Avner Bar-Ilan

The Timing and Intensity of Investment

Although there has been extensive analysis of the timing of investment, the intensity of investment has received far less attention. This paper analyzes both. For incremental investment, the intensity of investment proceeds as does timing in the fixed intensity new-view models. For lumpy investment, intensity and timing behave in strikingly different ways. Changes that encourage earlier investment can lead to lower intensity when investment occurs. Thus, the effect of such changes on the capital stock is ambiguous. The paper also makes a general comparison of intensity under incremental and lumpy investment, showing that both the capital stock and the uncertainty-investment relationship are different in the two regimes.

Consumer Durables: Evidence on the Optimality of Usually Doing Nothing

The authors argue that lumpy, nonconvex transaction costs are the norm for a wide range of economic decisions, which are thus characterized by inertial behavior. Application of this idea to the consumption of durable goods yields an (S,s) decision rule, which, when aggregated, highlights the different expected behavior of average expenditure per purchase versus the number of purchases. The empirical implications of this rule are presented and compared to other theories. A battery of empirical tests generally supports the predictions of the model; in particular, it does a good job of explaining the time pattern of response of spending on durables to a change in income. Copyright 1992 by Ohio State University Press.

A generalized impulse control model of cash management

Abstract This paper presents a general model of cash management, viewed as an impulse control problem for a stochastic money flow process. Generalizing classical approaches, we represent this process by a superposition of a Brownian motion and a compound Poisson process, controlled by two-sided target-trigger policies. For phase-type distributions for the upward and downward jumps we determine all pertinent cost functionals explicitly. Moreover, the controlled process is studied in steady state. The closed-form results can be used to determine optimal values for the target and trigger values numerically.

Time-to-build and capacity choice

Abstract This paper studies how demand uncertainty and time-to-build interact in affecting irreversible investment activity. Using impulse control methods we find the optimal timing and size of investment for a firm such as an electric utility that considers expanding its capacity in order to meet an uncertain demand. When the construction lag is short, uncertainty delays investment while increasing its size once it takes place. However, for comparatively long, and realistic, times-to-build the sensitivity to uncertainty is drastically reduced and the results can even be reversed; more uncertainty can speed up investment and reduce its size.

Explicit solution of inventory problems with delivery lags

We consider a continuous-time inventory system with fixed delivery lag, subject to a demand modelled as a diffusion process with drift. Excess demand is backlogged. We prove that the optimal ordering policy is a function of the sum of the stock on hand and the stock ordered but not yet delivered. Moreover, we state a relation linking the value function when orders are pending with the value function when no order is pending. As a consequence, the a priori infinite dimensional Quasi-Variational inequality QVI satisfied by the value function reduces to a finite dimensional one. The one-product inventory problem is then solved explicitly in the case of linear holding and shortage costs with fixed and proportional ordering cost. The optimal policy is determined; it is an s, S policy applied to the sum of stock on hand and orders pending, which means that when this sum decays below a critical level s, an order to level S is placed.

The Response of Criminals and Noncriminals to Fines

We use traffic data from a series of experiments in Israel and San Francisco to examine how illegal behavior is deterred by higher fines and whether deterrence varies with personal characteristics such as criminal record, driving record, income, and age. We find that red‐light running decreases sharply in response to an increase in the fine. The elasticity of violations with respect to the fine is larger for younger drivers and drivers with older cars. Criminals convicted of violent offenses or property offenses run more red lights on average but have the same elasticity as drivers without a criminal record. Within Israel, members of ethnic minority groups have the smallest elasticity with respect to a fine increase.

A Macroeconomic Perspective on Reserve Accumulation

This paper nests the buffer stock model within a standard open-economy model to capture two motives for international reserves accumulation—the insurance motive and the export-led growth motive. The model is solved for two exchange-rate policies, discretion and a rule with escape clause. It illustrates the behavior of international reserves and other macroeconomic variables when the policymaker pursues output and inflation stabilization and recognizes the supply of reserves can constrain the choice of exchange rate and the choice of exchange rate affects the supply of reserves. When output is below potential, it is optimal under both discretion and the rule to adopt a weak currency and promote export-led growth to achieve output and inflation stabilization. This policy leads to reserve accumulation and is consistent with the behavior of China. When reserves are low initially, welfare is higher when the policymaker follows a rule.

The Life Cycle Permanent-Income Model and Consumer Durables

This paper presents an extension of the life cycle permanent-income model of consumption to the case of a durable good whose purchase involves limpy transactions costs. By integrating the advancement/postponement decision in the individuals analysis, the implications of the model are different in some respects from those of standard consumption theory. Using explicit aggregation it is shown that expenditures on durables display very large short-run elasticity to changes in permanent income. Empirical tests generally produce results that are in line with the theory.

An algorithm for evaluating the number of controls in trigger--target models

Abstract We present an algorithm for evaluating the distribution of the number of controls in trigger-target models. This algorithm can be applied to study the distribution of capital installed in a certain time period, the distribution of quantity of money demanded, as well as other applications.