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Bank of Japan Working Paper Series Financial Markets, Monetary Policy and Reference Rates: Assessments in DSGE Framework Nao Sudo * nao.sudou@boj.or.jp No.12-E-12 December 2012 Bank of Japan 2-1-1 Nihonbashi-Hongokucho, Chuo-ku, Tokyo 103-0021, Japan * Financial System and Bank Examination Department Papers in the Bank of Japan Working Paper Series are circulated in order to stimulate discussion and comments. Views expressed are those of authors and do not necessarily reflect those of the Bank. If you have any comment or question on the working paper series, please contact each author. When making a copy or reproduction of the content for commercial purposes, please contact the Public Relations Department (post.prd8@boj.or.jp) at the Bank in advance to request permission. When making a copy or reproduction, the source, Bank of Japan Working Paper Series, should explicitly be credited. Financial Markets, Monetary Policy and Reference Rates: Assessments in DSGE Framework Nao Sudo December 28, 2012 Abstract In this paper, we explore the roles played by reference rates in business cycle ‡uctuations using a medium-scale full-‡edged dynamic stochastic general equilibrium (DSGE) model. Our model is an extended model of chained-credit-contract model developed by Hirakata, Sudo, and Ueda (2011b) estimated by the Japanese data. In our economy, there are interbank as well as lending markets. Credit spreads determined in the markets are a¤ected by the borrowers’creditworthiness and degree of informational friction in the credit markets. Focusing on the role of reference rates that a¤ects economic decisions through the delivery of information about the nature of economy, we evaluate channels through which the reference rates a¤ects credit spreads and macroeconomic activities. We …nd that (i) reference rates may mitigate informational friction in the credit markets, leading to a higher investment, output, and in‡ation, (ii) reference rates may contribute to economic stabilization by providing accurate economic forecast, and (iii) reference rates may bring about unintended consequence of monetary policy implementation by adding a noise to the credit spreads. Our results indicate the importance of reliable reference rates, particularly under the environment where uncertainty prevails, from the perspective of resource allocation, stabilization, and policy implementation. Keywords: Reference Rates; Credit Spreads; Informational Friction, Signal Extraction, Monetary Policy Director, International Division, Financial System and Bank Examination Department, Bank of Japan (E-mail: nao.sudou@boj.or.jp). The author would like to thank Kosuke Aoki, Ichiro Fukunaga, Jacob Gyntelberg, Daisuke Ikeda, Selahattin Imrohoroglu, Sohei Kaihatsu, Koichiro Kamada, Ryo Kato, Tomiyuki Kitamura, Shun Kobayashi, Marco Lombardi, Koji Nakamura, Kenji Nishizaki, Yukisato Ohta, Masashi Saito, Yuki Teranishi, Yuki Uchida, Yoichi Ueno, and Hiromi Yamaoka for their useful comments. Views expressed in this paper are those of the author and do not necessarily re‡ect the o¢ cial views of the Bank of Japan. 1 1 Introduction Since the …nancial crisis starting in 2007, a growing attention has been paid to the role played by the reference rates in …nancial transactions among both policy makers and scholars. Although there is a strong agreement about the usefulness of the reference rate in guiding pricing of …nancial products, some recent studies emphasize a negative side of a coin. For instance, Abrantez-Mtez et. al (2012), investigating empirically if manipulations have been in place particularly during the …nancial crisis, suggest that Libor rates may have su¤ered, though not materially, from manipulation problem.1 In this paper, we ask roles of reference rates in business cycle ‡uctuations.2 To this end, we make use of a medium-scale full-‡edged dynamic stochastic general equilibrium (DSGE) model developed by Muto, Sudo, and Yoneyama (2012, hereafter MSY)3 and discuss how reference rate a¤ects economic behavior of agents, credit spreads in …nancial transaction, and macroeconomic performance. Our model is built upon a chained-credit-contract model developed by Hirakata, Sudo, and Ueda (2009, 2011a, b, hereafter HSU) and is estimated using Japanese data from the 1980s to 2000s. In our economy, there are credit constrained …nancial intermediaries (hereafter FIs) as well as credit constrained goods producing …rms and those borrowing sectors raise external funds from the interbank market and lending market, respectively. Similarly to Bernanke, Gertler, and Gilchrist (1999), there is informational friction between lenders and borrowers. That is, while borrowers’output are diverse, lenders cannot observe realization of each borrower’s output unless monitoring is conducted. When lenders recognize that either borrowers’ riskiness or expense associated with monitoring goes up, then lenders charge higher spread on their lending rates. While credit spreads are primarily a¤ected by the borrowers’ creditworthiness measured by size of net worth, degree of informational friction in credit markets also plays the important role in determining the spreads. We study three distinct channels through which reference rate a¤ects macroeconomy. The …rst channel stresses in‡uence of reference rate on informational friction in the credit markets. We consider a case where a reliable reference rate reduces cost of monitoring activities associated with …nancial intermediation and a case where it reduces borrowers’diversity regarding perceived idiosyncratic productivity from lenders’perspective. When monitoring cost is less costly, expected default cost falls and credit spread tightens, facilitating …nancial intermediation and boosting the economy. Similarly, when lenders perceive that idiosyncratic productivity converges across borrowers, because expected portion of defaulting borrowers falls, credit spreads shrink, giving way to economic expansion. The second channel stresses in‡uence of reference rates on agents’forecast and its implication for macroeconomic stability. We consider a case where agents today receive news about future economic events. While agents decide the current economic activities taking the information contained in the news into their consideration, the news is contaminated with noises and agents’expectation of the future events conditional on the news may depart from what will actually materialize. The discrepancy between the today’s forecast and realization of the future events yields an additional source of business cycle ‡uctuations. When reference rates deliver accurate information about the future economic events, the discrepancy shrinks, achieving economic stability. 1 By contrast, Kuo, Skeie, and Vickery (2012) discuss that Libor rates generally comove with other measures of borrowing rates although they …nd that Libor quotes sometimes lie below these measures and less disperse compared to them. See also Snider and Youle (2010) for related discussion. 2 In contrast to our study that focuses on the role of reference rates in the macroeonomic activity, Muto (2012) studies the role in the interbank interest rates. 3 See also Kawata et al. (2012) for the evaluation of role of reference rates in the macroeconomic ‡uctuations using a …nancial macro-econometric model. 2 The third channel stresses in‡uence of reference rates through a monetary policy implementation. We consider a case where a monetary authority cannot observe a noise in the credit spreads separately from the fundamental variations. While the noise itself is a non-fundamental innovation, when a policy rate systematically responds to credit spreads that contains the noise, the noise causes an unintended consequence from the central bank’s perspective. From the private agents’ perspective, the response of the policy rate acts as a shock to the monetary policy rule, adversely a¤ecting macroeconomic stability. This paper is organized into six sections. Section 2 brie‡y describes our model. The model consists of two categories of …nancial markets, interbank market and lending markets, and three types of market participants, investors, FIs, and entrepreneurs. Credit spreads in the model are determined by two factors: creditworthiness of borrowers and degree of informational friction between borrowers and lenders. Here, reference rate a¤ects both two factors. In section 3, 4, and 5, we propose three channels through which reference rate a¤ects credit spreads and macroeconomic activities by providing agents information regarding the nature of the economy. Section 3 discusses the role of reference rate in reducing degree of informational friction in credit markets. When the friction is mitigated, credit spreads shrink and aggregate investment becomes less costly. Section 4 discusses the role of reference rate in helping agents’expectation formation about future economic events and stabilizing business cycle ‡uctuations. Section 5 explores the case when reference rate contains non-fundamental noises and a¤ects monetary policy implementation. Section 6 draws a conclusion. 2 The economy This section describes our model structure. The model is borrowed from MSY (2012) and the model outline is shown in Figure 1. The economy consists of …ve sectors: the household sector, the …nancial intermediary (FI) sector, the non-durables sector, the durables sector, and the government sector. The household sector consists of two agents, the representative household and the investors. The representative household supplies labor inputs to the goods-producing sectors, earns wage, makes a deposit to the investors, and receives repayment in return. The investors collect deposits from the household and lend them to the FI sector by making credit contracts called IF contracts with the FIs. The FIs raise the external funds from the investor through the IF contracts and lend them to the goods-producing sectors by making credit contracts with each of the sectors. We call each of the contracts, the FEC and the FED contract, respectively. Each goods-producing sector consists of three agents, the entrepreneurs, the capital goods producers, and the goods producers. The entrepreneurs raise external funds from the FIs, purchase capital goods from the capital goods producers using the funds, and provide the capital goods to the goods producers. They then earn the rental price of the capital goods in return, accumulating the earnings as the net worth. The capital goods producers purchase investment goods from the durables sector and produce the capital goods. The goods producers produce goods from labor input, capital goods, and intermediate goods. Government sector consists of the government and the central bank. The government collects tax from the household sector and spends the tax revenue for the government purchase. The central bank adjusts the nominal interest rate so as to stabilize the in‡ation rate. 3 2.1 Credit Contracts 2.1.1 FEC and FED Contracts Basic Setting The FEC and FED contract are made between a FI and a continuum of the entrepreneurs in the two goods-producing sectors. In period t; each type i FI o¤ers a loan contract to an in…nite number of group ji entrepreneurs in sector . An entrepreneur in group ji owns net worth N ;ji (st ) and purchases capital of Q (st ) Kji (st ), where st is the whole history of states until period t, Q (st ) is the price paid per unit of capital and Kji (st ) is the quantity of capital purchased by the group ji entrepreneur in sector : Since the net worth N ;ji (st ) of the entrepreneur is smaller than the amount of the capital purchase Q (st ) Kji (st ) ; the entrepreneur raises the rest of the funds Q (st ) Kji (st ) N ;ji (st ) from the type i FI. The net return to a capital of a group ji entrepreneur is a product of the two elements: an aggregate return to capital R (st+1 ) in sector and an idiosyncratic productivity shock ! ;ji (st+1 ) ; that is speci…c to the group ji entrepreneur.4 There is informational asymmetry between lenders and borrowers and the FI cannot observe the realization of the idiosyncratic shock ! ;ji (st+1 ) without paying the monitoring cost : Under this informational friction, the FEC and FED contracts specify: amount of debt that the group ji entrepreneur borrows from a type i FI, Q (st ) Kji (st ) N ;ji (st ) ; and cut-o¤ value of idiosyncratic productivity shock ! ;ji (st+1 ) ; which we denote by ! such that the group ji entrepreneur repays its debt if ! the default if otherwise. (st+1 ) ;ji ! ;ji ;ji (st+1 ) ; (st+1 ) and declares Entrepreneurs’participation constraint A group ji entrepreneur joins the FEC or FED contract only when the return from the credit contract is at least equal R 1 to the opportunity cost. Based on the FEC or FED contract, a portion of the entrepreneurs ! (st+1 ) dF (! ) does not default and the rest of them default. If they do ;ji not default, ex post, they receive the net return to its capital holdings: ! ;ji st+1 ! The entrepreneurial loan rate in sector r 4 Here, ! ;ji ;ji s t+1 ! st+1 ;ji R ! ;ji st Kji st : is therefore given by ;ji (st+1 ) R (st+1 ) Q (st ) Kji (st ) Q (st ) Kji (st ) N ;ji (st ) : (1) (st ) is a unit mean, lognormal random variable distributed independently over time and across entrepreneurs in sector . We express its density function by f by F st+1 Q : 4 ! ;ji ; and its cumulative distribution function Instead of participating in the FEC or FED contract, a group ji entrepreneur can purchase capital goods using only its own net worth N ;ji (st ) : In this case, ex ante, the entrepreneur expects to receive the earning R (st+1 ) N ;ji (st ) ; and ex post it receives the earning ! ;ji (st+1 ) R (st+1 ) N ;ji (st ). Therefore, the FEC and FED contract between a type i FI and group ji entrepreneur is agreed by the group ji entrepreneur only when the following inequality is expected to hold: st+1 Q R st Kji 0 st @ Z 1 ! ;ji ! ! (st+1 jst ) ;ji 1 dF (! )A st+1 jst R st+1 N ;ji st for 8ji : (2) FIs’pro…t from the credit contracts with the goods-producing sectors Based on equation (2), the expected earnings of the type i bank from the FEC and FED contracts are given by XZ st+1 jst R st+1 jst Q st Kji st dji ; i =c;x ji where i s t+1 t js Z ! 1 ;ji ! (st+1 jst ) ;ji s t+1 t js dF (! ) Z ! ;ji ! dF (! ) ; for = c; x: (3) 0 Note that term associated with accounts for the ex post monitoring cost that a type i FI pays when a group ji entrepreneur in the sector declares the default. The type i FI makes a contract with a in…nite number of group ji entrepreneurs in sector , and as shown in HSU (2009), the cut-o¤ value ! ;ji that is chosen by the type i FI is identical across all entrepreneurs in sector that make contract with the type i FI: Consequently, the FI’s expected total return from both the FEC and FED contracts is given by X st+1 jst R st+1 jst Q st Ki st ; i =c;x where Ki s t Z Kji st dji ; for = c; x: ji For the convenience of analysis below, we de…ne the total amount of net worth held by the group ji entrepreneur in sector . Z t N ;i s N ;ji st dji ; for = c; x: ji 2.1.2 IF Contracts Basic setting 5 The IF contract is made between an investor and a continuum of the FIs. In period t; each type i FI holds the net worth NF;i (st ) and makes loans to group ji entrepreneurs in the sector at an amount of Q (st ) K ;i (st ) N ;i (st ) : Since the P FI’s net worth is smaller than its loans to the t t entrepreneurs in the two sectors, it borrows the rest N ;i (st )] NF;i (st ) =c;x [Q (s ) K ;i (s ) from the investor. Similarly to the FEC and FED contracts, there is informational asymmetry between the lender and the borrowers. Each type i FI faces an idiosyncratic productivity shock ! F;i (st+1 ) : This shock ! F;i (st+1 ) represents technological di¤erences across the FIs, for example, those associated with risk management, maturity mismatch control, and loan securitization5 . Incorporating this idiosyncratic shock, the FI’s receipt from the loans to the entrepreneurs is given by6 " # X ! F;i st+1 st+1 jst R st+1 jst Q st Ki st : i =c;x The investor can observe the realization of the shock only by paying the monitoring cost F : Under this credit friction, the IF contract speci…es: P t t N ;i (st )] amount of debt that a type i FI borrows from the investor, =c;x [Q (s ) K ;i (s ) NF;i (st ) ; and cut-o¤ value of idiosyncratic shock ! F;i (st+1 ) ; which we denote by ! F;i (st+1 jst ) ; such that the FI repays debt if ! F;i (st+1 ) ! F;i (st+1 jst ) and declares the default if otherwise. FIs’pro…t from the credit contracts R1 According to the IF contract, a portion of the FIs !F;i (st+1 jst ) dFF (! F ) do not default while the rest of them default. The net pro…t of a non-default FI i equals its receipt from the FEC and the FED contract multiplied by the idiosyncratic shock ! F;i (st+1 ) minus repayment to the investor: ! X ! F;i st+1 jst ! F;i st+1 st+1 jst R st+1 jst Q st Ki st : i =c;x The FIs’loan rate is therefore given by rF s t+1 js t ! F;i (st+1 jst ) P P =c;x =c;x i (st+1 jst ) R (st+1 jst ) Q (st ) Ki (st ) [Q (st ) K ;i (st ) N ;i (st )] NF;i (st ) : Investors’participation constraint There is a participation constraint for the investor in the IF contract. Given the risk-free rate of return in the economy R (st ) ; the investor’s pro…t from the investment in the loans to the banks must at least equal to the opportunity cost of lending. That is " # X t+1 t js st+1 jst R st+1 jst Q st Ki st F;i s i =c;x 5 See HSU (2010) for the alternative interpretations for ! F;i (st ) : Similarly to the entrepreneurial riskiness ! ;ji ; the FIs’riskiness ! F;i is a unit mean, lognormal random variable distributed independently over time and across FIs i. Its density function and its cumulative distribution function are given by fF (! F;i ) and FF (! F;i ) ; respectively. 6 6 R st where F;i 2.1.3 s t+1 js t " X st K Q st ;i N ;i NF;i st st =c;x Z 1 ! F;i s t+1 ! F;i (st+1 jst ) t js dFF (! F ) F Z # for 8i; st+1 jst ; ! F;i (st+1 jst ) (4) (5) ! F dFF (! F ) : 0 Optimal Credit Contract Given the structure of the FEC, FED, and IF contract, a type i FI optimally chooses capital goods purchased from capital goods producing sectors, the cut-o¤ value in the three classes of contracts, respectively. As shown in HSU (2009), since all FIs are identical in terms of i ;the expected pro…t of a type i FI is given by Z 1 ! F st+1 jst !F ! F (st+1 jst ) dFF (! F ) " X st+1 jst R =c;x st+1 jst Q s t Ki st # : (6) The FI then maximizes the term (6), subject to the investor’s participation constraint (4) and entrepreneurial participation constraints (2). 2.1.4 Dynamic Behavior of Net Worth The net worth of the FIs and the entrepreneurs in the two goods-producing sectors depend on their earnings from the credit contracts and their labor income. Both FIs and entrepreneurs inelastically supply a unit of labor to goods producers in the goods-producing sectors and receive labor income WFc (st ) ; WEc (st ) ; WFx (st ) ; and WEx (st ).7 The aggregate net worths of the FIs and the entrepreneurs are given by NF st+1 = N st+1 = t t F VF s + "NF s + V st + X WF (st ) ; t P CP I (s ) =c;x WE (st ) + "N for PCP I (st ) (7) (8) = c; x; with VF st Z 1 !F st V Z ! !F (st+1 jst ) 1 (st+1 jst ) ! ! F st+1 jst ! st+1 jst dFF (! F ) ! dF (! ) R 7 " X =c;x st+1 Q st+1 jst R st K st+1 Q st ; for st K st = c; x: See Bernanke, Gertler, and Gilchrist (1999), Christiano, Motto, Rostagno (2008) and HSU (2011a, b) for the technical background on introducing inelasitc labor supply from the FIs and the entrepreneurs. 7 # ; Here, for = F; c; and x are probabilities that each FIs or entrepreneurs survive to the next period. The FIs and the entrepreneurs who are in business in period t and fail to survive in period t + 1 consume 1 V (st ) ; respectively. The net worth accumulations in the three sectors are a¤ected by exogenous shocks represented by "N (st ) that is orthogonal to the fundamental earnings from the credit contracts. We assume these shocks are i.i.d. They are …nancial shocks that capture an “asset bubble,” “irrational exuberance,” or an “innovation in the e¢ ciency of credit contracts,”hitting the FI sector or the goods-producing sectors. 2.2 Households Set up Household h is an in…nitely-lived representative agent with preference over the non-durables consumption, C (h; st ) ; service from the stock of durables, D (h; st ) ; and work e¤ort, L (h; st ) for = c; x, as described in the expected utility function, (9) 3 2 1+v P t 1 X 6 =c;x L (h; s ) 7 t t t (9) ' U0 E0 5; 4log C c h; s D d h; s 1+v t=0 where 2 (0; 1) is the discount factor, v > 0 is the inverse of the Frisch labor-supply elasticity, and ' is the weighting assigned to leisure. The parameters 2 (0; 1) for = c; d represents relative weights on utility from consuming each goods. The budget constraint for household h is given by X st P 2 P 6 6 4 h; st + S i; st =c;x =c;x P W (h; st ) L (h; st ) W (h;st ) w =c;x W (h;st 2 1) +R (st 1 ) S (h; st 1 ) + 2 1 3 7 W (st ) L (st ) 7 5; (10) (h; st ) + (h; st ) where P (st ) denotes nominal prices of goods , S (h; st 1 ) is the saving, Rs (st ) is the nominal rate on deposit, (h; st ) is the nominal pro…t returned to the household, and (st ) is the lump-sum nominal transfer from the government. W (h; st ) is the nominal wage and W (st ) is aggregate indices of the nominal wage in sector . The second term in the right hand side of the equation stands for the nominal cost associated with adjusting nominal wage W (h; st ), and w is parameter that governs the size of the cost. Labor supply decision Household h has the monopolistic power in its di¤erentiated labor input L (h; st ) in sector . The demand of the di¤erentiated labor is given by L h; s t = W (h; st ) W (st ) W (st ) st for L where L (st ) is aggregate indices of labor input in sector L s t = Z 1 L ;t h; s t ( W (st ) 1)= W 0 8 (st ) W dh (11) = c; x; that is de…ned as (st )=( W (st ) 1) for = c; x; where W c (st ) and Wx (st ) 2 (1; 1) deliver time-varying elasticity of labor demand for di¤erentiated labor input with respect to wages. Durables accumulation The law of motion for the stock of durables is given by D h; s t = (1 d ) Dt 1 h; s t 1 + 1 2 where d 2 (0; 1) is the depreciation rate of the durables stock, and with durable stock adjustment. 2.3 2 Xt (h; st ) Xt 1 (h; st 1 ) dd 1 dd ! Xt h; st ; (12) is the parameter associated Goods Producers Set up The economy consists of two distinct sectors of production: the non-durables sector and the durables sector. We assume that both sectors contain a continuum of …rms, each producing di¤erentiated products, as indexed by l 2 [0; 1] and m 2 [0; 1] ; respectively. We use Cg (st ) to denote a gross output of composite of di¤erentiated non-durables fCg (l; st )g l2[0;1] , and Xg (st ) to denote a gross output of composite of di¤erentiated durables fXg (m; st )g m2[0;1] : The production functions of the two composites are Cg st = Z 1 Cg l; st ( Pc Xg m; s t ( (st ) 1)= Pc (st ) Pc (st )=( Pc (st ) 1) dl ; 0 Xg s t = Z 1 Px (st ) 1)= Px (st ) Px (st )=( Px (st ) 1) dm ; 0 where P c (st ) and Px (st ) 2 (1; 1) denote the time-varying elasticity of substitution between products. The composite products are produced in an aggregation sector that faces perfect competition. The demand functions for the non-durables …rm l and for the durables …rm m are derived from the optimization behavior of the aggregation sector, represented by Cg l; s t Pc (l; st ) = Pc (st ) Pc (st ) Cg s t and Xg m; s t Px (m; st ) = Px (st ) These prices are related to the prices of the non-durables fPc (l; st )g fPx (m; st )g m2[0;1] by Pc s t = Z 1 Pc l; s t (1 Pc (st )) 1=(1 Pc (st )) and Px s dl 0 t = Z Px (st ) Xg st : l2[0;1] 1 Px m; st (13) and the durables (1 Px (st )) dm : 0 Resource constraint The composites serve either as …nal goods and as intermediate production inputs. The allocation of the gross output of the non-durables is 9