Columbia Business School Research

Improvements in computational methods have resulted in the faster solution of general equilibrium economic models This paper gives a nontechnical introduction to the octahedral algorithm for the solution of economic models.

This paper presents a macroeconomic model containing optimizing, inventory-holding firms that is consistent with a number of prominent empirical regularities concerning fluctuations in output, exchange rates, relative prices, and money. Prices are sticky, but they are not predetermined. Still, our model is consistent with exchange rate overshooting in the sense of Dornbusch. Typical sticky-price models allow a divergence between current production and current demand, but this divergence is never allowed to feed back into the model.

This paper relates New York City's experience since 1975, a period characterized by local economic and fiscal crisis and a gradual recovery from it, to four prevailing themes in the contemporary literature of cities and public administration.

The paper analyzes the use of information in companies planning strategically versus those which are not. This contrast is used to build the case for developing strategic forecasting capability which focuses on a variety of environments, is proactive and interactive, and creates a need for different kinds of data bases and forecasting techniques.

This paper establishes a simple existence proof for a solution to the optimality equations arising in finite undiscounted Markov Renewal Programs, by applying Brouwer's fixed point theorem to the so-called reduced value-iteration operator. Because of its simplicity, our approach lends itself to new existence results for more general models.

This paper adds to recent evidence on market inefficiency in processing information in earnings reports. It documents that short positions taken in sample stocks which did not report earnings by the date expected during the sample period, 1971–1976, would have been abnormally profitable, before transaction costs. This is because late reports, on average, revealed bad news which was not anticipated in market prices prior to the report date.

We examine a queueing system with multiple primary servers and a fewer number of auxiliary servers. There are two classes of customers—those who require service from a primary server working alone and those who require service from a primary server who is assisted by an auxiliary server. Though the apparent Markovian state space is five-dimensional, we show that an aggregation results in an exact two-dimensional representation which is Markovian. Matrix geometric theory is used to obtain approximations for the mean delay and blocking probability of each customer type.

Many queueing situations such as computer, communications and emergency systems have the feature that customers may require service from several servers at the same time. They may thus be delayed until the required number of servers is avialable and servers may be idle when customers are waiting. We consider general server-completion-time distributions and derive approximation methods for the computation of the steady-state distribution of the number of customers in queue as well as the moments of the waiting-time distribution. Extensive computational results are reported.

We develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree (m.c.s.t.) game. The first procedure requires O(n 2) elementary operations to obtain each additional point in the core, wheren is the number of users. The efficiency of the second procedure, which is a natural strengthening of the first procedure, stems from the special structure of minimum excess coalitions in the core of an m.c.s.t. game.

This paper attempts to contribute to two rapidly growing branches in economic theory: asset pricing and “overlapping generations” models. The model is formulated and it is shown that equilibrium prices exist, and some of their properties are discussed. Then the model is applied to an asymmetric information environment to see if randomness in the number of informed agents could confuse the uninformed. Surprisingly, it could not.

This paper presents a successive approximation method for solving systems of nested functional equations which arise, e.g., when considering Markov renewal programs in which policies that are maximal gain or optimal under more selective discount — and average overtaking optimality criteria are to be found. In particular, a successive approximation method is given to find the optimal bias vector and bias-optimal policies. Applications with respect to a number of additional stochastic control models are pointed out.

How many patrol cars staffed with a single police officer are needed to provide equivalent police service to an existing system with n two-officer patrol cars? This question is explored for New York City using a multiple patrol car per call priority queueing model. It is shown that a one-officer patrol program is feasible, yet pitfalls exist which could adversely affect its performance. The paper details the process of data analysis and model building and emphasizes the subjective elements that remain in a highly technical OR study.

We explain the observed negative relati between market value of firms and their fund raising activities. Ours is not a signalling model. The firm's objective is to maximize the present value of its income. Considerations of cash availability (liquidity) and unfolding of uncertainty drive our model. Income from operations is an important source of liquidity. Low earnings are associated with low liquidity. Whether earnings are low or not is known to some extent in advance of the realization itself.

Group planning practices of leading American and Australian manufacturing firms are compared and contrasted. Despite some differences, a broad pattern of similarity emerges across many elements of the planning systems.

One of the primary concerns of urban police departments is the effective use of patrol cars. In large cities, police assigned to patrol cars typically account for more than 50% of total police manpower and their allocation has become particularly crucial in light of recent fiscal cutbacks.

The performance of adult females on information acquisition tasks is shown to be related to their performance on information integration tasks; both are shown to be related to basic measures of cognitive ability derived from formal operations theory.

In this paper, we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are Cobb-Douglas with stochastic constant returns to scale. The following main results are established. (i) When there is no relative price uncertainty, it is shown that the equilibrium interest rate exhibits a mean reverting tendency. A nontrivial steady state distribution is found to exist for the equilibrium interest rate.

In many practical applications of multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs.

A reply correcting feedback from another economist. It explains in detail an aspect of the flotation cost adjustment.

We establish sufficient conditions for the recoverability and uniqueness of utility functions (preferences) generating consumption and asset demands in a two-period setting under uncertainty.

We address the combined problem of allocating a scarce resource among several locations, and planning deliveries using a fleet of vehicles. Demands are random, and holding and shortage costs must be considered in the decision along with transportation costs. We show how to extend some of the available methods for the deterministic vehicle routing problem to this case. Computational results using one such adaptation show that the algorithm is fast enough for practical work, and that substantial cost savings can be achieved with this approach.

We show that any triangulation of the 5-cube I⁵ by complete truncation, i.e., "slicing off" the even (or the odd) vertices, cannot use less than 67 or more than 68 pieces.

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem.

This paper presents an algorithm to compute an optimal (s,S) policy under standard assumptions (stationary data, well-behaved one-period costs, discrete demand, full backlogging, and the average-cost criterion). The method is iterative, starting with an arbitrary, given (s,S) policy and converging to an optimal policy in a finite number of iterations. Any of the available approximations can thus be used as an initial solution. Each iteration requires only modest computations. Also, a lower bound on the true optimal cost can be computed and used in a termination test.

Consider a central depot (or plant) which supplies several locations experiencing random demands. Orders are placed (or production is initiated) periodically by the depot. The order arrives after a fixed lead time, and is then allocated among the several locations. (The depot itself does not hold inventory.) The allocations are finally received at the demand points after another lag. Unfilled demand at each location is backordered. Linear costs are incurred at each location for holding inventory and for backorders. Also, costs are assessed for orders placed by the depot.

Clark and Scarf [1960] characterize optimal policies in a two-echelon, two-location inventory model. We extend their result to the infinite-horizon case (for both discounted and average costs). The computations required are far easier than for the finite horizon problem. Further simplification is achieved for normal demands. We also consider the more interesting case of multiple locations at the lower echelon. We show that, under certain conditions, this problem can be closely approximated by a model with one such location.

We examine a multi-server queueing system with Poisson arrivals in which customers require simultaneous service from a random number of servers. Servers assigned to the same customer begin and end service concurrently. Service times are, in general, assumed to be exponentially distributed. A system point approach is presented as a framework for obtaining the waiting time distribution for each customer type. Explicit solutions are derived for the two-server system.

In this paper we examine the effect of filing form 10-K on EDGAR on the incidence of small and large trades.

We focus on two commonly observed insurance policy provisions: upper limits on coverage and deductibles. We suggest that upper limits on coverage result from the effective limited liability obtained through the bankruptcy statutes. We show that absent moral hazard, if the administrative cost structure has fixed costs and scale economies, deductibles are not optimal. But the optimal contractual form leads to a moral hazard problem, which deductibles control.

This paper compares the properties of dividend announcements and management earnings forecasts as predictors of earnings and firm value. First, the two predictors are compared on the basis of their ability to predict earnings. Then the information they convey about firm value is assessed by comparison of the performance of investment strategies based on values of the two predictors. Finally, the effects of dividend announcements on stock prices are considered.

Corporate investment in an economy without a complete set of contingent claims markets has the characteristic of a public good in the sense that the stockholders' consumption plans cannot be separated from, but depend on, the specific investment plans of the firms. The purpose of this article is to develop an internal allocation mechanism capable of attaining production plans that are unanimously preferred by stockholders and that satisfy a natural notion of optimality applicable to the stock market economy.

This paper establishes the existence of a solution to the optimality equations in undiscounted semi-Markov decision models with countable state space, under conditions generalizing the hitherto obtained results. In particular, we merely require the existence of a finite set of states in which every pair of states can reach each other via some stationary policy, instead of the traditional and restrictive assumption that ever stationary policy has a single irreducible set of states.