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.
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.
Identification of Time-Varying Transformation Models with Fixed Effects, with an Application to Unobserved Heterogeneity in Resource Shares (2021, with Chris Muris and Krishna Pendakur)
Conditionally accepted at Journal of Econometrics
We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women’s resource shares decline with household budgets and that half of the variation in women’s resource shares is due to unobserved household-level heterogeneity.
This paper considers the transitory-permanent model for the earnings process, where the transitory and permanent shocks have variances that vary across individuals and time in an arbitrary way. The variances are drawn from unknown density functions at each time period. Sufficient conditions for the nonparametric identification of the density functions are provided, under different assumptions on the time series behavior of the transitory shock. The method proposed is then applied to earnings data to document a high degree of cross-sectional heterogeneity in the distributions of the transitory and permanent variances.
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 coefficients, the time-varying link function, the distribution of the counterfactual outcomes, and certain (time-varying) average partial effects. We propose estimators for the regression coefficient, the link function, the average partial effects, and study their asymptotic properties. We show the relevance of our model by obtaining new results for a nonlinear version of the canonical dynamic panel data model.
Identifying Higher-Order Earnings Risks and Asymmetric Marginal Propensities to Consume (with Silvia Sarpietro and Yuya Sasaki)
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