Financial Intermediation and Real Estate Prices Impact on Business Cycles: A Bayesian Analysis

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1 Financial Intermediation and Real Estate Prices Impact on Business Cycles: A Bayesian Analysis Carlos A. Yépez This version: April 217. (First version: April, 212.) Abstract How do financial intermediation and real estate prices impinge on the business cycle? I develop a two-sector stochastic general equilibrium model with financial intermediation and real estate collateral to assess the impact of financial conditions and land prices on aggregate fluctuations. I estimate the model with Bayesian methods using a novel data set that includes U.S. macro and financial variables during the period The results from the estimated model show that financial conditions have a sizable effect on the variability of investment spending, while productivity shocks are the main source of consumption fluctuations. Specifically, on the macro side, 1) financial shocks explain about three quarters of investment spending variability and one third of the variance in hours worked. On the financial side, 2) financial shocks explain most of the variability in land prices, credit spread, and aggregate net worth of the financial sector. The model also accounts for observed unconditional moments of macro and financial variables. Our quantitative results are suggestive of the impact of diverse sources of financial instability, and as such relevant for macro prudential policy analysis. Keywords: Financial Frictions; Banking; Net Worth; Leverage; Credit Spread; Land Prices; Business Cycles; Bayesian Estimation. JEL Codes: E21, E22, E32, E44 I am grateful to Markus Brunnermeier, Paolo Gelain, Fabio Ghironi, George Hall, Matteo Iacoviello, Alberto Ortiz, Dan Tortorice, Kei-Mu Yi, anonymous referees, and seminar participants at the Bank of Canada, Midwest Macroeconomics Meetings, Computing in Economics and Finance, Federal Reserve Bank of Atlanta, the 22nd School in Economic Theory at Hebrew University in Jerusalem, Boston College, and Brandeis University for helpful discussions, comments, and suggestions. This paper was previously entitled Financial and Real Estate Cycles on Business Cycles. University of Manitoba, Economics Department. Rm. 51 Fletcher Argue, Winnipeg, MB. R3T 5V5. carlos.yepez@umanitoba.ca 1

2 1 Introduction The Great Recession (27-29) underscored the importance of real estate prices and financial intermediation on business fluctuations. This recent episode of economic turmoil reignited interest on the structural linkages between financial conditions and real outcomes (see Bernanke and Gertler (1989), Kiyotaki and Moore (1997) for seminal contributions). Prior to 29, studies that investigated the sources of aggregate fluctuations during the period known as the Great Moderation ( ) ascribed an increasingly important role to non-productivity shocks (Gali and Gambetti (29), Smets and Wouters (27), henceforth SW (27), among others). After 29, a growing strand of macro literature focused on studying the role of financial market conditions on real activity (Christiano et al. (214), Gilchrist and Zakrajsek (212), Iacoviello (215), Justiniano et al. (21), Gertler and Kiyotaki (21), Gertler and Karadi (211), and Liu, Wang, and Zha (213), henceforth LWZ (213)). Most studies have focused on the prices of financial assets while the role of real estate prices has not been explored to the same extent. 1 I contribute to the literature with a quantitative study of the joint effects of real estate prices and financial intermediation on aggregate fluctuations. Specifically, in this study I ask: How much do real estate and financial conditions impinge on the volatility of macro and financial variables? I approach this question in two steps. First, on the theoretical side, I extend a two-sector real business cycle (RBC) model with heterogeneous households to include a credit channel through financial intermediaries whose function is to channel funds from lenders to borrowers and firms. I draw on the financial intermediation framework of Gertler and Karadi (211) (henceforth GKI (211)) and Gertler and Kiyotaki (21), where the financial accelerator mechanism (Bernanke, Gertler, and Gilchrist (1999)) is introduced to model the dynamics of the financial intermediary s balance sheet. In this framework, an increase in financial intermediary s assets favors the supply of credit and a subsequent expansion of aggregate economic activity; in a similar fashion, poor balance sheet conditions in the financial intermediary reduce the credit that borrowing households and firms can obtain, subsequently reducing aggregate economic activity. As a result, the financial accelerator operating through financial intermediation effectively propagates the transmission of financial shocks (i.e., shocks which affect the balance sheet of the bank). Second, I estimate the model using Bayesian methods applied to a novel data set of U.S. macroeconomic and financial variables during the period The 1 Important exceptions are Goodhart and Hofmann (27), Iacoviello (25), Iacoviello and Neri (21), Leamer (27), and LWZ (213). 2

3 results of the estimated model suggest that the credit (i.e., bank lending) channel is a quantitatively important mechanism for the transmission of financial shocks that ripple into the real economy. Importantly, the joint effect of credit supply, net worth, real estate, and quality of capital shocks accounts for a sizable share of the variability of key macroeconomic and financial variables over U.S. business cycles. Recent studies suggest mixed evidence on the importance of real estate markets in determining aggregate fluctuations. On the one side, studies by Claessens et al. (29), Goodhart and Hofmann (27), and Leamer (27) provide ample empirical evidence that credit and housing cycles are strongly associated with the business cycle. On the other side, quantitative studies such as Iacoviello (25) and Iacoviello and Neri (21) find that housing shocks have a small effect on the economy. In contrast, the study by LWZ (213) argues that land prices are a quantitatively important mechanism for the transmission and amplification of aggregate fluctuations. 2 Other studies focus on the role of financial intermediation and credit in driving aggregate fluctuations. Important contributions are studies by Gertler and Kiyotaki (21), GKI (211), and Iacoviello (215). These studies develop models in which asymmetric information applied to financial intermediation plays an important role in influencing real outcomes. The aforementioned separation in the two strands of the literature is startling given that it is widely accepted that major financial disruptions are associated with disturbances in (i) asset markets as well as (ii) disruptions in financial intermediation. This study aims to bridge this gap on two fronts. First, by explicitly decomposing real and financial linkages through the joint role of financial intermediaries and real estate collateral on aggregate fluctuations. Specifically, I extend the financial intermediation framework of Gertler and Kiyotaki (21) and GKI (211) to a twosector real RBC model (saver and borrower households) with two asset classes: firm equity and housing collateral. 3 Second, I use a novel data set that combines key macro and financial variables to estimate the model and quantify the importance of financial conditions over U.S. business cycles during the period I use seven macro and financial time series and estimate the model with Bayesian methods. The new financial data include corporate bond credit spread, total (household and business) debt, land prices, and aggregate net worth of financial institutions. 2 Studies such as Davis and Heathcote (27) and LWZ (213) use land price data arguing that most of the variation in house prices comes from land prices rather than the cost of structures. 3 This study uses a simplified RBC framework in order to abstract from important modeling challenges associated with the zero lower bound (ZLB) of nominal interest rates. We acknowledge that a richer version of the model can be developed with nominal rigidities and monopolistic competition as to provide insight on the role of non-conventinional monetary policy. 3

4 The quantitative analysis of the estimated model indicates that financial conditions have a sizable impact in driving U.S. business cycles for the period under study. Specifically, financial conditions, defined as the joint effect of credit supply, net worth, quality of capital, and real estate shocks, explain 77% of the variation in private business investment and 33% of the variation in hours worked. Moreover, these shocks explain 96% of the variability in financial intermediation net worth, 96% of the variability in credit spread, 64% of the variability in land prices, and 34% of the variability in total debt. 4 Last, I show that the estimated model is a good fit in matching a key set of macro and financial statistics over U.S. business cycles during the period The rest of the paper proceeds as follows. Section 2 describes the model. Section 3 discusses the solution and estimation methods. Section 4 analyzes the workings of the model and discusses the quantitative implications of different sources of aggregate fluctuations. Section 5 examines the empirical fit of the model in matching unconditional moments of both macro and financial variables. Section 6 checks for robustness of the results, and Section 7 concludes. 2 Model To study the role of financial and real estate linkages in aggregate fluctuations I develop a two-sector RBC model where I introduce i) a housing sector, and ii) financial intermediation. There are three agents in the economy. 1) Households who enjoy utility from consumption, leisure, and housing holdings; 2) Financial intermediaries who channel funds by borrowing from (saver) households and lending to firms and (borrowing) households; and 3) Firms that use capital, labor, and land as factors of production. 2.1 Households As in Iacoviello (25) there are two types of households in the economy, unconstrained or patient households (savers) and constrained or impatient households (borrowers). 4 Our quantitative results are meant to be suggestive of a large effect of financial shocks on aggregate fluctuations, yet these results need to be taken with caution as this study focuses on the size of the balance sheet of financial intermediaries, rather than its composition. We conjecture that the composition effect of the balance sheet may be dominant due to important asset return differentials. 4

5 2.1.1 Savers Savers derive utility from consumption, leisure and real estate holdings. Savers are composed by a continuum of unconstrained households who maximize expected future utility: E t t= βt su(c s t, L s t, H s t ) where C s t is consumption, L s t is labor supply, and H s t is real estate holdings. Saver households are owners and shareholders of financial and non-financial firms in the economy. The saver household s problem is given by: max C s t,hs t,ls t s.t. E t βs[ln(c t t s h s Ct 1) s + ζ t ln Ht s t= ϕ t 1 + η L1+η s,t ] (1) C s t + q t H s t + R t 1 B D t 1 = B D t + W t L s,t + Π t (2) where β s is the discount factor, η determines the Frisch labor elasticity coefficient, h s denotes the habit parameter in consumption. The saver household is subject to two shocks: A real estate demand shock (ζ t ), and a shock to labor supply (ϕ t ). Equation (2) is the saver household s budget constraint where q t is the price of land, W t and R t are the wage and gross interest rates respectively, Bt D are saver s deposits on the financial intermediary, and Π t denotes the net profits received by households from owning financial and non-financial firms in the economy. The shock processes are given by: where Θ t = ρ Θ Θ t 1 + σ Θ ɛ Θ t Θ t = {ζ t, ϕ t } and ɛ t N(, 1) Given the problem in (1) and (2), the optimality conditions for the unconstrained household are given by: λ s t = U C (C s t, L s t, H s t ) + β s he t [ UC (C s t+1, L s t+1, H s t+1) ] (3) λ s tw t + U L (C s t, L s t, H s t ) = (4) 5

6 q t = 1 λ t U H (C s t, L s t, H s t ) + E t [m t+1 q t+1 ] (5) and E t [m t+1 ] = 1 R t (6) where m t+1 denotes the unconstrained household s stochastic discount factor which is given by: [ ] λ s E t [m t+1 ] β s E t+1 t (7) λ s t where λ s t is the Lagrange multiplier associated with the resource constraint. Equations (3) and (4) are standard optimality conditions for intertemporal consumption and the marginal rate of substitution between labor and consumption. Equation (5) equates the price of real estate to the discounted present value of marginal utilities of land holdings. Equation (6) is the Euler equation Borrowers Borrower households consume, work, and demand real estate. Borrowers lease a fixed share (1 ς) of their real estate holdings to firms for which they earn rents r h t. Firms use real estate as factory space for production. Borrower households maximize expected future utility: E t t= βt eu(c e t, L e t, ςh e t ). Borrowers are more impatient than savers (β s > β e ), which makes borrowers constrained households in the economy. The amount of borrowing Bt e at any period t depends on the expected value of real estate collateral at time t and the borrowing gross interest rate Rt L. Thus, the borrower s problem is given by: max C e t,he t,le t s.t. βe[ln(c t t+1 e h e Ct e ) + ζ t ln(ht e ) t= ϕ t 1 + η L1+η e,t ] (8) C e t + q t H e t + R L t 1B e t 1 = B e t + W t L e,t + r h t (1 ς)q t H e t 1 (9) and the borrowing constraint: B e t m e E t [ qt+1 H e t R L t 6 ] (1)

7 where m e represents the loan-to-value (LTV) ratio of the borrower. The optimality conditions associated with the borrower are: λ e t = U C (C e t, L e t, ςh e t ) + β e he t [ UC (C e t+1, L e t+1, ςh e t+1) ] (11) q t = 1 λ e t and U H (Ct e, L e t, ςht e ) + µ [ ] t m e qt+1 E λ e t t Rt L λ e tw t + U L (C e t, L e t, ςh e t ) = (12) 1 = µ t λ e t [ ] λ e + β e E t+1 t q λ e t+1 (1 + (1 ς)rt+1) h t (13) [ ] λ e + β e E t+1 t R λ e t L (14) t where µ t is the shadow price associated with the borrowing constraint (1). 5 Equations (11) and (12) are standard optimality conditions for intertemporal consumption and the marginal rate of substitution between labor and consumption. Equation (13) equates the price of real estate to the current value of holding one unit of real estate plus the discounted present value of next period s rent revenue and next period s real estate price adjustment. Last, equation (14) relates the shadow price of consumption with the shadow price of borrowing plus the discounted value of next period s interest rate adjustment on borrowing. 2.2 Financial Intermediaries Financial intermediaries are owned by saver households; their function is to channel funds between borrowers (constrained households and firms) and lenders (unconstrained households). I model the representative financial intermediary as an extension of the financial intermediation framework posited by Gertler and Kiyotaki 21 and GKI (211) with two asset classes. Namely, i) equity capital, and ii) real estate collateral. A continuum of mass one financial intermediaries raises funds from the saver households by issuing one-period non contingent deposit claims Bt D that pay R t interest at the end of period t. In turn, each financial intermediary j uses these assets to fund borrowing by households and firms. On the one hand, the intermediary funds investment in the productive side of the economy by issuing one period loans to firms B f jt. On the other hand, it issues one period loans to borrowing households 5 Since borrowers are more impatient than savers the constraint (1) binds in equilibrium. 7

8 B e jt. Borrowing households and firms pay back R L t+1 in interest to the intermediary at the end of the period. The difference of assets and liabilities is the net worth of the intermediary, N jt. Thus, the balance sheet of financial intermediary j is: Assets B L jt Liabilities Bjt D Net Worth N jt where intermediary j assets B L jt are composed of claims to both firm s equity capital B f jt and real estate collateral Be jt 6 : ] [ Bjt L = e [B χt f jt + Be jt = e χt E t Q t K jt+1 + me q t+1 Hjt e ] Rt L where χ t represents a credit credit supply shock to assets of financial intermediaries: χ t = ρ x χ t 1 + σ χ ɛ t, ɛ t N(, 1). The participation constraint for intermediary j to operate is given by: E t [ mt+1 (R L t+1 R t+1 ) ], t where m t+1 is the stochastic discount factor of the unconstrained household, and (R L t+1 R t+1 ) represents the premium or credit spread between the return on capital and risk-free deposits. The law of motion for net worth of intermediary j is given by: (15) N jt+1 = R L t+1b L jt R t+1 B D jt. (16) 6 In this study I focus on size effects, rather than composition effects of the balance sheet. Therefore, I assume that the two assets are substitutes and payoff the same return Rt L. The analysis of the composition effect (i.e., portfolio choice) of the balance sheet is of great relevance but requires the use of non-linear solution and estimation methods, which are outside the scope of the present study. 8

9 The optimization problem of intermediary j consists in maximizing its expected future wealth: V jt = max E t (1 θ)θ t m t+1 N jt+1 (17) t = max E t (1 θ)θ t m t+1 [(Rt+1 L R t+1 )Bjt L + R t+1 N jt ]. t where θ the probability that the financial intermediary will survive next period so that its average lifetime is given by 1. 1 θ To solve this problem we guess and verify a solution to the value function of the form: V jt = υ t Bjt L + η t N jt (18) with B υ t = E t [(1 θ)m t+1 (Rt+1 L jt+1 L R t+1 ) + θm t+1 υ Bjt L t+1 ] (19) η t = E t [(1 θ) + θm t+1 N jt+1 N jt η t+1 ] where υ t represents the marginal gain of an additional unit of assets B L jt and η t is the marginal gain of a unit of net worth N jt. 7 To rule out the possibility of self-financing we consider an agency problem where the intermediary diverts a fraction λ of equity to his/her household. Monitoring is costly for the households so they can only recover a fraction 1 λ of their deposits when the financial intermediary walks away. Hence, the incentive constraint for the intermediary equates the marginal value of staying in business with the marginal gain of walking away, as follows: η t N jt + υ t B L jt λb L jt (2) when the incentive constraint binds, the relationship between intermediary j s assets and its equity capital is determined by: B L jt = η t λ υ t N jt (21) = φ t N jt 7 Refer to Appendix B for the derivation of the solution regarding the dynamic problem of the financial intermediary. 9

10 where φ t = ηt λ υ t represents the (intermediary) leverage ratio and is independent of intermediary j specific factors. The constraint binds when λ > υ t >, an increase in λ tightens the constraint. Since the components of the leverage ratio φ t do not depend on intermediary j specific factors we can substitute this result on the law of motion of net worth (16) to obtain: N jt+1 = [(Rt+1 L R t+1 )φ t + R t+1 ] N jt. (22) As in Mimir (215), we consider Ñt as aggregate net worth of financial intermediation at the beginning of period t and before the realization of any exogenous disturbance to bank equity. Ñ t is composed by the net worth of both existing intermediaries Ñet and new entrants Ñnt, Ñ t = Ñet + Ñnt, with Ñet given by: Ñ et = θ [ (R L t R t )φ t + R t ] Nt 1. (23) To determine Ñnt for new entering intermediaries we assume that households transfer a small fraction of seed funds to new intermediaries. This seed funding is equivalent to γ/(1 θ) of previous period s exiting intermediaries equity. Thus, Ñ nt = γn t 1. (24) Substitute equations (23) and (24) to derive the expression for the law of motion of aggregate net worth as: Ñ t = { θ [ (R L t R t )φ t + R t ] + γ } Nt 1. (25) Last, aggregate net worth at the end of period t is N t = e κnw t Ñ t, where κt nw an exogenous disturbance to bank equity: represents κ nw t = ρ n κ nw t 1 + σ κ ɛ t, ɛ t N(, 1). 2.3 Firms Firms hire labor from constrained and unconstrained households, use capital and land to produce final goods and are owned by unconstrained households. The representative firm produces final goods using the following technology: Y t = e zt (U t K t ) ν ((1 ς)ht 1) e σ L (1 ν σ)α s,t L (1 ν σ)(1 α) e,t. 1

11 The factors of production are capital K t, labor L t, and land rented from borrower households (1 ς)h e t 1. U t denotes the utilization rate of capital. Similar to GKI (211), each period firms raise funds B f t from intermediaries to finance their working capital bills. Each firm issues claims equal to the number of units of working capital K t+1, with each claim of capital priced at price Q t. Thus, the amount of funding that the firm can raise from the intermediary is limited by its capital collateral: B f t = Q t K t+1. (26) Each period, the firm makes revenues from sale of new production and the resale of undepreciated capital. Firms use intra-period loans to buy new capital, pay their real estate rental bills, and their wage bills. The intra-period loan that pays rental and wage bills carries a zero interest rate and is different from the loan that the firm uses to finance investment, which carries a positive interest rate. Firms pay back their intra-period loans at the end of the period upon realization of their revenues. Thus, the firm s problem is given by: max Π t+1 = max E t [m t+1 {Y t+1 + (Q t+1 δ(u t+1 ))e ξ t+1 K t+1 (27) K,H e,l s,l e,u (Rt+1Q L t K t+1 + rt+1(1 h ς)q t+1 Ht e + W t+1 L i t+1)}] s.t. i={s,e} Y t = e zt (U t K t ) ν ((1 ς)ht e ) σ L (1 ν σ)α s,t L (1 ν σ)(1 α) e,t (28) where the shocks z t and ξ t are standard AR(1) processes that represent exogenous variation to total factor productivity and the quality of capital respectively. The latter, quality of capital shock, is proposed Gertler and Kiyotaki (21) and GKI (211) as a key source of fluctuations, and thus can be interpreted as a financial source of exogenous variation in the price of capital. 8 The optimality conditions associated with the firm s problem include the marginal products of labor and utilization: W t = (1 υ σ)α Y t (L s t) (29) υ Y t U t = δ (U t )e ξt K t, (3) 8 The shock ξ t affects capital (a stock variable) and entails a first order effect on the dynamics of the price of capital, which in turn affects the asset side of the balance sheet of financial intermediaries. 11

12 the rental rate of real estate: ] E t rt+1 h Y t+1 = E t [σ, (31) (1 ς)q t Ht+1 e and the ex-post rate of return on capital: 2.4 Capital Producers E t R L t+1 = E t [ ν Y t+1 K t+1 + [Q t+1 δ(u t+1 )]e ξ t+1 Q t ]. (32) As in GKI (211), capital producers buy used capital from the representative firm at the end of period t. The cost of buying depreciated capital is normalized to one unit. Capital producers build new capital and refurbish old capital to sell it to firms at price Q t per unit at the beginning of next period. Unconstrained households own capital producers and receive any profits from their operation. Let I nt denote net capital investment and I t gross capital investment. Capital producers maximize net investment flow I nt subject to adjustment costs of investment. The maximization problem of the capital producer is: where max E t I nt m t {(Q t 1)I nt S t= ( Int I nt 1 ) ( I } nt ) I nt 1 (33) I nt = I t δ(u t )e ξt K t. (34) Consistent with Christiano, Eichenbaum, and Evans (25), the adjustment cost function S( ) has the following properties: S(1) =, S (1) =, and S (1) >. Similarly, we impose standard restrictions on the utilization cost function. i) Ū = 1 in steady state, ii) δ(1) = δ captures full depreciation in steady state, and iii) δ (1)/δ (1) = η u captures the elasticity of capital utilization. The optimal solution to the capital producer s problem yields the price of capital relation: Q t = 1 + S( ) + I nt I nt 1 S ( ) E t [ m t+1 ( Int+1 I nt ) 2 S ( )]. (35) 12

13 2.5 Competitive Equilibrium } Let s t = {B et, B ft, K t, N t ; Λ t denote the state of the world at time t, where Λ t is the state-space matrix of shock processes Λ t = ϱλ t 1 + ɛ t. A competitive equilibrium is a set of household s allocations { C s t (s), Ct e (s), Ht s (s), Ht e (s), L s t(s), L e t(s), Bt+1(s), D Bt+1(s) } e, a set of firm s and intermediary s decision rules { } L s t(s), L e t(s), Bt+1(s), f Ht e (s), K t (s), U t (s), I nt (s), N t+1 (s), φ t (s), and a set of prices { R t (s), Rt L (s), Q t (s), q t (s), rt h (s) } ; such that, given the prices, the decision rules of the household, firm, and financial intermediary solve their respective optimization problems. Further, the aggregate resource constraint holds every period ( ) Y t = Ct s + Ct e Int + I t + S ( I nt ), (36) I nt 1 I nt 1 and factor markets clear. Namely, the labor market L s t + L e t = L t, (37) the real estate market and the credit market H s t + H e t = H, (38) B L t = B f t + B e t. (39) 3 Estimation 3.1 Model Solution To solve the model I first stationarize the system of model equations around the balance growth path, then I derive the non-stochastic steady state, and linearize the model around the steady state. This yields a system of linear rational expectations equations that I solve using the Dynare toolbox. Last, I simulate model to examine its dynamic implications vis-a-vis the data. 9 9 The full system of linearized model equations is available from the author upon request. 13

14 3.2 Calibration As a preliminary step to the estimation procedure, I calibrate a key set of model parameters which are difficult to estimate and therefore are better identified using other information. Table 1 in Appendix C summarizes the calibrated parameters. I draw preference parameters from relevant values suggested by Iacoviello and Neri (21). Namely, the discount factors of constrained and unconstrained households in the model are set to β e =.97 and β s =.9925 respectively. The unconstrained household discount factor implies a steady state real interest rate of 4.8% annualized. The loan-to-value (LTV) ratio in the borrower s constraint is m e =.85. The steady state depreciation parameter is δ =.368 as in LWZ (213), which corresponds to an annualized depreciation rate of 14.7%. The share of borrower household s real estate rented to firms is ς =.73, based on Florance et al. (21) estimate of the size of U.S. commercial real estate. In the financial intermediary, the fraction transferred to existing bankers is set to γ =.2 as in GKI (211). The other parameters are calibrated to pin down specific steady state targets. I set the land preference parameter to ι =.637 to match a steady state housing wealth to annual GDP ratio of 1.34 similar to Iacoviello and Neri (21). In the case of the financial intermediary, the key steady state ratio is the financial leverage ratio or the ratio of total household and business liabilities to total financial net worth (B L /N). A value of 27 is obtained from the sample mean of this variable in the historical series indicating a highly leveraged financial sector. In addition, the steady state external financial premium is set to the average credit spread over the sample period equivalent to 2.1% annualized. To pin down these steady state ratios, I calibrate the following parameters. The survival rate of bankers is θ =.8261, the fraction of capital that can be diverted is λ =.121, and the elasticity of marginal depreciation η u = Finally, I set the dis-utility weight on labor at ϕ = 1.5, to pin down a steady state labor endowment equivalent to 3% of the time. 3.3 Estimation I estimate the structural parameters of the model and the parameters that govern the structural shocks using standard Bayesian estimation techniques applied to DSGE models as described in Schorfheide (2). The data set is composed of seven seasonally adjusted time series of key U.S. macroeconomic and financial variables at quarterly frequency, namely: log difference of real per capita private consumption 1 The parameters {θ, λ, η u } need to be calibrated simultaneously for two targets in order to have enough range of values as required by the steady state ratios in the data. 14

15 (non-durables, non-housing services), log difference of real per capita investment, log of hours worked (computed as ratio of total time endowment), log difference of real price of land, log difference of real per capita total household plus business (corporate and non-corporate) liabilities, log difference of total financial net worth, and real bond credit spread. Total financial net worth is calculated as the difference between total assets and total liabilities of an aggregate of financial institutions (commercial banks, asset backed securities (ABS) issuers, finance companies, funding corporations, among others). 11 For credit spread, I use Moody s seasoned BAA corporate bond relative to 1-year treasury bonds, which is a widely used default risk indicator. I use credit spread [ series as it ] is a plausible proxy for the model s external finance premium s t = E t r L t+1 r t+1 (Levin et al. (26), Gilchrist and Zakrajsek (212), GKI (211)). The data spans over the period 1975:1-21:4 and is described in more detail in Appendix A. 12 The measurement equation used in estimation is: Y t = ln Cons t ln Inv t ln Q L t ln Debt t ln NW t ln Hrs t CS t = c t i t q t b t nw t l t s t + g γ,t g γ,t g γ,t g γ,t g γ,t + where the left hand side denotes the observables and the right hand side contains the model counterparts of the stationarized variables as well as their respective stochastic growth trend and deterministic growth parameters. The symbol denotes the first difference operator, ḡ γ = 1(g γ 1) is the quarterly trend growth rate common to consumption, investment, land prices, total assets, and net worth; s is the steady state bond credit spread, and l is steady-state log of hours worked. There is a vector Ξ t of seven structural shocks, equal to the number of observables used in estimation. Namely, housing demand (ζ t ), dis-utility of labor supply (ϕ t ), 11 Adrian and Shin (21) provide evidence that market-based financial institutions of this type have become, along with commercial banks, the most dominant sources of financing over the last three decades. 12 In the robustness section I report results of the estimates I obtain using the GZ credit spread proposed by Gilchrist and Zakrajsek (212), which accounts for the possibility of maturity mismatch. The estimates are fairly close to the benchmark model estimates. The bond credit spread time series used in the benchmark model closely tracks the GZ credit spread with a correlation coefficient of.85. ḡ γ ḡ γ ḡ γ ḡ γ ḡ γ l s 15

16 investment (ξ t ), permanent productivity (A P t ), transitory productivity (A T t ), credit supply (χ t ), and net worth (κ nw t ): Ξ t = {ζ t, ϕ t, ξ t, A P t, A T t, χ t, κ nw t }. I estimate eight structural parameters, namely: Quarterly trend growth ḡ γ, capital adjustment cost ϕ k, habit persistence for constrained (h s ) and unconstrained (h e ) households, the capital share of output ν, the share of commercial real estate in production σ, the labor income share of saver households α, and the elasticity of labor supply η. Tables 2 and 3(A, B), columns 1 to 3, summarize the assumptions on the prior distributions of the estimated parameters. I draw most of the priors from relevant Bayesian estimation studies for these parameters (Smets and Wouters (27), Gilchrist et al. (29), Iacoviello and Neri (21), and LWZ (213)). The Bayesian estimation technique consists of two stages: 1) Estimation of the mode of the posterior distribution by maximizing the log of the posterior distribution based on assumptions for the prior distribution of parameters and likelihood of the data, and 2) a detailed characterization of the posterior distribution from the Metropolis-Hastings (MH) sampling algorithm. For the latter step I use a sample of 5. draws (from which I discard the first half). 13 Prior Posterior Dist. a b Mode Mean 1% 9% 1(ḡ γ 1) G(a,b) ϕ k G(a,b) h s B(a,b) h e B(a,b) ν B(a,b) σ B(a,b) α B(a,b) η G(a,b) Table 2. Priors and Posteriors of Structural Parameters (B=Beta, G=Gamma) 13 I use a step size of.5, which led to an acceptation rate of.29. I check the stability of the sample using the standard Brooks and Gelman (1998) test for parameter convergence and also examine the posterior distributions. The estimated parameters converge and are stable. Diagnostic tests are available upon request from the author. 16

17 Table 2, columns 1 to 3, summarize the prior distributions of the structural parameters. The quarterly trend growth rate (ḡ γ ) is assumed to be gamma distributed with shape parameters a=.4 and b=.1. The investment adjustment cost parameter (ϕ k ) is assumed to follow a gamma distribution with shape parameters a=2 and b=2. The habit in consumption parameters (h s, h b ) follow a beta distribution with shape parameters a=.7 and b=.1. The capital share parameter (ν) follows a beta distribution with shape parameters a=.3 and b=.5. The real estate share parameter (σ) follows a beta distribution with shape parameters a=.3 and b=.1. The labor income share of saver households (α) follows a beta distribution with shape parameters a=.33 and b=.24. Finally, the labor elasticity parameter (η) follows a gamma distribution with shape parameters a=2. and b=.75. Tables 3A and 3B, columns 1 to 3, summarize the prior distributions of the shock processes. These distributions are harmonized to rather loose priors. The standard errors follow an inverse-gamma distribution with shape parameters a=.1 and b=2, while the persistence of the autoregressive parameters are assumed to follow a beta distribution with shape parameters a=.33 and b=.24. Posterior Parameter Estimates Tables 2 and 3 (A, B), columns 3 to 5, show the mode, mean, and the 1 and 9 percent HPD interval of the posterior distribution of the structural and shock parameters. Standard Deviations Prior Distribution Posterior Distribution Description Dist. a b Mode Mean 1% 9% σ A P TFP (P) IG(a,b) σ A T TFP (T) IG(a,b) σ z Housing Pref. IG(a,b) σ ϕ Labor Supply IG(a,b) σ ξ Quality of K IG(a,b) σ χ Net Worth IG(a,b) σ n Credit Supply IG(a,b) Table 3A. Priors and Posteriors of Shock Parameters (B=Beta, IG=Inverse Gamma) 17

18 Autocorrelation Coefficients Prior Distribution Posterior Distribution Description Dist. a b Mode Mean 1% 9% ρ A P TFP (P) B(a,b) ρ A T TFP (T) B(a,b) ρ z Housing Pref. B(a,b) ρ ϕ Labor Supply B(a,b) ρ ξ Quality of K B(a,b) ρ n Net Worth B(a,b) ρ χ Credit Supply B(a,b) Table 3B. Priors and Posteriors of Shock Parameters (B=Beta, IG=Inverse Gamma) Table 2 shows the posterior estimates of modes of the structural parameters. The estimates indicate that the trend growth rate is estimated to be.38, fairly close to the average growth rate of output per capita over the sample at.4. The modes of the habit parameters of constrained and unconstrained households are.92 and.96 respectively, denoting strong habit persistence in both types of households. The mode of the investment adjustment cost parameter is estimated to be.3 lower than the estimate of LWZ (213) at.18. The capital share of income estimate is.15 similar to the estimate of Kaihatsu et al. (214) at.16. The real estate share of production is.1, lower than the value used in Iacoviello (25) at.3. The mode of the labor income share of saver households is.52 within the range of estimates in the literature (Iacoviello and Neri (21)). Finally, the labor supply parameter in the utility functions is.12, implying an elastic Frisch labor elasticity coefficient. In terms of the disturbance parameters, the volatility estimates indicate that two shocks: i) housing preference, and 2) credit supply have the largest standard deviations. The estimates of autocorrelation coefficients show two very persistent shocks, namely: i) housing preference, and ii) net worth. Overall, the 1%-9% HPD intervals show that the shock parameters are significant and tightly estimated. 4 Model Analysis and Results In this section I discuss the quantitative implications of the estimated model as follows. First, I summarize the steady state ratios implied by the estimated model. Second, I analyze the workings of the model through its key transmission mechanisms, as well as the transitional dynamics implied by the impulse response 18

19 functions. Third, I assess the relative importance of shocks in aggregate fluctuations by examining the variance decomposition of key macro and financial variables. Finally, I examine the conditional and historical variance decompositions implied by the estimated model. Table 4 presents the steady state ratios implied by the model. Note that in the data as well as in the model output is defined as consumption plus investment. Hence, other components of GDP are excluded (government and net exports) which are not within the scope of this (closed economy) model. The ratio of consumption to output is 87% which is close to the average U.S. consumption share of income in the data at 8%. The ratio of (non-housing) business capital to output is 3.3. The ratio of housing to annual GDP is 1.34 similar to Iacoviello and Neri (21). The steady state household debt to total debt ratio is.36, close to the average over the sample at.4. The leverage ratio is 27, consistent with the average leverage ratio of total household and business liabilities to net worth over the sample period. The annualized interest rate is 4.8%. Finally, the annualized gross external finance premium is 2.1%, consistent with average corporate (BAA) bond spread over the sample period. Description Parameter Value Consumption-to-GDP ratio C/Y.87 Capital-to-GDP ratio K/Y 3.28 Housing wealth-to-gdp (annual) ratio QH/(4 Y ) 1.34 Household Debt-to-Total Debt ratio B E /B L.36 Leverage ratio B L /NW External finance premium (% p.a.) ef p 2.1 Annualized interest rate (% p.a.) 4 r Model analysis Table 4. Steady state ratios We now discuss the key transmission mechanisms in the model. Endogenous Leverage One of the key equilibrium conditions of the financial intermediary is the equation that describes the dynamic behavior of the leverage ratio: φ t = BL t N t = eχte t[q tk t+1 +m e q t+1 H e t /RL t ] N t 19

20 The equation above indicates that leverage co-moves negatively with net worth and positively with total intermediary s assets. All else equal, shocks to the asset side of the intermediary s balance sheet, equity capital or land collateral, will impinge in the dynamics of the leverage ratio. In terms of net worth, the relationship with leverage is somewhat more complex. Recall from the evolution of net worth in the intermediary s balance sheet: Ñ t = { θ[(r L t R t )φ t + R t ] + γ } N t 1 The above relationship indicates that net worth is positively associated with credit spread, leverage, and its own lagged value. Importantly, excluding exogenous variation to net worth (κt nw ), and to the extent that either endogenous adjustments in credit spread or endogenous leverage dominate, the behavior of the financial net worth will follow. Rate of Return on Capital E t [ R L t+1 ] = Et [ ν Y t+1 K t+1 + [Q t+1 δ(u t+1 )]e ξ t+1 Firm s ex-post return on capital is the key determinant of the dynamics of credit spread. The rate of return of capital depends on two components. The marginal product of capital and the stochastic capital gains from selling undepreciated firm s equity. Importantly, a positive quality of capital shock that increases investment on impact, also increases the stochastic component of the return on capital, thereby increasing credit spread. Real Estate Demand To study the effect of real estate demand on real estate prices I examine the land Euler equation of the constrained household: q t = 1 [ ] ζ t λ e + β λ e t Ht e e E t+1 t q λ e t+1 (1 + (1 ς)rt+1) h + µ [ ] t m e qt+1 E t λ e t t Rt L This equation indicates that the marginal cost of an additional unit of land (left hand side) is equal to the marginal benefit (in consumption units) of land services plus the discounted present value of land rents, and the discounted present value of land holdings used as collateral, scaled by the shadow value of land holdings. Notice that when the borrowing constraint binds, the latter term is positive and it directly affects the volatility of current land prices. Hence, the above relationship underscores the importance of land demand and credit conditions in explaining the volatility of land prices. 2 Q t ]

21 Model Dynamics Here, I examine the model dynamics through the impulse responses to different sources of shocks. Figure 1 in Appendix D shows the transitional dynamics in response to a one standard deviation transitory productivity shock. The main -and expected- result is the amplification of real variables, which is reflected in the large humped shaped increase of consumption, investment, and output. In terms of financial variables, households substitute land holdings for consumption leading to a drop in land prices and net worth. Figure 2 shows the model response to a positive credit supply shock that increases debt and net worth on impact. The increase in credit leads to a drop in the premium (credit spread), which has a positive effect on investment and output. Notice that since net worth increases more than debt, leverage falls. In figure 3, a one standard deviation increase in the quality of capital leads to a large increase of investment spending coupled with a rise of output, and a weak increase of consumption with a lag. In terms of financial variables, capital gains lead to a small rise in the external finance premium along with a large increase in debt, and an eventual rise in net worth. The increase in investment leads equity prices to rise and land prices to fall, but eventually land prices increase as investment spending declines. Figure 4 shows the impulse responses to a one standard deviation housing demand shock that is reflected in an amplified positive response of land prices and debt. The increase in financial intermediation assets (debt) leads to a rise in net worth and a corresponding decline in leverage. The effect on investment and output is positive but small. 14 Figure 5 illustrates the response of the model to a positive shock to the dis-utility of labor which decreases aggregate labor on impact. As expected, the fall in labor is coupled with a drop in output and investment. As firms lower investment, the premium and real estate prices drop, banks deleverage and debt falls. Last, figure 6 illustrates the response to an increase in financial intermediation net worth. The impact on aggregate net worth is large and persistent, leading to a drop in debt and leverage. As a result, land prices drop, which coupled with the increase in the external finance premium, depresses investment and output. In sum, and most notably, the impulse response analysis of the estimated model suggests an important role of financial intermediation in amplifying productivity and 14 A drawback of our model is that since intermediaries are indifferent between housing and capital assets, hence the large housing demand shock has a small effect on credit spread, investment and output. We conjecture that the observed large swings in house prices and mortgage rates in the data do indeed have a much larger effect on credit spread, investment, and output. 21

22 quality of capital shocks. On the other hand, although real estate demand shocks have a large impact on financial variables, their impact on consumption and output is minor. 4.2 Results: What Shocks are Important? Table 5 summarizes the posterior variance decomposition of the seven observable macro and financial variables used in estimation. First, I discuss the drivers of the volatility of aggregate economic activity. In terms of private (non-residential) investment, the results quality of capital shocks explain about 31%, while credit supply and net worth shocks account for 44% of investment fluctuations. Next, productivity shocks explain 66% of the variability in hours worked, while another 33% of that volatility is explained by financial shocks combined. Last, consumption variability is explained by technology shocks alone. 15 Series/Shock Produc. Labor Housing Invest. Credit Net Worth Investment Consumption Hours Land Price Spread Debt Net Worth Table 5. Posterior Variance Decomposition of Observables Second, I examine what drives fluctuations in terms of financial variables. I find that 58% of the change in land prices is driven by land preference shocks alone, while another 33% is explained by labor supply shocks. Movements in credit spread are mainly driven by net worth (73%) shocks. Similarly, aggregate debt is driven mainly by labor supply (64%), and financial shocks (33%) shocks. Last, most of the variability in aggregate net worth is explained by credit supply (55%), housing preference (32%), and net worth (8%) shocks. Next, I examine the forecast error variance decomposition of the model s macro and financial variables over different horizons. Figures 7 to 13 in Appendix E show the conditional decompositions at horizons ranging from 1 quarter to 24 quarters. 15 Recall that the consumption time series excludes both durable and housing services, which helps explain the negligible effect of financial shocks on consumption. 22

23 In terms of GDP (defined as consumption plus investment), technology shocks contribute between 5% 7% of the variability of output at all horizons. However, a more detailed picture of the drivers of output fluctuations is better obtained from its components, consumption and investment. Most of the variability of consumption at short and medium horizons is driven by technology shocks, while financial shocks weakly increase in importance at longer horizons. In contrast, investment variability is highly associated with financial shocks at both short and long horizons with net worth shocks increasing in prominence at longer horizons. In terms of hours worked, technology shocks explain between 4% 7% of the variability of hours at different horizons, with financial shocks explaining at least 3% of fluctuations in hours worked at all horizons. In terms of financial variables, land preference shocks alone explain, not surprisingly, 7% of the variability of land prices one quarter ahead, and almost all the variability at other forecast horizons. In terms of credit spread variability, net worth shocks explain at least 6% of its variability at all horizons, while credit supply shocks explain at least 2% of fluctuations in credit spread at all horizons. Next, over 6% of the variability of aggregate debt one quarter ahead is due to labor supply shocks, while financial shocks explain at least 6% of debt variability from medium to long horizons. Last, financial shocks combined explain at least 8% of the variability of financial intermediation leverage at all forecast horizons. Finally, I exploit an advantage of the Bayesian approach which allows to quantify the importance of shocks to aggregate fluctuations along the historical sample. Figures 15 to 22 in Appendix F show the historical decomposition of key macro and financial variables. Figure 15 shows that consumption fluctuations are driven mostly by productivity shocks. Figure 16 shows that supply (productivity and labor) shocks and quality of capital shocks have been historically the drivers of investment fluctuations. Although more recently, during the Great Recession (27-29), the results show that credit supply, net worth, and housing demand shocks explain large part of the drop in investment. Figure 17 shows that fluctuations in hours worked are mainly due to variation in productivity. Although more recently, during the Great Recession, financial shocks combined became more prominent in explaining the large drop in hours worked. Figures 19 to 22 show the historical decomposition of financial variables. The results show that the joint effect of credit supply, net worth, and housing shocks drive most of the fluctuations in land prices, credit spread, net worth and aggregate debt over the historical sample. Moreover, during the Great Recession, the large drop in house prices was due mainly to housing demand shocks (figure 19), while fluctuations in credit spread were largely a result of financial shocks. 23

24 Overall, the variance decomposition results suggest that productivity shocks remain a dominant factor in determining the variability of consumption and hours, while financial shocks combined have played a central role in driving fluctuations of investment spending as well as financial variables (land prices, credit spread, debt, and net worth) in the U.S. during Empirical Performance In this section I examine how well the estimated model matches the in-sample unconditional moments. Although the Bayesian estimation method does not aim at matching a specific set of moments of the data as in Classical estimation methods, it is nevertheless informative to assess how the estimated model performs vis-a-vis the data. Table 6 summarizes the key moments. Both data and model statistics are computed from their corresponding HP-cyclical component at quarterly frequency with smoothing parameter 16. Note that the absolute volatility of output in the data is 1.5% while the model counterpart is 1.6%. σ i /σ y ρ(1) ρ i,y Series Data Model Data Model Data Model Output.9.8 Consumption Investment Hours Spread Land price Debt Net Worth Table 6. Moments of Macro and Financial Variables: Data vs. Model Columns 2 and 3 show the data and model s volatilities of macro and financial variables relative to income volatility. In terms of consumption and hours worked, the model s relative volatilities are not far from their data counterpart. However, the model overestimates the volatility of investment, which is not surprising as the estimated value of the capital adjustment cost parameter is very low. In terms of 16 Additional results on the impact of shocks on the cyclical properties of disaggregated measures of debt (household vs. firm), as well as historical decomposition of the observables are available upon request from the author. 24