NANCY STOKEY AND ROBERT LUCAS, JR., and Ed Prescott have produced an exceptionally useful, thorough, and timely introduction to stochastic economic dynamics. Dynamic optimization techniques developed in Operations Research, formulated initially by Richard Bellman (1957), have been used extensively in economics, particularly in macroeconomics, finance, and public finance. Economic theorists have extended dynamic programming theory in several valuable directions. Of particular note for this book is the concept of recursive equilibrium introduced in Edward Prescott and Rajnish Mehra (1980). While these techniques have been used extensively, there has been no broad, unified, and comprehensive presentation of the concepts, tools, and applications of recursive dynamic techniques that is written for economists and demands no more mathematics than a typical student is exposed to in a good graduate program. This book succeeds marvelously in filling this need. Furthermore, given the depth of development, it is also a valuable reference for researchers. Before describing the book's contents in detail, we should discuss what is distinctive and important about the recursive approach to dynamic economic problems. To do this, let's examine a simple problem and an alternative approach to its solution. The canonical problem for economic dynamics is the infinite horizon deterministic growth problem. Let k, be the capital stock at the beginning of period t, f(kt) a neoclassical production function expressing period t production as a function of kt, ct consumption in period t chosen at the end of the period, u(c) a concave utility function, and I the discount factor. Then a social planner for this infinitely lived economy will solve the problem

This paper shows that Edgeworth expansions for option valuation are equivalent to approximating option payoffs using Hermite polynomials. Consequently, the value of an option is the value of an infinite series of replicating polynomials. The resultant formulas express option values in terms of skewness, kurtosis, and higher moments. Unfortunately, the Hermite series diverges for fat-tailed models, so we provide alternative moment-based formulas. These formulas are a computationally efficient alternative to Fourier transform valuation and can value options even when the characteristic function is unknown. Applications include the first convergent solution for Hull and White’s stochastic volatility model.Received February 1, 2016; accepted June 27, 2016 by Editor Wayne Ferson.

Fragile by Design by Charles W. Calomiris and Stephen H. Haber introduces a framework for understanding financial crises and credit abundance with politics at its center. Using the historical experiences of five nations to illustrate, the authors propose that democracies such as the United States and Canada can have stable banks and ample credit so long as populist forces do not dominate the policy agenda, and that strong autocratic states such as Mexico can also achieve stability at the cost of restricting credit. Weak autocracies, such as Brazil over much of its history, often require inflationary finance and suffer from the banking fragility that comes with it. The authors identify populist ideologies and related policy decisions (such as unit banking, deposit insurance, and the Community Reinvestment Act) as underlying causes of banking instability in the United States as typified by the recent subprime crisis. Canada, in contrast, by holding populist forces in check through calculated political choices, remains crisis-free. (JEL D72, E44, G01, G21, N20, O16, O17)

Abstract We document that defined benefit pension plans with significant holdings in private equity (PE) earn substantially greater returns than plans with small holdings, in both the 1990s and the 2000s. A one standard deviation increase in PE holdings is associated with 4% greater returns per year. Up to one-third of this outperformance comes from lower costs that we link to economizing on costly intermediation by avoiding fund-of-funds and investing directly. The bulk of the outperformance comes from superior gross returns only partially explained by access and experience. We conjecture that larger PE investors have superior due diligence and ability to bridge information asymmetries in PE.

In the past 30 years, wage inequality has increased steeply while real minimum wages have fallen. This paper demonstrates that a general equilibrium model with endogenous skill choice is required to correctly evaluate the implications of minimum wage changes. The minimum wage not only truncates the wage distribution but also affects skill prices and therefore changes the incentives that people face when making educational decisions. The calibrated model suggests—in line with recent empirical literature—that even though minimum wages affect the bottom end of the wage distribution more, their impact on the top end is significant as well.

Hence, even if the partial equilibrium analyst knows full well that the actual situation is not really a competitive one, he probably will still make a first try using the competitive model with good old-fashioned profit maximization. And if the results appear too odd, appropriate qualifications may still be able to take care of them more simply than if he had started with a cumbersome managerial model. (In saying this, I am showing my bias.) [18, p. 30]

ECONOMICS, we all recite, deals with allocation of limited resources towards satisfaction of unlimited wants. Resources are typically identified as land, labor, and capital plus a technology that determines their transformation into consumer goods. Disparity between the available goods and services and the desired gives rise to scarcity and the question of what, how, and for whom to produce. The focus then shifts to description and evaluation of alternative resource allocation mechanisms for making the choices. The Pareto criterion, by which an allocation of resources is deemed efficient if any reallocation improving the position of some individual worsens the position of others, is a commonly employed gauge of a mechanism's performance. In the absence of externalities, increasing returns to scale, and uncertainty, a perfectly competitive market system yields a Pareto optimal allocation of resources; this underlies the view that individual self-interest is compatible with society's interest. The further conclusion that Pareto optimality may not be achieved via the market system in the presence of monopoly elements provides an economic rationale for antitrust laws. The objective of a resource allocation mechanism appears to be, according to the analysis described above, to make the best of available resources. The alternative objective of relaxing constraints through expanding the resource base or developing new technology seems to be beyond its scope. Thus, until rather recently, technical advance had been regarded, in the mainstream of economic theory, as unmotivated by the quest for profits and substantially unaffected by resource allocation. Instead, as J. Schmookler observed, technology had been viewed as a parameter like the weather, affecting the outcome of resource allocations but itself unaffected by them [84, 1965]. Evidence that technological progress has significantly contributed to growth in productivity, together with a substantial increase in research and development activity, largely financed by government and carried out by industry (see F. Machlup [51, 1962]), may have spurred reconsideration of this view. Once technical advance is regarded as an economic variable, it is natural to in-