Of Nickell Bias and its Cures: Comment on Gaibulloev, Sandler, and Sul

Abstract

Gaibulloev, Sandler, and Sul (2014) (here after GSS) present two methodological suggestions for estimating dynamic panel models with fixed effects and provide an empirical application using them. Our interest is only in their methodological suggestions, so we do not discuss the empirical application here. One of their methodological suggestions is that analysts account for crosssectional dependence by adjoining to the model a common factor which relates to events going on in the world that are not explained by the unit-level covariates. This is surely an interesting way to proceed, though we await further evidence on whether the recommended method is superior to standard spatial econometric approach. Since GSS do not discuss this comparison, we do not either, but their approach is clearly of potential interest. The second suggestion, that there is a problem with Nickell (1981) bias when the number of cross-sectional units (N) is considerably greater than the number of time points (T), and that this problem can be solved by simply analyzing subsets of the units independently, is on its face puzzling. In fact, we will argue that it is misguided. This suggestion is puzzling because usually in statistical analysis more data are better than less data. GSS suggest that less data, or equivalently, independent analyses of subsets of the data, is superior to using all the data simultaneously. As with any suggested fix for a methodological problem, we ask: (1) does the problem exist; (2) is the problem serious in applied work; and (3) does the proposed solution do more good than harm? The answer to the first question is yes, but the answers to the last two questions are clearly no. We note that GSS are not suggesting that we should subset the units because they believe that there may be unmodeled heterogeneity. Analysts, of course, should worry about any possibly unmodeled heterogeneity. For example, it may well be in their empirical application that there is heterogeneity across regions. However, this is not the argument that GSS make for subsetting. Obviously, heterogeneity is just as important an issue regardless of the ratio of N to T.

Stepping up during Elections: Independent Central Banks and Inflation

“…However, Beck and Katz (2011) and Beck et al (2014) argue that when T is 30 or 40 -in our case is 32 -the bias is significantly reduced. 16 Interestingly enough, Beck and Katz (2011) conclude that regardless of the number of cross-sectional units (N) -in our case is between 119…”

“…Several studies of opportunistic political business use country-quarter as unit of analysis.Arguably, that unit of analysis is appropriate to observe finer changes in inflation levels as the election-day approaches. However, that unit of analysis is not appropriate for our analysis because all other control variables are registered yearly.16 InBeck et al (2014) for T=40 and N=200 the bias in their point estimate is only -0.01.…”

Practical and Effective Approaches to Dealing With Clustered Data

“…The work of Cameron, Gelbach and Miller (2008), Angrist and Pischke (2009), and Harden (2011) suggests that data sets with fewer than about 40 clusters are at substantively elevated risk of having downward-biased CRSEs. However, this threshold can vary under different circumstances; for example, simulations by MacKinnon and Webb (2017) indicate that CRSEs Gaibulloev, Sandler and Sul, 2014;Beck, Katz and Mignozzetti, 2014). 5 Indeed, one very simple proposal to correct downward bias in CRSEs is to use G − 1 degrees of freedom (rather than N − k, with k the number of estimated parameters) when conducting t-tests; unfortunately, this procedure still results in excess false positive results (Cameron and Miller, 2015, p. 29), as we confirm in our own Monte Carlo simulations.…”

“… 3 Another alternative to dealing with serial dependence, explicitly including a lagged dependent variable, can be problematic if it creates “Nickell bias” due to the presence of fixed effects in the model (Nickell 1981; Beck, Katz and Mignozzetti 2014; Gaibulloev, Sandler and Sul 2014). …”

Fiscal Transparency, Elections and Public Employment: Evidence from the OECD

“…However, the structure of the dataset with a relative limited total number of time periods and its unbalanced nature means that the number of time periods for some countries is fairly low . So the risk of Nickell bias by implementing a lagged‐dependent variable together with unit‐fixed effects would increase substantially (Nickell, ), given that the number of time periods in the panel is relatively low compared to the number of time periods, which minimizes the Nickell bias (Beck et al., , 275)…”