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This paper proposes a model-free approach to analyze panel data with heterogeneous dynamic structures across observational units. We first compute the sample mean, autocovariances, and autocorrelations for each unit, and then estimate the parameters of interest based on their empirical distributions. We then investigate the asymptotic properties of our estimators using double asymptotics and propose split-panel jackknife bias correction and inference based on the cross-sectional bootstrap. We illustrate the usefulness of our procedures by studying the deviation dynamics of the law of one price. Monte Carlo simulations confirm that the proposed bias correction is effective and yields valid inference in small samples.

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This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and then apply kernel smoothing to compute their density functions. The dependence of the kernel estimator on bandwidth makes asymptotic bias of very high order affect the required condition on the relative magnitudes of the cross-sectional sample size (N ) and the time-series length (T ). In particular, it makes the condition on N and T stronger and more complicated than those typically observed in the longpanel literature without kernel smoothing. We also consider a split-panel jackknife method to correct bias and construction of confidence intervals. An empirical application and Monte Carlo simulations illustrate our procedure in finite samples.

We develop identification and estimation methods for treatment effect models with strategic interaction in the treatment decisions. We consider models where one's treatment choice and outcome can be endogenously affected by others' treatment choices. We formulate the interaction of the treatment decisions as a two-player complete information game with potential multiple equilibria. For this model, using a latent index framework and the assumption of a stochastic equilibrium selection rule, we prove that the marginal treatment effect from one's own treatment and that from his/her partner's can be separately point-identified with potential over-identifiability. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. The proposed estimator is shown to be uniformly consistent and asymptotically normal. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents' academic performance.1 To the best of our knowledge, few studies address treatment evaluation in the presence of strategic interaction, where the treatment decisions are explicitly modeled as games. One important exception is Balat and Han (2018), who mainly investigate the partial identification of average treatment effects (ATE). Thus, our main parameters of interest (MTE) are different from theirs (ATE). In addition, the key identification assumptions in Balat and Han (2018) are shape restrictions on the conditional mean outcome functions, while we mainly rely on a stochastic equilibrium selection rule, as stated below.2 As another related work, Mogstad et al. (2019) introduce partial monotonicity to deal with issues due to multiple instruments. However, partial monotonicity is not designed for settings with multivalued or multidimensional treatments such as our situation.