Abstract
The collective household model is based upon the assumption that decision makers have achieved efficient outcomes. This paradigm, which has become one of the leading approaches in family economics, is seldom, if ever, rejected, raising doubt about its falsifiability. We show that the standard approach to test the collective model may yield misleading inferences. We develop a new test procedure to assess its validity. Our approach extends to households that potentially include more than two decision makers. We provide an informal meta-analysis that suggests that much of the evidence in favor of collective rationality in the empirical literature appears to be inconsistent with our test. We illustrate the latter using data from a survey we have conducted in Burkina Faso. Consumption efficiency within monogamous households is not rejected using the standard testing procedure while it is clearly rejected using our proposed test procedure. Furthermore, our test also rejects consumption efficiency for bigamous households. We conclude that intra-household efficiency does yield empirically falsifiable restrictions despite being scarcely rejected in the literature.
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Notes
Distribution factors are variables, such as the state of the marriage markets, that influence the decision process within the household but neither individual preferences nor the household budget set.
See the first sentence of their Proposition 2.
A distribution factor cannot influence a single demand since, by definition, it cannot affect the household budget constraint.
In a somewhat complementary paper, Udry (1996) investigated production outcomes of rural Burkina Faso households and strongly rejected efficiency. Our analysis of household efficiency in consumption can be interpreted as conditional on the household production choices.
Strictly speaking, testing the joint “all or nothing” hypothesis would require knowledge of the covariance between different parameter estimates. Since we do not have this information, and since we do dot compare the studies between themselves, we will refer to our discussion as an informal meta-analysis.
Note that Dauphin et al. (2011) investigate the efficiency of households comprising three potential decision-makers (couples with an adult child) using price-based statistical tests.
This assumes that the household does not produce any of these N goods, or that the goods produced within the household can be freely sold and purchased on the market.
This notation is used to simplify the presentation. Note that if a good is purely private to member i, then the marginal utility of the other members for that good will simply be zero.
Henceforth, we will omit m from the argument to simplify the notation.
When N ≤ 2 or K = 1, collective rationality imposes no restrictions on the demand system.
An earlier extension of Proposition 2.ii of BBC2009 to multiple decision makers can also be found in Dauphin and Fortin (2001).
When N ≤ I + 1 or K < I + 1, collective rationality imposes no restrictions on the demand.
In the case where each Pareto weight depends on all distribution factors, one has \({\bf{z}}_L^* = {{\bf{z}}_{ - J}}\).
Note that just as for Proposition 2, Proposition 3 does not require any of the distribution factors to affect all the demands.
This analysis is based on point hypothesis testing, that is, on inspection of the marginal p-values of various estimates of \({D_{\bf{z}}}{x_n}\left( {\bf{z}} \right),\forall n = 1, \ldots ,N.\) Of course, as noted earlier, to . test the “all or nothing” joint hypothesis would require information on the covariance between the various coefficient estimates, which is unavailable. However, in papers where one distribution factor is random (e.g., generated from a randomized experiment), the covariance between the two distribution factors is likely to be close to zero.
Rookhuizen (1986), p. 59, free translation.
Lallemand (1977), p. 263, free translation.
Consequently, we implicitly ignore the whole area of the household decisions that concern time allocation, and in particular leisure choices. Note that the original formulation of the collective model did the exact opposite (see Apps and Rees 1988; Chiappori 1988): It focused on household labor supply but omitted the allocation of consumption goods, thanks to the Hicksian composite-good theorem. In that framework, wage rates were the main distribution factors.
According to the National 2006 Census.
An alternative approach would be to implement a joint hypothesis test. The latter would lead to the same decision rule as long as the covariance between the estimates of our two distribution factors is negligible. Otherwise, a more complex test must be implemented.
As long as the covariance between the estimates of our two distribution factors can be neglected
Portier and Delyon (2014) developed a so-called constrained bootstrap method which allows to compute the bootstrap distribution of three distinct rank-test statistics proposed in the literature under the null hypothesis that the rank of the matrix is of a given size. Among the three available statistics, we have chosen that of Li (1991) since the consistency of its associated constrained bootstrap test relies on less stringent conditions than the other two. The Li (1991) statistics is the following:
\({\hat {\rm \Lambda }} = n\mathop {\sum}\nolimits_{p = m + 1}^P {{{\hat \lambda }_p}} ,\)
where \(n\) is the sample size, \(\left( {{{\hat \lambda }_1}, \ldots ,{{\hat \lambda }_P}} \right)\) are the singular values of the matrix \({D_{\bf{z}}}{\bf{x}}({\bf{z}})\)arranged in descending order and m > 0 is the assumed rank of D z x(z). The null assumption is \({H_0}:rank\left[ {{D_{\bf{z}}}{\bf{x}}\left( {\bf{z}} \right)} \right] = m\) against \({H_1}:rank\left[ {{D_{\bf{z}}}{\bf{x}}\left( {\bf{z}} \right)} \right] >m\). Since this procedure cannot test whether \({H_0}:rank[{D_{\bf{z}}}{\bf{x}}({\bf{z}})] = 0\), we begin with an F test that all the distribution factors are simultaneously statistically significant in all the demand functions. If rejected, the next step is to test \({H_0}:rank[{D_{\bf{z}}}{\bf{x}}({\bf{z}})] = 1\) with a constrained bootstrap test of \({\hat {\rm \Lambda}}\), and so on until the maximum rank of \({D_{\bf{z}}}{\bf{x}}\left( {\bf{z}} \right)\) (i.e., I) is reached.
Few, if any, papers ever report tests of weak instruments in the empirical literature. For instance, no paper in Table 1 using a z-conditional demands approach reports such tests.
We acknowledge that the approach we use may raise questions about the presence of a pretest bias, as the choice of which demand to invert depends on the statistical significance of the estimated coefficients. Note that this issue is present in all the studies that use the z-conditional demand condition approach.
References
Apps, P. F., & Rees, R. (1988). Taxation and the household. Journal of Public Economics, 35(3), 355–369.
Attanasio, O., & Lechene, V. (2014). Efficient responses to targeted cash transfers. Journal of Political Economy, 122(1), 178–222.
Bayudan, C. (2006). Wives’ time allocation and intrahousehold power: Evidence from the Philippines. Applied Economics, 38, 789–804.
Becker, G. (1973). A theory of marriage: Part I. Journal of Political Economy, 81, 813–846.
Becker, G. (1974). A theory of social interactions. Journal of Political Economy, 82, 1063–1093.
Becker, G. (1981) A treatise on the family. Cambridge, MA: Harvard University Press.
Bobonis, G. (2009). Is the allocation of resources within the household efficient? New evidence from a randomized experiment. Journal of Political Economy, 117(3), 453–503.
Bourguignon, F., Browning, M., & Chiappori, P.-A. (2009). Efficient intra-household allocations and distributions factors: Implications and identification. Review of Economic Studies, 76, 503–528.
Bourguignon, F., Browning, M., Chiappori, P.-A., & Lechene, V. (1993). Intra--household allocation of consumption: A model and some evidence from French data. Annales d'Économie et de Statistique, 29, 137–156.
Browning, M., & Chiappori, P.-A. (1998). Efficient intra-household allocations: A general characterization and empirical tests. Econometrica, 66(6), 1241–1278.
Browning, M., Bourguignon, F., Chiappori, P.-A., & Lechene, V. (1994). Income and outcomes: A structural model of intrahousehold allocation. Journal of Political Economy, 102(6), 1067–1096.
Browning, M., Chiappori P.-A., & Weiss Y. (2014) Economics of the family. Cambridge: Cambridge University Press.
Camba-Mendeza, G., & Kapetanios, G. (2009). Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling. Econometric Reviews, 28, 581–611.
Chen, Z., & Woolley, F. (2001). A Cournot-Nash model of family decision making. Economic Journal, 111(474), 722–748.
Chiappori, P.-A., & Ekeland, I. (2006). The microeconomics of group behavior: General characterization. Journal of Economic Theory, 130(1), 1–26.
Chiappori, P.-A., Fortin, B., & Lacroix, G. (2002). Marriage market, divorce legislation and household labor supply. Journal of Political Economy, 110(1), 37–72.
Chiappori, P.-A. (1988) Rational household labor supply. Econometrica: Journal of the Econometric Society 56, 63–90
Dagenais, M., & Dufour, J.-M. (1991). Invariance, nonlinear models, and asymptotic tests. Econometrica, 59(505), 1601–1615.
Dauphin, A., El Lhaga, A., Fortin, B., & Lacroix, G. (2011). Are children decision-makers within the household ? Economic Journal, 121, 871–903.
Dauphin, A., & Fortin, B. (2001). A test of collective rationality for multi-person households. Economics Letters, 71(2), 211–216.
Gray, J. S. (1998). Divorce-law changes, household bargaining, and married women’s labor supply. American Economic Review, 88, 628–642.
Grossbard, A. (1976). An economic analysis of polygyny: The case of maiduguri.Current Anthropology 17, 701–707.
Grossbard-Shechtman, A. (1984). A theory of allocation of time in markets for labor and marriage. Economic Journal, 94, 863–882.
Haddad, L., & Kanbur, R. (1992). Intra-Household Inequality and the Theory of Targetting. European Economic Review, 36, 372–378.
INSD (2010) Enquête démographique et de santé à indicateurs multiples. Institut national de la statistique et de la démographie, Burkina Faso.
Lallemand, S. (1977). Une famille Mossi. Paris, Ouaguadougou: Recherche Voltaque. C.N.R.S.-C.V.R.S.
Lechene, V., & Preston, I. (2011). Noncooperative household demand.. Journal of Economic Theory, 146(2), 504–527.
Li, K.-C. (1991). Sliced inverse regression for dimension reduction. Journal of the American Statistical Association, 86, 316–342.
Lundberg, S., & Pollak, R. A. (1993). Separate spheres bargaining and the marriage market. Journal of Political Economy, 101(6), 988–1010.
Manser, M., & Brown, M. (1980). Marriage and household decision making: A bargaining analysis. International Economic Review, 21, 31–44.
McElroy, M. B. (1990). The empirical content of nash-bargained household behavior. Journal of Human Resources, 25(4), 559–583.
Montiel, O., & Pflueger, C. (2013). A robust test for weak instruments. Journal of Business and Economic Statistics, 31(3), 358–369.
Naidoo, J. (2015) The Power of Tests for Pareto Efficiency Within the Family. Mimeo, Department of Economics, University of Chicago.
Portier, F., & Delyon, B. (2014). Bootstrap testing of the rank of a matrix via least-squared constrained estimation. Journal of the American Statistical Association, 109(505), 160–172.
Quisumbing, A. R., & Maluccio, J. A. (2003). Resources at marriage and intrahousehold allocation: evidence from Bangladesh Ethiopia, Indonesia, and South Africa. Oxford Bulletin of Economics and Statistics, 65(3), 283–327.
Rookhuizen, M. (1986). Femmes de Rana: les besoins et possibilités des femmes d’un village Mossi au Burkina Faso. Femmes et développement, Burkina Faso.
Staiger, D., & Stock, J. H. (1997). Instrumental variables regression with weak instruments. Econometrica, 65(3), 557–586.
Stock, J., & Yogo, M. (2005). Testing for weak instruments in iinear IV regression. In D. W. K. Andrews (Ed.). Identification and Inference for Econometric Models (pp. 80–108). New York, NY: Cambridge University Press.
Thomas, D., & Chen C. L. (1994). Income shares and shares of income: empirical tests of models of household resource allocations. RAND Labor and Population Program Working Paper Series, 94–08.
Thomas, D., Contreras D., & Frankenberg E. (1999). Distribution of power within the household and child health. UCLA, mimeo, Economics Department, University of California Los Angeles.
Udry, C. (1996). Gender, agriculture production, and the theory of the household. Journal of Political Economy, 104(5), 1011–1046.
UNDP (2014). Human development report. United Nations, New York.
Vermeulen, F. (2005). And the winner is… An empirical evaluation of unitary and collective labour supply models. Empirical Economics, 30, 711–734.
Acknowledgment
We thank two anonymous referees for their valuable comments which helped improve the paper. We are grateful to Pierre-André Chiappori, Jesse Naidoo, Idrissa Diagne, Marion Goussé, Olivier Donni, Nicolas jacquemet, Carolin Pflueger, and François Portier, as well as numerous seminar participants for useful discussions and comments.
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Dauphin, A., Fortin, B. & Lacroix, G. Is consumption efficiency within households falsifiable?. Rev Econ Household 16, 737–766 (2018). https://doi.org/10.1007/s11150-016-9359-4
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DOI: https://doi.org/10.1007/s11150-016-9359-4