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Licensed Unlicensed Requires Authentication Published by De Gruyter Oldenbourg June 2, 2017

Matching as Non-Parametric Preprocessing for the Estimation of Equivalence Scales

Christian Dudel, Jan Marvin Garbuszus, Notburga Ott and Martin Werding

Abstract:

Empirically analyzing household behavior usually relies on informal data preprocessing. That is, before an econometric model is estimated, observations are selected in such a way that the resulting subset of data is sufficiently homogeneous to be of interest for the specific research question pursued. In the context of estimating equivalence scales for household income, we use matching techniques and balance checking at this initial stage. This can be interpreted as a non-parametric approach to preprocessing data and as a way to formalize informal procedures. To illustrate this, we use German micro-data on household expenditure to estimate equivalence scales as a specific example. Our results show that matching leads to results which are more stable with respect to model specification and that this type of formal preprocessing is especially useful if one is mainly interested in results for specific subgroups, such as low-income households.

JEL Classification: C18; D10; D12

References

Abadie, A., G.W. Imbens (2008), On the Failure of the Bootstrap for Matching Estimators. Econometrica 76: 1537–1557.10.3386/t0325Search in Google Scholar

Abadie, A., G.W. Imbens (2011), Bias-Corrected Matching Estimators for Average Treatment Effects. Journal of Business and Economic Statistics 29: 1–11.10.1198/jbes.2009.07333Search in Google Scholar

Angrist, J.D., G.W. Imbens, D.B. Rubin (1996), Identification of Causal Effects using instrumental variables. Journal of the American Statistical Association 91: 444–455.10.3386/t0136Search in Google Scholar

Bargain, O., O. Donni, P. Kwenda (2014), Intrahousehold Distribution and Poverty: Evidence from Cote d’Ivoire. Journal of Development Economics 107: 262–276.10.1016/j.jdeveco.2013.12.008Search in Google Scholar

Bellemare, C., B. Melenberg, A. van Soest (2002), Semi-Parametric Models for Satisfaction with Income. Portuguese Economic Journal 1: 181–203.10.1007/s10258-002-0006-zSearch in Google Scholar

Blundell, R., M. Browning, I. Crawford (2003), Nonparametric Engel Curves and Revealed Preference. Econometrica 71: 205–240.10.1111/1468-0262.00394Search in Google Scholar

Browning, M., P.-A. Chiappori, A. Lewbel (2013), Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household argaining Power. Review of Economic Studies 80: 1267–1303.10.1093/restud/rdt019Search in Google Scholar

Caliendo, M. S. Kopeinig (2008), Some Practical Guidance for the Implementation of Propensity Score Matching. Journal of Economic Surveys 22: 31–71.10.1111/j.1467-6419.2007.00527.xSearch in Google Scholar

Coulter, F. A. E., F. A. Cowell, S. P. Jenkins (1992), Equivalence Scale Relativities and the Extent of Inequality and Poverty. Economic Journal 102: 1067–1082.10.2307/2234376Search in Google Scholar

Deaton, A., J. Muellbauer (1980), Economics and Consumer Behavior. Cambridge, MA, Cambridge University Press.10.1017/CBO9780511805653Search in Google Scholar

Deaton, A., J. Muellbauer (1986), On Measuring Child Costs: With Application to Poor Countries. Journal of Political Economy 94: 720–744.10.1086/261405Search in Google Scholar

Dettmann, E., C. Becker, C. Schmeißer (2011), Distance Functions for Matching in Small Samples. Computational Statistics and Data Analysis 55: 1942–1960.10.1016/j.csda.2010.11.022Search in Google Scholar

Donaldson, D., K. Pendakur (2004), Equivalent-Expenditure Functions and Expenditure-Dependent Equivalence Scales. Journal of Public Economics 88: 175–208.10.1016/S0047-2727(02)00134-2Search in Google Scholar

Dudel, C. (2014), A Nonparametric Partially Identified Estimator for Equivalence Scales. Ruhr Economic Papers 526.Search in Google Scholar

Dudel, C., J. M. Garbuszus, N. Ott, M. Werding (2013), Überprüfung der bestehenden und Entwicklung neuer Verteilungsschlüssel zur Ermittlung von Regelbedarfen auf Basis der Einkommens- und Verbrauchsstichprobe 2008. Research Report for the Federal Ministry of Labour and Social Affairs.Search in Google Scholar

Engel, E. (1857), Die Productions- und Consumptionsverhältnisse des Königsreichs Sachsen. Zeitschrift des Statistischen Bureaus des Königlich Sächsischen Ministeriums des Inneren 3: 8+9.Search in Google Scholar

Hagenaars, A., K. de Vos, M. Zaidi (1994), Poverty Statistics in the Late 1980s: Research Based on Micro-data. Luxembourg, Office for Official Publications of the European Communities.Search in Google Scholar

Heckman, J. J. (2008), Econometric Causality. International Statistical Review 76: 1–27.10.1111/j.1751-5823.2007.00024.xSearch in Google Scholar

Ho, D. E., K. Imai, G. King, E. A. Stuart (2007), Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal inference. Political Analysis 15: 199–236.10.1093/pan/mpl013Search in Google Scholar

Iacus, S.M., G. King, G. Porro (2011), Multivariate Matching Methods that are Monotonic Imbalance Bounding. Journal of the American Statistical Association 106: 345–361.10.1198/jasa.2011.tm09599Search in Google Scholar

Iacus, S.M., G. King, G. Porro (2012), Causal Inference Without Balance Checking: Coarsened Exact Matching. Political Analysis 20: 1–24.10.1093/pan/mpr013Search in Google Scholar

Imbens, G.W. (2004), Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review. Review of Economics and Statistics 86: 4–29.10.3386/t0294Search in Google Scholar

Imbens, G.W., J.M. Wooldridge (2009), Recent Developments in the Econometrics of Program Evaluation. Journal of Economic Literature 47: 5–86.10.3386/w14251Search in Google Scholar

Kapteyn, A., B. Van Praag (1975), A New Approach to the Construction of Family Equivalence Scales. European Economic Review 7: 313–335.10.1016/0014-2921(78)90009-0Search in Google Scholar

King, G., L. Zeng (2006), The Dangers of Extreme Counterfactuals. Political Analysis 14: 131–159.10.1093/pan/mpj004Search in Google Scholar

Koulovatianos, C., C. Schröder, U. Schmidt (2005), On the Income Dependence of Equivalence Scales. Journal of Public Economics 89: 967–996.10.1016/j.jpubeco.2004.09.005Search in Google Scholar

Lancaster, G., R. Ray (1998), Comparison of Alternative Models of Household Equivalence Scales: The Australian Evidence on Unit Record Data. Economic Record 74: 1–14.10.1111/j.1475-4932.1998.tb01899.xSearch in Google Scholar

Lechner, M. (2008), A Note on the Common Support Problem in Applied Evaluation Studies. Annales d’Économie et de Statistique 91/92: 217–235.10.2307/27917246Search in Google Scholar

Lelli, S. (2005), Using Functionings to Estimate Equivalence Scales. Review of Income and Wealth 51: 255–284.10.1111/j.1475-4991.2005.00154.xSearch in Google Scholar

Lise, J., S. Seitz (2011), Consumption Inequality and Intra-Household Allocations. Review of Economic Studies 78: 328–355.10.1093/restud/rdq003Search in Google Scholar

Morgan, S. L., D. J. Harding (2006), Matching Estimators of Causal Effects: Prospects and Pitfalls in Theory and Practice. Sociological Methods and Research 35: 3–60.10.1177/0049124106289164Search in Google Scholar

Nelson, J. A. (1988), Household Economies of Scale in Consumption: Theory and Evidence. Econometrica 56: 1301–1314.10.2307/1913099Search in Google Scholar

Pendakur, K. (1999), Semiparametric Estimates and Tests of Base-Independent Equivalence Scales. Journal of Econometrics 88: 1–40.10.1016/S0304-4076(98)00020-7Search in Google Scholar

Pollak, R. A., T. J. Wales (1978), Estimation of Complete Demand Systems from Household Budget Data: The Linear and Quadratic Expenditure Systems. American Economic Review 68: 348–359.Search in Google Scholar

R Core Team (2014), R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.Search in Google Scholar

Rosenbaum, P. R., D. B. Rubin (1983), The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika 70: 41–55.10.21236/ADA114514Search in Google Scholar

Rothbarth, E. (1943), Note on a Method of Determining Equivalent Income for Families of Different Composition. in: C. Madge (Ed.), War Time Pattern of Saving and Spending. Cambridge, Cambridge University Press. pp. 123–130.Search in Google Scholar

Rubin, D. B. (1973), The Use of Matched Sampling and Regression Adjustment to Remove Bias in Observational Studies. Biometrics 29: 185–203.10.1017/CBO9780511810725.008Search in Google Scholar

Rubin, D. B. (1979), Using Multivariate Matched Sampling and Regression Adjustment to Control Bias in Observational Studies. Journal of the American Statistical Association 74: 318–328.10.1017/CBO9780511810725.013Search in Google Scholar

Rubin, D. B., N. Thomas (2000), Combining Propensity Score Matching with Additional Adjustments for Prognostic Covariates. Journal of the American Statistical Association 95: 573–585.10.1080/01621459.2000.10474233Search in Google Scholar

Schröder, C. (2009), Variable Income Equivalence Scales: An Empirical Approach. New York, Springer.Search in Google Scholar

Sekhon, J. S. (2011), Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching Package for r. Journal of Statistical Software 42: 1–52.10.18637/jss.v042.i07Search in Google Scholar

Statistisches Bundesamt (2012), Einkommens- und Verbrauchsstichprobe 2008. Wiesbaden, Qualitätsbericht.Search in Google Scholar

Szulc, A. (2009), A Matching Estimator of Household Equivalence Scales. Economics Letters 103: 81–83.10.1016/j.econlet.2009.01.027Search in Google Scholar

Szulc, A. (2014), Empirical Versus Policy Equivalence Scales: Matching Estimation. Bank i Kredyt 45: 37–52.Search in Google Scholar

Received: 2016-8-8
Revised: 2017-2-13
Accepted: 2017-5-9
Published Online: 2017-6-2
Published in Print: 2017-6-27

© 2017 Oldenbourg Wissenschaftsverlag GmbH, Published by De Gruyter Oldenbourg, Berlin/Boston