Paul Johnson, Steven Durlauf and Jonathan Temple 1149effects, especially in the context of smallT, to obtain imprecise sets of parameter
estimates. Given the potentially unattractive trade-off between robustness and effi-
ciency, Barro (1997), Temple (1999), Pritchett (2000a) and Wacziarg (2002) all argue
that the use of fixed effects in empirical growth models has to be approached with
care. The price of eliminating the misleading component of the between variation
- namely, the variation due to unobserved heterogeneity – is that all the between
variation is lost. This is costly, because growth episodes within countries inevitably
look a great deal more alike than growth episodes across countries, and therefore
offer less identifying variation. Restricting the analysis to the within variation elim-
inates one source of bias, but makes it harder to identify growth effects with any
degree of precision. Many of the explanatory variables currently used in growth
research are either highly stable over time, or tending to trend in one direction.
Without useful identifying variation in the time series data, the within-country
approach is in trouble. Moreover, growth is quite volatile at short horizons. It will
typically be hard to explain this variation using predictors that show little varia-
tion over time, or that are measured with substantial errors. The result has been a
number of panel data studies suggesting that a given variable “does not matter,”
when a more accurate interpretation is that its effect cannot be identified using the
data at hand.
Depending on the sources of heterogeneity, even simple recommendations, such
as including a complete set of regional dummies, can help to alleviate the biases
associated with omitted variables (Temple, 1998). More than a decade of growth
research has identified a host of fixed factors that could be used to substitute for
country-specific intercepts. A growth model that includes these variables can still
exploit the panel structure of the data, and the explicit modeling of the country-
specific effects is directly informative about the sources of persistent income and
growth differences.
In practice, the literature has focused on another aspect of using panel data
estimators to investigate growth. Nickell (1981) showed that within-groups esti-
mates of a dynamic panel data model can be badly biased for smallT, even asN
goes to infinity. The direction of this bias is such that, in a growth model, out-
put appears less persistent than it should (the estimate ofβis too low) and the
rate of conditional convergence will be overestimated. The Nickell bias explains
why the within-groups estimator is often avoided when estimating dynamic mod-
els. The most widely-used alternative is to difference the model to eliminate the
fixed effects, and then use 2SLS or generalized method of moments (GMM) to
address the correlation between the differenced lagged dependent variable and the
induced MA(1) error term. To see the need for instrumental variable procedures,
first-difference (24.31) to obtain:
logyi,t=( 1 +β)logyi,t− 1 +Xi,tψ+Zi,tπ+μi+εi,t−εi,t− 1 , (24.32)and note that (absent an unlikely error structure) the logyi,t− 1 component of
logyi,t− 1 will be correlated with theεi,t− 1 component of the new composite
error term, as is clearly seen by considering equation (24.31) lagged one period.