A Monte Carlo Study of Growth Regressions

Abstract

Using Monte Carlo simulations, this paper evaluates the bias properties of common estimators used in growth regressions derived from the Solow model. We explicitly allow for measurement error in the right-hand side variables, as well as country-specific effects that are correlated with the regressors. Our results suggest that using an OLS estimator applied to a single cross-section of variables averaged over time (the between estimator) performs best in terms of the extent of bias on each of the estimated coefficients. The fixed-effects estimator and the Arellano-Bond estimator greatly overstate the speed of convergence under a wide variety of assumptions concerning the type and extent of measurement error, while between understates it somewhat. Finally, fixed effects and Arellano-Bond bias towards zero the slope estimates on the human and physical capital accumulation variables.

Human capital and state-level economic growth: what is the contribution of schooling?

“…The growth empirics method directly estimates the transitional growth equations (6) and (7), which allows the explicit estimation of the education share β. Holtz-Eakin (1993), Vohra (1996), Vohra (1997), Garofalo and Yamarik (2002), Mullen and Williams (2005), Yamarik (2006) use the growth empirics approach and estimate an education share β ranging from less than 0.20 (Vohra 1996(Vohra , 1997 to over 0.50 (Mullen and Williams 2005). As predicted by Hauk and Wacziarg (2009), the cross-sectional estimates of β are higher than the panel FE and GMM-D estimates.…”

“…The validity of the additional first-difference instruments can be tested using a Difference-in-Hansen test comparing the Hansen test results of the first-differenced and system GMM estimators. Hauk and Wacziarg (2009) conduct Monte Carlo simulations on Eq. (9) allowing for measurement error and correlation between the regressors and state-specific effects.…”

“…However, Blundell and Bond (1998) show that the first-differenced GMM estimator is likely to perform poorly when the series are close to random walks. In particular, Monte Carlo evidence by Hauk and Wacziarg (2009) show that the first-difference GMM and fixed effects estimators will bias the estimate for the capital share, particularly human capital, to zero in the presence of measurement error. This paper improves upon the existing empirical framework in three important ways.…”

The elusive inequality-economic growth relationship: are there differences between cities and the countryside?

“…Moreover, in the presence of measurement error, mainly in the income distribution variables, fixed effects estimation would exacerbate the measurement-error bias and produce unreliable results. Hauk and Wacziarg (2004) find that cross-sectional (OLS) approaches lead to 6 If there are omitted variables that are simultaneously correlated with (1) past events, (2) the initial values of the explanatory variables, and (3) the regression residual, endogeneity bias may be introduced in a cross-sectional setting such as this one. However, using a long 10-year window minimizes these problems.…”

“…In a Monte Carlo examination of growth empirics with modest measurement error,Hauk and Wacziarg (2004) found that the biases from omitting the fixed effects in a cross-sectional approach tended to offset the measurement error bias, generating relatively accurate estimates. However, in fixed effects models, the measurement error was exacerbated by the fixed effects (within) differencing, which led to results that were multiple fold more biased than cross-sectional approaches, producing results that were often the wrong sign (also seePartridge 2005).9 All variables are listed in AppendixTable 5, which also includes weighted descriptive statistics of all the variables for the entire sample, as well as for MA and non-MA counties.…”