Knowledge that Transforms

The authors introduce a class of alternating-move, infinite-horizon models of duopoly. The timing captures the presence of short-run commitment s. They apply this framework to a natural monopoly in which costs are so large that at most one firm can make a profit. The firms install short-run capacity. In the unique symmetric Markov perfect equilibriu m, only one firm is active and practices the quantity analogue of lim it pricing. For commitments of brief duration, the market is almost c ontestable. The authors conclude with a discussion of more general mo dels where the alternating timing is derived rather than imposed. Copyright 1988 by The Econometric Society.

Social experiments are characterized by their high cost. A tempting alternative to the establishment of a contemporaneous statistical control group is preexempt observat ion of the treatment group. In this paper, the authors analyze the tr ade-off between these two types of "con-trol" as functions of their relative cost and information content in a multiperiod error compone nts framework, where the allocation of observations across the two gr oups is always done in an optimal manner. Solutions for the optimal p roportion of the sample to be devoted to the contemporaneous control group are presented and their behavior as a function of relevant para meters is studied. Copyright 1988 by The Econometric Society.

The authors provide game theoretic foundations for the classic kinke d demand curve and Edgeworth cycle. In their alternating-move model, there are multiple Markov perfect equilibria of both the kinked deman d curve and Edgeworth cycle variety. In any Markov perfect equilibria , profit is bounded away from the Bertrand equilibria level. A kinked demand curve at the monopoly price is the unique symmetric "renegot iation proof" equilibrium when there is little discounting. The auth ors then endogenize the timing by allowing firms to move at any time. They find that firms end up alternating, thus vindicating the fixed timing assumption of the simpler model. Copyright 1988 by The Econometric Society.

The problem of controlling a stochastic process, with unknown parameters over an infinite horizon, with discounting is considered. Agents express beliefs about unknown parameters in terms of distributions. Under general conditions, the sequence of beliefs converges to a limit distribution. The limit distribution may or may not be concentrated at the true parameter value. In some cases, complete learning is optimal; in others, the optimal strategy does not imply complete learning. The paper concludes with examination of some special cases and a discussion of a procedure for generating examples in which incomplete learning is optimal. Copyright 1988 by The Econometric Society.

It is of interest to know when the incentive compatibility conditio n in principal-agent problems can be replaced by the condition that the agent's expected utility be stationary in effort. The Mirrlees-Rogerson conditions do not work if the principal can observe more than one observable statistic. Also, the Mirrlees-Rogerson assumption that the distribution function of output is convex in the agent's action is unsatisfactory even in the context of the basi c model; it is too restrictive. The paper presents a suite of conditio ns that are applicable to the multistatistic case and replaces the objectionable convex distribution function assumption. Copyright 1988 by The Econometric Society.

One type of semiparametric regression is b8X A u(Z), where b and u(Z) are an unknown slope coefficient vector and function. Estimates of b based on incorrect parametrization of u are generally inconsist ent, whereas consistent nonparametric estimates converge slowly. An e stimate, bC, is constructed by inserting nonpar-ametric regression es timates in the nonlinear orthogonal projection on Z. Under regularity conditions bC is shown to be N1/2-consistent for b and asymptoticall y normal, and a consistent estimate of its limiting covariance matrix is given. The author discusses the identification problem and bC's e fficiency. Extensions to other econometric models are described. Copyright 1988 by The Econometric Society.

A great deal of research on the empirical behavior of inventories examines some variant of the production smoothing model of finished goods inventories. The overall assessment of this model that exists in the literature is quite negative: there is little evidence that manufacturers hold inventories of finished goods in order to smooth production patterns. This paper examines whether this negative assessment of the model is due to one or both of two features: costs shocks and seasonal fluctuations. The reason for considering costs shocks is that if firms are buffeted more by cost shocks than demand shocks, production should optimally be more variable than sales. The reasons for considering seasonal fluctuations are that seasonal fluctuations account for a major portion of the variance in production and sales, that seasonal fluctuations are precisely the kinds of fluctuations that producers should most easily smooth, and that seasonally adjusted data is likely to produce spurious rejections of the production smoothing model even when it is correct. We integrate cost shocks and seasonal fluctuations into the analysis of the production smoothing model in three steps. First, we present a general production smoothing model of inventory investment that is consistent with both seasonal and non-seasonal fluctuations in production, sales, and inventories. The model allows for both observable and unobservable changes in marginal costs. Second, we estimate this model using both seasonally adjusted and seasonally unadjusted data plus seasonal dummies. The goal here is to determine whether the incorrect use of seasonally adjusted data has been responsible for the rejections of the production smoothing model reported in previous studies. The third part of our approach is to explicitly examine the seasonal movements in the data. We test whether the residual from an Euler equation is uncorrelated with the seasonal component of contemporaneous sales. Even if unobservable seasonal cost shocks make the seasonal variation in output greater than that in sales, the timing of the resulting seasonal movements in output should not necessarily match that of sales. The results of our empirical work provide a strong negative report on the production smoothing model, even when it includes cost shocks and seasonal fluctuations. At both seasonal and non-seasonal frequencies, there appears to be little evidence that firms hold inventories in order to smooth production. A striking piece of evidence is that in most industries the seasonal in production closely matches the seasonal in shipments, even after accounting for the movements in interest rates, input prices, and the weather.

APPROXIMATE POWER FUNCTIONS FOR SOME ROBUST TESTS OF REGRESSION COEFFICIENTS Thomas J . Rothenberg Department o f Economics U n i v e r s i t y o f C a l i f o r n i a , Berkeley Research Papers i n Economics No. 84-1 Summary Edgeworth expansions are developed f o r the d i s t r i b u t i o n functions o f some t e s t s t a t i s t i c s i n the normal l i n e a r regression model where the e r r o r covariance matrix i s unknown. Tests based on generalized l e a s t squares estimates and also on ordinary l e a s t squares estimates are considered. In both cases, adjustments t o the asymptotic c r i t i c a l The approxi values are found and approximate l o c a l power c a l c u l a t e d . and a u t o c o r r e l a t i o n . mations are applied to a number o f examples, i n c l u d i n g h e t e r o s c e d a s t i c i t y

IN SPITE OF ITS IMPORTANCE, the exploration process has not received much attention in the economics of nonrenewable resources. Among the researchers who investigated this problem, we might mention Arrow and Chang (1982), Deshmukh and Pliska (1980), Pindyck (1978, 1980), and Gilbert (1979, 1981). For earlier work on this subject, we might also mention Gaffney (1967) and Herfindahl (1974). Basically, an exploration program is a search for potential deposits whose sizes and locations are both uncertain. Furthermore, exploration technology exhibits a high degree of scale economies. Our paper represents an attempt to deal with these rather neglected aspects of the exploration process in a model of simultaneous extraction and exploration.