Household portfolios and financial preparedness for retirement
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Crawford, Rowena; O'Dea, Cormac Article Household portfolios and financial preparedness for retirement Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Crawford, Rowena; O'Dea, Cormac (2020) : Household portfolios and financial preparedness for retirement, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 11, Iss. 2, pp. 637-670, https://doi.org/10.3982/QE725 This Version is available at: https://hdl.handle.net/10419/217198 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/
Quantitative Economics 11 (2020), 637–670 1759-7331/20200637 Household portfolios and financial preparedness for retirement Rowena Crawford Institute for Fiscal Studies Cormac O’Dea Department of Economics, Yale University and Institute for Fiscal Studies Using a lifecycle model of consumption, saving and portfolio choice combined with linked survey and administrative data on wealth and lifetime earnings we evaluate measures of retirement preparedness. We estimate heterogeneous discount factors for households and compare these estimates of their patience to their replacement rates—the simple measure often used to evaluate the adequacy of retirement savings. We find first that the specification of the model’s asset structure matters quantitatively for preference parameter estimates—households appear to be much more patient when they are assumed to have access only to a riskfree asset compared to when we account for the fact that much of their wealth is stored in higher-return tax-advantaged private pensions and in housing. Second, we find that only the most patient households achieve the replacement rates out of final earnings that are often recommended by policymakers and industry as sensible benchmarks for retirement preparedness. Notwithstanding this, we find that even quite impatient households in the population we study achieve high replacement rates out of lifetime average income—a more sensible summary measure of preparedness for retirement. Keywords. Lifecycle model, wealth, savings, pensions, patience, discount factors. JEL classification. D14, D31, D91, E21, H55. 1. Introduction Many countries are implementing policies to encourage saving for retirement. Examples include: mandatory private pension saving in Australia (introduced in 1992), a compulsion for all employers to auto-enroll employees into private pension saving in the United Kingdom (introduced from 2012) and auto-enrollment in the US army in 2010, with a number of US states now implementing or piloting similar initiatives. The rationale for Rowena Crawford: [email protected] Cormac O’Dea: [email protected] Thanks to James Banks, Richard Blundell, Uta Bolt, Thomas Crossley, Mariacristina De Nardi, Carl Emmerson, Scott Findley, Eric French, Hamish Low, Rory McGee, Aneesha Parvathaneni, Ananth Seshadri, Stephanie Weber, and four anonymous referees for very helpful comments and to the Economic and Social Research Council (via ESRC-NCRM Node PEPA ref: ES/I02574X/1; Centre for Microeconomic Analysis of Public Policy ref: ES/M010147/1; Secondary Data Analysis grant ref: ES/N011872/1 and ESRC grant ES/P001831/1) and to the Joseph Rowntree Foundation for funding. Correspondence to Cormac O’Dea. Any errors are our own. ©2020 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0. Available at http://qeconomics.org.https://doi.org/10.3982/QE725
638 Crawford and O’Dea Quantitative Economics 11 (2020) such policies is that individuals, left to their own devices, will not save enough for retirement. This paper examines the evidence for the presumption, implicit or explicit, that there is systematic undersaving. We have two distinct approaches. The first develops a lifecycle model of consumption and saving and combines this with microdata on the wealth holdings (from household survey data) and lifetime earnings histories (from linked administrative data) for a sample of English households. The model is a rich one: households can save in each of pension and nonpension wealth; they face risks over earnings, pension fund returns, and longevity; and they are heterogeneous in their earnings processes, their fertility, and their patience. We use this model to estimate the implied level of patience, for each household in our sample, that would rationalize observed wealth holdings. The data which, together with our lifetime earnings data and model, is used to identify the discount factor is wealth close to retirement. Our estimates of discount factors, therefore, summarize how households trade-off consumption during working life and saving for retirement and, as such, the estimated discount factor gives a summary measure of the extent to which households have planned for their retirement. We complement this approach by estimating a more conventional summary measure of how households trade-off working life consumption and saving—replacement rates out of lifetime earnings (see, e.g., Munnell and Soto (2005)andBanks, Emmerson, Oldfield, and Tetlow (2005)). Comparisons of observed or projected replacement rates (out of either career average or of final earnings) to target levels are often used by policymakers to assess adequacy of savings among cohorts approaching retirement (e.g., Bridges and Choudhury (2005), Pension Commission (2004)) and by financial advisers in recommendations to clients (e.g., TIAA (2018)). While such approach has the advantage of simplicity, any threshold selected as the appropriate one for saving is necessarily ad hoc. Furthermore, assuming a single replacement rate for all households, regardless of their personal circumstance (trajectory of income, number of children, life expectancy, etc.) is “conceptually flawed” (Scholz and Seshadri (2009), building on earlier work by Gokhale, Kotlikoff, and Warshawsky (1999)). We show the relationship between our estimated replacement rates and the estimated discount factors from our first approach and highlight some implications for users of the simple replacement rate approach. We have four principle findings. First, we can match the distribution of wealth with modest heterogeneity in the degree of patience. The interquartile range for estimates of the discount factor from our preferred model stretches from 092 to 097.Themedian discount factor is 095, close to conventional values estimated (or assumed) by papers using lifecycle models that assume homogeneous discounting. We validate these estimates of discount factors in a number of ways. In particular, we show that those with higher education are estimated to be more patient (as has been previously found in the literature), the estimates are associated with other known correlates of patience (e.g., smoking behavior) and that our estimated discount factors correlate with self-reported measures of patience elicited from the same survey respondents. Second, we highlight the importance of capturing the richness of the savings environment available to households for the estimation of discount factors. The median discount factor estimated using a simple one-risk-free-asset model would be 104,with
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 639 an interquartile range that stretches from 101 to 108. When we take account in the model of the fact that households, in reality, have access to a tax-advantaged pension fund which incentivizes saving for retirement, the median estimate falls to 099. Neither of the models underlying these estimates accounts, though, for the particular features of housing as a store of wealth (e.g., that it returns a flow of services and that it tends to be purchased using leverage). Once we account for these features in the return on nonpension wealth, the median estimated discount rate factor falls to 095—our preferred estimate. Third, few of the cohorts that we study (those born in England in the 1940s) will have substantially lower income in retirement than their average earnings over the course of their working life. The median replacement rate is 845%, and only around one-third would have pension income at age 65 of less than 70% of their average lifetime earnings. However, replacement rates are lower when pension income is compared to a proxy for final pre-retirement earnings (which is common practice among policymakers and industry). In particular, the median replacement of the average of the best 5years of earnings is 47%, and almost nine out of ten households are found to replace less than 70% of this measure of earnings in retirement. Finally, bringing together our two approaches, we show that these estimated replacement rates out of a measure of final earnings are low—compared to thresholds for “adequacy” commonly used—even when wealth holdings can be justified without appealing to high levels of individual impatience. This suggests that those using replacement rates to assess retirement preparedness must be careful with their choice of replacement rate and the associated threshold against which adequacy is assessed. While the ease of communicating simple replacement rate benchmarks is clear, those recommending them need to (a) be clear that suggesting high replacement rates out of final earnings represents an extremely demanding threshold and (b) be cognizant of the importance of individual circumstances and preferences when recommending savings choices. Our paper contributes to two distinct literatures. The first is that which has used lifecycle models to assess household retirement saving (most notably Engen, Gale, and Uccello (1999) and Scholz, Seshadri, and Khitatrakun (2006)). Our paper is most similar to Scholz, Seshadri, and Khitatrakun (2006), who showed that levels of wealth accumulated by the vast majority of households in a now-retired cohort in the US were more than an “optimal” level of wealth that the authors derive. “Optimal” wealth in that paper is pinned down using a lifecycle model in which a homogeneous discount rate is assumed, which is set approximately equal to the rate of return on the model’s (single) asset. We add to their paper by (a) enriching the asset structure, primarily by including a risky, higher expected return and tax-advantaged pension asset; (b) estimating the distribution of discount rates rather than assuming a value; and (c) showing the relationship between those discount rates and the instrument central to notions of optimal saving used by policymakers—replacement rates. The second literature to which we contribute is that concerning the estimation of discount factors. Lifecycle models have typically assumed homogeneity of discount rates (or homogeneity conditional a set of observable characteristics, e.g., education).
640 Crawford and O’Dea Quantitative Economics 11 (2020) Early estimated structural models include Attanasio, Banks, Meghir, and Weber (1999), Gourinchas and Parker (2002), and Cagetti (2003); more recently (and focusing on those papers most relevant to the current paper), papers studying Medicaid (De Nardi, French, and Jones (2016)), old-age means-tested transfers (Braun, Kopecky, and Koreshkova (2016)), and intergenerational transfers (Lockwood (2018)) have assumed that agents all have the same degree of patience. This assumption of a homogeneous discount factor is a strong one. Experiments have provided evidence in support of heterogeneous discount rates (Andersen, Harrison, Lau, and Rutström (2008), Andreoni and Sprenger (2012)), and such heterogeneity has been proposed as a candidate explanation for observed wealth inequality (Krusell and Smith (1998), Hendricks (2007), Hubmer, Krusell, and Smith (2019)). Using a “semistructural approach,” Alan and Browning (2010)andAlan, Browning, and Ejrnæs (2018) used, respectively, data on the consumption growth and on the comovements of income and consumption to estimate distributions of discount rates, finding substantial dispersion in measures of patience. Samwick (1998)andGustman and Steinmeier (2005) both solved lifecycle models and identified, as we do, a discount factor for each household by matching wealth levels in the data. Samwick (1998) solved a model with income uncertainty and estimates a discount factor for each household in a cross-sectional data set as that which rationalizes wealth to current income ratios; Gustman and Steinmeier (2005) solved a lifecycle model with deterministic income and estimate a discount factor for each household as that which rationalizes wealth stocks conditional on life-history of earnings. Computational advances, combined with our rich data, allow us to relax many of the assumptions made in those papers. We broaden the asset structure beyond the “single-safe-asset” workhorse model to make it more reflective of the assets in which households save for retirement, and we incorporate uncertainty in multiple dimensions (earnings, returns, and survival). The rest of this paper proceeds as follows. Section 2introduces the linked survey and administrative data that we use. Section 3outlines the model, while Section 4discusses the estimation and parameterization of features of the model. Section 5discusses our results. Section 6concludes. Appendices A-1 may be found in the Online Supplemental Material (Crawford and O’Dea (2020)). 2. Data Our data is formed by linking survey and administrative data. The survey data come from the English Longitudinal Study of Ageing (ELSA)—a biennial longitudinal survey of the household population of England aged 50 and over.1ELSA contains detailed data on demographics, labor market circumstances, income and, most importantly for our purposes, the level and composition of wealth holdings. 1ELSA is part of a family of international aging surveys, including the Health and Retirement Study (HRS) in the US and the Survey of Health, Ageing and Retirement in Europe (SHARE), that collect a similar set data using broadly comparable methodologies.
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 641 ELSA respondents were also asked for their National Insurance number (the equivalent of a US Social Security number) and permission to link to their history of National Insurance contributions. Almost 80% of ELSA respondents agreed to the linking of their survey records with their administrative data. Data on these contributions allow us to calculate individuals’ state pension entitlements, and (subject to some top-coding) to obtain a detailed history of their earnings. Appendix D.1 discusses how we convert our administrative data on National Insurance contributions into a panel of earnings. We use the 2002/03 ELSA data (the year for which the sample was linked) together with the linked National Insurance data. 2.1 Sample We restrict our attention to couple households that contain a man born between 1940 and 1949. There are 1615 couples of this type in the 2002/03 ELSA data. These individuals would be aged between 52 and 63 (and, therefore, approaching the UK public pension age of 65) when observed in 2002/03. We exclude households where either partner refused permission to link to their administrative data, since for these households we cannot obtain lifetime earnings. We also exclude households where the man is observed in the NI data for fewer than 5years and/or where households have more than 5 years of self-employment activity (since the NI data are less well suited to calculating the earnings histories of the self-employed—as is discussed in more detail in Appendix D.1). After applying these restrictions, 995 couples, or approximately 62% of couples, remain. Table 1provides descriptive statistics for our sample of households and for all ELSA couples in the relevant cohort. The average age of men in our sample when they are observed in 2002/03 is just under 57, with women on average being 54. Nearly 70% of men in our sample reported still being in work, and only 15% defined themselves as retired. Home ownership was the norm for this cohort—in our sample, nearly 90% of households own their home (either outright or still mortgaged). A comparison of the descriptive statistics from the survey data for our sample and the descriptives for all couples in ELSA in the relevant cohort suggests a close match along most observables between our sample and the full sample of couples in the cohort of interest. An exception to this is with regard to self-employed individuals who are underrepresented in our sample. This is unsurprising given that we drop those with significant histories of self-employment though this is accentuated by the self-employed being less likely to grant permission to link to their administrative records (see Bozio, Crawford, Emmerson, and Tetlow (2010)). 2.2 Wealth measures in ELSA Our model contains each of private pension wealth and nonpension wealth (which, in turn, comprises each of housing and more liquid wealth). Therefore, we must define an empirical analogue for each of these. The sum of these components is referred to as “private wealth.” Private pension wealth includes both Defined Benefit (DB) and Defined Contribution (DC) pensions. Wealth is calculated differently for each of these. DC pension wealth
642 Crawford and O’Dea Quantitative Economics 11 (2020) Table 1. Descriptive statistics for couples in ELSA of cohort 1940–1949. Our Sample All Male Female Male Female Individual characteristics Mean age 568541569540 Low education 353% 435% 365% 419% Mid education 273% 322% 266% 311% High education 374% 243% 368% 224% Employee 605% 595% 554% 529% Self-employed 110% 36% 152% 46% Retired 149% 111% 143% 108% Other 136% 258% 150% 272% Household characteristics Owner occupier 896% 876% Median total income £22,544 £22,166 Median employment income £17,870 £17,189 Median asset income £185 £182 Median private pension wealth £95,593 £72,384 Median housing wealth £120,000 £121,000 Median nonpension, nonhousing wealth £32,200 £30,625 Sample size 995 1615 is the reported value of funds held. We calculate DB pension wealth as the capital sum that would be required in our survey year to purchase the projected stream of DB income to which the household is entitled given their reported accrual of rights to date and the rules of the pension scheme. To calculate this, we first calculate the capital sum required at age 65, given annuity rates at that age.2The capital sum required in 2002/03 is then calculated by assuming that households would achieve a real rate of return equal to the model’s mean return on DC wealth between 2002/03 and the year in which they reach the age of 65. Housing wealth is the gross value of owner-occupied housing less any mortgage debt. Liquid wealth is the sum of all other nonpension wealth less any outstanding nonmortgage debt. The largest component of this is cash (and we refer to this form of wealth as “cash” below), but it also includes other liquid financial wealth, net nonprimary housing wealth and other wealth (business wealth and physical assets such as land, antiques, and collectibles). Table 2summarizes, for our sample of couples, the distribution of wealth held in each of these components. The mean level of total wealth is £407,400,ofwhicharound 369% is held in housing, 343% in private pension wealth, and 288% in cash and other liquid assets. This compares to mean lifetime earnings of £985,400. Holdings of wealth and each of its components rise with lifetime earnings, and ratios of mean total wealth 2The annuity rate is calculated using the model’s risk-free interest rate and survival probabilities (details are given below).
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 643 Table 2. Observed private net wealth (£, 000s), by lifetime earnings. Lifetime Earnings Total Pension Cash Housing Median Mean Median Mean Median Mean Median Mean Median Mean All 8889 9854 2807 4074956 1398322 1172 1200 1505 Lifetime earnings decile: Lowest 2998 2876643 251914035520 1525235639 2 5174 5103 1462 2167357656102534750977 3 6633 6583 1767 3029520805193 1092895 1132 4 7680 7654 2087 27466259401947199 50 1087 5 8517 8495 2422 3310723 1096272885 1005 1329 6 9326 9358 2525 3366981 1188300820 1150 1358 7 10517 10491 3481 3765 1095 1323469941 1325 1501 8 12022 12014 3197 4134 1252 1487345767 1400 1880 9 14409 14476 5466 6193 1962 24136 65 1447 2213 2334 Highest 18940 21557 6837 9527 2874 3723 1037 2988 2500 2816 to mean lifetime earnings are highest among those at the bottom and top of the lifetime earnings distribution (see also Venti and Wise (1999), Gustman and Steinmeier (1999), Bozio, Emmerson, O’Dea, and Tetlow (2017)), although the very large difference between mean and median wealth in the bottom decile highlights the fact that wealth is particularly skewed at that part of the distribution and that many households who have had low lifetime earnings hold little private wealth. 3. A model of saving for retirement We solve and estimate a lifecycle model of consumption, saving and portfolio choice. Details are given in this section. Briefly, its key features include: decisions made (collectively) by households that differ in their patience, uncertainty over employment, earnings, returns on a pension fund and mortality; exogenous heterogeneity over the earnings process and fertility; and a careful specification of the tax and benefit system. 3.1 Preferences and the economic environment 3.1.1 Preferences Household utility in each period (1year in the model) is assumed to exhibit constant relative risk aversion in equivalized consumption, multiplied by the number of equivalized adults in the household: U(ct)=nt ct nt1−γ 1−γ where (ct nt)is household equivalized consumption and ntis the number of equivalized adults in the household. The subscript trefers to the age of the household (taken to be the age of the male).
644 Crawford and O’Dea Quantitative Economics 11 (2020) 3.1.2 Employment and earnings Employment starts at age 20 and can continue until age 64, at which point employment is no longer possible. In each period, households get an employment offer with probability πj,wherejrepresents education group. Households are divided into three education groups: high-school drop outs, high school graduates, and those with at least some college.3 Earnings (eit) are therefore given by eit =˜ eit w.p. πj 0w.p. 1−πj where (˜ e) is household productivity, defined below. 1−πjcan therefore be interpreted as the probability of a spell of long-term unemployment (lasting a year) for both members of the couple. The log productivity of a household (the sum of earnings of both members of the couple) is given by the sum of a fixed effect, a quadratic in age (t) and a stochastic process which contains a first-order autoregressive process with normally distributed innovation. Households receive this value unless they receive an unemployment shock: ln ˜ eit =αi+δj 1t+δj 2t2+uit(1) uit =ρjuit−1+ξit ξ∼N0σ2 j The coefficients of the earnings process depend on education. 3.1.3 Household heterogeneity Households are ex ante heterogeneous. They differ by their education. Let ¯ jindex the combination of education levels of each member of a couple (and so takes one of nine values).4They also differ in the fixed effect in their earnings process (αi) which they are assumed to know from the start of life. We also include in the vector of fixed effects the number of children in the household at each age ({kit}100 t=20). The implication of this assumption is that couples know with certainty from the age of 20 exactly how many children they will have and when those children will be born.5In what follows, we summarize the “type” of household iby θi=(¯ jiαi{kit}100 t=20). Each household has its own type (θi) which will be part of the state space, and so each household faces a different optimization problem which must be individually solved. 3In the UK context, these are defined as having compulsory education only, compulsory but no postsecondary education and those with some post-secondary education. We use the (better known) US terminology though in this paper. 4While we assume that the education of the husband only determines the earnings process, the education of both spouses will be relevant for survival probabilities (and, therefore, also for annuity pricing). 5An alternative assumption—that children arrive probabilistically according to a process that depends on age (see Hong and Ríos-Rull (2012) and Jørgensen (2017))—would add substantially to the computational cost (as we would have to add the number of children as a state variable and include an additional dimension of integration) and would, we conjecture, be no closer to reality than assuming that households know how many children they will have.
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 651 4.1 Step 1: Parameterization This section discusses the model parameterization. First, the parameters that set the economic conditions (rates of return, policy environment) faced by our cohort of interest, and second, demographic and preference parameters. 4.1.1 Economic environment Return on cash The rate of return on cash is set at the average real return on cash balances, which was 16% between 1952 and 2012 (see Table 1of Barclays Capital (2012)). Share of nonpension wealth in housing To calculate s(at)—the share of nonpension wealth held in housing—we use data from the Wealth and Assets Survey which is a dedicated wealth survey of the British population that started in 2006. We regress the proportion of nonpension wealth held in housing wealth on a quadratic in total wealth. We also include cohort dummies and a set of time dummies constrained to sum to zero (a normalization suggested by Deaton and Paxson (1994) given the identification problem implied by the collinearity of age, period, and cohort). We do this only for those who own a house (recall that 90% of the households in our sample are homeowners). The modeled relationship is shown in Figure 16 in Appendix E—the share of wealth held in housing is high for those with the lowest wealth levels (approximately 09), falling to 065 for those with £1mofnonpensionwealth. Return on housing To specify the return on housing (given in equation (2)), we need to specify two rates of return (rhcg —the housing capital gain and rhr—the rental income from owner occupied housing), the mortgage interest rate (rmort ), and the leverage ratio (lev(t)). In setting rates of return, we follow the broad approach outlined by Kaplan and Violante (2014). The average real capital gain over the period 1976 to 2002—the first year that we have data to the year in which our sample of households are observed—was 32% (Nationwide Building Society (2014)). Our model abstracts from housing risk, so we follow Kaplan and Violante (2014) by subtracting the variance of returns, giving a real capital gain of 228%. The service flow from housing is calculated using the ratio of the estimate of aggregate housing consumption to the estimate of the value of the housing stock in the National Income and Product Accounts. This yields an average of 84%. We risk-adjust by subtracting the variance of returns and also subtract depreciation (1%, using data from the National Income and Product Accounts) and insurance costs (035%, taken from Kaplan and Violante (2014)). This yields a return of 702%.13 The mortgage rate is set at 59% and is calculated using data from the Bank of England (Bank of England (2017)). This is the average rate over time and over all products where historical data is available. Finally, the leverage ratio (lev(t)) is set in a manner 13This is the consumption value from having access to owner-occupied housing. We assume that this value does not increase as the value of a given quantity of housing increases. Therefore, households earn this 702% return on the value of their current stock of gross housing in 2002 housing prices (all other quantities in the model are also expressed in prices of this year). We convert housing wealth in other years to these prices by deflating (inflating) values in years after (before) that year by rhcg per year.
652 Crawford and O’Dea Quantitative Economics 11 (2020) similar to the housing share. Using the Wealth and Asset Survey, we regress the observed leverage ratio on a quadratic in age, as well as cohort and time dummies. The estimated function is given in Figure 17 in Appendix E. Pension fund returns We base the mean and standard deviation of pension fund returns on an index known as the “DCisions index.” This is an index of total fund returns that reflects the asset allocation decisions made by leading DC pension plans in their default investment strategies. This index provides information on returns stretching back to 1994. For years prior to 1994 when the DCisions index is not available, we estimate φt using the FTSE all-share index (on which data is available back to the early 1960s) and the ratio between the FTSE all-share index and the DCisions index over the period where both are available (1994–2010). We discuss how this is estimated in Appendix H. We use the mean and standard deviation of this time series in our model. These parameters are, respectively, ¯ φ=397% and σφ=138%. Unemployment rate The period in our model is a year. We consider a household in the data to be unemployed for a year if they have total earnings of less than £4402—the level of unemployment benefit payable to an unemployed couple in 2002/03. In our data, the incidence of unemployment, so defined, between the ages of 25 and 50 is 84%,65%, and 64% for our low, medium and high education groups, respectively. These are the unemployment probabilities used in the model. Public pension We model public pension entitlements as a quadratic in decile of fixed effect and decile of “final earnings” where the coefficients are allowed to vary by education. Final earnings in the data are measured as the average decile of the last 5years of observed earnings. For estimating this process, we only use data on those aged over 60 (for whom public pension entitlements are largely determined). Figure 1illustrates the relationship between modeled public pension entitlements and each of final earnings and earnings fixed effect. In the left hand panel, we give predicted public pension as final earnings decile varies (where for each earnings decile we set the fixed effect decile equal to its average for that group). In the right hand panel, we Figure 1. Public pension process.
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 653 give public pension as fixed effect decile increases (with final earnings similarly set at its group-specific mean). In the case of both state variables, there is only a slight gradient with respect to decile. Annuity rates The actuarially fair annuity rates are calculated using survival probabilities (the estimation of which are described below) and the risk-free interest rate. The administrative load is assumed to be 10% of the value of the DC fund to be annuitized. This is taken from Murthi, Orszag, and Orszag (2000) who apply the methodology of Mitchell, Poterba, and Warshawsky (1999) to the UK. We give the annuity rates in Appendix I (with the formula given in Section 3 of the Online Supplemental Material accompanying this paper). 4.1.2 Demographic and preference parameters Survival probabilities Our objective is to have survival curves for each gender and education group for our cohort of interest. The UK’s Office for National Statistics (ONS) produces period and cohort survival curves by gender but not by education. Period survival curves give survival probabilities by age given the age-specific mortality rates at a particular point in time—they therefore make no allowance for any later actual or projected changes in mortality. Cohort survival curves give survival probabilities by age for a given cohort and allow age-specific mortality rates to vary for known or projected changes in mortality over time. Cohort survival curves are thus more appropriate for our purposes. We use observed deaths in the ELSA panel between 2002/03 and 2012/13 to estimate asetofperiod survival curves by gender and education. Using these, we calculate the difference between these education-age-gender period survival probabilities and the ONS’ age-gender period survival probabilities. We then adjust the ONS’ age-gender cohort survival curves (for the 1945 cohort) using these differences to obtain education-agegender cohort survival probabilities. Equivalence scale The number of equivalent adults in a household nis set using the “modified OECD equivalence scale” (see Anyaegbu (2010) for a discussion). The first adult in a household counts for one equivalent adult, subsequent adults and children aged 14 and over count for half an equivalent adult, while children aged 13 or younger account for 30% of an equivalent adult. Coefficient of relative risk aversion The coefficient of relative risk aversion has proved a difficult coefficient to identify.14 Our approach is to set the coefficient of relative risk aversion to 3, following the most closely-related work (Scholz, Seshadri, and Khitatrakun (2006)). Summary These parameters of the model and values assigned are summarized in Table 3. 14See Chiappori and Paiella (2011) for a review and recent empirical contribution.
654 Crawford and O’Dea Quantitative Economics 11 (2020) Table 3. Parameterization. Parameter Symbol Value/Source Unemployment rate {π}3 j=186%,65%,64% Return on cash rc16% Housing capital gain rhcg 23% Housing rental yield rhhr70% Mortgage interest rate rmort 59% Mean return on DC fund ¯ φ40% Variance of return on DC fund σ2 φ138% Survival probabilities sjm t,sjf tONS life tables adjusted for education using survival differences by education observed in ELSA Administrative load on annuities z10% Coefficient of relative risk aversion γ3 Equivalence scale nModified OECD scale 4.2 Step 2: Estimation 4.2.1 Estimation of earnings processes To estimate the parameters of the earnings process, we aggregate individual earnings histories into household earnings histories. We then divide households into three groups according to the education of the man in the couple (indexed by j). The parameters to be estimated are {αi}N i=1and {δj 1δj 2ρjσ2 j}3 j=1. To allow for measurement error in earnings, we augment the earnings process given in equation (1)withani.i.d. measurement error term mit . The assumed data generating process for our earnings data is given in equations (11)–(13): ln ˜ edata it =αi+δj 1ti+δj 2t2 i+vit(11) vit =uit +mit(12) uit =ρjuit−1+ξit(13) The approach to estimation is a standard one (see, e.g., Low, Meghir, and Pistaferri (2010)). It involves first running a fixed effects regression and estimating the household fixed effect and quadratic in age. Residuals (r) are then obtained: rit =ln ˜ edata it −ˆαi−ˆ δj 1ti−ˆ δj 2t2 i The parameters of the wage process are obtained by choosing those that minimize the distance between the empirical covariance matrix of differences in these residuals and the theoretical covariance matrix implied by equations (11)–(13). Estimates of the parameters of the earnings process for each of three education groups are given in Table 15 in Appendix I. 4.3 Estimation of discount factor Conditional on a discount factor, the model solution gives decision rules for each household. We can use these rules, combined with realized earnings and investment returns
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 655 that they receive to simulate behavior (consumption, savings in each asset and, therefore, total wealth (A=a+DC)) at each age: Asim it =fiβiθi{eiτ }t τ=1(14) where βiis patience, θiis household type and {eiτ }t τ=1contains earnings shocks up to t. The discount factor estimate is that for which simulated wealth and observed wealth coincide in 2002 (when wealth is observed). Adata i2002 =Asim i2002 =fiˆ βiθi{eiτ }2002 τ=1(15) We calculate a discount factor for all households whose wealth can be rationalized with a discount factor in the range 05to 15.973% of households in our sample have wealth levels that can be rationalized with patience in this range (and 960% in the narrower range of 08to 12). 5. Results The model laid out in the previous section has three purposes. First, it will be used to estimate the distribution of discount factors which would rationalize observed household wealth holdings. Second, it will be used to understand the importance of accounting for household portfolios in models of saving for retirement. Third, it will be used to document a link between measures of preparedness for retirement used by policymakers (replacement rates) and discount factors, the preference parameter which bears most heavily on the preparedness for retirement of agents in lifecycle models. 5.1 Estimates of discount factors Table 4summarizes the distribution of discount factors for each of three versions of our model. The first row, which we give as a benchmark, gives estimates derived from a simple one-asset lifecycle model where all wealth accrues the risk-free rate (16%)asa return. The median discount factor is 1042 with an interquartile range stretching from 1011 to 1080. These rates are extremely high relative to those which have been found in the literature. The second row adds the capacity for agents to save in an illiquid taxadvantaged pension asset, which earns an expected return that is higher than the safe return but is risky. All of nonpension wealth still earns the safe rate of return. The median estimated discount factor falls to 0999. Additionally, the distribution shows less variation, with an interquartile range of 0976 to 1021, as part of heterogeneity in wealth is Table 4. Distribution of discount factors—baseline models. Model Mean p10 p25 Median p75 p90 One asset 1052 0980 1011 1042 1080 1125 No housing treatment 1002 0949 0976 0999 1021 1052 Modeled housing 0947 0894 0923 0950 0975 1002
656 Crawford and O’Dea Quantitative Economics 11 (2020) Figure 2. Distribution of discount factors. explained by differential (across households of different income and with different fertility profiles) incentives to avail of the tax breaks associated with pension saving. Neither model takes into account that much of nonpension wealth is held in housing. The third row gives estimates from our preferred version of our model that, in addition to including the pension asset, also calibrates the return on nonpension wealth to take into account housing (as discussed in Section 3.1.4). The median discount factor is 0950, with an interquartile range of 0923 to 0975. Figure 2illustrates the three distributions summarized in Table 4. 5.1.1 Validation of discount factor estimates The discount factors we estimate are identified by fitting total private wealth simulated by our model to observed total private wealth holdings. One test of the model is therefore how holdings of individual components of wealth fit the data. Figure 3illustrates how modeled non-pension wealth (left-hand panel) and modeled pension wealth (right-hand panel) compare to that observed in the data for each household. Nonpension wealth (which includes housing and nonhousing assets) is strongly clustered around the 45-degree line—the correlation coFigure 3. Portfolio composition—preferred model (housing modeled).
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 657 Table 5. Observed and modeled wealth, means (£, 000s). Total Pension Nonpension Data Modeled Data Modeled Data Modeled All 3874 3873 1429 1208 2445 2665 Lifetime earnings decile: Lowest 1728 1729412226 1316 1502 2 2189 2186663453 1526 1733 3 2401 2400785503 1616 1898 4 2774 2770949727 1825 2043 5 2965 2962 1106752 1859 2210 6 3437 3433 1212951 2225 2482 7 3765 3766 1323 10452443 2721 8 4134 4133 1487 1263 2648 2870 9 6193 6192 2413 2168 3781 4024 Highest 8817 8826 3783 3846 5034 4980 Note: The totals in the data columns differ slightly from those in Table 2as the sample used here are only those for whom we can rationalize observed wealth holdings with a discount factor between 05and 15. efficient between modeled and observed nonpension wealth is 08577. Pension wealth is more clustered around low levels, but is also strongly correlated, with a correlation coefficient of 07282.Table5shows the mean holdings of each of pension and nonpension wealth in the data and the mean holdings implied by the model by decile of lifetime earnings. Figure 9c in Appendix B uses the quantities in this table to graph the ratio of mean pension wealth to mean total wealth—showing that, in addition to matching the level, the model also replicates the increase in the pension share by lifetime wealth. The model therefore performs well in terms of fitting household portfolio choices. An additional test of the validity of our estimates is that we can use the breadth of data collected in ELSA to validate the estimated discount factors using information that is not used at all in the modeling process. More specifically, we can examine how the estimated discount factors vary with individual characteristics thought to correlate with, or be indicative of, individuals’ time preference. We examine three particular characteristics: education, self-reported financial planning horizon, and current and former smoking behavior. The left-hand panel of Figure 4illustrates how the distribution of estimated discount factors varies for our three education groups. The distribution of those with lower education lies to the left of those with more education. This is consistent with the bulk of existing literature on education and discount factors (e.g., Lawrance (1991), Cagetti (2003), Dohmen, Falk, Huffman, and Sunde (2010)). The right-hand panel of Figure 4illustrates how the distribution of estimated discount factors varies according to individuals’ answers to the question “In deciding how much of your income to spend or save, people are likely to think about different financial planning periods. In planning your family’s saving and spending, which of the following time periods is more important to you?” The options given to respondents are: the next few weeks, the next few months, the next year, the next few years, the next 5–10 years,
658 Crawford and O’Dea Quantitative Economics 11 (2020) Figure 4. Validation of discount factors—distributions by education. longer than 10 years. For ease of illustration, we group individuals into those who respond with a period up to “the next year” and those who respond with a period “the next few years” or longer (a finer categorization is used later in Table 6). Those reporting longer planning horizons are estimated to have higher discount factors. This is strong validation that at least some of the heterogeneity in discount factors estimated through the modeling process is indeed reflective of heterogeneity in individuals’ preferences. Samwick (1998) showed the relationship between a similar question and his estimates of discount rates and also finds that the estimated and stated measures of patience correlate. In Table 6, we report the results of median regression analysis examining the correlation between estimated discount factors and individuals’ self-reported planning horizon, education level, smoking behavior, and these three characteristics simultaneously. These confirm statistically significant differences in median discount rates between the groups illustrated in Figure 4and also show that estimated discount factors are significantly negatively correlated with current smoking behavior (see Khwaja, Silverman, and Sloan (2007) which documents, in a different setting, a correlation between some measures of time preference and smoking behavior). We also find that the correlation between discount factors and each characteristic holds up even when the others are being controlled for. We take this as evidence that the distribution of discount factors we have estimated is indeed reflective of heterogeneity in time preferences. 5.2 Household portfolios and saving for retirement 5.2.1 The role of pensions The previous section illustrated the importance of the asset structure of our lifecycle model for the estimated distribution of discount factors. To examine the role of household portfolios in more detail, we can use our model to evaluate what would happen, at our estimated discount factors, if some of the features of the asset structure we have added were removed. Table 7shows how the distribution of each of total private wealth and its two components, pension wealth, and nonpension wealth, vary with the characteristics of the model’s asset structure. We show four scenarios: 1. Our baseline.
Quantitative Economics 11 (2020) Household portfolios and financial preparedness 659 Table 6. Median regressions of estimated discount factor on household characteristics. (1)(2)(3)(4) Planning (weeks) — — (—)(—) Planning (up to a year) 0017 0011 (0005)(0005) Planning (a few years) 0033 0019 (0005)(0005) Planning (5+years) 0036 0023 (0005)(0004) Low educ. — — (—)(—) Mid educ. 0030 0027 (0003)(0003) High educ. 0040 0033 (0004)(0004) Never smoked — — (—)(—) Former smoker −0007 −0004 (0004)(0003) Smoker −0018 −0007 (0005)(0004) Constant 0923 0932 0956 0921 (0004)(0002)(0003)(0004) Observations 954 943 964 930 Note: Standard errors in parentheses. 2. Removing the pension tax advantage. Pension saving is now done out of net income, and yields a nontaxable annuity in retirement (rather than being done out of gross income and yielding a taxable annuity). The pension remains risky and earns a higher expected return than cash. 3. Removing the pension asset entirely (and so retirement funds are all saved in the composite nonpension wealth asset). 4. Additionally, removing access to housing (and so all wealth is held in cash). Comparing the baseline with the third row of the top panel shows that removal of the pension would, holding the distribution of discount factors constant, reduce mean accumulated wealth from approximately £451,000 to approximately £353,000.Theproportionate reduction is greater at the top of the wealth distribution (where the fall was approximately 20% at the 90th percentile) than at the middle and bottom (where the fall was just over 10% at the median and just under 10% at the 10th percentile). The result that, conditional on a set of discount factors, wealth accumulation would be less in the absence of access to the pension is isomorphic to the result presented in Section 5.1 that estimated discount factors would be higher if no access to the pension was assumed. Pension wealth differs from nonpension wealth in two respects that are quantitatively important for increasing saving. First, it is treated advantageously by the tax
660 Crawford and O’Dea Quantitative Economics 11 (2020) Table 7. Distribution of modeled wealth: pension tax advantage counterfactual analysis at age 64. p10 p25 Median p75 p90 Mean Total wealth Baseline 850 1856 3346 5785 8836 4509 No pension tax adv. 812 1729 3158 5227 7979 4112 No pension asset 778 1645 2953 4801 7113 3536 No pension and no housing 05254802 1680 2791 1207 Pension wealth Baseline 147499 1180 2402 3947 1921 No pension tax adv. 00196607 1370 2374 1172 No pension asset 000000000000 No pension and no housing 000000000000 Nonpension wealth Baseline 591 1268 2238 3507 5082 2588 No pension tax adv. 789 1481 2436 3947 5686 2940 No pension asset 778 1645 2953 4801 7113 3536 No pension and no housing 05254802 1680 2791 1207 system. Second, it has a higher expected return than the cash portion of nonpension wealth.15 The second row of each panel in Table 7allows the effects of these two aspects to be disentangled. Of the approximately 22% fall in mean wealth with the removal of the pension asset (from £450,900 to £353,600), two-fifths is due to the favorable tax treatment (removal of which would lead to a fall from in mean wealth from £450,900 to £411,200); with the remaining three-fifth due to the returns available from the risky asset. Finally, removing access to housing (which forces all of nonpension wealth to be held in cash and so substantially reduces the rate of return on offer) dramatically reduces wealth further. Mean wealth would fall to £120,700 and private wealth in the bottom 10% is very close to zero. Those at the bottom of the lifetime earnings distribution have reasonable earnings replacement from the public pension as well as an asset-tested transfer that essentially taxes wealth accumulation over a certain range. Both of these factors mean that they have limited incentives to save for retirement; these incentives are further reduced in the counterfactuals studied here. We can use these counterfactual estimates to place our results in the context of the literature which estimates the extent to which household responses to pension tax incentives represent new saving or whether households respond to them by saving more in pension wealth at the expense of other forms of wealth. Poterba, Venti, and Wise (1995) and, more recently, Gelber (2011) argued that 401(k) saving is largely “new” saving that would not have been saved in the absence of the savings vehicle being offered; while Engen, Gale, and Scholz (1994) and, more recently, Chetty et al. (2014) argued that subsidies largely increase pension wealth at the expense of other forms of wealth. Our results are intermediate to these sets of studies—the approximately £75,000 fall in pension 15In our setting, the pension asset also gives access to an annuity though the effect of this on wealth accumulation is small.
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