Abstract
This article uses time-use and household expenditure data to measure the substitutability between time and money within the Beckerian household production framework. The elasticity of substitution is estimated for five commodity groups and across two developing countries: Ecuador and Guatemala. The estimated elasticities are positive, indicating substitutability, and much larger for all other goods compared to food. Our results raise some interesting questions regarding the policy effects of an intervention that does not consider the money/time trade-offs in consumption.
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Notes
Note that the general Becker model will collapse to a single budget constraint if all time decisions are choice variables (e.g. importantly labour) and time at work and time at home are completely fungible. Furthermore, the empirical approach to the household production function requires the household’s technology to exhibit constant returns and no joint production; otherwise, implicit commodity prices depend on the household’s preferences as well as on its technology and on the prices of market goods (Pollak and Wachter 1975).
As pointed out by one of the referees, output is not assumed constant in the strict sense of the word in this case. When we take the ratio of inputs via Shepard’s Lemma, output cancels out due to the multiplicative form of the cost function for homothetic technologies.
An earlier version of this paper provides an estimate of the opportunity cost derived from a structural model of domestic production. It’s mean is around one half of the household’s average wage rate and it is positively correlated with it. The resulting elasticities of substitution using this estimate of the opportunity cost instead of the wage rate are roughly in the same range as those reported in this paper.
The imputation procedure is detailed in the Appendix.
Estimates drawn from the ENCOVI surveys place the indigenous population at 37 per cent in 2006. The indigenous population in Ecuador has been estimated at 7 per cent in 2010 according to the official statistics (INEC).
Note that ‘Eating’ time for Guatemala does not include the time a person takes to eat.
Refer to Canelas and Salazar (2014) for further discussion and information on these statistics.
Canelas and Gisselquist (2018) show that in spite of a broad trend towards greater equality, horizontal inequalities in educational and labour market outcomes between indigenous and non-indigenous groups in Guatemala are persistent. In particular, all indigenous ethnic groups experience earning gaps with respect to ladinos (non-indigenous) at the mean and across the earnings distribution.
See Canelas et al. (2014) for calculations of income elasticities for these commodities and the classification of necessity and luxury goods.
See Canelas et al. (2014) for results concerning the price and income elasticities of these goods.
Note that while in developing countries payment in-kind is common, i.e. labour can be used to pay for food or as a form of rental payment, in our samples this is rather marginal.
An earlier version of this paper provides similar estimations for the eating commodity in Canada and France.
See Alpman and Gardes (2015) for an analysis of the great recession in the US.
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Acknowledgements
We thank the editor and the two reviewers. Their comments and suggestions were extremely useful and constructive helping us to considerably improve the quality of our paper. Gardes and Merrigan thank Fonds de recherche société culture - Québec, FRQSC, for their financial support
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Appendix
Appendix
Appendix 1. Statistical matching Ecuadorian data
Because the dataset on expenditures does not include any information on time use variables in Ecuador, we use statistical matching to impute time use for households in the expenditure survey. For this, we use two different samples (ENEMDU and ECV) drawn from the same population and that follow the same sampling process.
The statistical matching between the surveys was done by a tobit regression of the time use for each activity on a common set of socio-economic characteristics of households which are present in both surveys. The set of variables includes: age of the individual, annual household income, household size, a dummy variable equal to one if the spouse works, and dummy variables for 10 geographical regions.
Because the imputation procedure is done on individuals and not households, we choose in the expenditure survey males and females who are in households corresponding to our selection criteria in the Time-Use survey and perform separate regressions of time use on household characteristics available in both datasets.
The regression coefficient estimates of the time surveys are used to predict time use for different activities corresponding to the consumption of different goods in the expenditure survey. The aggregated time use for the household is obtained by adding up the predicted time use for the male and female adults in the household.
Appendix 2. Wage regression
To account for the endogeneity of wages and the selection of women and men into the labour market, we follow the standard procedure in the literature and use the Heckman two-step slection procedure to predict wages and use these predicted wages in Eq. (1).
The probit model for labour force participation is estimated separately for men and women controlling for the presence of children aged 5 years old or less, marital status, age, age squared, educational level, ethnic group, and area of residence. Identification of the sample selection wage equation is achieved by way of exclusion restrictions in the wage equation (i.e. we exclude from the wage equation the presence of children aged 5 years old or less and the marital status of the individual).
We then estimate the wage equation, regressing the log of real weekly earnings on the same set of explanatory variables listed above plus the inverse Mills ratio while applying the exclusion restrictions. The predicted log wage obtained from the wage equation is then used to estimate the EOS in Equation 1.
Appendix 3. Tables
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Canelas, C., Gardes, F., Merrigan, P. et al. Are time and money equally substitutable for all commodity groups in the household’s domestic production?. Rev Econ Household 17, 267–285 (2019). https://doi.org/10.1007/s11150-018-9425-1
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DOI: https://doi.org/10.1007/s11150-018-9425-1