Knowledge that Transforms

A solution method and an estimation method for nonlinear rational expectations models are presented in this paper.The solution method can be used in forecasting and policy applications and can handle models with serial correlation and multiple viewpoint dates.When applied to linear models, the solution method yields the same results as those obtained from currently available methods that are designed specifically for linear models.It is, however, more flexible and general than these methods.The estimation method is based on the maximum likelihood principal.It is, as far as we know, the only method available for obtaining maximum likelihood estimates for nonlinear rational expectations models.The method has the advantage of being applicable to a wide range of models, including, as a special case, linear models.The method can also handle different assumptions about the expectations of the exogenous variables, something which is not true of currently available approaches to linear models.

[We present a definition of factor structure that is less restrictive than the one typically used in arbitrage pricing models. Our factor structure restrictions build on the following intuitive distinctions between factor variance and idiosyncratic variance: (i) A well-diversified portfolio contains only factor variance. (ii) If a portfolio is uncorrelated with the well-diversified portfolios, then it contains only idiosyncratic variance; so if a sequence of such portfolios becomes well-diversified, the limiting variance should be zero. Our factor structure restrictions imply Ross' [5] arbitrage pricing formula. We obtain upper and lower bounds on the approximation error in that formula; these bounds may be useful in empirical work. They imply that arbitrage pricing is exact if and only if there is a risky, well-diversified portfolio on the mean-variance frontier. If all mean-variance efficient portfolios are well-diversified, then the well-diversified portfolios provide mutual fund separation. Our factor structure restrictions are satisfied (with K factors) if and only if the covariance matrix of asset returns has only K unbounded eigenvalues as the number of assets increases.]

[Fix-price equilibria à la Benassy are shown to be unique under a condition, closely related to the macroeconomic stability condition, at any price system p extgreater extgreater O.]

IN THIS PAPER we present a multiperiod model of investment and reinvestment in which the investor's goal is the maximization of terminal wealth over the finite horizon in which economic activity occurs. The model entails the absence of risk, constant returns-to-scale, stationarity, and a borrowing constraint. The main point is to characterize the relationship between an investment project's asymptotic (internal) growth rate and its set of internal-rates-of-return, thereby provid

When is the Pareto optimal amount of public goods independent of income distribution? Subject to some regularity conditions, the answer is when preferences of every individual i can be represented by a utility function of the form U(X_i,Y)=A(Y)X_i+B_i(Y) where X_i is i's consumption of private goods and Y is the amount of public goods.

We consider an open question in applied price theory: Without a priori knowledge of a firm's cost function or a consumer's indirect utility function, is it possible to estimate price and substitution elasticities consistently by observing a demand system? As the work of White [30], Guilkey, Lovell, and Sickles [19], and others has shown, ordinary flexible functional forms such as the translog cannot achieve this objective. We find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the Fourier flexible form provided the number of fitted parameters increases as the number of observations increases. This result obtains with any of the commonly used statistical methods as, for example, multivariate least squares, maximum likelihood, and three-stage least squares. It obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule. We approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail.

[In most statistical estimation problems, the distribution of errors is unknown, and the traditional assumption of normality is used for convenience. We investigate here the fragility of the inferences based on normality by hypothesizing a neighborhood of distributions around the normal distribution, and by identifying the set of alternative maximum likelihood estimates corresponding to the set of error distributions.]

MODELS WHICH INCORPORATE both uncertainty and the dynamic behavior of economic agents are difficult to analyze.2 Moreover, even when a solution is obtained, it can seldom be simply stated and rarely lends itself to straightforward interpretations. An example of an appealingly understood result is a turnpike theorem, which states that if the planning horizon is distant then the optimal policy can be approximated by a wealth-independent policy. Our paper develops an analogous result in a stochastic intertemporal model of portfolio selection. In fact, we obtain necessary and some sufficient conditions for a turnpike. The problem considered in this essay is that of an investor-a von NeumannMorgenstern expected utility maximizer-who invests for a finite horizon and consumes only his terminal wealth. At the beginning of the first period the investor allocates his wealth, w, among various assets, and at the end of the first