IO economists often estimate demand for differentiated products using data sets with a small number of large markets. This paper addresses the question of consistency and asymptotic distributions of instrumental variables estimates as the number of products increases in some commonly used models of demand under conditions on economic primitives. I show that, in a Bertrand–Nash equilibrium, product characteristics lose their identifying power as price instruments in the limit in certain cases, leading to inconsistent estimates. The reason is that product characteristic instruments achieve identification through correlation with markups, and, depending on the model of demand, the supply side can constrain markups to converge to a constant quickly relative to sampling error. I find that product characteristic instruments can yield consistent estimates in many of the cases I consider, but care must be taken in modeling demand and choosing instruments. A Monte Carlo study confirms that the asymptotic results are relevant in market sizes of practical importance.

Is the stock market boom a result of the baby boom? This paper develops an overlapping generations model in which a baby boom is modeled as a high realization of a random birth rate, and the price of capital is determined endogenously by a convex cost of adjustment. A baby boom increases national saving and investment and thus causes an increase in the price of capital. The price of capital is mean–reverting so the initial increase in the price of capital is followed by a decrease. Social Security can potentially affect national saving and investment, though in the long run, it does not affect the price of capital.

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This paper examines the implications of adverse selection in the private annuity market for the pricing of private annuities and the consequent effects on constrption and bequest behavior. With privately known heterogeneous mortality probabilities, adverse selection causes the rate of return on private annuities to be less than the actuarially fair rate based on population average mortality. However, a fully funded social security system with compulsory participation can offer an implied rate of return equal to the actuarially fair rate based on population average mortality. Thus, since social security offers a higher rate of return than private annuities, consumers cannot completely offset the effects of social security by transacting in the private annuity market. Using an overlapping generations model with uncertain lifetimes, we demonstrate that the introduction of actuarially fair social security reduces the steady state rate of return on annuities and raises the steady state levels of average bequests and average consumption of the young. The steady state national capital stock rises or falls according to the strength of the bequest motive.

Expected value maximizing sequential search rules can be expressed in terms of reservation values. In search with learning the reservation value at any stage of the search is unknown until that stage is reached. Thus calculating ex ante (and subsequent) probabilities of search duration and the offer accepted is difficult if these probabilities are expressed in terms of reservation values. This paper shows, for a wide class of learning procedures, how re-expressing these probabilities in terms of fixed points allows their direct calculation and, thereby, calculation of the expected value of adaptive search. Examples and comparative statics results are presented.

THE DRAMATIC INCREASE in energy prices in the 1970s has stimulated interest in the effect of energy prices on the demands for various factors of production. In analyzing the choice of energy-using characteristics of capital, it is important to recognize that a firm's energy-capital ratio is much more flexible prior to undertaking a capital investment than it is after the capital is put in place. In this paper we examine factor intensity choices in a stochastic putty-clay model. Ex ante, when the firm is making investment decisions, the price of energy is unknown. The energy/capital ratio is flexible ex ante and the firm chooses the optimal energy intensity based on the probability distribution of energy prices. Ex post, the energy/capital ratio is fixed and the price of energy is known. The firm cannot adjust the energy/capital ratio but can choose not to use its capital if the realized price of energy is too high.2 Recently, Kon [3] has studied factor demands in a stochastic putty-clay model in which the price of output is random and the prices of factors of production are known with certainty. In this paper, we focus on the effects of energy prices and thus treat factor prices as random and the output price as known with certainty. This difference in the source of randomness appears to make little difference in the comparison of optimal factor intensity under certainty and under uncertainty; indeed Proposition 1 in this paper corresponds to Kon's Proposition 1. In this paper we then go on to examine the effects on optimal factor intensity of changes in the mean and variance of the price of energy.3 The option to shut down during unfavorable price regimes plays an important role in our analysis. In Section 1 we develop a stochastic putty-clay model and compare a risk-neutral firm's behavior under certainty and uncertainty. The effects on energy-intensity of changes in the mean and variance of energy prices are analyzed in Section 2.

central objective of this paper is to present a series expansion of nonlinear estimators in order to facilitate an analysis of the distributions of such estimators. Where the estimator under consideration is a maximum likelihood estimator, the method provides somewhat more information, as well as higher order approximations to the distributions of the nonlinear estimators than does the usual theory which demonstrates asymptotic normality. The method is also useful for a wide class of estimators including those defined only implicitly by the estimating procedure. Approximations to the distributions of the nonlinear estimators can be obtained in many cases even when the moments do not exist. In any event, it is to be hoped that the analytic procedures discussed in this paper will simplify the analysis of specific cases and will shed more light on the general formulation of nonlinear estimation problems. The remainder of this paper is in four sections. The first section presents the basic theory and analyzes the asymptotic distributions of nonlinear estimators in correctly specified models. This is followed in the second section by a brief discussion of a number of interesting examples. The third section compares the approach outlined in this paper with the traditional maximum likelihood and general nonlinear series expansions. In the fourth section the approximate asymptotic distribution of the regression residuals is derived. The general statement of the model to be considered in the following sections is given by:

[This paper demonstrates how a two or three component error structure can be used with seemingly unrelated regressions. Its application may be particularly useful with large panel data sets when the researcher wishes to estimate several equations simultaneously and believes that errors both between and within equations are correlated over time and across units. Relatively simple algorithms are presented for estimation of the error covariance matrix and generalized least squares coefficients.]