Fundación de Estudios de Economía Aplicada

Expenditures at retirement by Spanish households by José M. Labeaga^** *** Rubén Osuna DOCUMENTO DE TRABAJO 2007-36 Serie Nuevos Consumidores CÁTEDRA Fedea - BBVA

November 2007

* We are grateful to Sergi Jiménez-Martín and María Navarro for several useful comments. We also acknowledge funding from project SEJ2005-08783-C04-04. ** Department of Economic Analysis, UNED and FEDEA. jmlabeaga@fedea.es *** Department of Economic Analysis, UNED. Paseo Senda del Rey 11. 28040 Madrid. Voice +34 91 398 78 19. Fax +34 91 398 87 68. rosuna@uned.cee.es

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Abstract

The life cycle theory predicts the smoothing of consumption over time by forward-looking agents with concave utility functions. However, many empirical studies have shown a significant drop in expenditures after retirement in US, Italy, Germany, UK, Spain and other countries. This contradicts the main result of the life cycle model, and this gap between theory and reality is known as the retirement consumption puzzle since the seminal paper by Banks, Blundell and Tunner (1998). In this study, we analyze the impact of retirement on income and a breakdown of expenditures by estimating complete demand systems and single equations using an unbalanced panel of Spanish households. Although in terms of the non-durable expenditures modelled we observe the puzzle, the categories related to a decrease in consumption are only those subsidized for retirees (health expenditures and public transport).

Key words: consumption puzzle, life cycle, panel data JEL Class.: C33, D12, J26.

1. Introduction

The retirement-savings or retirement-consumption puzzle has been analyzed in several studies. The life cycle theory predicts the smoothing of consumption over time by forward-looking agents with concave utility functions (Modigliani and Brumberg, 1954). Whether the retirement and death dates are known, there are no bequest motives and capital markets are perfect, the model explains the consumption patterns by the variables ‘rate of interest’ (r) and ‘rate of time preference’ . If consumption will increase with age, and if the contrary will be the case. No drastic drops are compatible with the model since rational agents choose to smooth consumption as to keep marginal utility constant over time. The original life cycle model can be expanded to consider bequest motives or to include some consequences of uncertainty (about the date of death, for instance) or risk aversion on individual decisions (Levhari-Mirman, 1977). When retirement is expected, consumption should not be affected even if income drops.

However, many empirical studies have shown a significant drop in expenditures after retirement in US, UK, Italy, Germany, Spain and other countries (see, for instance, Hamermesh, 1984; Bernheim, Skinner, and Weinberg 2001; Haider and Stephens, 2007; Banks, Blundell and Tanner, 1998; Miniaci, Monfardini and Weber, 2003; or Lührmann, 2006). This contradicts the main result of the life cycle model, and the gap between theory and reality is known as the retirement consumption puzzle. Several hypotheses for this observed drop in consumption has been proposed, as we will see later on.

On the contrary, other studies have not observed the puzzle at all. For instance, Christensen (2004) uses a true panel data, the Spanish Encuesta Continua de Presupuestos Familiares (ECPF), for the period 1985-1997. She doesn’t find significant drop in income at the moment of retirement. Moreover, the budget shares for several non-durable goods are not affected by retirement, even for those work-related goods. The estimated demand equations do not reject the hypothesis of no-change in consumption around retirement. Similarly, Hurd and Rohwedder (2005), using cross-section and panel data, find no evidence of a lack of forward-looking behaviour: the expectations on spending before retirement broadly matches with effective spending after retirement, and the median actual spending change is approximately zero.

When the puzzle is effectively observed, the first candidate of causing changes in consumption is income. But even if income drops at retirement, the smoothing of consumption predicted by the life-cycle model is in contradiction with the observed change in consumption patterns. In a seminal study, Hamermesh (1984), using the US Retirement History Survey, explains the drop in consumption after retirement by a drop in income that would erode the accumulated wealth if a correction to consumption is not applied. One assumption of the original life-cycle model does not hold: people want the wealth to be positive at the date of death due to bequest motives. The effects of this preference is undistinguishable from the over accumulation of wealth due to uncertainty about the moment of death in risk-averse individuals. Denton, Mountain and Spencer (2002) use repeated cross-sections from the Canadian FAMEX for simulations based on an adapted version of the Deaton and Muellbauer’s Almost Ideal Demand System. They conclude that the cause of changes in consumption patterns is a drop in income instead of changes in tastes. The problem is how to explain a change in consumption if the drop in income was expected, as we have seen, because it is in contradiction with the life-cycle consumption model.

Other hypotheses point to non-separabilities as the culprit of the observed drop in consumption (see, for arguments in favour of the adoption of nonseparable preferences, Attanasio and Weber, 1993; Meghir and Weber, 1996; and Battistin, Brugiavini, Rettore and Weber, 2007). This would provide an acceptable explanation within the life-cycle model. For instance, some workrelated expenditures suddenly drop after retirement. Moreover, work-related expenditures affect the wealth accumulation during the working life, and retirement also induces a drop in expenditures due to this wealth-effect of past working activity. A different way of focusing this issue would be to relax separability between consumption and leisure into the utility function. Whether the utility function is not separable in these two goods, the marginal utility of one of them will depend on the other, so retirement is endogenous. Consumption and leisure can be substitutes or complements, and therefore, after retirement, consumption could increase or decrease (leisure increases in any case). Only if they are substitutes we can solve the consumption puzzle, explaining the observed drop in consumption in accordance with the life-cycle model, which predicts a smoothing in utility throughout the entire life.

The hypothesis of non-separability cannot explain the whole observed drop in consumption after retirement, and therefore this explanation is incomplete. For instance, Banks, Blundell and Tanner (1998) find that non-separabilities between work and consumption is one of the possible explanations of the puzzle, but not the only one. The authors conclude that only unexpected shocks could complete the explanation of the observed phenomenon (the other possibility is irrational behaviour). They use repeated cross-section data from the British Family Expenditure Survey. Laitner and Silverman (2005) employ data from the US Consumer Expenditure Survey to explain the drop in consumption after retirement (a 16 percent) by introducing into the life cycle model intratemporal utility that is non-separable in consumption and leisure, discrete work options and retirement age that emerges from household choice. Instead of explaining the puzzle, they seek to rationalize it into this new model that predicts a drop in consumption at retirement.

In the same way, retirement implies a substantial increase in leisure, and the opportunity costs of home production will abruptly drop. This increases home production, which replaces expenditure in some consumption goods (Laitner and Silverman, 2005; Aguiar and Hurst, 2005). In addition, shopping activities are also less costly than before, and therefore the same purchases can be obtained at lower prices. Home production and shopping would reduce the total monetary expenses, but not consumption. The problem of this approach is how to explain drops in consumption spending on goods that cannot be produced at home. Moreover, the use of data on food expenditures as a proxy to non-durable expenditures, as many studies do, is not completely correct. The reason is that these expenditures are necessities and therefore their income elasticity is very low and, on the other hand, these expenditures have a high sustitutability by time (see Attanasio and Weber, 1995). There are also several references in this line of research. Hurd and Rohwedder (2003) employ the cross-sectional Consumption and Activities Mail Survey (CAMS) on time use. They find that, after retirement, people substitute market goods for home production, which explains the observed drop in consumption. Aguiar and Hurst (2005) look for evidence about home production substitution of food at home and food out of home. The quality or quantity of food is not altered, but home production replaces market purchases of goods and services. They use the US Continuing Survey of Food Intakes by Individuals, for testing the connections between home production, food consumption and food expenditures after retirement. They find a reduction of a 17 percent in food expenditures and an increase of a 53 percent in time spent in home production after retirement. Therefore, consumption is smoothed throughout the lifetime, but expenditures are not, and a drop can be observed. Miniaci, Monfardini and Weber (2003) and Lührmann (2006) combine data on expenditures and data on time use in order to verify a causal connection between home production and drops in expenditures on several consumption goods. In particular, Miniaci, Monfardini and Weber (2003) use the Italian cross-sectional Survey on Family Budgets (SFB) and find non-separabilities (a drop in work-related goods and an increase in home production after retirement). They also find that there are not unanticipated shocks on income due to retirement. Lührmann (2006) investigates how retirement affects the consumer expenditures after retirement, also considering an increase in home production as a hypothesis for the observed drop in consumption. She finds a significant drop of about 17 percent in expenditures after retirement, at the same time of a 30 percent increase of time spent on home production.

An obvious alternative explanation is to hypothesize unexpected shocks at the moment of retirement, affecting expenditures or income. An unanticipated negative shock affecting income, or incorrect expectations about income after retirement, will induce a change in the expenditures, as pointed to by Hamermesh (1984). Health shocks, for instance, might increase unexpectedly medical expenditures. Other possible effect of one such health shock is an early and unexpected retirement. This would reduce total expected income perceived during the entire life. Smith (2004) employs a true panel database–the British Household Panel–but restricted to food expenditures. If retirement is voluntary, food spending is largely smoothed through retirement, but if retirement is involuntary, food spending falls. This supports the hypothesis of negative wealth shocks as the cause of the retirement consumption puzzle.

Other hypotheses are far more sophisticated. Lundberg, Startz and Stillmann (2001) claim that after retirement a change in marital bargaining power occurs, in favour of women. Women know their life expectancy is longer and they are interested in a drop in consumption in order to increase savings for the period in which their husbands have passed away. Zamora (2004) explains the relative bargaining power of the man and the woman as a function of the labor activity, employing Spanish data very similar to those used by us in this study (a true panel data). The structure of the consumption in the household depends on the woman decision on labour participation. Expenditure-elasticities for woman labor participation can be calculated, and the consumption of some goods will increase if the woman works (feminine goods, related the woman’s power) whereas others will increase if the woman doesn’t work (masculine goods, related to man’s power). Bernheim, Skinner and Weinberg (2001) find difficult to reconcile the data–the U.S. Panel Study of Income Dynamics (PSID) and the Consumer Expenditure Survey (CEX)–with the life-cycle model. The framework of rational, farsighted optimization seems to be inadequate for a correct understanding of the observed behaviour. The typical modifications of the basic life-cycle model, incorporating differences in wealth due to differences in time-preferences, bequest motives, non-separabilities between consumption and leisure or unexpected shocks, do not provide a valid or sufficient explanation for the change in consumption just after retirement. Angeletos,

Laibson, Repetto, Tobacman and Weinberg (2001) share this view about the rationality of the agents. A more realistic model is proposed, integrating conflicting preferences. Short-run preferences endorse immediate gratification and long-run preferences recommend patience and precaution. The combination of those time preferences is known as “hyperbolic” preferences (see Laibson, 1997), and a model of consumption based on hyperbolic discount functions seems to approximate the data much better than conventional models based on exponential discount functions. This new model allows for changes in preferences depending on circumstances. Long-run plans are not met due to short-run behaviour. Gruber and Köszegi (2001) develop a new model for addictive behaviour based on the "rational addiction" model, but incorporating time-inconsistent preferences. Battistin, Brugiavini, Rettore, and Weber (2007) estimate (p. 20) a 9,8 percent consumption drop (with a 5,7 percent standard error) after correcting for the endogenous nature of the retirement decision implied by a model without separability between consumption and leisure.

In this paper, we analyze the impact of retirement on income and a breakdown of expenditures by estimating complete demand systems and single equations. We use an unbalanced panel of Spanish households taken from the Encuesta Continua de Presupuestos Familiares (ECPF) during the period 1985- 1997. Most studies on the subject do not employ panel data, or they are time panels that do not allow having enough observations before and after the retirement to do the tests. The ECPF, however, offers a maximum of 8 observations for each household, providing detailed data for several quarters before and after retirement. The consumption puzzle is observed, with a significant drop in expenditures after retirement of around a 5 percent, which does not correspond with any significant drop in disposable income. Alternative estimations, differing in the degree of sophistication, from single equation estimation to complete demand systems, clearly show that only a few categories of consumption are significantly affected by retirement. These categories are health expenditures and public transport, two heavily subsidized (for the elderly) public goods. Further, we analyze a finer classification of work-related goods as well as health and transport goods and services and we only find significant reductions in the demand for some health and transport items after retirement. These results point to the fact that no substantial change in the structure of consumption occurs after retirement, which is a remarkable result of our paper.

The rest of the paper is structured as follows. In the next section we present the data and the grouping of goods. We also present the sample selection process done before estimating the specifications proposed. In section 3 we provide a first look at the data on income and consumption at retirement.

Section 4 is devoted to present the results of single equations and we report in section 5 the results of the complete demand system estimated under different assumptions. Section 6 concludes.

2. Data and sample selection

2.1. The data

The ECPF is a true panel in which the households collaborate up to a maximum of 8 quarters. When a household drops, a new household replaces it, so the survey constitutes a rotating panel. This is a self-reported survey, but the detailed reports are filled with the supervision of an interviewer. The information provided is very rich, including expenditures on 279 groups of goods classified on the basis of a four digits nomenclature (linked to an EUROSTAT classification). The ECPF continued from the third quarter of 1997 to our days, but under a slightly different methodology (the linkage of the two waves is easy though). In addition to expenditure, households provide information on family composition, income and occupation. Income and expenditures are two of the key variables to be addressed within the information of the ECPF. Household income is differentiated between monetary and in-kind income. Moreover, income categories are household earnings, self-employed income, capital and property income and income from transfers.

Each quarter the survey provides information for about 3,200 households. The amount of data collected from each household does the collaboration exhausting. Due to this reason, households are asked for collaborating a maximum of 8 quarters, though some of them drop before reaching the maximum period of collaboration. This introduces the possibility of attrition, although our opinion is that attrition is non-random in consumption or demand models. The collaboration ranges between 1 to 8 quarters. Table 1 shows the distribution of the collaborations. The total number of observations (households and quarters) can be calculated from the first two columns, and it amounts to 151,672, from the 49 quarters available, from the first quarter of 1985 to the first quarter of 1997. This sample period coincides with a period of rather stable rules in the Spanish pension system, which reduces uncertainty for those retired during the sample period.

Income is a key variable in this study. It is narrowly correlated with expenditures. The life- cycle consumption theory assumes anticipated changes in income and, therefore, consumption smoothing. Disposable household income includes total earnings of the household members, self-employed income, income in kind, pensions, unemployment benefits and other sources of income. The expenditures also are referred to the household level. The ECPF has a remarkable property: it includes information on expenditures of a broad range of commodities, durables and non-durables. We only analyze expenditures on non-durables, assuming they are separable from durables. The effect of retirement on durable expenditure is more difficult to grasp, considering that the household reports expenditures on durables at the moment of the interview or in the three previous months.

Table 1. Distribution of households according to collaboration in the ECPF

Expenditures on non-durables are grouped for the purposes of this study in the following 14 categories: food and non-alcoholic drinks; alcoholic drinks; tobacco; clothing; housing and other non-durables related to housing; energy at home; health; private transport; public transport; communications (telephone, mail, etc.); leisure, restaurants and bars; education and cultural goods and price services; petrol; other non-durable goods. Clothing only includes cloth and footwear repairs, because cloth and footwear goods are considered durables. This explains the relative small weight of this group in the total expenditures. We have also check that the results do not change when clothing and footwear items are considered non-durables. The Appendix has a detailed description of the goods included in the 15 groups.

We have elaborated specially suited price indexes for each household. In order to get them, we used prices of each commodity weighted by the average expenditure shares for each household. This household specific price index is then employed in the calculating a generic Stone index price using the mean values of the expenditure shares. We use this Stone index for deflating economic variables. This price index is far more accurate in describing the changes in the relevant consumption good than the Retail Price Index (RPI) reported in the ECPF and used by Christensen (2004), although she claims that the value of the

RPI is quite similar to the value of the household specific Stone index. However, since we also opt for estimating a complete demand system, we need as much variation in prices as possible in order to be able to identify their responses.

2.2. Sample selection

We are interested in the analysis of the changes experienced around retirement, affecting income and consumption.¹ Due to this reason, we need at least three observations for each household, one for the quarter previous to retirement, other for the quarter in which retirement is reported and another one for the quarter after retirement. Therefore, households with only one or two collaborations (the first two rows of the previous table) are not of interest to us. In addition, households with three or more collaborations but that retire during the quarter of the first or the last collaboration must be discarded as well, because no change can be observed in these cases. In order to do that, we need to count the number of transitions for each household head and preserve those for which only one transition is observed. Information by types of transitions into and out of retirement is reported in Table 2. We also drop from our final sample those households in which the family head changes, due to death or any other reason. It can be easily detected by looking at changes in the age of the household head.

There are a good number of cases of early retirement (see Boldrin, Jiménez and Peracchi, 1997). The Spanish pension system allows retirement before the age of 65 is reached. During the period considered, there are several programs of public pensions: the General and Social Security Scheme (RGSS) cover most workers from the private and public sectors, including a total of 8.7 million people; the Special Social Security Schemes (RESS) cover selfemployed, agricultural workers, domestic workers, sailors and miners, including a total of 3.7 million people; finally, there is a government employees scheme (RCP), covering 800,000 people. There are other programs and pension plans for particular institutions (for instance, employees of the Bank of Spain) and special funds that supplement the pensions provided by one of the before mentioned programs. People affiliate to the RGSS before 1967 are allowed to early retirement at 60, although the legal retirement age is 65. The RESS does not allow early retirement, but self-employed people can perceive a pension and still be working as self-employed. The RCP allows civil servants to retire at age 60 without penalization if they have at least 30 years of contribution. Boldrin, Jiménez and Peracchi (1997) find strong incentives to early retirement but, as we have seen, this is allowed only for ages of 60 or higher and under some conditions depending on the particular program. Those reporting to be retired at lower ages will be excluded from the sample. Table 3 shows retirement ages for the household heads that meet the conditions mentioned, i.e., only 1 transition into retirement; retired at least 1 quarter after the first collaboration and 1 quarter before the last one.

Christensen (2004) considers that a household is “retired” if the husband is retired, “since the wives work as housewives for nearby 70 percent of the sample”. Lührmann (2006), however, adopts a more sophisticated procedure based of two different definitions of “retired” for the households. Following the first definition, a household is considered as “retired” if the household head reports to be retired or to perceive pension income. The second definition considers “retired households” to those in which the head is older than 65 and is not selfemployed or one person is retired and the other inactive (out of the labor force). Age is not a good criterion for determining the retirement status of a person in the case of Spain, due to the peculiarities of the Spanish pension system explained by Boldrin, Jiménez and Peracchi (1997).

Table 2. Transitions into and out of retirement in the ECPF

Since early retirement is allowed at 60, whether a person is retired before there exist a possibility of a shock of any kind that could have caused it. We will keep these observations, and we introduce a dummy that identifies those retiring before 60. These retirements are normally preceded by long unemployment periods, unstable working histories or work accidents. This seems to explain a large part of the total retirements observed at early ages. After 60, people working full time can retire, because there are incentives to early retirement in many cases. Voluntary retirement seems to explain the relatively large proportion of retirements from full-time work observed at 60 or older. Many cases can be observed of people retiring from unemployment at 60 or later (see Table 4). These are typical cases of people becoming unemployed a few years before normal retirement age. After 65, no cases of retirement from unemployment or instability are observed (see Table 3). The final sample size is reduced in terms of number of observations and households and Table 5 presents the different sub-samples. We have 325 households and 2,192 observations in our final sample of household heads retired at normal ages (panel A of Table 5). We report in panel B of Table 5 the structure of the unbalanced panel for those retiring before 60. They will be added to the sample in several estimations. These people can be considered as unexpectedly retired. Panel C and panel D present the structure of the sample by normal and early retirement ages, respectively. The sample thus created allow us to built a retirement dummy in order to count the number of households retired in each quarter as well as the number of quarters each household is observed before and after retirement.

Table 3. Retirement ages at the ECPF

Table 4. Retirement ages in the ECPF

Table 5. Different sub-samples of retired individuals

3. Income and post-retirement consumption

In order to get a preliminary picture of the change in consumption after retirement, we have calculated the total amount of expenditures in non-durables before and after retirement. We sum quarterly expenditures in the periods preretirement and post-retirement and we evaluate the changes. An average increment of a 7.4 percent is observed. The variation between different groups is important, but the distribution of expenditure shares presents a high number of zeros and, consequently, the calculated average of increments in expenditures is not very informative. This specially affects the groups of alcoholic drinks (45.7 per cent of zeros), tobacco (44.2), clothing (86.8), health (47.8), private transport (61.1), public transport (51.8), education (70.3) and petrol (55.5). The median provides a less contaminated measure of the change in expenditure. The median increase in non-durable expenditures after retirement is 2.5 percent, being the median increases negative for alcoholic drinks, tobacco, clothing, health, public transport, education, petrol and other non-durables, and positive for food, housing, energy at home, private transport, communications and leisure. The impact of retirement on consumption can be estimated jointly considering these medians and the average of the expenditure shares. For instance, clothing (-12.1 per cent), health (-21.3 per cent) and petrol (-11.5 per cent) show large drops in quarterly consumption after retirement, but the relative weight of these groups is small (0.1 per cent for clothing, 2.2 for health and 3.1 for petrol). On the other hand, small (positive) increments in the quarterly expenditures occur in more important groups, like food and non-alcoholic drinks (2.0 per cent median increment for a 35.7 per cent weight of its share), housing (3.6 per cent median increment for a 27.6 relative weight of the share) or leisure (9.0 per cent of increment for a 12.0 per cent of the share). Looking at the aggregate, the surprising result is that the consumption does not drop after retirement, but it registers a slight increase.

In this section, we present a regression-based analysis for analyzing the impact of retirement on income and expenditure. We regress the logarithm of real total household income and the log of real total household expenditure on a retirement dummy. We also include in the specification quarterly and yearly dummies for a better consideration of seasonality, mainly due to the fourteen payments scheme in Spain, business cycle effects, and different temporal placement of the households into the sample (see Browning and Collado, 2001). Boldrin, Jiménez and Peracchi (1997) refer to two characteristics of the ECPF and the Spanish payment tradition –affecting both pensions and work earnings– to take account of (see also a summary in Christensen, 2004). Firstly, wage earners receive twelve payments, plus two extra payments in July and December. This implies some quarterly variation in household income, although these positive shocks are fully anticipated and it does not necessarily affect expenditures. Browning and Collado (2001) find evidence about smoothing of consumption even accounting for the extra payments. Secondly, the members of the household are asked to inform about their actual labour force status, referred to the moment of the interview, although the reported income refers to the three previous months.²

We adjust log income and consumption regressions on the retirement dummy using three different methods: pooled, fixed-effects and random effects models. We report these results in Table 6. In panel A we report results for the specification without quarterly and yearly dummies. Only the coefficient and tstatistic of the retirement dummy are reported. In panel B of the table we also report the p values associated to the F statistic for testing the significance of the time dummies. These variables must be included for controlling seasonal or cyclic variations in the dependent variable. Jointly considered, however, these variables are significant, especially in the pooled regression and random effects estimations. We repeat the regression incorporating a set of quarterly and yearly dummies, and we show the results on panel C.

The impact of retirement on income (log income) and non-durable expenditure (log expenditure) is always negative, and clearly significant for expenditure (except in the fixed effects specification). The coefficient of the retirement dummy points to 5 to 10 percent drop in expenditures after retirement. Retirement has not significant impact on the logarithm of income in the fixed and random effects models. These results seem to suggest reduction in expenditures after retirement, without a correspondence to a similar reduction on income, which is the basic stylized fact known as consumption puzzle.

² The same difference exists between non-durable expenditures and durable expenditures. The former are referred to the moment of the interview and the later to the previous quarter.

Table 6. Log income and log consumption regressions

Note. 1. The coefficients correspond to the retirement dummy, which variable gets value 1 from the moment of retirement onwards.

4. Estimating some demand equations

In this section we study the effects of retirement on non-durable expenditure shares estimating single equations for several non-durable goods. We would like to identify the goods for which we observe a decrease in expenditure. We estimate a model based on a simple form of a Working-Leser demand equation. We estimate the model by OLS (i.e., under the assumption of absence of unobserved heterogeneity) and using three different methods for controlling unobserved heterogeneity: GLS under uncorrelated random effects and two models based on transformations to first differences and within groups. The first set of estimates arises from the next simple Working-Leser specification:

\[w _ {i h t} = \alpha_ {i} + \beta_ {i} l n x _ {h t} + \delta_ {i} D _ {h, r e t i r e d} + \gamma_ {i} Z _ {h t} + \varepsilon_ {i h t}\tag{1}\]

where the indexes i, h and t refer to goods, households and time respectively is the logarithm of total non-durable expenditure deflated with a Stone price index; the demographic vector includes a dummy which takes value 1 from period t to the end of the sample period if the household head is retired at time t, the number of adults in household h at time t, the number of children in the household, a dummy variable identifying working wives, quarterly dummies and yearly dummies. Our aim in adjusting this model is to compare it with the basic model estimated by Christensen (2004). However, we expand the set of variables by including additional ones, as the square of the logarithm of the total expenditures for allowing non-linear relationships, a set of family composition dummies (identifying single households, childless couples and couples with one, two, three or more children), a dummy identifying the gender of the household head, a dummy taking into account the tenure regime of the house, a dummy that identifies retired wives, another collecting the working situation of the wife (working or not), a dummy identifying for self-employed individuals, another for the condition of being a white collar worker, a dummy showing whether the head of household is a part-time worker, and the same for the wife, a set of dummies controlling the size of the municipality where the household lives (rural for households living in towns of less than 10,000 inhabitants, and urban for households living in towns of more than 500,000 inhabitants) and plus three educational dummies (no educational background, high school and university degree).

We report the results (coefficients and t-ratios) for the retirement dummy for the 14 expenditure shares on Table 7. We have incorporated a dummy identifying those retired before 60. Since the first-differences and within-groups procedures transform the variables to differences in time and from time means, respectively, non-time varying covariates are not identified in those models. The only groups significantly affected by retirement are public transport, energy at home and health. Public transport and health goods and services are subsidized for retired people in Spain, what explains their negative sign. The increase of time spent at home can explain the positive significant effect in the group of energy at home.

Table 7. Estimates of the effects of retirement on demand (single equations)

The hypothesized non-separabilities between work activity and the consumption of work-related goods can be tested by looking at whether retirement has some significant impact on them. It is difficult to select a set of goods related to work. For instance, food-out could be linked to work activity, but also to leisure. We will follow the same classification of Banks, Blundell and Tanner (1998, p. 781) for these goods, which include clothing, private and public transport, petrol and food-out. The last row of Table 7 shows that retirement does not have a significant impact on these work-related goods. Even more, and not reported in Table 7, we have included communications to this work-related group. The reasoning is that some private consumption of these services could be done at work, like telephone calls, internet connecting, faxes or parcels, etc. No significant effects of retirement on this amplified group have been found.

We have selected four different groups of work-related goods and have proceeded to a separate analysis, employing all the estimation methods with the full set of explanatory variables. The idea is that the aggregate of work-related goods could be masking the significant influence of particular sets of goods narrowly related to work activities. The first of such disaggregated subgroups is composed by public transport services, including train, subway and bus. The second one is composed by leisure activities, like cinema, theatre, concerts, museums, sports spectacles and sports practice, etc., hotels and package tours. The third includes free meals at work, and the fourth group only includes package tours separately. Only public transport and free meals are significantly and negatively affected by retirement. Therefore, the final effect on the workrelated aggregate has been compensated by positive and negative effects, resulting in a non-significant overall impact.

Finally, although we do not report these results in Table 7, we have estimated two quantile regression models, for the median and the 75 percent quantile in an attempt to check whether some items are affected at different levels of expenditure on these groups. The significant variables detected in the estimations reported in Table 7 are quite similar to those obtained with the quantile regression. As we have explained in the previous section, the expenditure shares have many zeros, and this could introduce a severe bias in the mean and in the models based on the mean. The median regression is immune to this strong asymmetry in the sample. It identifies a significant influence (at 5 per cent level) of retirement on tobacco, health and public transport. This holds for people retired before and after 60 years old. The 75 per cent quantile regression estimation is interesting because of the incidence of the zeros on some of these goods. However, the results point to the same significant effects of retirement on health and public transport.

5. A Complete Demand System

The results obtained in single demand equations impose separability restrictions which can hide relationships among goods and bias parameter estimates. The next goal is to estimate a more complete model to overcome this problem. Our choice is the quadratic extension of the Deaton and Muellbauer's Almost Ideal Demand Model (1980), proposed by Banks, Blundell and Lewbel (1997, p. 533-534) –called Quadratic Almost Ideal Demand System (QUAIDS). One of the aims for proposing this demand system is to allow for flexible income and price responses. Nicol (2001, 2003) and Banks, Blundell and Lewbel (1997) show the importance of rank-three models in demand systems using data from the US CEX or the Canadian FAMEX consumer expenditure surveys.

A general expression for Engel curves that match the empirical evidence is

\[w _ {i h t} = A _ {i h t} (\pmb {p} _ {h t}) + B _ {i h t} (\pmb {p} _ {h t}) l n x + C _ {i h t} (\pmb {p} _ {h t}) g (x _ {h t})\tag{2}\]

for goods , households , H and periods , a N-vector of prices , and and differentiable functions. The allows for non-linearities observed in the Engel curves for some goods. Equation (2) must satisfy homogeneity and symmetry.

When is zero equation (2) is linear in log income. It also occurs when is equal to for some function which does not depend on i. In these two cases, model (2) has rank 2. However, it is observed that whereas it can occur for some goods, others have strong non-linearities. Moreover, because does not depend on it, the ratio of the coefficients on and should be constant, and the empirical evidence rejects it. Then, model (2) must have rank 3 either if is not zero or it can be reduced to a function of . Notice, for instance, that the AI model has constant (independent of prices) and for all i. Other extended versions of the AI model have and independent of prices (see Blundell, Pashardes and Weber 1993).

The rank 3 quadratic logarithmic budget share systems have indirect utility functions of the form

\[\ln V _ {h t} = \left\{\left[ \frac {\ln m _ {h t} - \ln a (\mathbf {p} _ {h t})}{b (\mathbf {p} _ {h t})} \right] ^ {- 1} + \lambda (\mathbf {p} _ {h t}) \right\} ^ {- 1}\tag{3}\]

when the is independent of prices the indirect utility function reduces to a form suitable for any model of the PIGLOG class, including the translog or the AI models. Particularly, when is set to zero we have the indirect utility function of the AI model.

Following Banks, Blundell and Lewbel (1997) we define instead

\[\lambda \left(\mathbf {p} _ {h t}\right) = \sum_ {i = 1} ^ {n} \lambda_ {i h t} \ln p _ {i h t} \quad \text { where } \quad \sum_ {i} \lambda_ {i h t} = 0\tag{4}\]

Applying Roy’s identity we have the budget shares, quite similar to those of other models belonging to the PIGLOG class, but incorporating a quadratic term:

\[w _ {i h t} = \frac {\partial \ln a (\mathbf {p} _ {h t})}{\partial \ln p _ {i h t}} + \frac {\partial \ln b (\mathbf {p} _ {h t})}{\partial \ln p _ {i h t}} (\ln x _ {h t}) + \frac {\partial \lambda_ {h t}}{\partial \ln p _ {i h t}} \frac {1}{b (\mathbf {p} _ {h t})} (\ln x _ {h t}) ^ {2}\tag{5}\]

where is a linear homogeneous price index, and are zero homogeneous in prices, is the price vector faced by households at each time period, is total expenditure of household h at time t and is the participation of good i in total expenditure by household h at moment t. It is easy to see that and

We derive the demand equations for goods, by taking the Almost Ideal parameterisation of Deaton and Muellbauer (1980) for and

\[\ln a \left(\mathbf {p} _ {\mathrm{ht}}\right) = \alpha_ {0} + \sum_ {\mathrm{i} = 1} ^ {\mathrm{I}} \alpha_ {\mathrm{i}} \ln p _ {\mathrm{iht}} + \frac {1}{2} \sum_ {\mathrm{i} = 1} ^ {\mathrm{I}} \sum_ {\mathrm{j} = 1} ^ {\mathrm{I}} \gamma_ {\mathrm{ij}} ^ {*} \ln p _ {\mathrm{iht}} \ln p _ {\mathrm{jht}}\tag{6}\]

\[\ln b \left(\mathbf {p} _ {\mathrm{ht}}\right) = \sum_ {\mathrm{i} = 1} ^ {\mathrm{I}} \beta_ {\mathrm{i}} \ln p _ {\mathrm{iht}}\tag{7}\]

where represent consumer goods considered by the model.

Equations (3), (4), (6) and (7) define the QUAIDS. By replacing equations (6) and (7) in (5) we get the expenditure equation system

\[w _ {i h t} = \alpha_ {i} + \sum_ {j = 1} ^ {I} \gamma_ {i j} \ln p _ {i h t} + \beta_ {i} \ln \left[ \frac {m}{a \left(\mathbf {p} _ {h t}\right)} \right] + \frac {\lambda_ {i}}{b \left(\mathbf {p} _ {h t}\right)} \left\{\ln \left[ \frac {m}{a \left(\mathbf {p} _ {h t}\right)} \right] \right\} ^ {2}\tag{8}\]

Since we have several observed demographics , the model is flexible enough to allow functions of the parameters in (5) to affect demand. They can shift both the intercept and the slopes of the share equations by defining and

Table 8 presents parameter estimates and t-ratios for our quadratic specification, under symmetry and homogeneity restrictions. Additional demographic variables are included in the model: quarterly dummies, number of adults and children in the household and dummies for gender of head of household, housing tenure, retirement of the wife, self-employment, white-collar workers, working wives, head of household part-time workers, wife part-time worker, size of municipality and education level. The retirement dummy is clearly significant for health and public transport with negative effects and marginally significant for communications with positive effects. Expenditures on energy at home are not affected by retirement in this case, despite the increase in time spent at home. While health and public transport are subsidized goods when retirement occurs in a way such that negative effects on consumption at retirement are expected, the positive effect on communications expenditure can be possibly explained because postal and electronic mail as well as internet and telephone services which were done at work, are now done at home. The dummy identifying those retired before 60 is significant at 10 percent level for clothing with negative sign. We can argue that it is a good related to work, but this is not the case since this dummy is not significant in the workrelated goods group. The possible explanation is the accommodation of the unexpected shock that retirement supposes for these individuals.

We further investigate the effects of retirement on consumption by making a final exercise reducing the 14 expenditure categories into 4: energy at home, health, work-related goods (including clothing, private and public transport, petrol and food-out) and other non-durable goods. Panel B of Table 8 presents parameter estimates and t-ratios for our quadratic specification on these four groups, under symmetry and homogeneity restrictions. Retirement only affects health expenditures with a negative sign, as expected. Work-related goods are unaffected and we cannot detect non-separabilities between workrelated consumption and labour supply. Although the results are not reported, the dummy identifying early retirement does not show any effect on the demand of work-related goods.

Table 8. Estimates of the effects of retirement on demand (complete system)

6. Some conclusions

The main result of this paper, which is not common to many other studies, is that the consumption-retirement puzzle is not observed, in the sense of reduction of expenditure at retirement. We have a significant impact of retirement on income and expenditures, but this does not translate to a significant impact on a wide range of non-durable expenditures. The expected negative impact on several expenditure groups is not observed in our results (see also Christensen, 2004). Only public transport, health and communications expenditures are significantly affected by retirement, with negative (the former two mentioned groups) and positive (the last one). The explanation seems to rely on a crowding out effect. Retired people keep the level of the non-durable consumption unchanged in order to keep constant the marginal utility of consumption, but they slightly change the structure according to changes in the relative prices of goods.

In Spain, public transport is heavily subsidized for retired people, as it is also the case of health goods and services. The increase in expenditure on the communications group can be possibly explained because postal and electronic mail as well as internet and telephone services which were done at work are now done at home. On the other hand, retirement does not have significant influence on the remaining expenditure groups, and this is a remarkable and unexpected result. Work-related goods, an aggregation of several expenditure groups (clothing, transportation, private and public, gasoline and food-out), are not affected either.

The life-cycle model is compatible with a consumption drop at retirement if the marginal utility of consumption is affected by leisure, but it does not seem to be the case with Spanish data.

Further work is needed for detecting, measuring and explaining the impact of retirement on subsidized goods. This additional research effort must be concentrated on a better separation of the goods and on an explicit analysis of how retired people slowly change their habits after retirement. Even if retirement is expected, habits are powerful enough to make the necessary adaptations in a non-instantaneous way. We only had 8 quarters so, at best, we can observe a retired household for 6 quarters after retirement. Any permanent change in consumption habits is gradual and slow enough to be unobservable in that short period of time. Whenever retired people suffer any physiological shock affecting their behaviour and since they have not longer the necessity to go to work everyday, medium run effects of retirement on consumption could perfectly be different to short run effects and so we need longer panels in order to answer these questions.

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Appendix. Consumption groups.