Mostly Panel Econometrics : Essays on Asymptotic Analysis and Enhanced Inference

Abstract: This thesis consists of five chapters which focus on panel data theory. Four of them analyze explicit panel data models and one chapter deals with time series forecasting model, where external panel data help us estimate unobserved explanatory variables. The broad topics discussed in the thesis include i) simplification of distribution of a statistical test under double asymptotics, ii) elimination of fixed effects and bias correction in dynamic panels, iii) accounting for cross-section dependence and estimation of latent factors when they can be non-stationary and iv) usage of latent factors to improve out-of-sample forecasts and testing competing forecast models. In Chapter I, we re-visit a problem posed by Phillips and Lee (2015, Econometric Reviews). They considered a simple bivariate vector autoregression (VAR), where both series exhibited different degrees of non-stationarity: near unit root and mild explosiveness. While one is interested in testing whether both series are in the lower vicinity of unit root and share the same persistence features, unfortunately, Wald test statistic degenerates under the null. We re-consider this setup in the context of panel data, where we use extra observations from the cross-section to simplify asymptotic distributions in order to obtain chi-square-based inference. Chapter II looks into very popular factor augmented linear forecast models and tests to evaluate out-of-sample forecasting accuracy. In large macroeconomic datasets, various series tend to co-move together and it is modelled by employing a small number of latent factors (see e.g. Stock and Watson, 1999 and 2002). Instead of using a large number of available variables, researchers reduce the dataset dimension by estimating the driving factors and use those estimates directly. We further explore two tests of equal forecasting accuracy for nested models to investigate if factor augmented model outperforms parsimonious model with known set of variables. Unlike Gonçalves el. al (2017, Journal of Econometrics), where the factors are estimated using Principal Components (PC) under presumably known number of factors, we employ Common Correlated Effects (CCE) estimator which is very user friendly and employs a common thematic block structure of large macro datasets. Factors are estimated as block averages to proxy the common underlying information given by factors. We continue discussing latent factors in Chapter III and Chapter IV. Here we focus on panel data, where unobserved factors model strong cross-section dependence among the panel units and possible endogeneity within the individual time series. Pesaran (2006, Econometrica) suggested solving these issues by augmenting the regression with cross-section averages of the dependent and independent variables. This is CCE estimator. While very simple, pooled version of CCE (CCEP) is asymptotically biased under homogeneous slopes, unless the number of individuals dominates the length of time series in the panel. Moreover, typically the bias is inestimable and analytic correction is not possible. In Chapter III, we analyze the properties of a simple ‘pairs’ bootstrap algorithm discussed in Kapetanios (2008, Econometrics Journal) in the context of CCE and develop bootstrap-based bias correction procedure. In Chapter IV, we continue the study of Westerlund (2018, Econometrics Journal), where CCE was extended to non-stationary factors of a very general type. In the latter study, however, only CCEP under homogeneous slopes was examined, but we extend the analysis to heterogeneous slopes and explore the properties of the mean group (CCEMG) estimator in order to further model unobserved heterogeneity. The thesis concludes with Chapter V, where we re-visit at a classical problem in dynamic panels with fixed effects known as Nickel Bias. De-meaning the data to purge individual-specific effects in dynamic panels makes the model errors correlated, and the bias accumulates if the time dimension is large. On the other hand, if we estimate the fixed effects, we run into incidental parameter problem. Bai (2013, Econometrica) considered the so-called Factor Analytical (FA) estimator, which circumvents these issues by estimating the sample variance of individual effects rather than the effects themselves. In the latter study, panel AR(1) model with autoregressive parameter in the stationary region was explored. We extend this to autoregressive coefficient tending to unity and incidental trends, similarly to Moon and Phillips (2004, Econometrica) in order to account for trending and drifting variables.