Natural conjugate priors for the instrumental variables regression model applied to the Angrist–Krueger data

We propose a natural conjugate prior for the instrumental variables regression model. The prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior. The Jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator. We construct informative priors for the Angrist–Krueger [1991. Does compulsory school attendance affect schooling and earnings? Quarterly Journal of Economics 106, 979–1014] data and show that the marginal posterior of the return on education in the US coincides with the marginal posterior from the Southern region when we use the Jeffreys prior. This result occurs since the instruments are the strongest in the Southern region and the posterior using the Jeffreys prior, identical to maximum likelihood, focusses on the strongest available instruments. We construct informative priors for the other regions that make their posteriors of the return on education similar to that of the US and the Southern region. These priors show the amount of prior information needed to obtain comparable results for all regions.     

Randomization and simplification in dynamic decision-making

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision-maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in noninteractive deterministic environments where the decision-maker's choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components: an action selection rule and a behavior modification rule. In noninteractive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.     

The evolution of rationality and the Red Queen

Strategic rationality is subjected here to natural selection. In a zero-sum repeated game of incomplete information, one long-run individual is informed of the state of the world, and plays against a sequence of short-run opponents who are not. Strategies are noisy and have bounded recall. An equilibrium in these is shown to exist. Relative to any such equilibrium, sufficiently greater recall enjoys an advantage that is not decreasing in the original level of recall, thus capturing the Red Queen effect. The selection pressure to reduce a small amount of noise is less than that to increase recall.     

Innovation timing games: a general framework with applications

We offer a new algorithm for analyzing innovation timing games. Its main advantage over the traditional approach is that it applies to problems that had previously been intractable. We use the algorithm to examine two classical innovation problems. We find that the competition takes the form of a waiting game with a second-mover advantage either for any level of R&D costs (process innovation) or for high R&D costs (product innovation). Moreover, both models predict that the second-mover advantage is monotonically increasing in the costs of R&D.     

Employment changes, the structure of adjustment costs, and plant size

In this paper, we analyze the pattern of employment adjustment using a rich panel of Norwegian plants. The data suggest that the frequency of episodes of zero net employment changes is inversely related to plant size. We develop and estimate a simple “q” model of labor demand, allowing for the presence of fixed, linear and quadratic components of adjustment costs. The econometric evidence supports the existence of purely fixed components, unrelated to plant size. As a result, the range of inaction is wider for smaller plants. The quadratic component of costs is also always important. In most specifications fixed costs are higher for employment contractions. The quadratic component is higher during employment contractions compared to expansions for small plants, while this is not true for larger plants.     

Unit and Fractional Roots at the Long Run and the Seasonal Frequencies in Macroeconomic Time Series

In this article, we show that macroeconomic time series may contain unit and fractional roots at both, at zero and at zero and at the seasonal frequencies. The importance of the root at the long run or zero frequency requires in many cases to consider this root at both, separately in an independent polynomial, and also included in the seasonal one. Several Monte Carlo experiments are conducted to examine cases when the root at the zero frequency is not appropriately considered. An empirical application based on the tests of Robinson, Peter M. “Efficient Tests of Nonstationary Hypotheses,” Journal of the American Statistical Association, 89, 1994, pp. 1420–37 is also carried out at the end of the article.The author gratefully acknowledges financial support from the Government of Navarra (“Ayudas de Formación e Investigación y Desarrollo”).     

Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

Summary In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.I thank Scott Freeman, Katsuhiko Kawai, and two referees for proofreading this text; all lead to clarifications.     

Overnight borrowing, interest rates and extreme value theory

We examine the dynamics of extreme values of overnight borrowing rates in an inter-bank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates using pre-crisis data. The examination of tails (extreme values) provides answers to such issues as to what are the extreme movements to be expected in financial markets; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat-tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations.     

Redistribution as a selection device

This paper studies the role of the wealth distribution for the market selection of entrepreneurs when agents differ in talent. It argues that the redistribution of initial endowments can increase an economy's surplus because more talented individuals get credit for their risky investment projects. Moreover, the redistribution of initial endowments may lead to a Pareto-improvement although all agents are non-satiable. An agent's entrepreneurial ability is his private information and there is moral hazard in production. I find conditions such that unproductive rich entrepreneurs crowd out productive poor ones on the capital market. Then redistribution of initial endowments may lead to a new equilibrium where market participants are better informed about the entrepreneurs’ ability. The new equilibrium is characterized by (i) the selection of better entrepreneurs, (ii) a higher riskless rate of return on capital, (iii) lower repayments of successful entrepreneurs to their creditors and (iv) the fact that all agents are better off.     

Complex solutions of nonconcave dynamic optimization models

Summary In this paper we consider a class of time discrete intertemporal optimization models in one dimension. We present a technique to construct intertemporal optimization models with nonconcave objective functions, such that the optimal policy function coincides with any pre-specifiedC ² function. Our result is a variant of the approach presented in a seminal paper by Boldrin and Montrucchio (1986). Whereas they solved the inverse problem for the reduced form models, we address the different question of how to construct both reduced and primitive form models. Using our technique one can guarantee required qualitative properties not only in reduced, but also in primitive form. The fact that our constructed model has a single valued and continuous optimal policy is very important as, in general, nonconcave problems yield set valued optimal policy correspondences which are typically hard to analyze. To illustrate our constructive approach we apply it to a simple nonconcave model.We are grateful for the helpful comments of L. Montrucchio, K. Nishimura, T. Mitra and an anonymous referee. Financial support of the Austrian Science Foundation under contract No. P7783-PHY and No. J01003-SOZ is gratefully acknowledged. This paper was written while M. Kopel was visiting the Department of Economics, Cornell University.