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A test of weak exogeneity in the simultaneous equation Tobit model is proposed and illustrated using a female labour supply model estimated using cross-section data. The test statistic can be simply output from any standard Tobit maximum likelihood package, and is asymptotically efficient. The procedure provides consistent estimators for the simultaneous Tobit model whose asymptotic covariance matrix is a simple extension of the usual Tobit formula. We also provide the Lagrange Multiplier test of weak exogeneity. (This abstract was borrowed from another version of this item.)
A NUMBER OF AUTHORS argue that a Bayesian posterior odds criterion is appropriate for model selection.2 This paper considers how to derive this criterion when there is minimal prior information. We propose minimizing measures of prior information relative to the models in question rather than relative to the parameters of the particular models. In so doing, we obtain an expression for the odds that is invariant to the parameterization of the particular models and overcomes certain well known finite sample limiting problems. We illustrate this procedure using two popular measures of information derived from the well known Shannon [26] measure. By minimizing these measures with the sample size held fixed, we obtain the same model selection criterion that Schwarz [25] derived asymptotically for large sample sizes. This expression has a number of desirable properties and is computationally no more
[The estimation and testing of a singular equation system in the context of a general dynamic specification is considered. In an application to factor demand equations, hypotheses suggested by economic theory are expressed in terms of the long run structure of the system under alternative dynamic specifications. Variations in the dynamic specification are found to have a significant impact upon the inferences that can be made about the long run structure.]
Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.
[Models of the behavior of populations of self-reproducible natural resources in an economic framework have rarely anticipated the consequences of different forms of production functions. This paper investigates sufficient conditions for extinction in a very general model as well as a model having a specific production function. In the second section additional considerations relating to extinction are deduced as well as the existence of a watershed level of population. These conclusions are exemplified using data from one particular population of red deer.]
This paper provides necessary and sufficient conditions for it to be optimal to base decisions on estimates of the parameters that characterize a decision problem (e.g., profit maximization with an estimated price elasticity of demand). We show that the separation of parameter estimation from decision making generally yields lower utility than an integrated approach which takes account of estimation uncertainty. We evaluate the decision in the parameter estimation method and show that the resulting utility loss can be substantial. MANY ACTUAL DECISIONS are based on statistical estimates of parameters that help to characterize the decision environment. For example, a firm maximizing the expected utility of profit might find that its input and output decisions depend on unknown parameters of its demand function. Econometric estimates of such parameters might then be derived and utilized in making these decisions. The first purpose of this paper is to rigorously investigate whether it is correct to make decisions in this manner; in general, it is not. The second purpose is to investigate the decis'ion bias in decisions based on commonly employed parameter estimates. We will determine, for example, whether a price setting monopolist is mistakenly setting prices too high or too low when he bases his pricing decision on the maximum likelihood estimate of his demand equation. Finally, we provide a detailed numerical example to show that basing decisions on conventional parameter estimates can lead to large losses of utility. In Section 2, we introduce all notation, explain the procedure commonly used when basing decisions on values of unknown underlying parameters, and exhibit the decision-theoretic correct alternative procedure. When the optimal decisions under these two procedures are identical, we call the proper. We use the term summary value to refer not only to standard parameter estimates but to any single substituted for an unknown parameter in order to make decisions. This generalized concept is necessary because a that is appropriate for making decisions, in a sense defined below, need not have any of the properties of conventional parameter estimators. In Section 3, we derive under general assumptions necessary and sufficient conditions for the existence of proper values that are independent of the decision maker's utility function, U( ). This independence restriction is
Basu and Bundick, 2017 showed an intertemporal preference volatility shock has meaningful effects on real activity in a New Keynesian model with Epstein and Zin, 1991 preferences. We show that when the distributional weights on current and future utility in the Epstein–Zin time aggregator do not sum to 1, there is an asymptote in the responses to such a shock with unit intertemporal elasticity of substitution. In the Basu–Bundick model, the intertemporal elasticity of substitution is set near unity and the preference shock only hits current utility, so the sum of the weights differs from 1. We show that when we restrict the weights to sum to 1, the asymptote disappears and preference volatility shocks no longer have large effects. We examine several different calibrations and preferences as potential resolutions with varying degrees of success.