This paper provides an introduction and "user guide" to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a "quasi-experimental" design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD.

Regression Discontinuity Designs in Economics

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects. This recent theoreti- cal literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas of empirical microeconomics. In this review, we discuss some of the recent developments. We focus primarily on practical issues for empirical research- ers, as well as provide a historical overview of the area and give references to more technical research.

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Recent developments in the econometrics of program evaluation

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

We apply an understanding of what computers do to study how computerization alters job skill demands. We argue that computer capital (1) substitutes for workers in performing cognitive and manual tasks that can be accomplished by following explicit rules; and (2) complements workers in performing nonroutine problem-solving and complex communications tasks. Provided these tasks are imperfect substitutes, our model implies measurable changes in the composition of job tasks, which we explore using representative data on task input for 1960 to 1998. We find that within industries, occupations and education groups, computerization is associated with reduced labor input of routine manual and routine cognitive tasks and increased labor input of nonroutine cognitive tasks. Translating task shifts into education demand, the model can explain sixty percent of the estimated relative demand shift favoring college labor during 1970 to 1998. Task changes within nominally identical occupations account for almost half of this impact.

/pdf/the-skill-content-of-recent-technological-change-an-120y2lva5p.pdf

The Skill Content of Recent Technological Change: An Empirical Exploration

This paper provides an introduction and “user guide” to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a “quasi-experimental” design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD. ( JEL C21, C31)

/pdf/regression-discontinuity-designs-in-economics-5foiogfcmd.pdf

Regression discontinuity designs in economics

Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regressio...

/pdf/local-polynomial-order-in-regression-discontinuity-designs-5dymhhfy9k.pdf

Local Polynomial Order in Regression Discontinuity Designs

During the 1980s, did the sharp increase in the college-high school wage differential represent a rise in the college premium, or a growth in the payoff to unmeasured ability or skill? Can the slowdown in black-white wage convergence or the widening black-white gap among young workers witnessed during the 1980s be explained by a rise in the return to pre-labor market factors correlated with race? In this study, we show that it is possible to use across-group variation in within-group wage variances from multiple periods to identify the change in the return to unobservable skill, within a relatively unrestrictive error-components model of wages. The identification does not require full specification of the time-series properties or the functional form of the errors. Male earnings data from the CPS show that there is useful variation in within-group wage variances -- enough to estimate a growth in the return to unobservable skill of about 10 to 20 percent during the 1980s. In our analysis, these magnitudes imply that even alter controlling for the effects of an increase in the payoff to unobservable skill, college-educated workers still gain substantially relative to high school-educated workers, while young black men still experience a significant wage decline relative to white men during the l980s.

Changes in Relative Wages in the 1980s: Returns to Observed and Unobserved Skills and Black-White Wage Differentials

Thin-wall titanium structural castings

We estimate the effect of new unionization on firms? equity value over the 1961-1999 period using a newly assembled sample of National Labor Relations Board (NLRB) representation elections matched to stock market data. Event-study estimates show an average union effect on the equity value of the firm equivalent to a cost of at least $40,500 per unionized worker. At the same time, point estimates from a regression-discontinuity design comparing the stock market impact of close union election wins to close losses are considerably smaller and close to zero. We find a negative relationship between the cumulative abnormal returns and the vote share in support of the union, allowing us to reconcile these seemingly contradictory findings. Using the magnitudes from the analysis, we calibrate a structural median voter model of endogenous union determination in order to conduct counterfactual policy simulations of policies that would marginally increase the ease of unionization.

Long-Run Impacts of Unions on Firms: New Evidence from Financial Markets, 1961-1999

A regression discontinuity (RD) research design is appropriate for program evaluation problems in which treatment status (or the probability of treatment) depends on whether an observed covariate exceeds a fixed threshold. In many applications the treatment-determining covariate is discrete. This makes it impossible to compare outcomes for observations "just above" and "just below" the treatment threshold, and requires the researcher to choose a functional form for the relationship between the treatment variable and the outcomes of interest. We propose a simple econometric procedure to account for uncertainty in the choice of functional form for RD designs with discrete support. In particular, we model deviations of the true regression function from a given approximating function -- the specification errors -- as random. Conventional standard errors ignore the group structure induced by specification errors and tend to overstate the precision of the estimated program impacts. The proposed inference procedure that allows for specification error also has a natural interpretation within a Bayesian framework.

David S. Lee

Papers

Local Polynomial Order in Regression Discontinuity Designs

Changes in Relative Wages in the 1980s: Returns to Observed and Unobserved Skills and Black-White Wage Differentials

Thin-wall titanium structural castings

Long-Run Impacts of Unions on Firms: New Evidence from Financial Markets, 1961-1999

Regression Discontinuity Inference with Specification Error