personal Computer Ownership

\[\widehat{PC} = \beta_0 + \beta_1hsGPA + \beta_2ACT + \beta_3parcoll + \beta_4colonial \] Christopher Lemmon, a former MSU undergraduate, collected these data from a survey he took of MSU students in Fall 1994. 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

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:

Chapter 9: More on Specification and Data Issues

Example 9.8: R&D Intensity and Firm Size

\[rdintens = \beta_0 + \beta_1sales + \beta_2profmarg + \mu\]

From Businessweek R&D Scoreboard, October 25, 1991. Load the data and estimate the model.

data("rdchem")
?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.

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 from the Economic Report of the President, 2004, Tables B-64, B-73, and B-79.

data("intdef")
?intdef

tbill_model <- lm(i3 ~ inf + def, data = intdef)

Example 10.11: Seasonal Effects of Antidumping Filings

C.M. Krupp and P.S. Pollard (1999), Market Responses to Antidumpting Laws: Some Evidence from the U.S. Chemical Industry, Canadian Journal of Economics 29, 199-227. Dr. Krupp kindly provided the data. They are monthly data covering February 1978 through December 1988.

data("barium")
?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)

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 from the Economic Report of the President, 1989, Table B-47. The data are for the non-farm business sector.

data("earns")
?earns

wage_time <- lm(lhrwage ~ loutphr + t, data = earns)

wage_diff <- lm(diff(lhrwage) ~ diff(loutphr), data = earns)

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_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

These are Wednesday closing prices of value-weighted NYSE average, available in many publications. Wooldridge does not recall the particular source used when he collected these data at MIT, but notes probably the easiest way to get similar data is to go to the NYSE web site, www.nyse.com.

\[return_t = \beta_0 + \beta_1return_{t-1} + \mu_t\]

data("nyse")
?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)

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)

Chapter 13: Pooling Cross Sections across Time: Simple Panel Data Methods

Example 13.7: Effect of Drunk Driving Laws on Traffic Fatalities

Wooldridge collected these data from two sources, the 1992 Statistical Abstract of the United States (Tables 1009, 1012) and A Digest of State Alcohol-Highway Safety Related Legislation, 1985 and 1990, published by the U.S. National Highway Traffic Safety Administration. \[\widehat{\Delta{dthrte}} = \beta_0 + \Delta{open} + \Delta{admin}\]

data("traffic1")
?traffic1

DD_model <- lm(cdthrte ~ copen + cadmn, data = traffic1)

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")

Chapter 15: Instrumental Variables Estimation and Two Stage Least Squares

Example 15.1: Estimating the Return to Education for Married Women

T.A. Mroz (1987), The Sensitivity of an Empirical Model of Married Women’s Hours of Work to Economic and Statistical Assumptions, Econometrica 55, 765-799. Professor Ernst R. Berndt, of MIT, kindly provided the data, which he obtained from Professor Mroz.

\[log(wage) = \beta_0 + \beta_1educ + \mu\]

data("mroz")
?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)

Example 15.2: Estimating the Return to Education for Men

Data from M. Blackburn and D. Neumark (1992), Unobserved Ability, Efficiency Wages, and Interindustry Wage Differentials, Quarterly Journal of Economics 107, 1421-1436. Professor Neumark kindly provided the data, of which Wooldridge uses the data for 1980.

\[\widehat{educ} = \beta_0 + sibs\]

data("wage2")
?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)

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

Data from D. Romer (1993), Openness and Inflation: Theory and Evidence, Quarterly Journal of Economics 108, 869-903. The data are included in the article.

\[inf = \beta_{10} + \alpha_1open + \beta_{11}log(pcinc) + \mu_1\] \[open = \beta_{20} + \alpha_2inf + \beta_{21}log(pcinc) + \beta_{22}log(land) + \mu_2\]

Example 16.6: INFLATION AND OPENNESS

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

data("openness")
?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)

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.

Chapter 18: Advanced Time Series Topics

Example 18.8: FORECASTING THE U.S. UNEMPLOYMENT RATE

Data from Economic Report of the President, 2004, Tables B-42 and B-64.

data("phillips")
?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.

phillips_train <- subset(phillips, year <= 1996)

unem_AR1 <- lm(unem ~ unem_1, data = phillips_train)

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

unem_inf_VAR1 <- lm(unem ~ unem_1 + inf_1, data = phillips_train)

Now, use the subset argument to create our testing data set containing observation after 1996. Next, pass the both the model object and the test set to the predict function for both models. Finally, cbind or “column bind” both forecasts as well as the year and unemployment rate of the test set.

phillips_test <- subset(phillips, year >= 1997)

AR1_forecast <- predict.lm(unem_AR1, newdata = phillips_test)
VAR1_forecast <- predict.lm(unem_inf_VAR1, newdata = phillips_test)

kable(cbind(phillips_test[ ,c("year", "unem")], AR1_forecast, VAR1_forecast))

Appendix