Households’ joint consumption spending and home production responses to retirement in the US

Abstract

We analyze the effect of retirement on households’ joint consumption spending and home production decisions using a micro panel with detailed spending and time use categories of US households. For causal identification, we use panel data regressions. Our results suggest that the spending drop at retirement is partially compensated by increases in home production of the retiring household member. Home production can particularly make up for losses in spending categories that are well-substitutable by home production, although only about 12% of total pre-retirement consumption spending, but there is no evidence that households fully replace consumption spending at retirement. In a Life-Cycle Model, we find no empirical evidence for full consumption smoothing at retirement.

1. Introduction

The Life-Cycle Model (LCM) has been widely studied, both theoretically and empirically, in the literature. Theoretically, the LCM predicts that agents smooth consumption over their life-time. Empirically, substantial drops in consumption spending are observed at retirement which is inconsistent with the LCM.¹ Two key parameters of the LCM determine the smoothing of consumption over the life-cycle: 1) the intertemporal elasticity of substitution between consumption and leisure (IES) and 2) the intratemporal elasticity of substitution between spending and leisure. Many studies using US data typically find a value of the IES beyond 0 (mostly between 0.4 and 0.8) suggesting that there is no full intertemporal smoothing of consumption. Therefore, smoothing should come from replacing spending by home production according to the LCM. However, unlike for the IES, there is little direct empirical evidence on the degree to which households replace spending by home production.

In his seminal work, Becker (1965) argues that consumption is ‘produced’ by two inputs: market expenditures (consumption spending) and time (home production). The relative price of time, the foregone wage, determines the share of market consumption in the consumption bundle. Hence, spending on consumption spending is a bad proxy for actual consumption as ‘time’ can be used to increase consumption beyond expenditures (Hurst, 2008). Moreover, the theory of home production of Becker (1965) suggests that people will substitute away from consumption spending to home production as the opportunity cost of time drops. This argument is often used to explain the substantial drops in consumption spending observed at retirement.

In this paper, we are the first to analyze households’ joint spending and home production decisions at retirement using micro panel data with detailed information on spending and time use categories of both spouses in a household.² The combination of detailed information on both spending and home production allows us to assess the potential use of home production to replace spending at retirement. Using the theoretical LCM of (Rogerson & Wallenius, 2016, 2019), we are the first to identify the smoothing of consumption over the life-cycle by assessing the elasticities of inter- and intratemporal substitution based on causal estimates of retirement on households’ consumption and home production. The detailed information on consumption and time use categories helps to assess to what extent households replace spending by home production at retirement beyond a single measure of food spending.

Due to limited availability of data sets that include information on both consumption and home production, prior studies have largely analyzed the effect of retirement on home production in isolation from consumption spending (Schwerdt, 2005; Stancanelli & Van Soest, 2012a; Velarde & Herrmann, 2014; Bonsang & Van Soest, 2020; Atalay et al., 2019). To assess the extent to which home production replaces spending, these papers suggest that increases in home production are sufficient evidence (Stancanelli & Van Soest, 2012a; Atalay et al., 2019), relate home production responses to income replacement rates of retirement income (Schwerdt, 2005),³ or compute the monetary value of home production and relate this to the income drop observed at retirement (Bonsang & Van Soest, 2020). Without exception, these studies conclude that the increase in home production is sufficient to replace spending at retirement. However, the home production increases are not related to actual spending changes at retirement. Therefore, it remains largely unclear to what extent increases home production can make up for consumption losses. Using food expenditures and time spend in preparing meals, Aguiar & Hurst (2005) are the first to use information on both consumption spending and home production and conclude that increased cooking replaces food spending at retirement. This is confirmed by Velarde & Herrmann (2014). Been et al. (2019) argue that conclusions regarding the ability of households to replace spending by home production depends on the consumption categories considered. This implies that the conclusion of Aguiar & Hurst (2005) may not hold for a wider array of consumption categories.

To estimate the effect of retirement on joint consumption spending and home production decisions, we exploit the panel nature of the data following Luengo-Prado & Sevilla (2012) and Bonsang & Van Soest (2020). Similar to Bonsang & Van Soest (2020), we use a multi-equation model and estimate a system of equations with Fixed Effects. In order to check the robustness of the results, we apply a fuzzy Regression Discontinuity Design (RDD) exploiting the US Social Security system which follows the approaches taken in Bloemen et al. (2010) and Stancanelli & Van Soest (2012a,b) using cross-sectional data.

To assess the size of the intratemporal elasticity of substitution between spending and home production we analyze to what extent increases in home production can replace spending at retirement. Our purpose is not to estimate the intratemporal elasticity of substitution, but to assess whether it is reasonable to assume that this elasticity is relatively large and sufficient to imply consumption smoothing with non-full intertemporal consumption smoothing as suggested by, among others, Rogerson & Wallenius (2016, 2019). We use three approaches to analyze the extent to which households replace spending by home production: 1) Identifying near-retirees’ share of consumption spending that is potentially replaceable by home production. For home production to be able to fully replace spending drops, we need to identify how much of pre-retirement spending is potentially replaceable. 2) Estimating shadow wages based on the effects of retirement on joint consumption spending and home production changes. Shadow wages relate the value of the decrease in spending to the hours increase in home production. Home production fully protects against consumption drops at retirement if the value of the increase in home production is bigger than or equal to the drop in consumption spending, e.g. a shadow wage that is smaller than or equal to the price of time. 3) By combining 1 and 2, we analyze the substitution between potentially replaceable spending categories and home production to identify the extent to which households replace spending for which home produced counterparts are likely to exist. These three indicators should inform us on how likely a high intratemporal elasticity of substitution is empirically.

Our estimation results suggest that retirement induces a drop in consumption (16% men, 6% women) spending while jointly increasing the time spend in home production of the retiring household member (3.5 hours men, 3 hours women). We find that substitutable consumption spending is reduced by about 42% (men) and 13% (women) which indicates that primarily substitutable consumption categories are reduced at retirement. However, substitutable spending is only about 12% of households’ total consumption spending. This result suggests that home production is likely to replace these substitutable spending categories, but full replacement of total spending is unlikely. This is confirmed by the estimated shadow wages which are substantially higher than the costs of performing (or hire) an hour of home production indicating that full replacement is unlikely for total consumption. For substitutable consumption, shadow wages show that substitution of spending by home production is not unlikely. The quantitative implications of our results for the LCM outlined by Rogerson & Wallenius (2019) is that the intratemporal elasticity of substitution is likely to be around 1 (e.g. no smoothing by home production) which implies an intertemporal elasticity of substitution of about 0.7. Hence, US households are unlikely to smooth consumption over the life-cycle.

2. Data

2.1. Data and definitions of consumption and home production

For our analysis, we use micro level panel data with detailed information on both spending and time use of US households from the combination of HRS and CAMS surveys. More specifically, combining the HRS and CAMS allows us to analyze 39 spending categories and 33 time use categories for a representative sample of the US population aged 50 and over and their spouses and follow these households over time. The quality of the data from CAMS is high since spending totals aggregate closely to those in the CEX (Hurd & Rohwedder, 2009) and the time use data aggregate closely to time use in the American Time Use Study (Hurd & Rohwedder, 2007). For a more detailed description of survey methodology in the HRS/CAMS, we refer to Appendix A.

The HRS/CAMS data is unique in the design to explicitly facilitate studies of home production and possible substitution with market purchased goods. Only some of the time use categories can be used in home production as a substitute for market purchased goods. For example, time spent cooking can substitute for spending on dining out whereas time spent taking a nap has no substitution possibilities. The time use section asks about time spent on various home production activities and there is a direct mapping of these to elicited categories of spending that potentially lend themselves to substitution with home production. We follow this design in the categorization of home production activities and substitutable spending. For details on the 33 time use categories, see Table A2. Time in home production is the sum of the following time use categories:

• House cleaning

• Washing, ironing or mending clothes

• Yard work or gardening

• Shopping or running errands

• Preparing meals and cleaning up afterwards

• Taking care of finances or investments, such as banking, paying bills, balancing the checkbook, doing taxes, etc.

• Doing home improvements, including painting, redecorating, or making home repairs

• Working on, maintaining, or cleaning car(s) and vehicle(s)

The CAMS data allows to map the aforementioned time use categories to spending categories. By the same token we can quantify the fraction out of total spending that is substitutable, and note that in an industrialized setting like the U.S., many spending categories cannot be home produced, such as utilities, mortgage/rent, insurances, subscriptions, trips/vacation/hobbies, etc. Table A3 gives an overview of the consumption spending definitions in CAMS and the classification into substitutable consumption. We define the sum of these spending categories as ”substitutable consumption” since the good or service has both market and home versions. The following shows the mapping between the market purchases on the left and time used in home production on the right.

• Housekeeping services ⇔ House cleaning, washing, ironing or mending clothes

• Washing/drying machine (durable) ⇔ Washing, ironing or mending clothes

• Gardening services ⇔ Yard work or gardening

• Dining out ⇔ Preparing meals and cleaning up afterwards

• Dishwasher (durable) ⇔ Preparing meals and cleaning up afterwards

• Home repair services ⇔ Doing home improvements, including painting, redecorating, or making home repairs

• Vehicle maintenance services ⇔ Working on, maintaining, or cleaning car(s) and vehicle(s)

Thanks to the richness of the CAMS data we can take a broader view on substitutable consumption spending than one that focuses only on a single market good such as dining out like Aguiar & Hurst (2005), yet we do not assume that all (non-durable) consumption can be replaced which would be inappropriate in an economy that has moved far beyond subsistence.

The mapping between aforementioned categories may mean that we miss some relevant categories of home production or of substitutable spending despite having a data set particularly designed for such mapping. Given the HRS is a general-purpose survey, there were limits on the level of detail and hence survey time that could be spent on eliciting time use and spending. Firstly, the CAMS data lack detail on to whom some time spending categories are devoted. ‘Helping others’ can pertain helping both household members and people outside of the own household. The first might be a form of informal care for a spouse that can be considered as home production. Especially, if it replaces a spending category such as ‘health services’. However, since we do not know to what extent this category addresses people within the household, we do not consider it as home production. Secondly, the limits in the level of detail imply that we cannot differentiate between types of spending within aforementioned categories such as pre-cooked food purchases versus other groceries as used in Hicks (2015). Thirdly, not all substitutable consumption fits in the 39 spending categories. For example, financial management is a category of time use recorded in CAMS but the hiring of a financial advisor is not explicitly a category of consumption spending. Therefore, it is likely that our estimated share of substitutable consumption spending is a lower bound. However, according to the categorization of consumption spending in Table A3 a great deal of spending cannot be substituted by time use, so the actual share is probably not much greater than our definition of substitutable spending for the whole sample. Finally, we should note that spending on (grand)child care services is not a part of the survey. Since the data consists of people aged 50+, most child care is regarding grandchildren who are not a part of the household and were therefore not considered as home production in constructing the survey.

In the analysis, we primarily focus on two types of consumption measures. Firstly, we use total consumption spending (per year) excluding durable goods which is common practice in the literature. Several sensitivity analyses show that our main conclusions are robust to different definitions of total consumption spending.⁴ Secondly, we use substitutable consumption spending which are the spending categories that are mapped by time use categories of home production.

2.2. Sample and summary statistics

For our analytical sample, we exploit the 2005, 2007, 2009, and 2011 waves of the combined HRS/CAMS data. Following Stancanelli & Van Soest (2012a) we restrict the sample to heterosexual couples, in which both spouses are aged between 51–80, both spouses filled out the time use survey, and couples are dropped if neither spouse was employed at the beginning of observing the household. The latter should reduce possible underestimation of the effect of retirement on consumption and home production as those people are already likely to have lower levels of consumption and higher levels of home production. Also, it makes sure we only keep households for whom we observe a within-household change in retirement status which is important for our identification strategy explained in Section 4. Table A1 in the Appendix shows how much observations are associated with each step of restricting the sample.

Definitions of retirement are based on respondents’ self-reported labor market situation.⁵ We define retirement as those who report to be (partially) retired. Non-retired implies that the respondent is either working (full time or part time), unemployed, disabled, or out of the labor force (e.g. housekeeper).^6,7

Table 1 shows summary statistics of the most important variables in the regression analyses for our analytic sample.⁸ Most interestingly, we observe that about 12% of total consumption spending is potentially substituted by home production. Much of this replaceable consumption spending consists of dining out expenses. Furthermore, women spend almost 10 hours per week more on home production than men, on average, which is consistent with prior documented gender inequalities in home production (Sevilla-Sanz et al., 2010; Gimenez-Nadal & Sevilla, 2014).

Table 1:

Summary statistics^a

	Mean	SD	Min.	Max.	P50
Consumption spending (USD/y)
Dining out	2,228	3,127	0	58,049	1,382
Substitutable consumption	5,416	6,842	0	146,309	3,472
Consumption w/o durables	47,187	29,171	0	296,984	40,688
Time use (h/w) b
Male home production	16.0	16.2	0.0	409.7	12.4
Female home production	25.9	19.1	0.0	183.2	22.1
Male leisure	78.6	46.2	0.0	509.8	72.7
Female leisure	87.8	53.3	0.0	570.9	80.3
Male characteristics c
1(Retired)	0.72	0.45	0.00	1.00	1.00
Age	66.6	7.6	51.0	80.0	67.0
1(Age ≥ 62)	0.72	0.45	0.00	1.00	1.00
1(Badhealth)	0.06	0.25	0.00	1.00	0.00
ADL (0–5)	0.17	0.62	0.00	5.00	0.00
Female characteristics
1(Retired)	0.67	0.47	0.00	1.00	1.00
Age	63.8	7.5	51.0	80.0	64.0
1(Age ≥ 62)	0.59	0.49	0.00	1.00	1.00
1(Badhealth)	0.06	0.24	0.00	1.00	0.00
ADL (0–5)	0.20	0.69	0.00	5.00	0.00
Household characteristics
Household size > 2	0.26	0.44	0.00	1.00	0.00
Wave 2007	0.25	0.43	0.00	1.00	0.00
Wave 2009	0.24	0.43	0.00	1.00	0.00
Wave 2011	0.27	0.44	0.00	1.00	0.00

^aSummary statistics are presented for our sample of 5,610 observations. Monetary measures are expressed in 2011 US dollars using the Consumer Price Index of the Bureau of Labor Statistics.

^bThe CAMS survey assumes multi-tasking such that the total number of hours per week reported by respondents may exceed 168 hours per week. We do not know if values beyond 168 hours per week are due to multi-tasking or can be considered as an error. However, values beyond the 99th percentile (Men: 69 h/w, Women: 92 h/w) may be considered as outliers. Deleting outliers from the analysis, either by deleting the top 1%, by deleting those beyond 168 h/w, or by capping the values to 168 does not alter our conclusions (not reported here). Leisure excludes time spend sleeping.

^cFor men, being retired and being at least 62 years old is both 72% of the sample. However, this does not imply that the two perfectly coincide. In the data, 13% of the men aged 62+ is not yet retired while 34% of men aged 61- is already retired.

2.3. Descriptive statistics by retired and non-retired households

Table 2 presents the average amount of spending (in $ per year) for non-retired couples, couples in which the male is retired and the female is not, couples in which the female is retired and the male is not and couples in which both spouses are retired.⁹ Please note that these descriptives should not be interpreted causally as we compare the cross-section of four household types here. The descriptives show that total consumption spending is substantially lower in households in which the male is retired.¹⁰ Female retirement does not seem to be associated with a substantial reduction in consumption spending. Female retirement seems to matter much less for spending decisions than male retirement.

Table 2:

Household consumption spending ($ per year)

	Non-retired (m), Non-retired (f)		Retired (m), Non-retired (f)
	Mean	S.D.	Mean	S.D.
Dining out	2,360.36	2,746.58	2,139.93	2,717.91
Substitutable consumption	6,237.31	8,226.39	5,056.10	5,676.95
Consumption w/o durables	53,792.18	29,654.00	48,093.84	27,647.10
Observations	996		878
	Non-retired (m), Retired (f)		Retired (m), Retired (f)
	Mean	S.D.	Mean	S.D.
Dining out	2,611.73	3,414.12	2,140.73	3,281.80
Substitutable consumption	6,764.34	9,432.65	5,013.21	5,995.21
Consumption w/o durables	53,798.86	35,153.00	43,654.91	27,615.95
Observations	574		3,162

A similar pattern is observed when focusing on consumption spending that could directly be substituted for by home production such as dining out, housekeeping services, gardening services, home repair services and vehicle maintenance. The total of home production substitutable consumption is about 12% of total consumption spending and, therefore, a non-negligible component of total consumption spending.¹¹ In all defined groups of couples, expenditures on dining out are the most substantial component of home production substitutable consumption (about 40%). Table 2 also shows that substitutable consumption is more responsive to households’ retirement decisions than total consumption which is likely due to the fact that these consumption components are partially substituted by increased home production at retirement. For example, comparing households with a retired male and a non-retired female to non-retired households shows a drop of about 11% and 19% in total consumption spending and substitutable spending respectively.

Table 3 shows the time spent in home production and leisure differentiated over non-retired, partially-retired and retired couples. Looking at the total time spent in home production indicates that men and women in non-retired couples spend, on average, about 14 hours and 24 hours per week respectively. Women devote more of their time to home production than men which is consistent with prior findings (Hersch & Stratton, 2002). Men spend about 2 hours more time in home production in couples in which the male is retired while the female is not. Women in these households do not devote substantially more time to home production than households in which both spouses are non-retired. In households in which the female is retired and the male is not, we see that the total sum of home production in the household is higher compared to households in which both spouses are non-retired. This is mainly due to a substantially higher number of hours spend in home production by the female (27 hours), while males only spend about 14 hours. The total time devoted to home production is highest in couples with spouses that are both retired. In these households, men spend about 17 hours per week in home production while women spend about 27 hours per week.

Table 3:

Time spend in total home production and leisure (hours per week)

	Non-retired (m), Non-retired (f)				Retired (m), Non-retired (f)
	Male		Female		Male		Female
	Mean	S.D.	Mean	S.D	Mean	S.D.	Mean	S.D.
Home production	14.52	14.59	24.09	16.80	16.50	20.52	24.68	19.14
Leisure (ex. sleep)	78.56	44.91	88.10	53.29	78.64	55.54	89.47	56.17
Observations	996				878
	Non-retired (m), Retired (f)				Retired (m), Retired (f)
	Male		Female		Male		Female
	Mean	S.D.	Mean	S.D.	Mean	S.D.	Mean	S.D.
Home production	13.63	13.89	26.66	19.72	16.84	15.70	26.70	19.51
Leisure (ex. sleep)	75.22	40.56	84.45	53.88	79.20	44.76	87.82	52.39
Observations	574				3,162

With total household home production of 38, 42, 41 and 44 hours per week respectively, we see that retirement is associated with increased home production although the increase is fairly small for couples in which one spouse has retired already. These descriptives also suggest that most of the increased home production is due to the partner that retires and that cross-effects between the partners are relatively small. Despite substantial increases in home production of women at retirement, it is primarily male retirement that matters for spending decisions. Regarding leisure time, we find remarkably little differences between the four household types, although leisure seems to be a bit higher for those in retirement. Especially, if both spouses are retired.

3. Retirement incentives

3.1. US pension system

The US pension system consists of both a public pension system and a voluntary private pension system. The public pension system, or Social Security, consists of various elements and operates as a pay-as-you-go system financed through mainly social security taxes paid by employers and employees. The old-age public pension system consists of a minimum pension, an earnings-related pension, and a means-tested supplement for those who would otherwise fall below the subsistence level. The voluntary private system consists of occupational pensions (both DB and DC, including 401(k) plans) and personal pension mostly consisting of individual retirement accounts (IRAs) and annuities/life insurances. Occupational pensions are not mandatory and only 61% of all private-sector workers are covered by company-sponsored pension plans of which 55% have access to a DC plan. The exact rules of these private pensions related to premiums and benefits strongly depend on the employer, but most plans typically use a normal retirement age of 65. Employers can also contribute to the IRAs. Unlike the other pension plans, IRAs are owned by the person such that benefits are available at any time. However, if the IRA is withdrawn before the age of 59.6, a 10% tax is applicable. Also, savers must start withdrawing the IRA before the age of 70.5. For a more detailed overview, we refer to OECD (2009).

Summing public pensions and private occupational pensions, OECD (2009) shows that retirees can potentially expect 75%−85% of their final earnings replaced by their pensions depending on the DB or DC nature of their pension plan. In both cases, the Social Security ensures about 40% of final earnings. However, retirees can top up their retirement income by additional sources from personal pension plans and savings. Also, these number are based on a fictional person with a full career. In practice, many people do not have a full career due to periods of unemployment, sickness, or early retirement. Butrica et al. (2012) use microsimulation to analyze the importance of different retirement resources for actual US households and show that about 95% of retired American households receive Social Security. Income from Social Security (excluding the means-tested supplement) accounts for about a third of the sum of all retirement sources, including personal pension plans and savings, on average. This percentage is bigger than any other source of retirement income including all private pensions which are in total even less than a quarter of total income during retirement. Although Social Security is an important source of income on average, Butrica et al. (2012) also shows that the importance of social security is likely to be very heterogeneous among subgroups of the population. They show that primarily singles, non-whites, low-educated, and low-income people have less access to employer-sponsored pensions which makes them more reliable on Social Security benefits at retirement. Nonetheless, from these figures we conclude that Social Security is a non-negligible source of retirement income for US households, on average. This justifies our interest in households’ responses to Social Security.

3.2. Statutory retirement ages in Social Security

The earliest age at which retirees are eligible to claim Social Security benefits is 62, i.e. Early Retirement Age (ERA). Social Security benefits can be claimed up to the age of 70. The Full Retirement Age (FRA) is the age at which people can start claiming unreduced Social Security benefits. The Social Security Amendments of 1983, increased the FRA depending on the year of birth. Individuals born before 1938, have an FRA of 65. People born in 1938–1943 face a stepwise increase of the FRA by 2 months per birth year cohort until the age of 66. People born from 1943–1954 face an FRA of 66. People born in 1955–1960 face a stepwise increase again until the FRA of 67. People born after 1959 face an FRA of 67.

People claiming benefits after the FRA, which is possible up to the age of 70, receive an actuarially fair premium. Claiming benefits before the FRA results in actuarially fair reductions in the benefit payments. Hence, the penalty for claiming benefits at the early retirement age of 62 was increased by the amendments. The actuarially fair reduction increases as the FRA rises so to equalize lifetime payments for workers who claim at different ages.¹² These reductions are substantial: for a person with an FRA of 67 retiring at age 62, 63, 64, 65, or 66 reduces the monthly benefit amount by about 30%, 25%, 20%, 13.3%, and 6.7% respectively. For those born before 1938 the reduction for retiring at age 62 is 20%. This percentage increases with birth year cohort. For all cohorts the US Social Security system is such that claiming prior to the age of 62 does not give right to claim any monthly Social Security benefits. Given the fact that Social Security benefits are an important source of income during retirement, it makes retiring prior to the age of 62 unlikely for the average US household.

4. Empirical model

Since retirement decisions are likely to be endogenous to consumption and home production decisions due to unobserved preferences for consumption and leisure, simple OLS parameter estimates are likely to be biased and inconsistent. Most likely, those households that retire relatively early have high unobserved preferences for leisure that may lead to an underestimation of the effect on consumption spending and home production. Nonetheless, failing to control for such unobserved preferences most likely gives estimates that can be interpreted as a lower bound for the effect of retirement on consumption spending and home production.

To control for unobserved preferences and estimate a causal relationship between retirement decisions (R_k = {0, 1} with k = {m, f}) and consumption spending $\left(\frac{dln\left(C_k^m\right)}{d{R}_k}\right)$ and home production $\left(\frac{dln\left(H_k^h\right)}{d{R}_k}\right)$, we exploit the panel nature of the data following the approach of Luengo-Prado & Sevilla (2012) and Bonsang & Van Soest (2020). They argue that exploiting the panel structure of the data should be sufficient to estimate the effect of retirement on consumption spending and home production. Under the assumption that people’s unobserved preferences for consumption and leisure are time-invariant and correlated with the independent variables, controlling for household specific effects through Fixed Effects regressions solves the endogeneity between retirement and consumption/time use decisions as the within-household changes at retirement estimated by the Fixed Effects regressions control for the unobserved preferences that effect both retirement and consumption/time use decisions.

Similar to Bloemen et al. (2010), Stancanelli & Van Soest (2012b), Stancanelli & Van Soest (2012a), Bonsang & Van Soest (2020), and Fonseca et al. (2017) we estimate a Simultaneous Equation Model (SEM) to allow for joint decisions in consumption spending and home production decisions similar to SEM models.¹³ The SEM exists of the following system of equations in which we define $C_{it}^m$ as consumption spending of household i at time t, H_itm and H_{it f} as time spent in home production activities by men and women in a household respectively, and R_itm and R_{it f} the dummies indicating whether the male or female is retired respectively. Following Stancanelli & Van Soest (2012a), we specify $C_{it}^m$ as the log of market consumption¹⁴ and H_itm and H_{it f} in levels.

$$C_{it}^m=Z_{itm}{\beta }^{cm}+Z_{itf}{\beta }^{cf}+X_{it}{\zeta }^c+A_{itm}{\delta }^{cm}+A_{itf}{\delta }^{cm}+R_{itm}{\gamma }^{cm}+R_{itf}{\gamma }^{cf}+{\alpha }_i^c+{\epsilon }_{it}^c$$ (1)

$$H_{itm}=Z_{itm}{\beta }^{hmm}+Z_{itf}{\beta }^{hfm}+X_{it}{\zeta }^{hm}+A_{itm}{\delta }^{hmm}+A_{itf}{\delta }^{hfm}+R_{itm}{\gamma }^{hmm}+R_{itf}{\gamma }^{hfm}+{\alpha }_i^{hm}+{\epsilon }_{itm}^{hm}$$ (2)

$$H_{itf}=Z_{itm}{\beta }^{hmf}+Z_{itf}{\beta }^{hff}+X_{it}{\zeta }^{hf}+A_{itm}{\delta }^{hmf}+A_{itf}{\delta }^{hff}+R_{itm}{\gamma }^{hmf}+R_{itf}{\gamma }^{hff}+{\alpha }_i^{hf}+{\epsilon }_{itf}^{hf}$$ (3)

with

$$A_{itk}=\left[ag{e}_{itk},ag{e}_{itk}^2\right]$$ (4)

The main coefficients of interest are ${\gamma }^{ck}=\frac{dln\left(c_k^m\right)}{d{R}_k}$ and ${\gamma }^{hkk}=\frac{dln\left(h_k^h\right)}{d{R}_k}$. These coefficients measure the spouses’ (cross-)effects of retirement on consumption spending and home production. Z is a vector of characteristics of the individual, including health and ADL’s. Vector X captures characteristics that are similar for both spouses in the household, including period effects and household size. α_i is the individual- and household-specific time-invariant unobserved heterogeneity.

Similar to Fonseca et al. (2017), we control for the time-invariant unobserved heterogeneity following Mundlak (1978) in all equations in the system. This method assumes a parametrization of unobserved heterogeneity by adding the individual mean of time-varying regressions to the estimation procedure and is approximately similar to Fixed Effects regression based on demeaning of the variables (Wooldridge, 2010).¹⁵

$${\alpha }_i^c={\overline{A}}_{im}{\xi }_1^{cm}+{\overline{A}}_{if}{\xi }_2^{cf}+{\overline{D}}_{im}{\xi }_3^{cm}+{\overline{D}}_{if}{\xi }_4^{cf}+{\overline{Z}}_{im}{\xi }_5^{cm}+{\overline{Z}}_{if}{\xi }_6^{cf}+{\overline{X}}_i{\xi }_7^c+u_i^c$$ (5)

$${\alpha }_i^{hk}={\overline{A}}_{im}{\xi }_1^{hm}+{\overline{A}}_{if}{\xi }_2^{hf}+{\overline{D}}_{im}{\xi }_3^{hm}+{\overline{D}}_{if}{\xi }_4^{hf}+{\overline{Z}}_{im}{\xi }_5^{hm}+{\overline{Z}}_{if}{\xi }_6^{hf}+{\overline{X}}_i{\xi }_7^{hk}+u_i^{hk}$$ (6)

Here, $v_{itk}^{jk}=u_i^j+{\epsilon }_{itk}^{jk}$ with $v^{jk}~N\left(0,{\Sigma }_{v^{jk}}\right)$ and j = {c,hm,hf}. Σ is the variance-covariance matrix of the error-terms.

Equations 1–8 are jointly estimated using (Full Information) Maximum Likelihood (FIML), following Bloemen et al. (2010), Stancanelli & Van Soest (2012a), Stancanelli & Van Soest (2012b), Bonsang & Van Soest (2020), and Fonseca et al. (2017), which explicitly accounts for contemporaneous correlation that might exist between the error terms of Equations 6–8.¹⁶ The estimation of each equation in isolation ignores the information about the covariances between the equations and information about the exclusion restrictions on all other equations. The error terms ${\epsilon }_{it}^c$, ${\epsilon }_{itm}^{hm}$, and ${\epsilon }_{itf}^{hf}$ are normally distributed with mean zero and variance ${\sigma }_{{\epsilon }^c}$, ${\sigma }_{{\epsilon }_m^{hm}}$, and ${\sigma }_{{\epsilon }_f^{hf}}$ respectively. In other words, we assume linear models for consumption spending and home production. In this way, we follow the error assumptions in Stancanelli & Van Soest (2012b).

5. Estimation results

5.1. Simultaneous Equations Model with Fixed Effects

The results in Table 4 suggest that both male $\left({\gamma }_1^{jm}\right)$ and female retirement $\left({\gamma }_1^{jf}\right)$ reduces household consumption spending significantly (see Table A6 in the Appendix for the extended results including control variables). Household consumption spending drops by 16% when the male retires. On average (see Table 2), this means that male retirement decreases total household consumption spending per year by about $9,145. When the female retires, household consumption spending drops by 5% which is, on average, a drop of about $2,934. Jointly, male retirement also increases the time spent in home production by males by about 3.7 hours per week. Female retirement increases the amount of time spent in home production by 3.2 hours per week. The results of a smaller drop in consumption spending and a bigger increase in home production of females upon female retirement is in line with the descriptive statistics in Table 2: Female retirement matters much less for spending decisions than male retirement despite substantial increases in home production of women at retirement.

Table 4:

The effect of retirement on spending and home production decisions^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.03	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−0.18	0.73	3.15***	0.72

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include control variables.

Unlike Stancanelli & Van Soest (2012b) (positive effects, Italy) and Bonsang & Van Soest (2020) (negative effects, Germany) we do not find strong cross-effects of retirement on home production of spouses, on average.¹⁷ Section D extends the baseline estimates by allowing for heterogeneous effects of retirement by retirement resources, health, and the Great Recession. Allowing for such heterogeneity in retirement resources, health, and the business cycle does not alter our main conclusions.

Conclusions from our baseline model are robust to different spending definitions (Table B1), partial and full retirement (Table B2), including labor supply at the intensive margin, excluding Fixed Effects from the SEM (Table B3), estimating separate equations (Table B4), different functional forms of age effects (Table B5), and a smaller age interval (Table B6). We rule out that the drop in consumption spending found at retirement is driven by drops in work-related expenses such as clothing and transportation costs (Table B1). We also rule out that the drop in consumption spending found at retirement is entirely driven by shopping for lower prices. Aguiar & Hurst (2007) suggest that a doubling of shopping frequency can lower prices by up to 10%. Although we find significant effects of retirement on time spend shopping, the increases in hours spend shopping are only about 0.71 hours per week (26%) and 0.44 hours per week (11%) for men and women, respectively (Table B7). Price effects instead of quantity effects are therefore unlikely to drive the drop in total spending. Here, it should be noted that price effects, either from increased shopping or shifting from more expensive pre-produced productions to cheaper unprocessed alternatives (which is not observed in our data), may cause the actual effects of retirement on consumption to be smaller than approximated by our spending measure.

In interpreting the results, we should also note that increased home production can increase spending if spending-complementary categories such as grocery shopping as a complement to increased cooking (and decreased dining out). Such spending-complements to home production would lead to a lower elasticity of substitution for consumption spending. However, estimating the effect of retirement on a system of equations related to dining out spending, groceries spending, and time spend on cooking of both the male and female, we find no evidence for such complements. Instead, we find significant decreases in dining out spending as well as groceries spending despite significant increases in time spend on cooking (see Table B8).

Estimated correlations between the three error terms are presented in Table 5.¹⁸ A significant correlation between two error terms suggests that there is a latent variable that affects both equations, e.g. both outcomes respond to a common shock in the model. Moreover, Stancanelli & Van Soest (2012a) suggest that the sign of a significant correlation reveals substitution patterns between the different outcomes. We find no significant correlation between consumption spending and home production (males) or a very small negative correlation (females). This suggest that negative shocks, other than retirement on which we condition, do not induce substantial substitution from consumption spending to home production.

Table 5:

Estimated correlations between error terms^a

$C_{it}^m$	Coeff.	S.E.	H itm	Coeff.	S.E.	H it f	Coeff.	S.E.
${\sigma }_c^2$	0.67***	0.04	${\sigma }_{hm}^2$	16.00***	1.03	${\sigma }_{hf}^2$	18.76***	0.38
σc,hm	−0.02	0.04	σhm,hf	0.12***	0.02
σc,hf	−0.03*	0.02

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level.

5.2. Sensitivity to a fuzzy Regression Discontinuity Design

By exploiting the US Social Security system, as outlined in Section 3.2, we have a potentially strong approach to test the robustness of our conclusions from the Fixed Effects model to a different method of causal inference. This approach follows earlier papers that analyze the responsiveness of retirement decisions to Social Security.¹⁹ Theoretically, the earliest possible age to retire (ERA) and claim Social Security benefits is 62. Theoretically, the ERA creates a discontinuity in the probability of retirement running through the age of a person. The probability of retirement is higher for persons that can claim Social Security benefits than for persons who can not: $P(R_{it}\mid ag{e}_{it}=ERA)\gg P\left(R_{it}\mid ag{e}_{it}<ERA\right)$ with ERA = 62.

Figure 1 shows the discontinuities in the retirement rate by age. There seems to be a discontinuous jump in the probability of retirement at the ERA among men. Women’s jump at the ERA is less pronounced hinting that they are less responsive to pension incentives consistent with earlier findings (Song & Manchester, 2007). At age 65, the FRA for the older cohorts, the discontinuity is less pronounced than at the ERA for both men and women. Figures 2 and 3 show how the discontinuities at the ERA affect our variables of interest: consumption spending and home production. Both seem rather smooth around the ERA suggesting the absence of a retirement-consumption puzzle.

To capture the effect more formally, we estimate the following fuzzy Regression Discontinuity Design (RDD). For an excellent overview of (fuzzy) RDD, we refer to Lee & Lemieux (2010). Since there is no deterministic assignment rule here, we only observe a change in the probability of retirement for those below and above the ERA. Therefore, we cannot rely on a sharp RDD but causal identification depends on a fuzzy RDD. Hence, our approach reduces to an instrumental variable approach using the discontinuity at ERA as an instrumental variable which is likely to be both relevant (e.g. determines retirement) and valid (e.g. does not determine spending and time use other than through retirement). More specifically, we estimate the following model which is comparable to our Fixed Effects model except for 1) leaving out Fixed Effects and 2) adding two equations that estimate the effect of reaching the ERA on the probability to retire which can be considered as our first-stage estimates in the fuzzy RDD.

$$C_{it}^m=Z_{itm}{\beta }^{cm}+Z_{itf}{\beta }^{cf}+X_{it}{\zeta }^c+A_{itm}{\delta }^{cm}+A_{itf}{\delta }^{cm}+R_{itm}{\gamma }^{cm}+R_{itf}{\gamma }^{cf}+{\epsilon }_{it}^c$$ (7)

$$H_{itm}=Z_{itm}{\beta }^{hmm}+Z_{itf}{\beta }^{hfm}+X_{it}{\zeta }^{hm}+A_{itm}{\delta }^{hmm}+A_{itf}{\delta }^{hfm}+R_{itm}{\gamma }^{hmm}+R_{itf}{\gamma }^{hfm}+{\epsilon }_{itm}^{hm}$$ (8)

$$H_{itf}=Z_{itm}{\beta }^{hmf}+Z_{itf}{\beta }^{hff}+X_{it}{\zeta }^{hf}+A_{itm}{\delta }^{hmf}+A_{itf}{\delta }^{hff}+R_{itm}{\gamma }^{hmf}+R_{itf}{\gamma }^{hff}+{\epsilon }_{itf}^{hf}$$ (9)

$$R_{itm}=Z_{itm}{\beta }^{rmm}+Z_{itf}{\beta }^{rfm}+X_{it}{\zeta }^{rm}+D_{itm}{\theta }^{rmm}+A_{itm}{\delta }^{rmm}+D_{itf}{\theta }^{rmf}+A_{itf}{\delta }^{rmf}+{\epsilon }_{itm}^{rm}$$ (10)

$$R_{itf}=Z_{itm}{\beta }^{rmf}+Z_{itf}{\beta }^{rff}+X_{it}{\zeta }_{rf}+D_{itm}{\theta }^{rfm}+A_{itm}{\delta }^{rfm}+D_{itf}{\theta }^{rff}+A_{itf}{\delta }^{rff}+{\epsilon }_{itf}^{rf}$$ (11)

with

$$A_{itk}=\left[\left(ag{e}_{itk}-ERA\right),{\left(ag{e}_{itk}-ERA\right)}^2\right]$$ (12)

$$D_{itk}=1\left(ag{e}_{itk}\ge ERA\right)$$ (13)

and ERA = 62. θ^jkm and θ^{jk f} estimate the discontinuous jump of reaching the FRA on the probability to retire for men and women, respectively. Table 6 presents the estimation results from the fuzzy RDD. The results suggest that reaching the ERA increases the probability of retiring by about 10% and 9% for men and women, respectively. This discontinuity is important in explaining retirement behavior with joint significance showing p-value well below 0.000 suggesting that the discontinuity is a strong instrument. This is confirmed by the F-statistic that is bigger than the rule-of-thumb of 10 in all regressions. Also, following Chernozhukov & Hansen (2008), the reduced form estimates in Table C1 provide reasons to believe that our estimates do not show significant effects by chance due to having weak instruments while the actual effect may be absent (e.g. no retirement-consumption puzzle).

Table 6:

Regression Discontinuity using ERA^ab

		$C_{it}^m$		H itm		H it f		R itm		R it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.18***	0.04	4.82***	0.95	2.62*	1.35
${\gamma }_1^{jf}$	R it f	−0.12***	0.03	0.65	0.86	6.68***	1.52
θjkm	D itm							0.10***	0.02	0.03	0.02
θjk f	D it f							0.03*	0.02	0.09***	0.02

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f,rm,r f. k = m,f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bJoint significance of RDD coefficients ${\theta }_1^{jkm}$ and ${\theta }_1^{jkf}$ gives p – value = 0.000 and p – value = 0.000 for men and women, respectively.

In contrast to Figures 2 and 3, the estimation results do suggest a drop in consumption spending and an increase in home production. However, even in the absence of control variables our RDD suggests a decrease in spending and increase in home production (see Table C2) consistent with our baseline estimates and the RDD with control variables. The differences between the figures and the estimate are not driven by the SEM as separate IV regression are in line with the estimation results (see Table C3).

Though comparable to our baseline results based on the Fixed Effects model, the estimated effects of retirement on consumption spending and home production are amplified in the fuzzy RDD, especially for women. Introducing Fixed Effects to the fuzzy RDD, like Fonseca et al. (2017), slightly reduces the effects of retirement on spending and home production, but most prominently for men (Table C4).

6. Are home production increases sufficient to replace spending?

6.1. Implied shadow wages

The estimation results show that spending (home production) decreases (increases) at retirement. A common approach to analyze to what extent the increase in home production can make up for spending losses is to monetize the value of home production (Bonsang & Van Soest, 2020). Frazis & Stewart (2011) have developed different methods to value home production in monetary terms. Two of the most common measures are the replacement cost approach and the minimum wage approach which value an hour of home production by the cost it would take to purchase the production in the market (e.g. the wage of hiring someone to do the work) and the minimum wage respectively.²⁰ Hence, in our case both approaches suggest a shadow wage of about 7.25 US dollars since a generalist wage for maids and housekeepers would be about the same as the minimum wage in the US. However, Ghez & Becker (1975) argue that a shadow wage below the minimum wage is plausible for retirees as the price of time drops due to a drop in opportunity costs.

Bonsang & Van Soest (2020) relate the monetary value of the increase in home production at retirement to the decrease in income at retirement and find that both are about equal such that retirees are able to compensate the income loss due to retirement. Instead of relating home production to income we relate home production to consumption spending which is arguably a better approximation of households’ well-being. Home production fully replaces the value of spending at retirement R = {0, 1} if the increase in home production hours $\left(h_t^h\right)$ times its monetary hourly value (w) is bigger than or equal to the drop in consumption spending $\left(c_t^m\right)$:

$$w\cdot \frac{d{h}_t^h}{dR}\ge -\frac{d{c}_t^m}{dR}$$ (14)

The average shadow wages we estimate from $w=\frac{d{h}_t^h}{dR}/\frac{d{c}_t^m}{dR}$ are about $45 per hour for males²¹ and about $15 per hour for females.²² Since this estimated shadow wage is much higher than the assumed monetary value of home production of 7.25 US dollars indicates that the increase in home production is too small to make up for the drop in consumption spending. Hence, it is unlikely that households fully replace the monetary value of consumption spending by home production.²³

6.2. Substitutable consumption spending

Despite clear increases in home production at retirement, our estimated shadow wages suggest that the increase in home production is insufficient to cover the full drop in consumption spending. So far, these conclusions are based on all spending categories. Unlike prior attempts to analyze the extent to which households can replace spending by home production, we are able to estimate a model that only includes potentially substitutable consumption spending. Section 2.2 showed that, on average, 12% of total pre-retirement consumption is consumption that can be substituted by home production in our used sample. Even if households fully replace spending categories by home production, they can only replace about 12% of total spending. Households’ ability to use home production to smooth consumption at retirement is therefore likely to be small.

In this section we estimate the effect of retirement on disaggregates of consumption spending. More specifically, we disaggregate consumption spending $c_i^m$ in $c_i^m=\left\{c_i^{m,ns},c_i^{m,s}\right\}$ with $c_i^{m,s}$ consumption categories that can potentially replaced by home production and $c_i^{m,ns}$ consumption categories that have no home produced counterpart. We define $c_i^{m,s}$ as the sum of spending on dining out, housekeeping services (including washing, drying, and dishwashing machines), gardening services, home repair services, and vehicle maintenance following Been et al. (2019).

Table 7 shows the estimation results for substitutable consumption spending, both including and excluding durables (washing, drying, and dishwashing machines). The main conclusions are robust to using different definitions of substitutable consumption spending. The main difference with our baseline estimates is that the drop in consumption spending observed at retirement is much bigger (about 42% men, 13% women) than the drop in total consumption spending. This can likely be explained by shifting away from spending to home production for these consumption categories. Estimates of non-substitutable consumption are highly similar to the baseline results which is likely to be a consequence of the small share of total consumption spending that is replaceable by home production.

Table 7:

Different definitions of consumption^a

		$C_{it}^{m,s}$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
Substitutable consumption
${\gamma }_1^{jm}$	R itm	−0.42***	0.06	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.13**	0.06	−0.18	0.73	3.15***	0.72
Substitutable consumption (excl. durables)
${\gamma }_1^{jm}$	R itm	−0.42***	0.06	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.13**	0.06	−0.18	0.73	3.15***	0.72
Non-substitutable consumption
${\gamma }_1^{jm}$	R itm	−0.14***	0.03	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−0.18	0.73	3.15***	0.72

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on dining out, housekeeping services (including washing, drying, and dishwashing machines), gardening services, home repair services, and vehicle maintenance per year. Durables are defined as yearly spending on washing, drying, and dishwashing machines. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The parameter estimates of these variables are not reported here. The Simulated Maximum Likelihood is ran with 100 Halton draws.

These estimation results imply shadow wages of about $14 and $4.5 for men and women respectively.²⁴ For men, this is still relatively high compared to the replacement cost approach and the minimum wage approach. Interestingly, our estimates using dining out and cooking in Table B8 produce a shadow wage of $16 that is very similar.²⁵ This observation suggests that using food-related spending and time use only, like Aguiar & Hurst (2005), approximates our conclusions better than using total spending or income, like Bonsang & Van Soest (2020), to evaluate the role of home production in replacing spending. For women, we find a shadow wage below the minimum wage, consistent with Ghez & Becker (1975), which implies full replacement of replaceable consumption spending by home production according to our definitions. However, it remains largely unknown whether households actually replace goods one-to-one and consume the same consumption bundle or whether households reduce spending on substitutable consumption with the aim to be able to spend more on non-substitutable consumption categories thereby changing the consumption bundle.

6.3. Elasticity between substitutable spending and home production

Been et al. (2019) were the first to estimate the elasticity between changes in home production and changes in substitutable spending. Using wealth shocks from the Great Recession they estimate an elasticity in the range of −0.56 to −0.65 and significantly different from zero and conclude that their estimated elasticity statistically implies full substitution consistent with Becker (1965). Compared to Been et al. (2019), our analysis differs in mainly two ways. One, we focus on the effects of retirement and not on changes in housing wealth induced by the Great Recession. This also implies the need for a different approach for causal identification exploiting the panel nature of the data. Two, whereas Been et al. (2019) analyze substitution between spending and time use at the personal level, we explicitly take into account spending and time use behavior of both spouses which helps us understand the within-household decisions made at retirement.

With the estimates in Table 7 we can also approximate the elasticity that is estimated by Been et al. (2019). $\frac{dln\left(h_t^h\right)}{dR}$ is 0.26²⁶ and 0.13²⁷ for men and women, respectively, and $\frac{dln\left(c_t^{m,s}\right)}{dR}$ is −0.42 and −0.13 for men and women, respectively. Hence, $\frac{dln\left(h_t^h\right)}{dR}/\frac{dln\left(c_t^{m,s}\right)}{dR}$ is −0.62 and −1 for men and women, respectively. These approximated elasticities of substitution are highly comparable to the estimated elasticity on the same data by Been et al. (2019). Therefore, full substitution between substitutable spending and home production at retirement seems likely. Especially, for retiring women. Based on the comparison with Been et al. (2019), we conclude that the estimated elasticity does not depend on whether a consumption drop is initiated by a wealth shock or an income shock at retirement.

7. Implications for the Life-Cycle Model

Thus far, the paper has focused on the degree to which households are able to replace consumption spending by home production at retirement. We have shown the limited extent to which home production can replace total consumption, although it is successful in replacing substitutable spending categories. However, so far, our results cannot indicate to what extent US households smooth consumption at retirement. To argue to what extent our results imply consumption smoothing or not, we use the two-person Life-Cycle Model (LCM) of Rogerson & Wallenius (2019).

Rogerson & Wallenius (2016) propose a theoretical life-cycle framework that shows that the intertemporal elasticity of substitution between consumption and leisure and the intratemporal elasticity of substitution between spending and home production are positively related. Both are important to determine the degree of consumption smoothing at retirement. Their framework shows that consumption smoothing is either mainly due to intratemporal or due to intertemporal substitution. Rogerson & Wallenius (2019) have extended this framework to two-person households. Assuming a simple Life-Cycle Model with a CES-utility function and additively separable preferences for consumption and leisure in a two-person household, they show that the ratio of the intertemporal elasticity (γ) and intratemporal elasticity (η) can be estimated from couples’ changes in hours of home production (H_k) and leisure (L_k):

$$\frac{\gamma }{\eta }=\frac{\left(\Delta \text{ln}{L}_m-\Delta \text{ln}{L}_f\right)}{\left(\Delta \text{ln}{H}_m-\Delta \text{ln}{H}_f\right)}$$ (15)

γ and η determine the curvature of the utility function and the extent to which expenditures can be substituted by home production, respectively. γ = 0 yields full intertemporal smoothing. η → ∞ yield full intratemporal smoothing. Note that η and the elasticity between substitutable spending and home production from Section 6.3 are different concepts, though related. Full smoothing by home production gives an elasticity of −1 implying η → ∞ in the LCM. No smoothing by home production gives an elasticity of 0 implying η = 1 in the LCM. Rogerson & Wallenius (2019) note that the two-person household is key to deriving $\frac{\gamma }{\eta }$ without requiring information on consumption spending unlike Rogerson & Wallenius (2016) for the unitary household model.

We estimate $\frac{\gamma }{\eta }$ for transitions into retirement by extending our baseline estimates with two equations. One equation for male leisure time and one equation for female leisure time. Estimation results are shown in Table 8. The average time spend on leisure (without sleeping) and home production for non-retired males is 77.34 hours and 14.19 hours, respectively. Similarly, this is 88.74 and 24.37 for non-retired women, respectively. Together with the estimation results in Table 8, these statistics imply $\frac{\gamma }{\eta }$ = 0.72. The value of this ratio falls in the interval that is considered to be a typical retirement transition in Rogerson & Wallenius (2019).

Table 8:

The effect of retirement on spending, home production, and leisure decisions^a

		$C_{it}^m$		H itm		H it f		L itm		L it f
		Coeff.	S.E.	Coeff	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.03	3.66***	0.58	−0.96	0.71	6.26***	1.74	3.08	1.98
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−0.18	0.73	3.15***	0.72	0.55	1.78	0.66	1.94

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. Leisure is total leisure time excluding sleeping time. The Simulated Maximum Likelihood is ran with 100 Halton draws.

Typical values of η reported in the literature are in the range of 1.7–2.5 (Rogerson & Wallenius, 2016). According to $\frac{\gamma }{\eta }$ = 0.72, these imply an interval of γ of 1.2–1.8. This γ is above unity and suggests relatively weak intertemporal consumption smoothing, but depends on relatively high values of substitution between spending and home production. However, our empirical analysis shows that intratemporal substitution is likely to be small or absent for total consumption. Therefore, assuming η = 1, gives γ = 0.72 which is closer to unity than to zero. So, even if US households do not smooth consumption intratemporally by replacing spending by home production, there is evidence that these households do not fully smooth consumption intertemporally either. Therefore, our results imply that US households are unlikely to fully smooth consumption at retirement.

8. Conclusion

The Life-Cycle Model (LCM) theoretically predicts that agents smooth consumption over their life-time. Empirically, however, substantial drops in consumption spending are observed at retirement.²⁸ Becker’s theory on time allocation decisions (Becker, 1965) suggests that people will substitute away from consumption spending to home production as the opportunity cost of time drops and should reconcile theory and empirics of the LCM. However, prior studies on the role of home production in replacing consumption spending have relied on partial information on spending and home production.

In the current paper, we are the first to analyze households’ joint spending and home production decisions at retirement using micro panel data with detailed information on spending and time use categories of both spouses in a household. The combination of detailed information on both spending and home production allows us to assess the potential use of home production to replace spending at retirement. Using the theoretical LCM of (Rogerson & Wallenius, 2016, 2019), we are the first to identify the smoothing of consumption over the life-cycle by assessing the elasticities of inter- and intratemporal substitution based on causal estimates of retirement on households’ consumption and home production. The detailed information on consumption and time use categories helps to assess to what extent households replace spending by home production at retirement.

To estimate the effect of retirement on joint consumption spending and home production decisions, we follow Luengo-Prado & Sevilla (2012) and Bonsang & Van Soest (2020) and exploit the panel nature of the data. Additionally, we use a Fuzzy Regression Discontinuity Design (RDD) in the spirit of Bloemen et al. (2010); Stancanelli & Van Soest (2012a,b); Fonseca et al. (2017) to check the sensitivity of the results to identification method. Our estimation results suggest that male retirement induces a substantial drop in consumption spending while both male and female retirement substantially increase time spend in home production of the retiring household member. Contrasting prior evidence from studies with home production but no spending information (Aguiar & Hurst, 2005; Schwerdt, 2005; Stancanelli & Van Soest, 2012a; Velarde & Herrmann, 2014; Bonsang & Van Soest, 2020; Atalay et al., 2019), our findings suggest that households cannot fully replace the consumption drop at retirement by increasing home production.

Firstly, the share of substitutable consumption spending is only about 12% of total pre-retirement household consumption which leaves the scope for substitution, and hence, full replacement of consumption by home production small. Nonetheless, substitutable consumption spending is more substantially reduced at retirement. Secondly, estimated shadow wages are substantially higher than the costs of performing (or hire) an hour of home production which indicates that consumption drops more than the monetary value of home production increases and, hence, retirees are unlikely to fully replace consumption. Thirdly, even for substitutable consumption spending, shadow wages are relatively high for full smoothing, but it is not unlikely that retiring households are able to replace these categories of spending. This is confirmed by approximations of the elasticity between changes in home production and changes in spending.

To assess the degree of consumption smoothing and the role of home production, we interpret our estimation in the context of the LCM proposed by (Rogerson & Wallenius, 2019). Based on this model and our empirics, we conclude that it is unlikely that US households fully smooth consumption at retirement. Future research can help identify whether the lack of consumption smoothing among US households is due to preferences or due to insufficient retirement resources. This has important implications for social policy as the first suggests that retirement saving should not be mandatory while the latter can be solved by making retirement saving mandatory.

A. Online Appendix: Data Background

A.1. HRS/CAMS surveys

The data for our empirical analyses come from the Health and Retirement Study (HRS), a longitudinal survey that is representative of the U.S. population over the age of 50 and their spouses. The HRS conducts core interviews of about 20,000 persons every two years. In addition the HRS conducts supplementary studies to cover specific topics beyond those covered in the core surveys. The time use and spending data we use in this paper were collected as part of such a supplementary study, the Consumption and Activities Mail Survey (CAMS).

Health and Retirement Study – Core interviews

The first wave of the HRS was fielded in 1992. It interviewed people born between 1931 and 1941 and their spouses, irrespective of age. The HRS re-interviews respondents every other year. Additional cohorts have been added so that beginning with the 1998-wave the HRS is representative of the entire population over the age of 50. The HRS collects detailed information on the health, labor force participation, economic circumstances, and social well-being of respondents. The survey dedicates considerable time to elicit income and wealth information, providing a complete inventory of the financial situation of households. In this study we use demographic and asset and income data from the HRS core waves spanning the years 2002 through 2010.

Consumption and Activities Mail Survey

The CAMS survey aims to obtain detailed measures of time use and total annual household spending on a subset of HRS respondents. These measures are merged to the data collected on the same households in the HRS core interviews. The CAMS surveys are conducted in the HRS off-years, that is, in odd-numbered years. Questionnaires are sent out in late September or early October. Most questionnaires are returned in October and November. CAMS thus obtains a snap-shot of time use observed in the fall of the CAMS survey year.

Since the timing of the fielding of the HRS (even years) and CAMS (odd years) surveys are different, the variables in CAMS are merged to the preceding HRS wave, e.g. CAMS 2005 to HRS 2004, etc. Since the timing of the fielding of the HRS (even years) and CAMS (odd years) surveys are different, the variables in CAMS are merged to the preceding HRS wave, e.g. CAMS 2005 to HRS 2004, etc. The retirement age depends (i.e. forcing variable) on the information in the HRS whereas consumption spending and time use depend (i.e. outcome variables) on the information in CAMS. Both HRS and CAMS have been made comparable so that all the relevant variables are contemporaneous.

Starting in the third (2005) wave of CAMS, both respondents in a couple household were asked to complete the time use section, so that the number of respondent-level observations on time use in each wave was larger for the waves from 2005 and onwards compared to the first two 2001 and 2003 waves. Households were chosen at random from the entire pool of households who participated in the prior HRS core interview. In this study we use CAMS data from 2005, 2007, 2009 and 2011. The CAMS data can be linked to the rich background information that respondents provide in the HRS core interviews. Rates of item non-response are very low (mostly single-digit), and CAMS spending totals aggregate closely to those in the CEX (Hurd & Rohwedder, 2009). The time use data aggregate closely to categories of time use in the American Time Use Study (Hurd & Rohwedder, 2007).

Respondents were asked about a total of 31 time use categories in wave 1; wave 2 added two more categories; wave 4 added 4 additional categories. Thus, since CAMS 2007 the questionnaire elicits 37 time use categories. Using wave 3 to 6 in this paper, we have 33 time use categories available longitudinally. For most activities respondents are asked how many hours they spent on this activity ”last week.” For less frequent categories they were asked how many hours they spent on these activities ”last month.” Hurd & Rohwedder (2008) provide a detailed overview of the time use section of CAMS, its design features and structure, and descriptive statistics. A detailed comparison of time use as recorded in CAMS with that recorded in the American Time Use Survey (ATUS) shows summary statistics that are fairly close across the two surveys, despite a number of differences in design and methodology (Hurd & Rohwedder, 2007).

Respondents were asked about a total of 39 spending categories in the CAMS waves. For nondurable goods and services, the respondent is asked how much was spent in each category and is sometimes given the option, depending on the survey wave and category, of reporting the amount spent weekly, monthly, or yearly. For frequent spending categories, such as gasoline and food, respondents are given the option of reporting all three periodicities, while less frequent spending categories such as mortgage and utilities are only given monthly or yearly options. For durable goods, the respondent is asked to indicate whether the household purchased the item in the ”past 12 months,” and, to the best of their ability, provide the purchase price.

A.2. Selection and definitions

Table A1:

Sample selection in HRS/CAMS

	Definition	Total observations
(1)	CAMS waves 3–6a	14,972
(2)	(1) + Time use component filled out	14,941
(3)	(2) + Couple households	7,088
(4)	(3) + Heterosexual couples	7,044
(5)	(4) + Age 51–80	5,654
(6)	(5) + Both spouses filled out	5,634
(7)	(6) + Both spouses not always (in)activeb	5,610

^aFor comparability of time use categories we use four waves of CAMS (2005, 2007, 2009, and 2011) merged with the RAND HRS version M data file. Since the timing of the fielding of the HRS (even years) and CAMS (odd years) surveys are different, the variables in CAMS are merged to the preceding HRS wave, e.g. CAMS 2005 to HRS 2004, etc.

^bBased on the variable self-reported labor market status (RwLBRF) in the HRS data.

Table A2:

Home production in HRS/CAMS 2005–2011 (h/week)^a

	Mean	SD	% Total
Home production activities
House cleaning	4.4	5.9	2.7
Laundry	2.4	3.5	1.5
Gardening	2.7	5.1	1.6
Shopping	3.9	4.4	2.4
Cooking	6.2	6.8	3.8
Financial management	1.0	1.9	0.6
Home maintenance	1.0	2.8	0.6
Vehicle maintenance	0.4	1.0	0.2
Home production	21.8	18.6	13.2
Non home production activities
Watching TV	20.4	16.0	12.4
Reading newspapers or magazines	5.2	5.4	3.2
Reading books	3.6	6.0	2.2
Listening to music	6.3	10.0	3.8
Playing games	1.2	3.1	0.7
Attending concerts/movies	0.3	1.0	0.2
Singing/playing instrument	0.3	1.3	0.2
Arts and crafts	0.6	2.5	0.4
Dining out	1.5	2.2	0.9
Personal hygiene	6.5	6.5	3.9
Caring for pets	2.6	7.9	1.6
Managing medical condition	1.9	10.6	1.2
Walking	6.3	10.6	3.8
Sports and exercise	2.3	4.9	1.4
Visiting in-person with friends/family	6.8	11.7	4.1
Communication by telephone/letters/e-mail	4.9	7.0	3.0
Physically showing affection	2.9	5.8	1.8
Helping others	1.8	5.8	1.1
Attending religious services	1.0	1.7	0.6
Attending meetings/clubs	0.4	1.1	0.2
Working for pay	12.1	19.2	7.3
Volunteer work	0.9	3.5	0.5
Using computer	1.8	2.6	1.1
Sleeping and napping	47.9	17.8	29.0
Praying/meditating	3.5	7.1	2.1
Total time use	165.0	64.5	100.0

^aStatistics are presented for our subsample of 5,610 observations.

Table A3:

Substitutable consumption spending in HRS/CAMS 2005–2011 (USD/year)^a

	Mean	SD	% Total
Substitutability - Possible
Dining out	2,228	3,127	4.6
Dishwasher	31	135	0.1
Housekeeping services	429	1,158	0.9
Washing/Drying machine	86	311	0.2
Gardening services	368	1,146	0.8
Home repair services	1,487	4,529	3.1
Vehicle maintenance	788	930	1.6
Substitutability - Possible, Clear relation to substitutes
Housekeeping supplies	447	648	0.9
Gardening supplies	356	805	0.7
Home repair supplies	1,096	2,710	2.3
Substitutability - Possible, Not likely
Clothing	996	1,716	2.1
Substitutable consumption	5,416	6,842	11.3
Substitutable consumption (incl. suppl.)	7,315	8,130	15.2
Substitutable consumption (incl. suppl., clothing)	8,310	8,829	17.3
Substitutability - Impossible
Health insurance	2,653	3,137	5.5
Health services	1,439	3,869	3.0
Drugs	1,190	2,039	2.5
Medical supplies	233	669	0.5
Car payments	2,233	4,833	4.6
Car insurance	1,347	932	2.8
Home insurance	943	1,040	2.0
Mortgage interest	3,569	6,844	7.4
Property tax	2,421	3,002	5.0
Rent	842	3,499	1.7
Household furnishings	776	1,935	1.6
Electricity	1,818	1,818	3.8
Heat	989	1,392	2.1
Water	529	791	1.1
Phone/Cable/Internet	1,688	1,547	3.5
Tickets	236	634	0.5
Trips/vacations	2,532	3,895	5.3
Refrigerator	95	352	0.2
Computer	155	425	0.3
Television	190	560	0.4
Hobbies	352	947	0.7
Sports	307	1,291	0.6
Contributions	2,131	3,857	4.4
Cash gifts	2,202	6,341	4.6
Personal care	638	992	1.3
Food/drink grocery	5,384	4,778	11.2
Total consumptionb	48,140	29,305	100.0
Total consumption (ex. durables)	47,187	29,171	98.0

^aStatistics are presented for our subsample of 5,610 observations. Monetary measures are expressed in 2011 US dollars using the Consumer Price Index of the Bureau of Labor Statistics.

^bWe define total consumptions as the total of durable and nondurable consumption excluding the categories car purchases and car use.

A.3. Full summary statistics

Table A4:

Summary statistics^a

	Mean	SD	Min.	Max.	P50
Consumption spending (USD/y)
Dining out	2,228	3,127	0	58,049	1,382
Housekeeping services	429	1,158	0	20,870	10
Gardening services	368	1,146	0	27,642	0
Home repair services	1,487	4,529	0	130,184	152
Vehicle maintenance	788	930	0	8,298	542
Dishwasher	31	135	0	1,095	0
Washing/Drying machine	86	311	0	2,831	0
Total Substitutable	5,416	6,842	0	146,309	3,472
Total	47,187	29,171	0	296,984	40,688
Time use male (h/w)
House cleaning	2.3	3.8	0.0	56.0	1.0
Laundry	0.9	2.1	0.0	60.0	0.0
Gardening	3.5	5.8	0.0	160.0	2.0
Shopping	3.2	4.0	0.0	100.0	2.0
Cooking	3.3	5.1	0.0	120.0	2.0
Financial management	0.8	1.8	0.0	46.5	0.5
Home maintenance	1.3	3.2	0.0	57.7	0.5
Vehicle maintenance	0.6	1.4	0.0	49.3	0.2
Total home production	16.0	16.2	0.0	409.7	12.4
Time use female (h/w)
House cleaning	6.2	7.2	0.0	150.0	4.0
Laundry	3.7	3.9	0.0	60.0	3.0
Gardening	1.7	3.6	0.0	48.0	0.0
Shopping	4.2	4.2	0.0	60.0	3.0
Cooking	8.5	7.2	0.0	120.0	7.0
Financial management	0.9	1.7	0.0	55.8	0.5
Home maintenance	0.6	1.8	0.0	58.1	0.0
Vehicle maintenance	0.2	0.6	0.0	14.0	0.0
Total home production	25.9	19.1	0.0	183.2	22.1
Male characteristics
1(Retired)	0.72	0.45	0.00	1.00	1.00
Age	66.6	7.6	51.0	80.0	67.0
1(Age ≥ 62)	0.72	0.45	0.00	1.00	1.00
1(Badhealth)	0.06	0.25	0.00	1.00	0.00
ADL (0–5)	0.17	0.62	0.00	5.00	0.00
Female characteristics
1(Retired)	0.67	0.47	0.00	1.00	1.00
Age	63.8	7.5	51.0	80.0	64.0
1(Age ≥ 62)	0.59	0.49	0.00	1.00	1.00
1(Badhealth)	0.06	0.24	0.00	1.00	0.00
ADL (0–5)	0.20	0.69	0.00	5.00	0.00
Household characteristics
Household size > 2	0.26	0.44	0.00	1.00	0.00
Wave 2007	0.25	0.43	0.00	1.00	0.00
Wave 2009	0.24	0.43	0.00	1.00	0.00
Wave 2011	0.27	0.44	0.00	1.00	0.00

^aSummary statistics are presented for our sample of 5,610 observations. Monetary measures are expressed in 2011 US dollars using the Consumer Price Index of the Bureau of Labor Statistics.

Table A5:

Household consumption spending ($ per year)

	Non-retired (m), Non-retired (f)		Retired (m), Non-retired (f)
	Mean	S.D.	Mean	S.D.
Dining out	2,360.36	2,746.58	2,139.93	2,717.91
Housekeeping services	487.55	1,090.72	397.14	1,186.40
Gardening services	331.16	1,043.25	290.24	996.32
Home repair services	1,871.17	6,252.26	1,302.10	3,341.12
Vehicle maintenance	1,045.41	1,067.86	797.67	853.04
Substitutable consumption	6,237.31	8,226.39	5,056.10	5,676.95
Consumption w/o durables	53,792.18	29,654.00	48,093.84	27,647.10
Observations	996		878
	Non-retired (m), Retired (f)		Retired (m), Retired (f)
	Mean	S.D.	Mean	S.D.
Dining out	2,611.73	3,414.12	2,140.73	3,281.80
Housekeeping services	626.80	1,529.21	383.44	1,086.40
Gardening services	456.06	1,122.55	385.89	1,217.26
Home repair services	2,063.00	6,978.01	1,312.67	3,466.83
Vehicle maintenance	903.14	1,108.63	683.31	846.28
Substitutable consumption	6,764.34	9,432.65	5,013.21	5,995.21
Consumption w/o durables	53,798.86	35,153.00	43,654.91	27,615.95
Observations	574		3,162

A.4. Full estimation results

Table A6:

Full estimates baseline regression^abc

		$C_{it}^m$		H itm		H it f		R itm		R it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\beta }_1^{jm}$	A itm	0.06	0.07	1.61	1.65	−3.38*	2.05	0.00	0.02	0.00	0.02
${\beta }_2^{jm}$	$A_{itm}^2\left(/1,000\right)$	−0.35	0.45	−14.02	10.71	27.20**	13.90	0.06	1.08	1.01	1.14
${\beta }_3^{jm}$	1(badhealthitm)	0.02	0.04	0.66	1.07	−2.06	1.73	0.09**	0.04	0.01	0.03
${\beta }_4^{jm}$	ADL itm	−0.03	0.05	−1.13**	0.50	−0.28	0.60	−0.01	0.02	0.00	0.01
${\beta }_1^{jf}$	A it f	0.01	0.06	2.10	1.56	3.88**	1.82	0.02	0.02	0.00	0.02
${\beta }_2^{jf}$	$A_{itf}^2\left(/1,000\right)$	−0.16	0.45	−8.45	11.28	−30.26**	13.38	0.40	0.84	2.04***	0.76
${\beta }_3^{jf}$	1(badhealthit f)	−0.01	0.10	−0.91	1.52	−2.69	2.25	−0.05	0.03	0.10**	0.04
${\beta }_4^{jf}$	ADL it f	−0.02	0.03	−0.41	1.18	−1.86***	0.63	0.03*	0.02	0.03	0.02
${\zeta }_1^j$	Constant	8.66***	1.41	17.56	27.48	50.37	39.07	0.17	0.36	−0.11	0.17
${\zeta }_2^j$	1(2007it)	−0.04	0.05	−3.09**	1.55	−1.35	1.65	−0.01	0.03	0.10***	0.03
${\zeta }_3^j$	1(2009it)	−0.08	0.10	−4.95	3.15	−3.26	3.17	0.01	0.06	0.19***	0.07
${\zeta }_4^j$	1(2011it)	−0.10	0.15	−7.07	5.13	−4.57	5.01	0.02	0.09	0.30***	0.11
${\zeta }_5^j$	1(Householdsizeit > 2)	0.02	0.04	0.85	0.69	1.05	0.86	0.02	0.02	−0.01	0.02
${\gamma }_1^{jm}$	R itm	−0.17***	0.05	4.36***	1.25	2.11	1.71
${\gamma }_1^{jf}$	R it f	−0.11***	0.04	1.14	1.07	6.21***	2.06
	Mundlak p-value	0.00		0.00		0.04		0.03		0.00
	Log likelihood	−56,807.16
	Chi2 p-value	0.00

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include the individual mean of time-varying covariates: Mundlak-variables are jointly significant. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bJoint significance of RDD coefficients gives p – value = 0.001 and p – value = 0.000 for men and women, respectively.

^cEstimated correlations between the error terms are presented in Table 5.

B

B. Online Appendix: Robustness of baseline results

Table B1:

Estimation results: Work-related and health expenses^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
Excl. work-related expenses
${\gamma }_1^{jm}$	R itm	−0.15***	0.03	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.04	0.03	−0.18	0.73	3.15***	0.72
Excl. health expenses
${\gamma }_1^{jm}$	R itm	−0.15***	0.03	3.66***	0.58	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.06*	0.03	−0.18	0.73	3.15***	0.72

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year excluding clothing and transport spending or excluding drugs, health services, and medical supplies. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The Simulated Maximum Likelihood is ran with 100 Halton draws.

Table B2:

Retirement definitions^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
Work to retirement only
${\gamma }_1^{jm}$	R itm	−0.15***	0.03	5.06***	0.77	−0.47	1.05
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−1.13	0.92	5.19***	1.04
Excl. partial retirement
${\gamma }_1^{jm}$	R itm	−0.15***	0.02	4.23***	0.56	−0.19	0.63
${\gamma }_1^{jf}$	R it f	−0.07**	0.03	−1.02	1.67	3.40***	0.67
Market work hours (W, per week)
${\gamma }_1^{jm}$	Witm/100	0.44***	0.05	−11.89***	1.29	3.44**	1.62
${\gamma }_1^{jf}$	Wit f/100	0.23***	0.07	5.70	1.51	−12.47***	1.67

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year excluding clothing and transport spending or excluding drugs, health services, and medical supplies. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The Simulated Maximum Likelihood is ran with 100 Halton draws.

Table B3:

SEM without Fixed Effects^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.03	3.54***	0.58	−0.85	0.70
${\gamma }_1^{jf}$	R it f	−0.06**	0.03	−0.12	0.71	3.11***	0.72

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include control variables.

Table B4:

Separate equations with Fixed Effects^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.03	3.66***	0.59	−0.96	0.71
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−0.18	0.73	3.15***	0.72

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include control variables.

Table B5:

Linear age effects^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.14***	0.03	3.86***	0.59	−0.98	0.70
${\gamma }_1^{jf}$	R it f	−0.05	0.03	−0.14	0.72	3.22***	0.71

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include control variables.

Table B6:

Households with male aged 57–67^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.10***	0.03	3.10***	0.76	−0.13	0.95
${\gamma }_1^{jf}$	R it f	−0.05	0.04	0.00	0.76	2.89***	0.97

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. All regressions include control variables.

Table B7:

The effect of retirement on spending, home production, and shopping time decisions^a

		$C_{it}^m$		H itm		H it f		Shop itm		Shop it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.03	3.66***	0.58	−0.96	0.71	0.71***	0.13	−0.10	0.16
${\gamma }_1^{jf}$	R it f	−0.05*	0.03	−0.18	0.73	3.15***	0.72	0.11	0.20	0.44***	0.15

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. Leisure is total leisure time excluding sleeping time. The Simulated Maximum Likelihood is ran with 100 Halton draws.

Table B8:

The effect of retirement on cooking, groceries, and dining out^a

		$C_{it}^{\mathit{\text{dining}}}$		$C_{it}^{\mathit{\text{grocery}}}$		$H_{itm}^{\mathit{\text{cook}}}$		$H_{itm}^{\mathit{\text{cook}}}$
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.36***	0.10	−0.09*	0.06	1.04***	0.19	−0.56**	0.28
${\gamma }_1^{jf}$	R it f	−0.13	0.09	−0.04	0.06	−0.39*	0.22	1.36***	0.28

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on dining out and groceries per year. Home production is hours spend on cooking per week. The Simulated Maximum Likelihood is ran with 100 Halton draws.

C

C. Online Appendix: Regression Discontinuity

C.1. Discontinuity figures

Figure 1:

Fraction of retirees by age of men (a-c) and women (d-f)

Figure 2:

Household consumption spending ($ per year) of men (a) and women (b)

Figure 3:

Home production (hours per week) of men (a) and women (b)

C.2. Regression Discontinuity specifications

Table C1:

Reduced form results^a

		Y it		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\theta }_1^{jkm}$	D itm	−0.11***	0.02	1.75***	0.46
${\theta }_1^{jkf}$	D it f	−0.13***	0.02			2.29***	0.51

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Income is the Inverse Hyperbolic Sine transformation of total gross household income per year. Home production is the sum of hours spend in home production activities per week.

Table C2:

Separate Instrumental Variable estimations without control variables^a

		$C_{it}^m$		H itm		H it f		R itm		R it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.25***	0.04	2.27***	0.83
${\gamma }_1^{jf}$	R it f	−0.28***	0.04			5.30***	1.21
${\theta }_1^{jkm}$	D itm							0.28***	0.02
${\theta }_1^{jkf}$	D it f									0.24***	0.02

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week.

Table C3:

Regression Discontinuity without control variables^ab

		$C_{it}^m$		H itm		H it f		R itm		R it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.11**	0.05	3.37***	0.93	0.60	1.65
${\gamma }_1^{jf}$	R it f	−0.16***	0.04	−1.19	0.82	3.58***	1.47
${\theta }_1^{jkm}$	D itm							0.11***	0.02	0.03	0.02
${\theta }_1^{jkf}$	D it f							0.03*	0.02	0.08***	0.02

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bJoint significance of RDD coefficients ${\theta }_1^{jkm}$ and ${\theta }_1^{jkf}$ gives p – value = 0.000 and p – value = 0.000 for men and women, respectively.

Table C4:

Regression Discontinuity with Fixed Effects^ab

		$C_{it}^m$		H itm		H it f		R itm		R it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.16***	0.04	4.59***	1.06	2.62*	1.33
${\gamma }_1^{jf}$	R it f	−0.12***	0.03	0.78	0.90	6.44***	1.69
${\theta }_1^{jkm}$	D itm							0.09***	0.02	0.02	0.02
${\theta }_1^{jkf}$	D it f							0.03*	0.02	0.08***	0.02

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Marginal effects are presented. Standard errors are clustered at the individual level. j = c,hm,h f ,rm,r f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year. Home production is the sum of hours spend in home production activities per week. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bJoint significance of RDD coefficients ${\theta }_1^{jkm}$ and ${\theta }_1^{jkf}$ gives p – value = 0.000 and p – value = 0.000 for men and women, respectively.

D

D. Online Appendix: Heterogeneity analyses

According to the results in Table D1, people who worry a lot about not having enough income to get by have substantially higher drops in consumption spending at retirement. Households that worry a lot tend to react by primarily increasing the home production of the wife when the male and female retire. Allowing for heterogeneous effects by available income does not alter our main conclusions. According to the results in Table D2, we particularly find that men increase their home production substantially if their wife retires and is in bad health. Such an effect is not found among women whose husband is in bad health. Neither do we find an effect of health on own home production decisions or household consumption spending. The results shown in Table D3 indicate that consumption responds stronger to male retirement during the Great Recession and less strong to female retirement. A possible explanation is that men, often being the main earner in the household, had to retire involuntarily during the recession. Women, on the other hand are more likely to complement the household income which is also suggested by the cross-spouse effects in the probability to retire induced by the recession. Having a husband of age 62 increases the probability of women to retire during the recession while having a wife of age 62 decreases the probability of retirement among men during the recession (not shown in the table for brevity).

Table D1:

Heterogeneity in retirement income^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.15***	0.03	3.60***	0.59	−1.11	0.71
${\gamma }_2^{jm}$	Ritm · 1(Worryit−1m)b	−0.17***	0.04	1.04	0.89	2.85**	1.31
${\gamma }_1^{jf}$	R it f	−0.03	0.03	−0.24	0.74	2.80***	0.73
${\gamma }_2^{jf}$	Rit f · 1(Worryit−1f)b	−0.19***	0.03	0.44	0.78	2.88***	1.08

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year excluding clothing and transport spending or excluding drugs, health services, and medical supplies. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bThe variable Worry equals one if the person answers to worry a lot about not having enough income to get by and equals zero if the person answers to worry somewhat, a little, or not at all.

Table D2:

Heterogeneity in health^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.17***	0.03	3.75***	0.59	−0.95	0.71
${\gamma }_2^{jm}$	Ritm · 1(Badhealthitm)b	0.40	0.29	−2.37	2.60	−1.15	3.93
${\gamma }_1^{jf}$	R it f	−0.06***	0.03	−0.32	0.74	3.33***	0.72
${\gamma }_2^{jf}$	Rit f · 1(Badhealthit f)b	0.23	0.15	5.38***	2.09	−7.09*	4.23

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year excluding clothing and transport spending or excluding drugs, health services, and medical supplies. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bThe variable badhealth equals one if the person answers to be in a bad or fair health and equal zero if they answer to be in excellent, very good, or good health.

Table D3:

Heterogeneity due to Great Recession^a

		$C_{it}^m$		H itm		H it f
		Coeff.	S.E.	Coeff.	S.E.	Coeff.	S.E.
${\gamma }_1^{jm}$	R itm	−0.10**	0.04	3.33***	0.77	−1.05	0.69
${\gamma }_2^{jm}$	Ritm · 1(GRitm)b	−0.10**	0.04	0.67	1.04	0.20	1.30
${\gamma }_1^{jf}$	R it f	−0.11**	0.05	−0.04	0.69	2.97***	0.99
${\gamma }_2^{jf}$	Rit f · 1(GRit f)b	0.08*	0.05	−0.28	1.27	0.36	1.33

^a* Significant at the 0.10 level; ** at the 0.05 level; *** at the 0.01 level. Standard errors are clustered at the individual level. j = c,hm,h f. k = m, f. Consumption is the Inverse Hyperbolic Sine transformation of spending on non-durable consumption per year excluding clothing and transport spending or excluding drugs, health services, and medical supplies. Home production is the sum of hours spend in home production activities per week. All regressions include the variables included in the baseline model. The Simulated Maximum Likelihood is ran with 100 Halton draws.

^bThe variable GR equals one if for the waves 2009 and 2011 and equals zero for the waves 2005 and 2007.