Justin McCrary

New Evidence on the Finite Sample Properties of Propensity Score Reweighting and Matching Estimators

Frölich (2004) compares the finite sample properties of reweighting and matching estimators of average treatment effects and concludes that reweighting performs far worse than even the simplest matching estimator. We argue that this conclusion is unjustified. Neither approach dominates the other uniformly across data-generating processes (DGPs). Expanding on Frölichs analysis, this paper analyzes empirical as well as hypothetical DGPs and also examines the effect of misspecification. We conclude that reweighting is competitive with the most effective matching estimators when overlap is good, but that matching may be more effective when overlap is sufficiently poor.

The Deterrence Effect of Prison: Dynamic Theory and Evidence

Using administrative, longitudinal data on felony arrests in Florida, we exploit the discontinuous increase in the punitiveness of criminal sanctions at 18 to estimate the deterrence effect of incarceration. Our analysis suggests a 2 percent decline in the log-odds of offending at 18, with standard errors ruling out declines of 11 percent or more. We interpret these magnitudes using a stochastic dynamic extension of Beckers (1968) model of criminal behavior. Calibrating the model to match key empirical moments, we conclude that deterrence elasticities with respect to sentence lengths are no more negative than -0.13 for young offenders.

Dynamic Perspectives on Crime

* I think David Lee for collaboration on related projects and Pat Kline and Demian Pouzo for unusually helpful comments. Mike Elsby provided a set of extremely detailed and insightful comments on an earlier draft. I am responsible for any errors.

FOLLOWING GERMANY'S LEAD: USING INTERNATIONAL MONETARY LINKAGES TO ESTIMATE THE EFFECT OF MONETARY POLICY ON THE ECONOMY

Forward-looking behavior on the part of the monetary authority makes it difficult to estimate the effect of monetary policy interventions on output. We present instrumental variables estimates of the impact of interest rates on quarterly real output for several European countries, using German interest rates as the instrument. These estimates confirm a strong forward-looking bias in least squares estimates that persists even conditional on standard controls for the history of the system. Due to the potential for correlation of output shocks across countries, we interpret our estimates as lower bounds for the effect of monetary policy on real output.

Are U.S. Cities Underpoliced? Theory and Evidence

We document the extent of measurement errors in the basic data set on police used in the literature on the effect of police on crime. Analyzing medium to large U.S. cities over 1960 to 2010, we obtain measurement error-corrected estimates of the police elasticity. The magnitudes of our estimates are similar to those obtained in the quasi-experimental literature, but our approach yields much greater parameter certainty for the most costly crimes, the key parameters for welfare analysis. Our analysis suggests that U.S. cities are substantially underpoliced.

Measuring Benchmark Damages in Antitrust Litigation

Abstract We compare the two dominant approaches to estimation of benchmark damages in antitrust litigation, the forecasting approach and the dummy variable approach. We give conditions under which the two approaches are equivalent and present the results of a small simulation study.

Conservative Tests under Satisficing Models of Publication Bias

Publication bias leads consumers of research to observe a selected sample of statistical estimates calculated by producers of research. We calculate critical values for statistical significance that could help to adjust after the fact for the distortions created by this selection effect, assuming that the only source of publication bias is file drawer bias. These adjusted critical values are easy to calculate and differ from unadjusted critical values by approximately 50%—rather than rejecting a null hypothesis when the t-ratio exceeds 2, the analysis suggests rejecting a null hypothesis when the t-ratio exceeds 3. Samples of published social science research indicate that on average, across research fields, approximately 30% of published t-statistics fall between the standard and adjusted cutoffs.

Dark Trading at the Midpoint: Pricing Rules, Order Flow and High Frequency Liquidity Provision

We examine the competitive advantage enjoyed by dark venues over stock exchanges due to rules regulating the minimum price variation (MPV) for quoting equity securities. The MPV rule requires quotes above

Subsidizing Liquidity with Wider Ticks: Evidence from the Tick Size Pilot Study

1.00 per share to be in pennies, but it permits subpenny trades to facilitate price improvement for marketable orders. This exception to the penny quote rule benefits dark venues by allowing broker-dealers to intercept market orders by offering subpenny trading opportunities. However, a growing chorus of critics allege that (a) dark venues exploit this exception by offering little or no price improvement for market orders, and (b) allowing dark venues to intercept market orders harms the incentive to display liquidity on exchanges on which markets depend for efficient securities pricing. Using a novel regression discontinuity design and over eight trillion observations on market data from 2011-2014, we provide evidence that is inconsistent with both critiques. First, increasing the incentive to use the exception to the penny quote rule increases the rate of trading in dark venues at the midpoint of the national best bid and offer, thus offering liquidity takers price improvement in the form of the quoted half-spread. Second, while enhanced order flow to dark pools decreases price competition on exchanges, this reduction is primarily because of reduced quoting among high frequency trading (HFT) firms. Consistent with concerns about HFT, we show HFT market-making increases price volatility and that overall trading volume increases when it occurs in dark pools rather than on exchanges.

Dark Trading at the Midpoint: Does SEC Enforcement Policy Encourage Stale Quote Arbitrage?

Using data from the 2016-2018 tick size pilot study, we examine the efficacy of using wider tick sizes to subsidize market-making in small capitalization stocks. We demonstrate that realized spreads decay quickly within the initial microseconds of a trade. The effect reduces the subsidy offered by wider tick sizes, particularly for non-HFT market makers. The profit subsidy from wider tick sizes is also compromised by a significant shift in trading to “taker/maker” exchanges and to midpoint trading in non-exchange venues. The pilot’s exception for midpoint trades also accounts for the fact that nearly a third of trading remains in non-exchange venues despite the inclusion of a trade-at rule. Overall, these findings point to considerable inefficiencies in the pilot study’s goal of using wider tick sizes to subsidize liquidity provision in small capitalization stocks