Asymptotic and bootstrap inference for inequality and poverty measures

A random sample drawn from a population would appear to offer an ideal opportunity to use the bootstrap in order to perform accurate inference, since the observations of the sample are IID. In this paper, Monte Carlo results suggest that bootstrapping a commonly used index of inequality leads to inference that is not accurate even in very large samples, although inference with poverty indices is satisfactory. We find that the major cause is the extreme sensitivity of many inequality indices to the exact nature of the upper tail of the income distribution. This leads us to study two non-standard bootstraps, the m out of n bootstrap, which is valid in some situations where the standard bootstrap fails, and a bootstrap in which the upper tail is modelled parametrically. Monte Carlo results suggest that accurate inference can be achieved with this last method in moderately large samples.     

Global estimates of growth–inequality–poverty (GIP) triangle: evidence from World Bank’s classification countries

This study extended the concept of ‘growth–inequality–poverty (GIP) triangle’ by using the principle component approach which allows us to composite different poverty and inequality indicators into one single index that contains most of the useful information from the original dataset. Using the idea of GIP triangle, this study examines the long-run relationship among weighted poverty index (which comprises headcount ratio, poverty gap and squared poverty gap); weighted inequality index (i.e., Watts Index, Gini Index and MLD Index) and average monthly per capita income in the designated 138 countries according to World Bank’s classification over a period of 2005–2010. The data set mainly contain countries’ unit record household survey at least one which is conducted between the countries during the sample period. The regression model encompassing the impact of economic growth and income inequality on poverty reflects that income inequality increases poverty while economic growth decreases poverty. It indicates that the impact of inequality in increasing poverty is a somewhat greater than that of growth in average income in reducing overall poverty in a sample countries. The other regression model encompassing the impact of economic growth and poverty on income inequality showed that the poverty itself is also likely to be a barrier for poverty reduction; and inequality seems to predict lower future growth rates. The final regression model depicting the impact of poverty and income inequality on mean income of the household suggests that poverty itself reduces mean income of the household while income inequality increases economic growth. The results are interesting and simply suggest that whenever social institutions malfunction, the incidence of damage would usually be distributed unevenly over the society’s members.     

Mobility and the dynamics of poverty in Iran: Evidence from the 1992–1995 panel survey

In the last three decades, revolutionary Iran has experienced large shocks to its political and economic system with likely effects on poverty, inequality, and economic mobility. While poverty has declined, inequality has remained relatively high and stable over nearly four decades. In this paper, for the first time, we examine poverty and inequality in a dynamic context using a 4-year panel data, collected during 1992–1995. We show that short-term income mobility is relatively high, which helps mitigate persistent high inequality. We offer a range of estimates of transition probabilities, indicating that, for example, someone in the lowest (highest) quintile has between 25% and 50% chance of moving up (down) the income ladder. Focusing on the dynamics of poverty, we distinguish between short- and long-term poor and between chronic and transient poverty. Surprisingly, we find that chronic poverty is a more serious problem in urban than rural areas, while transient poverty is geographically more uniformly distributed. Finally, using Tobit and quantile regression, we examine the correlates of these two types of poverty. Both chronic and transient poverty are higher for households headed by women and by younger and less educated men. While minorities suffer more from transient poverty, they are less likely to be chronically poor. We discuss the implications of these findings for policy to alleviate chronic and transient poverty.     

Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index

Zenga’s new inequality curve and index are two recent tools for measuring inequality. Proposed in 2007, they should thus not be mistaken for anterior measures suggested by the same author. This paper focuses on the new measures only, which are hereafter referred to simply as the Zenga curve and Zenga index. The Zenga curve Z(α) involves the ratio of the mean income of the 100α % poorest to that of the 100(1?α)% richest. The Zenga index can also be expressed by means of the Lorenz Curve and some of its properties make it an interesting alternative to the Gini index. Like most other inequality measures, inference on the Zenga index is not straightforward. Some research on its properties and on estimation has already been conducted but inference in the sampling framework is still needed. In this paper, we propose an estimator and variance estimator for the Zenga index when estimated from a complex sampling design. The proposed variance estimator is based on linearization techniques and more specifically on the direct approach presented by Demnati and Rao. The quality of the resulting estimators are evaluated in Monte Carlo simulation studies on real sets of income data. Finally, the advantages of the Zenga index relative to the Gini index are discussed.     

UNCERTAINTY AND DENSITY FORECASTS OF ARMA MODELS: COMPARISON OF ASYMPTOTIC,BAYESIAN, AND BOOTSTRAP PROCEDURES

The objective of this paper is to analyze the effects of uncertainty on density forecasts of stationary linear univariate ARMA models. We consider three specific sources of uncertainty: parameter estimation, error distribution, and lag order. Depending on the estimation sample size and the forecast horizon, each of these sources may have different effects. We consider asymptotic, Bayesian, and bootstrap procedures proposed to deal with uncertainty and compare their finite sample properties. The results are illustrated constructing fan charts for UK inflation.     

Bootstrapping cointegrating regressions

In this paper, we consider bootstrapping cointegrating regressions. It is shown that the method of bootstrap, if properly implemented, generally yields consistent estimators and test statistics for cointegrating regressions. For the cointegrating regression models driven by general linear processes, we employ the sieve bootstrap based on the approximated finite-order vector autoregressions for the regression errors and the first differences of the regressors. In particular, we establish the bootstrap consistency for OLS method. The bootstrap method can thus be used to correct for the finite sample bias of the OLS estimator and to approximate the asymptotic critical values of the OLS-based test statistics in general cointegrating regressions. The bootstrap OLS procedure, however, is not efficient. For the efficient estimation and hypothesis testing, we consider the procedure proposed by Saikkonen [1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] and Stock and Watson [1993. A simple estimator of cointegrating vectors in higher order integrating systems. Econometrica 61, 783–820] relying on the regression augmented with the leads and lags of differenced regressors. The bootstrap versions of their procedures are shown to be consistent, and can be used to do asymptotically valid inferences. A Monte Carlo study is conducted to investigate the finite sample performances of the proposed bootstrap methods.     

Estimation of poverty measures with auxiliary information in sample surveys

The analysis of poverty measures has been receiving increased attention in recent years. This paper contributes to the literature by developing percentile ratio estimators based on the pseudo empirical likelihood method. In practice, variances of poverty measures could be not expressible by simple formulae and consequently other techniques should be used in the variance estimation stage. Assuming percentile ratios, resampling techniques are investigated in this paper. A numerical example based on data from the Spanish Household Panel Survey is taken up to illustrate how suggested procedures can perform better than existing ones. The effect of a model-misspecification on the proposed estimators is also evaluated by using simulated populations.     

Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures

This paper presents estimators of distributional impacts of interventions when selection to the program is based on observable characteristics. Distributional impacts are calculated as differences in inequality measures of the marginal distributions of potential outcomes of receiving and not receiving the treatment. The estimation procedure involves a first non‐parametric estimation of the propensity score. In the second step weighted versions of inequality measures are computed using weights based on the estimated propensity score. Consistency, semi‐parametric efficiency and validity of inference based on the percentile bootstrap are shown for the estimators. Results from Monte Carlo exercises show its good performance in small samples. Copyright © 2015 John Wiley & Sons, Ltd.     

ESTIMATION OF CENSORED PANEL‐DATA MODELS WITH SLOPE HETEROGENEITY

This paper considers estimation of censored panel‐data models with individual‐specific slope heterogeneity. The slope heterogeneity may be random (random slopes model) or related to covariates (correlated random slopes model). Maximum likelihood and censored least‐absolute deviations estimators are proposed for both models. The estimators are simple to implement and, in the case of maximum likelihood, lead to straightforward estimation of partial effects. The rescaled bootstrap suggested by Andrews (Econometrica 2000; 68 : 399–405) is used to deal with the possibility of variance parameters being equal to zero. The methodology is applied to an empirical study of Dutch household portfolio choice, where the outcome variable (portfolio share in safe assets) has corner solutions at zero and one. As predicted by economic theory, there is strong evidence of correlated random slopes for the age profiles, indicating a heterogeneous age profile of portfolio adjustment that varies significantly with other household characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes

Besides a brief historical outline of the Gini index decomposition proposals, we compare, in a subgroups framework, the decompositions of the Gini index and of the uniformity and inequality indexes recently proposed by Zenga. The two decompositions follow a similar scheme: in both cases the overall index can be at first expressed as a weighted average of convenient "cross" measures, with their own interpretation, and afterwards it is decomposed into a within and a between term by merely distinguishing measures evaluated within the same subgroup from the ones regarding different subgroups. This procedure does not depend on an a priori definition of the within or the between term and allows their contribution to be naturally evaluated preserving the structure of the index itself. In the last section the two decompositions are applied to the Italian net household wealth provided by the 2006 central Bank of Italy sample survey on household budgets.     

Semiparametric Bayesian inference in smooth coefficient models

We describe procedures for Bayesian estimation and testing in cross-sectional, panel data and nonlinear smooth coefficient models. The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement—for example, estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model.     

Cross-sectional dependence robust block bootstrap panel unit root tests

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the group-mean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data, originally proposed for a setting of no cross-sectional dependence beyond a common time effect. The tests, suited for testing for unit roots in the observed data, can be easily implemented as no specification or estimation of the dependence structure is required. Asymptotic properties of the tests are derived for T going to infinity and N finite. Asymptotic validity of the bootstrap tests is established in very general settings, including the presence of common factors and cointegration across units. Properties under the alternative hypothesis are also considered. In a Monte Carlo simulation, the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests. The power properties of the bootstrap tests appear to be similar to those of the asymptotic tests.     

Dynamics of productivity in higher education: cross-european evidence based on bootstrapped Malmquist indices

This study examines patterns of productivity change in a large set of 266 public higher education institutions (HEIs) in 7 European countries across the time period 2001–2005. We adopt consistent bootstrap estimation procedures to obtain confidence intervals for Malmquist indices of HEI productivity and their components. Consequently, we are able to assess the statistical significance of changes in HEI productivity, efficiency and technology. Our results suggest that, assessed vis-à-vis a common ‘European’ frontier, HEI productivity rose on average by 4 % annually. Statistically significant changes in productivity were registered in 90 % of observations on the institutions in our sample, but statistically significant annual improvements in overall productivity took place in only 56 % of cases. There are considerable national differences, with German, Italian and Swiss HEIs performing better in terms of productivity change than HEIs from the other countries examined.     

Estimation of Poverty Transition Matrices with Noisy Data

This paper investigates measurement error biases in estimated poverty transition matrices. We compare transition matrices based on survey expenditure data to transition matrices based on measurement‐error‐free simulated expenditure. The simulation model uses estimates that correct for measurement error in expenditure. We find that time‐varying measurement error in expenditure data magnifies economic mobility. Roughly 45% of households initially in poverty at time t ? 1 are found to be out of poverty at time t using data from the Korean Labor and Income Panel Study. When measurement error is removed, this drops to between 26 and 31% of households initially in poverty. Copyright © 2016 John Wiley & Sons, Ltd.     

The Effect of Income Distribution on the Ability of Growth to Reduce Poverty: Evidence from Rural and Urban African Economies

The present study examines the extent to which income distribution affects the ability of economic growth to reduce poverty, based on 1990s data for a sample of rural and urban sectors of African economies. Using the basic‐needs approach, an analysis‐of‐covariance model is derived and estimated, with the headcount, gap, and squared gap poverty ratios serving as the respective dependent variables, and the Gini coefficient and PPP‐adjusted incomes as explanatory variables. The study finds that the responsiveness of poverty to income growth is a decreasing function of inequality, albeit at varying rates for the three poverty measures: lowest for the headcount, followed by the gap and fastest for the squared gap. The ranges for the income elasticity in the sample are estimated at: 0.02–0.68, 0.11–1.05, and 0.10–1.35, respectively, for these poverty measures. Furthermore while, on average, the responsiveness of poverty to income growth appears to be the same between the rural and urban sectors, there are substantial sectoral differences across countries. The results suggest the need for country‐specific emphases on growth relative to inequality.     

收入流动性对收入不平等的影响

虽然收入流动性在收入分配研究领域正在逐渐升温,但收入流动性对收入不平等的影响这一关键问题的研究不足。文章推导了Gini系数在绝对收入流动性矩阵中对应的表达式,分析了收入流动性矩阵对不平等程度的作用途径。并利用1998年-2002年的收入面板数据验证了该理论分析。实证分析表明,由于向收入高低两端流动的力量增长较快并在势头上超过了同样增长的向中等收入水平流动的力量,整体的收入不平等程度恶化了。     

An Improved Test for Earnings Management Using Kernel Density Estimation

Abstract

This paper describes improvements on methods developed by Burgstahler and Dichev (1997, Earnings management to avoid earnings decreases and losses, Journal of Accounting and Economics, 24(1), pp. 99–126) and Bollen and Pool (2009, Do hedge fund managers misreport returns? Evidence from the pooled distribution, Journal of Finance, 64(5), pp. 2257–2288) to test for earnings management by identifying discontinuities in distributions of scaled earnings or earnings forecast errors. While existing methods use preselected bandwidths for kernel density estimation and histogram construction, the proposed test procedure addresses the key problem of bandwidth selection by using a bootstrap test to endogenise the selection step. The main advantage offered by the bootstrap procedure over prior methods is that it provides a reference distribution that cannot be globally distinguished from the empirical distribution rather than assuming a correct reference distribution. This procedure limits the researcher's degrees of freedom and offers a simple procedure to find and test a local discontinuity. I apply the bootstrap density estimation to earnings, earnings changes, and earnings forecast errors in US firms over the period 1976–2010. Significance levels found in earlier studies are greatly reduced, often to insignificant values. Discontinuities cannot be detected in analysts’ forecast errors, while such findings of discontinuities in earlier research can be explained by a simple rounding mechanism. Earnings data show a large drop in loss aversion after 2003 that cannot be detected in changes of earnings.     

Dilation bootstrap

We propose a methodology for combining several sources of model and data incompleteness and partial identification, which we call Composition Theorem. We apply this methodology to the construction of confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap methodology to deal with sampling uncertainty without reference to the hypothesized economic structure. It requires bootstrapping the quantile process for univariate data and a novel generalization of the latter to higher dimensions. Once the dilation is chosen to control the confidence level, the unknown true distribution of the observed data can be replaced by the known empirical distribution and confidence regions can then be obtained as in Galichon and Henry (2011) and Beresteanu et al. (2011).     

BOOTSTRAPPING A STABLE AD MODEL: WEAK VS STRONG EXOGENEITY*

Through Monte Carlo experiments the effects of a feedback mechanism on the accuracy in finite samples of ordinary and bootstrap inference procedures are examined in stable first- and second-order autoregressive distributed-lag models with non-stationary weakly exogenous regressors. The Monte Carlo is designed to mimic situations that are relevant when a weakly exogenous policy variable affects (and is affected by) the outcome of agents’ behaviour. In the parameterizations we consider, it is found that small-sample problems undermine ordinary first-order asymptotic inference procedures irrespective of the presence and importance of a feedback mechanism. We examine several residual-based bootstrap procedures, each of them designed to reduce one or several specific types of bootstrap approximation error. Surprisingly, the bootstrap procedure which only incorporates the conditional model overcomes the small sample problems reasonably well. Often (but not always) better results are obtained if the bootstrap also resamples the marginal model for the policymakers’ behaviour.     

Imputation of Missing Item Responses: Some Simple Techniques

Among the wide variety of procedures to handle missing data, imputingthe missing values is a popular strategy to deal with missing itemresponses. In this paper some simple and easily implemented imputationtechniques like item and person mean substitution, and somehot-deck procedures, are investigated. A simulation study was performed based on responses to items forming a scale to measure a latent trait ofthe respondents. The effects of different imputation procedures onthe estimation of the latent ability of the respondents wereinvestigated, as well as the effect on the estimation of Cronbach'salpha (indicating the reliability of the test) and Loevinger'sH-coefficient (indicating scalability). The results indicate thatprocedures which use the relationships between items perform best,although they tend to overestimate the scale quality.