The present paper shows that cross-section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T, is small and only the number of cross-sectional units, N, is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components-based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small-T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects. 1 While the results reported in the present paper are not restricted to the treatment effects case, we will use it as a motivating example. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Summary The presence of unobserved heterogeneity and its likely detrimental effect on inference has recently motivated the use of factor‐augmented panel regression models. The workhorse of this literature is based on first estimating the unknown factors using the cross‐section averages of the observables, and then applying ordinary least squares conditional on the first‐step factor estimates. This is the common correlated effects (CCE) approach, the existing asymptotic theory for which is based on the requirement that both the number of time series observations, T, and the number of cross‐section units, N, tend to infinity. The obvious implication of this theory for empirical work is that both N and T should be large, which means that CCE is impossible for the typical micro panel where only N is large. In the current paper, we put the existing CCE theory and its implications to a test. This is done by developing a new theory that enables T to be fixed. The results show that many of the previously derived large‐T results hold even if T is fixed. In particular, the pooled CCE estimator is still consistent and asymptotically normal, which means that CCE is more applicable than previously thought. In fact, not only do we allow T to be fixed, but the conditions placed on the time series properties of the factors and idiosyncratic errors are also much more general than those considered previously.
Recent literature mainly examines the causal relationship between the insurance market and economic activity, while agreeing on presence of cointegration. The bulk of this evidence relies on Pedroni's (Econom Theory 20(03):597-625, 2004) very popular residual-based panel cointegration test. However, this test not only requires that the number of time periods is large, but also that it is large relative to the number of cross section units. In this paper, we demonstrate that violating this requirement leads to Pedroni's test over-rejecting the null hypothesis of no cointegration. We then re-investigate cointegration between insurance market activity and real output using a dataset covering 49 countries over 36 years. While Pedroni's test rejects the null, using a more suitable test procedure yields no evidence of cointegration. This suggests that much of the earlier evidence should be re-evaluated. Equally important, if the evidence on cointegration is misleading, then subsequent causality results are also likely to be misleading.
Abstract. While adopting the contextualized hidden Markov model (CHMM) framework for unsupervised Russian POS tagging, we investigate the possibility of utilizing the left, right, and unambiguous context in the CHMM framework. We propose a backoff smoothing method that incorporates all three types of context into the transition probability estimation during the expectation-maximization process. The resulting model with this new method achieves overall and disambiguation accuracies comparable to a CHMM using the classic backoff smoothing method for HMM-based POS tagging from [17].
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