Housing Wealth E ect and Retirement

Transcription

1 Housing Wealth E ect and Retirement Bo Zhao yz University of Oslo July Abstract The empirical part of the paper estimate the e ect of asset price uctuations on retirement probability using the most updated data from the Households Retirement Survey and the Current Population Survey. Regression results predict that a % increase in local housing price level would increase the mean retirement probability for home owners by 2.8%-6.7% and the same amount of increase in stock price would increase the mean retirement probability for stock owners by.%. However, the magnitude of housing wealth e ect is not signi cantly di erent from stock wealth e ect. In the theoretical part of the paper, I investigate the housing wealth e ect on retirement decision through three channels, i.e., the resizing e ect, collateral borrowing, and the bequest motive. More speci cally, I model explicitly housing as a durable consumption goods in a life cycle incomplete market model, in which households choose endogenous retirement age subject to the persistent income risk, housing price risk, and mortality risk. Numerical simulation show how retirement age response to housing price shocks through the three channels and estimate the welfare cost of housing price shock to the near-retirement group and its e ect on the current pension system. K eywords: Housing Wealth E ect, Retirement JEL classi cation: E2 E24 J26. Introduction It is particular important to understand the key factors that in uence retirement decisions in the country where the whole population is aging over time. Most previous research emphasizes the role of social security, private pension, health insurance, and health risk (French, 04; Yogo, 09; Imrohoro¼glu and Kitao, ). From a di erent perspective, this paper is going to answer two questions. What is the e ect of wealth change (stocks wealth or housing wealth) on retirement timing? Is the standard incomplete market life cycle model with housing asset and exogenous price risks able to quantify such wealth e ect? The questions are important because the U.S. households are gradually shifting their portfolios towards 2 more risky asset, which is mainly re ected in the increased participation rate in the de ned contribution plan and the boom in home ownerships from 994 (Chambers et. al., 09). Households are faced with great bo.zhao@econ.uio.no. Phone Number: (+) Postal Address: Research Department of Federal Reserve Bank of Minneapolis, United States. 90 Hennpine Ave, 04 MN, U.S. y I appreciate comments from Kjetil Storesletten, José-Víctor Ríos-Rull, Jonathan Heathcote, Fabrizio Perri, Greg Kaplan, Richard Rogerson, Kaiji Chen, Low Hamish, Fatih Guvenen. I also thank all the seminar participants at NHH-UiO Macro Dynamics Workshop, Labor Workshop at University of Minnesota. All errors are my own. z I acknowledge nancial support from Norwegian Research Council.

2 Housing Wealth Effect and Retirement 2 changes in the net worth if their portfolios are heavily concentrated in those assets. One way for them to insure against asset price risks is to adjust labor at both extensive margin and intensive margin. For old households, this usually takes the form of altering retirement planning. If the wealth e ect on retirement turns out be quantitatively important, it can potentially have big welfare implications for the households near the retirement age. The government should take it into consideration when making tax and transfer policy under the current pension system. Using the most updated data from Household Retirement Survey and the Current Population Survey, this paper estimate the e ect of wealth uctuations on old households retirement. More speci cally, I look at the retirement behavior for the near-retirement households, who subject to exogenous stock price and housing prices risks. I especially focus on the role of housing wealth by exploiting the housing price variation across 9 census divisions and metropolitan statistical areas. I nd home owners are more likely to retire when housing price are above the trend, while renters hardly respond. Similarly, stock owners are more responsive to stock prices uctuations than non-stock owners. By running both panel and cross-sectional regression, I nd that a % increase in local housing price would increase the mean retirement probability for home owners by 2:8% 6:7% and the same amount of increase in stock price would increase the mean retirement probability for stock owners by :%. However, the magnitude of housing wealth e ect is not signi cantly di erent from stock wealth e ect. There are mainly three reasons why housing price, like stock price, can a ect households retirement decisions. First, housing price changes can a ect households budget constraint. When housing price are high, old households may want to downsize their houses (Banks et. al., 07). They can even sell their houses and become renters or move into the nursing home. The recent development in equity borrowing makes it possible for old people aged above 62 to use reverse mortgage to cash out their home value. Households don t have to pay back the loan until they die or move out of the house. Second, it can a ect households borrowing constraint. Housing not only provides services ows, but 2 also can be used as collateral. When interest is low and housing price is high, households can re nance their mortgages or apply home equity line of credit. Moreover, interest rate on these loans is tax deductible. Even for those who were not borrowing constrained before, their borrowing constraint maybe binding in the presence of the big decline in the housing price. Third, housing is also an important asset as the bequest. Although households consume out of savings For example, during this period, the annualized returns to stocks and housing asset vary from -% to 0%. The median household whose age is now between 7-62 hold 22.3% of their total net worth (including social security wealth) in housing market, 9.2% in stocks market at year 06 (Gustman, Steinmeier and Tabatabai, 09). Since then, both stocks market and housing market have been declining by 30%, which is equal to % of their total wealth, nearly $3,700 in 06 dollars. The loss is even larger than the median household income, which is $0,233 in 07 according to the U.S. Census Bureau.

3 Housing Wealth Effect and Retirement 3 after retirement, most households leave bequest to their children after they die. Housing assets account for the largest fraction of non-pension wealth for the median U.S. households, even if one think of de ned contribution plans as indirect stocks holdings. In the theoretical part of the paper, I investigate the wealth e ect of housing price shocks on households retirement decision through the three channels, i.e., the resizing e ect, collateral borrowing, and the bequest motive. I set up a life cycle incomplete market model with housing being modeled explicitly as a dual asset. Households choose endogenous retirement age subject to the persistent income risk, housing price risk and mortality risk. By doing this, I am able to separate three channels by running counterfactual experiment and evaluate the e ect of them on retirement respectively. In the end, I estimate the welfare cost of housing price shock to the near-retirement group and its e ect on the current pension system. There is a small literature on the wealth e ect and households consumption. Holtz-Eakin et al. (993) and Imbens et al. (0) use exogenous wealth variations, such as inheritances or lottery winnings, to identify the wealth e ect on consumption. The virtue of this method is to avoid the endogeneity problem of wealth accumulation. Other studies, including Paker (999) and Juster et al. (999), estimate the marginal propensity to spend out of household wealth using households survey data. Estimates by those authors range between 3% and 8%. Recent studies look at another important component of household wealth, housing asset. Case et al. (0) use aggregate data to nd a % increase in housing wealth increases aggregate consumption by 0:4% for the US and roughly :% for international panel. Meanwhile, they nd only insigni cant e ect of rising nancial wealth on aggregate consumption. Campell and Cocco (07) investigate the response of household consumption to house price by constructing a pseudo panel. They nd the largest e ect of house prices on consumption for old home owners and smallest e ect for young renters. In their benchmark regression, a % increase in housing value increase the non-durable consumption of the old homeowner by around :22%, which accounts for 8% of the increase in housing value. A growing literature is trying to estimate the wealth e ect on labor supply and retirement. Early studies 2 use household level data to estimate the stock market boom on the retirement decision. Bottazzi et. al. (0) build up a structural model to explain why female supply is higher in households with mortgage debt. Cheng and French (0) show that the run-up in the stock market in 990s, which has brought greater than $0; 000 gains to more than % of individuals aged and above, decreases the participation rate for people older than 0 by 3:2%. Sevak (02) exploit the HRS data to nd an increase of $0; 000 wealth shock would 30 lead to a :9% increase in retirement probability among individuals aged between and 60. Coronado and Perozek (03) use the same data set and nd that households who held corporate equity immediately prior to the bull market of the 990s retired 7 months earlier than other respondents on average. Later on,

4 Housing Wealth Effect and Retirement 4 Farnham and Sevak (07) nd that a % increase in housing wealth would reduce the expected retirement age by 3: months to months. More recently, Gustman et al.(09) and Coile and Levine (09) estimate the e ect of recent stock market and housing market downturns on household retirement respectively. The former concludes that recent stock market decline lead the early boomers to postpone retirement by : months on average. However, the latter found no evidence that old workers respond to uctuating housing market. The paper consists of 4 sections. In Section 2, I describe the estimation strategy and give regression results from two di erent datasets. In Section 3, I write down a life cycle model with housing to explain the housing wealth e ect. Section 4 concludes. 2. Empirical Analysis 2.. Datasets and Descriptive Statistics Two datasets I use in this paper are Household retirement Survey (HRS) and Current Population Survey (CPS). The HRS is a national, biennial panel survey of individuals over age 0 and their spouses. The survey include detailed information about demographics, income, assets, health, cognition, family structure and connections, health care utilization and costs, housing, job status and history, expectations, and insurance. In this paper, I use the Rand version of HRS data The Current Population Survey (known as the Monthly CPS) is a monthly U.S. household survey conducted jointly by the U.S. Census Bureau and the Bureau of Labor Statistics from 940s. A set of labor force and demographic questions, known as the "basic monthly survey", is asked every month in order to measure unemployment. Over time, supplemental inquiries on special topics have been added for particular months. For example, the March Annual Demographic File and Income Supplement (the March CPS) provide information on household income as well as personal income statistics. I use the public monthly CPS data from NBER. Table shows the distribution of asset portfolios over the life cycle using data from the Survey of 2 Consumer Finances (SCF) 07, which is conducted every three years to provide detailed information on the nances of U.S. families. The dataset is also cross-sectional with about 400 households in each survey. The household s age is de ned as the age of householders. The households total assets include nancial asset, real asset, and business asset. The net value of nancial asset is de ned by the sum of liquid asset, certi cates of deposit, directly held pooled investment funds, savings bonds, directly held stocks, cash value 30 of whole life insurance, other managed assets, quasi-liquid retirement accounts, and other nancial asset, net

5 Housing Wealth Effect and Retirement value of bonds, bond funds, and other savings minus debt, including lines of credit not secured by residential real estate, credit card balances after last payment, installment loans and other debt. The net value of real asset is the sum of net primary residence value, residential property excluding primary residence, vehicles, net equity in non-residential real estate such as land, rental real estate, a partnership, or money owed to households on a land contract or mortgage. The stocks ownerships include directly held stocks, investment funds, IRA account, and the de ned contribution plans. First, asset pro les and stocks ownerships are hump-shaped, both of which peak at the 6-69 age group; labor income pro le is also hump-shaped but reaches the maximum earlier than the asset pro les; second, the real asset to total net worth ratio is U-shaped. This is due to that households mainly use accumulated nancial asset for consumption at older age. third, the proportion of households re nance their rst lien mortgage is decreasing after age 0 and the proportion of retired households is nonlinearly increasing after age 0. Households can cash out their housing by re nancing their mortgage, home equity line of credit or reverse mortgage. Before age 70, more than 30% of households re nance their rst mortgage. Nakajima and Telyukova (09) document that more and more households are cashing out their housing through home equity line of credit or reverse mortgage. The total combined volume of Case-out and 2nd Mortgages/Home equity line of credit have increased from only 2.7 billion in 99 to 346 billion in 06 when the housing price peaked. After that, it drops to only 30.9 billion in 08 when the housing market goes down dramatically. In the HRS data, a mention of retirement can be made either through the employment status or the questions that ask the respondent whether he/she considers himself retired. In the rst case, labor force status can be classi ed into 7 categories: work full time, work part time, unemployed, partly retire, retired, disabled, and not in the labor force. Retirement can be regarded as a transition from the other 6 states. In the second case, households are asked whether they think themselves as fully retired, partly retired, or not retired. The rst measurement on average have large response rate and less missing value due to the way 2 questions were asked in each wave. The Rand HRS says its derivation uses many di erent questions that are available each wave. A respondent can give evidence of working, being retired, and disability alone or in combination with other statuses. This measurement attempts to pull information from several sources, and sort through the discrepancies. Working and retirement take precedence in its derivation. In this paper, I choose to use the rst de nition. 30 De ne retirement as "failure" or "death" using the terminology of survival analysis. Then the discrete- time hazard function as the probability of transition at discrete time t j ; j = ; 2; :::; given survival to time t j

6 Housing Wealth Effect and Retirement 6 is de ned as j = Pr (T = t j jt t j ) () and the discrete-time cumulative hazard function is j (t) = X jjt jt j (2) Figure, 2, 3, and 4 show the nonparametric estimates of retirement transition of male respondents across di erent wealth quintiles and ownerships groups using the HRS data The wealth is de ned as the total net worth including real asset. The ownerships groups include the home owner who directly own stocks, home owner who do not hold stocks, and renter who do not hold stocks. They account for 30.2%, 2.%, and 4.8% of the total sample respectively. Since the renter who own stocks only account for less than 2.% of the total sample, I decide not to include them in the gure. In all cases, I exclude self-employed respondents. Two points can be made about these gures: rst, the retirement hazards rate is increasing both in age and in wealth. For example, the retirement hazard rate for respondents at age 6 in the rst quintile is twice as large as the fth quintile. Second, because the strong positive correlation between wealth and home/stock ownerships, the retirement pattern also di er systematically among di erent ownerships. Respondents who hold both stocks and home equity are twice more likely to retire than people who do not own any of this assets. In this paper, I use housing price index on both census division levels (CDs) and metropolitan statistical areas (MSAs). This rst one I choose is the constant quality housing price index from Federal Housing Finance ncy (the FHFA Index) in 9 census divisions, in which the standard deviation of the most volatile region is 63% higher than the least volatile region (See Table 2). 2 The second housing price index is the S&P/Case-Shiller Home Price Index. It measures the residential housing market, tracking changes in the value of the residential real estate market in metropolitan regions across the United States. It is not surprising to see that the CS index is much more volatile than the FHFA Index (Table 2). The standard deviation of the most volatile MSA is 683% higher than the least volatile MSA and 3% higher than the 2 second least volatile one. I use the S&P00 Stock Price Index in the paper. 2 This index is estimated using repeated observations of housing values for individual single-family residential properties on which at least two mortgages were originated and subsequently purchased by either Freddie Mac or Fannie Mae since January 97. The use of repeat transactions on the same physical property units helps to control for di erences in the quality of the houses comprising the sample used for statistical estimation.

7 Housing Wealth Effect and Retirement The HRS Data Retirement can be modeled as a binary decision problem, where households choose to retire when the discounted future value of being a retiree is larger than the value of being a worker. Since the value function for each individual is unobservable, the regression model simply assumes that the underlying value function can be written as a linear combination of exogenous variables. Under di erent assumptions about distribution of error terms, the problem can be formulated as logit, probit, or linear probability model. To make the interpretation of coe cients much easier, I choose the linear probability model in the paper, although the quantitative results might slightly di er among these models. More speci cally, the conditional probability of retirement given Xt i can be written as follows: Pr(Retire i t = jx i t) = i + T t X i t + " i t (3) Where Retire i t equals to if the respondent i report to be retired at time t. X i t is a vector of fundamental variables, which include households labor earnings of at previous year, the interaction term between home ownership and housing price index, the interaction term between stock ownership and stocks price index, social demographic variables, geographical dummies, etc. i is the unobservable individual xed e ect, which may be correlated with X i t: Questions about households earnings are retrospective. In the regression, I de ne total labor income as the sum of wage income, bonuses, overtime pay, commissions, tips, 2nd job or military reserve earnings, professional practice, and trade income in the previous year. I did not include the pension income, social security income, or unemployment compensation. Stock ownerships include holdings of stocks, mutual funds, investment trusts, individual retirement ac- count, and de ned contribution plan. 3 It is a binary variable, which equals to if the households own any form of stocks. Home ownerships is also a binary variable. It equals to if the household owns his primary residence. I use monthly housing price index for 9 census divisions from Federal Housing Finance ncy. The index is estimated by using sales price data, rather than appraisal data. I use monthly S&P00 index 2 for stock price in the model. Both the S&P00 Index and the FHFA housing price index included in the regression are yearly average of BP- ltered monthly data. 4 All indices are de ated using CPI index. Social demographic variables include a full set of dummies for education years, race, age, and whether the respondent is covered by any health insurance plan. I also include the self-reported health status, the 3 Here I simply assume that all wealth in individual retirement account and de ned contribution plan are invested in the stocks market. 4 In order to take out the long term trend in price, I use a band-passing lter with standard parameter, i.e., 6 and 32 for quarterly data, 8 and 96 for monthly data. This preserves the components of the cycle with frequency between. and 8 years.

8 Housing Wealth Effect and Retirement 8 annualized federal funds rate, conventional mortgage interest rate, and unemployment rate in each census division to control for the local economics prospective. The sample includes male respondents aged between 0 and 70 over , who are wage and salary workers. This gives me a sample of 7; 339 households. I exclude self-employed respondents because they behave quite di erently in terms of retirement behavior. I also run the regression with same set of covariates for the subsample of home owners. Table 3 shows the linear probability regression results for the both groups. T-statistic is given shown in the parenthesis and all standard errors are clustered at household level. I focus on three speci cations of the model. The speci cation I is the random e ect model. The underlying assumption is that the unobserved heterogeneity is uncorrelated with other explanatory variables. The statistics for Breusch and Pagan Lagrangian multiplier test for random e ects is 2 () = 7393:8 with p = 0:000. Therefore, the absence of individual e ect is rejected and the random e ect model dominates pooled OLS regression. The speci cation II shows the results for xed e ect model. The statistic for Hausman speci cation test is 2 (36) = 38:9 with p = 0:000: Therefore, the null hypothesis that there is no signi cant di erence between the rand e ect model and xed e ect model is rejected, and the xed e ect speci cation gives consistent estimates while the random e ect speci cation does not. The speci cation III uses Hausman-Taylor method to estimate the same equation, taking into consideration that the endogeneity of home ownerships and stock ownerships. In the following part of this section, I will focus on regression results from speci cation II and III. For both speci cations II and III, the coe cient before earnings is negative, which is not surprising since labor earnings is the opportunity cost of retirement. It means that 0; 000 dollars (in 08 dollars) increase in earnings will reduce the retirement probability by 6:6% to 7:9%. The coe cient before the interaction term between housing price and home ownerships represent the housing wealth e ect on home owners. In the xed e ect model, it is interpreted as % increase in the 2 yearly average housing price level would increase the retirement probability for home owners by 6:7%. The coe cient before the interaction terms before stocks price and stock ownerships has the similar interpretation. A % increasing in stock prices level would increase the retirement probability for stock owners by :6%: How large is this e ect? The mean house value for wage and salary worker in HRS is $2,000 and the mean value for stocks and individual retirement account is $87,000 at year 06 (08 dollars). Since the 30 sample period in HRS covers , the regression can be used to predict the e ect of recent housing price decline on household retirement decision. In some regions, for example, the Paci c region and New England, housing price level drops around %. According to the estimation results, the mean retirement

9 Housing Wealth Effect and Retirement 9 rate for home owners in these regions should drop as large as 3:4%. The mean age for home owners in my regression sample is 60:8 and the mean retirement probability at the sample mean is 0:46. Suppose that the conditional retirement probability is the same for all ages. Then, the expected time to retirement is around 2:7 years. A drop from retirement probability from 0:46 to 0:336 would increase the expected mean retirement age for home owner by 0:9 year, or months. The result is close to Farnham and Sevak (07), in which they nd that a % increase in housing wealth would reduce the expected retirement age by 3: months to months. For the stock prices, a % drop would increase the expected retirement age at the sample mean by 0:6 year, or 2 months. The magnitude of this stock wealth e ect is close to the ndings in Gustman et al.(09), which concludes that recent stock market decline lead the early boomers to postpone retirement by : months on average. Now I am comparing the relative magnitude of housing wealth e ect and stocks wealth e ect. The rst null hypothesis is H 0 : housing wealth e ect = stock wealth e ect. For all the three speci cations, this cannot be rejected at % signi cance level, i.e., the two e ect are not signi cantly di erent from each other, although the point estimate for housing wealth e ect is larger. The second null hypothesis is H 0 : housing wealth e ect < stock wealth e ect. From the bottom of Table 3, it can be seen that the null hypothesis cannot be rejected in Speci cations II and III at % signi cance level. Therefore, if there is any support for larger housing wealth e ect, it is very weak. This result is also consistent with ndings of Goodstein (08), in which he cannot reject the hypothesis that two wealth e ects are equal. The health index ranges from to, where the most excellent health status is indexed by. The coe cient before health is positive, which means that the worse health status is, the more likely householders choose to 2 retire earlier. For one extra level increase in health indicator, the retirement probability increase by 0:76% in the xed e ect model. For a person with excellent health, his retirement probability is 3% smaller than the person with poor health. Health insurance also plays an important role in households retirement planning. The retirement probability of worker covered by employer provided health insurance plans is 7:% smaller than their non-insured counterparts. On the other hand, government provided health insurance, like Medicare and Medicaid, is positively correlated with worker s retirement probability. This is partly because medicaid is for those aged above 6. The estimates from home owner alone give higher estimates about housing wealth e ect. It suggests that these results are robust to the selection of home owners.

10 Housing Wealth Effect and Retirement 2.3. The CPS Data In order to verify the ndings from the HRS data and to get comparable results with other similar studies (Coile and Levine, 09; Gustman et al., 09), I choose the monthly CPS data. The dataset contains more frequent data about households home ownerships, labor force status, and geographic information on the monthly basis, which allows me to investigate the wealth e ect of regional housing price changes. I select the monthly CPS data from 989 to from NBER. This is mainly because the housing price index for di erent MSAs on monthly level is not available until 987. Before 982, the housing tenure question is not asked in the CPS. Because the cross-sectional properties of CPS data, the previous xed e ect model cannot be identi ed. Now, the new econometric model is written as follows: Pr(Retire i t = jx i t) = + T t X i t + " i t (4) where X i t contains the usual set of demographic and geographic variables, the interaction term between home ownerships and housing price index, a measure of stock wealth e ect, etc. The binary variable Retire i t equals if individual i retires at time t. The retirement status is listed as a separate term in CPS labor force status after 994 because the redesign of CPS questionnaire. Before that, retirement cannot be identi ed using the labor force status alone. I combine the labor force status with the major labor activity last week (item 9) to identify the retirement status. I de ne a person to be retired if his major activity last week is reported as retirement, and his labor force status in CPS is coded as being not in the labor force. The whole sample consists of male householders aged between 0 and 70 from 989M to 09M9. For the same reason as before, I exclude self-employed workers from the sample. Some months in the sample (99M, 99M6, 99M7) are dropped in Speci cation I because the lack of information on detailed geographic level makes the identi cation of housing wealth e ect impossible for these months. In Speci cation I, I focus on the subsample of households who are living in the largest metropolitan 2 statistics areas (MSAs) (See Table 2 for the list the classi cation of those MSAs in the CPS using CMSA codes). I use the interaction term between home ownership and MSA-speci c Case-Shiller home price index to identify the housing wealth e ect. The identi cation of stock wealth e ect is more di cult in the CPS because there is no question about stock ownerships. Following Coile and Levine (09), I include the interaction term between college graduates group and S&P00 index to see whether stocks price a ect this 30 education groups in a di erent way. If the stocks wealth e ect does exist, we would expect to see a signi cant and positive coe cient before the interaction term, given that there is high correlation between education

11 Housing Wealth Effect and Retirement attainment and stock ownerships. For example, 77% of household head with college degree own stocks in HRS 06. Only.% of household head with high school degree own stocks. All housing price index and stock price index included in the regression are ltered monthly logarithm value de ated by the CPI Index. In the monthly CPS, only those who are going to leave the sample (The ongoing rotation group), which only accounts for less than 2% of the whole sample, are asked detailed question about individual earnings. However, there is question about the household income each month, which is recorded as categorical variable. I impute the value of household income using the cell mean and include this variable in the regression. Social demographic and geographic variables contain dummies for a full set of age, race, states, MSAs, census divisions. I also include federal funds rate, conventional mortgage rates, number of person living in the household, and the MSA-speci c unemployment rate for male householders aged between 0 and 70 to control for local labor market conditions. In Speci cation II, I estimate the model based on the full sample, and look at the wealth e ect from aggregate housing prices. The wealth e ect of housing is identi ed by the interaction term between the census-division-speci c FHFA home price index and home ownership. I also include the census-divisionspeci c unemployment rate for male householders aged between 0 and 70 to control for the local economic perspective. The Speci cation III, I am trying to identify the housing wealth e ect from aggregate level. To do this, I include the interaction term between the national FHFA housing price index and home ownerships and include aggregate unemployment rate for male householders aged between 0 and 70. The regression results for the CPS data are shown in the Table 4. The MSA level regression estimates that % increase in housing price would increase the retirement probability for home owners by 2:8%. The magnitude is half the size of the housing wealth e ect point estimate from the HRS data. It also shows that a % increase in stock prices would increase the mean retirement rate by 0:73% for the college degree group. Both coe cients are signi cantly di erent from zero at % signi cance level. 2 A 0,000 dollars increase in household earnings would reduce the retirement probability by 9.27%, the magnitude of which is comparable to the ndings of HRS data. The coe cient before the conventional mortgage rate is negative. A % increases in the mortgage rate decrease the retirement rate by.3%. It may be due to that householders have to work longer period in order to pay back their mortgage. Or it is a sign of increasing tightness of borrowing constraints. 30 The result from census division level and national level regression show a much smaller size of housing wealth e ect and stock wealth e ect. When I only include the home owners in the regression, the retirement The earliest FHFA monthly housing price index starts from 99M. The Sample period before 99 is dropped.

12 Housing Wealth Effect and Retirement 2 does not response to housing prices. This suggests that the way housing wealth a ect retirement behavior is through local housing price movement rather than aggregate level. The coe cient before aggregate unemployment rate and census division level is positive. However, the coe cient before MSA local unemployment rate is negative. When I include the aggregate unemployment rate as well in speci cation I, the coe cient before MSA local unemployment rate becomes insigni cant. Overall, the ndings con rm the ndings by Coile and Levine (07) that retirement is positively correlated with unemployment rate. There may be concerns about the endogeneity of housing and stock ownerships in the regression equation. Although the HRS data allows me to use some lagged variables as instruments for ownerships, the CPS is not designed for panel studies and the simple cross-sectional dimension does not allow me to isolate the unobserved individual e ect which may be correlated with other regressors. For the HRS data, the regression on home owner alone does not give quite di erent estimates about housing wealth e ect. While for the CPS data, the correlation between unobserved characteristics of householder and home ownerships may be a potential problem. In the next section, I am going to write down a structural model with housing size decision to address this problem. 3. A Benchmark Life-cycle Model 3.. Demographics The model economy is inhabited by J overlapping generations. Each generation consists of a continuum number of households with total measure. Households face mortality risk drawn from age-speci c distribution. They enter the labor market at age and the maximum age is J: The conditional survival probability from age j to age j + is denoted as s j, where s J = 0: Assume aggregate population growth rate is zero: When the population structure is stationary, the fraction of new born is = JX + j= j () where j Q j i= s i is the unconditional survival rate. The fraction of age j can be computed recursively 2 from j+ = s j j (6) where j = ; :::; J :

13 Housing Wealth Effect and Retirement Preferences and Endowments Each household is endowed with one unit of indivisible labor. Retirement is an absorbing state, i.e., once households retire, they can not go back to work. In addition to age and initial wealth, households also di er in their idiosyncratic labor income risk. The stochastic process for wage before retirement is assumed to be ln w j = e j + z j + " j (7) which consists of three parts: e j is the age-speci c labor e ciency unit; z j is a persistent shock to wage; " j is the transitory shock, " j i:i:d:n 0; 2 " z j = z z j + j (8) where j i:i:d:n 0; 2 : After retirement, the households collect lump sum retirement bene t b (the de ned contribution plan) w j = b (9) for all J j j r ; where j r is the endogenous retirement age. Alternatively, the retirement bene t can be modeled as the de ned bene t plan. The households receive payment which is a fraction of their preretirement income w j = w j r () Households derive utility from consuming non-housing consumption good c j, housing services h j+, leisure l j, and from bequest x j : l j can take two values: if the household has retired and 0 if he still works. The utility function can be written as JX j j u (c j ; h j+ ; l j ) + ( j j+ ) u B (x j ) () j= where u B (x j ) is the bequest utility Housing Market Housing plays a dual role in the model. It not only provides service ows, but also can be used as a collateral asset. The down payment ratio is ; i.e., the households can borrow up to fraction of total 2 housing value.

14 Housing Wealth Effect and Retirement 4 The only risky asset in the economy is housing. The housing price follows a AR() process ln p j = p ln p j j i:i:d:n + j 0; 2 : Housing depreciate at a rate of h : (2) In the benchmark model, I assume all households are home owners. Housing asset is divisible. The selling or buying house does not incur any transaction cost Households Households are heterogenous in dimensions = fx; z; "; p; jg ; which denote total wealth at the beginning of period, persistent income shock, transitory income shock, housing price, and age respectively. The timing of the economy is the following. At the beginning of period, housing price shocks and income shocks are randomly drawn. Households decide the amount of house to buy and weather to work or not. If they work, they receive labor income. If they retire, they receive social security payment. Households receive the return from nancial asset, consume non-durable goods, and decide how much to borrow against their house and to save in risk-free bond. At the end of period, mortality risk is revealed. If households die, the amount of nancial asset and housing asset are left as accidental bequest. Households can borrow up to a xed fraction of the value of their house. They can not leave negative accidental bequest. The dynamic programing problem for households can be formulated as follows: Before the retirement, households solve the problem 8 >< l j max u (cj ; h j+ ; l j ) + E j sj V R ( j+ ) + ( s j ) u B ( j+ ) + c j;h j+ V W ( j ) = max l j2f0;g >: ( l j ) max c j;h j+ u (cj ; h j+ ; l j ) + E j sj V W ( j+ ) + ( s j ) u B ( j+ ) 9 >= (3) >; subject to x j+ = R (x j + ( ) w j l j c j p j h j+ ) + p j+ h j+ ( h ) (4) x j+ max fp j+ h j+ ( h ) ; 0g () c j > 0 h j+ > 0 (6) (7) where l j is a binary variable for retirement/work decision.

15 Housing Wealth Effect and Retirement The endogenous retirement age j r is determined by j r min fjjl j = ; J j g (8) Once become retired, the households can not choose to go back to work, i.e., l j ; j j r. After the retirement, the household s value function is V R ( j ) = max c j;h j+ u (cj ; h j+ ; l j ) + E j sj V R ( j+ ) + ( s j ) u B ( j+ ) (9) subject to (4), (), (6), and (7). 3.. Characterization of Partial Equilibrium When the borrowing constraint is not binding, the partial equilibrium can be characterized by Euler equations 6 u c (j) = RE j sj u c (j + ) + ( s j ) V B x (j + ) () u h (j) = s j E j [u c (j + ) (Rp j p j+ )] + ( s j ) E j (Rpj p j+ ) V B x (j + ) (2) where () is the standard consumption Euler equation, and (2) is the housing Euler equation. See Appendix for a proof Calibration Assume that the household utility function takes the form u (c j ; h j+ ; l j ) = "!c j + (!) h # j+ + l j (22) Following Fernandez and Krueger (), I calibrate the elasticity of substitution between consumption and housing services to be. The relative risk aversion parameter is chosen to be 2. is the xed bene t from leisure when retire (or can be interprated as xed cost of working), which is endogenously determined by the model (See below). The utility from leaving bequest is assumed to be u B (x j ) = x j 6 The notation here is a little bit loosely written. The policy function should also depend on whether households have retired or not. (23)

16 Housing Wealth Effect and Retirement 6 which is assumed to have the same curvature as the utility function. measure the bequest strength. This is also endogenously pinned down by the model. The share of consumption in the utility function!, the discount rate, xed bene t from retirement, and bequest strength are calibrated to match the following four moments: the average share of housing asset in total networth for householders aged between 0 and 70, the average net worth (normalized by labor income) for households aged between 6 and 69, the average cumulative retirement rate of households aged between 60 and 64, the mean wealth ratio between householders aged 8-89 and aged These give! = 0:90; = 0:960; = 0:7; = 36:0: Risk free interest rate is assumed to be 2:0%: Nagaraja et al. (09) estimate the housing price process for metropolitan areas using FHFA quarterly housing price index Their model consists of a xed time e ect, a random ZIP code e ect, and an autoregressive component. The autoregression coe cients ranges from to The variance of persistent shocks is between to When translate into yearly frequency, this gives p 2 [0:929; 0:990]; p 2 [0:092; 0:0997]: In the benchmark model, I set the p = 0:98 and p = 0:06: I approximate housing price process by methods proposed by Kopecky and Suen () using a 9-state markov chain (see Table ). The housing depreciation rate h is set to be 0:%: Heathcote et al. (08) estimate income process using PSID data I set the persistency of income shock z = 0:9733; the standard variance of persistent shock = 0:242; and the standard variance of transitory shock " = 0:2: I use the same method to approximate the persistent income shocks and transitory shocks with markov chain. After retirement, the household received retirement bene t. I set b = 0:3 to match the mean ratio of pension income to household labor income at age 0, where I normalize the average labor income at age 0 to be. The payroll tax for social security is set to :0%. 8 Table summarize all parameters used in benchmark model Simulation 2 This main objective of this part is to show quantitatively the magnitude of housing wealth e ect on retirement decision in the model and compare it with ndings in the empirical part. First, I use a di erence-in-di erence method to identify the housing wealth e ect on retirement. More speci cally, I compare two economies, with each consists of 30,000 households. All households are born at the same year and followed from age 0 to 90. The only di erence between the two economies is the housing 7 The wealth pro le is estimated using SCF 07 data. The cumulative retirement rate is from the HRS data. 8 Social Security payroll-tax rate in the US is.3 percent. Since I focus on retirement bene ts, I subtract the part of the tax rate due to Medicare and Disability Insurance.

17 Housing Wealth Effect and Retirement 7 price sequence. Housing price in the rst economy (the experiment group) follows the same stochastic process as the second economy (the control group), except that it always increases by a xed proportion (23% in the simulation) at the same date, i.e., households in the experiment group always enjoy a positive housing price shock at some age (age 60 for example) despite the housing price is drawn from the given distribution before and after that speci c age; households in the control group can experience either positive or negative housing price shock depending on the random draws at that speci c age. I use the di erence in the age-speci c conditional retirement rate between two economies to identify the housing wealth e ect. I also compare the average households consumption, net worth, and housing value in the two groups. In order to focus on the retirement decision and to align the model with the data, I simulate the model for households aged between 0 and 90. All households enter the model economy at age 0 with initial wealth distribution calibrated to match the SCF 07 data. They consume housing as well as non-durable goods and choose labor supply subject to the income risk, housing price risk, and mortality risk. Figure?? and Figure?? plot the mean value of these statistics after 00 draws of di erent housing price series. Table 8 list the di erence in the mean retirement age between two economies. In the benchmark model, households in the experiment group retire 2.2 years earlier than their counter- parts in the control group when housing price shocks hit at age 0. The di erence in the mean retirement age tends to be decreasing as this speci c age increases. This is because younger households have more time to adjust labor supply and housing price shock is very persistent. Second, I estimate the xed e ect model using the model generated panel data. The aim is to compare the regression result with the housing wealth e ect estimated from the empirical data. To do this, I generate a rotated panel including 0 cohorts. Each cohort consists of,000 households, which are followed from age 0 to 70. Therefore, the panel covers 70 years. I run a panel regression of retirement status on housing price, income, asset level, and age dummies. Table 6 shows the regression result of xed e ect model. The coe cient before housing price is 0:3 in the xed e ect model. This estimate is between the point estimate 2 from CPS data and the HRS data. The coe cient before income level is 6:907e-04, a magnitude close to the previous estimate. It would also be interesting to look at the housing wealth e ect on consumption as well. Table 7 show this result. The coe cient before housing price in the consumption regression is 0:303, which means % increase in housing price level would increase consumption level by 3%. This is smaller than the estimate by Campbell and Cocco (07), which does not consider endogenous labor supply. When 30 taking endogenous retirement into account, the housing wealth e ect on consumption reduce by two thirds.

18 Housing Wealth Effect and Retirement Experiment A: No Bequest Motive The rst experiment is to see the e ect of bequest motive. I remove the bequest motive by setting = 0 and keeping other parameters constant. Table 6 is the regression results. The absence of bequest motive cause the households to retire earlier and accumulate less wealth. The composition of asset is more concentrated in housing asset. Figure 7 plot the average asset and consumption pro le for the case when positive housing price shocks happens at age for experiment group and compare it with the control group. The housing wealth e ect on retirement drops by half. However, the housing wealth e ect on consumption was little a ected (see Table 7) Experiment B: No Borrowing Constraint The second experiment is to shut down the channel of collateral borrowing. I assume that households can not use housing as a collateral asset by setting the downpayment ratio to be : Under this new no borrowing constraint, households hold less housing asset than in the benchmark model. It turns out that housing wealth e ect on retirement drops by % in this case (see Table 6 and Table 7). The housing wealth e ect on consumption also drop by 7%. This is due to that not many households aged between 0 and 70 are borrowing constrained. Figure 8 plot the average asset and consumption pro le for the case when positive housing price shocks happens at age for experiment group and compare it with the control group Experiment C: In nite Adjustment Cost The third experiment is to investigate the channel of wealth e ect through buying and selling the house. Households are assumed to be endowed with xed amount of housing h. It is too costly to sell and buy house in this economy. In the simulation parts, I calibrate the size of house to match the average housing value for households aged between 0 and 70. The resizing channel is very important for the housing wealth e ect. Table 6 shows that when households was forbidden from selling the house when housing asset appreciate, the housing wealth e ect on retirement drop by 78%. % increase in housing value would only increase the average retirement rate in the sample by 7%. Moreover, Table 7 shows that the housing wealth e ect on 2 consumption drop more than 90%. Housing wealth e ect does not disappear in the in nite adjustment cost case is because: rst, households have bequest motive. Instead of leaving nancial asset, households choose to leave housing asset as a bequest; second, the model allows them to consume out of their housing asset when they still live in them.

19 Housing Wealth Effect and Retirement Welfare analysis This part explore the welfare e ects of housing price shocks. Keep in mind that it is a partial equilibrium model with interest rate and housing prices are exogenously determined. Following the literature, the welfare e ects of housing price shocks are measured by the compensating variations, denoted as CV. Given two economies with housing price equal to i and i + respectively, the compensating variations measure how much (in percent) the consumption index, de ned as c! h!, must be increased at each period and each contingency in the economy with housing price level i so that a given type of agent is indi erent between the two economies. 9 The compensation of variation for households aged j at housing price level i is de ned as CV (i; j) = R V (xj ; p i+ ; z; "; j) dzd" R V (xj ; p i ; z; "; j) dzd" (24) where x j is the average networth for age j households. Table 9 shows the compensation of variation for households at age 0. Worker aged 0 who are living under housing price level need 6:% increase in their consumption index level to be indi erent between living under housing price level and level 2. The retiree s CV is higher than the worker s. Table also shows that the CV is a decreasing function of baseline housing price level Balance Sheet of Pension The pension collected after retirement is assumed to be constant in the benchmark model (the de ned contribution plan). Therefore, I de ne the present discounted value of total amount of pension for age j cohort to be 90X k=j+ p (l j = ) Nb ( + r) k j (2) where N is the total population, which is normalized it to. p (l j = ) is the fraction of households being retired at age j: Using this measure, I calculate the di erence in the total amount of pension between the experiment group and the control group. Not surprisingly, the total amount of pension collected is on average higher in experiment group because households retire earlier. Table 8 shows the percentage changes in total amount 2 of pension for age j cohort as well as the total economy. For the age 0 cohort, the sudden positive housing price shock at age increase the total amount of pension collected in the experiment group by.3%. For 9 In the simulation part, I use a 9-state markovian chain to approximate the housing price process. Hence i = :::8