This essay reviews Kenneth I. Wolpin's (2013) monograph The Limits of Inference without Theory, which arose from lectures he presented at the Cowles Foundation in 2010 in honor of Tjalling Koopmans. While I readily agree with Wolpin's basic premise that empirical work that eschews the role of economic theory faces unnecessary self-imposed limits relative to empirical work that embraces and tries to test and improve economic theory, it is important to be aware that the use of economic theory is not a panacea. I point out that there are also serious limits to inference with theory: 1) there may be no truly “structural” (policy invariant) parameters, a key assumption underpinning the structural econometric approach that Wolpin and the Cowles Foundation have championed; 2) there is a curse of dimensionality that makes it very difficult for us to elucidate the detailed implications of economic theories, which is necessary to empirically implement and test these theories; 3) there is an identification problem that makes it impossible to decide between competing theories without imposing ad hoc auxiliary assumptions (such as parametric functional form assumptions); and 4) there is a problem of multiplicity and indeterminacy of equilibria that limits the predictive empirical content of many economic theories. I conclude that though these are very challenging problems, I agree with Wolpin and the Cowles Foundation that economists have far more to gain by trying to incorporate economic theory into empirical work and test and improve our theories than by rejecting theory and presuming that all interesting economic issues can be answered by well-designed controlled, randomized experiments and assuming that difficult questions of causality and evaluation of alternative hypothetical policies can be resolved by simply allowing the “data to speak for itself.” (JEL B41, C18)

This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the curse of dimensionality for a subclass of MDPs known as discrete decision processes (DDPs).

This paper formulates a simple, regenerative, optimal-stopping model of bus-eng ine replacement to describe the behavior of Harold Zurcher, superinte ndent of maintenance at the Madison (Wisconsin) Metropolitan Bus Comp any. Admittedly, few people are likely to take particular interest in Harold Zurcher and bus engine replacement per se. The author focuses on a specific individual and capital good because it provides a simp le, concrete framework to illustrate two ideas: (1) a "bottom-up" a pproach for modeling replacement investment and (2) a "nested fixed point" algorithm for estimating dynamic programming models of discre te choice. Copyright 1987 by The Econometric Society.

[It is commonly believed that textbook publishers attempt to "kill off" competition from used textbooks through yearly edition changes. In the context of Wicksell's model of durable goods, Peter Swan has shown that such "planned obsolescence" is never optimal: a monopolist seller of durable goods maximizes profits by setting product durability equal to the competitive or socially optimal level, and efficiently extracts consumer surplus through sales price alone. This paper formulates a monopolist seller's choice of price and durability as the solution to a Stackelberg game between the monopolist and consumers. We employ a new equilibrium model of a durable goods market which, unlike Wicksell's model, recognizes that scrappage of durables is endogenously determined. We show that with endogenous scrappage, consumers have a substitution possibility which constrains the profits of a monopolist seller. This constraint on profits causes the monopolist to distort durability from the socially optimal level. We derive conditions under which this distortion takes its most extreme form: the monopolist kills off competition from used durables by producing new assets of zero durability.]

[This paper presents a dynamic model of consumer trading on the primary, secondary, and scrap markets for a stochastically deteriorating durable good in a stationary economy with perfect information and no transaction costs. We explicitly model the trading process by tracking each durable from its "birth" in the primary market, through its sequence of owners in the secondary market, until its "death" in the scrap market. We prove that a stationary equilibrium tests, characterize the distribution of consumer holdings of durables, and show that equilibrium asset prices are shadow prices to a particular regenerative optimal stopping problem. We show that each heterogeneous agent equilibrium is observationally equivalent to a homogeneous agent equilibrium. We derive a differential equation for equilibrium rental rates, and a functional equation which links rental rates to asset prices. These equations show precisely how the structure of durable prices and rental rates embody the functional form and population distribution of preferences and the technological characteristics of durable goods.]

Why is the price of renting an automobile “flat” as a function of its age or odometer value? Specifically, why is it that car rental companies do not offer customers the option of renting older cars at a discount, instead of offering only relatively new cars at full price? We also tackle a related puzzle: why do car rental companies trade-in their vehicles so early? Most US companies purchase brand new rental cars and replace them after 2 years or when their odometer exceeds 34,000 km. That is a very costly strategy due to the well-known by rapid depreciation in used car prices. We show that in a competitive rental market, prices are a declining function of odometer and cars are rented over their full economic lifespan. Our solution to these puzzles is that actual rental markets are not fully competitive and firms may be behaving suboptimally. We provide a case study of a large car rental company that provided us access to its operating data. We develop a model of the company's operations that predicts that the company can significantly increase its profits by keeping its rental cars twice as long as it currently does, discounting the rental prices of older vehicles to induce its customers to rent them. The company undertook an experiment to test our model's predictions. We report initial findings from this experiment which involved over 4500 rentals of over 500 cars in 4 locations over a 5-month period. The results are consistent with the predictions of our model, and suggest that a properly chosen declining rental price function can increase overall revenues. Profits also increase significantly, since doubling the holding period of rental cars cuts discounted replacement costs by nearly 40%.

This paper provides an empirical analysis of how the U.S. Social Security and Medicare insurance system affect the labor supply of older males in the presence of incomplete markets for loans, annuities, and insurance. We estimate a detailed dynamic programming (DP) model of the joint labor supply and Social Security acceptance decision, focusing on a sample of males in the low to middle income brackets whose only pension is Social Security. The DP model delivers a rich set of predictions about the dynamics of retirement behavior, and comparisons of actual vs. predicted behavior show that the DP model is able to account for wide variety of phenomena observed in the data, including the pronounced peaks in the distribution of retirement ages at 62 and 65 (the ages of early and normal eligibility for Social Security benefits, respectively). We identify a significant fraction of health insurance constrained individuals who have no form of retiree insurance other than Medicare, and who can only obtain fairly priced private insurance via their employer's group plan. The combination of significant individual risk aversion and a long tailed (Pareto) distribution of care expenditures implies that there is a significant security value for these individuals to remain employed until they are eligible for Medicare coverage at age 65. Overall, our model suggests that a number of heretofore puzzling aspects of retirement behavior can be viewed as artifacts of particular details of the Social Security rules, whose incentive effects are especially strong for lower income individuals and those who do not have access to fairly priced loans, annuities, and insurance.

We define a class of dynamic Markovian games, directional dynamic games (DDG), where directionality is represented by a strategy-independent partial order on the state space. We show that many games are DDGs, yet none of the existing algorithms are guaranteed to find any Markov perfect equilibrium (MPE) of these games, much less all of them. We propose a fast and robust generalization of backward induction we call state recursion that operates on a decomposition of the overall DDG into a finite number of more tractable stage games , which can be solved recursively. We provide conditions under which state recursion finds at least one MPE of the overall DDG and introduce a recursive lexicographic search (RLS) algorithm that systematically and efficiently uses state recursion to find all MPE of the overall game in a finite number of steps. We apply RLS to find all MPE of a dynamic model of Bertrand price competition with cost-reducing investments which we show is a DDG. We provide an exact non-iterative algorithm that finds all MPE of every stage game, and prove there can be only 1, 3, or 5 of them. Using the stage games as building blocks, RLS rapidly finds and enumerates all MPE of the overall game. RLS finds a unique MPE for an alternating move version of the leapfrogging game when technology improves with probability 1, but in other cases, and in any simultaneous move version of the game, it finds a huge multiplicity of MPE that explode exponentially as the number of possible cost states increases.