Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence

Cross-country differences in output persistence are well documented in the literature. Further, Fatás (2000) finds a strong positive correlation between the persistence of fluctuations and long-term average growth rates for a sample that includes the G7 countries and eight additional OECD countries. We confirm these findings for a larger sample of 101 countries with data extending over the period 1970-2008. The standard RBC models with exogenous productivity shocks cannot account for this evidence, while Fatás (2000) shows that the standard AK endogenous growth model is able to generate this positive correlation. Moreover, empirical evidence documents large differences in capital utilization rates across countries and a positive correlation between capital utilization and per capita income as well as between depreciation and long-term average per capita income growth. Both standard exogenous and endogenous growth models, however, assume that capital services are a constant proportion of the underlying capital stock and treat depreciation as an exogenous parameter. We extend the existing evidence on the relationship between output growth and depreciation rates through dynamic panel data estimations by using a sample of 101 countries over the period 1970-2008. The evidence is not consistent with the predictions of standard exogenous growth and AK-type endogenous growth models, for which the depreciation rate affects negatively either transitional growth or long-run growth, respectively. We then attempt to reconcile empirical evidence and the predictions on persistence, long-term growth and capital utilization rates by allowing the depreciation rate to be sensitive to the rate of capital utilization in an otherwise standard AK model. We find that, in this setting, a full utilization rate of capital is not optimal, depreciation is endogenously determined, and the implications of the model are consistent with the observed cross-country evidence showing that: (1) the degree of persistence is an increasing function of output growth, and (2) output growth is positively associated with the depreciation rate. As far as the empirical part is concerned, we estimate conventional dynamic panel data specifications that regress real per capita output growth on its main growth determinants according to standard growth theory, thereby paying particular attention to the relationship between depreciation rates and output growth. Arellano and Bover (1995) and Blundell and Bond (1998) show that in the case of persistent regressors, lagged levels of the variables are weak instruments for the first-differenced regressors. This leads to a fall in precision as well as to biased coefficients. To overcome these shortcomings, we employ the system estimator proposed by Arellano and Bover (1995) and Blundell and Bond (1998), which utilizes instruments in levels and first-differences to improve efficiency. Regarding the theoretical part, we extend the RBC model of Fatás (2000) by studying the dynamics of growth and persistence in a model where both the depreciation rate and growth are endogenous and procyclical. We find that the model’s predictions become consistent with the empirical evidence on persistence, long-term growth and depreciation rates. In addition, we show that the standard AK growth model (compared to the AK model with endogenous capacity utilization) overstates the long-run impact of a shock on the level of output. Despite the fact that temporary shocks become persistent in both models (since they have an impact on the amount of resources allocated to capital accumulation), it turns out that when the depreciation rate is endogenous, temporary shocks affect capital accumulation through two channels: the marginal product of capital and the depreciation rate. Since it is optimal to utilize capital less than fully, shocks have a lower impact on the marginal product of capital than in a standard AK model, which leads to a lower effect on capital accumulation. Moreover, the procyclicality of the depreciation rate further smooths the impact on capital accumulation, which results in a lower persistence measure of short-term fluctuations than in a traditional AK model.