Axioms for an individual's preferences over time, taken from the present perspective, usually assume that the individual will live, or expects to live, throughout a given horizon span. This paper offers an axiomatization that explicitly recognizes the uncertainty of an individual's lifetime. It divides a horizon span into n periods and assumes that if death is not immediate then it will occur at the end of one of the periods. The theory is based on an unconditional preference relation over potential future consumption streams that accounts for uncertain lifetime, along with a conditional preference order that is based on the hypothesis that death will occur at the end of period i. There is a conditional order for each i from 1 to n. The utility representation involves an order-preserving utility function for each of the n conditional orders such that one potential consumption stream is unconditionally preferred to another if, and only if, the sum of the conditional utilities for the first stream exceeds the sum of the conditional utilities for the second. It is argued that the theory seems fairly reasonable only if probability of survival does not depend significantly on past consumption.

Is one distribution (of income, consumption, or some other economic variable) among families or individuals more or less equal in relative terms than another? Despite the seeming straightforwardness of this question, there has been and continues to be considerable debate over how to go about finding the answer. There are two points of contention. One is the issue of cardinality vs. ordinality. Practitioners of the cardinal approach compare distributions by means of summary measures such as a Gini coefficient, variance of logarithms, and the like. For purposes of ranking the relative inequality of two distributions, the cardinality of the usual measures is not only a source of controversy, but it is also redundant. Accordingly, some researchers prefer an ordinal approach, adopting Lorenz domination as their criterion. The difficulty with the Lorenz criterion is its incompleteness, affording rankings of only some pairs of distributions but not others. Current practice in choosing between a cardinal or an ordinal approach is now roughly as follows: Check for Lorenz domination in the hope of making an unambiguous comparison; if Lorenz domination fails, calculate one or more cardinal measures. This raises the second contentious issue: which of the many cardinal measures in existence should one adopt? The properties of existing measures have been discussed extensively in several recent papers. Typically, these studies have started with the measures and then examined their properties. In this paper, we reverse the direction of inquiry. Our approach is to start by specifying as axioms a relatively small number of properties which we believe a ?good? index of inequality should have and then examining whether the Lorenz criterion and the various cardinal measures now in use satisfy those properties. The key issue is the reasonableness of the postulated properties. Work to date has shown the barrenness of the Pareto criterion. Only recently have researchers begun to develop an alternative axiomatic structure. The purpose of this paper is to contribute to such a development.

The purpose of this paper is to examine within the context of a patieular U.S. exammetric model the sensitivity of fiscal policy effects to alternative assumptions about the behavior of the Federal Reserve. Five cases are considered, four in which Fed behavior is exogenous and one in which Fed behavior is endogenous. In each of the four exogenous cases the Fed is assumed to control a particular variable, which is then taken to be exogenous for purposes of the fiscal-policy experiments. For the endogetmus case an estimated equation explaining Fed behavior is added to the model. and the expanded mcdel is used to perform the experiments. The rewlts of some optimal control experiments are also reported in this paper. These latter experiments are designed to examine the sensitivity of optimal fiscal policies to alternative assumptions about Fed behavior. The main conclusion of this paper is that fiscal policy effects and optimal fiscal policies are quite sensitive to assumptions about the behavior of the Fed. 1. IN-cROD”cTION MOST EXAMINATIONS OF FISCAL POLICY EFFECTS in U.S. econometric models are based on the assumption that the behavior of the Federal Reserve (henceforth called the “Fed”) is exogenous, i.e., that the behavior of the Fed is not influenced by the state of the economy. The typical procedure is to assume that the Feds has control over a particular variable in the model and then to take this variable as exogenous for purposes of the fiscal policy experiments. An alternative procedure, if one believes that the behavior of the Fed is not exogenous, is to estimate an equation explaining Fed behavior (i.e., explaining the variable that the Fed is assumed to control), add this equation to the model, and use this expanded model to perform the fiscal policy experiments. The purpose of this paper is to examine within the context of a particular U.S. econometric model the sensitivity of fiscal policy effects to alternative assumptions about Fed behavior. Five cases are considered, four in which Fed behavior is exogenous and one in which Fed behavior is endogenous. In each of the four exogenous cases the Fed is assumed to control a particular variable, which is then taken to be exogenous for purposes of the fiscal policy experiments. The control variables in the four cases are: (1) the amount of government securities outstanding; (2) the money supply; (3) nonborrowed reserves; and (4) the bill rate. For the endogenous case an estimated equation explaining Fed behavior is added to the model, and the expanded model is used to perform the fiscal policy experiments. Section 2 contains a brief description of the econometric model used for purposes of this paper. The model, which is described in detail in Fair [9], is particularly suited for examining the effects of monetary and fiscal policies ‘The research described in this paper was financed by grant SOC77-03274 from the National

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