Optimal education and pensions in an endogenous growth model

March 29, 2010

By Elena Del Rey and Miguel Lopez-Garcia


It is well known that, in OLG economies with life-cycle saving and exogenous growth, competitive equilibria will in general fail to achieve optimality and may even be dynamically inefficient. This is a consequence of individuals accumulating amounts of physical capital that differ from the level which would maximize welfare along a balanced growth path (the Golden Rule). With human capital, a second potential source of departure from optimality arises, to wit: individuals may not choose the correct amount of education investment. However, the Golden Rule concept, widely used in exogenous growth frameworks, has not found its way into endogenous growth models. In this paper, we propose to recover the Golden Rule of physical and also human capital accumulation. The optimal policy to decentralize the Golden Rule balanced growth path when there are no constraints for individuals to finance their education investments is also characterized. It is shown that it involves positive pensions and negative education subsidies (i.e., taxes).

Interesting idea to check out the Golden Rule for human capital with the counterintuitive result that education should be taxed. The reason is that as individuals get more educated, it exerts a negative externality on the others to raise more physical capital to maintain the interest rate. Equilibria off the Golden Rule, however, are welfare improving with subsidies to education. Is the Golden Rule then the right welfare criterion?


New Monetarist Economics: Models

March 24, 2010

By Stephen Williamson and Randall Wright


The purpose of this paper is to discuss some of the models used in New Monetarist Economics, which is our label for a body of recent work on money, banking, payments systems, asset markets, and related topics. A key principle in New Monetarism is that solid microfoundations are critical for understanding monetary issues. We survey recent papers on monetary theory, showing how they build on common foundations. We then lay out a tractable benchmark version of the model that allows us to address a variety of issues. We use it to analyze some classic economic topics, like the welfare effects of inflation, the relationship between money and capital accumulation, and the Phillips curve. We also extend the benchmark model in new ways, and show how it can be used to generate new insights in the study of payments, banking, and asset markets.

This is a companion paper (with 100+ pages) to a chapter to appear in the Handbook of Monetary Economics. It summarizes the principles of the money search agenda, now named New Monetarist Economics, and offers a succession of models, like when you would cover the topic in a graduate class. Bookmark this page to refer to it…

Time Preference and the Distributions of Wealth and Income

March 14, 2010

By Richard M. H. Suen


This paper presents a dynamic competitive equilibrium model with heterogeneous time preferences that can account for the observed patterns of wealth and income inequality in the United States. This model generalizes the standard neoclassical growth model by including (i) a demand for status by the consumers and (ii) human capital formation. The first feature prevents the wealth distribution from collapsing into a degenerate distribution. The second feature generates a strong positive correlation between earnings and wealth across agents. A calibrated version of this model succeeds in replicating the wealth and income distributions of the United States.

It is surprisingly difficult to replicate the distribution of wealth. One way to do it is by assuming heterogeneous preferences, but this requires more heterogeneity than what would be reasonable. Richard Suen gets here increasing returns to heterogeneity by adding human capital formation (richer people can get even richer) and wealth in the utility function (people want to hold wealth, not just consume it). Are these reasonable assumptions?

Stochastic Search Equilibrium

March 8, 2010

By Giuseppe Moscarini and fabien Postel-Vinay


We analyze a stochastic equilibrium contract-posting model. Firms post employment contracts, wages contingent on all payoff-relevant states. Aggregate productivity is subject to persistent shocks. Both employed and unemployed workers search randomly for these contracts, and are free to quit at any time. An equilibrium of this contract-posting game is Rank-Preserving [RP] if larger firms offer a larger value to their workers in all states of the world. We show that every equilibrium is RP, and equilibrium is unique, if firms differ either only in their initial size, or also in their fixed idiosyncratic productivity but more productive firms are initially larger, in which case turnover is always efficient, as workers always move from less to more productive firms. The RP equilibrium stochastic dynamics of firm size provide an explanation for the empirical finding that large employers are more cyclically sensitive (Moscarini and Postel-Vinay, 2009). RP equilibrium computation is tractable, and we simulate calibrated examples.

There was a time where macro models had only Taylor-type contracts at their disposal. Now we have contracts that specify a full set of contingent outcomes, with heterogeneity in firms and workers, and this is still tractable. One could even ask: is the real world really this complex?

Money and Credit With Limited Commitment and Theft

March 2, 2010

By Stephen Williamson and Daniel Sanchez


We study the interplay among imperfect memory, limited commitment, and theft, in an environment that can support monetary exchange and credit. Imperfect memory makes money useful, but it also permits theft to go undetected, and therefore provides lucrative opportunities for thieves. Limited commitment constrains credit arrangements, and the constraints tend to tighten with imperfect memory, as this mitigates punishment for bad behavior in the credit market. Theft matters for optimal monetary policy, but at the optimum theft will not be observed in the model. The Friedman rule is in general not optimal with theft, and the optimal money growth rate tends to rise as the cost of theft falls.

Money can compensate for the lack of commitment and for imperfect record keeping, however it can also be stolen. What does this imply for the money supply? Under which conditions are money and credit robust? This is an incredibly rich model that allows to understand when money and credit can both be used, and when not. It shows that money can be so powerful that it shuts down lending, under the Friedman rule. I will need more time to digest this paper, maybe others have some comments on it as well.