Evaluating Macroprudential Policy in a DSGE Framework with Financial Frictions

Transcription

1 Evaluating Macroprudential Policy in a DSGE Framework with Financial Frictions Sherry Xinrui Yu Boston University October 15, 213 Abstract This paper studies the effectiveness of macroprudential policy in a New Keynesian DSGE model with financial frictions. The financial sector is modeled vis-à-vis Gertler and Karadi (211) with endogenous bank leverage ratio. Simulation results show that macroprudential policy can mitigate shocks and stabilize the economy. More specifically, two types of macroprudential instrument are examined. First, a countercyclical Taylor-type rule to regulate the loan-to-value (LTV) ratio of the borrowing household is imposed. Furthermore, a lump-sum tax policy is administered to reduce the leverage ratio of financial intermediaries during economic booms. Both policies aim to stabilize the credit cycle and interact with a standard monetary policy. The LTV ratio regulation significantly dampens economic fluctuations but creates credit shifting towards the business sector. Comparatively, the tax policy stabilizes the aggregate credit market more effectively by directly controlling the balance sheet of financial intermediaries. Additional welfare analysis selects the optimal simple rules and provides further insights to the search for a competent and implementable macroprudential policy. Keywords: Macroprudential Policy, Financial Frictions, Loan-to-Value (LTV) Ratio, Optimal Macroprudential Policy JEL classification: E22, E32, E44, E5, E61 address: xinruyu@bu.edu

2 1 Introduction The 28 financial crisis and the subsequent Global Recession have raised the discussion among researchers and policymakers regarding the role of traditional monetary policy and the need of macroprudential policy to restore economic stability. Blanchard et al. (21) comments on the failure of financial regulation in preventing and mitigating the systematic risk in financial markets. In addition, traditional monetary policy was not suffi cient to generate a quick and effective recovery. The crucial role of the financial system in this crisis has triggered the search for macroprudential tools to promote financial and economic stability. These tools target the broad financial markets instead of individual institution. The objective of this type of supervision and regulation is to mitigate the transmission of shocks to the general economy. However, debates have been raised regarding the design of macroprudential instruments and their interaction with monetary policy. This paper contributes to the literature by addressing three key issues. First, it incorporates the housing sector to study the interaction between asset prices and business cycle fluctuations. This aims to shed some light on the recent financial crisis, which initiated with a housing boom in the U.S.. A major portion of domestic borrowing is secured by real estate (Iacoviello (25)) and the housing market has been found to play an important role in driving business cycles (Case (2), Higgins and Osler (1997)). Second, this paper models financial frictions in the traditional New Keynesian DSGE framework. Incorporating the financial market captures the key element of the recent crisis and can then be used to study the impact of financial regulation on the transmission of shocks. Furthermore, this paper studies two types of macroprudential instrument. A countercyclical loan-to-value (LTV) ratio rule that targets households borrowing constraints and a lump-sum tax policy that directly affects the balance sheet of financial intermediaries. Using both monetary and macroprudential tools, I further conduct welfare analysis to find the optimal and implementable rules that can effectively dampen economic fluctuations. The model mechanism works as follows. Suppose there is a positive housing demand shock. Consumption and housing prices increase as a response, expanding the borrowing constraint of the households. Higher consumer prices reduce the net value of debt and deteriorate lender s balance sheet. Profit-maximizing banks facing increasing demand for loans expand lending in the economy and raise their leverage ratio. This leads to greater liquidity risk in the financial market and increases the systematic risk. 1

3 Nonetheless, macroprudential policy can be used to mitigate the impact from the demand shock. More specifically, the regulatory authority lowers the target LTV ratio of the households causing the collateral value to drop. This generates a contractionary effect on the borrowing constraint, which releases the tension on financial intermediaries. Credit expansion is limited, which lowers the liquidity risk in the financial market. Macroprudential instruments target the overall financial system and suppress credit growth in response to positive shocks. The opposite applies for negative shocks. The target LTV ratio is raised to stimulate lending in the economy, which promotes a fast and effective recovery. This paper is organized as follows. Section 2 reviews existing literature on housing market, financial frictions and macroprudential policies. Section 3 presents the model. Section 4 reports the calibration of key parameters and Section 5 analyzes the model implications. Section 6 conducts the welfare analysis and Section 7 concludes. 2 Literature Review This paper is related to at least three major strands of literature. The first line of research studies the relationship between credit and housing. Theoretically, Kiyotaki and Moore (1997) models collateral constraints tied to the real estate value of entrepreneurs. Iacoviello (25), Iacoviello and Neri (21) comment on the importance of housing in business cycle fluctuations. More recently, Liu, Wang and Zha (213) also identifies the crucial role of land prices in driving macroeconomic variables. Furthermore, the authors argue that land price is the dominant factor that affects housing price. Davis and Heathcote (27) finds similar results using empirical analysis. Research by the IMF finds that credit and housing cycles are tightly linked to business cycles (IMF (29)). Fitzpatrick and Mcquinn (27) finds that the housing boom and credit liberalization are mutually reinforcing in the long-run using data from Ireland. Similar results are found in Norway from Anundsen and Jansen (211). Favara and Imbs (21) finds that bank deregulation in the U.S. has significant impact on housing price. The model is also tightly related to the growing literature that incorporates financial frictions into DSGE models. Carlstrom and Fuerst (1997), Kiyotaki and Moore (1997) and Bernanke, Gertler and Gilchrist (1999) are few pioneer works. The important role of financial friction is stressed and carefully studied in a variety of context in the recent decade (see Christiano, Trabandt and Walentin (211), Smets and Wouters (27), 2

4 Gilchrist, Ortiz and Zakrajsek (29), Gertler, Gilchrist and Natalucci (27) for a few examples). Recent studies also focus on the crucial role of financial intermediation in driving business cycles. Christiano, Motto and Rostagno (21) draws attention to the nominal friction (from the fact that lending contracts are denominated in nominal terms) that accounts for a significant portion of business cycle fluctuations. Gertler and Kiyotaki (21) investigates how interruptions in the financial market lead to a crisis and the effectiveness of several market interventions in mitigating the crisis. Gertler and Karadi (211) further searches for a more effective but unconventional monetary policy in a simulated financial crisis. Macroprudential policy refers to the financial regulation that directly targets financial stability and systematic risk. It is often mentioned as an alternative or complementary approach to the traditional monetary policy. Common macroprudential tools target bank s capital buffer and leverage ratio as well as household s debt-to-income ratio and LTV ratio. Gelati and Moessner (213) provides an excellent survey on the research of macroprudential policy and the current policy debate. Suh (212) studies the interaction between monetary and macroprudential policy in a DSGE model with financial accelerator. The findings suggest that macroprudential policy is effective in stabilizing the economy but creates a regulatory arbitrage that reallocates credit to a less regulated sector. Gelain et al. (213) incorporates housing into standard DSGE model and finds that a permanent tightening of household s collateral constraint is most effective in reducing excessive volatility. Lima et al. (212) searches for the optimal monetary and macroprudential policy in a DSGE model with financial frictions. The authors find that a tax-subsidy scheme aiming to reduce bank s leverage ratio is effective in stabilizing the economy and is also welfare-improving. A common ground for the most effective and appropriate macroprudential policy has not been reached in the literature. Some policies are sector-specific while others can be diffi cult to implement. The objective of this paper is to find a practical, effective and welfare-improving macroprudential policy that can be used jointly with traditional monetary policy. In the next section, I present a model that is useful in addressing the recent financial crisis and can be utilized to study the issues mentioned above. 3 Model The model is adapted from Iacoviello (25), where two types of households differ by their discount factors. The impatient households (indexed j = b) are subject to 3

5 a higher discount factor than the patient household (indexed j = s), and borrow funds to consume each period (β b < β s ). Patient households optimally choose the amount of savings each period earning the risk-free rate R t. Using capital, household labor and housing input, the non-financial firms produce intermediate goods and sell to monopolistically competitive retailers. The capital good producers purchase used capital from intermediate-good producers, buy new capital, refurbish the old capital and sell to the firms next period. The financial sector is modelled vis-à-vis Gertler and Karadi (211). The existence of credit friction creates a wedge between the saving and lending rates. The central bank conducts monetary policy via a simple Taylor-type rule that responds to the deviations of output and inflation. The model is then augmented to include macroprudential policies, with restrictions on the LTV ratio of borrowers and leverage ratio of financial intermediaries. 3.1 Households There exist two types of infinitely-lived, utility maximizing households. The patient households deposit savings into the banking sector and receive the risk-free interest rate. The impatient households borrow from banks to consume and face a credit constraint limited by the value of their house, served as collateral. The difference in time preferences implies that in the equilibrium, the patient households will always save and the impatient households will always borrow. I assume a continuum of households in each type with equal population. Both types of households obtain utility from housing goods and offer labor services in a competitive labor market Patient Households Patient households, denoted by s, are subject to a discount rate β s. In addition, they lease a fraction (1 κ) of housing goods to non-financial firms and earn rent r h t. Firms use this real estate for production of intermediate goods. The representative household makes consumption, C t,s, housing, H t,s and labor, L t,s choices each period by maximizing the life-time expected utility given by max C s,h s,l s,d E { β t s[υ c log C t,s + v h ε H t t= L 1+ϕ } L t,s log(κh t,s ) v l 1 + ϕ L (1) 4

6 subject to budget constraint C t,s + P H t (H t,s H t 1,s ) + D t R t D t 1 + W t,s L t,s + r h t (1 κ)p H t H t 1,s + Π t (2) ε H is a preference shock on housing goods, where a positive ε H leads to a rise in housing demand. The parameter υ c controls the utility from consumption, v h governs the utility from housing goods and v l dictates the disutility of labor supply. Pt H denotes the housing price in units of consumption. Patient households make real bank deposit D t, earning real return R t+1 in the following period. In addition, W s is the real wage and Π t denotes the net profits received from owning financial and non-financial firms. All variables are in real terms and the optimal choices are characterized by the following first order conditions: v c C t,s P H t v l L ϕ L t,s = v c C t,s W t,s (3) 1 1 = β C s E t R t+1 (4) t,s C t+1,s = v hε H t H t,s + β s E t v c c t+1,s P H t+1[1 + r h t+1(1 κ)] (5) Equation (3) is the labor supply decision and (4) is the standard Euler equation. (5) characterizes the housing demand for patient households, which shows that the shadow price of housing goods in period t is the sum of period t marginal utility from housing goods and the discounted value of the shadow price in t Impatient Households The impatient households make consumption, labor and housing decisions every period. The representative household, denoted by b, with discount factor β b maximizes the expected utility given by max C b,h b,l b,b E { β t b [υ c log C t,b + v h ε H t t= L 1+ϕ } L t,b log H t,b v l 1 + ϕ L C t,b + P H t (H t,b H t 1,b ) + R L t B t 1,b W t,b L t,b + B t,b (7) (6) B t,b m t E t [ P t+1 H Rt+1 L H t,b ] (8) 5

7 In equation (8), m t represents the maximum allowable LTV ratio and E t P H t+1 H t,b is the expected future value of the borrower s real estate. The households borrow B t,b in period t and repay R L t+1 B t,b in period t + 1. Constraint (8) implies that during period t, the impatient households may only borrow up to a fraction m t of the expected value of their housing stock in period t + 1 less interest payment. In the equilibrium, this constraint binds given the assumption that borrowers are more impatient than the savers. Let λ t be the Lagrange multiplier associated with the borrowing constraint, then the first order conditions that characterize the optimal choices are: v l L ϕ L t,b = v c C t,b W t,b (9) v c C t,b P H t v c v c = λ t E t Rt+1 L + β C b E t Rt+1 L (1) t,b C t+1,b = v hε H t H t,b + β b E t v c c t+1,b P H t+1 + λ t m t E t P H t+1 (11) Comparing the first order conditions of the patient and impatient households, we immediately see the importance of the collateral constraint. From (1), a strictly positive λ t associated with binding constraint implies that the traditional intertemporal optimal condition fails to hold with equality. In addition, the marginal utility of investment in housing increases with the magnitude of the Lagrange multiplier. Moreover, equation (11) shows that the borrower s marginal return on housing goods depends on the LTV ratio. In a financially frictionless economy, the borrowing rate would be equivalent to the savings rate, R L t = R t. 3.2 Financial Intermediaries A banking sector as in Gertler and Karadi (211) is introduced in this section to create a wedge between the deposit and lending rates. Credit frictions are essential to capture the role of bank capital in the transmission of shocks to the economy. Financial frictions are imbedded in the funds available to banks, but I assume frictionless transfer of funds between financial intermediaries and borrowers. There exists a continuum of mass one banks owned by the households with the timeline summarized as follows: In the beginning of period t, bank j raises deposit D j t at deposit rate R t+1 payable in period t + 1 from the patient household Bank j issues one-period loans to the impatient households with real estate col- 6

8 lateral, B j t,b = m te t [ P t+1 H H j Rt+1 L t,b ] Bank j also issues one-period loans to non-financial firms backed with equity capital, B j t,e = Q tk j t+1 All loans are subject to interest rate R L t+1 payable in period t + 1 Here, K t+1 is the capital holding of firms with unit price Q t. This can be interpreted as the value of financial claims the banks hold against non-financial firms. Intermediary j s balance sheet consists of assets given by B j t = Bj t,b + Bj t,e = m te t [ P t+1 H Rt+1 L H j t,b ] + Q tk j t+1 (12) In addition, with liabilities D j t and the residual net worth N j t, the following condition holds for every period: The law of motion of intermediary j s net worth is simply B j t = Dj t + N j t (13) N j t+1 = RL t+1b j t R t+1d j t (14) The banker will only fund projects with expected return no less than the discounted cost of borrowing. Therefore, the following inequality must hold: E t Λ t,t+1+i (R L t+1+i R t+1+i ), i (15) where Λ t,t+1+i is the stochastic discount factor applied in period t to earnings in t i. The survival rate of the financial intermediary is θ, a probability independent of job history. This implies that the average lifetime of a banker in any period is 1 1 θ. Similar to the birth-and-death assumption of banks in Bernanke, Gertler and Gilchrist (1999), a positive exit probability prevents bankers from accumulating suffi cient net worth to finance equity investments internally. In each period, (1 θ) of bankers exit and become workers while a similar amount of workers take up jobs as financial intermediaries. Bankers who exit from the financial sector transfer their earnings back to the corresponding household, and the household provides some start-up funds for new bankers. 7

9 Financial intermediary j maximizes its expected discounted terminal net worth, V j t, by choosing the amount of assets it purchases: V j t = max E t i= (1 θ)θ i β i+1 s Λ t,t+1+i [(R L t+1+i R t+1+i )B j t + R t+1+in j t+i ] (16) Similar to Gertler and Karadi (211), V j t can be rewritten as follows: V j t = υ t B j t + η tn j t (17) with υ t = E t [(1 θ)β s Λ t,t+1 (Rt+1 L R t+1 ) + β s Λ t,t+1 θ Bj t+1 B j υ t+1 ] (18) t η t = E t [(1 θ) + β s Λ t,t+1 θ N j t+1 N j η t+1 ] (19) t υ t is the expected discounted marginal benefit to banker j for a unit increase in asset holdings B j t, keeping N j t constant. Analogously, η t is the expected discounted marginal gain for a unit increase in net worth, holding total assets constant. Following Gertler and Karadi (211), I introduce a moral hazard/costly enforcement problem to limit the liability of the financial intermediaries. This aims to prevent intermediaries from borrowing indefinitely from households given positive expected risk premium, as shown in (15). At the beginning of any period, the banker can choose to divert a fraction λ of all available funds from the projects and transfer back to its corresponding household. Upon this action, depositors can force the intermediary into bankruptcy and recapture the remaining fraction 1 λ of total assets. Costly enforcement implies that it is too costly for the depositors to recover the diverted fraction λ of funds. To assure depositors are willing to supply funds to bankers each period, the following incentive constraint must be satisfied: V j t = υ t B j t + η tn j t λbj t (2) The left hand side of (2) is the cost of diverting funds for banker j, or the value of operating the intermediary. The right hand side is the gain from diverting a fraction λ of available assets. The financial intermediary chooses not to divert only when the value of operating the intermediary is greater than or equal to the benefit from diverted assets. 8

10 Free of agency problems, the financial intermediary would continue to expand borrowing until Rt+1 L is adjusted to ensure υ t =. With the incentive compatibility constraint in place, the intermediary s asset holdings are restricted by its equity capital. When the constraint binds, (2) can be rewritten as B j t = η t λ υ t N j t (21) = φ t N j t where φ t is the endogenous leverage ratio of the banks that depositors will tolerate. Proposition 1 The incentive compatibility constraint binds if and only if < υ t < λ. Proof. This is proven by contradiction. Suppose υ t λ. Then given η t N j t >, the left hand side of (2) is always greater than the right hand side. Therefore the constraint is not binding. This implies that the value of operating a bank is always greater than the benefit from diverting funds. Now, suppose υ t. Then the marginal gain of increasing investment in financial assets is less or equal to zero, implying that the financial intermediary will not take deposits from household to acquire assets B j t, resulting in a slack constraint. The credit condition tightens when λ increases. When the constraint binds, the law of motion of intermediary j s net worth becomes: N j t+1 = [(RL t+1 R t+1 )φ t + R t+1 ]N j t (22) The leverage ratio does not depend on any bank-specific characteristics, therefore aggregate variables can be simply obtained by summing across all intermediaries. Let N t be the aggregate net worth of all banks, it can be written as the sum of the net worth of existing bankers, N et, and the net worth of new bankers, N nt. B t = φ t N t = φ t (N et + N nt ) (23) Recall that only a fraction θ of bankers at t 1 survive through period t, using equation (22), we can express N et as N et = θn t = θ[(r L t R t )φ t 1 + R t ]N t 1 (24) New bankers receive start-up funds from their respective households. It is assumed that this fund equals to a fraction of the value of assets that exiting bankers intermediated 9

11 in their final operating period, given by (1 θ)b t. The households are assumed to transfer ϖ 1 θ of the total final period assets of exiting bankers to newly entering financial intermediaries. N nt can then be written as N nt = ϖb t (25) Therefore, we can rewrite the law of motion for N t+1 as follows N t = θ[(r L t R t )φ t 1 + R t ]N t 1 + ϖb t (26) 3.3 Entrepreneurs There is a continuum of infinitely lived entrepreneurs of measure one, who produce a homogeneous good utilizing household labor, capital and housing stock. Entrepreneurs use a standard Cobb-Douglas production function with constant return-to-scale. Note that there is imperfect substitution between impatient and patient household labor, which may be explained by assuming the patient households to be managers of firms and impatient households to be workers. The representative entrepreneur produces an intermediate good Y t, using capital goods K t, housing stock (1 κ)h t,s and labor input of the patient and impatient households according to the production function: Y t = A t (U t ξ t K t ) η [(1 κ)h t,s ] υ L α(1 η υ) t,s L (1 α)(1 η υ) t,b (27) A t is the technology shock, ξ t is an exogenous shock to the quality of capital and U t is the utilization rate of capital. ξ t K t is the effective quantity of capital at time t. Firms raise fund from the financial intermediaries by issuing claims against working capital K t+1 at price Q t. More specifically, B t,e = Q t K t+1 (28) The endogenous borrowing constraints are only applicable to banks since non-financial firms face no frictions. Banks have perfect information about the firm and there is perfect enforcement. The constraints discussed in Section 3.2, however, directly affect the supply of funds to the firms. Intermediate-good producer chooses a capital utilization rate U t, capital K t and 1

12 labor rate (L t,s, L t,b ) to produce Y t, and sells the product at price P mt. The firm solves max U,L s,l b,k P mty t +Q t ξ t K t δ(u t )ξ t K t W t,s L t,s W t,b L t,b R L t Q t 1 K t r h t (1 κ)p H t H t 1,s where δ( ) is the depreciation rate on capital. The first order conditions are given by (29) L t,s : W t,s = P mt (1 η υ)α Y t L t,s (3) L t,b : W t,b = P mt (1 η υ)(1 α) Y t L t,b (31) U t : δ (U t )ξ t K t = P mt η Y t U t (32) The firm pays out the ex-post return to capital to the banks given that they earn zero profit in each state. The ex-post return to capital is given by R L t+1 = [P mt+1η Y t+1 ξ t+1 K t+1 + Q t+1 δ(u t+1 )]ξ t+1 Q t (33) The intuition is that the ex-post gross rate of return on capital equals to the sum of the marginal productivity of labor and the capital gain from changes in capital prices. Note that the valuation shock ξ t+1 provides additional variation to the return on capital. The value of capital stock at the end of period t + 1 is ξ t+1 U t+1 [Q t+1 δ(u t+1 )]. Similarly, the non-financial firm pays ex-post return to housing stock as rents to the patient households. Taking derivative with respect to H t,s, the ex-post rent is given by rt+1 h P mt+1 Y t+1 = υ (1 κ)pt+1 H H t,s (34) 3.4 Capital Producers Capital producers are essential to introduce capital adjustment costs in a tractable way. Following the literature on financial accelerator, capital adjustment costs would induce variations in the price of capital in response to changes in capital stock. At the end of period t, competitive capital producing firms purchase used capital from intermediate-good producers, re-polish old and produce new capital. They sell both repaired and new capital. Assuming the cost of replacing depreciated capital is one, the price of a unit of new or repaired capital is denoted by Q t. Let I t be the gross 11

13 capital created, I nt be the net capital created and Ī be the steady state value of I t, the capital goods producer solves max I nt E t= β t sλ,t [(Q t 1)I nt Φ( I nt + Ī I nt 1 + Ī )(I nt + Ī) (35) s.t.i nt = I t δ(u t )ξ t K t (36) Φ( ) is the capital adjustment cost function, with Φ(1) = Φ (1) = and Φ (1) >. The first order condition that characterizes the net investment Q relation is given by Q t = 1+Φ( I nt + Ī I nt 1 + Ī )+Φ ( I nt + Ī I nt 1 + Ī ) (I nt + Ī) I nt 1 + Ī E tβ s Λ t,t+1 Φ ( I nt+1 + Ī I nt + Ī )(I nt+1 + Ī I nt + Ī )2 Note that given no idiosyncratic shock among capital-good producers, all firms choose the same net investment rate. In this setup, the price of capital increases when total investment expenditure expands. Depreciation rate and adjustment cost function are assumed to take the following functional forms δ(u t ) = δ (37) δ 1 + ω + δ 1 + ω U 1+ω t (38) Φ( I nt + Ī I nt 1 + Ī ) = φ I 2 ( I nt + Ī I nt 1 + Ī 1)2 (39) where δ is determined by the steady state, ω and φ I are parameters. 3.5 Retail Firms Retail firms are present in the model to introduce sticky prices. There is a continuum of monopolistic competitive retailers who purchase intermediate output from intermediate-good producers and produce final output, Y t. The CES composite of final goods is given by Y st is the output by retailer s, Y t = [ 1 Y ε 1 ε st ds] ε ε 1 (4) Y st = ( P st ) ε Y t (41) P t P t = [ 1 P 1 ε st ds] 1 1 ε (42) 12

14 One unit of intermediate goods can be used to produce one unit of final goods. The marginal cost is simply the price of intermediate output, P mt. To introduce nominal rigidities, only a fraction 1 γ of retailers can reset price freely in any period. Retailers that do not re-optimize prices will index their prices with respect to inflation and the parameter γ P. Specifically, the retailer chooses the optimal reset price P t max P t E t i= γ i β i sλ t,t+i [ P t P t+i to solve i (1 + π t+k 1 ) γ P P mt+i ]Y st+i (43) π t is the rate of inflation from t i to t. The first order condition is E t i= γ i β i sλ t,t+i [ P t P t+i [ k=1 i (1 + π t+k 1 ) γ P ] 1 ε k= /ε P mt+i]y st+i = (44) Using the law of large numbers, we can derive the law of motion for the price level P 1 ε t = (1 γ)(p t ) 1 ε + γ((1 + π t 1 ) γ P P t 1 ) 1 ε (45) Let P t = P t /P t, the law of motion for the relative price level is given by 1 = (1 γ)( P t ) 1 ε + γ[ (1 + π t 1) γ P 1 + π t ] 1 ε (46) 3.6 Central Bank and Monetary Policy The central bank in this economy administers a log-linearized Taylor rule of the following form: where i t is the nominal interest rate. î t = ρ r (î t 1 ) + (1 ρ r )[γ πˆπ t + γ Y Ŷ t )] + ε R t (47) The central bank sets to adjust interest rate according to the log deviation of inflation and output from their steady state levels. γ π > and γ Y > are the parameters chosen by the central bank to conduct the monetary policy. When ρ r >, this rule also includes a first-order autoregressive component that captures the interest rate inertia à la Woodford (2). The relationship between real and nominal interest rates is characterized by the Fisher equation 1 + i t = R t+1 E t P t+1 P t = R t+1 E t (1 + π t+1 ) (48) ε R t is a random monetary shock with zero mean and variance σ 2 R. 13

15 3.7 Macroprudential Policy Dynamic Loan-to-Value (LTV) Ratio The impatient households can only borrow up to a fraction of the expected value of their housing stock, characterized by equation (8). The regulatory authority controls for the loan-to-value ratio as a way to moderate credit growth in the economy. Under the assumption that the impatient households are subject to a lower discount factor than the patient households, the borrowing constraint will always bind. Therefore, a high LTV ratio releases the tension of the collateral constraint and induces borrowing. Lower LTV ratio implies a tighter constraint that restricts the amount of lending in the real economy. The first experiment is to allow fixed LTV ratio for the impatient households. More specifically, I set m t = m in the baseline model. With the constraint binding, changes in the maximum LTV ratios directly signal credit liberalization or tightening policies. This assists the study of the impact of credit conditions on the real economy. The 28 financial crisis grew out of great economic conditions associated with a period of housing price boom and credit liberalization. Fixed LTV ratio is unable to capture the dynamic and corrective measures the policymakers may want to implement. A countercyclical LTV ratio is thus desired to limit lendings during booms and stimulate the economy during downturns. In an alternative experiment, I adopt a dynamic simple Taylor rule of the form: ˆm t = ρ m ˆm t 1 ϕ Y Ŷ t ϕ P ˆP H t (49) where ϕ Y > and ϕ P > are the parameters chosen by the regulatory authority. In this setup, policymakers adjust the LTV rule corresponding to the log deviations of output and housing price from their steady state values. In the literature, Gerlach and Peng (25) documents the regulation of household credit as a stabilizing tool for housing prices in Hong Kong and South Korea during the 1997 East Asian crisis Pigouvian Lump-Sum Tax The financial intermediaries face an endogenous capital-to-loan ratio of Nt B t = 1 φ t, which is the reciprocal of their leverage ratio. Similar to the discussion above, regulatory authority wants to raise bank s capital and restrict credit growth during economic upturns. Here, I introduce a Pigouvian lump-sum tax scheme adapted from Lima et 14

16 al. (212). In this setup, the government collects tax on bank s loans and uses the proceeds to subsidize the bank s net worth. This tax-subsidy policy directly affects the leverage ratio and allows policymakers to stabilize the credit market via the balance sheet of financial intermediaries. Let τ s t be the subsidy rate on net worth and τ t be the tax rate on loans, we can rewrite the balance sheet of the bank (equation 13) as follows (1 τ t )B t = D t + (1 τ s t)n t (5) The new law of motion for the bank s net worth is given by N t+1 = (R L t+1 R t+1 )(1 τ t )B t + (1 τ s t)r t+1 N t + τ s tn t (51) The last term on the right-hand side of equation (51) is the lump-sum subsidy. Intermediary j now solves a new problem V j t = max E t i= (1 θ)θ i β i+1 s Λ t,t+1+i [(R L t+1+i R t+1+i )(1 τ t+i )B j t+i (52) +((1 τ s t+i)r t+1+i + τ s t+i)n j t+i ] = υ m t B j t + ηm t N j t with υ m t = E t [(1 θ)β s Λ t,t+1 (Rt+1 L R t+1 )(1 τ t ) + β s Λ t,t+1 θ Bj t+1 B j υ t+1 ] (53) t η m t = (1 θ)(1 τ s t) + E t [(1 θ)β s Λ t,t+1 τ s t + β s Λ t,t+1 θ N j t+1 N j η t+1 ] (54) t Equation (26) can be rewritten as N t = θ[(r L t R t )(1 τ t 1 )φ t 1 + (1 τ s t 1)R t + τ s t 1]N t 1 + ϖ(1 τ t )B t (55) The aggregation across banks is identical to section 3.2 with a newly added balanced budget condition τ t B t = τ s tn t (56) In addition, there exists a cost of administering this tax scheme, which is quadratic in 15

17 the tax rate, ψτ 2 t B t. The tax rate is administered through a Taylor rule that corresponds to changes in output. The log-linearized rule is given by ˆτ t = ρ τ ˆτ t 1 + θ Y Ŷ t (57) where θ Y > is a parameter selected by the regulatory authority. When output increases above its steady state level, the positive tax rate imposed on bank s lending asserts a negative pressure on the leverage ratio. Subsequent subsidy on bank s net worth leads to a further decrease in leverage, which increases the capital-to-loan ratio. During economic recessions, the tax and subsidy revert their positions and there will be taxes on bank s capital holdings to stimulate borrowing. As a result, leverage ratio falls and credit expansion is achieved to enhance economic recovery. Unlike Lima et al. (212), the steady state tax rate in this model is zero instead of some small positive value. This implies that the economy bears no cost of raising taxes in the equilibrium and only faces such burden in response to a random shock. This allows us to better compare across models as the steady state values remain unchanged. The central bank, regulatory authority and the government play different roles in shaping the economy. First, the central bank determines the nominal interest rate through monetary policy, which then affects the real interest rate via the Fisher equation. This influences the funding cost of financial intermediaries and their lending rates. Secondly, the regulation on LTV ratio has a direct impact on household borrowing, which further passes onto the bank s balance sheet. However, the borrowing conditions of the entrepreneurs are only influenced indirectly through lending rates. Furthermore, the Pigovian tax scheme targets the leverage ratio of financial intermediaries directly. This has an impact on both business and household borrowing conditions. Provided that each policy affects different agents via different channels, the interaction between monetary policy and macroprudential tools is further examined in Section Competitive Equilibrium The shocks to productivity, housing preference, monetary policy and quality of capital follow AR(1) process in a log-linearized form: â t = ρ A â t 1 + ɛ A t (58) ˆε H t = ρ Hˆε H t 1 + ɛ H t (58.1) 16

18 A competitive equilibrium is a sequence of allocations ˆε R t = ρ Rˆε R t 1 + ɛ R t (58.2) ˆξt = ρ Qˆξt 1 + ɛ ξ t (58.3) {H t,s, H t,b, L t,s, L t,b, C t,s, C t,b, D t, B t,b, B t,e, B t, K t+1, Y t, N t, I t, I nt, υ t, η t, φ t, τ t, τ s t, m t } t= (59) together with a sequence of prices {W t,s, W t,b, Λ t,t+1, U t, P H t, P mt, P t, Q t, λ t, R t+1, R L t+1, i t, r h t+1, π t } t= (6) and exogenous processes {A t, ε R t, ε H t, ξ t } t= (61) such that i) the allocations solve each household s, entrepreneur s, retailer s maximization problem at equilibrium prices given pre-determined variables and ii) all markets clear. The aggregate clearing conditions are given by H t,s + H t,b = H (62) L t,s + L t,b = 1 Y t = C t,s + C t,b + I t + Φ( I nt + Ī I nt 1 + Ī )(I nt + Ī) + ψτ 2 t B t (63) τ t B t = τ s tn t (64) Equation (64) and the term ψτ 2 t B t in (63) only appear when the Pigovian tax scheme is imposed. The full log-linearized model is presented in appendix A.2. 4 Calibration Table 1 in the appendix provides a summary of parameters and their calibrated values. The time period in the model is one quarter. Parameter values are mostly taken from Gertler and Karadi (211) and Iacoviello (25). The discount factors for the saving and borrowing households are chosen to be.985 and.95, respectively. This implies that the annual net equity return for the patient households is 6.1%. The weight of consumption goods and housing goods in the utility function (v c, v h ) are calibrated as.9 and.1. The weight of labor in the utility function (v l ) is set to 17

19 be 2. The inverse of Frisch elasticity of labor supply (ϕ L ) is.276. According to the Bureau of Economic Analysis, investments in commercial real estates as a percentage of GDP is on average twice of investments in residential property. In this model, I assume patient households lease a fraction 1 κ =.67 of housing stock to firms. This is also consistent with estimation results from Yepez (212), where the posterior mean of 1 κ from Bayesian estimation is around.6. The financial sector consists of three suggestive parameters (θ, λ, ϖ), which are the survival rate of bankers, the fraction of wealth a banker could divert and the proportional wealth transfer to the entering banks. The parameters are chosen to meet two goals. First, the steady state interest rate spread is one percent. Moreover, the steady state leverage ratio of banks is four. In Gertler and Karadi (211), the fraction of assets a banker can divert (λ) is extraordinarily high at more than 3%. This is set to achieve a life expectancy of a decade for the bankers. In this model, I set the survival rate of bankers (θ) to be.948, which implies an average career horizon of five years. This lowers the fraction of assets a banker can divert to 17%. Entering bankers get a wealth transfer (ϖ) of.2 as in Gertler and Karadi (211). In the production sector, the share of capital and housing stock in the Cobb-Douglas production function are set to be.33 and.3. The patient household s labor share (α) is set to be.64. The steady state utilization rate is normalized to 1 with rate of depreciation δ(u) =.25. This implies that capital takes an average of ten years to fully depreciate. The capital adjustment cost parameter φ I is 4 and the elasticity of marginal depreciation with respect to the utilization rate (w) is 7.2. The retail firm s elasticity of substitution is 4.167, implying a steady state real markup to be The probability of keeping prices fixed (γ) is.779 and the measure of inflation indexation (γ P ) is.241. The baseline calibration for the degree of intervention in monetary policy is set according to Gertler and Karadi (211) where γ π = 1.5 and γ Y =.125. The degree of inertia (ρ r ) is.8. The autoregressive coeffi cients in the exogenous processes are ρ A =.85, ρ H =.95, ρ R =.8 and ρ ξ =. The steady state consumption ratio between impatient and patient households (C b /C s ) is.89 and the ratio of labor supply (L b /L s ) is Annualized household debt-to-gdp ratio (B b /Y ) is.26 and 3.9 for the business-to-household credit ratio (B e /B b ). The aggregate consumption-to-gdp ratio (C/Y ) is.82, the investment to GDP ratio (I/Y ) is.12 and the capital-to-gdp ratio (K/Y ) is 5.2. The steady state LTV ratio (m) and leverage ratio (φ) are.7 and 4, respectively. The tax and subsidy 18

20 rates are zero in equilibrium. lending rate (R L ). The real interest rate (R) is 1.15 and 1.25 for the 5 Model Analysis This section reports simulation results from three alternative specifications with four shocks. First, the baseline model ("BLM") considers a fixed LTV ratio with m =.7, which is the steady state value for m t. This implies that the impatient households can only borrow up to 7% of the expected value of their housing stock. In fact, this number is compatible with the average LTV ratio for US residential mortgages (76%) before the financial recession in 28 (IMF 211). The central bank conducts monetary policy according to equation (47) without other active regulatory policy. The second model adopts a dynamic LTV ratio rule ("LTVM") characterized by (49). The regulatory authority lowers the LTV ratio during economic booms to limit credit expansion and increases the ratio during recessions. The degree of inertia (ρ m ) is.85 and the degrees of intervention are ϕ P = 1.5 and ϕ Y =.15. In the last specification, the baseline model is augmented with the Pigovian tax scheme ("PTM") characterized by equation (57). The government sets positive tax and subsidy rates during economic booms to increase the capital-to-loan ratio of financial intermediaries. The degree of inertia (ρ τ ) is.75 with the degree of intervention (θ Y ) to be.57, taken from Lima et al. (212). The monetary policy is effective in all three models with no change in the parameter values. The impulse response functions from positive productivity, housing demand, capital quality shocks and expansionary monetary policy are displayed in Figure 1 to 4 in the appendix. The standard deviation for each shock is σ A = σ ξ =.1, σ R =.1 (annualized) and σ H =.21. The magnitude of the housing demand shock is taken from Suh (212), which matches the historical volatility of housing price in the U.S.. Moreover, one percent productivity and capital quality shocks are standard as in Gertler and Karadi (211).The macroprudential policies, if effective, should stabilize the economy relative to the baseline model. Furthermore, fluctuations of household lending and housing price should be significantly dampened. 5.1 Technology Shock In the baseline model, output, consumption, investment increase and inflation decreases in response to a 1% technology shock (Figure 1 solid lines). Increase in 19

21 consumption drives up housing demand, causing its price to rise under fixed housing supply. Consequently, household lending expands resulting in a higher leverage ratio for financial intermediaries. It should be emphasized that the leverage ratio has increased more than 15% in comparison to the steady state level, which creates excessive liquidity risk in the credit market. Consistent with findings in Gertler and Karadi (211), the credit spread falls in response to positive productivity shock that causes the bank s net worth to fall. With a dynamic LTV ratio rule, the impulse response functions are moderately dampened for consumption, investment, output, inflation and housing price (Figure 1 dashed lines). The LTV ratio decreases by around 6% in response to higher output and housing price. The contractionary LTV ratio further leads to a decrease in household lending since the impatient households now face lower collateral value of housing stock. However, decreasing net worth along with an increasing leverage ratio cause the aggregate lending to increase in response to the shock (evidently from equation 21). This suggests that the financial intermediaries seek to expand business lending when the household credit market is regulated. This causes a credit shift from the impatient households to entrepreneurs, consistent with findings in Suh (212). The regulatory authorities should consider this possibility when choosing the appropriate macroprudential policy. The tax policy, PTM, is comparably more effective (Figure 1 dash-dotted lines). Leverage ratio remains stable as the government imposes a 1% tax on aggregate lending and simultaneously subsidizes the bank s net worth. Furthermore, the percentage change in all other variables are significantly smaller in comparison to the BLM and LTVM. Household lending and housing price slightly increase in response to the technology shock but revert back to the steady state levels quickly. Small changes in the leverage ratio and bank s net worth suggests minimal evidence of credit shifting. Both macroprudential policies are effective in stabilizing the economy, but the tax policy may be more desirable in this particular setup. 5.2 Housing Demand Shock Figure 2 displays the impulse response functions from a housing demand shock of 21 bps, calibrated from Suh (212). A positive shock implies that both the patient and impatient households now obtain more utility from housing stock. Given exogenous and fixed housing supply, the price is completely driven by demand. In the BLM, consumption, output and inflation increase while investment falls. As more people demand for housing, price increases and lending expands. The financial intermediaries 2

22 also become more leveraged. In the LTVM, impatient households face a 1% drop in the target LTV ratio that limits the maximum loan size. This reduces household lending and dampens the growth in housing price. In addition, the increase in leverage ratio is reduced by more than 5% in comparison to the BLM. This significantly limits the liquidity risk of financial intermediaries. Similar to the technology shock, a small decrease in bank s net worth and relatively large increase in leverage ratio imply a rise in aggregate lending. The increase in business lending exceeds the change in aggregate lending provided that household lending has decreased in response to the shock. When financial intermediaries are restrained in the housing sector, profit-maximizing behavior motivates them to expand business in the production sector. In contrast, the PTM is also effective in response to a housing demand shock. All variables other than the housing price are associated with small fluctuations, and the tax rate is positive at around 3 bps. Housing price increases slightly less than the LTVM but reverts back to the steady state level quickly. Both figures 1 and 2 suggest that the dynamic LTV ratio rule is competent in controlling for household lending and housing price, but creates additional volatility in the business sector. The tax policy is effective under both shocks but achieves a better stabilizing role in response to technology disturbance. 5.3 Capital Quality Shock In figure 3, a 1% capital quality shock is imposed to examine the effects on housing market. The disturbance is considered temporary with an autoregressive coeffi cient of zero. The overall effect takes two stages. First, a positive shock to the quality increases the effective quantity of capital, which enhances the balance sheet of financial intermediaries. Consequently, increasing demand for capital drives up the price, Q t and bank s leverage ratio. Effects of the shock are amplified by the presence of financial frictions. Demand for housing drops initially as resources are directed toward the production sector, causing the housing price to fall. In the second stage, positive income growth naturally induces greater housing demand and adds additional pressure on the credit market. In the BLM, the housing prices first decreases by 4% then quickly rises to 2% above the steady state level. Consumption and leverage ratio are humpshaped given the two-stage adjustment process and the bank s net worth grows by 3%. The introduction of the dynamic LTV ratio effectively dampens the effects from the shock and restricts credit expansion. Because housing price falls immediately after 21

23 the shock, the target LTV ratio first increases above its steady state level then drops significantly. The borrowing limit for impatient households increases first, which leads to greater household lending. As output and housing prices both rise, the LTV ratio falls below the long-run level and leads to a gradual decrease in household loans. This macroprudential policy actively adjusts the borrowing constraints to reduce fluctuations in the credit market. As a result, disturbances in the economy are effectively mitigated. In contrast with technology and housing demand shocks, business lending expands naturally in response to higher price and quantity of capital with little evidence of credit shifting. The tax policy is more effective in stabilizing the credit market but not the aggregate economy. Positive tax on total lending reduces the growth of household borrowing and alleviates the increase in housing price. Changes in the net worth of financial intermediaries involve two parts. The first part comes from increases in the quantity and price of capital, as shown in the BLM. However, the positive subsidy further enhances the bank s net worth. As a result, the net present value of financial intermediaries increases nearly 4% in response to the capital quality shock. Consequently, the credit market is more restricted with a smaller increase in the leverage ratio. Since households own the financial intermediaries, consumption and output growths are higher in comparison to the LTVM, but are still noticeably smaller than those from the BLM. 5.4 Monetary Shock Figure 4 displays the impulse response functions from an unexpected 1% (annualized) decline in nominal interest rate. Consumption, investment, output and inflation rise in response to the shock. This expansionary shock lowers the borrowing expense of banks and induces more lending. Leverage ratio, housing price and household lending increase significantly in the BLM. The greater risk premium also raises the bank s net worth. With only monetary policy in effect, the economy experiences large fluctuations and faces higher financial risk. In contrast, the countercyclical loan-to-value ratio policy is effective in stabilizing the economy. In the LTVM, percentage deviations are evidently smaller. The LTV ratio decreases to around 2% before gradually returning to the steady state level. Housing price and household lending increase about 5% less than in the baseline case. However, business lending significantly expands and creates the credit shifting problem mentioned previously. As the cost of borrowing decreases, financial intermediaries face larger incentive to expand lending in all sectors. Regulatory control in the housing sector promotes a more active lending market in the business sector. 22

24 The tax scheme is more effective in mitigating economic response to disturbances, as demonstrated in previous sections. The tax rate increases by 1% in response to a 2% rise in output. Although the initial deviation of output is greater than in the LTVM, the recovery is also more rapidly. The tax policy effectively reduces changes to the bank s balance sheet, resulting in small fluctuations of the housing price and household lending. In this case, business lending also expands more than household lending due to lower borrowing cost of the banks, suggesting some evidence of credit shifting. However, the magnitude is smaller in comparison to the LTVM. 5.5 Volatility of Economic Variables Macroprudential policy aims to stabilize the economy and dampen fluctuations caused by unexpected shocks. The impulse response functions presented above provide direct measures of the percentage change of major variables in response to shocks. However, evaluation of the relative volatility is essential for a complete assessment. More specifically, a successful macroprudential policy should not only reduce the relative change of an economic variable, but also lessen the overall variation. Table 2 summarizes the unconditional standard deviation of consumption, output, investments, inflation, housing price, bank s net worth, household lending and business lending. The percentage difference between the baseline model and other models are listed in brackets. Both the dynamic LTV ratio rule and Pigovian tax policy could significantly reduce the volatility of housing price. In addition, household lending is around 1% less volatile in models with macroprudential policy. However, the results are not uniform among other variables. In the LTVM, standard deviations of investment and business lending are higher than the baseline model. This suggests that the banks reallocate towards the less regulated production sector when restriction is applied on household lending. The financial intermediaries expand business lending to maximize profit, which leads to a more volatile credit market. Since the ratio of business to household lending is 3.9 in the steady state, the aggregate lending in the economy fluctuate even more than in the case with fixed LTV ratio. The tax policy is more effective in stabilizing the economy. Except for the bank s net worth, all other variables are less volatile in comparison to the BLM and LTVM. Furthermore, the standard deviation of business lending and investments are significantly lessened. In summary, the regulatory authority needs to take consideration of possible trade-off between the business and household sectors when choosing the appro- 23