HOW TO MEASURE LIVING STANDARDS AND PRODUCTIVITY

I set out a general algorithm for calculating true cost‐of‐living indices when demand is not homothetic and when the number of products may be large. The non‐homothetic case is the important one empirically (Engel's Law). The algorithm can be applied in both time series and cross section. It can also be used to estimate true producer price indices and Total Factor Productivity in the presence of input‐biased economies of scale and technical change. The basic idea is to calculate a chain index of prices but with actual budget (cost) shares replaced by compensated shares, i.e. what the shares would have been if consumers (firms) faced actual prices but their utility (output) were held constant at some reference level. The compensated shares can be derived econometrically from the same data as are required for the construction of conventional index numbers. The algorithm is illustrated by applying it to estimating true PPPs for 141 countries and 100 products within household consumption, using data from the World Bank's latest International Comparison Program.     

Violation of the Law of Demand

Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. We show when the widely cited Mitjuschin and Polterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or hyperbolic absolute risk aversion) class of utility functions are fully characterized in terms of preference parameters. For a natural extension of the constant elasticity of substitution member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur.     

PETROLEUM REFINING INDUSTRY: AN ASSESSMENT OF ITS PRODUCTION STRUCTURE*

Cost structure of petroleum refining industry in Kuwait has been examined, with specific focus on factor substitution, and economies of scale and utilisation. This has been done by estimating translog cost functions, both long‐run and short‐run, using annual time‐series data covering the period from 1976 to 1998. The results indicate that the implied production structure is non‐homothetic, and the pattern of scale effect is labour and capital saving but material using. The evidence also supports presence of induced exogenous technical change, which is non‐neutral (labour and capital using, and material saving). The elasticity of substitution between capital and labour is negative, implying that the two inputs are complements. The results also indicate absence of economies and diseconomies of scale in the petroleum refining industry.     

ω‐Homothetic Preferences: Theory and Applications

This paper develops a new class of homothetic preferences which generate Marshallian demand curves for individual goods which can be concave, convex or linear in own price under the assumption that agents treat aggregate price indices as given (as in Dixit‐Stiglitz, 1977). The preferences are represented by a cost function which has two parameters: one determining the curvature of the Marshallian demand; the other determining the elasticity of demand when all prices are equal. The elasticity of demand varies with relative prices. Illustrative examples are given of Cournot duopoly and exchange rate pass‐through.     

Consumption externality, efficiency and optimal taxation in one-sector growth model

In an economy with consumption externalities, existing studies find that a competitive equilibrium is efficient in the long run and remains efficient in transitions if preferences are homothetic. This paper revisits the efficiency issue in an otherwise standard one-sector growth model where consumption externalities affect a utility via their effects on the time preference. We find that even if preferences are homothetic, the externality changes the marginal rate of substitution between now and future and leads to a disparity in the intertemporal elasticity of substitution between the centrally planned economy and a decentralized economy. As a result, a competitive equilibrium is inefficient in transition dynamics. We characterize an optimal tax/subsidy structure that enables the allocation in a decentralized economy to replicate the social optimum.     

Global restrictions on the parameters of the CDES indirect utility function

This paper extends the analytical and empirical application of the basic indirect utility function of Houthakker–Hanoch—called the CDES specification (constant differences of elasticities of substitution). The non-homothetic CDES preferences are the natural parametric extension on the global domain of the homothetic CES preferences with many commodities, and CDES can conveniently be used in specifying CGE multisector models with a demand side satisfying observable Engel curve patterns. Moreover, all Marshallian own-price elasticities are no longer restricted to exceed one, and positive and negative cross-price effects are allowed for in empirical demand analyses. Explicit calculations of the Allen elasticities of substitution are instrumental in demonstrating the economic implications of the parameters of indirect utility functions with global regularity properties and flexibility of the derived demand systems.     

Multifactor CES general equilibrium: Models and applications

Sector-specific multifactor CES elasticities of substitution and the corresponding productivity growth are jointly measured by regressing the growth of per-factor cost shares against the growth of factor prices. We use linked input-output tables for Japan and the Republic of Korea as the data source for factor price and cost shares in two temporally distant states. We then construct a multisectoral general equilibrium model using the system of estimated CES unit cost functions and evaluate the economy-wide propagation of an exogenous productivity stimulus in terms of welfare. Further, we examine the differences between models based on a priori elasticities such as Leontief and Cobb-Douglas.     

The Consumer Tax Equivalent of a Tariff with Imperfect Substitutes

In estimating the Consumer Tax Equivalent (CTE) and Producer Subsidy Equivalent (PSE) of a tariff, it is often assumed that the imported good is a perfect substitute for the relevant locally made good. However, in evaluating the economy-wide effects of a change in tariff using general equilibrium models, it is common to assume that the imported good is an imperfect substitute (so-called Arming-ton assumption)¹ This paper estimates CTE assuming imperfect substitution in order to be consistent with the assumption commonly used in general equilibrium models. It shows how estimates of the CTE and PSE are sensitive to assumptions about the substitution elasticity of demand and the price elasticity of supply for the locally made good.     

The CES‐‐Translog Production Function, Returns to Scale and AES

The translog functional form imposes no a priori restrictions on the substitution possibilities between the factor inputs, by relaxing the assumption of strong separability, and the CES–translog cost function specification allows for testing homothetic technology with Hicks‐neutral technical change. In this paper an n ‐factor CES–translog production function is presented which develops the parameters to directly assess scale effects from those due to technology in the production structure. In addition, by applying Shephard's lemma it was possible to derive the input demand functions, as well as the partial elasticities of substitution and the cross‐partial price elasticities of demand for a generalized CES–translog production structure.     

中国长期煤炭需求:影响与政策选择

本文采用协整技术研究中国煤炭需求的长期均衡关系,估计出中国煤炭需求的长期收入弹性、价格弹性、结构弹性以及运输成本弹性;预测未来长期煤炭需求并分析其对环境、煤炭供给和煤炭价格的影响;模拟解释变量不同增长率下煤炭需求的演变并给出政策选择。中国高速经济增长是煤炭需求增长的主要原因。GDP是引导煤炭需求的原因,但煤炭需求不是引导GDP增长的原因,这也说明了将GDP作为解释变量的合理性。变量模拟得出的政策选择是工业结构的调整,即便是微调,也会对煤炭需求有很大的抑制作用;煤炭出厂价格的变动对煤炭需求变动的影响不太大,但煤炭需求对运输成本相当敏感,因而煤炭的最终价格对煤炭需求影响很大。     

The role of labour demand elasticities in tax incidence analysis with heterogeneous labour

Whether labour bears full burden of household level income and consumption taxes ultimately depends on the degree of substitutability among different types of labour in production. We find more variation in incidence patterns across households with less than perfectly substitutable heterogeneous labour than with perfectly substitutable homogeneous labour in production. This finding is based on results obtained from homogeneous and heterogeneous labour general equilibrium tax models calibrated to decile level income and consumption distribution data of UK households for the year 1994. We use labour supply elasticities implied by the substitution elasticity in households' utility functions and derive labour demand elasticities from the substitution elasticity in the production function. First version received: March 1998/Final version received: April 1999     

Fiscal policy simulations – a comparison of UK models

The problem of endowing large applied general equilibrium models with numerical values for parameters is formidable. For example, a complete set of own- and cross-price elasticities of demands for the MONASH model of the Australianeconomy involves in excess of 50000 items. Invoking the minimal assumptions that demand is generated by utility maximization reduces the load to about 26000 - obviously still a number much too large for unrestrained econometric estimation. To obtain demand systems estimates for a dozen or so generic commodities at a top level of aggregation (categories like ‘food’, ‘clothing and footwear’, etc.), typically Johansen's lead has been followed, and directly additive preferences imposed upon the underlying utility function. With the move beyond one-step linearized solutions of applied general equilibrium models, the functional form of the demand system adopted becomes an issue. The most celebrated of the additive-preference demand systems, the linear expenditure system (LES), has one drawback for empirical work; namely, the constancy of marginal budget shares (MBSs) - a liability shared with the Rotterdam system. To get around this, Theil and Clements used Holbrook Working's Engel specification in conjunction with additive preferences; unfortunately both Working's formulation and Deaton and Muellbauer's AIDS have the problem that, under large changes in real incomes, budget shares can stray outside the [0, 1] interval. It was such behaviour that led Cooper and McLaren to devise systems with better regularity properties. These systems, however, are not globally compatible with any additive preference system. In this paper we specify, and estimate, at the six-commodity level, an implicitly directly additive-preference demand system which allows MBSs to vary as a function of total real expenditure and which is globally regular throughout that part of the the price-expenditure space in which the consumer is at least affluent enough to meet subsistence requirements.     

Balanced‐Budget Rules,Elasticity of Substitution,and Macroeconomic (In)Stability

This paper examines the relation between factor substitution and (local) stability of equilibria in a one‐sector real business cycle model under balanced‐budget rules. We show that under non‐unitary elasticity of factor substitution, the Schmitt‐Grohé‐Uribe indeterminacy result can be altered. Using the two‐step normalization procedure, we highlight two opposing effects of factor substitution, namely, the efficiency effect and the distribution effect, on aggregate stability. With endogenous distortionary taxes and gross substitutability between capital and labor, the existing literature overlooks the distribution effect and finds that balanced‐budget rules are likely to deliver indeterminacy. However, if capital stock is relatively more abundant, a higher elasticity of substitution generates a source of stability due to the distribution effect. Our calibration shows that the distribution effect is always the dominating force.     

The supply of non‐renewable resources

There exists no formal treatment of non‐renewable resource (NRR) supply, systematically deriving quantity as function of price. We establish instantaneous restricted (fixed reserves) and unrestricted NRR supply functions. The supply of a NRR at any date and location depends not only on the local contemporary price of the resource but also on prices at all other dates and locations. Besides the usual law of supply, which characterizes the own‐price effect, cross‐price effects have their own law. They can be decomposed into a substitution effect and a stock compensation effect. We show that the substitution effect always dominates: a price increase at some point in space and time causes NRR supply to decrease at all other points. Our new—although orthodox—setting takes into account not only NRR supply limitations but also the heterogeneity of NRR deposits, and the endogeneity of their development and opening. Our analysis extends to NRRs the partial‐equilibrium analysis of demand and supply policies. Thereby, it provides a generalization of results about policy‐induced changes on NRR markets.     

Product Market Imperfection and the Two‐sector Harris–Todaro Economy

This paper examines the ramifications of market imperfection for a dual economy in the context of the two‐sector Harris–Todaro model with the agricultural (manufacturing) sector under perfect competition (monopoly). Based on a utility function of constant elasticity of substitution variety, it demonstrates (i) existence of a unique equilibrium at which the consumer price ratio and the producer price ratio are synchronized; (ii) several fundamental properties of the model (crucial to extended research on this subject area); (iii) contrary to an earlier result obtained under an oligopolistic manufacturing sector, trade liberalization for a small economy may be immiserizing.     

Price Effects on Compound Commodities

We examine the effect of simultaneous price changes on the total demand for a group of goods, which we call a compound commodity. Specifically, we consider unit and proportional cost components (e.g., taxes, transportation costs) imposed on compound commodities. If the unit cost is positive, then the proportional cost raises the relative price of the more expensive good, and thus induces substitution towards the less expensive good within this group. Then, the substitution effect of the proportional cost for a compound commodity is non‐negative if and only if the compound commodity and the other goods are, on average, not strongly substitutable.     

A model of benefit and tax share discrimination by a monopoly bureau

This paper integrates the theory of demand for publicly provided goods in a democracy with the theory of bureaucratic supply in order to develop a model of benefit share and tax share discrimination by a monopoly bureau. The demand side of the political market is based on a utility maximizing model of voter behavior with voters' demands aggregated through a majority voting process. The supply side of the political market is based on a budget maximizing model of bureaucratic behavior. The bureau is assumed to possess monopoly power as a result of either its control over benefit shares or tax shares and, hence, implicit tax prices or its control over budget proposals placed on the agenda. Different degrees of discrimination are examined and in each case the equilibrium of the model yields a total budget for the bureau as well as distributions of benefit shares or tax shares across voters.     

Optimally eating a stochastic cake: a recursive utility approach

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion.     

Capacity Investment with Dynamic Operation and Intertemporal Budget Balance

We characterize the optimal investment and production path in a project characterized by indivisible capacity and stochastic inverse demand curve. At first best (without budget requirements), the investment is made earlier the lower the price elasticity of demand, causing the trajectory of production to be below the trajectory of capacity. At second best (when the investor is required to break even), the investment delay is upward distorted, the distortion being larger the lower the price elasticity of demand. Moreover, in the particular case of constant elasticity demand, investment is delayed but production remains at its first‐best level.     

A FURTHER EXAMINATION OF THE PRICE AND VOLATILITY IMPACT OF STOCK DIVIDENDS AT EX‐DATES*

We examine the price and volatility reaction around stock dividend ex‐dates for an Australian sample, over the period January 1992 to December 2000. We find that price reaction around stock dividend ex‐dates provides positive abnormal returns both prior, and subsequent, to the abolishment of par value of shares in July 1998. When we partitioned the sample into financial, industrial non‐financial and mining firms, the price reaction is found to be positive and significant only for industrial non‐financial companies. Volatility of daily returns for periods subsequent to ex‐dates is significantly greater than corresponding periods prior to announcement dates, while cumulative raw returns subsequent to ex‐dates are significantly lower than periods prior to announcement dates for industrial non‐financial companies. The magnitude of the price reaction is statistically significantly related to an increase in the volatility of daily returns and to a reduction in cumulative raw returns subsequent to the ex‐dates, for industrial non‐financial companies. These findings support buying pressure hypothesis suggested by Dhatt et al. (1994, 1996 ).