Studies in the econometrics of panel data with applications to
- Autores: Elena Manresa
- Directores de la Tesis: Enrique Sentana Iváñez (dir. tes.), Stéphane Bonhomme (codir. tes.)
- Lectura: En la Universidad Internacional Menéndez Pelayo (UIMP) ( España ) en 2015
- Idioma: español
- Tribunal Calificador de la Tesis: Cesare Robotti (presid.), Xavier D'Haultfoeuille (secret.), Áureo de Paula (voc.), Jesús M. Carro (voc.), Bryan S. Graham (voc.)
- Materias:
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- Resumen
The main objective of this thesis was to develop new methodologies that can inform researchers about some aspects of their model that are not informed by economic theory. To this end I have combined model selection features with more traditional panel data econometric models.
The different methodologies are useful in different economic settings. I have shown the capabilities of each of the new methodologies by using them in specific economic questions with real data. In all of them I have obtained novel results that add to the different economic literatures.
In the case of grouped patterns of heterogeneity I have studied the link between income and democracy of countries and found that the unobserved heterogeneity found among countries is consistent with Huntington’s 3rd wave of democracy theories. In terms of recovering the structure of interactions I have shown how the methodology is able to uncover the structure of knowledge spillovers resulting from R&D investments among firms in the US. Finally, I have explored the suitability of the Epstein Zin model and found that there is evidence of overspecification.
In what follows I summarize the conclusions reached for each of the methodologies, outline the main findings, and discuss future lines of research that I think are worth exploring.In Chapters 2 and 3 I have proposed, jointly with Stéphane Bonhomme, the Grouped fixed-effects (GFE) framework, that offers a flexible yet parsimonious approach to model unobserved heterogeneity. The approach delivers estimates of common regression parameters, together with interpretable estimates of group-specific time patterns and group membership. The framework allows for strictly exogenous covariates and lagged outcomes. It also easily accommodates unit-specific fixed-effects in addition to the time-varying grouped patterns, and grouped heterogeneity in coefficients. Importantly, the relationship between group membership and observed covariates is left unrestricted. The GFE approach should be useful in applications where time-varying grouped effects may be present in the data. As a first example, the empirical analysis of the evolution of democracy shows evidence of a clustering of political regimes and transitions. More generally, GFE should be well-suited in difference-in-difference designs, as a way to relax parallel trend assumptions. Other potential applications include models of social interactions and spatial dependence where the reference groups or the spatial weights matrix are estimated from the panel data.
The extension to nonlinear models is a natural next step. While it is possible to define GFE estimators in more general models (see for example equation (2.9)), the analysis raises statistical challenges. One area of applications is static or dynamic discrete choice modelling, where a discrete specification of unobserved heterogeneity may be appealing (Kasahara and Shimotsu, 2009, Browning and Carro, 2013). See Saggio (2012) for a first attempt in this direction. Lastly, another interesting extension is to relax the assumption that there is a finite number of well-separated groups in the population. As an alternative approach, one could view the grouped model as an approximation to the underlying data generating process, and characterize the statistical properties of GFE as the number of groups G increases with the two dimensions of the panel.
In Chapter 4 I present a methodology to estimate both the structure of interactions and the spillover effects when the structure of interactions is not observable to the econometrician. This method is useful when the structure of interactions is sparse and persistent over time. Both of these assumptions can be partially relaxed: Sparsity can be relaxed by adding a priori information on the structure of interactions. Persistence over time can be relaxed by splitting the sample, parametrizing the spillover effects as a function of time, or by augmenting the number of regressors as explained in Appendix C.1.
Spillovers arise when characteristics have an impact on the outcome of other individuals in the sample. This model is useful in at least two cases: First, in the context of randomized treatment experiments, when the treatment is subject to generate externalities. Second, in production function frameworks, where productivity generates spillovers.
I propose a new estimator, the Pooled Lasso estimator, that can be seen as a panel data counterpart of the Lasso estimator. I provide an iterative computation method that combines the Lasso estimator with OLS pooled regression.
Computation is fast, in relation to the large number of potential structures of interactions, given the global convex nature of the criterion.
I analyze the properties of the Pooled Lasso estimator in a simplified model with no common parameters under assumptions of Gaussian and independent errors, both in the time and cross-sectional dimension. Based on a recent paper by Lam and Souza (2013), these strong conditions on the errors are likely to be relaxed. First, gaussianity can be replaced by conditions on the tail probability of errors. Second, limited time-series dependence can also be incorporated using Nagaev-type inequalities. Finally, mild cross-sectional dependence in the errors is also likely to be incorporated.
I study the rate of convergence of cross-sectional spillover effects and, more generally, aggregate spillover effects. These quantities can be interpreted as relevant policy parameters depending on the application. Under conditions of cross-sectional independence on the error in estimation of the spillover effects, average spillover effects are estimated at a much better rate than individual spillover effects.
Inference methods in the context of the Lasso are hard to derive due to the non-differentiability of the criterion. However, recent work in econometrics and statistics show good progress in this direction. For instance, Belloni et al.. (2013), show how to conduct inference in a post-lasso setting. That is, after using Lasso as a model selection devise, an ex-post OLS regression is run conditional on the estimated model. In particular, after using a Lasso-type estimator twice to select relevant controls in a treatment effect framework, they derive the asymptotic distribution of the treatment effect estimator and provide a formula for confidence intervals. One of the main features of their work is that, even in spite of imperfect model selection, their results hold uniformly for a large class of DGPs. Another recent work, by Lockhart et al., (2013) focus in developing a significance test of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path of LARS (e.g. Efron et al., 2004). The Lasso solution path are the different solutions that the Lasso delivers when the penalty parameter decreases.
