查看更多>>摘要:I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment effects on the treated (ATTs) are identified for each cohort and calendar time period in which a cohort was subjected to the intervention. The pooled quasi-maximum likelihood estimators in the linear exponential family extend pooled ordinary least squares estimation of linear models. By using the conditional mean associated with the canonical link function, imputation and pooling across the entire sample produce identical estimates. Generally, pooled estimation results in very simple computation of the ATTs and their standard errors. The leading cases are a logit functional form for binary and fractional outcomes- combined with the Bernoulli quasi-log likelihood (QLL)-and an exponential mean combined with the Poisson QLL.
查看更多>>摘要:Each year, The Econometrics Journal organises a Special Session on a subject of current interest and importance at the Annual Conference of the Royal Economic Society. With these sessions, the journal intends to promote econometric theory and methods of substantive direct or potential value in applications and their actual empirical application. At the Society's online 2022 Conference, Xavier D'Haultfoeuille (CREST-ENSAE) and Jeffrey Wooldridge (Michigan State University) presented in a Special Session on The New Difference-in-Differences. Difference-in-differences (DiD) is a popular approach to estimating treatment effects from observational data. In its simplest form, it compares the change in outcomes over two periods between a treatment group that switches into treatment in the second period and a control group that remains untreated in both periods. Under the 'parallel-trends' assumption that the treatment group would have seen the same trend in outcomes as the control group if it would not have been treated, such a DiD estimates an average treatment effect on second-period outcomes in the treatment group. In empirical practice, this is often implemented by estimating a two-way fixed-effects (TWFE) model that specifies mean outcomes to be linear in group and time effects and the effect of treatment. Simply differencing outcomes over time kills the group effects, but leaves both the treatment effect (for the treatment group) and any time trend. A second difference, across groups, subsequently isolates the treatment effect. Indeed, the usual (least-squares) TWFE estimator of the slope parameter on the treatment indicator is the DiD estimator.
查看更多>>摘要:Linear regressions with period and group fixed effects are widely used to estimate policies' effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. It has recently been shown that those regressions may produce misleading estimates if the policy's effect is heterogeneous between groups or overtime, as is often the case. This survey reviews a fast-growing literature that documents this issue and that proposes alternative estimators robust to heterogeneous effects. We use those alternative estimators to revisit Wolfers (2006a).
查看更多>>摘要:There are many kinds of exogeneity assumptions. How should researchers choose among them? When exogeneity is imposed on an unobservable like a potential outcome, we argue that the form of exogeneity should be chosen based on the kind of selection on unob-servables it allows. Consequently, researchers can assess the plausibility of any exogeneity assumption by studying the distributions of treatment given the unobservables that are consistent with that assumption. We use this approach to study two common exogeneity assumptions: quantile and mean independence. We show that both assumptions require a kind of nonmonotonic relationship between treatment and the potential outcomes. We discuss how to assess the plausibility of this kind of treatment selection. We also show how to define a new and weaker version of quantile independence that allows for monotonic selection on unobservables. We then show the implications of the choice of exogeneity assumption for identification. We apply these results in an empirical illustration of the effect of child soldiering on wages.
查看更多>>摘要:This paper develops a first-stage linear regression representation for an instrumental variables (Ⅳ) quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first stage. We then suggest procedures to evaluate the validity of instruments by evaluating their statistical significance using the first-stage representation. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power. An empirical application illustrates the methods.
查看更多>>摘要:In heterogeneous treatment effect models with endogeneity, identification of the local average treatment effect (LATE) typically relies on the availability of an exogenous instrument monotonically related to treatment participation. First, we demonstrate that a strictly weaker local monotonicity condition-invoked for specific potential outcome values rather than globally-identifies the LATEs on compliers and defiers. Second, we show that our identification results apply to subsets of compliers and defiers when imposing an even weaker local compliers-defiers assumption that allows for both types at any potential outcome value. We propose estimators that are potentially more efficient than two-stage least squares (2SLS) in finite samples, even in cases where 2SLS is consistent. Finally, we provide an empirical application to estimating returns to education using the quarter of birth instrument.
查看更多>>摘要:In the interactive effects panel data literature information criteria are commonly used to consistently determine which of the estimated principal components factors to include. The present paper shows that the same approach can be applied to factors estimated by taking the cross-sectional averages of the observables, as prescribed by the popular common correlated effects (CCE) approach. This should be useful to practitioners because at the moment there is no other theory that justifies the use of information criteria in CCE.
查看更多>>摘要:This paper investigates three-way gravity models with multiplicative unobserved effects, which are popular in bilateral trade analysis and many other contexts. Such models are usually estimated by the fixed effects Poisson pseudo maximum likelihood method. As an alternative, we extend the estimation strategy proposed by Jochmans (2017) to our new settings by constructing moment conditions that are independent of the unobserved effects. Our method entails estimation of the conditional mean of a variety of functional forms. The generalized method of moments (GMM) estimator based on these moment conditions is Inconsistent and asymptotically normally distributed. We also discuss the estimation of dynamic models by extending the linear feedback models to our three-way settings. Through various simulation designs, we show that our GMM estimator outperforms the competing Poisson pseudo maximum likelihood estimator. As an empirical application, we estimate the effects of the currency unions on exports.
查看更多>>摘要:In this paper, we estimate the path of daily SARS-CoV-2 infections in England from the beginning of the pandemic until the end of 2021. We employ a dynamic intensity model, where the mean intensity conditional on the past depends both on past intensity of infections and past realized infections. The model parameters are time-varying, and we employ a multiplicative specification along with logistic transition functions to disentangle the time-varying effects of nonpharmaceutical policy interventions, of different variants, and of protection (waning) of vaccines/boosters. Our model results indicate that earlier interventions and vaccinations are key to containing an infection wave. We consider several scenarios that account for more infectious variants and different protection levels of vaccines/boosters. These scenarios suggest that, as vaccine protection wanes, containing a new wave in infections and an associated increase in hospitalizations in the near future may require further booster campaigns and/or nonpharmaceutical interventions.
查看更多>>摘要:We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against the alternative that there is an 'abnormal' period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process. Simulations in the Appendix show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e., the Bitcoin returns.