Regression Discontinuity Applications with Rounding Errors in the Running Variable

Many empirical applications of regression discontinuity (RD) models use a running variable that is rounded and hence is discrete, e.g., age in years, or birth weight in ounces. This paper shows that standard RD estimation using a rounded discrete running variable leads to inconsistent estimates of treatment effects, even when the true functional form relating the outcome and the running variable is known and is correctly specified. This paper provides simple formulas to correct for this discretization bias. The proposed approach does not require instrumental variables, but instead uses information regarding the distribution of rounding errors, which is easily obtained and often close to uniform. The proposed approach is applied to estimate the effect of Medicare on insurance coverage in the US, and to investigate the retirement-consumption puzzle in China, utilizing the Chinese mandatory retirement policy.Regression discontinuity; Rounding; Rounding errors; Discrete running variable

Simple Estimators for Binary Choice Models with Endogenous Regressors

This paper provides simple estimators for binary choice models with endogenous or mismeasured regressors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can be used with limited, censored, continuous, or discrete endogenous regressors, and they also allow for latent errors having heteroskedasticity of unknown form, including random coefficients. The variants of special regressor based estimators we provide are numerically trivial to implement. We illustrate these methods with an empirical application estimating migration probabilities within the US.Binary choice; Binomial response; Endogeneity; Measurement error; Heteroskedasticity; Discrete endogenous regressor; Censored regressor; Random coefficients; Identification; Latent variable model

Regression Discontinuity Marginal Threshold Treatment Effects

In regression discontinuity models, where the probability of treatment jumps discretely when a running variable crosses a threshold, an average treatment effect can be nonparametrically identified. We show that the derivative of this treatment effect with respect to the threshold is also nonparametrically identified and easily estimated, in both sharp and fuzzy designs. This marginal threshold treatment effect (MTTE) may be used to estimate the impact on treatment effects of small changes in the threshold. We use it to show how raising the age of Medicare eligibility would change the probability of take up of various types of health insurance.Regression discontinuity; Sharp design; Fuzzy design; Treatment effects; Program evaluation; Threshold; Running variable; Forcing variable

Jumpy or Kinky? Regression Discontinuity without the Discontinuity

Regression Discontinuity (RD) models identify local treatment effects by associating a discrete change in the mean outcome with a corresponding discrete change in the probability of treatment at a known threshold of a running variable. This paper shows that it is possible to identify the RD model treatment effect without a discontinuity. In particular, identification can come from a slope change (a kink) instead of a discrete level change (a jump) in the treatment probability. The intuition is based on L'hopital's rule. The identification results can also be interpreted using instrumental variables models. Estimators are proposed that can be applied in the presence or absence of a discontinuity, by exploiting either a jump, or a kink, or both. The proposed estimators are applied to investigate the "retirement-consumption puzzle." In particular, I estimate the impact of retirement on household food consumption by exploiting changes in the retirement probability at 62, the early retirement age in the US.Regression discontinuity; Fuzzy design; Local average treatment effect; Identification; Jump; Kink; Threshold; Retirement; Consumption

Mandatory Retirement and the Consumption Puzzle: Prices Decline or Quantities Decline?

This paper investigates household consumption changes at retirement by utilizing a comprehensive, diary-based household survey from China. The survey contains both consumption quantity and price information, which permits separating quantity changes from price changes. The mandatory retirement policy in China provides a quasi-experimental setting for identification of the true causal effects of fully anticipated retirement. Using regression discontinuity models, we show that food expenditure declines at retirement, particularly among the low-education group, and that the decline is driven by price declines instead of quantity declines. Shopping time for food increases at retirement, consistent with the price and quantity changes

Microeconometric Models with Endogeneity -- Theoretical and Empirical Studies

Thesis advisor: Arthur LewbelThis dissertation consists of three independent essays in applied microeconomics and econometrics. Essay 1 investigates the issue why individuals with health insurance use more health care. One obvious reason is that health care is cheaper for the insured. But additionally, having insurance can encourage unhealthy behavior via moral hazard. The effect of health insurance on medical utilization has been extensively studied; however, previous work has mostly ignored the effect of insurance on behavior and how that in turn affects medical utilization. This essay examines these distinct effects. The increased medical utilization due to reduced prices may help the insured maintain good health, while that due to increased unhealthy behavior does not, so distinguishing these two effects has important policy implications. A two-period dynamic forward-looking model is constructed to derive the structural causal relationships among the decision to buy insurance, health behaviors (drinking, smoking, and exercise), and medical utilization. The model shows how exogenous changes in insurance prices and past behaviors can identify the direct and indirect effects of insurance on medical utilization. An empirical analysis also distinguishes between intensive and extensive margins (e.g., changes in the number of drinkers vs. the amount of alcohol consumed) of the insurance effect, which turns out to be empirically important. Health insurance is found to encourage less healthy behavior, particularly heavy drinking, but this does not yield a short term perceptible increase in doctor or hospital visits. The effects of health insurance are primarily found at the intensive margin, e.g., health insurance may not cause a non-drinker to take up drinking, while it encourages a heavy drinker to drink even more. These results suggest that to counteract behavioral moral hazard, health insurance should be coupled with incentives that target individuals who currently engage in unhealthy behaviors, such as heavy drinkers. Essay 2 examines the effect of repeating kindergarten on the retained children's academic performance. Although most existing research concludes that grade retention generates no benefits for retainees' later academic performance, holding low achieving children back has been a popular practice for decades. Drawing on a recently collected nationally representative data set in the US, this paper estimates the causal effect of kindergarten retention on the retained children's later academic performance. Since children are observed being held back only when they enroll in schools that permit retention, this paper jointly models 1) the decision of entering a school allowing for kindergarten retention, 2) the decision of undergoing a retention treatment in kindergarten, and 3) children's academic performance in higher grades. The retention treatment is modeled as a binary choice with sample selection. The outcome equations are linear regressions including the kindergarten retention dummy as an endogenous regressor with a correlated random coefficient. A control function estimator is developed for estimating the resulting double-hurdle treatment model, which allows for unobserved heterogeneity in the retention effect. As a comparison, a nonparametric bias-corrected nearest neighbor matching estimator is also implemented. Holding children back in kindergarten is found to have positive but diminishing effects on their academic performance up to the third grade. Essay 3 proves the semiparametric identification of a binary choice model having an endogenous regressor without relying on outside instruments. A simple estimator and a test for endogeneity are provided based on this identification. These results are applied to analyze working age male's migration within the US, where labor income is potentially endogenous. Identification relies on the fact that the migration probability among workers is close to linear in age while labor income is nonlinear in age(when both are nonparametrically estimated). Using data from the PSID, this study finds that labor income is endogenous and that ignoring this endogeneity leads to downward bias in the estimated effect of labor income on the migration probability.Thesis (PhD) — Boston College, 2009.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Economics

Endogenous Regressor Binary Choice Models Without Instruments, With an Application to Migration

Abstract This paper shows the semiparametric identification of a binary choice model having an endogenous regressor without relying on outside instruments. A simple estimator and a test for endogeneity are provided based on this identification. These results are applied to analyze working age male's migration within the US, where labor income is potentially endogenous. Identification relies on the fact that the migration probability among workers is close to linear in age while labor income is nonlinear in age. Using data from the PSID, this study finds that labor income is endogenous and that ignoring this endogeneity leads to downward bias in the estimated effect of labor income on the migration probability. JEL Codes: C35, J6

Jumpy or Kinky? Regression Discontinuity without the Discontinuity

Regression Discontinuity (RD) models identify local treatment effects by associating a discrete change in the mean outcome with a corresponding discrete change in the probability of treatment at a known threshold of a running variable. This paper shows that it is possible to identify RD model treatment effects without a discontinuity. The intuition is that identification can come from a slope change (a kink) instead of a discrete level change (a jump) in the treatment probability. Formally this can be shown using L'hopital's rule. The identification results are interpreted intuitively using instrumental variable models. Estimators are proposed that can be applied in the presence or absence of a discontinuity, by exploiting either a jump or a kink