Department of Economics
Research field: Econometrics
This paper develops nonparametric identification and estimation results for a single-spell hazard model, where the unobserved heterogeneity is specified as a Lévy subordinator. The identification approach solves a nonlinear Volterra integral equation of the first kind with an unknown kernel function defined on a non-compact support. Both the kernel of the integral operator, which models the distribution of the unobserved heterogeneity, and the functions that enter it nonlinearly are identified given regularity conditions and minimal variation in the observed covariates. The paper proposes a shape-constrained nonparametric two-step sieve minimum distance estimator. The second step estimates the kernel of the integral operator, exploiting a monotonicity property. Rates of convergence are derived and Monte Carlo experiments show the finite sample performance of the estimator.
On the Role of Covariates in the Synthetic Control Method (2019, with Bruno Ferman).
The Econometrics Journal, 22(2): 117-130. Included in the Virtual Issue: The Econometrics of Treatment Effects
Abadie et al. (2010) derive bounds on the bias of the Synthetic Control estimator under a perfect balance assumption on both observed covariates and pretreatment outcomes. In the absence of a perfect balance on covariates, we show that it is still possible to derive such bounds, but at the expense of relying on stronger assumptions on the effects of observed and unobserved covariates and of generating looser bounds. We also show that a perfect balance on pre-treatment outcomes does not generally imply an approximate balance for all covariates, even when they are all relevant. Our results have important implications for the implementation of the method.
Nonparametric Heteroskedasticity in Persistent Panel Processes: An Application to Earnings Dynamics (2018, with Yuya Sasaki).
Journal of Econometrics, 203(2): 283-296.
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This paper considers a dynamic panel model where a latent state variable follows a unit root process with nonparametric heteroskedasticity. We develop constructive nonparametric identification and estimation of the skedastic function. Applying this method to the Panel Survey of Income Dynamics (PSID) in the framework of earnings dynamics, we found that workers with lower pre-recession permanent earnings had higher earnings risk during the three most recent recessions.
This paper considers the difference‐in‐differences (DID) method when the data come from repeated cross‐sections and the treatment status is observed either before or after the implementation of a program. We propose a new method that point‐identifies the average treatment effect on the treated (ATT) via a DID method when there is at least one proxy variable for the latent treatment. Key assumptions are the stationarity of the propensity score conditional on the proxy and an exclusion restriction that the proxy must satisfy with respect to the change in average outcomes over time conditional on the true treatment status. We propose a generalized method of moments estimator for the ATT and we show that the associated overidentification test can be used to test our key assumptions. The method is used to evaluate JUNTOS, a Peruvian conditional cash transfer program. We find that the program significantly increased the demand for health inputs among children and women of reproductive age.
We consider the class of fixed-T panel models where the response variable is an unknown function of a linear latent variable with fixed effects, regressors, and an error term. The key distinctions from existing models are that: the unknown function may be weakly monotonic and time-varying; the error term may be nonparametric; and the fixed effects are unrestricted. We provide new identification results for the structural parameters, and features of the conditional distribution of the fixed effects.
We construct a new full-commitment intertemporal collective household model that implies time-varying monotonic demand equations. Here, fixed effects are (logged) resource shares of household members, and depend on household-level unobserved heterogeneity. Using a two-period Bangladeshi panel dataset, we show that half the variation in women’s resource shares is due to unobserved heterogeneity. Further, women’s resource shares decline with household budgets, casting doubt on some previously used identification strategies.
In nonlinear panel models with fixed effects and fixed-T, the incidental parameter problem poses identification difficulties for structural parameters and partial effects. Existing solutions are model-specific, likelihood-based, impose time homogeneity, or restrict the distribution of unobserved heterogeneity. We provide new identification results for the structural function and for partial effects in a large class of Fixed Effects Linear Transformation (FELT) models with unknown, time-varying, weakly monotone transformation functions. Our results accommodate continuous and discrete outcomes and covariates, require only two time periods, and impose no parametric distributional assumptions. First, we provide a systematic solution to the incidental parameter problem in FELT. Second, we identify the distribution of counterfactual outcomes and a menu of time-varying partial effects without any assumptions on the distribution of unobserved heterogeneity. Third, we obtain new results for nonlinear difference-in-differences that accomodate both discrete and censored outcomes, and for FELT with random coefficients. Finally, we propose rank- and likelihood-based estimators that achieve square root-n rate of convergence.
Linear Forms with Random Coefficients, with an Application to Earnings Volatility (2020)
This paper considers a new panel model with heteroskedasticity, where the parameter of interest is the probability density function of the heteroskedasticity. The nonparametric identification results are established sequentially via a deconvolution argument (in the first step) and by establishing a sufficient condition under which a linear Fredholm integral equation of the first kind has a unique solution (in the second step). The identification results are constructive and give rise to nonparametric estimators. Applied to data from the Panel Study of Income Dynamics, the method developed in this paper uncovers a high degree of heterogeneity in earnings risk. In particular, the evolution over time of the quantiles of the conditional shock variance shows that it is those in the right tail of the distribution who experience the highest volatilities, with lower quantiles experiencing relatively constant volatilities during the sample period.
This paper considers a class of fixed-T nonlinear panel models with time-varying link function, fixed effects, and endogenous regressors. We establish sufficient conditions for the identification of the regression coefficient and the time-varying link function. We also establish identification of time-varying partial effects. We propose a new estimator for the regression coefficient and the link functions, and establish their asymptotic properties. We also study the properties of the implied estimator for the time-varying partial effects. We show the relevance of our model with two examples. In the first, we obtain new results for the nonlinear version of the canonical dynamic panel data model. In the second, we obtain new results in the context of production function estimation. In particular, compared to existing methods, we allow for more flexible functional forms than currently available in the literature.
Nonparametric Identification and Estimation of a Potential Hazard Model
Identification of a Duration Model with Time Deformed Unobserved Heterogeneity
A Duration Model with Dynamic Unobserved Heterogeneity. TSE working paper 11-262