Optimal monetary policy, asset purchases, and credit market - PowerPoint PPT Presentation

Optimal monetary policy, asset purchases, and credit market frictions Andreas Schabert, University of Cologne June, 2014

2 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

3 INTRODUCTION This paper � How do …nancial market frictions matter for the conduct of monetary policy? – Trade-o¤ of a welfare maximizing central bank (CB) � Is there a role for central bank purchases (not creation) of loans? – A CB asset exchange is typically irrelevant � Main idea – CB asset purchases can matter when money supply is rationed

4 INTRODUCTION The model � A sticky price model where money is essential and private agents borrow/lend – To facilitate aggregation, we consider ex-ante identical agents (Shi, 1997) � Household members draw preference shocks – High valuation of consumption ! borrowing money from other members � Financial market friction – Private debt contracts are not perfectly enforceable – Loans secured by pledgeable assets (Kiyotaki and Moore, 1997)

5 INTRODUCTION Monetary policy � Central bank supplies money against eligible assets – Money supply is fully backed (e.g. by treasury securities) – Central bank sets the price of money in terms of eligible assets � When the policy rate equals the marginal valuation of money – Conventional regime where asset purchases are irrelevant � When the policy rate is set below marginal valuation of money – Eligible asset are scare and quantitative instruments can matter

6 INTRODUCTION Results � Positive in‡ation rates are not desirable – Intraperiod loans: real debt burden cannot be reduced by higher in‡ation – In‡ation raises the loan rate and ampli…es the credit market friction � Optimal monetary policy (without money rationing) – Under sticky prices: central bank mainly aims at stabilizing prices – When prices are more ‡exible, monetary policy eases the borrowing constraint � CB can enhance welfare by purchasing asset at a favorable price

7 INTRODUCTION Related studies � Studies on optimal monetary policy under …nancial market frictions – Monacelli (2008): household borrowing constrained by collateral – De Fiore et al. (2011): optimal monetary policy under imperfect monitoring � Studies on unconventional monetary policies – Curdia and Woodford (2011): direct central bank lending under costly banking – Gertler and Kiyotaki (2011): balance sheet constraint of …nancial intermediaries – Araújo et al. (2013): asset purchases without a speci…c role of currency

8 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

9 THE MODEL Timing Beginning of the period: Household members hold money, gov. bonds, and housing – Aggregate productivity shocks are realized – Money supplied against treasuries at policy rate – Idiosyncratic preference shocks are realized – Loans are originated and might be purchased by the central bank – Household members buy goods from …rms with money as means of payment – Borrowers repay loans and government bonds are issued End of the period

10 THE MODEL Households I/IV � In…nitely many households of measure one, each with members i 2 [0 ; 1] – household wealth equally distributed at the beginning of each period (Shi, 1997) – Utility depends on consumption c i;t , housing h i;t , labor n i;t h 1 � � h n 1+ � c 1 � � � 1 � 1 i;t i;t i;t u ( � i;t ; c i;t ; h i;t ; n i;t ) = � i;t + � � � 1 + �; 1 � � 1 � � h – i.i.d. shocks � i 2 f � b , � l g with equal probabilities and � l < � b � End-of-period stock of housing h i;t might di¤er between both types of members – Supply of housing is …xed at h

11 THE MODEL Households II/IV � Money injections I i;t against eligible assets discounted with the policy rate R m t I i;t � � B t � B i;t � 1 =R m t ; (1) � Drawing � b implies b orrowing, partially constrained by collateral � L b;t � z t P t q t h b;t ; where L b;t < 0 (2) where z t is the liquidation value and q t the real price of the housing good. � Lenders can re…nance secured loans L l;t = � L b;t at the CB I L l;t � � t � L l;t =R m (3) t

12 THE MODEL Households III/IV � Households rely on money for purchases of consumption goods h i I l;t + I L l;t + M H (1 + � ) L l;t + L r =R L P t c l;t � l;t � 1 � t l;t h i I b;t + M H (1 + � ) L b;t + L r =R L P t c b;t � b;t � 1 � t b;t – Loans funded by proceeds of CB purchases L r l;t = � L r b;t � L r l;t =R L t – Unsecured loans �L l;t and re…nanced loans L r l;t are not pledgeable � Lenders are willing to sell all secured loans to the CB if R m t < R L t – Money supply constraint (1) and (3) are then binding (money rationing)

13 THE MODEL Households IV/IV � Maximizing E P 1 t =0 � t u i;t s.t. money, goods, and asset market constraints – Borrower’s credit demand is a¤ected by the borrowing constraint ( � b;t � 0 ) 0 : 5( � b c � � b;t +1 + � l c � � l;t +1 ) � b;t 1 = �E t + ; � b c � � � b c � � R L b;t � t +1 b;t (1 + � ) t – Lender’s credit supply a¤ected by possible CB loan purchases " !# 0 : 5( � b c � � b;t +1 + � l c � � l;t +1 ) R L 1 � t t = �E t 1 + � 1 ; � l c � � R m R L 1 + � l;t � t +1 t t – � b;t = 0 and R m t = R L t lead to a standard consumption Euler equations.

14 THE MODEL Firms � Typical New Keynesian set-up – Identical intermediate goods producing …rms produces with labor and receive a constant subsidy that eliminates average mark-ups – Monopolistically competitive retailers buy intermediate goods and set prices like according to Calvo/Yun � Price dispersion leads to short-run and long-run ine¢ciency – Minimized by price stability

15 THE MODEL Central bank � Central bank supplies money outright and temporarily, – sets the price of money in terms of eligible assets R m t � 1 – decides how many assets are purchased/repoed � t 2 [0 ; 1] and � B t 2 (0 ; 1] – and transfers its interest earnings to the treasury � � � � P t � m t = (1 � 1 =R t ) B c t + R m M H � M H + ( R m M L t + M R t � 1) ; t t t � 1 t leading to the end-of-period balance sheet B c t = M H t :

16 THE MODEL Government � Government issues one-period bonds, pays a subsidy at a constant rate, and – has access to lump-sum taxes/transfers � t ( B T t =R t ) + P t � m t = B T t � 1 + P t � t + P t � p : � Supply of short-term government bonds is speci…ed in a simple way, B T t = � B T t � 1 where � > � and bond market clearing requires B T t = B t + B c t .

17 THE MODEL First best allocation Proposition 1: The …rst best allocation f c � b;t ; c � l;t ; n � b;t ; n � l;t , h � b;t ; h � l;t g 1 t =0 satis…es � b;t ( c � b;t ) � � � l;t ( c � l;t ) � � , = n � n � = l;t ; b;t h � h � = l;t ; b;t b;t ) � � = [ �= ( a t � )]0 : 5 � ( n � � b ( c � t ) 1+ � � � ; h � b;t + h � l;t = h and c � l;t + c � b;t = a t ( n � t ) � . � Competitive equilibrium – Three frictions: borrowing constraint, cash vs. credit goods, and sticky prices

18 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

19 CONSTRAINED BORROWING AND MONETARY POLICY Long-run properties � Suppose that money supply is not rationed ( R m = R L ) – loan rate equals lender’s marginal rate of intertemporal substitution � =c � � � R L = ( �=� ) � � l c � � l where c � � = 0 : 5 � l c � � + 0 : 5 � b c � � : l b – If the borrowing constraint is slack, � b;t = 0 , relative consumption satis…es � l c � � = � b c � � l b – If borrowing is constrained � b;t > 0 , relative consumption of the lender satis…es c l > ( � l =� b ) 1 =� c b ! Tighter borrowing constraints lead to lower loan rates

20 CONSTRAINED BORROWING AND MONETARY POLICY 1.025 0.303 0.175 z= 0.8 1.02 z= 0.4 0.302 0.1745 F r ictionles s 1.015 0.301 0.174 1.01 1.005 0.3 0.1735 1 0.299 0.173 0.995 0.99 0.298 0.1725 0.99 0.995 1 1.005 1.01 0.99 0.995 1 1.005 1.01 0.99 0.995 1 1.005 1.01 0.64 0.326 0.62 0.3255 -3.12 0.6 0.325 -3.125 0.58 0.3245 0.56 0.324 -3.13 0.54 0.3235 -3.135 0.52 0.323 -3.14 0.5 0.3225 0.99 0.995 1 1.005 1.01 0.99 0.995 1 1.005 1.01 0.99 0.995 1 1.005 1.01 Steady state values for di¤erent in‡ation rates

21 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

22 OPTIMAL POLICY AND ASSET PURCHASES Flexible prices Proposition 2: A long-run e¢cient allocation can, in general, neither be imple- mented under rationed money supply nor under non-rationed money supply. � E¢ciency would require the Friedman rule and a slack borrowing constraint – Under R L = 1 , borrowing constraint will in general be binding – Money cannot be supplied in a rationed way, since R m � R L = 1 � Under second best with ( R L > 1 ) – Money rationing ( R m < R L ) and purchasing loans can enhance welfare