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A Simple Method for Predicting Distributions by Means of Covariates with Examples from Poverty and Health Economics
Swiss Journal of Economics and Statistics volume 152, pages49–80(2016)
We present an integration based procedure for predicting the distribution f of an indicator of interest in situations where, in addition to the sample data, one has access to covariates that are available for the entire population. The proposed method, based on similar ideas that have been used in the literature on policy evaluation, provides an alternative to existing simulation and imputation methods. It is very simple to apply, flexible, requires no additional assumptions, and does not involve the inclusion of artificial random terms. It therefore yields reproducible estimates and allows for valid inference. It also provides a tool for future predictions, scenarios and ex-ante impact evaluation. We illustrate our procedure by predicting income distributions in a case with sample selection, and both current and future doctor visits. We find our approach outperforms other commonly used procedures substantially.
Atkinson, Anthony B., and François Bourguignon (2000), Handbook of Income Distribution, Amsterdam: North-Holland.
Azzarri, Carlo, Gero Carletto, Benjamin Davis, and Alberto Zezza (2006), “Monitoring Poverty without Consumption Data”, Eastern European Economics 44(1), pp. 59–82.
Berzel, Andreas, Gillian Z. Heller, and Walter Zucchini (2006), “Estimating the Number of Visits to the Doctor”, Australian & New Zealand Journal of Statistics 48, pp. 213–224.
Biewen, Martin, and Stephen P. Jenkins (2005), “A Framework for the Decomposition of Poverty Defferences with an Application to Poverty Defferences Between countries”, Empirical Economics 30, pp. 331–358.
Birkin, Mark, and Martin Clarke (1989), “The Generation of Individual and Household Incomes at the Small Area Level Using Synthesis”, Regional Studies 23(6), pp. 535–548.
Chaudhuri, Shubham, Jyotsna Jalan, and Asep Suryahadi (2002), “Assessing Household Vulnerability to Poverty from Cross-Sectional Data: A Methodology and Estimates from Indonesia”, Discussion Paper Series, Department of Economics, Columbia University.
Chernozhukov, Victor, Iván Fernández-Val, and Blaise Melly (2013), “Inference on Counterfactual Distributions”, Econometrica 81(6), pp. 2205–
Chotikapanich, Duangkamon (2008), Modeling Income Distributions and Lorenz Curves, Series: Economic Studies in Inequality, Social Exclusion and Well-Being 5, Springer.
Davis, Benjamin (2003), Choosing a Method for Poverty Mapping, Food and Agriculture Organization of the United Nations, Rome, www.fao.org/docrep/005/y4597e/y4597e00.htm.
DiNardo, Jone, Nicole M. Fortin, and Thomas Lemieux (1996), “Labor Market Institutions and the Distribution of Wages, 1973–1992: A Semiparametric Approach”, Econometrica 65, pp. 1001–1046.
Donald, Stephen G., Yu-Chin Hsu, and Garry F. Barrett (2012), “Incorporating Covariates in the Measurement of Welfare and Inequality: Methods and Applications”, Econometrics Journal 15, pp. C1–C30.
Elbers, Chris, Jean O. Lanjouw, and Peter Lanjouw (2003), “Micro-Level Estimation of Poverty and Inequality”, Econometrica 71(1), pp. 355–364.
Filmer, Deon, and Lant H. Pritchett (2001), “Estimating Wealth Effects without Expenditure Data — Or Tears: An Application to Educational Enrollments in States of India”, Demography 38(1), pp. 115–132.
Gasparini, Leonardo, Martín Cicowiez, Federico Gutierrez, and Mariana Marchionni (2003), “Simulating Income Distribution Changes in Bolivia: A Microeconometric Approach”, The World Bank Bolivia Poverty Assessme
González-Manteiga, Wenceslao, and Rosa M. Crujeiras (2013), “An Updated Review of Goodness-of-Fit Tests for Regression Models”, Test 22(3), pp. 361–411.
Härdle, Wolfgang, Sylvie Huet, Enno Mammen, and Stefan Sperlich (2004), “Bootstrap Inference in Semiparametric Generalized Additive Models”, Econometric Theory 20, pp. 265–300.
Heller, Gillian Z. (1997), “Who Visits the GP? Demographic Patterns in a Sydney Suburb”, Technical report, Department of Statistics, Macquarie University.
Hentschel, Jesco, Jean Olson Lanjouw, Peter Lanjouw, and Javier Poggi (2000), “Combining Census and Survey Data to Trace the Spatial Dimensions of Poverty: A Case Study of Ecuador”, World Bank Economic Review 14(1), pp. 147–165.
Horton, Nicholas J., and Stuart R. Lipsitz (2001), “Multiple Imputation in Practice: Comparison of Software Packages for Regression Models with Missing Variables”, The American Statistician 55(3), pp. 244–254.
Juhn, Chinhui, Kevin M. Murphy, and Brooks Pierce (1993), “Wage Inequality and the Rise in Returns to Skill”, The Journal of Political Economy 101(3), pp. 410–442.
Little, Roderick J. A., and Donald B. Rubin (2002), Statistical Analysis with Missing Data (Second Edition), John Wiley, New York.
Lombardía, María J., and Stefan Sperlich (2008), “Semiparametric Inference in Generalized Mixed Effects Models”, Journal of Royal Statistical Society: Series B 70(5), pp. 913–930.
McLachlan, Geoffrey, and David Peel (2000), Finite Mixture Models, Wiley Series in Probability and Statistics.
MELLY, BLAISE (2005), “Decomposition of Differences in Distribution Using Quantile Regression”, Labour Economics 12(4), pp. 577–590
MISHRA, SATISH C. (2009), “Economic Inequality in Indonesia: Trends, Causes, and Policy Response”, Strategic Asia, commissioned by UNDP Regional Office, Colombo.
Noufaily, Angela, and M. C. Jones (2013), “Parametric Quantile Regression Based on the Generalized Gamma Distribution”, Journal of the Royal Statistical Society, Series C, Applied Statistics 62(5), pp. 723–740.
Paulin, Geoffrey D., and David L. Ferraro (1994), “Imputing Income in the Consumer Expenditure Survey”, Monthly Labor Review 117(12), pp. 23–31.
Politis, Dimitris N., Joseph P. Romano, and Michael Wolf (1999), Subsampling, Springer, New York.
Ravallion, Martin (2001), “Growth, Inequality and Poverty: Looking Beyond Averages”, World Development 29(11), pp. 1803–1815.
Rigby, R. A., and Stasinopoulos, D. M. (2005), “Generalized Additive Models for Location, Scale and Shape”, Applied Statistics 54, pp. 507–554.
Rothe, Christoph (2010), “Nonparametric Estimation of Distributional Policy Effects”, Journal of Econometrics 155, pp. 5670.
Royston, Patrick (2004), “Multiple Imputation of Missing Values”, The Stata Journal 4(3), pp. 227–241.
Sahn, David E., and David C. Stifel (2000), “Poverty Comparison Over Time and Across Countries in Africa”, World Development 28(12), pp. 2123–
Sperlich, Stefan, Oliver B. Linton, and Wolfgang Härdle (1999), “Integration and Backfitting Methods in Additive Models — Finite Sample Properties and Comparison”, Test 8, pp. 419–458.
Sperlich, Stefan (2014), “On the Choice of Regularization Parameters in Specification Testing: a critical discussion”, Empirical Economics 47, pp. 427–450.
Stock, sc James H. (1989), “Nonparametric Policy Analysis”, Journal of the American Statistical Association 84(406), pp. 567–575.
Su, Yu-Sung, Andrew Gelman, Jennifer Hill, and Masanao Yajima (2011),“Multiple Imputation with Diagnostics (mi) in R: Opening Windows into the Black Box”, Journal of Statistical Software 45(2), pp. 1–31.
Tarozzi, Alessandro, and Angus Deaton (2009), “Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas”, Review of Economics and Statistics 91(4), pp. 773–792.
Van Kerm, Philippe (2013). “Generalized Measures of Wage Differences”, Empirical Economics 45(1), pp. 465–482.
Yee, T. W., and C. J. Wild (1996), “Vector Generalized Additive Models”, Journal of Royal Statistical Society, Series B, Methodological 58, pp. 481–493.
Zeller, Manfred, Julia Johannsen, and Gabriela Alcaraz V. (2005), “Developing and Testing Poverty Assessment Tools: Results from Accuracy Test in Peru”, College Park, IRIS Center, University of Maryland.
We thank the editors and an anonymous referee for helpful discussion and comments. We also appreciated the discussions with the participants of the Annual meetings of the German Statistical Society 2010, and of the Swiss Statistical Society in 2011.
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Dai, J., Sperlich, S. & Zucchini, W. A Simple Method for Predicting Distributions by Means of Covariates with Examples from Poverty and Health Economics. Swiss J Economics Statistics 152, 49–80 (2016). https://doi.org/10.1007/BF03399422
- predicting distributions
- missing values
- household expenditures
- income distribution
- health economics
- impact evaluation