Introduction Model Results Home Ownership, Savings and Mobility Over The Life Cycle Jonathan Halket Gopal Vasudev NYU January 28, 2009 Jonathan Halket, Gopal Vasudev To Rent or To Own
Introduction 30 percent of households rent in U.S. 46 percent of households aged 21-35 rent 19 percent of households aged 36-50 rent What are the determinants of the life cycle prole of home ownership? Why are young households more likely to rent than middle-aged households?
Home Ownership 1 0.9 Proportion of Home Owners 0.8 0.7 0.6 0.5 0.4 0.3 0.2 20 30 40 50 60 70 Age
(Too) Many Explanations For Home Ownership Financial constraints in the mortgage market Mobility and Transactions costs of housing Portfolio Concerns Circumstantial evidence in favor of each. All are conrmed, but they haven't been quantied.
Financial Constraints Young households cannot pay down payment to buy house rent instead of buying smaller house Evidence: Young households are poor lower wealth, lower income Literature: Haurin, Hendershott and Wachter, J. of Housing Research (1997) Barakova, Et Al., J. of Housing Economics (2003) Chambers, Garriga & Schlagenhauf, IER (Forthcoming)
Mobility Mobility and Housing transaction costs Career Concerns Young are more likely to move to a new U.S. state or for job reasons Literature: Cameron & Tracy (1997) Young are more mobile than old and renters are more mobile than owners - particularly when young
Portfolio Concerns Implicit: Incomplete Markets House values are stochastic and correlated with labor earnings Literature: Ortalo-Magne & Rady, J. Housing Economics (2002), (2005) Davido, J. of Urban Economics (2006) Owning as hedge against changes in rents Literature: Sinai & Souleles, QJE (2005)
Model Elements Incomplete Markets > Portfolio Concerns Life cycle: OLG Bewley-Aiyagari-Huggett model Down payment > Financial Constraints Locations (Islands): Job-related mobility With GE, stochastic house values > Portfolio Concerns A reason to own: Mortgage interest is tax-deductable. Health Warning: A bunch of institutional assumptions to close model
What we do Build and calibrate quantitative GE model that can match data on: Family size (calibrated) Earnings (calibrated) Ownership (Endogenous) Mobility (Endogenous) Turn on/o family changes, insurance opportunities, and down payment requirements observe eects on ownership prole.
What's New In this model: Location, Location, Location Locations exogenously dier in their labor market quality Cost of housing endogenously tied to quality of location New equilibrium denition and proof for Bewley Models with some discrete choices In the results: Most young are not credit constrained. Young rent because: They are mobile They want to consume Ownership is a good hedge against rents for older households that live in cheap areas.
Households and Locations Measure 1 of households ι and locations ε. Households age deterministically, with age (a) dependent survival prob λ(a) New households born, replacing dying households
Technology Non-durable consumption good c Durable housing good h c produced globally: F (K,L) H(ε) = H
Preferences u(c, h, a) = ( ) 1 γ c 1 σ h σ S(a) 1 γ Family size equivalent consumption S(a) constant across households of same age. Growing families have higher inter-temporal marginal rates of substitution.
Productivity Household supplies eciency units: l(i, j) = l i (i)l j (j) Household ability i Age component - deterministic over life cycle Permanent component i p follows random walk Purely transitory component i t iid Location productivity, j transition probabilities: π j Moving cost: θ m l(i, j)
Housing Housing rented from or bought/sold from/to risk-neutral, competitive real estate industry Rental unit-price: q(j) Buying unit-price: p(j) Household must work and live in the same location. Household can either rent or own, but not both. No short-selling housing.
Housing Per period cost of housing: κp(j)h Transactions Costs: Buying and Selling cost: θ h p(j)h Zero prots for real estate industry: q(j) = (κ + r 1 + r )p(j) 1 1 + r E(p(j ) p(j) j)
Assets Risk-free, one period bond paying r No uncollateralized borrowing Renters cannot borrow Homeowners can borrow up to 1 d percent of their house value or may role over current principal on mortgage if it doesn't move. No borrowing for oldest households
Reason to own Income tax rate: τ y Mortgage interest payments are tax deductible. Gov collects all taxes and accidental bequests, funds initial wealth and throws remainder into ocean.
Household's Problem V (i, j,τ, h, b, a,ε) = sup c,h,b,τ, j,ε u(c, h, a)+βλ(a)ev (i, j,τ, h, b, a+1,ε ) c + b + h ((1 τ )q( j) + τ p( j)(κ + 1 + 1m θ h )) w t l(i, j)(1 1m θ m ) + b(1 + r t ) + τhp(j)(1 1 m θ h ) b min{ (1 d)p( j)τ h, (1 1 m )b} ε {ε : j(ε) = j} 1 m = { 0 if h = h,τ = τ,ε = ε 1 else
Existence of Equilibrium Intuition: Conditional on choosing to move, households are indierent over locations with the same productivity. Challenge: Bewley-type models with discrete choices may not have continuous demand and supply curves. Solution: Use mixed allocation to allocate households that are indierent Similar to Sharing Rule in Simon & Zame, Econometrica (1990) Provides UHC and convexity - enough for Kakutani FPT Doesn't matter for computational results Works for other discrete choice Bewley models.
Equilibrium A Stationary Competitive Equilibrium is: A set of prices - which for housing are dependent on the location's productivity Capital, Labor and Housing supply and demand and Government expenditures such that markets clear and budget is balanced An optimal policy correspondence over the state space which solves the household's problem A measure over the state space how many households are at each point in the state space A mixed allocation set of measures, one for each point in the state space, whose supports are the ranges of the optimal policy correspondence at that point in the state space.
Calibration & Estimation Data used for calibration/estimation is U.S. data from 1970-1993 Home ownership stable over sample PSID available at annual frequency Parameters calibrated From literature: θ h,γ, α, τ y From data: Earnings process - using panel data from PSID Initial wealth distribution - using SCF Parameters estimated In closed form: δ,δ h,τ p,d, and family-size prole. Estimated using SMM: β,σ,θ m, jointly with house price vector p.
Home ownership 70 Homeownership rate 69 68 67 Percent 66 65 64 63 62 1965Q11970Q11975Q11980Q11985Q11990Q11995Q12000Q12005Q1 date quarterly
Calibration & Estimation Parameter Description Value d(a < 65) Down payment 0.2 θ h Transaction cost 0.035 γ Risk aversion 5 τ y Income tax rate 20% δ h Maintenance.02 Parameter Value Moment Data Model K β 1.055(.975) 2.00 1.97 Y ph σ.12 1.22 1.26 Y θ m.025 Moving rate 12.42% 11.6%
Tenure 1 0.9 Proportion of Home Owners 0.8 0.7 0.6 0.5 0.4 0.3 Tenure (Sim) Tenure (Data) 0.2 0.1 20 30 40 50 60 70 Age
Moving 0.5 0.25 Proportion of Movers 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 Prop of Movers (Sim) Prop of Movers (Data) Proportion of Inter State Movers 0.2 0.15 0.1 0.05 Prop of Inter State Movers (Sim) Prop of Inter State Movers (Data) Prop of Job related Movers (Data) 0.05 0 20 30 40 50 60 70 Age 0 20 30 40 50 60 70 Age
Prole of home ownership What are the main determinants of the home ownership prole?: Expected duration Motives for savings
Average Duration 25 Expected Duration (Renters) Expected Duration (Owners) 20 15 Years 10 5 0 20 30 40 50 60 70 Age
Mobility, Ability and Wealth Young households have higher mobility: Option value of moving higher: Longer earnings horizon Higher uncertainty Income growing over life cycle > can aord to move into bigger house in mid-life Family size growing over life cycle > want to move into bigger house in mid-life
Savings and Risk 5 4.5 4 exp(average log earnings) 3.5 3 2.5 2 1.5 1 0.5 20 30 40 50 60 70 80 90 100 Age
Savings and Risk Young households want to borrow against future earnings but cannot Young households save only for precautionary reasons Can save using Risk-free bond Housing risky and correlated with earnings not as good for insurance
Heterogeneity V (i p, i t, j,τ, h, b, a,ε) = V (0, i t, j,τ, h e i p, b e i p, a,ε) (ei p ) 1 γ Discrete choices are determined by the relative level of nancial wealth to ability Renters with high wealth to ability have more of their permanent income in riskless form Less likely to adjust housing consumption in the future Becomes owner sooner
Counterfactuals Take baseline model and: Eliminate permanent uncertainty Set σ ip = 0. Eliminate down payment constraint Set d = 0 for non-retired households. For each alternative model: Repeat GE/calibration exercise and assess eect on tenure decision. Assess eect on tenure decision in partial equilibrium, using prices from baseline model.
More Insurance Expected Duration of Stay of Home Owners 45 40 35 30 25 20 15 Base σ ip =0 Net Wealth 1500 1000 500 Base σ ip =0 10 20 30 40 50 60 70 Age 0 20 30 40 50 60 70 Age
More Insurance 1 0.9 0.8 Proportion of Home Owners 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Base σ ip =0 0 20 30 40 50 60 70 Age
Down Payment 1 0.9 0.8 Proportion of Home Owners 0.7 0.6 0.5 0.4 0.3 Base d=0 0.2 0.1 20 30 40 50 60 70 Age
Down Payment Relatively small eects from changing down payment constraint Average increase in age of rst ownership: 2.06 years 30.5% of household buy a smaller rst home (>5% smaller) instead of waiting. Conditional Mobility drops but so does Unconditional Average Duration of owners Continuous housing choice set important Change in GE prices small - housing demand similar.
Conclusions Young households value mobility and wish to insure but not save for retirement. Buying a house limits mobility and is poor insurance. Most young households would rent even with no down payment required for owning.
Future Research Housing supply: What is the relative availability of rental and owner-occupied housing across regions and sizes? House prices: Why is the cross-sectional dispersion of rents so low compared to wages? Housing returns: What are the main determinants of the cross-section of housing returns at the regional vs. MSA vs. zip code level? Recent past: Cheaper borrowing rather than more available borrowing may be key