Dale Jorgenson

Samuel W. Morris University Professor

WELFARE: Volume Two -- Preface

This volume is the second of two volumes containing my empirical studies of consumer behavior and presents a new conceptual framework for normative economics. The first of the two volumes, Modeling Consumer Behavior , focuses on econometric modeling at the aggregate level. My initial goal was to incorporate the implications of utility maximization into a model for aggregate time series data, employing the concept of a representative consumer. Subsequently, my objective expanded to include the implications of aggregation over utility-maximizing consumers. This required pooling aggregate time series with cross-section data for individual households.

The new approach to normative economics presented in this volume exploits the econometric model of aggregate consumer behavior that resulted from my earlier investigations. The model takes the form of a system of aggregate demand functions obtained by aggregating over individual demand functions. Measures of welfare are then recovered from the individual demand functions and combined into a single indicator of social welfare, reflecting concepts of horizontal and vertical equity. This approach was summarized in my presidential address to the Econometric Society, published in 1990 and reprinted as chapter 1 below.

Problems of normative economics have a number of common features. The initial step in the solution of each problem is to establish and implement the relevant measure of individual welfare. This is a natural consequence of formulating a model of individual consumer behavior on the basis of utility maximization. However, the theory of consumer behavior that has been the standard since the seminal work of John Hicks and Roy Allen (1934) is based on an ordinal concept of individual welfare that is not comparable among individuals.

Economic policies are commonly compared by means of index numbers representing consumer's surplus. Given the limitations of the traditional index number approach discussed below, attention has shifted toward lineal descendants of Jules Dupuit's (1844) concept of consumer's surplus--the compensating and equivalent variations introduced almost a century later by Hicks (1942). The issue that remains is to relate these changes in individual welfare to changes in social welfare. This is essential if the changes are to be decomposed into changes in economic efficiency and distributional equity.

Since the pioneering work of Anthony Atkinson (1970) and Serge Kolm (1969), the measurement of social welfare has been based on explicit social welfare functions. However, the social welfare functions introduced by Atkinson and Kolm are defined on the distribution of income rather than the distribution of individual welfare. John Muellbauer (1974b) and Kevin Roberts (1980c) have shown that measures of social welfare based on income coincide with measures based on individual welfare if and only if preferences are identical and homothetic for all consumers.

To overcome objections to social welfare functions defined on income, Muellbauer (1974b) has defined social welfare functions on the distribution of Hicks's equivalent variation. Roberts (1980c) has characterized the conditions under which these measures of social welfare coincide with measures based on the distribution of individual welfare. In the absence of restrictions on social welfare functions, individuals must have identical and homothetic preferences. With no restrictions on preferences, the social welfare function must be dictatorial in the sense of Kenneth Arrow (1963).

Dictatorial social welfare functions are obviously unsatisfactory as a conceptual basis for normative economics. The objection to the assumption of identical and homothetic preferences is empirical rather than conceptual. Econometric models of consumer behavior, like the one presented in chapter 1, exhibit income elasticities of demand that are different from unity, implying that preferences are not homothetic. These models also reveal differences in preferences among households with different characteristics, so that the assumption of identical preferences is also empirically untenable.

At this point the literature on normative economics bifurcates. The first branch, at one time denominated the New Welfare Economics, follows Hicks (1940) in applying the "compensation principle." Under this principle any change in policy in which the winners can compensate the losers improves social welfare. Paul Samuelson (1950) demonstrated that this principle gives rise to inconsistent orderings. John Chipman and James Moore (1973 ,198Oa ) showed that the compensation principle provides a valid indicator of social welfare only if measures of individual welfare are identical and homothetic.

The second branch of normative economics reverts to a much earlier tradition, invoking the Pareto principle. Under this principle a change in policy improves social welfare only if it makes at least one individual better off while leaving other individuals at least as well off. The concept of Pareto optimality plays a central role in the theory of general competitive equilibrium of Arrow and Gerard Debreu (1954) through the two Fundamental Theorems of Welfare Economics, relating Pareto optimality to competitive equilibrium.

By itself the useful idea of Pareto optimality is much too weak to provide a satisfactory foundation for normative economics. On the other hand, the compensation principle depends for its validity on empirically untenable assumptions about individual preferences. Fortunately, the concept of a social welfare function, originated by Abram Bergson (1937) and discussed by Samuelson (1947), provides a means of overcoming these difficulties. As Amartya Sen (1977) has argued persuasively, this requires dispensing with ordinal measures of individual welfare that are not comparable among individuals.

The model of a representative consumer illustrates the essential ideas. The most transparent version of this model is based on identical and homothetic preferences for all individuals. Aggregate demand functions then assume the same form as individual demand functions. Welfare for each individual is proportional to total expenditure and inversely proportional to an index of the cost of living. These measures can be combined into an indicator of social welfare based on Bergson's concept of a social welfare function.

Construction of a model of consumer behavior by aggregation over utility-maximizing consumers is possible without requiring the untenable restrictions of identical and homothetic preferences. However, such a model retains the most important feature of the model of a representative consumer-measures of individual welfare that are cardinal and interpersonally comparable. Obviously, this formulation of the theory of consumer behavior is far more restrictive than that of Hicks and Allen (1934).

While a cardinal measure of individual welfare that is fully comparable among individuals is implicit in the index number approach to welfare economics, differences among individuals are ignored and preferences are assumed to be homothetic. By overcoming these restrictions the econometric approach to normative economics presented in chapter 1 opens up a richer and more satisfactory methodology for comparison of alternative economic policies. This methodology exploits the measurability and comparability of welfare measures for different individuals to construct an indicator of social welfare.

Replacing the ordinal concept of individual welfare that is not comparable among individuals will require a great deal of relearning for generations of economists schooled on Hicks and Allen (1934) and Arrow and Debreu (1954). However, this concept has effectively neutered many of these same economists in debates about economic policy. Only modest consolation is available from the influential teaching of Lionel Robbins (1938) that an economist qua economist has little to contribute to these debates -- beyond announcing those rare instances when the principle of Pareto optimality can be invoked.

For practitioners of normative economics the application of an econometric model to the measurement of social welfare is a highly innovative but also unfamiliar and even disturbing idea. Multi-million dollar budgets are involved in statistical reporting of price index numbers. This well-established practice does not require explicit modeling of consumer behavior. The index number approach to the cost of living is evaluated in chapter 2 below and, perhaps surprisingly, found to be conceptually sound and empirically robust.

However, the successful implementation of a cost-of-living index is far from trivial. The U.S. Bureau of Labor Statistics compiles a Consumer Price Index (CPI) based on the index number approach. During the period 1964-1989 the CPI incorporated an upward bias of more than ten percent, due to an inconsistent treatment of the cost of owner-occupied housing before and after 1983. More recently, the CPI has been subject to a persistent upward bias of 1.5 percent per year. This experience shows that implementation of price index numbers is highly problematical.

Similarly, the standard of living appears at first glance to be one of the most straightforward ideas in the conceptual toolkit of the normative economist. The value of transactions is divided by a cost-of-living index to obtain an index of the standard of living. The first issue is the scope of the transactions to be included; this issue is implicit in the definition of the cost of living. The second issue is how to allow for changes in distributional equity. A satisfactory resolution of this issue requires combining measures of individual welfare into an overall indicator of social welfare.

The U.S. Bureau of the Census constructs a measure of the standard of living based on median real family income. According to this mea-sure, the U.S. standard of living has been stagnant for the past two decades. The fundamental difficulty with the Census approach is that the standard of living is defined in terms of consumption rather than income. However, the standard of living measure presented in chapter 1 grows more than forty percent faster than a conventional measure based on real consumption per capita. Important biases in this conventional measure can be traced to biases in the CPI, the definition of the population, and the omission of equity considerations.

Given empirically satisfactory measures of individual and social welfare, it is very straightforward to formulate a concept of the standard of living that reflects distributional equity as well as economic efficiency The measure of equity implied by this formulation is a natural starting point for a measure of inequality that reflects society's willingness to pay for the redistribution of individual welfare. A similar measure of poverty reflects society's willingness to pay for redistributions that bring all individuals to the minimum level of well-being represented by a poverty line.

Inequality is usually measured by considering dispersion in the distribution of "income" for cross sections of individual households, but inequality, like the standard of living, is defined in terms of consumption rather than income. Once again, a critical issue is the scope of transactions pertinent to individual welfare. More sophisticated approaches to inequality take into account differences in the cost of living, especially in comparisons at different points of time. Only rarely do differences in the composition of individual households come into play, but these differences are obviously germane to distributional equity, the central issue in measuring inequality.

The Bureau of the Census publishes a measure of inequality based on a Gini coefficient for family income. This measure shows a widely reported U-turn with decreases in inequality until 1973, followed by a rise in inequality. By contrast the measure of equity presented in chapter 1 shows a steady rise throughout the period 1947-1985. This is due to differences between the distributions of income and consumption and incorporation of an appropriate adjustment for changes in the composition of families.

Poverty measurement traditionally focuses on the head-count ratio of individuals and families below a stipulated poverty line. This initially appears as a problem in the enumeration of the relevant populations. However, comparison of head-count ratios for different points of time or different sub-groups of the population inevitably requires more careful scrutiny of the poverty line itself. Differences in the cost of living and demographic characteristics of the relevant populations immediately come to the fore, just as in the measurement of inequality.

Head-count measures of poverty published by the Bureau of the Census show the same U-turn for poverty as for inequality. These measures are based on real income per household equivalent member. By contrast consumption-based measures of inequality and poverty presented in chapter 7 show that inequality has declined over the period 1947-1985 and poverty has been a declining proportion of inequality. Important biases in the Census measure can be attributed to the use of income rather than consumption, equivalence scales for different family members based on food consumption rather than household budgets for all items, and biases in the CPI.

In short, the econometric approach to normative economics unifies the treatment of inequality, poverty, and the cost and standard of living. However, this approach brings to light some very significant flaws in statistical programs that cover these important areas. The stagnation of the U.S. standard of living and the U-turns in inequality and poverty are revealed as statistical artifacts. The most important deficiency in the Census programs that generate these statistics is the use of income rather than consumption. Serious deficiencies also arise from biases in the CPI and the use of household equivalence scales.

In the studies presented in this volume my objective is to provide a detailed alternative to the empirically untenable index number approach. Dispensing with index numbers will undoubtedly remain an unsettling prospect for many practitioners. However, the reader steeped in traditional methods will find much that is familiar, despite the radical restructuring implied by the econometric approach. For example, I have preserved the logical structure of the index number approach by employing cardinal and interpersonally comparable measures of individual welfare.

The basic concepts of normative economics are introduced in section 1.2 of chapter 1. The concept of individual welfare is derived from the theory of the utility-maximizing household. Individual welfare is transformed into a money metric by defining an individual expenditure function as the minimum expenditure required to attain a given level of individual welfare. All of this is standard apparatus in the theory of consumer behavior, but it is important to note that the individual units are households, which are social entities, rather than biological individuals.

Only ordinal measures of welfare that are not comparable among households are required for applications of the Pareto principle. However, individual welfare depends on the characteristics of households as well as prices and total expenditure. The conditions required for aggregation imply the existence of measures of individual welfare that are cardinal and fully comparable among individuals. In section 1.4 of chapter 1 I present these measures and a class of social welfare functions defined on them.

The first step in determining social welfare is to evaluate individual welfare functions for all households. The second step is to evaluate the social welfare function. Social welfare is transformed into a money metric by defining a social expenditure function in terms of the minimum aggregate expenditure required to attain a given level of welfare, as in section 1.4 of chapter 1. While the social expenditure function is a much less familiar concept than the individual expenditure function, the application of these concepts is precisely analogous.

I decompose social welfare into equity and efficiency components in section 1.2 of chapter 1. Efficiency is the maximum level of social welfare attainable by redistributing aggregate expenditure among individual households. Welfare losses from an inequitable distribution are eliminated by this maximization. The resulting level of welfare can be expressed as a function of prices and aggregate expenditure. Equity reflects the gain in welfare from moving toward a more egalitarian distribution.

To illustrate the basic concepts of the econometric approach to normative economics, I present a model ,of aggregate consumer behavior in section 1.3. I then recover measures of individual welfare from demand functions and incorporate this information into a social welfare function. The class of social welfare functions I consider combines the average level of welfare with a measure of dispersion. Utilitarian social welfare functions are a limiting case where the dispersion drops out.

I define measures of the standard of living and its cost in chapter 1 and implement these measures for the United States for the period, 1947-1985. My 1983 paper with Daniel Slesnick , reprinted in chapter 2, discusses individual and social cost of living indexes in much greater detail. Slesnick and I present a third concept of the cost of living, defined for sub-groups of the population. For this purpose we introduce group welfare and expenditure functions analogous to the social welfare and expenditure functions of chapter 1. Finally, we present a nonparametric approach to the cost of living based on the price index formula introduced by Leo Tomqvist (1936).

The most striking empirical finding in chapter 2 in that cost-of-living indexes for typical households, indexes for sub-groups of the population, and the social cost-of-living index give nearly identical results for the twenty year period 1958-1978. In short, the cost-of-living index is unaffected by substantial differences in the definition of the group under consideration. In addition, the nonparametric cost-of-living index is very similar, so that the index number approach pro- duces the same results.

Slesnick (1991a) has compared alternative social cost-of-living indexes for the U.S. for the substantially longer period 1947-1988. He shows that those presented in chapters 1 and 2 and others discussed in the literature give similar results. He also presents two different nonparametric indexes-the Laspeyres index used by the U.S. Bureau of Labor Statistics in constructing the Consumer Price Index (CPI) and the Tomqvist index of chapter 2. Again, the index number and econometric approaches produce essentially the same measures of the cost of living.

Erwin Diewert's (1981) theory of exact index numbers suggests a rationale for the empirical results of chapter 2 and Slesnick (1991a). Diewert shows that the Tomqvist index formula is exact for preferences that take the translog parametric form employed in the econometric models of chapters 1 and 2. If the preferences of an individual consumer take this form, the corresponding cost-of-living index can be obtained by applying the Tomqvist formula; econometric modeling is not required.

The social cost-of-living index number of chapter 1 is based on a model of a representative consumer. This model corresponds to the concept of a maximizing society introduced by Samuelson (1956) and discussed by Robert Pollak (1981). The model also underlies the group cost-of-living index in chapter 2. I conclude that the cost-of-living index for an individual consumer provides the conceptual basis for cost-of-living measurement at all levels. The index number approach is conceptually sound as well as empirically robust.

However, empirical implementation of the index number approach to the cost of living has proven to be highly problematical. Slesnick (1991b) has estimated that the CPI incorporated an upward bias of about ten percent during the period 1964-1989, due to differences in the treatment of the cost of owner-occupied residential housing before and after 1983. More recently, the Advisory Commission to Study the Consumer Price Index (1995) has carefully evaluated the biases in the CPI, revealing a persistent bias of 1.5 percent per year.

The standard of living index presented in chapter 1 is a money measure of actual social welfare. This index can be represented as a product of measures of economic efficiency and distributional equity. Economic efficiency is an indicator of potential social welfare, the maximum that can be attained through redistributions. This can be represented as the ratio of aggregate expenditure to the cost of living and is independent of society's aversion to inequality. Finally, equity is defined as the ratio of money measures of actual and potential social welfare.

Chapter 8, reprinted from my 1989 paper with Slesnick , discusses the social standard of living in more detail. The standard of living measure grows more than forty percent faster than real expenditure per capita. This conventional measure of the standard of living is defined as the ratio of aggregate expenditure per capita to the CPI. Important biases can be traced to the CPI and the head-count definition of the population. In addition, per capita real expenditure omits equity considerations altogether, giving rise to a significant bias.

Slesnick (1991a) has compared alternative social standard of living indexes for the U.S. for the period 1947-1988. By contrast with the cost of living, indexes of the standard of living differ substantially, reflecting different measures of equity. Slesnick (1991b) has compared indexes based on income, like that of the Census, with the consumption- based measures presented in chapters 1 and 8. Consumption-based measures do not exhibit the stagnation of the past two decades reported by the Census.

Chapter 3, reprinted from my 1984 paper with Slesnick , discusses measures of equity and efficiency in detail. In section 3.8 we define a measure of relative inequality as one minus the measure of equity presented in chapter 1. Relative inequality, defined in this way, lies between zero and one and is equal to zero for perfect equality. The money measures of inequality and efficiency that underly this definition are expressed in terms of the social expenditure function introduced in chapter 1. The money measure of inequality expresses societies willingness to pay for perfect equality.

Table 3.9 of chapter 3 contains the important empirical finding that inequality decreases throughout the period 1958-1978. Table 1.1 of chapter 1 gives a parallel result, showing that equity has risen for the longer period 1947-1985. However, growth in equity occurred only during 1958-1978 and 1983-1985.

Slesnick (1994) has extended these results to the period 1947-1991, showing little change in inequality since the early 1970s. The widely reported U-turn in inequality, reported by the Census, is not reflected in any of these measures of inequality. Slesnick (1994) has compared consumption-based measures of inequality with measures based on income, like that of the Census. Important differences between the distributions of income and consumption account for most of the discrepancies. However, changes in the composition of families play a significant role in the measures of inequality presented in chapters 1 and 3. The Census adjusts family income for these changes in measuring poverty, but not in measuring inequality. Biases in the CPI, which contribute to biases in the Census measure of the standard of living, are unimportant for inequality.

The decomposition of a social welfare function presented in chapter 3 is a very significant innovation. The initial step is to define group welfare functions, Like those presented in chapter 2, for a set of mutually exclusive and exhaustive groups, for example, age groups. A between group welfare function is then defined on the group welfare functions in the same way a social welfare function is defined on individual welfare functions in chapter 1. Using these concepts and the corresponding expenditure functions we show that relative inequality can be decomposed into the sum of between and within group components.

Focusing on groups defined in terms of age of the head of household, we first consider relative inequality for each group. These measures of inequality have declined over the period 1958-1978, but much of the decline is concentrated in the early part of the period. Overall, inequality within groups falls steadily from 1958 to 1970 and then remains almost unchanged through the remainder of the period. Inequality between groups falls after 1958 and then rises to a peak in 1969, falling gradually through 1978. The great predominance of inequality for U.S. is within rather than between age groups.

Slesnick (1994) has considerably extended the decomposition of inequality between and within groups. Inequality between age groups is a relatively small proportion of overall inequality and changes relatively little over the period 1947-1991. The decline in overall inequality through the 1970s is largely within age groups. Inequality between groups classified by size of household is about half of total inequality, but there is little change during the period. A fall in inequality within sire groups accounts for the decline in overall inequality.

Inequality between regions falls sharply over the period 1947-1980, &reflecting the rise in the standard of living of the South. However, most of the fall in overall inequality can be attributed to a reduction in inequality within regions. Inequality between farm and nonfarm groups of the population is a very small part of overall inequality and nearly vanishes over the period 1947-1991. Inequality between racial groups is a very modest proportion of total inequality and has not changed over this period. Inequality by gender of the household head is also a very small part of total inequality and has not changed substantially.

The concept of equity presented in chapter 1 rests on society's willingness to pay to eliminate inequality. Chapter 7, reprinted from my 1989 paper with Slesnick , introduces a poverty threshold specified in terms of individual welfare. Holding aggregate expenditure constant, the optimal policy for alleviation of poverty is to transfer expenditure from the most affluent households to households below the poverty threshold. The gain in social welfare from this redistributional policy is a measure of poverty analogous to the measure of inequality presented in chapter 3.

Inequality is measured by the gain in social welfare that results from redistributions of aggregate expenditure to eliminate inequality. This measure of inequality can be represented as the sum of two components. The first is associated with the elimination of poverty, while the second corresponds to the inequality that remains after poverty has been eliminated. Similarly, we decompose relative inequality between relative measures of poverty and the remaining inequality. Finally, we consider the transfers required to eliminate poverty and the remaining inequality.

The most important empirical result of chapter 7 is that poverty has decreased steadily over the period 1947-1985. By the end of the period a transfer of $4.742 billions in constant dollars of 1972, had it been feasible, would have brought about the elimination of poverty Inequality has declined over the period and poverty has been a declining proportion of inequality. While almost three-quarters of inequality can be attributed to individuals below the poverty line in 1947, less than six percent can be so attributed in 1985.

The advantage of approaching the elimination of poverty in terms of redistributional policy is that poverty and inequality can be viewed from the same perspective. However, measures of poverty are more commonly based on head-count ratios, like those regularly compiled by the Census. Chapter 6 shows that thirty-four percent of households and forty-one percent of individuals fell below the poverty line in 1947, but only slightly more than three percent of households and five percent of individuals fell below the line in 1985.

Slesnick (1993) has compared head-count ratios like those presented in chapter 7 with ratios compiled by the Census for the period 1947-1989. The Census measures fall to a minimum in 1973 and rise afterward, paralleling the U-turn in inequality already discussed. Slesnick traces this to the use of income rather than consumption in measuring poverty, the construction of equivalence scales from food budgets rather than household budgets for all items, and the use of the CPI, which is subject to very substantial biases during the 1970s and 1980s.

In chapter 7 Slesnick and I exploit the decomposition of social welfare into within and between group components. Poverty within groups can be defined in terms of group welfare gains due to redistribution within the group so as to eliminate poverty. Poverty between groups can then be defined in terms of additional gains in social welfare that result from redistribution between groups. Poverty differs substantially among age groups. Gains from allowing redistribution between groups to eliminate inequality are modest, while these gains are negligible for poverty elimination.

One of the common features of the problems of normative economics presented in this volume is adjusting for changes in the composition of families. Chapter 5, reprinted from my 1987 paper with Slesnick , discusses the household equivalence scales used for this purpose in chapters 1 ,7 , and 8. As a starting point, we take the econometric model of aggregate consumer behavior presented in chapter 1. The individual demand functions that underly this model incorporate the demographic characteristics of individual households.

To define commodity-specific household equivalence scales we take utility to be a function of effective quantities consumed for all commodities. These quantities are defined as ratios of the actual quantities to commodity-specific equivalence scales. We can define general household equivalence scales by comparing budgets for different households. The key to estimating household equivalence scales is to view households as social entities, rather than collections of biological individuals. Households distribute total expenditure among family members in accordance with socially determined welfare objectives.

General equivalence scales are defined in terms of household expenditure functions by analogy with cost-of-living indexes. The individual cost of living index is the ratio of expenditures required to make a given household equally well off at two different sets of prices. The general equivalence scale defined in chapter 5 is the ratio of expenditures required to make two different households equally well off at a given set of prices. This scale can be interpreted as the number of equivalent members for each household.

Chapter 5 gives general and commodity-specific equivalence scales for households classified by size, age of head, and region of residence. The conditions required for aggregation over individual demand functions imply that equivalence scales are independent of utility levels. This has the important advantage that comparisons between two households require only their characteristics, not their levels of utility. A cost of living index independent of utility levels requires the empirically untenable assumption of homothetic preferences.

The Census employs household equivalence scales in constructing a poverty line for different types of households. Inexplicably, the Census employs household equivalence scales in measuring poverty, but not in measuring inequality or the standard of living. In addition, these scales are based on food consumption, rather than household expenditure on all commodities. Slesnick (1993) shows that this produces a substantial bias in the Census poverty measures and con-tributes to the statistical artifact that measured poverty rises during the 1970s and 1980s.

The evaluation of alternative economic policies uses the same framework for normative economics as the measurement of inequality, poverty, and the cost and standard of living. Policies can be compared in terms of levels of individual welfare by appealing to the Pareto principle. The econometric model generates measures of individual welfare that can be combined into an indicator of social welfare. Policies can be compared in terms of levels of social welfare and these comparisons can be further decomposed between levels of economic efficiency and distributional equity.

My 1985 paper with Slesnick , reprinted in chapter 4, compares alternative policies for petroleum price regulation and taxation of petroleum production in the United States . We take the prevailing policy as a reference case. Under this policy petroleum price controls were eliminated in 1981; a windfall profits tax was levied on petroleum production at the same time. The alternative policies include continued controls with no taxation of petroleum production and elimination of controls with a reformed windfall profits tax, beginning in 1983. Finally, we consider a third alternative policy of eliminating controls with no tax.

We compare social welfare under the policy prevailing in 1985 with welfare under each of the three alternative policies and translate these comparisons into money measures. Although the measures depend on American society's degree of aversion to inequality, we find that the comparisons are almost identical in qualitative terms. Under continued controls money metric social welfare is positive for three years and then becomes negative. Eliminating the windfall profits tax reduces welfare for one year, but increases it for all remaining years. Reforming the windfall profits tax is an improvement over the prevailing policy, but produces lower welfare levels than simply eliminating the tax.

Social welfare can be decomposed between efficiency and equity, where efficiency corresponds to the potential gain in welfare. The prevailing policy results in lower efficiency than eliminating the windfall profits tax, except for the initial year of the policy change. While eliminating the tax has a negative impact on equity, this is outweighed by the gains in efficiency. Eliminating the tax produces greater gains in efficiency than either of the alternative policies, but this is partially offset by losses in equity. We conclude that both efficiency and equity comparisons are essential for the evaluation of alternative policies.

My 1987 paper with Slesnick , reprinted as chapter 6, compares alternative policies for natural gas price regulation. The reference case for policy analysis is gradual decontrol of natural gas prices under the National Gas Policy Act of 1978. We also consider continued controls and immediate decontrol, both presented as legislative proposals to the Congress in 1983. Under continued controls the impact on social welfare is positive for the years 1983 to 1989, but then becomes negative. Welfare increases under immediate decontrol throughout the period 1983 to 2000, so that this policy is superior to the prevailing policy and continued controls.

The impact of continued controls on efficiency is positive for the period 1983 to 1989 and negative for the rest of the period, while efficiency gains under immediate decontrol are positive throughout the period. Continued controls also reduce equity for the period 1983 to 1989, while immediate decontrol reduces equity throughout the period. Efficiency and equity move in opposite directions and both are essential for the evaluation of alternative policies.

The comparisons of alternative policies for petroleum taxation and petroleum and natural gas price regulation presented in chapters 4 and 6 are based on simulations of U.S. economic growth under alternative policies. These simulations employ a dynamic general equilibrium model of the U.S. economy that I constructed with Edward Hudson (1974). In my 1992 paper with Slesnick and Peter Wilcoxen , reprinted in chapter 9, we consider simulations of the impact of a carbon tax to reduce emissions of carbon dioxide. For this purpose we use a far more detailed model of the growth of the U.S. economy that I have constructed with Wilcoxen (1990a, 1990b).

To estimate the impact of a carbon tax on the distribution of individual welfare we consider a population of infinitely-lived households or "dynasties." Households are classified by demographic characteristics, as in the earlier chapters, but each household type is linked to similar types in the future through intergenerational altruism. Measures of individual welfare are based on time paths of consumption for the corresponding dynasty. As before, we define social welfare on the distribution of individual welfare over households or dynasties.

We consider a sequence of carbon taxes that holds emissions of carbon dioxide in the U.S. constant at the 1990 level. The direct effect of the tax is to increase purchasers' prices of fossil fuels, which contain carbon, especially coal and crude oil. This results in substitution away from fossil fuels by both producers and consumers, reducing emissions of carbon dioxide fourteen percent by the year 2020. Higher energy prices reduce capital formation and produce a decline in output; about half of this decline is due to lower capital formation and the rest to lower productivity growth.

The welfare cost of a carbon tax is dominated by a loss in efficiency amounting to $234 billion in 1990 dollars. The equity impact of the tax can be positive or negative, depending on the degree of aversion to inequality. The welfare cost must be compared with the benefits of internalizing the externality associated with carbon dioxide emissions. Of course, this externality affects the whole planet, while a carbon tax is the responsibility of an individual government like the U.S.

The econometric approach to welfare economics summarized in this volume is based on a straightforward extension of the conventional index number approach. The essential idea is that preferences of individual households are revealed by their market behavior. An econometric model of household behavior makes it possible to dispense with the limitation to identical and homothetic preferences that characterizes the index number approach. Using much weaker restrictions required for aggregation over utility~maximizing households, we obtain measures of individual welfare that are cardinal and interpersonally comparable.

Measures of individual welfare can be combined into an indicator of social welfare by means of Bergson's concept of a social welfare function. Changes in social welfare can be decomposed between changes in economic efficiency and distributional equity. This approach has been applied to the measurement of inequality, poverty, and the cost and standard of living. It has also been applied to the evaluation of alternative tax and regulatory policies, separating the impacts of policy changes into impacts on efficiency and equity.

Practitioners of normative economics may be relieved to find that the construction of a consumer price index, perhaps the most important application of the index number approach, is conceptually sound and empirically robust. However, the implementation of this approach in the official statistics leaves a great deal to be desired. The official statistical programs that generate measures of poverty, inequality, and the standard of living are deeply flawed and give highly misleading results. These programs will require a total overhaul.

A great deal remains to be done to exploit the new conceptual framework for normative economics. The new methodology presented in chapter 9 provides comparisons among different growth paths resulting from alternative policies. Economic impacts are summarized in terms of wealth rather than consumption. An important objective that remains is to incorporate labor-leisure choice into a model of aggregate consumer behaviorism that measures of individual welfare depend on leisure as well as goods and services.

Each extension of the econometric approach to normative economics generates new information about individual welfare. This information can be incorporated into an indicator of social welfare by bringing to bear ethical judgements about horizontal and vertical equity. We have found it useful to translate changes in social welfare into monetary terms for the applications presented in this volume. The scope of normative economics will be extended by this research program to encompass a broader and broader range of issues in the evaluation of economic performance.

I would like to thank June Wynn of the Department of Economics at Harvard University for her excellent work in assembling the manuscripts for this volume in machine-readable form. Renate d'Arcangelo of the Editorial Office of the Division of Engineering and Applied Sciences at Harvard edited the manuscripts, proofread the machine-readable versions and prepared them for typesetting. Warren Hrung , then a senior at Harvard College , checked the references and proofread successive versions of the typescript. William Richardson and his associates provided the index. Gary Bisbee of Chiron Incorporated typeset the manuscript and provided camera-ready copy for publication. The staff of The MIT Press, especially Terry Vaughn, Victoria Richardson, and Michael Sims, has been very helpful at every stage of the project. Financial support was provided by the Program on Technology and Economic Policy of the Kennedy School of Government at Harvard. As always, the author retains sole responsibility for any remaining deficiencies in the volume.