Credit Disruptions and the Spillover Effects between the Household and Business Sectors

Credit Disruptions and the Spillover Effects between the Household and Business Sectors Rachatar Nilavongse Preliminary Draft Department of Economics, Uppsala University February 20, 2014 Abstract This paper studies the effects of credit supply disruptions in a New Keynesian DSGE framework. First, I examine the effects of credit supply disruptions in the business sector. The model with financially constrained households generates a bigger decline in aggregate consumption and GDP than the model, which excludes financially constrained households. With financially constrained households in the model, the collateral channel strengthens the spillover effects and amplifies business cycles. I also use the model with financially constrained households to analyze the effects of credit supply disruptions in the household sector. A tightening of household credit conditions creates a bigger drop in aggregate consumption and GDP than a tightening of business credit conditions. The interaction between working capital, credit shocks and the collateral channel are important to understand the movement in inflation rate. A tightening of business credit conditions can lead to an increase in the inflation rate whereas a tightening of household credit conditions can generate deflation. JEL Codes: E31, E32, E44, G01 Keywords: Financially Constrained Households, Entrepreneurs, Credit Conditions, Spillover Effects, Housing Prices, Collateral Value, Inflation I am grateful to Mikael Bask and Nils Gottfries for their generous feedback at various stages. I would like to thank seminar participants at Department of Economics, Uppsala University and Stockholm University. Postal address: Department of Economics, Uppsala University, P.O. Box 513, SE-751 20 Uppsala, Sweden. E-mail address: rachatar.nilavongse@nek.uu.se

1 Introduction The U.S. faced credit market disruptions in 2007 and then the U.S. entered the worst recession since the Great Depression. There are few papers that examine the effects on the real economy of credit supply disruptions in a New Keynesian DSGE framework. In existing studies, credit supply disruptions in the business sector spill over into the household sector mainly through labor income channel. In this paper, the collateral channel strengthens the transmission of credit supply disruptions from the business sector to the household sector and amplifies business cycles. This paper also focuses on the effects of different type of credit shocks on inflation rate. Different types of credit supply shocks do not necessarily generate the same response of the inflation rate. Credit supply disruptions are modeled as a tightening of credit conditions for business loans and household loans. The Federal Reserve Board conducts a survey among senior loan offi cers of banks asking whether they have recently tightened their credit conditions for commercial and consumer loans. Figure 1 plots the index of tightening credit conditions on commercial and industrial loans while figure 2 plots the corresponding index for consumer loans. The figures show that credit conditions for commercial and consumer loans were severely tightened in the 2008, and just before the U.S. began to experience a deep recession. 1 This paper seeks to understand the macroeconomic effects of credit supply disruptions and the spillover effects from the business sector to the household sector and vice versa. I set up a DSGE model that includes the household sector and the business sector. The household sector splits in two groups: unconstrained households and financially constrained households. The business sector is represented by entrepreneurs who are borrowing constrained. Financially constrained households and entrepreneurs use houses as collateral. First, I analyze the effects of a tightening of business credit conditions on the economy, 1 The data are from Senior Loan Offi cer Opinion Survey on Bank Lending Practices from the Federal Reserve Board 2013. 2

the inflation rate and the spillover effects from the business sector to the household sector. Second, I examine the macroeconomic effects of a tightening of household credit conditions, and the spillover effects from the household sector to the business sector. In a model with unconstrained households, a tightening of business credit conditions generates spillover effects from the business sector to the household sector through labor income channel. With financially constrained households in the model, there are spillover effects from the business sector to the household sector through labor income and the value of housing collateral. The main results are as follows: the model with financially constrained households generates a bigger decline in aggregate consumption and GDP than the model, which excludes financially constrained households. The reason is that with financially constrained households in the model, the collateral channel strengthens the spillover effect from the business sector to the household sector. Therefore, the effects of a tightening of business credit conditions are amplified. I also use the model to analyze the effects of a tightening of household credit conditions. The main result is that a tightening of household credit conditions creates a bigger recession than a tightening of business credit conditions. In the model, I assume that the household sector has a higher debt ratio than the business sector in the steady state. The assumption is based on empirical evidence from the U.S. by Cecchetti, Mohanty and Zampolli 2011. As the household sector has a higher debt ratio than the business sector, the household sector is more sensitive to a change in credit conditions than the business sector. As a result, a tightening of household credit conditions creates a bigger drop in aggregate consumption and GDP than a tightening of business credit conditions. The interaction between the working capital, credit shocks and collateral channel are important to understand the movement of inflation rate. According to the sensitivity analysis in this paper, a tightening of business credit conditions can lead to an increase in the inflation rate whereas a tightening of household credit conditions can generate deflation. 3

This paper is related to a literature on collateral constraints such as Kiyotaki and Moore 1997 and Iacoviello 2005. Quadrini 2011 points out collateral constraints amplify the macroeconomic impact of exogenous shocks. The exogenous shocks such as producitivity and monetary shocks do not directly affect collateral constraints of borrowers. Hence, these shocks would create a recession in the absence of collateral constraints. However, a model with collateral constraints generate a bigger recession. Jermann and Quadrini 2012 and Liu, Wang, and Zha 2013 study the macroeconomic effects of a tightening of business credit conditions. A tightening of credit conditions can directly affect collateral constraints, and thus it can directly generate a recession. In their models, the spillover effect from the business sector to the household sector arises through labor income. Their models do not include financially constrained households. With financially constrained households, credit supply disruptions in the business sector transmit to the household sector both through labor income and through the collateral value of housing. Hence, the effects of a tightening of business credit conditions are amplified and the size of the recession becomes bigger. In addition to the analysis of credit supply disruptions in the business sector, I also study the effects of credit supply restrictions in the household sector. Gerali, Neri, and Signoretti 2010 have a tightening of business and household credit conditions in their model; however, the spillover effects in their model does not include the housing collateral channel because firms and households do not have a common asset as collateral. Bahadir and Gumus 2012 study household credit and business credit shocks in an open economy model. The unconstrained household does not include in their model because the business and the financially constrained household sector can directly borrow from an international financial market. Their model is a real business cycle model which assumes prices are flexible. Iacoviello 2010 study the effects of financial shocks on the economy, but the inflation rate is absence in the model. My model is a closed economy with sticky prices; therefore, credit shocks can affect the movement in inflation and 4

debt-deflation may arise. Understanding the movement in the inflation rate is important for conducting monetary policy during a period of financial distress. This paper is structured as follows. Section 2 describes theoretical framework. Section 3 presents calibration strategy. Section 4 discusses the impulse responses of the economy to tightening of credit conditions. Section 5 carries out sensitivity analyses. Section 6 concludes. 2 Theoretical framework The economy is populated by unconstrained households, financially constrained households and entrepreneurs as in Iacoviello 2005. Both types of households get utility from housing services provided by their houses. The supply of housing stock is fixed. Financially constrained households use their houses as collateral in order to get loans, which are used for houses and consumption. Both types of households consume, work and demand housing. The business sector is represented by entrepreneurs who use capital, labor and houses to produce an intermediate good. Entrepreneurs use their housing stock as collateral. Entrepreneurs receive intertemporal loans to finance their consumption, capital and investment in the housing market. Additionally, there is a need for intraperiod loans working capital loans that are used to pay the wage bill. An intertemporal loan is obtained in the current period, and the loan is repaid in the next period. An intraperiod loan is obtained in the beginning of the current period, and it is repaid at the end of the current period without interest. Moreover, Monopolistic retailers generate nominal rigidity in the model. Retailers purchase the intermediate good from entrepreneurs, costlessly differentiate it and then resell the differentiated goods in the final goods market. Households and entrepreneurs consume final goods. 5

3 Unconstrained Household An unconstrained household maximizes expected lifetime utility given by L U η t E 0 t=0 β Ut ln C U t + j ln H U t where the unconstrained household is denoted with a superscript U, C U t η 1 is consumption at t, H U t denotes the holding of housing stock, L U t denotes labor hours. The parameter β U is the discount factor, η is the inverse of labor supply elasticity, j is a weight on housing services. The unconstrained household faces the following budget constraint: Ct U + q t H U t Ht 1 U R t 1 b U + t 1 = b U t + wt U L U t + S t. 2 π t where q t is the real house price, w U t is the real wage, L U t is the unconstrained household s labor supply and S t is the lump-sum profit received from the ownership in the retail firm described below. The inflation rate is denoted by π t. R t 1 is the nominal interest rate on bonds at period t 1. The unconstrained household is endowned with bonds b U t. The unconstrained household purchases bonds b U t 1 and the bonds are subjected to real interest rate Rt 1 π t the unconstrained household provides loans to the financially constraint household and the entrepreneur and make a loss as the real interest rate goes up. The labor income is w U t L U t. The first order conditions for housing demand, consumption and labor supply respectively are: q t Ct U = j β U q t+1 Ht U + E t Ct+1 U 1 β U R t Ct U = E t π t+1 Ct+1 U 3 4 w U t = L U η 1 t C U t. 5 Equation 3 determines the optimal holdings of housing stock. The marginal cost of accumulating a marginal unit of housing is qt C U t and equals the marginal benefit of holding the marginal unit of housing stock, which consists of the marginal utility of housing stock j Ht U and the expected resale value of house 6

E β U q t+1 t. Equation 4 is a standard consumption Euler equation. The Ct+1 U labor supply choice is represented by equation 5. The marginal benefit of working w U t equals the marginal cost of working L U η 1 t C U t. 3.1 Financially Constrained Household The utility function of a financially constrained household is: L F η t E 0 t=0 β F t ln C F t + j ln H F t η 6 where the superscript F denotes the financially constrained household, and β F is the financially constrained household s discount factor which is lower than the unconstrained household s discount factor β F. C F t is the consumption of final good while H F t is the demand for housing stock. L F t is the labor supply. The financially constrained household maximizes their utility 6 subject to two constraints. The budget constraint is: Ct F + q t H F t Ht 1 F R t 1 b F + t 1 = b F t + wt F L F t. 7 π t The financially constrained household does not have the ownership in the retail firm, so the financially constrained household does not receive the lumpsum profit from the retail firm. The financially constrained household receives loans b F t. Rt 1bF t 1 π t is the repayment of the loans, and this reflects the assumption that debt contracts are set in nominal terms; hence, the movement of inflation rate can affect the real interest rate and the cost of debt payment. As the inflation rate decreases, the cost of debt payment goes up. The labor income is w F t L F t. The collateral constraint is: R t b F t m F t E t qt+1 H F t π t+1. 8 The amount of loans that the financially constrained household can get are restricted by the collateral constraint, which depends on the value of the house E t qt+1 Ht F π t+1 /R t and the tightness of credit conditions for loans to the financially constrained household m F t. I assume that the tightness of household credit conditions m F t follows an AR1 stochastic process: m F t = a+ρ F m F t +ε F t, 7

where a is a constant, ρ F ɛ 0, 1 is the persistence parameter, and ε F t is an i.i.d. white noise process with mean zero and variance σ 2 F. Solving the problem gives the first order conditions with respect to housing demand, consumption and labour supply respectively: q t C F t 1 C F t = j H F t = E t β F q t+1 + E t Ct+1 F + λ F t m F t q t+1 π t+1 β F R t π t+1 C F t+1 9 + λ F t R t 10 w F t = L F η 1 t C F t. 11 Equation 9 determines the optimal demand for housing stock when the household faces a credit constraint. The marginal cost of purchasing an extra unit of house is q t C F t. The marginal gain of holding an additional unit of housing comprises of the utility gain of an extra unit of having housing stock, the Ht F expected gain of house E β F q t+1 t and the marginal utility of relaxing the bor- Ct+1 F rowing constraint λ F t m F t E t q t+1 π t+1. Equation 10 is an Euler condition for j consumption with the borrowing constraint. λ F t is the multiplier on the borrowing constraint 8. In the case when the borrowing constraint is not binding, equation 9 and 10 reduce to a standard optimal demand for housing stock and a standard Euler consumption equation respectively. The financially constrained household s labor supply choice is represented by equation 11 which is similar to the labor supply choice of unconstrained household. 3.2 Entrepreneur An entrepreneur has the following utility function: E 0 t=0 β Et ln C E t 12 where E denotes the entrepreneur, C E t is the consumption of the final good. β E is entrepreneur s discount factor, which is smaller than the unconstrained household, but is greater than the financially constrained household s discount factor. Entrepreneurs use a Cobb-Douglas technology that uses capital, house 8

and labor as inputs to produce an intermediate good t. The production function is: t = K µ t 1 H E t 1 v L U t α1 µ v L F t 1 α1 µ v 13 where K t 1 is capital that depreciates at rate δ, Ht 1 E is housing input, L U t and L F t are the unconstrained and financially constrained household labors α measures the relative importance of each group. The parameters µ ɛ 0, 1 and v ɛ 0, 1 measure the capital share and housing share respectively. As in Iacoviello 2005, output cannot be transformed immediately into consumption. Therefore, retailers purchase the intermediate good from entrepreneurs at the wholesale price and transforms it into final goods, which will be sold to the both types of households and entrepreneurs. The entrepreneur sells the output in a competitive market and faces the flow of funds constraint as follows: t /X t + b E t = C E t + q t H E t H E t 1 + Rt 1 b E t 1/π t +w U t L U t + w F t L F t + I t + ξ k,t. 14 Intertemporal loans are denoted by b E t. Demand for housing stock is H E t. The value of output in terms of the final good is t /X t, where X t is the markup which equals the price of the final good relative to the wholesale price. The cost of investing additional housing stock in the current period is q t H E t H E t 1, the repayment of last-period intertemporal debt is R t 1 b E t 1/π t, the wage payments to the households are w U t L U t +w F t L F t. Capital investment is defined as I t = K t 1 δ K t 1, the adjustment costs of capital is assumed to be equal to ξ k,t = 2 ψk I t 2δ K t 1 δ Kt 1, and ψ k reflects the importance of capital adjustment costs. The entrepreneur s borrowing constraint is: w U t L U t + w F t L F t + R t b E t m E t E t qt+1 H E t π t+1. 15 The entrepreneur uses intertemporal loans to purchase capital and to invest in housing market and using the loans for consumption. The entrepreneur also need working capital loans intraperiod loans. I follow Jermann and Quadrini 2012 and assume that wage payment need to be financed by working capital. The 9

within-period working capital loans are repaid at the end of the current period. Intertemporal loans are subjected to the interest rate payment R t while intraperiod loans are not. Thus, total loans include intraperiod loans wt U L U t + wt F L F t and intertemporal loans R t b E t. Total loans are constrained by the value of house Ht E E t q t+1 π t+1 and the tightness of credit conditions on loans to entrepreneurs m E t, which follows the AR1 stochastic process: m E t = b + ρ E m E t + ε E t, where b is a constant, ρ E ɛ 0, 1 is the persistence parameter, and ε E t is an i.i.d. white noise process with mean zero and variance σ 2 E. The first-order conditions with respect to housing demand, consumption, demand for unconstrained household and financially constrained household labor and investment respectively are: [ ] q t β E v t+1 β E Ct E = E t X t+1 Ht E + E t q t+1 + λ E t m E t E t q t+1 π t+1 16 1 C E t C E t+1 C E t+1 = βe Rt Ct+1 E + λ E t R t 17 π t+1 wt U L U α 1 µ v t = t 18 1 + R t λ E t Ct E X t wt F L F 1 α 1 µ v t = t 1 + R t λ E t Ct E X t 19 µ t = 1 Ct E 1 + ψ k It δ δ K t 1 20 µ t = γ 1 ψ It+1 It+1 Ct+1 E δ ψ 2 It+1 δ δ K t K t 2δ K t [ ] µ t+1 +γe t Ct+1 E X + µ t+1 1 δ. 21 t+1k t Equation 16 determines optimal housing stock holdings by the entrepreneur. The marginal cost of investing an additional unit house qt C E t [ yields benefits the future marginal product of house E β E v t Ct+1 E expected gain from investing in the housing market E β E t equals the marginal gain of holding an additional unit of house. Investing a marginal unit of house ], and the C E t+1 t+1 X t+1h E t q t+1, and from a benefit of having house as a collateral asset. Equation 17 is the entrepreneur s Euler consumption condition with the borrowing constraint. λ E t is the 10

multiplier on the entrepreneur s borrowing constraint 15. In the case when the borrowing constraint is binding, equations 16 and 17 reduce to a standard optimal demand for housing stock and a standard Euler consumption condition respectively. Equations 18 and 19 are the labor demand equations. They differ from the usual formulations because of the presence of λ E t. When the collateral constraint becomes more tighter λ E t becomes higher, the access to working capital loans is reduced. This induces entrepreneurs to decrease labor demand. Equations 20 and 21 determine the process of capital investment. An increase in entrepreneur s consumption reduces the cost of investment as the marginal utility of consumption decreases. This induces the entrepreneur to increase investment. 3.3 Retailers To have sticky prices in the model, I follow Bernanke, Gertler, and Gilchrist 1999, which allows for monopolistic competition and implicit costs of adjusting nominal prices. A continuum of retailers of mass 1, indexed by z, purchase the intermediate good t from entrepreneurs at the wholesale price P w t in a competitive market, and transform it into t z and sell t z at the price P t z. Total final goods production is a composite of individual retail goods: f t = 1 0 t z ɛ 1/ɛ dz ɛ/ɛ 1 22 where ɛ > 1. The corresponding price index is given by P t = 1 0 P t z 1 ɛ dz 1/1 ɛ. 23 Given the two last equations, the demand curve facing each retailer is given by t z = P t z/p t ε f t. Each retailer then chooses a sale price P t z and take the price of wholesale goods P w t and the demand curve as given. Each retailer can change his price in every period only with probability 1 θ. Let P t z be the price set by retailers who are able to change their price at t. The corresponding demand is t+k z = P t z/p t+k ɛ t+k. The optimal P t z is 11

found by maximizing expected discounted profits: k=0 { P θ k E t Λ t z t,k X } t+k z = 0 24 P t+k X t+k where Λ t,k = β C I t /C I t+k is the unconstrained household intertemporal marginal rate of substitution, and X t Pt P w t denotes the markup of final over intermediate goods the price of final goods relative to the price of wholesale goods. The aggregate price level is: P t = θp ε t 1 + 1 θ P t 1 ε 1/1 ε. 25 Following standard derivations and combining equations 24 and 25 and the log-linearizing one can obtain a forward-looking Phillips curve, which states that the current inflation rate depends positively on expected inflation rate and negatively on the current markup X t : ˆπ t = β U E tˆπ t+1 κ X t 26 where κ 1 θ 1 βθ /θ. 3.4 Monetary Policy Monetary policy takes the form of an interest rate rule, R t R = Rt 1 R ρr [ πt π ρy ] 1 ρr ρπ t 27 where ρ r, ρ π and ρ y are parameters. The central bank sets the interest rate R t according to a Taylor rule that responds to inflation and output growth deviations from the steady state. 3.5 Market equilibrium Market clearing condition for good is: t = C U t + C F t + C E t + I t. 28 Market clearing condition for the housing market is: 1 = H U t + H F t + H E t. 29 12

Bond market clearing condition is: 0 = b U t + b F t + b E t. 30 4 Calibration I begin with short descriptions of the two models that are used for analyzing the effects of a tightening of business and household credit conditions. The basic model consists of unconstrained households and entrepreneurs. The basic model has the spillover effect from the business sector to the household sector only via labor income channel. The full model comprises unconstrained households, financially constrained households and entrepreneurs. The full model has the spillover effects from the business sector to the household sector via labor income and collateral value of housing. Table 1 summarizes the full model calibration and table 2 summarizes the basic model calibration. One period corresponds to one quarter. Discount factors: β U, β F, β E are 0.99, 0.97, and 0.98 respectively. The value of β U implies a steady state annual interest rate of about 3 percent. The parameters such as steady-state gross markup X, the Frisch labor supply elasticity η, capital share µ, depreciation rate δ, and the probability fixed price θ are chosen in line with the business cycle literature as reported in Iacoviello 2005. The Frisch labor supply elasticity η is set to 1.01. This value implies that a relatively flat labor supply curve to match the weak observed response of real wages to macroeconomic disturbances. The steady-state gross markup X is set to 1.05 and the probability fixed price θ is set to 0.75. I set capital share µ to 0.3. The depreciation rate of capital δ is set to 0.03, which corresponds to an annual rate of depreciation of 12 %. The unconstrained household wage share α is set to 0.64 and the financially constrained households wage share is 0.36. This value corresponds to the estimate by Campbell and Mankiw 1989 and Iacoviello 2005. Their estimates strongly support the presence of financially constrained households. The capital adjustment cost ψ k is set to 2 as in Iacoviello 2005 and the value is consistent with an empirical study by Chirinko 1993. Finocchiaro 13

and Heideken 2012 estimate m F and m E to be 0.83 and 0.64 based on the U.S. data. These values indicate that the household sector has higher debt ratio to GDP than the business sector. I set m F and m E according to the Finocchiaro and Heideken 2012 estimates. These estimates are consistent with an empirical study by Cecchetti, Mohanty and Zampolli 2011. The weight on housing services in both household utility functions j is calibrated to imply a steady state ratio of residential housing to annual output around 145 %. The elasticity of output to entrepreneurial real estate υ is calibrated to match a steady state ratio of commercial real estate to annual output around 70 %. Regarding specification of coeffi cients in the Taylor rule, I adopt the values from Jermann and Quadrini 2012. The persistence of a shock to the tightness of household s borrowing constraint a tightening of household credit conditions ρ F is set at 0.95 and the persistence of a shock to the tightness of entrepreneur s borrowing constraint a tightening of business credit conditions ρ E is also 0.95. The standard deviation of the both shocks σ F and σ E are set to unity. Table 1. The full model Discount factor for unconstrained households β U = 0.99 Discount factor for financially constrained households β F = 0.97 Discount factor for entrepreneurs β E = 0.98 Markup X = 1.05 Capital depreciation rate δ = 0.03 Capital adjustment cost ψ k = 2 The weight on housing services in both household utility function j = 0.022 The elasticity of output to entrepreneurial real estate v = 0.0102 Labor supply aversion η = 1.01 Unconstrained household wage share α = 0.64 Probability fixed price θ = 0.75 Leverage ratio for financially constrained households m F = 0.83 Leverage ratio for entrepreneurs m E = 0.64 Taylor rule interest rate parameter ρ r = 0.745 Taylor rule inflation parameter ρ π = 2.41 Taylor rule output parameter ρ y = 0 Shock to the tightness of household s borrowing constraint ρ F = 0.95 Shock to the tightness of entrepreneur s borrowing constraint ρ E = 0.95 Standard deviation household credit shock σ F = 1 Standard deviation business credit shock σ E = 1 14

Table 2. The basic model Discount factor for unconstrained households β U = 0.99 Discount factor for entrepreneurs β E = 0.98 Markup X = 1.05 Capital depreciation rate δ = 0.03 Capital adjustment cost ψ k = 2 The weight on housing services in both household utility function j = 0.0205 The elasticity of output to entrepreneurial real estate v = 0.0098 Labor supply aversion η = 1.01 Probability fixed price θ = 0.75 Leverage ratio of entrepreneurs m E = 0.64 Taylor rule interest rate parameter ρ r = 0.745 Taylor rule inflation parameter ρ π = 2.41 Taylor rule output parameter ρ y = 0 Shock to the tightness of entrepreneur s borrowing constraint ρ E = 0.95 Standard deviation business credit shock σ E = 1 5 Impulse responses 5.1 Effects of a tightening of business credit conditions Business credit conditions became tighter during the financial crisis as it can be seen in the figure 1. In this section, I attempt to answer two questions. What are the effects of a tightening of business credit conditions on the economy and the inflation rate?. What are the spillover effects of credit supply disruptions in the business sector on the household sector?. I begin with descriptions of the two models that are used in this section. The basic model consists of unconstrained households and entrepreneurs. The basic model has the spillover effect from the business sector to the household sector only via labor income channel. The full model comprises unconstrained households, financially constrained households and entrepreneurs. The full model has spillover effects from the business sector to the household sector via labor income and collateral value of housing. Figure 3 shows the impulse responses of the economy to a tightening of credit conditions for loans to the business sector. The solid line represents the full model while the dotted line represents the basic model. The main results of the basic model and their intuition are as follows. A tightening of business credit conditions yields a negative response in aggregate consumption, employment, investment, GDP, house prices but yields a posi- 15

tive response in inflation. A tightening of credit business standards directly tightens entrepreneurs borrowing constraints; consequently, entrepreneurs decrease the demand for housing. The decrease in the demand for housing leads to a decline in house prices. Entrepreneurs borrowing constraints become even tighter as house prices go down; hence, entrepreneurs have less available funds for consumption and investment which both decrease. Since entrepreneurs need working capital loans to make wage payments, a tightening of entrepreneurs borrowing constraints has a direct negative effect on labor demand. This induces entrepreneurs to reduce the number of workers. The basic model yields a positive response in inflation. A tightening of business credit conditions has a negative impact on consumption of the final good and thus on demand for the intermediate good, which creates downward pressure on the wholesale price. On other hand, a tightening of business credit conditions decreases the access to working capital loans and thus increases the cost of labors. This induces entrepreneurs to raise the price of the intermediate good. This supply side effect on the intermediate good is greater than the demand side effect. As the wholesale price increases relative to the price of the final good and the markup decreases and this pushes up the inflation rate. The central bank responses to a rise in inflation by raising the nominal interest rate. The basic model has a spillover effect from the business sector to unconstrained households through labor income. The credit tightening in the business sector restricts the access to working capital financing. This induces entrepreneurs to decrease labor demand. The decrease in labor demand pushes down the wage rate and leads to the fall of the labor income of unconstrained households. Unconstrained households respond to lower labor income by reducing their consumption. As an increase in collateral requirements for entrepreneurs by 1 percentage point leads to a decrease in unconstrained household consumption by about 0.026 percentage point. The main results of the full model are as follows. The full model yields a negative response in aggregate consumption, employment, investment, GDP, 16

house prices and a negative response in inflation. The spillover effects from the business sector to the financially constrained household sector go via labor income and collateral value of housing. A tightening of credit business standards induces entrepreneurs to decrease the demand for housing. The decrease in the demand for housing leads to a decline in house prices. The decline in house prices leads to a decline in financially constrained households collateral value of housing. In addition to labor income channel, the decrease in the collateral value of housing reinforces a drop in financially constrained household consumption. Hence, the full model generates a bigger decline in aggregate consumption than the basic model. Aggregate consumption with credit constrained households declines by about 0.33 percentage point. Without credit constrained households in the model, aggregate consumption declines by about 0.18 percentage point. The difference is substantial. Thus, Jermann and Quadrini 2011 and Liu, Wang and Zha 2013 may underestimate a decline in aggregate consumption and GDP when there are credit supply disruptions in the business sector because their models do not take account of the effects on financially constrained households via the collateral channel. In their models, the spillover effect from the business sector to the household sector goes through labor income channel. 2 The full model generates a negative response in inflation when there are credit supply disruptions in the business sector. With financially constrained households in the model, the decline in house prices reinforces a drop in aggregate consumption. As a result, the demand side effect is greater than the supply side effect and the price of the intermediate good decreases relative to the price of the final good and the inflation rate is reduced. Hence, the full model generates a negative response in inflation which is contrary to the basic model. Debt deflation plays a role as bonds are not indexed to the inflation rate. Hence, deflation rises the cost of debt payments, which further depresses consumption, labor demand and investment. The central bank responds to a 2 Entrepreneurs and financially constrained households do not have a common asset as collateral in the model by Gerali et al 2010. Hence, the spillover effect between credit constrained households and entrepreneurs arises mainly through labor income in their model. 17

decrease in inflation by lowering the nominal interest rate, and thus the real interest rate decreases. We have learned that the model with financially constrained households generates a bigger decline in aggregate consumption and GDP than the model that excludes financially constrained households.with financially constrained households in the model, collateral channel strengthens the spillover effects from the business sector to the household sector. Thus, the effects on the economy of credit supply disruptions in the business sector are amplified. Also, the effects on financially constrained households via collateral channel is important for the result of the inflation rate. 5.2 Effects of a tightening of household credit conditions As we have seen in the figure 2, household credit conditions became tighter in the summer of 2007. This section examines the macroeconomic effects of a tightening of household credit conditions and the spillover effects of credit supply disruptions from the household sector to the business sector. Figure 4 shows the impulse responses of the economy to a tightening of credit conditions for loans to financially constrained households. A tightening of household credit conditions drives down aggregate consumption, employment, GDP, house prices and the inflation rate. Financially constrained households have a higher leverage ratio than entrepreneurs in the steady state. Hence, financially constrained households are more sensitive to a change in credit conditions than entrepreneurs. As a result, a tightening of household credit conditions creates a much bigger drop in aggregate consumption than a tightening of business credit conditions. When collateral requirements for the households increases by 1 percentage point, aggregate consumption drops by about 0.64 percentage points. Since a tightening of household credit conditions leads to a substantial decline in aggregate consumption, a tightening of household credit conditions generates a larger decline in inflation than a tightening of business credit conditions. Hence, debt deflation plays a more important role in the economy when credit 18

supply disruptions directly affect household collateral constraints than credit supply disruptions directly impact entrepreneurs collateral constraints. Deflation raises the real cost of debt payments, which further depresses consumption, labor demand and investment. A tightening of household credit conditions yields a drop in GDP by about 0.13 percentage points while a tightening of business credit conditions generates a decline in GDP by about 0.08 percentage points. The implication of these results is that credit supply disruptions in the household sector can generate a deep recession as the one which the U.S. experienced in the Great Recession. I will now discuss the spillover effects of credit tightening in the household sector on the business sector. A contraction of credit supply in the household sector spills over into the business sector through the collateral channel. The credit tightening in the household sector has negative impacts on entrepreneurs consumption and investment. A tightening of household credit conditions induces financially constrained households to decrease the demand for housing. The decrease in the demand for housing leads to a decline in house prices. The decrease in house prices decreases entrepreneurs collateral value; hence, entrepreneurs decrease their consumption and investment. When collateral requirements for the households increase by 1 percentage point, this leads to a drop in entrepreneurs consumption by about 0.1 and investment by about 0.05 percentage points. The credit tightening in the household sector has negative spillover effects on entrepreneurs labor demand. The decrease in the collateral value tightens the access to working capital financing; consequently, it raises the cost of labor and the demand for labor. This pushes down the wage rate, and this induces both types of households to decrease their labor supply. The decline in labor demand and labor supply leads to a decrease in employment level. The credit tightening in the household sector has negative spillover effects on entrepreneurs demand for housing via the collateral channel. However, the decrease in the real interest rate induces entrepreneurs to increase the demand for housing. 19

6 Sensitivity analysis In this section, I conduct three experiments where I vary parameters that directly affect the spillover effects between the business sector and the household sector and the response of inflation. The parameters are varied one at a time and keeping the remaining parameters at their baseline values. In the first experiment, I carry out a sensitivity analysis of the spillover effects from the business sector to the household sector. The household leverage ratio m F is varied between 0.73 and 0.93. A higher household leverage ratio means financially constrained households become more sensitive to their collateral value of housing. Thus, an increase in household leverage ratio strengthens the spillover effects from the business sector to the household sector. A sensitivity analysis of a tightening of business credit conditions delivers the following results. A higher household leverage ratio amplifies the effects of a tightening of business credit conditions on financially constrained household consumption and the GDP. In the second experiment, I carry out a sensitivity analysis of the spillover effects from the household sector to the business sector. The leverage ratio for entrepreneurs m E is varied between 0.54 and 0.74. A higher entrepreneurs leverage ratio implies that entrepreneurs become more sensitive to their collateral value of housing. An increase in the leverage ratio in the business sector strengthens the spillover effects from the household sector to the business sector. The results from a tightening of household credit conditions are as follows. The credit tightening in the household sector has negative effects on entrepreneurs consumption and investment. A higher leverage ratio in the business sector amplifies the effects of tightening of household credit conditions on investment, entrepreneurs consumption and the GDP. Third experiment, I vary a parameter that directly affects the dynamic of inflation. A change in the probability fixed price θ has a direct impact on the response of inflation rate. I vary θ between 0.65 and 0.85. First, I conduct 20

a sensitivity analysis of the response of inflation when there is a tightening of business credit conditions. The results are as follows. The sign of the response of inflation to a tightening of business credit conditions is ambiguous. The full model yields a positive response in inflation when θ is above 0.84. Therefore, the sign of the response of inflation is sensitive to a choice of θ when collateral constraints of entrepreneurs are directly affected by credit supply disruptions. However, the basic model still generate a positive response in inflation when I vary θ between 0.65 and 0.85. Second, I examine a sensitivity of the response of inflation when household collateral constraints are directly affected by credit supply disruptions. A change in θ does not alter the sign of the response of inflation to a tightening of household credit conditions. A tightening of household credit conditions still yields a negative response in inflation when I vary θ between 0.65 and 0.85. 7 Conclusion This paper shows that collateral value of housing plays an important role in the transmission of credit supply disruptions in the business sector to the household sector and vice versa. First, I examine the effects of a tightening of business credit conditions. Specifically, entrepreneurs collateral constraints are directly affected by credit supply disruptions. The model with financially constrained households generates a bigger decline in aggregate consumption and GDP than the model, which excludes financially constrained households. The reason is that the spillover effect from the business sector to the household sector is through labor income channel. With financially constrained households in the model, credit supply disruptions in the business sector transmit to the household sector through labor income and the value of collateral. As a consequence, the effects of tightening of business credit conditions are amplified. Second, I use the model to analyze the effects of tightening of household credit conditions. Financially constrained households have a higher leverage ratio than entrepreneurs in the steady state. Thus, financially constrained house- 21

holds are more sensitive to a change in credit conditions than entrepreneurs. A tightening of household credit condition creates a bigger drop in aggregate consumption than a tightening of business credit conditions. As a result, a tightening of household credit conditions generates a larger decline in inflation than a tightening of business credit conditions. The implication of the results is debt deflation plays a more important role in the economy when household collateral constraints are directly affected by credit supply disruptions than entrepreneurs collateral constraints are directly affected by credit supply disruptions. Deflation rises the real cost of debt payments, which further depress consumption, labor demand and investment. Therefore, a contraction of the credit supply in the household sector can generate a sharp drop in aggregate consumption and GDP. According to the sensitivity analysis, a tightening of business credit conditions can lead to an increase in the inflation rate whereas a tightening of household credit conditions still generate deflation. The next step of this paper is to explore optimal monetary policy in the model and the interest rate spreads. References [1] Bahadir, B., & Gumus, I. 2012. Credit Decomposition and Business Cycles in Emerging Economies. Technical Report. [2] Bernanke, B. S., Gertler, M., & Gilchrist, S. 1999. The Financial Accelerator in A Quantitative Business Cycle Framework. Handbook of Macroeconomics, vol. 1C, edited by J. B. Taylor and M. Woodford, 1341-1393. New ork: Elsevier Science, North-Holland. [3] Campbell, J.., & Mankiw, N. G. 1989. Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence. In NBER Macroeconomics Annual, vol. 4, MIT Press, 185-216.. [4] Cecchetti, S. G., Mohanty, M. S., & Zampolli, F. 2011. The Real Effects of Debt. BIS Working Paper No. 352. 22

[5] Chirinko, R. S. 1993. Business Fixed Investment Spending: Modeling Strategies, Empirical Results, and Policy Implications. Journal of Economic Literature, 314, 1875-1911. [6] Federal Reserve Board. Senior Loan Offi cer Opinion Survey on Bank Lending Practices. 2013. Retrieved from http://www.federalreserve.gov/boarddocs/snloansurvey/. [7] Finocchiaro, D., & Queijo von Heideken, V. 2012. Do Central Banks React to House Prices?. Riksbank Research Paper, No. 217. [8] Gerali, A., Neri, S., Sessa, L., & Signoretti, F. M. 2010. Credit and Banking in a DSGE Model of the Euro Area. Journal of Money, Credit and Banking, 42s1, 107-141. [9] Iacoviello, M. 2005. Housing Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle. American Economic Review, 95, 739-764 [10] Iacoviello, M. 2010. Financial Business Cycles. Technical Report. [11] Jermann, U. and Vincenzo, Q. 2012. Macroeconomic Effect of Financial Shocks. American Economic Review, 102, 238-271. [12] Kiyotaki, N. and Moore, J. 1997. Credit Cycles. The Journal of Political Economy, 105, 211-248. [13] Liu, Z., Wang, P., and Zha, T. 2013. Land-Price Dynamics and Macroeconomic Fluctuations. Econometrica, forthcoming. [14] Quadrini, V. 2011. Financial frictions in macroeconomic fluctuations. Economic Quarterly, 973, 209-254. 8 Appendix Steady state π = 1 23

R = 1 β [ ] X 1 S = X β U β E λ = λ F = I = δ K qh E C E β U β F C F = βe v 1 1 γ e X γ e m E β U + 1 m E β E w U L U = α 1 µ v 1 1 + β U β E X w F L F 1 α 1 µ v = 1 1 + β U β E X b E qh = me β U E w U L U β C E C F = + wf L F = 1 X + 1 R be wu L U wf L F I 1 β F m F β U β F [1 β F m β ] F U β F + jm 1 F β U w U L U qh F b F C U = j [1 β F m F qh = mf β U F β U β F ] CF = 1 R be 1 R bf + wu L U H E β E v = β E v + 1 γ e XΓ 1 H E β E v = β E v + 1 γ e XΓ 1 + S j C U Γ 1 = 1 β + j C [1 β F m β ] F F β F U 24

H U j CU = 1 β Γ 2 + j CU Γ 2 = βe v 1 1 γ e X + j C F [1 β F m β ] F U β F H F = j CF [1 β F m F β U β F ] Γ 3 + j CF Γ 3 = βe v 1 1 γ e X + j C U 1 β U 8.1 Log-linearized equations 1. Aggregate demand Ŷ t = CE ĈE t + CU ĈU t + CF ĈF t + I Ît Ĉ U t = ĈU t+1 rr t rr t ˆR t E tˆπ t+1 Î t ˆK t 1 = γît+1 ˆK 1 γ 1 δ t + Ŷt+1 ψ ˆX t+1 ˆK t + 1 ĈE ψ t t+1 ĈE 2. Housing/consumption margin ˆq t = γ eˆq t+1 + 1 γ e Ŷt+1 ˆX t+1 ĤE t +1 m E β U ĈE t ĈE t+1 m E t β U rr t + β U β E m E m E t ˆq t = γ hˆq t+1 1 γ h ĤF t +1 m F β U ĈF t ωĉf t+1 γ h β F + m F β U β F ω β F m F β F /1 m F β F ˆq t = β U ˆq t+1 1 β U Ĥt U + ĈU t β U Ĉt+1 U ˆm F t β rr t + β U β F m F ˆm F t 25

3. Borrowing constraint ˆbF t = ˆq t+1 + ĤF t rr t + ˆm F t b E ˆb E t w U L U = m E β E qh E = ˆq t+1 + ĤE t be rr t β U w U L U α 1 µ ν 1 + R 1 ˆX t X β E Ŷt X + R ˆR t 1 β E ˆπ t+1 1 ĈE β E t+1 ĈE t β U w F L F w F L F = 1 α 1 µ ν 1 + R 1 ˆX t X β E Ŷt X + R ˆR t 1 β E ˆπ t+1 1 ĈE β E t+1 ĈE t 4. Aggregate supply ˆL U t = 1 η Ŷt ˆX t 1 η ĈU t + 1 η 1 β U β E + β E β U β E ˆRt β U ˆπ t+1 β U Ĉt+1 E ĈE t ˆL F t = 1 η Ŷt ˆX t 1 η ĈF t + 1 η 1 β U β E + β E β U β E ˆRt β U ˆπ t+1 β U Ĉt+1 E ĈE t Ŷ t = µ ˆK t 1 + νĥe t 1 + α 1 µ ν ˆL U t + 1 α 1 µ v ˆL F t ˆπ t = β U ˆπ t+1 κ ˆX t κ 1 θ 1 βθ /θ 5. Flows of funds/evolution of state variables ˆK t = δît + 1 δ ˆK t 1 b F ˆb F t = CF ĈF t + qhf ĤF t 1 ĤF + R bf ˆRt 1 + ˆb F w t 1 ˆπ t F L F 26

b E ˆb E t = CE ĈE t + qh ĤE t 1 ĤE + I Ît 1 Ŷt X ˆX t + be R ˆRt 1 + ˆb F t 1 ˆπ t + w U L U + w F L F 6. Shocks to tightness of borrowing constraint ˆm F t = ρ F ˆm F t + ε F t ˆm E t = ρ E ˆm E t + ε E t 7. Monetary policy rule ˆR t = 1 ρ r ρ π ˆπ t + ρ y Ŷ t + ρ r ˆRt 1 27

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