Knowledge that Transforms

THE EFFECT OF MONETARY GROWTH on an economy's investment has long been of interest to economists, and monetary growth models provide a convenient tool for the analysis of this question. The standard optimizing growth model postulates that money is injected into the private sector through transfer payments which typically either are of lump sum form or are proportional to wealth, income, or money holdings. (See, for example, Brock (1974), Calvo (1979), Fischer (1979), and Gertler and Grinols (1982).) In these models monetary changes are tied directly to changes in subsidy or tax rates, and greater expected money growth generally either has no effect on investment or increases it through a Tobin (1965) effect. In this paper we analyze the effects that a stochastic monetary policy has on investment in an economy with individual optimization, rational expectations, and a government which makes expenditures and finances them through borrowing, money creation, and proportional income taxes. With such a formulation, money can be injected into the private sector through government purchases and open market operations as well as through transfers, and the link between money growth and subsidy or tax rates is weakened or nonexistent. We assume that the nominal income tax rates are constant over time. Given tax rates and (stochastic) government consumption, the stochastic monetary growth rule followed by the government induces a stochastic government debt policy. The effects that changes in the stochastic monetary growth rate have on investment depend on the nature of the depreciation deduction and on the relationship between the coefficient of relative risk aversion and the tax rate on production income. When depreciation deductions are based on historical costs, an equilibrium is unique so long as the coefficient of relative risk aversion is greater than the tax rate applicable to production income. In this case an increase in the mean rate of money growth decreases equilibrium investment while a mean preserving spread in the money growth rate increases investment. Given Friend and Blume's (1975) finding that the coefficient of relative risk aversion is substantially greater than one, this seems to be the empirically relevant case. If the coefficient of relative risk aversion is less than the tax rate on production income, multiple equilibria are possible, and the effects on investment of changes in the stochastic money growth rate are generally indeterminate. When depreciation deductions are based on replacement costs, investment is independent of the stochastic money growth rate. The paper is organized as follows. Section 2 develops the optimization problem of the representative individual when depreciation deductions are based on historical costs. Section 3 describes the behavior of the government and develops the rational expectations equilibrium for this economy. Section 4 examines the effects on investment of changes in the stochastic money growth rate. Section 5 briefly reconsiders the model when depreciation deductions are based on replacement costs.

This paper shows that: (1) the "preference reversal" phenomenon can be consistent with transitive preferences if these preferences violate the independence axiom of expected utility theory and (2) for the class of experiments that were used to produce the evidence concerning "preference reversal, " the elicitation of certainty equivalents is possible if, and only if, the respondent's preferences can be represented by functionals that are linear in the probabilities. Furthermore, a more general class of experiments is not immune to "preference reversal" if nonexpected utility preferences are admitted. Copyright 1987 by The Econometric Society.

Comparative static properties of optimal nonlinear income taxes are obtained for a finite population version o f the Mirrlees income-tax model with a weighted utilitarian social we lfare function and quasilinear preferences. The parameters which are varied are the weights in the welfare function, the slope of the prod uction constraint, and a parameter in the utility function. The endog enous variables are the consumers' consumption levels, pretax incomes (labor supplies in efficiency units), utility levels, and marginal t ax rates. Copyright 1987 by The Econometric Society.

This paper presents a finite-horizon search model that is econometrically implemented using all of the restrictions impli ed by the theory. Following a sample of male high school graduates fr om the youth cohort of the National Longitudinal Surveys from graduat ion to employment, search parameters are estimated. Reservation wages and offer probabilities are estimated to be quite low. Simulations a re performed of the impact of changing the parameters on the expected duration of unemployment. Copyright 1987 by The Econometric Society.

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We consider the problem of providing incentives over time for an agent with constant absolute risk aversion. The optimal compensation scheme is found to be a linear function of a vector of N accounts which count the number of times that each of the N kinds of observable events occurs. The number N is independent of the number of time periods, so the accounts may entail substantial aggregation. In a continuous time version of the problem, the agent controls the drift rate of a vector of accounts that is subject to frequent, small random fluctuations. The solution is as if the problem were the static one in which the agent controls only the mean of a multivariate normal distribution and the principal is constrained to use a linear compensation rule. If the principal can observe only coarser linear aggregates, such as revenues, costs, or profits, the optimal compensation scheme is then a linear function of those aggregates. The combination of exponential utility, normal distributions, and linear compensation schemes makes computations and comparative statics easy to do, as we illustrate. We interpret our linearity results as deriving in part from the richness of the agent's strategy space, which makes it possible for the agent to undermine and exploit complicated, nonlinear functions of the accounting aggregates.

We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect. A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations. Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional sales by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.

In an economy with one public and one private good, egalitarian-equivalent cost sharing consists of finding the highest public good level, x*, such that consuming x* for free yields a feasible utility distribution. The corresponding feasible allocation (typically unique), called egalitarian-equivalent, is in the core of the economy. Conversely, any cost sharing method satisfying Pareto optimality, cost monotonicity (nobody suffers a utility loss if the production technology improves upon, ceteris paribus), and individual rationality (no single-agent coalition objects) or no private transfers (no agent receives a positive amount of private good), must select an egalitarian-equivalent allocation in every economy. Copyright 1987 by The Econometric Society.

This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).