Is the basic life-cycle theory of consumption becoming more relevant? Evidence from Portugal

Abstract

In this paper we report and discuss estimates of life-cycle consumption profiles obtained using microdata for Portuguese households. The estimated profiles are much flatter than the profiles usually reported in the literature for other countries, namely the Netherlands, the UK and the USA. In addition, we also report estimates of cohort and business cycle effects on consumption. The estimated cohort effects are consistent with the post-war progress in median standards of living. However, there is a deceleration in the trend of consumption growth for more recent cohorts. The business cycle estimates suggest that the recent debt crisis has had a strong negative impact on household consumption.

Appendices

Appendix 1: Classification of household expenditures

In this paper we follow the approach of Fernández-Villaverde and Krueger (2007) in dividing total expenditure among five categories: nondurables, durables, health, clothing and footwear, and education. For the last three categories we used the corresponding categories in the Portuguese Household Budget Survey (IDEF). We then classified the remaining categories in IDEF as either durable or nondurable expenditure. Our classification is presented in Table 4.

Table 4 IDEF—expenditure category codes

However, as a result of differences in the classification of household expenditures, comparison of our results with results presented in other papers in the literature is not straightforward. While the IDEF uses the United Nations’ Classification of Individual Consumption According to Purpose (COICOP), the Consumer Expenditure Survey (CEX) data used by Fernández-Villaverde and Krueger (2007) does not. Passero et al. (2014) provide a thorough discussion of the relationship between these data and the ‘Personal consumption expenditures’ (PCE) data, released by the US Bureau of Economic Analysis, which is based on the COICOP. Their discussion is helpful for understanding the problems arising when comparing studies that use different classifications of expenditures.

The major difference between our categories and those in Fernández-Villaverde and Krueger (2007) concerns Education. In IDEF this category includes only fees (tuition and administrative). Other education related expenditures are considered to be part of other categories. Most notably, books are part of recreation and culture expenditures, while school transportation is part of transport services. In CEX, these expenditures (and others such as “Food or board while attending school”) are included in the Education category.

In Fernández-Villaverde and Krueger (2007) expenditures on durables include owned dwelling, rented dwelling, house equipment, vehicles, books and electronic equipment. Our measure expands on this by including insurances connected with dwelling. Note that according to Passero et al. (2014, p. 192), the PCE (COICOP) measures of insurance do not match those in CEX. Likewise, our classification of expenditure on nondurables includes, for example, social protection, travel insurance, other insurance or financial services, but the COICOP definition of these items also does not match that in CEX.

IDEF includes the major components of health expenditure, as the CEX does. However, a significant part of the Portuguese population has access to the National Health Service for free. Over time, free access has been restricted, which may help explain the decreasing frequency of zero values in the sample—see Table 1.

Appendix 2: Imputation of age

Our IDEF dataset only contains the age of the household’s reference person for the 2010 survey. For the other surveys, we know the age class of the reference person. In the cases of the 2000 and 2015 surveys, the age classes are five years long, from [25;29] until [70;74]. In the case of the 2005 survey, the age classes are [25;29], [30;44], [45;64] and [65;74]. Therefore, we used two versions of the multinomial logit model for imputing the age, one for the 2000 and 2015 surveys, the other for the 2005 survey.

The multinomial logit model assumes that, given $J$ possible values (${V}_{j}$) for the outcome variable ${Y}_{i}$ (the value taken for individual $i$), the probability of observing alternative $j$ is given by:

$$P({Y}_{i}\,=\,{V}_{j}\vert {\bf{x}}_{i})\,=\,\frac{\exp ({\bf{x}}_{i}^{\prime}{\boldsymbol{\beta}}_{j})}{{\sum \limits_{k\,=\,1}^{J}}\exp ({\bf{x}}_{i}^{\prime}{\boldsymbol{\beta}}_{k})}$$

(4)

where ${{\bf{x}}}_{i}$ is a vector of characteristics of individual $i$ and ${{\boldsymbol{\beta }}}_{j}$ ($j\,=\,1,\ldots ,J$) is the matching vector of coefficients corresponding to alternative $j$. To identify the coefficients, a normalization restriction, such as ${{\boldsymbol{\beta }}}_{J}\,=\,{\bf{0}}$, is required.

To impute the age, we estimated the model represented by Eq. (4) using the observations of the 2010 survey for each five-year age class. In other words, we estimated the model 10 times, one for each subset (corresponding to one of the age classes) of the 2010 survey. The ${Y}_{i}$ variable is the age of the reference person. The possible values are the ages in the corresponding age class (e.g. in the case of the [25;29] age class these are the values 25, 26, 27, 28 and 29). We used the resulting estimates of the ${{\boldsymbol{\beta }}}_{j}$’s to impute the ages of the reference persons in the 2000 and 2015 surveys. For the 2005 survey we had to estimate the model for each subset of the 2010 data corresponding to one of the age classes reported in the 2005 survey: [25;29], [30;44], [45;64] and [65;74]. The explanatory variables (${{\bf{x}}}_{i}$) were the same in all cases and their choice was limited by the data available in IDEF: the gender of the reference person, whether the reference person has a partner, the number of ancestors in the household, the number of descendents in the household, the level of education of the reference person, the NUTS 2 region where the household resides, the work status of the reference person and the share of each category of expenditure in total expenditure.

The age imputed to each household was the age to which the model assigned the highest probability. Does our result on the flatness of the life-cycle consumption profile depend on this choice? To answer this question we constructed 500 alternative age samples. Each age sample was obtained by randomly drawing an age for each individual from the distribution implied for that individual by the estimated model. We re-estimated the consumption profile using each of these 500 age samples instead of the maximum-probability age. Then, for each of the newly estimated 500 consumption profiles, we computed the percent difference between maximum total expenditure across the life cycle and total expenditure at age 25. Table 5 presents the results. The maximum relative variation was always under 20%. It was below 14% for 81% of the simulated age samples. Using the maximum-probability age, in Section 4.1 we reported this change to be 13%. Therefore, our conclusion regarding the flatness of the consumption profile appears to be robust to the imputed age.

Table 5 Distribution of the maximum increase in total expenditure