Slutsky Matrix Research Articles

English title is not available [SLUTSKY DENKLEMi VE ESNEKLIK TOPLULASTIRMA (AGREGASYON) KOSULLARININ TURKIYE EKONOMISI OZELiNDE IRDELENMESI

In this study it is created a two goods model (imports and domestically produced goods) using the datafrom the Turkish eeonomy for the 1975-2003 period; and it is estimated a total -10 demand elasticities- namely, the price and income elasticities for this goods (6); the elasticities of substitution (4). It is first estimated the priee and ineome elastieities of imported goods and then using the Slutsky and elasticity aggregation equations, it is calculated the other 8 coefficient of elasticities. The quantitative analysis yielded results that verified our theoretical expectations.

Estimating Managers' Utility-Maximizing Demand for Agency Goods

An empirical model of managers' demand for agency goods is derived and estimated using the Almost Ideal Demand System of Deaton and Muellbauer (AER 1980). As in Jensen and Meckling (JFE 1976), we derive managers' demand for agency goods by maximizing a managerial utility function where managers allocate the potential value of their firm's assets to the consumption of agency goods and the production of market value (which, given their ownership stake, determines their wealth). The utility function is defined over wealth and the value of agency goods and is conditioned on managers' holdings of stock options, the proportion of the firm owned by outside block-holders, and the firm's capital structure. We obtain the maximum potential value of firms' assets by fitting a stochastic frontier (upper envelope) to the market value of assets given the investment in those assets. The difference between the potential market value of a firm's investment in its assets and their actual market value (corrected for statistical noise) is used to gauge managers' consumption of agency goods. The demand function for agency goods (lost market value) is estimated using U. S. data on publicly traded bank-holding companies. Using the adding-up condition, the demand for asset value is derived from it and restated as the utility-maximizing Q ratio. We apply Slutsky's equation to decompose the effect of a variation in the proportion of the firm owned by managers into a substitution and a wealth effect, which parallel the alignment-of-interest effect and the entrenchment effect. By estimating financial performance in a choice-theoretic framework, the alignment and entrenchment effects of ownership can be identified econometrically. We find evidence that the strength of both effects increases with insider ownership, but ownership by outside block-holders mitigates the entrenchment effect.

Generalized benefit functions and measurement of utility

Luenberger [8] introduced the so-called benefit function that converts preferences into a numerical function that has some cardinal meaning. This measure has a number of remarkable properties and is a powerful tool in analyzing welfare issues ([10], [12], [13], [14]). This paper studies the conditions for a general function to make it a relevant welfare measure. Therefore, we introduce a large class of measures, called generalized benefit functions. The generalized benefit function is derived from the minimization of a convex function over the complement of a convex set. We show this class encompases as a special case the benefit function and is suitable to provide an alternative characterization of preferences. We also make a connection to the expenditure function through Fenchel duality theory and derive a duality result from Lemaire [7] for reverse convex optimization. Finally, we study the relationship between our class of functions and Hicksian compensated demand and we establish a link to the Slutsky matrix.

Duality and consumption decisions under income and price risk

This paper uses duality to provide an analysis of compensated and uncompensated decisions under income and/or price risk. We focus on a two-good model, in which the individual maximizes expected utility subject to a stochastic budget constraint. A Slutsky equation is derived that decomposes the derivative of the optimal decision function with respect to any parameter in the model into an income effect and a substitution effect. The total effect of an increase in risk is controlled by the generalized preference intensity, while the compensated effect of an increase in risk is controlled by the generalized risk premium developed in the literature on aversion to one risk in the presence of another.

Interest-sensitive wealth and the life-cycle hypothesis: implications for fiscal policy

Summers (1981) shows interest-sensitive labor wealth has a substantial effect on the interest elasticity of consumption in a life-cycle model. Sweeney (1988) shows interest-sensitive non-labor wealth also affects consumption choice, if altruistic bequests do not dominate consumer choice. Yet, most life-cycle models exclude interest-sensitive non-labor wealth. This paper embeds interest-sensitive non-labor wealth in a life-cycle model, derives a Slutsky equation for consumption, and simulates the interest elasticity of consumption. The simulations indicate that non-labor wealth can have a sizable impact on consumption choice in life-cycle models. This suggests that the common practice of excluding interest-sensitive non-labor wealth from life-cycle models could produce misleading macroeconomic policy conclusions.

Comparative Statics of Money-goods Specifications of the Utility Function

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem.

SUBSTITUTION AND REVENUE EFFECTS WITH ENDOGENOUS IMPATIENCE

Building on a nonlinear additively separable representation for the generator of preferences, this article provides an extensive characterization of intertemporal consumption—leisure arbitrages with an endogenous measure of impatience. A joint characterization of the comparative dynamics of consumption and leisure is undertaken. An analytical approach first puts in evidence a classical Slutsky decomposition between revenue and substitution effects after various perturbations. Those conclusions are at a second stage illustrated by a three-dimensional geometric argument.

The Economic Record versus AER: Twenty Six Years Ahead on the Money-Goods Model

We prove that the symmetric and negative semidefinite modified Slutsky matrix derived by Samuelson and Sato (1984) for the money-goods model of the consumer, is identical to that derived by Pearce (1958) a quarter century before and restated sixteen years later by Berglas and Razin (1974). We also prove that these conditions are only sufficient for the problem at hand and are encompassed by a more general, modified Slutsky matrix that is necessary and sufficient as derived by Paris and Caputo (2001). These results have crucial relevance for testing the implications of consumer behavior.

A Non-homothetic Globally Concave Flexible Cost Function and its Application to Panel Data

A new non-homothetic globally concave flexible cost function is introduced and applied to a panel of firms in the Japanese paper and pulp industry. This cost function is a mixture of the generalized McFadden form and the generalized Ozaki form due to Nakamura (1990). A generalized index of technical change is used in place of the standard quadratic form of time-trend. The estimated cost function satisfied global concavity, and the symmetry condition of the Slutsky matrix was not rejected. Homotheticity was strongly rejected. JEL Classification Numbers: C33, D24.

Chromosomes and the Slutsky Equation: Lessons from 21st Century Genetics for 20th Century Economics

Reductionist scientific methodology has been at the forefront of economics research for much of the past 50 years. This short essay argues that recent discoveries in genetic engineering show that the study of complex phenomena might not be best served by such an approach, but rather by one that takes into consideration more evolutionary approaches. This provides a tremendous opportunity for the field of bioeconomics to establish itself as a major school of though, going into the future.

Comparative Statics of Money-Goods Specifications of the Utility Function

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem.

Imposing Local Curvature Conditions in Flexible Demand Systems

By reparameterizing the basic translog and the log translog demand systems and exploiting the fact that the Slutsky matrix must be negative semidefinite but cannot be negative definite, it is shown that a recently proposed simple procedure to maintain locally the curvature property of consumer theory can be applied to these popular translog models as well. The proposed procedure can also be applied to other demand-system specifications such as, for example, the nonseparable generalized linear expenditure system.

More on Slutsky's Equation as Pareto's Solution

More on Slutsky's Equation as Pareto's Solution

Efficient Intra-Household Allocations: A General Characterization and Empirical Tests

The neoclassical theory of demand applies to individuals, yet in empirical work it is usually taken as valid for households with many members. This paper explores what the theory of individuals implies for households that have more than one member. We make minimal assumptions about how the individual members of the household resolve conflicts. All we assume is that however decisions are made, outcomes are efficient. We refer to this as the collective setting. We show that in the collective setting household demands must satisfy a symmetry and rank condition on the Slutsky matrix. We also present some further results on the effects on demands of variables that do not modify preferences but that do affect how decisions are made. We apply our theory to a series of surveys of household expenditures from Canada. The tests of the usual symmetry conditions are rejected for two-person households but not for one-person households. We also show that income pooling is rejected for two-person households. We then test for our collective setting conditions on the couples data. None of the collective setting restrictions are rejected. We conclude that the collective setting is a plausible and tractable next step to take in the analysis of household behavior.

How quasi-rational are you?: A behavioral interpretation of a two form which measures non-integrability of a system of demand equations

The symmetrized Slutsky matrix is used to provide an income measure of non-integrability. This matrix, used as a two-form by Arnold to measure non-integrability of an exterior differential system, measures how far quasi-rational (systematic but not utility maximizing) demand is from being rational.

A difficulty in the search for Giffen behavior

Gilley and Karels [1991] argue that economists should search for Giffen goods in cases where two or three goods are chosen subject to two constraints. This paper reconsiders their three-good model. With a third good added, traditional comparative statics analysis, which is absent from the simpler model, becomes crucial. The Slutsky equation with a negative own substitution effect reappears, suggesting that one good which is automatically Giffen in the two-good, two-constraint model may have a downward-sloping demand curve when the third good is added to the model.

Approximating compensated income from ordinary demand functions

This paper proposes a REversible Second- ORder Taylor (RESORT) approximation to compensated income from ordinary demand functions. RESORT yields the Malmquist-Vartia (M-V) algorithm as a first-order case. Using the Slutsky equation, RESORT obtains the substitution matrix and checks it for symmetry and negative semi-definiteness to validate compensated income. This validation procedure is an improvement over M-V.

A food demand system based on demand for characteristics: If there is ‘curvature’ in the Slutsky matrix, what do the curves look like and why?

A food demand system is proposed based on demand for energy, variety, and tastes of foods. By specifying utility as an explicit function of these characteristics, the entire matrix of demand elasticities can be derived for n foods and one non-food from prior specification of just four elasticities, while avoiding any assumption of separability between foods. This framework can explain why poorest groups often are most price-responsive, but also can account for highest price-responsiveness by middle income groups. The system is applied to published food consumption data for urban and rural populations in Pakistan. Elasticities are compared with those obtained in a published Pakistan study applying an almost ideal demand system (AIDS).

The Potential for High-Value Agricultural Products Under the North American Free Trade Agreement: The Case of Beef in Mexico and Canada: Comment

In his recent article, Onianwa used the absolute price version of the Rotterdam demand model to estimate Mexican and Canadian import demands for U.S. beef products. The specification of the Rotterdam model allows straightforward testing of the basic theoretical properties of demand. Based on theory, a system of demand equations should obey adding up, homogeneity, symmetry, and negativity (Theil 1971, 1975; Deaton and Muellbauer). Adding up is guaranteed or automatically satisfied in the Rotterdam model and other similar demand models like the almost ideal demand system (AIDS). Hence, adding up cannot be tested. Negativity can be checked by calculating the eigenvalues of the Rotterdam Slutsky matrix (all eigenvalues should be nonpositive). The remaining two properties, homogeneity and symmetry, can be straightforwardly tested by using the likelihood ratio test, as in the present paper, or the Wald or Lagrange multiplier tests; homogeneity can also be tested separately for each demand equation using the F-test.

A discrete characterization of Slutsky symmetry

A smooth demand function is generated by utility maximization if and only if its Slutsky matrix is symmetric and negative semidefinite. Slutsky symmetry is equivalent to absence of smooth revealed preference cycles, cf. Hurwicz and Richter (Econometrica 1979). To observe such a cycle would require a continuum of data. We characterize Slutsky symmetry by means of discrete “antisymmetric” revealed preference cycles consisting of either three or four observations.