Welfare effects of housing price appreciation in an economy with binding credit constraints Welfare effects of housing price appreciation in an economy with binding credit constraints Lecture presentation Lecture presentation Ashot Tsharakyan Ashot Tsharakyan April 2008 April 2008

Presentation Outline Introduction and motivation The general model with endogenous housing price and binding credit constraints Special cases Definition of welfare adjustment The results of the model with exogenous housing price and binding credit constraints Endogenous housing price model: Supply-side shocks Comparison of the welfare adjustment in credit-constrained and unconstrained models Endogenous housing price model: Demand-side shocks US economy in : Actual aggregate welfare adjustment Summary

Introduction and motivation 1/5 Considerable housing price appreciation in the developed countries during last decade, particularly in US

Introduction and motivation 2/5 Existing research: 1. the effects of housing price appreciation on household’s consumption and welfare (Campbell and Cocco(2005),Li and Yao(2004),Bajari et all(2005)) 2. the effects of credit constraints on the housing market behavior (Ortalo-Magne and Rady(2005))

Introduction and motivation 3/5 Bajari et all (2005) conclude that up to first order approximation there are no effects of the housing price appreciation on aggregate welfare Two major limitations in their analysis: 1. The households are assumed to be not credit constrained 2. Housing price is given exogenously (no explicit equilibrium in the housing market) and it appreciates due to unspecified shocks In Bajari et all (2005) the beneficial effect of housing price appreciation which comes from relaxation of credit constraints and better consumption smoothing, is ignored The source of housing price appreciation should intuitively matter for its eventual welfare effects

Introduction and motivation 4/5  In reality credit constraints are important drivers of the housing market: a) Empirical evidence: over 65% of owner-occupied housing stock in US is mortgage financed, average actual LTV ratio in US very close to maximum allowed LTV (constraints are binding) b) From modeling perspective, Ortalo-Magne and Rady (2005) identify a crucial role of capital gains and losses experienced by credit-constrained individuals in explaining housing market fluctuations.  It should be important to model the source of housing price appreciation that is to make housing price endogenous

Introduction and motivation 5/5  First, aggregate welfare effects of housing price appreciation are explored in exogenous price model with binding credit constraints  Then the endogenous price model is constructed in which housing price appreciates due to different supply and demand side shocks  Change in building permit cost as a supply-side shifter (based on Glaeser and Guyorko (2005), changes in income and interest rates as demand-side shifter  Endogenous price model is analyzed in both credit constrained and unconstrained versions  Finally, cumulative aggregate welfare adjustment from the considered combination of shocks is computed by aggregating the results in credit constrained and unconstrained models

Housing price is determined endogenously and it changes endogenously due to demand or supply shocks Demand side is represented by the households and supply side is represented by competitive sector of construction firms Construction firms face CRS Cobb-Douglass technology (Amin and Cappoza(1993)), use capital and land as inputs and need to obtain building permit from zoning authority Housing stock depreciates with constant rate δ The model with endogenous housing price and binding credit constraints 1/4

The model with endogenous housing price and binding credit constraints 2/4 Possible forms of credit constraint:  Margin clause (Mendoza and Durdu(2004)) 1  Kiyotaki-Moore constraint 2 1 i.e households can borrow only up to fraction m<1 of total value of their housing stock 2 households can borrow as long as the gross repayment next period does not exceed the next period’s expected monetary value of the collateral.

The household’s optimization problem ( case with margin clause ) {c t,h t+1,b t+1 } s.t.

where k=K/L is capital to land ratio n is the regulatory cost of obtaining building permit ( which is the source of endogenous housing price appreciation, based on Glaeser and Guyorko(2005 )) Profit-maximizing input is given by: Construction firm’s optimization problem

Special cases a) Model with exogenous housing price and credit-constrained households: Housing price is not determined endogenously. It is exogenous and it is contained in the value function of the household as a state. It appreciates due to non-specified shock No construction firms in the model. Depreciation of housing is abstracted from and it is assumed that fixed stock of housing is traded b) Model with endogenous housing price but binding credit constraints Credit constraint is removed from household’s optimization problem

Definition of welfare adjustment Change in income necessary to keep household’s lifetime utility constant in case of housing price appreciation. For the exogenous price model it is derived from the following formula by solving for : For the endogenous price model it is derived from the following formula by solving for (case of change in building permit cost)

The results of the model with exogenous housing price and binding credit constraints Individual welfare adjustment is given by the following expression : Comparison with Bajari at al (2005) result : a) W elfare loss is lower (welfare gain is higher) because of the additional beneficial effect of housing price appreciation in form of relaxation of binding credit constraints. b) Homeowners do get a certain benefit from housing price appreciation even without participating in housing transactions (when x j,t =0)

Aggregate welfare adjustment Aggregate welfare adjustment is the sum of individual adjustments When summing up across households the first term drops out based on market clearing and aggregate welfare adjustment is given by : IMPORTANT FINDING The housing price appreciation in the economy subject to binding credit constraint implies improvement in the aggregate welfare (in case of exogenous housing price assumption)

Quantification of the result of exogenous housing price model

Endogenous price model: Supply side shocks 1/3 Solve household’s and firm’s problem, define equilibrium, derive steady state,analyze what happens in the steady state when building permit cost increases. Assume special case utility function of modified Cobb- Douglass form (Li and Yao (2004))

The welfare adjustment resulting from change in building permit cost in the model with credit constraints is given by: The welfare adjustment resulting from change in building permit cost in the model without credit constraints is given by: Endogenous price model: Supply side shocks 2/3

Endogenous price model: Supply-side shocks 3/3 Under the reasonable values of parameters (given in the table below) both of the welfare adjustments shown previously are positive, implying welfare loss Parameter Value in unconstrained model Value in the model with credit constraints i π0.02 δ0.025 ω0.56 m-0.8 β

Comparison of the welfare adjustment in credit- constrained and unconstrained models 1/2 Sensitivity analysis for different values of ω ωUnconstrainedConstrained

Comparison of the welfare adjustment in credit- constrained and unconstrained models 2/2 Relationship between welfare adjustments in the constrained and unconstrained economies depends on relative weight of housing in the utility function ( parameter ω) What is the proper value for ω ? Use the fact that is the function of ω and parameters only Calibrate shares of housing and non-durable consumption in the household’s expenditures (shares available from CES by BLS) Calculate ω from the resulting equation The plausible range for ω is

Endogenous price model: Demand-side shocks 1/5 Changes in household income are straightforward demand shocks

Endogenous price model: Demand-side shocks 2/5 Welfare adjustment resulting from housing price appreciation driven by income changes in the constrained model is given by: In the unconstrained model it is given by:

Endogenous price model: Demand-side shocks 3/5 Positive demand-side shock can also be generated by declines in the interest rates.

Endogenous price model: Demand-side shocks 4/5

Endogenous price model: Demand-side shocks 5/5 Welfare adjustment resulting from housing price appreciation driven by changes in the interest rates in the model with credit constraint is given by: Welfare adjustment resulting from housing price appreciation driven by changes in the interest rates in the unconstrained model is given by:

Endogenous price model: Demand-side shocks vs supply-side shocks Quantify welfare adjustments resulting from housing appreciation driven by changes in income and interest rates using already set values of parameters The results show that those adjustments are negative implying that housing price appreciation driven by changes in income and interest rates leads to welfare improvement As already shown, negative supply side shock in the form increase in building permit cost leads to welfare loss Modeling source of housing price appreciation is important when considering the welfare effects of housing price appreciation

US economy in : Actual aggregate welfare adjustment 1/2 It is reasonable to expect that combination of demand and supply shocks affected the real US economy and US housing market Apply theoretical results to actual US economy, and calculate the aggregate welfare effects of housing price appreciation driven by combination of considered demand and supply shocks for (period of significant housing price growth) Use US data to calculate changes in shock variables over the considered period, calculate resulting welfare adjustments for each shock and each model (credit-constrained and unconstrained), sum them up over shocks for each group of households

US economy in : Actual aggregate welfare adjustment 2/2 Calibrate the weights of credit constrained and unconstrained households in the economy, using data on net worth of US households by the age of the household head (available from Survey of Consumer Finance) Aggregate over the calibrated weights the results for credit constrained and unconstrained models to get final cumulative aggregate welfare change Result : Aggregate welfare improved, demand-side shocks dominated during the considered period

Summary In the exogenous housing price model with binding credit constraints housing price appreciation implies an improvement in aggregate welfare. The result is due to the fact that credit-constrained model takes into account the welfare improving effect of the housing price appreciation, which implies relaxation of binding credit constraints. In the model with endogenous housing price, welfare effect of housing price appreciation depends on whether it is caused by demand-side shock or supply-side shock The relationship between supply-driven welfare adjustments in the two modeling alternatives depends on the relative weight housing in the agent.s utility function The calculation of cumulative aggregate welfare adjustment shows that demand-side shocks dominated in US economy and aggregate welfare improved