Krishna Pendakur - Academia.edu (original) (raw)

Papers by Krishna Pendakur

Social Science Research Network, 2007

We invent Implicit Marshallian Demands, a new type of demand function that combines desirable fea... more We invent Implicit Marshallian Demands, a new type of demand function that combines desirable features of Hicksian and Marshallian demand functions. We propose and estimate the Exact Af ne Stone Index (EASI) Implicit Marshallian Demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can be polynomials or splines of any order in real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression.

Journal of Econometrics, Nov 1, 2009

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is every... more Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non-and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they o¤er powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the di¤ering convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and …nite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We …nd that our nonparametric analysis yields statistically sig-ni…cantly and qualitatively di¤erent results from traditional parametric estimators and tests.

The American Economic Review, Feb 1, 2013

This online supplementary appendix contains five main sections: Appendix A.1 states formally our ... more This online supplementary appendix contains five main sections: Appendix A.1 states formally our main identification theorems, providing the general conditions for identification under either the Similar Across People (SAP) or Similar Across Types (SAT) conditions. Appendix A.2 gives proofs of the Theorems in Appendix A.1. Appendix A.3 provides an example of a class of indirect utility functions that satisfy the assumptions of both of our main identification Theorems, and yields Engel curves having the functional form we assume for our empirical work. Appendix A.4 provides an example functional form within the general class of models given in appendix A.3. This functional form could be used if one wished to combine our results with other structural analyses, e.g., if one wished to introduce prices into the model. Appendix A.5 provides the results of extensive statistical tests of the adequacy of our model's assumptions. These are divided into sets of tests focusing on the general BCL methodology, our SAP and SAT restrictions on preferences, invariance of resource shares with respect to total expenditures at low total expenditure levels, and privateness of clothing expenditures.

arXiv (Cornell University), Aug 12, 2020

We provide new results showing identification of a large class of fixed-T panel models, where the... more We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity. * This paper partly supersedes and replaces an earlier working paper by Botosaru and Muris entitled "Binarization for panel models with fixed effects".

Journal of Political Economy, Aug 1, 2017

We model unobserved preference heterogeneity in demand systems via random Barten scales in utilit... more We model unobserved preference heterogeneity in demand systems via random Barten scales in utility functions. These Barten scales appear as random coefficients multiplying prices in demand functions. Consumer demands are nonlinear in prices and may have unknown functional structure. We therefore prove identification of Generalized Random Coefficients models, defined as nonparametric regressions where each regressor is multiplied by an unobserved random coefficient having an unknown distribution. Using Canadian data, we estimate energy demand functions with and without random coefficient Barten scales. We find that not accounting for this unobserved preference heterogeneity substantially biases estimated consumer-surplus costs of an energy tax.

RePEc: Research Papers in Economics, Sep 3, 2015

Because most principles for evaluating policies which result in population change require informa... more Because most principles for evaluating policies which result in population change require information about individual well-being as well as interpersonal comparisons, some way of assessing levels of well-being is essential to their use. In this paper, we look at one way of doing it using equivalent expenditures and equivalence scales. In certain circumstances, equivalent expenditures, which can be used to make interpersonal comparisons, can be estimated. This note examines this method in light of the demands of the critical-level generalized utilitarian family of principles. Properties of those principles are examined, and the problems of setting the critical level and of implementing priority for the less well off is included. In addition, the possibility of decisions based on theory and a few facts is investigated. The paper concludes with a discussion of population policy and the current world environmental crisis. Most principles for evaluating policies which result in population change require some information about the existence and utility levels of those who ever live in the histories which corresponding to policy options, which we alternative histories or alternative. Utilities are indexes of well-being, and in population ethics, they should be indexes of lifetime well-being. The utility estimates are hard to assess and, because lifetime utilities are needed, the problem is more difficult than the estimation of short-term well-being. One way to estimate utilities, at least in short periods, is to use equivalent expenditures and equivalence scales. They make interpersonal comparisons of utilities, accounting for heterogeneity of household characteristics, and can be estimated from available data in some circumstances. Although short-term utilities are not adequate for population ethics, estimation of their short-term values is an important first step. This paper presents an outline of one such method (Section 4). It is not the only possible one, but it does work and, if a reference utility function is specified and estimated, an economy can be converted, for welfare purposes, into one with identical reference single individuals. Children are included; no one is left out. In Section 1 and 2, we present several of the main principles and families of principles: classical utilitarianism, average utilitarianism, the critical-level generalized utilitarian

Social Science Research Network, 2007

Consumer demand microdata typically exhibit a great deal of expenditure variation but not very mu... more Consumer demand microdata typically exhibit a great deal of expenditure variation but not very much price variation. In this paper, we propose a semiparametric approach to the consumer demand problem in which expenditure share equations are nonparametric in the real expenditure direction and parametric (with …xed coe¢cients) in price directions. Here, Engel curves are unrestricted so that demands may have any rank. We also consider a 'varying coe¢cients' extension in which price e¤ects depend on real expenditure. Because the demand model is derived from a model of cost, it may be restricted to satisfy integrability and used for consumer surplus calculations. Since real expenditure is not observed, but rather estimated under the model, we face a semiparametric model with a nonparametrically generated regressor. We show e¢cient convergence rates for parametric and nonparametric components. The estimation procedures are introduced for both cases, under integrability restrictions and without. Further we give speci…cation tests to check these integrability restrictions. An empirical illustration with Canadian price and expenditure data shows that Engel curves display curvature which cannot be encompassed by standard parametric models. In addition, we …nd that although the rationality restriction of Slutsky symmetry is rejected in our …xed coe¢cients model, it is not rejected in the varying coe¢cients extension.

The Economic Journal, Mar 9, 2022

We propose a model of consumption inefficiency in collective households. Inefficiency depends on ... more We propose a model of consumption inefficiency in collective households. Inefficiency depends on a "cooperation factor", which can also affect both the allocation of resources within a household and the utility of household members. Households are conditionally efficient, conditioning on the value of the cooperation factor. This lets us exploit convenient modeling features of efficient households (like not needing to specify the bargaining process), while still accounting for, and measuring the dollar cost of, inefficient levels of cooperation.

Journal of Political Economy, Mar 1, 2022

We provide a method to estimate resource shares-the fraction of total household expenditure alloc... more We provide a method to estimate resource shares-the fraction of total household expenditure allocated to each household member-using linear (e.g., ordinary least squares) estimation of Engel curves. The method is a linear reframing of the 2013 nonlinear model of Dunbar, Lewbel, and Pendakur, extended to allow single-parent and other complex households, scale economies in assignable goods, and complementarities between nonassignable goods and supplemented with a linear identification test. We apply the model to data from 12 countries and investigate resource shares, gender gaps, and poverty at the individual level. We reject equal sharing and find large gender gaps in resource shares, and consequently in poverty rates, in some countries.

Lewbel and Pendakur (2021) propose a model of consumption inefficiency in collective households, ... more Lewbel and Pendakur (2021) propose a model of consumption inefficiency in collective households, based on “cooperation factors”. We simplify that model to make it empirically tractable, and apply it to identify and estimate household member resource shares, and to measure the dollar cost of inefficient levels of cooperation. Using data from Bangladesh, we find that increased cooperation among household members yields the equivalent of a 13% gain in total expenditures, with most of the benefit of this gain going towards men. JEL codes: D13, D11, D12, C31, I32.

Journal of Econometrics, 2021

We provide new results showing identification of a large class of fixed-T panel models, where the... more We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity. * This paper partly supersedes and replaces an earlier working paper by Botosaru and Muris entitled "Binarization for panel models with fixed effects".

An equivalence scale is a measure of the cost of living of a household of a given size and demogr... more An equivalence scale is a measure of the cost of living of a household of a given size and demographic composition, relative to the cost of living of a reference household (usually a single adult), when both households attain the same level of utility or standard of living. Equivalence scales are dif cult to construct because household utility cannot be directly measured, which results in economic identi cation problems. Applications of equivalence scales include: measurement of social welfare, economic inequality, poverty, and costs of children; indexing payments for social bene ts, life insurance, alimony, and legal compensation for wrongful death.

Because most principles for evaluating policies which result in population change require informa... more Because most principles for evaluating policies which result in population change require information about individual well-being as well as interpersonal comparisons, some way of assessing levels of well-being is essential to their use. In this paper, we look at one way of doing it using equivalent expenditures and equivalence scales. In certain circumstances, equivalent expenditures, which can be used to make interpersonal comparisons, can be estimated. This note examines this method in light of the demands of the critical-level generalized utilitarian family of principles. Properties of those principles are examined, and the problems of setting the critical level and of implementing priority for the less well off is included. In addition, the possibility of decisions based on theory and a few facts is investigated. The paper concludes with a discussion of population policy and the current world environmental crisis.

We provide a new full-commitment intertemporal collective household model to estimate resource sh... more We provide a new full-commitment intertemporal collective household model to estimate resource shares, defined as the fraction of household expenditure enjoyed by household members. Our model implies nonlinear time-varying household quantity demand functions that depend on fixed e↵ects. We provide new econometric results showing identification of a large class of models that includes our household model. We cover fixed-T panel models where the response variable is an unknown monotonic function of a linear latent variable with fixed e↵ects, regressors, and a nonparametric error term. The function may be weakly monotonic and time-varying, and the fixed e↵ects are unrestricted. We identify the structural parameters and features of the distribution of fixed e↵ects. In our household model, these correspond to features of the distribution of resource shares. Using Bangladeshi data, we show: women's resource shares decline with household budgets; and, half the variation in women's resource shares is due to unobserved heterogeneity.

We provide a new full-commitment intertemporal collective household model to estimate resource sh... more We provide a new full-commitment intertemporal collective household model to estimate resource shares, defined as the fraction of household expenditure enjoyed by household members. Our model implies nonlinear time-varying household quantity demand functions that depend on fixed e↵ects. We provide new econometric results showing identification of a large class of models that includes our household model. We cover fixed-T panel models where the response variable is an unknown monotonic function of a linear latent variable with fixed e↵ects, regressors, and a nonparametric error term. The function may be weakly monotonic and time-varying, and the fixed e↵ects are unrestricted. We identify the structural parameters and features of the distribution of fixed e↵ects. In our household model, these correspond to features of the distribution of resource shares. Using Bangladeshi data, we show: women's resource shares decline with household budgets; and, half the variation in women's resource shares is due to unobserved heterogeneity.

Journal of Political Economy, 2017

We prove a new identification theorem showing nonparametric identification of the joint distribut... more We prove a new identification theorem showing nonparametric identification of the joint distribution of random coefficients in general nonlinear and additive models. This differs from existing random coefficients models by not imposing a linear index structure for the regressors. We then model unobserved preference heterogeneity in consumer demand as utility functions with random Barten scales. These Barten scales appear as random coefficients in nonlinear demand equations. Using Canadian data, we compare estimated energy demand functions with and without random Barten scales. We find that unobserved preference heterogeneity substantially affects the estimated consumer surplus costs of an energy tax.

The Economic Journal, 2012

We consider an revealed preference based method which will partition consumer microdata into an a... more We consider an revealed preference based method which will partition consumer microdata into an approximate minimal number of preference types such that the data are perfectly rationalisable by standard utility theory. This provides a simple, nonparametric and theory-driven way of investigating unobserved preference heterogeneity in empirical data, and easily extends to any choice model which has a revealed preference characterisation. We illustrate the approach using survey data and …nd that the number of types is remarkably few relative to the sample size-only 4 or 5 types are necessary to fully characterise all observed choices in a dataset with 500 observations of choice vectors.

Social Choice and Welfare, 2011

For a change in prices, the common-scaling social cost-of-living index is the equal scaling of ev... more For a change in prices, the common-scaling social cost-of-living index is the equal scaling of every individual's expenditure level needed to restore the level of social welfare to its pre-change value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circular test requires the product of index values for successive price changes to be equal to the index value for the whole change. We show that both tests are satisfied if and only if the Bergson-Samuelson indirect social-welfare function is homothetic in prices, a condition which does not require individual preferences to be homothetic. If individual preferences are homothetic, however, stronger conditions on the Bergson-Samuelson indirect must be satisfied. Given these results, we ask whether the restrictions are empirically reasonable and find, in the case that individual preferences are not homothetic, that the restrictions make little difference to estimates of the index.

We propose a generalization of random coefficients models, in which the regression model is addit... more We propose a generalization of random coefficients models, in which the regression model is additive (or additive with interactions) rather than linear, and each regressor is multiplied by an unobserved error. We show nonparametric identification of the model. In addition to providing a natural generalization of random coefficients, we provide economic motivations for the model based on demand system estimation. In these applications, the random coefficients can be interpreted as random utility parameters that take the form of Engel scales or Barten scales, which in the past were estimated as deterministic preference heterogeneity or household technology parameters. We apply these results to consumer surplus and related welfare calculations.

Social Science Research Network, 2007

We invent Implicit Marshallian Demands, a new type of demand function that combines desirable fea... more We invent Implicit Marshallian Demands, a new type of demand function that combines desirable features of Hicksian and Marshallian demand functions. We propose and estimate the Exact Af ne Stone Index (EASI) Implicit Marshallian Demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can be polynomials or splines of any order in real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression.

Journal of Econometrics, Nov 1, 2009

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is every... more Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non-and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they o¤er powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the di¤ering convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and …nite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We …nd that our nonparametric analysis yields statistically sig-ni…cantly and qualitatively di¤erent results from traditional parametric estimators and tests.

The American Economic Review, Feb 1, 2013

This online supplementary appendix contains five main sections: Appendix A.1 states formally our ... more This online supplementary appendix contains five main sections: Appendix A.1 states formally our main identification theorems, providing the general conditions for identification under either the Similar Across People (SAP) or Similar Across Types (SAT) conditions. Appendix A.2 gives proofs of the Theorems in Appendix A.1. Appendix A.3 provides an example of a class of indirect utility functions that satisfy the assumptions of both of our main identification Theorems, and yields Engel curves having the functional form we assume for our empirical work. Appendix A.4 provides an example functional form within the general class of models given in appendix A.3. This functional form could be used if one wished to combine our results with other structural analyses, e.g., if one wished to introduce prices into the model. Appendix A.5 provides the results of extensive statistical tests of the adequacy of our model's assumptions. These are divided into sets of tests focusing on the general BCL methodology, our SAP and SAT restrictions on preferences, invariance of resource shares with respect to total expenditures at low total expenditure levels, and privateness of clothing expenditures.

arXiv (Cornell University), Aug 12, 2020

We provide new results showing identification of a large class of fixed-T panel models, where the... more We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity. * This paper partly supersedes and replaces an earlier working paper by Botosaru and Muris entitled "Binarization for panel models with fixed effects".

Journal of Political Economy, Aug 1, 2017

We model unobserved preference heterogeneity in demand systems via random Barten scales in utilit... more We model unobserved preference heterogeneity in demand systems via random Barten scales in utility functions. These Barten scales appear as random coefficients multiplying prices in demand functions. Consumer demands are nonlinear in prices and may have unknown functional structure. We therefore prove identification of Generalized Random Coefficients models, defined as nonparametric regressions where each regressor is multiplied by an unobserved random coefficient having an unknown distribution. Using Canadian data, we estimate energy demand functions with and without random coefficient Barten scales. We find that not accounting for this unobserved preference heterogeneity substantially biases estimated consumer-surplus costs of an energy tax.

RePEc: Research Papers in Economics, Sep 3, 2015

Because most principles for evaluating policies which result in population change require informa... more Because most principles for evaluating policies which result in population change require information about individual well-being as well as interpersonal comparisons, some way of assessing levels of well-being is essential to their use. In this paper, we look at one way of doing it using equivalent expenditures and equivalence scales. In certain circumstances, equivalent expenditures, which can be used to make interpersonal comparisons, can be estimated. This note examines this method in light of the demands of the critical-level generalized utilitarian family of principles. Properties of those principles are examined, and the problems of setting the critical level and of implementing priority for the less well off is included. In addition, the possibility of decisions based on theory and a few facts is investigated. The paper concludes with a discussion of population policy and the current world environmental crisis. Most principles for evaluating policies which result in population change require some information about the existence and utility levels of those who ever live in the histories which corresponding to policy options, which we alternative histories or alternative. Utilities are indexes of well-being, and in population ethics, they should be indexes of lifetime well-being. The utility estimates are hard to assess and, because lifetime utilities are needed, the problem is more difficult than the estimation of short-term well-being. One way to estimate utilities, at least in short periods, is to use equivalent expenditures and equivalence scales. They make interpersonal comparisons of utilities, accounting for heterogeneity of household characteristics, and can be estimated from available data in some circumstances. Although short-term utilities are not adequate for population ethics, estimation of their short-term values is an important first step. This paper presents an outline of one such method (Section 4). It is not the only possible one, but it does work and, if a reference utility function is specified and estimated, an economy can be converted, for welfare purposes, into one with identical reference single individuals. Children are included; no one is left out. In Section 1 and 2, we present several of the main principles and families of principles: classical utilitarianism, average utilitarianism, the critical-level generalized utilitarian

Social Science Research Network, 2007

Consumer demand microdata typically exhibit a great deal of expenditure variation but not very mu... more Consumer demand microdata typically exhibit a great deal of expenditure variation but not very much price variation. In this paper, we propose a semiparametric approach to the consumer demand problem in which expenditure share equations are nonparametric in the real expenditure direction and parametric (with …xed coe¢cients) in price directions. Here, Engel curves are unrestricted so that demands may have any rank. We also consider a 'varying coe¢cients' extension in which price e¤ects depend on real expenditure. Because the demand model is derived from a model of cost, it may be restricted to satisfy integrability and used for consumer surplus calculations. Since real expenditure is not observed, but rather estimated under the model, we face a semiparametric model with a nonparametrically generated regressor. We show e¢cient convergence rates for parametric and nonparametric components. The estimation procedures are introduced for both cases, under integrability restrictions and without. Further we give speci…cation tests to check these integrability restrictions. An empirical illustration with Canadian price and expenditure data shows that Engel curves display curvature which cannot be encompassed by standard parametric models. In addition, we …nd that although the rationality restriction of Slutsky symmetry is rejected in our …xed coe¢cients model, it is not rejected in the varying coe¢cients extension.

The Economic Journal, Mar 9, 2022

We propose a model of consumption inefficiency in collective households. Inefficiency depends on ... more We propose a model of consumption inefficiency in collective households. Inefficiency depends on a "cooperation factor", which can also affect both the allocation of resources within a household and the utility of household members. Households are conditionally efficient, conditioning on the value of the cooperation factor. This lets us exploit convenient modeling features of efficient households (like not needing to specify the bargaining process), while still accounting for, and measuring the dollar cost of, inefficient levels of cooperation.

Journal of Political Economy, Mar 1, 2022

We provide a method to estimate resource shares-the fraction of total household expenditure alloc... more We provide a method to estimate resource shares-the fraction of total household expenditure allocated to each household member-using linear (e.g., ordinary least squares) estimation of Engel curves. The method is a linear reframing of the 2013 nonlinear model of Dunbar, Lewbel, and Pendakur, extended to allow single-parent and other complex households, scale economies in assignable goods, and complementarities between nonassignable goods and supplemented with a linear identification test. We apply the model to data from 12 countries and investigate resource shares, gender gaps, and poverty at the individual level. We reject equal sharing and find large gender gaps in resource shares, and consequently in poverty rates, in some countries.

Lewbel and Pendakur (2021) propose a model of consumption inefficiency in collective households, ... more Lewbel and Pendakur (2021) propose a model of consumption inefficiency in collective households, based on “cooperation factors”. We simplify that model to make it empirically tractable, and apply it to identify and estimate household member resource shares, and to measure the dollar cost of inefficient levels of cooperation. Using data from Bangladesh, we find that increased cooperation among household members yields the equivalent of a 13% gain in total expenditures, with most of the benefit of this gain going towards men. JEL codes: D13, D11, D12, C31, I32.

Journal of Econometrics, 2021

We provide new results showing identification of a large class of fixed-T panel models, where the... more We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity. * This paper partly supersedes and replaces an earlier working paper by Botosaru and Muris entitled "Binarization for panel models with fixed effects".

An equivalence scale is a measure of the cost of living of a household of a given size and demogr... more An equivalence scale is a measure of the cost of living of a household of a given size and demographic composition, relative to the cost of living of a reference household (usually a single adult), when both households attain the same level of utility or standard of living. Equivalence scales are dif cult to construct because household utility cannot be directly measured, which results in economic identi cation problems. Applications of equivalence scales include: measurement of social welfare, economic inequality, poverty, and costs of children; indexing payments for social bene ts, life insurance, alimony, and legal compensation for wrongful death.

Because most principles for evaluating policies which result in population change require informa... more Because most principles for evaluating policies which result in population change require information about individual well-being as well as interpersonal comparisons, some way of assessing levels of well-being is essential to their use. In this paper, we look at one way of doing it using equivalent expenditures and equivalence scales. In certain circumstances, equivalent expenditures, which can be used to make interpersonal comparisons, can be estimated. This note examines this method in light of the demands of the critical-level generalized utilitarian family of principles. Properties of those principles are examined, and the problems of setting the critical level and of implementing priority for the less well off is included. In addition, the possibility of decisions based on theory and a few facts is investigated. The paper concludes with a discussion of population policy and the current world environmental crisis.

We provide a new full-commitment intertemporal collective household model to estimate resource sh... more We provide a new full-commitment intertemporal collective household model to estimate resource shares, defined as the fraction of household expenditure enjoyed by household members. Our model implies nonlinear time-varying household quantity demand functions that depend on fixed e↵ects. We provide new econometric results showing identification of a large class of models that includes our household model. We cover fixed-T panel models where the response variable is an unknown monotonic function of a linear latent variable with fixed e↵ects, regressors, and a nonparametric error term. The function may be weakly monotonic and time-varying, and the fixed e↵ects are unrestricted. We identify the structural parameters and features of the distribution of fixed e↵ects. In our household model, these correspond to features of the distribution of resource shares. Using Bangladeshi data, we show: women's resource shares decline with household budgets; and, half the variation in women's resource shares is due to unobserved heterogeneity.

We provide a new full-commitment intertemporal collective household model to estimate resource sh... more We provide a new full-commitment intertemporal collective household model to estimate resource shares, defined as the fraction of household expenditure enjoyed by household members. Our model implies nonlinear time-varying household quantity demand functions that depend on fixed e↵ects. We provide new econometric results showing identification of a large class of models that includes our household model. We cover fixed-T panel models where the response variable is an unknown monotonic function of a linear latent variable with fixed e↵ects, regressors, and a nonparametric error term. The function may be weakly monotonic and time-varying, and the fixed e↵ects are unrestricted. We identify the structural parameters and features of the distribution of fixed e↵ects. In our household model, these correspond to features of the distribution of resource shares. Using Bangladeshi data, we show: women's resource shares decline with household budgets; and, half the variation in women's resource shares is due to unobserved heterogeneity.

Journal of Political Economy, 2017

We prove a new identification theorem showing nonparametric identification of the joint distribut... more We prove a new identification theorem showing nonparametric identification of the joint distribution of random coefficients in general nonlinear and additive models. This differs from existing random coefficients models by not imposing a linear index structure for the regressors. We then model unobserved preference heterogeneity in consumer demand as utility functions with random Barten scales. These Barten scales appear as random coefficients in nonlinear demand equations. Using Canadian data, we compare estimated energy demand functions with and without random Barten scales. We find that unobserved preference heterogeneity substantially affects the estimated consumer surplus costs of an energy tax.

The Economic Journal, 2012

We consider an revealed preference based method which will partition consumer microdata into an a... more We consider an revealed preference based method which will partition consumer microdata into an approximate minimal number of preference types such that the data are perfectly rationalisable by standard utility theory. This provides a simple, nonparametric and theory-driven way of investigating unobserved preference heterogeneity in empirical data, and easily extends to any choice model which has a revealed preference characterisation. We illustrate the approach using survey data and …nd that the number of types is remarkably few relative to the sample size-only 4 or 5 types are necessary to fully characterise all observed choices in a dataset with 500 observations of choice vectors.

Social Choice and Welfare, 2011

For a change in prices, the common-scaling social cost-of-living index is the equal scaling of ev... more For a change in prices, the common-scaling social cost-of-living index is the equal scaling of every individual's expenditure level needed to restore the level of social welfare to its pre-change value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circular test requires the product of index values for successive price changes to be equal to the index value for the whole change. We show that both tests are satisfied if and only if the Bergson-Samuelson indirect social-welfare function is homothetic in prices, a condition which does not require individual preferences to be homothetic. If individual preferences are homothetic, however, stronger conditions on the Bergson-Samuelson indirect must be satisfied. Given these results, we ask whether the restrictions are empirically reasonable and find, in the case that individual preferences are not homothetic, that the restrictions make little difference to estimates of the index.

We propose a generalization of random coefficients models, in which the regression model is addit... more We propose a generalization of random coefficients models, in which the regression model is additive (or additive with interactions) rather than linear, and each regressor is multiplied by an unobserved error. We show nonparametric identification of the model. In addition to providing a natural generalization of random coefficients, we provide economic motivations for the model based on demand system estimation. In these applications, the random coefficients can be interpreted as random utility parameters that take the form of Engel scales or Barten scales, which in the past were estimated as deterministic preference heterogeneity or household technology parameters. We apply these results to consumer surplus and related welfare calculations.