Linearization and Higher-Order Approximations: How Good are They?: Results from an Endogenous Growth Model with Public Capital. This paper is a computational economics paper as it investigates the impact of linearization and higher-order approximation in the dynamic general equilibrium models on anlayzing economic policies impact on welfare. This paper examines the accuracy of computing transitional dynamics associated with fiscal policy reforms with linear and higher-order Taylorís series expansions of a core economic model in which there exists a public capital externality and growth that is determined endogenously as in Lucas (1988) and Uzawa (1965). By comparing the approximations of the post-policy reform transition paths and the welfare implications that they engender with those obtained from exact characterizations of the transitional dynamics found by the reverse-shooting methods described in Atolia and Buffie (2009), we find that the traditional approximation methods employed in performing policy analysis may induce significant errors that could lead to erroneous conclusions regarding the impact of fiscal policy reforms. Moreover, these problems may not be easily minimized by resorting to ever-higher approximations. The order of approximation required to obtain approximation errors that may be seen as acceptable (even when this minimum error in the estimation of welfare gains (losses) is as large as 1%) varies widely with the type of fiscal policy reform undertaken, the time horizon of the analysis, and the setting of deep parameters about which little may be known. In some cases, we find that even a fourth-order approximation of the core dynamic system is insufficient to come within the error bounds that any researcher would likely deem to be acceptable. While these results were obtained for a particular model economy, there is no reason to believe that similar problems will not be present in other models.We believe that the results we report in this paper strongly encourage the exercise of caution when undertaking an analysis whose conclusions require computations that entail the approximation of a significant set of transitional dynamics. The paper is published in the Journal of Computational Economics. See the paper's page for more information.
Consumption Taxation in an Endogenous Growth Model with Public Capital. This paper examines the consequences of shifting from a combination of distortionary taxes on capital income, labor income, and consumption expenditures to a less distortionary tax regime that relies solely on consumption taxes. The model allows for both productive government expenditures on public capital that enhances the economy's output and for an endogenous mechanism for economic growth that tax policy can affect. The model, therefore, accounts for the roles played by both public capital and human capital in the process of economic growth; roles which have been widely recognized in both theoretical and empirical literature. The results indicate that such a tax reform would signifcantly enhance economic growth and welfare in the long-run. However, there would be signifcant adverse welfare consequences. See the paper's page for more information.
Long-Run Growth versus Welfare: The Importance of Transitional Dynamics When Assessing Alternative Fiscal Policies. This paper examines the consequences of distortionary taxes on welfare and growth in the framework of an endogenous growth model. It incorporates the role of government capital in enhancing the productivity of the production process. The model, therefore, accounts for the roles played by both public capital and human capital in the process of economic growth; roles which have been widely recognized in both theoretical and empirical literature. When the model is calibrated to the U.S. economy and the consequences of shifts to alternative scal policies are analyzed, it is found that the implications for growth for various policy regimes are different from those for welfare. In particular, a scal policy delivering the highest long-run growth is not necessarily the one that maximizes the overall welfare. This difference arises from the very dierent welfare outcomes of these scal policies during the transition. An accurate overall welfare assessment of different policies, therefore, requires solving for the exact nonlinear transitional dynamics of the model which we do using the reverse-shooting technique. See the paper's page for more information.