The effect of college curriculum on earnings: An affinity identifier for non-ignorable non-response bias

We link information on graduates from many cohorts to their high-school and college records and demographics to infer the impact of college major on earnings. We develop an estimator to handle potential non-response bias and identify non-response using an affinity measure—the potential respondent’s link to the survey organization. This technique is generally applicable for adjusting for unit non-response. In the earnings model estimated using the identified (for non-response bias) selectivity adjustments, adjusted earnings differentials across college majors are below half as large as unadjusted differentials and ten percent smaller than those that do not account for selective non-response.     

Edgeworth expansions and normalizing transforms for inequality measures

Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n⁻¹)$O\left(n^{-1}\right)$. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n^−3/2)$O\left(n^{-3/2}\right)$. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.     

Calculating a Standard Error for the Gini Coefficient: Some Further Results*

Several authors have suggested using the jackknife technique to approximate a standard error for the Gini coefficient. It has also been shown that the Gini measure can be obtained simply from an artificial ordinary least square (OLS) regression based on the data and their ranks. We show that obtaining an exact analytical expression for the standard error is actually a trivial matter. Further, by extending the regression framework to one involving seemingly unrelated regressions (SUR), several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner.     

Testing for stochastic dominance using the weighted McFadden-type statistic

We demonstrate that when testing for stochastic dominance of order three and above, using a weighted version of the Kolmogorov–Smirnov-type statistic proposed by McFadden [1989. In: Fomby, T.B., Seo, T.K. (Eds.), Studies in the Economics of Uncertainty. Springer, New York, pp. 113–134] is necessary for obtaining a non-degenerate asymptotic distribution. Since the asymptotic distribution is complex, we discuss a bootstrap approximation for it in the context of a real application.     

Patient enrollment in medical trials: Selection bias in a randomized experiment

Self-selection can bias estimates of treatment effects from randomized experiments if one is interested in extrapolating results to the general population. This paper notes that there is an isomorphism between the Roy model for the sorting of workers into sectors and the decision of subjects to participate in randomized experiments. The main implication is that, as the probability of receiving active treatment rises, patients who are less optimistic about new treatment will begin to enroll and estimates of treatment effects will fall. This, in turn, implies that selection bias is positive. These findings are confirmed with data from trials of ulcer medications.     

Understanding Italian Inequality Trends*

This article develops a unifying framework for analysing the effects of: (i) the changing distribution of individual incomes by main factor sources, (ii) the increasing participation of wives in the labour force, and (iii) the changing distribution of family types on the distinctive trends towards inequality in equivalent household income in Italy between 1977 and 2004. Changes in the distribution of work and pension incomes explain most of the trend. The higher average likelihood of wage‐earning wives had an unequalizing effect on households on the left tail of the income distribution. Little is explained by the changing distribution of family types.     

Hierarchical Modelling of Disparities in Preferences for Redistribution*

We evaluate the magnitude of the disparities in the demand for redistribution across European countries and American states during the 2000s. Modelling the demand for redistribution in a multilevel framework, we identify the determinants that contribute the most in predicting support for redistribution. We observe that individual characteristics and contextual variables are associated with demand for redistribution in the same way in Europe and in the US, whereas others exert different influences on the probability of supporting redistribution. We find important differences from some well‐established evidence obtained from data collected for the 1980s and the 1990s.     

Partial Horizontal Inequity Orderings: A Non‐parametric Approach*

We provide a partial ordering view of horizontal inequity (HI), based on the Lorenz criterion, associated with different post‐tax income distributions and a (bistochastic) non‐parametric estimated benchmark distribution. As a consequence, several measures consistent with the Lorenz criterion can be rationalized. In addition, we establish the so‐called HI transfer principle, which imposes a normative minimum requirement that any HI measure must satisfy. Our proposed HI ordering is consistent with this principle. Moreover, we adopt a cardinal view to decompose the total effect of a tax system into a welfare gain caused by HI‐free income redistribution and a welfare loss caused by HI, without any additive decomposable restriction on the indices. Hence, more robust tests can be applied. Other decompositions in the literature are seen as particular cases.     

Reliable inference for the Gini index

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen’s poverty index and its modification known as the Sen–Shorrocks–Thon index.     

Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction

We provide analytical formulae for the asymptotic bias (ABIAS) and mean-squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. Our analytical formulae can be viewed as generalizing the bias and MSE results of [Richardson and Wu 1971. A note on the comparison of ordinary and two-stage least squares estimators. Econometrica 39, 973–982] to the case with nonnormal errors and stochastic instruments. Our approximations are shown to compare favorably with approximations due to [Morimune 1983. Approximate distributions of k$k$-class estimators when the degree of overidentifiability is large compared with the sample size. Econometrica 51, 821–841] and [Donald and Newey 2001. Choosing the number of instruments. Econometrica 69, 1161–1191], particularly when the instruments are weak. We also construct consistent estimators for the ABIAS and AMSE, and we use these to further construct a number of bias corrected OLS and IV estimators, the properties of which are examined both analytically and via a series of Monte Carlo experiments.     

Quadratic Engel Curves with Measurement Error: Evidence from a Budget Survey*

This paper examines the importance of accounting for measurement error in total expenditure in the estimation of Engel curves, based on the 1994 Ethiopian Urban Household Survey. Using Lewbel's [Review of Economics and Statistics (1996 ), Vol. 78, pp. 718–725] estimator for demand models with correlated measurement errors in the dependent and independent variables, we find robust evidence of a quadratic relationship between food share and total expenditure in the capital city, and significant biases in various estimators that do not correct for correlated measurement errors.     

Proportionally adjusted marginal pricing method to share joint costs

We consider the cost sharing problem with divisible demands of heterogeneous goods. We propose a cost sharing method called Proportionally Adjusted Marginal Pricing (PAMP) method. PAMP is a nonadditive (in the cost function) extension of average cost pricing. We introduce an axiom called Local Independence (LI) and use LI together with Continuity, Proportionality, and Scale Invariance to characterize PAMP. Received: 23 March 2001 / Accepted: 16 November 2001 I thank Yves Sprumont, Hervé Moulin, and Ahmet Alkan for discussions, comments and suggestions. Thanks also go to the associate editor and the referees, whose comments and suggestions greatly improve the paper.     

Simulating the Reform of Means‐tested Benefits with Endogenous Take‐up and Claim Costs*

Microsimulation models are commonly used to examine the distributional impact of reforms of the means‐tested benefit system. Take‐up behaviour is related to the level of entitlement, so reform may induce changes in take‐up. We develop a stochastic simulation method and apply it to a probit model of ‘income support’ take‐up by the UK pensioners. The method allows us to adjust net income for the welfare losses because of tangible or intangible claim costs. Endogenous take‐up and claim costs both have an important impact on the simulated outcomes of the policy reform.     

Examining bias in estimators of linear rational expectations models under misspecification

Most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value. We investigate the asymptotic bias of generalized method of moment (GMM) and maximum likelihood (ML) estimators in such models under misspecification. We consider several misspecifications, and focus more specifically on the case of omitted dynamics in the dependent variable. In a stylized DGP, we derive analytically the asymptotic biases of these estimators. We establish that in many cases of interest the two estimators of the degree of forward-lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter. We also propose a quasi-Hausman test of misspecification based on the difference between the GMM and ML estimators. Using Monte-Carlo simulations, we show that the ordering and direction of the estimators still hold in a more realistic New Keynesian macroeconomic model. In this set-up, misspecification is in general found to be more harmful to GMM than to ML estimators.     

Estimation of finite sequential games

I propose a new estimation method for finite sequential games that is efficient, computationally attractive, and applicable to a fairly general class of finite sequential games that is beyond the scope of existing studies. The major challenge is the computation of high-dimensional truncated integration whose domain is complicated by strategic interaction. This complication resolves when unobserved off-the-equilibrium-path strategies are controlled for. Separately evaluating the likelihood contribution of each subgame-perfect equilibrium that generates the observed outcome allows the use of the GHK simulator, a widely used importance-sampling probit simulator. Monte Carlo experiments demonstrate the performance and robustness of the proposed method.     

Estimating a Parsimonious Model of Inequality Aversion in Stackelberg Duopoly Experiments*

In the Stackelberg duopoly experiments in Huck et al. (2001) , nearly half of the followers’ behaviours are inconsistent with conventional prediction. We use a test in which the conventional self‐interested model is nested as a special case of an inequality aversion model. Maximum likelihood methods applied to the Huck et al. (2001) data set reject the self‐interested model. We find that almost 40% of the players have disadvantageous inequality aversion that is statistically different from zero and economically significant, but advantageous inequality aversion is relatively unimportant. These estimates provide support for a more parsimonious model with no advantageous inequality aversion.     

Accounting for heterogeneous returns in sequential schooling decisions

This paper presents a method for estimating returns to multiple schooling levels taking into account that returns may be heterogeneous among agents and that educational decisions are made sequentially. A sequential decision model explicitly considers that the level of education is the result of previous schooling choices and so, the variation of supply-side instruments over time will emerge as a source of identification of the desired parameters. A test for heterogeneity in returns from sequential schooling decisions is developed and expressions for Marginal Treatment Effects are obtained in this context. Returns are estimated and tested from cross-sectional data from a Spanish household survey that contains rich family background information and useful instruments. This methodology is used to analyze possible effects of the 1970 reform of the Spanish education system.     

Estimation of collective household models with Engel curves

The structural consumer demand methods used to estimate the parameters of collective household models are typically either very restrictive and easy to implement or very general and difficult to estimate. In this paper, we provide a middle ground. We adapt the very general framework of [Browning, M., Chiappori, P.A., Lewbel, A., 2004. Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power, Boston College Working Papers in Economics 588] by adding a simple restriction that recasts the empirical model from a highly nonlinear demand system with price variation to a slightly nonlinear Engel curve system. Our restriction has an interpretation in terms of the behaviour of household scale economies and is testable. Our method identifies the levels of (not just changes in) household resource shares, and a variant of equivalence scales called indifference scales. We apply our methodology to Canadian expenditure data.     

Chain indices of the cost-of-living and the path-dependence problem: An empirical solution

This paper proposes a new method for estimating true cost-of-living (Konüs) indices, for large numbers of commodities, using data only on prices, aggregate budget shares and aggregate expenditure. Conventional chain indices are path-dependent unless income elasticities are (implausibly) all equal to 1. The method allows this difficulty to be overcome. I show that to estimate a Konüs index, only income and not price elasticities are required. The method is applied to estimate a Konüs price index for 70 products covering nearly all the UK's Retail Prices Index over 1974–2004, using the Quadratic Almost Ideal Demand System. The choice of base year for utility has a significant effect on the index.     

Intragenerational mobility and the concept of the equalization of longer-term incomes: An estimation for a developing country

This paper calculates the degree of intragenerational income mobility and carries out the decomposition of the influence of observable characteristics on income mobility. Using the concept of mobility as the equalization of longer-term incomes, we quantify the class of measures called the E index using administrative records for social security contributions of formally employed young adults in Colombia between 2010 and 2018. In addition, we use the Recentered Influence Function (RIF) decomposition method to extend its application to the E index and decompose the influence of observable characteristics on our estimates. Our findings indicate Colombia's mobility is disequalizing. We also show that female mobility is even more disequalizing than male mobility. Our decomposition shows that disequalizing mobility depends on employees' type of contract, economic sector, and location.