The two sector endogenous growth model: an atlas

In this paper we investigate the underlying structure of the Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today

The impact of immigrant dynasties on wage inequality

I construct a set of dynamic macroeconomic models to analyze the effect of unskilled immigration on wage inequality. The immigrants or their descendants do not remain unskilled–over time they may approach or exceed the general level of educational attainment. In the baseline model, the economy’s capital supply is determined endogenously by the savings behavior of infinite-lived dynasties, and I also consider models in which the supply of capital is perfectly elastic, or exogenously determined. I derive a simple formula that determines the time discounted value of the skill premium enjoyed by college-educated workers following a change in the rate of immigration for unskilled workers, or a change in the degree or rate at which unskilled immigrants become skilled. I compare the calculations of the skill premiums to data from the U.S. Current Population Survey to determine the long-run effect of different immigrant groups on wage inequality in the United States

Capital-Skill Complementarity and the Immigration Surplus

Immigration, Capital-Skill Complementarity, Overlapping Dynasties

Evaluating Historical Episodes using Shock Decompositions in the DSGE Model

We present alternative methods for calculating and interpreting the influence of exogenous shocks on historical episodes within the context of DSGE models. We show analytically why different methods for calculating shock decompositions can generate conflicting interpretations of the same historical episodes. We illustrate this point using an extended version of Drautzburg and Uhlig's (2015) model of the U.S. economy, focusing on the periods 1964-1966, 1979-1987, 2007-2008 and 2016-2018. We argue that the best method for analyzing particular episodes is one which isolates the influence of the shocks during the period under consideration and where the initial conditions represent the system's distance from steady state at the beginning of the episode

On Deficit Bias and Immigration

How much can governments shift the cost of their expenditure from today's voters to tomorrow's generations of immigrants, without resorting to taxation that is explicitly discriminatory? I demonstrate that if their societies are absorbing continuous flows of new immigrants, we should expect governments that represent the interests of today's population to choose policies that shift some portion of the tax burden to the future, even if that population is altruistically linked to future generations. To measure the deficit bias, I analyse the dynamic behaviour of an optimal growth model with overlapping dynasties and factor taxation, calibrated for the US economy, and consider the welfare implications for today's population and their descendants of intertemporal shifts in the tax rates on labour and capital as well as transfer payments. Models with overlapping infinite-lived dynasties allow for a very clear distinction between natural population growth (an increase in the size of existing dynasties) and immigration (the addition of new dynasties). They also provide an alternative to the strict dichotomy between models with overlapping generations, where agents disregard the impact of their choices on future generations, and the quasi-Ricardian world of infinite-lived dynasties with representative agents that fully participate in both the economy and the political system in every period. The trajectory of the debt burden predicted by the model is a good match for the rise in US Federal Government debt since the early 1980's, as well as the increases in debt projected by the Congressional Budget Office over the next few decades

The two sector endogenous growth model: An atlas

In this paper we investigate the underlying structure of the . Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature-even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies-including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today. © 2012 Elsevier Inc

The Optimal Taxation of Asset Income when Government Consumption is Endogenous: Theory, Estimation and Welfare

This paper derives the Ramsey optimal policy for taxing asset income in a model where government expenditure is a function of net output or the inputs that produce it. Extending Judd (1999), I demonstrate that the canonical result that the optimal tax on capital income is zero in the medium to long term is a special case of a more general model. Employing a vector error correction model to estimate the relationship between government consumption and net output for the United States between 1947Q1 to 2013Q2, I demonstrate that this special case is empirically implausible, and show how the cointegrating vector can be used to determine the optimal tax schedule. I simulate a version of the model using the empirical estimates to measure the welfare implications of changing the tax rate on asset income, and contrast these results with those generated in a version of the model where government consumption is purely exogenous. The shifting pattern of welfare measurements confirms the theoretical results. I calculate that the prevailing effective tax rate on net asset income in the US between 1995 and 2011 averaged 0.441. Hence abolishing the tax completely does generate welfare improvements, though only by the equivalent of less than a one percent permanent increase in consumption---less than a third the implied welfare benefit when the endogeneity of the government consumption is ignored. The maximum welfare improvement from shifting part of the burden of tax from capital to labour is the equivalent of a permanent increase in consumption of between only 1.173 and 1.304% and is attained when the tax rate on asset income is lowered to between 0.18 and 0.2. Allowing the tax rate to vary over time raises the maximum welfare benefit to 1.31%. All the results are very robust to a wide range of elasticities of labour supply