Showing papers in "International Economic Review in 1969"

The Adjustment of Stock Prices to New Information

Abstract: There is an impressive body of empirical evidence which indicates that successive price changes in individual common stocks are very nearly independent. Recent papers by Mandelbrot and Samuelson show rigorously that independence of successive price changes is consistent with an "efficient" market, i.e., a market that adjusts rapidly to new information. It is important to note, however, that in the empirical work to date the usual procedure has been to infer market efficiency from the observed independence of successive price changes. There has been very little actual testing of the speed of adjustment of prices to specijc kinds of new information. The prime concern of this paper is to examine the process by which common stock prices adjust to the information (if any) that is implicit in a stock split

A Multinomial Extension of the Linear Logit Model

Abstract: A large number of analyses in the social sciences are concerned with the determinants of the probability that a particular event will occur. For example, one may be interested in the forces which motivate commuters to use their cars to go to work as against some form of mass transport. Time, cost, and other considerations will play a role. Let p be the probability that a car is used, and hence 1 — p the probability that mass transport is preferred; then one may want to apply a linear specification of the form $$p = a + b{{{T_1}} \over {{T_2}}} + c{{{C_1}} \over {{C_2}}} + {d_1}{Q_2} + {d_2}{Q_2} + {d_3}{Q_3},$$ where T 1 and T 2 are the times (minutes per day) needed for the two competing modes of transportation, C 1 and C 2 their costs (dollars per day), and Q l, Q 2, and Q 3 commuter characteristics which are considered to be relevant to the choice (income, family size, etc.).

Optimal investment and consumption strategies under risk, an uncertain lifetime, and insurance*

Abstract: sumption in period j, such that either the risk aversion index -u"(x)/u'(x), or the risk aversion index -xu"'(x)/u'(x), is a positive constant for all x > 0. In a second paper [6], it was further shown that this model, developed with the individual in mind, also gives rise to an induced theory of the firm under risk for the same class of utility functions. In the foregoing model, it was assumed that the individual's horizon was infinite (or known with certainty). In this paper, we consider the same basic model with three modifications. First, we postulate that the individual's, lifetime is a random variable with a known probability distribution. Second, we introduce a utility function intended to represent the individual's bequest motive. Third, we offer the individual the opportunity to purchase insurance on his life. It is found that when some or all of these modifications are made, all of the more important properties possessed by the optimal consumption and investment strategies under a certain horizon are preserved, albeit only under special conditions. In Section 2, the various components of the decision process are constructed. In the earlier model, the individual's objective was assumed to be the maximization of expected utility from consumption over time. Here, we postulate, more generally, that his objective is to maximize expected utility from consumption as long as he lives and from the bequest left upon his death. As before, the individual's resources are assumed to consist of an initial capital position (which may be negative) and a non-capital income stream. The latter, which may possess any time-shape, is assumed to be known with certainty and to terminate upon his death. In addition to insurance available at a "fair'" rate, the individual faces both financial opportunities (borrowing and lending) and an arbitrary number of productive investment opportunities. The interest rate is presumed to be known but may have any time-shape. The returns from the productive opportunities are assumed to be random variables, whose probability distributions may differ from period to period but are assumed to satisfy the "no-easy-money" condition. While no limit is placed on borrowing, the individual is required to be solvent at the time of his death with

Pure competition, coalitional power, and fair division*

Abstract: : Consideration of a new application of the mathematical theory of games to the conceptual foundations of the theory of economic competition. The Memorandum first gives a nontechnical discussion of three different types of solution to mathematical models of the marketplace, namely, the competitive equilibrium, the core, and the value, and relates them to three principles of distribution, namely, pure competition, coalitional power, and fair division. Several models are then analyzed in detail. First, numerical solutions are calculated for a class of symmetric market games, chosen to contrast the value with the other two solutions. Next, as the number of traders is increased, the convergence of all three solutions to a single outcome is proved for a general class of markets with money. Finally, an illustrative market model without money is evaluated explicitly as a function of the size of the market. This represents the first substantial application of a new definition of the value for games without side payments. The formal definitions are summarized in an appendix. (Author)

Factor price equalization and the stolper-samuelson tiieorem*

Abstract: It is important at the outset to remove an ambiguity in the statement just made. It is one thing to say that, given any initial equilibrium position, there exists a one-to-one association between commodities and factors such that a change in any commodity price will lead to a more than proportionate change (in the same direction) in the corresponding factor price. It is quite another thing to state that it is possible to find a one-to-one association between goods and factors in advance such that, starting from any equilibrium, a change in any commodity price will lead to a more than proportionate change in the price of the already specified factor. The first may be called the local version of the Stolper-Samuelson theorem, and the second the global version. Another distinction must be made. In the case of two factors and two commodities (the only case treated rigorously by Stolper and Samuelson), it turns out that if, as a result of an increase in the price of a good, one of the factor prices rises more than proportionately, then the other factor price must actually fall. In generalizing the theory to more than two commodities and two factors, it no longer holds that a more than proportionate increase in one factor price entails a fall in all the remaining factor prices. The case in which this does occur will be referred to as the strong form of the StolperSamuelson theorem, whereas the more general case will be called the weak form. We shall explore the various ways in which the theory first set forth by Stolper and Samuelson may be extended to n goods and factors. The main conclusions can be summarized as follows (the wording is necessarily vague, inasmuch as it constitutes a translation of mathematical conditions): (1) The Stolper-Samuelson theorem (strong, as well as weak form) is true locally (almost everywhere) for n 2, and globally whenever reversal of factor intensity is ruled out, as is, by now, quite well known. However, it is no longer true for n > 2, even under conditions which guarantee full factor price equalization. (2) Under certain special conditions, the weak form of

On the relation between commodity prices and factor rewards

Abstract: 1. 1. CONSIDER A COMPETITIVE ECONOMY with two commodities produced in positive amounts, two non-produced factors of production, and production functions concave and homogeneous of degree one. According to the StolperSamuelson Theorem [12], an autonomous increase in the price of one product gives rise to an increase in the real reward of one factor and to a decline in the real reward of the other. Specifically, an increase in the price of the i-th product results in an increase in the real reward of whichever factor is used vxith greater relative intensity in the i-th industry; and since one is free to number factors in any order, it is possible to associate the i-th factor with the i-th product (at least in a sufficiently small neighborhood of an initial equilibrium). 1.2. This is an exceedingly useful theorem. In a two-by-two model one finds oneself appealing to it in just about every exercise involving the distribution of income. The original article by Stolper and Samuelson was devoted to a single application of the theorem, the relation between tariff protection and real wages.2 But the theorem plays an equally important role in determining the incidence of a sales tax in a closed economy ([1], [4], [5]), and in making clear the distributional implications of capital accumulation [11]. The theorem would be even more useful if it could be extended to the case of n products and n factors. Can we in that more general case claim that an increase in the price of the i-th good results in an unambiguous increase

The Effect of Market Size on Concentration

Abstract: THE EFFECT OF market size on the concentration of output has long been of interest to students of industrial organization. It is generally thought that increases in the size of market reduce concentration. Unfortunately, the supporting evidence for this view is limited and hardly persuasive. On the one hand cross-sectional studies often show the combined market share of output of the four leading firms to be smaller in industries within the larger markets.2 Whether this inverse relation can be explained on economic or statistical grounds has not been discussed. Larger markets typically have a large number of firms. (The appropriate definition of market is discussed below.) The inverse relation between concentration and the number of firms in an industry could arise if random samples were selected from a common size distribution of firms. The larger the sample size, the lower the concentration ratio. The presence of an inverse relation may constitute verification of a hypothesis of economic theory or may be consistent with random sampling hypothesis.3 The explanatory value of the random sampling hypothesis is evaluated in Section 3 of the paper. Studies of changes in concentration over time often fail to show an inverse relationship between changes in concentration and changes in the size of market.4 The stability of U.S. concentration ratios over time has been noted

`Operation Twist' and the Movement of Interest Rates and Related Economic Time Series

Abstract: THIS PAPER PRESENTS the results of research on the question: Has "Operation Twist" succeeded in "twisting" the term structure of interest rates? Specifically, this paper contains a review of the generally accepted theory of the relationship between interest rates and selected economic time series; a report on the estimation of parameters of two interest rate equations, the variables of which are drawn from this theory; and a report on how these two equations may be used to draw inferences concerning "Operation Twist." Generally accepted theory is consistent with the hypothesis that, other things being equal, over a period of time the interest rate on a debt security varies directly with interest rates on alternative debt securities, yields on equity securities, prices of goods and services, and national income, and inversely with net free member bank reserves. This hypothesis is analyzed briefly in Section 1. In Section 2, this hypothesis is tested empirically in the form of a linear short-term interest rate equation and a linear long-term interest rate equation. The two-stage least squares method is used to estimate the parameters of these two linear equations from seasonally adjusted monthly data for the period 1953-1961. "Operation Twist" is analyzed in Section 3. This policy, which was initiated during President Kennedy's administration, seeks to maintain "relatively" high short-term rates, because of the balance of payments problem, and "relatively" low long-term rates because of the economic growth problem. The policy is based on the hypothesis that the Federal Reserve System and/ or the Treasury are able to modify the term structure of interest rates. The hypothesis specifically holds that the differential of long-term rates over short-term rates can be narrowed by governmental agencies.2 To oversimplify, this hypothesis is unacceptable to proponents of the "traditional" theory of the term-structure of interest rates.3 The "Operation Twist" hypothesis is

The Customs Union and the Theory of Second Best

Abstract: THE STUDY OF the customs union or free trade area is of great relevance, both from the practical point of view of international trade policies, and from the theoretical point of view of second best theory. The basic model in the economics of the customs union is that of two commodities and three countries-the home country, the partner country, and the foreign country (the rest of the world).2 By assuming infinite elasticity of foreign and partner supply and the nonexistence of tariffs imposed by the foreign and partner countries, it can easily be shown that the welfare of the home country is increased by the trade creation effect and diminished by the trade diversion effect, of the home country's granting a discriminatory elimination of its tariff on imports from the partner, while retaining its tariff on those from the foreign country.3 An optimum tariff rate for the home country on imports from its partner country can be calculated from the comparison of these two effects, i.e., in terms of the change of consumers' surplus of the home country. Such a rate is optimal simultaneously from the points of view of the home country, of the customs union (the home and partner countries), and of the world (three countries), since the welfare of the partner and foreign countries remains unchanged. The assumption of infinite elasticity of foreign supply is, however, inappropriate for this problem, since under this assumption there is no incentive for the home country to impose a tariff on its imports from the foreign country. Free trade should be considered the best solution and there is no place for arguing the optimal rate of tariff, i.e., a second best solution. Moreover, the assumption of the nonexistence of tariffs imposed by the foreign country cannot be considered realistic if the home country imposes a tariff on imports from the foreign country. If one drops the assumption of an infinitely elastic foreign supply and or that of no foreign tariff, one must solve the problem of the comparison of gains and losses of different countries. Optimality from the point of view of the customs union or of the world should, therefore, necessarily be that

Entrepreneurial Choice over Time under Conditions of Uncertainty

Abstract: IN THIS PAPER we analyze the way that a firm which operates under uncertainty will behave during the current period and over time. To do so, we develop a new multi-stage model of the firm which has-as we show belowinteresting implications both for economic theory and for econometric research. The paper's main results are summarized in two theorems in Section 2. The first of these theorems shows that an entrepreneur who operates under uncertainty will behave in each period as if he were attempting to maximizesubject to production and financial constraints-a strictly concave one-stage objective function whose arguments represent: (1) the dividends which the firm pays during the period, and (2) the firm's end-of-period asset-and-financing structure. The second theorem shows that, if it is possible to represent the behavior over time of prices and certain other parameters by random processes, then the firm's behavior over time (as reflected during each period in the inputs it uses, the output it produces, the dividends it pays, and the end-ofperiod asset-and-financing structure it selects) can also be represented by well-defined random processes. The proofs of both theorems are given in the Appendix.

On the Relationship among Different Members of the k-Class

Abstract: SINGLE EQUATION MODELS have been severely criticized on the ground that they neglect the simultaneity of jointly dependent variables. It is argued that in most instances, two or more variables in an equation are simultaneously determined by some larger system of equations. Bronfenbrenner [3], Haavelmo [6], and others have shown that in this event ordinary least squares will produce asymptotically biased parameter estimates. The limited information maximum likelihood method (see [9]) and two-stage least squares (see Theil [12], Zellner and Theil [13] and Basmann [2]) yield consistent, asymptotically unbiased parameter estimates. The k-class due to Theil can be viewed as a general estimation method which includes ordinary least squares (OLS), two-stage least squares (2SLS), and limited information as particular members. This paper presents an alternative derivation of the k-class method in which least squares is applied to a structural equation after suitable transformations have been applied to the jointly dependent variables. Different members of the k-class (differing in their posited values of k) correspond to different transformations of measured reduced-form residuals. The relationships among parameter estimates of different k-class members are then revealed by the analysis of specification errors. These relationships take the form of mathematical identities and are developed in Section 2. In Section 3, I examine the conditions under which the dispersion among different members of the k-class is a minimum. It can be shown that the k-class estimators are weighted averages of the OLS and 2SLS estimators.

A note on short-run employment and real wage rate under competitive commodity markets*

Abstract: THIS PAPER EXPLORES the effects upon aggregate employment and the real wage rate of a decline of aggregate demand in two economies in which the commodity market is competitive. In the first economy, all goods just produced are supplied to the market perfectly inelastically, the costs of storage being too great to warrant the holding of stocks at any non-negative market price. In the second type of economy, holding costs are low enough that producers will carry over some stock into the next market period when the current market price is low enough on the speculation that future sales will be possible at a higher price. This latter model has been studied by Edwin Mills [7, (chapter 4)] and Edward Zabel [9], and it will be supposed here that firms follow the optimal production and sales policies derived by Zabel [9]. Consider a decrease of aggregate demand for commodities which does not prevent the continued existence of a full-employment equilibrium. Under what conditions concerning the dynamics of the system will the fall of aggregate demand cause involuntary unemployment, at least transitionally? In particular, is a failure of money wages immediately to fall in proportion to the price level (at any given level of employment) a necessary condition for involuntary unemployment? That is, will involuntary unemployment occur only if the fall of aggregate demand causes a rise of the real wage rate? This is the principal question to be studied in this paper.

An Analysis of the Price-Inventory Nexus with Empirical Application to the Canadian Manufacturing Sector

Abstract: Most empirical work dealing with the behavior of prices focuses on the aggregate price level2. This is not surprising, given countries' concern with inflation and the fact that inflation is defined in terms of the movement in some aggregate price index, such as the consumer price index. In addition, this work has been most fruitful: policy-makers now, as well as economists, are talking in terms of "trade-offs" between prices and unemployment. Nevertheless, there is a cost involved in such analyses. By concentrating on the determinants of the aggregate price level, these studies take price behavior out of the context of the industry or firm where the decisions concerning prices are actually made. The result may well be that such studies fail to provide adequate explanations for the behavior of the components of the aggregate price level. Equally important, an analysis of industry price behavior may yield valuable insights into aggregate price behavior -insights not available from aggregate analyses. It is within this setting that the present paper attempts to proceedto investigate price movements at a disaggregated level and to interpret the findings in the context of the current empirical literature on price behavior. More specifically, the purpose of this paper is two-fold: (1) to investigate the determinants of short-run price movements at an industry level, and (2) to ensure that these price equations are suitable for integration into the context of a larger industry submodel, including other decision variables such as inventories, production, and unfilled orders. Happily, to anticipate the results, these turn out to be complementary objectives. This occurs primarily because we hypothesize (and verify empirically) that short-run price changes are determined, in part, by considerations involving inventories. In fact, the variable that satisfies both these objectives-equilibrium inventories minus actual inventories-is the only variable that bears a consistent empirical relationship to quarterly price movements over 1956-1962, the time period of

Stability of Growth Equilibrium in a Neoclassical Vintage Model

Abstract: IN A RECENT PAPER Solow, Tobin, Weizsacker and Yaari [4] have analyzed the properties of growth equilibria in a one-sector, vintage capital model with a fixed machine-output ratio and with a labor-machine ratio that is an exogenously given, exponentially decreasing function of time. Given constant rates of labor growth and of saving, they have shown that any path of growth equilibrium, starting with an arbitrary capital composition and labor force, converges asymptotically to a unique balanced growth path (whenever such path exists), in which the vintage distribution of capital remains stationary. Previously, Phelps [2] and Uzawa [6] have established the same result for a certain class of neoclassical vintage models in which variation in the amount of labor per unit of capital along some production function is possible at all times (ex-ante as well as eX-poSt).2 This class includes all those production functions for which it never pays to scrap old machines entirely prior to their expiration through wear and tear.3 A member of this class is the CobbDouglas function.4 In this paper we are interested in extending the above result to a neoclassical vintage model in which the length of life of machines (written m) is an economic variable that is determined by equibrium conditions. A condition for balanced growth is now that m should be constant over time. We shall prove that along any growth equilibrium path, m converges asymptotically to its corresponding balanced growth value. As our proof is based to a large extent on that in [4], the argument is presented in outline, rather than complete.

An investigation of commercial banks' aggregate portfolio adjustments*

Abstract: THE DEVELOPMENTS OF the last twenty years in the theory of choice under conditions of uncertainty have provided economists with the theoretical tools to handle problems of portfolio selection by individuals. These newlyfashioned tools have been applied subsequently to financial institutions such as commercial banks.2 This paper is an addition to the increasing stock of studies based on the framework provided by the relatively recent works of Markowitz [6], Tobin [9], and Farrar [2] in the field of asset choice. More particularly, this study provides an analysis of the observed aggregate commercial banks' portfolio of assets. The first part of the paper provides the theoretical development which leads to the identification of the variables determining the bankers' aggregate portfolio. The banker's view of the various assets is conceptualized in terms of expectations about future prices of assets. Then, from these expectations about prices, we derive the expectations about future returns from each asset. The banker's views of these returns are then transformed into a view of his expectations about linear combinations of assets, i.e., alternative portfolios. We assume that the banker determines which is the "best," or optimal, portfolio from among all those available under prevailing market conditions on the basis of maximum expected utility. While the development so far enables us to identify the specific variables which explain the optimal portfolio, the link between these variables and the observed (as opposed to the optimal) portfolio is still missing. To provide this connection between the optimal and observed portfolio, we introduce a Markov process which describes the dynamic adjustments of the aggregate banks' portfolio as it approaches the optimal, or equilibrium, portfolio. We then derive the equations determining the aggregate portfolio composition at each point of time. The second part of this paper deals with the estimation and analysis of the regression equations. Using the estimated coefficients we calculate the