Development of the extended linear expenditure system from simple saving assumptions

The extended linear expenditure system (ELES) can be developed as an atemporal maximization of a Stone-Geary utility function wherein saving is treated as a good in itself. The key to this development is the a priori specification of the ‘subsistence quantity’ of saving, γ_{n + 1}, to be zero. Thus, the intertemporal maximization approach to the ELES is equivalent to specifying a Klein-Rubin saving function with γ_{n + 1} = 0 for a linear expenditure system (LES) based on permanent income rather than total expenditure. Any income concept - current, normal, or permanent, for example - is acceptable for the ELES developed from the atemporal maximization.     

Measurement of Changes in Economic Welfare in India: 1970–2001

This paper provides time series estimates of measures of economic welfare, inequality, decile class specific true cost of living index and poverty measures based on 20 rounds of National Sample Survey data for the period 1970–2001. It has estimated piece-wise Linear Expenditure System (LES) for very poor, moderately poor, non-poor low and non-poor high expenditure groups for rural as well as urban areas. Money metric utility for deciles are derived from the money metric utility function and social welfare index is constructed by aggregating metric utility of the deciles. Using social welfare index as well as real per capita consumption, the paper analyses the changes in economic welfare over the three decades. Using conventional measures, the paper analyses the changes in poverty and inequality during 1970–2001. The paper also provides estimates of the welfare effects of commodity prices.

     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Taylor rules: Consequences for wealth and income inequality

This paper compares the consequences of “active” vs. “passive” Taylor rules for wealth and income inequality. Since the distinction is operative only along transitional paths, we compare the implications for two forms of government expenditure that generate such transitions. Our results confirm that the contrasting effects obtained previously for the aggregate economy have significant distributional consequences. For an active Taylor rule, whether the government increases its expenditure on consumption, or productively, wealth inequality will increase. Expenditure on the two public goods yields divergent paths for income inequality. Government consumption expenditure raises income inequality; productive government expenditure reduces it. If the Taylor rule is passive, an increase in either form of government expenditure reduces wealth inequality initially and over time. Income inequality initially increases, but declines over time, although remaining above its previous steady-state level.     

Aggregate behavior and microdata

It is shown how one can effectively use microdata in modelling the change over time in an aggregate (e.g. mean consumption expenditure) of a large and heterogeneous population. The starting point of our aggregation analysis is a specification of explanatory variables on the micro-level. Typically, some of these explanatory variables are observable and others are unobservable. Based on certain hypotheses on the evolution over time of the joint distributions across the population of these explanatory variables we derive a decomposition of the change in the aggregate which allows a partial analysis: to isolate and to quantify the effect of a change in the observable explanatory variables. This analysis does not require an explicit treatment of the unobservable variables.     

When is a tax neutral?

A proportional income tax is said to be neutral if variations in the tax rate do not affect the optimal composition of the consumption commodities of a utility maximizing consumer. It is shown that neutrality obtains if and only if the indirect utility function of the consumer is groupwise homothetic. If the income tax rates on labor and property incomes are allowed to differ, then neutrality obtains if and only if the indirect utility function of the consumer is homothetically separable. If, in addition, it is required that the proportional income tax be neutral with respect to not only consumption commodities but also to leisure, then 'the indirect utility function must have the form: $\text{V = V(f(w)+H}{}^1\text{(p))}$, where w and p are the normalized prices of leisure and consumption respectively, and H¹(p) is homogeneous of degree one in p.     

Resurrecting the weak credibility hypothesis in models of exchange-rate-based stabilization

We analyze how weak credibility affects the volatility of consumption spending in a model of exchange-rate-based stabilization that allows for both durable and nondurable goods. The inclusion of durables greatly improves the explanatory power of the weak credibility hypothesis. The hypothesis can account for the main qualitative properties of the boom–bust cycle provided the elasticity of durables expenditure with respect to Tobin's q is greater than the intertemporal elasticity of substitution. Moreover, the quantitative effects are very large. In numerical simulations based on conservative assumptions about the expenditure share of durables (20%) and wealth effects (none), aggregate consumption increases 17–22% and the real exchange rate appreciates 24–26% when the crawl decreases from 100% to zero for 3 years. In variants of the model that incorporate supply effects, the consumption boom is equally strong but appreciation of the real exchange rate rises to 30–40%.     

Conditions for Sustainable Optimal Economic Development

This paper shows that, for dynamic optimizing economies with different types of natural resource, environmental, and human‐made capital stocks, a necessary and sufficient condition for permanently sustaining an optimal utility/consumption level is the stationarity of the current‐value Hamiltonian. For economies whose development is not exogenously and directly affected by time (i.e., time‐autonomous economies), this stationarity condition generalizes Dixit et al.’s (1980 ) “zero‐net‐aggregate‐investment” rule of sustain‐ability, which in turn generalizes Solow‐Hartwick’s sustainability rule. For non‐autonomous economies, the stationarity condition is not generally fulfilled, and the current‐value Hamiltonian under (over) estimates the true welfare level by an amount equal to the discounted value of the net “pure time effect.” For the non‐autonomous case of a time‐dependent utility discount rate, a general condition on the discount rate function (of which the hyperbolic discount rate function is a special case) upholds the results obtained for autonomous cases. The paper concludes with a discussion of policies that promote both optimality and sustainability objectives.     

The macroeconomics of unbalanced growth and the expanding public sector: Some simple tests of a model of government growth

A now classic model of public sector growth is Baumol's (1967) ‘Macroeconomics of Unbalanced Growth’. That model implies that one cause of public sector expenditure growth is a low or zero rate of productivity growth in the public sector relative to the private sector. Previous studies have tested, and partially confirmed, the Baumol hypothesis by computing productivity indices for various public sector activities. In this paper I attempt to test that model in a more direct manner. The unbalanced growth model is used to predict growth rates of per capita government expenditures, government's share of GNP and the pattern of government expenditure growth. These predictions are compared with observed growth rates of aggregate government expenditures. The model predicts the growth rate aggregate government expenditures, the growth rate of government's share of GNP, and the pattern of government expenditure growth reasonably well, and the data tend to support the Baumol model.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Sensitivity of ‘optimal’ commodity tax rates to alternative demand functional forms: An econometric case study of India

This study investigates, on a nine commodity disaggregation of Indian budget data (NSS, 28th round), the sensitivity of ‘optimal’ commodity tax rates to alternative demand systems. LES and RNLPS. ‘Optimality’ is used here in the very special sense of being conditional on observed expenditure and fixed consumer prices. The alternative sets of tax rates agree at low levels of ‘inequality aversion’ but disagree widely at ‘Rawlsian’ levels. LES is heavily rejected in favour of its one-parameter generalisation, RNLPS. The results suggest that LES price elasticities should not be used in ‘optimal’ tax calculations. The ‘optimal’ tax rates imply only a modest redistribution.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Conspicuous consumption and generation replacement in a model of perpetual youth

This paper investigates household decisions in an overlapping generations model in which individual utility depends on a weighted average of consumption of one's peers. In contrast to representative agent economies, the consumption externality generally affects savings and growth rates. The effects critically depend on the rate at which labor productivity changes with age. For a high (low) rate, the externality lowers (raises) the steady state propensity to consume out of total wealth. The optimal allocation can be decentralized by a (reverse) unfunded social security system if the rate of labor productivity decline is high (low). In contrast to discrete time OLG models, the optimal steady state capital income tax is zero, in spite of the externality.     

Decreasing absolute risk aversion and utility indices derived from cake-eating problems

This paper establishes the following characterization of decreasing absolute risk aversion (DARA) utility indices: J exhibits DARA if and only if it is the indirect function corresponding to an infinite horizon cake-eating problem for some nondecreasing and concave utility function of consumption. The characterization is applied to the analysis of resource extraction under uncertainty and to an inverse optimal problem.     

‘Double dipping’: the combined effects of social security and civil service pensions on employee retirement

How do macro variables such as aggregate consumption, aggregate money demand, prices, and interest rates vary in response to government attempts to redistribute income across agents through selective tax-transfer policies? This question is investigated for an overlapping generations model consisting of heterogeneously endowed three-period lived agents. In the presumably most favorable case for invariance (identical log-linear utility functions), it is shown that positive interest rate macro equilibria are invariant with respect to redistributions in social security benefits if and only if all agents initially exhibit qualitatively identical liquidity preference behavior, i.e. positive money holding only in youth, only in middle-age, or never.     

On the interaction between public and private capital in economic growth

This paper introduces two forms of interaction between private and public capital in an endogenous growth model in which productive government expenditure takes the form of a stock-variable and public capital is used in part as an input in the production of final output and in part to increase its own supply. While the first form of interaction involves the stocks of the two capital-goods and takes place within the final output sector through the specification of the aggregate production function (Cobb?CDouglas vs. CES), the second one concerns the rates of investment in the two kinds of capital. The share of productive public expenditure devoted to output production can be either exogenous or endogenous. Our results suggest that when this share is exogenous, along the balanced growth path the optimal growth rate of the economy is a positive function of the degree of complementarity between the two forms of investment. When the share of productive public expenditure devoted to output production is endogenous, the public capital share in GDP becomes, along with the model??s preference parameters, an important determinant of the economy??s long run growth. We also find that the optimal growth rate is an increasing function of the elasticity of substitution between public and private capital inputs in goods production, and is independent of the complementarity/substitutability between the two forms of investment.     

Hoglex Demand Systems and Welfare Policy in Major Asean Developing Countries: A Bayesian Analysis Using Expenditure Unit Records

The HOGLEX demand system (Tran Van Hoa (1983, 1985)) is integrable and flexible in the sense that it is based on utility maximization and encompasses most other well-known demand systems (e.g., LINEX, AIDS) in the literature on consumer behaviour (Laitinen et al. (1983)). HOGLEX studies to date have been based on conventional OLS or MLE methods and panel aggregate income and price data, and restricted to investigating consumption patterns. The paper elaborates on three important subsets of the HOGLEX demand system and, using household expenditure unit records from two major ASEAN developing countries (i.e., Thailand and the Philippines), estimates by the Bayesian method these subsets for 20 socio-demographic cohorts, and discusses their substantial implications in social security and welfare policy analysis. We also estimate the models in the more practical case of measurement errors in total expenditure and compare the results with those without measurement errors.

     

A model with endogenously determined cycles, discounting and growth

Summary. This article reexamines the role of consumption in growth and emphasises the external effects of aggregate consumption, viewed as consumption standards, as an additional impediment in the growth process. These external effects raise the productivity of the individuals and are positively related to their valuation of the future. Conditions are established under which this results in a marginal value of wealth that is an increasing function of consumption. This brings new types of multiple steady states, local indeterminacies and cyclical motions. Imposing extra homogeneity restrictions, balanced growth solutions with endogenous impatience emerge. The possibility of multiple convergent paths is univocally related to endogenous discount effects. A comparison with a benchmark planning economy indicates an excessive value for the rate of time preference and emphasises its insufficient adaptation to future utility in a stationary setting. Discrepancies along the transition path that rest on endogenous impatience versus fixed discount appear in a non-stationary environment when the competitive balanced growth solution is indeterminate. Received: May 5, 1996; revised version: May 19, 1997     

International comparisons of expenditure patterns

The linear expenditure system (LES) of Stone (1954) is fitted to an eight-commodity classification of personal consumption expenditures in the national accounts data of 19 countries widely dispersed in the development spectrum. Cross-country comparison of the results reveals some discernible patterns in the variations of price and expenditure elasticities as a function of GNP per head. In particular, Food's own-price and expenditure elasticities are estimated to decline in absolute value as real GNP per head increases. Overall, own-price elasticities and cross-price elasticities with respect to food appear to account for about 80% of total price responsiveness in the fitted system.