Estimating dynamic panel data models: a guide for macroeconomists☆
Introduction
The revitalization of interest in long-run growth and the availability of macroeconomic data for large panels of countries has generated interest among macroeconomists in estimating dynamic panel models. However, microeconomists have generally been more avid users of panel data, and, thus, existing panel techniques have been devised and tested with the typical dimensions of microeconomic datasets in mind. These datasets usually have a time dimension far smaller and an individual (country) dimension far greater than the typical macroeconomic panel.
This difference is important in choosing an estimation technique for two reasons. First, it is well known that the LSDV (least squares dummy variable) model with a lagged dependent variable generates biased estimates when the time dimension of the panel (T) is small. Thus, for many macroeconomists, the question, ‘How big should T be before the bias can be ignored?’, is a critical one. A second reason that macro panels may require different estimation techniques than those used on micro panels is that recent work investigating the appropriateness of competing estimators has generated conflicting results, showing that the characteristics of the data influence the performance of an estimator.1
We evaluate several different techniques for estimating dynamic models with panels characteristic of many macroeconomic panel datasets; our goal is to provide a guide to choosing appropriate techniques for panels of various dimensions. Our work most closely follows Kiviet’s (1995); however, we focus our attention on data with the qualities normally encountered by macroeconomists while he focuses on the short (small T), wide (large N) panels typical of micro data.2
We have three main conclusions. First, macroeconomists should not dismiss the LSDV bias as insignificant. Even with a time dimension as large as 30, we find that the bias may be equal to as much as 20% of the true value of the coefficient of interest. However, using an RMSE criterion, the LSDV performs just as well or better than many alternatives when T=30. With a smaller time dimension, LSDV does not dominate the alternatives. Second, for panels of all sizes, a corrected LSDV estimator generally has the lowest RMSE. However, implementation of the corrected LSDV for an unbalanced panel has not been derived and therefore alternatives may be needed. When the corrected LSDV is not practical, a GMM procedure usually produces lower RMSEs relative to the Anderson–Hsiao estimator. Finally, we find that a ‘restricted GMM’ estimator that uses a subset of the available lagged values as instruments increases computational efficiency without significantly detracting from its effectiveness.
Section snippets
The problem and proposed solutions
We consider the dynamic fixed effects modelwhere ηi is a fixed-effect, xi,t is a (K−1)×1 vector of exogenous regressors and ϵi,t∼N(0, σϵ2) is a random disturbance. We assume
The fixed effects model we have chosen is a common choice for macroeconomists, and is generally more appropriate than a random effects model for two reasons. First, if the individual effect represents omitted variables, it is likely
Methodology
Our data generation process closely follows Kiviet (1995). The model for yit is given in Eq. (1); xit was generated withThus, in addition to β, ρ and σξ2 also determine the correlation between yit and xit. Kiviet defines a signal to noise ratio, σs2and shows that it can be calculated from other parameters of the model as followsThe higher the signal-to-noise ratio, the more useful x
Results
We first examine the bias of the OLS and LSDV estimators for various panel sizes. Table 1 summarizes the results from this initial experiment for a subset of parameter values.5 These results confirm several well-documented conclusions about these estimators: (1) in both cases, the bias of γ is more severe than that
Conclusion
The recommendations from our Monte Carlo analysis are summarized below.Summary of recommendations Empty Cell T≤10 T=20 T=30 Balanced panel LSDVC LSDVC LSDVC Unbalanced panel GMM1 GMM1 or AH LSDV
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This paper represents the views of the authors and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff.