Welfare-Enhancing Distributional E¤ects of Central Bank Asset Purchases Andreas Schabert University of Cologne November, 2017
2 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION
3 INTRODUCTION Central bank asset purchases � Should central banks (CBs) intervene in secondary markets for private debt securities? – Large scale purchases of debt securities were added into the CB instrument set – Several studies report gains of unconventional policies in times of …nancial stress � Recent experiences with asset purchases suggest measurable asset price e¤ects – Asset purchase reduced yields on long-term treasuries (De Fiore et al., 2016) – MBS purchases reduced yields and mortgage rates (Hancock and Passmore, 2014)
4 INTRODUCTION Redistributive e¤ects of asset purchases � Is there a useful role for asset purchases (AP) even in tranquil times and o¤ the ZLB? – Even if they are non-neutral, they might be equivalent to conventional policies � This paper – AP drive a wedge between the e¤ective rates for lenders and borrowers – Not possible by conventional instruments (interest rates or in‡ation target) – They can induce a redistribution of funds from lenders to borrowers
5 INTRODUCTION Welfare enhancing role of asset purchases � CB purchases of assets distort market prices and might raise or lower e¢ciency – Even if borrowers are constrained, redistribution can reduce social welfare � Novel insights – Financial constraint induces constrained ine¢ciency due to externalities – AP can serve as a Pigouvian subsidy and enhance welfare even further – State contingent asset purchases should be countercyclical
6 INTRODUCTION The framework � Endowment economy with idiosyncratic shocks and limited contract enforcement – Positive feedback loop between collateral demand, prices, and borrowing capacity � Fiat money as a medium of exchange – Fully backed by eligible assets (treasuries or collateralized debt ) – Conventional monetary policy is neutral
7 INTRODUCTION Related literature � Bene…cial unconventional monetary policies under stressed …nancial markets – Curdia and Woodford (2011), Gertler and Karadi (2011), Chen et al. (2012), Del Negro et al. (2016), Woodford (2016) and others � Redistributive e¤ects of conventional monetary policy – Akyol (2004), Berentsen et al., (2005), Algan and Ragot (2010), Lippi et al. (2015), Auclert (2016), Garriga et al. (2016) and others � Constrained ine¢ciency under pecuniary externalities and …nancial constraints – Lorenzoni (2008), Bianchi (2011), Stein (2012), Bianchi and Mendoza (2017), Jeanne and Korinek (2016), Davila and Korinek (2017) and others
8 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION
9 THE MODEL Overview � Households face idiosyncratic shocks, hold treasuries, money, and durables (housing) – They rely on …at money for purchases of non-durables – They can get money from the CB against eligible assets (treasuries) � A household with a relatively high valuation of non-durables – can borrow intraperiod from other households against collateral (durables) � Central bank buys treasuries and can further purchase collateralized debt – Treasury issues short-term debt in an ad-hoc way
10 THE MODEL Timing Beginning of the period – Aggregate shocks are realized – Money is supplied against treasuries – Idiosyncratic preference shocks are realized – Loans are originated and might be purchased by the central bank – Household members purchase goods with …at money – Loans are repaid, repos are settled, and assets are traded End of the period
11 THE MODEL Households I/III � In…nitely lived households i 2 [0 ; 1] with identical initial wealth and endowment – Utility depends on consumption c i;t and housing h i;t u i;t = u ( � i ; c i;t ; h i;t ) – i.i.d. preference shocks � i 2 f � b , � l g with equal probabilities and � l < � b � They can get money 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 where B i;t � 1 denotes treasuries and � B t the fraction of purchased treasuries.
12 THE MODEL Households II/III � Agents drawing � b borrow, � L i;t > 0 , at the loan rate R L t against collateral � L i;t � z t P t q t h i;t ; where z t 2 (0 ; 1) is a liquidation value, q t the housing price, and P t the price level. � CB might o¤er purchases of a fraction � t of secured loans L l;t = � L b;t I L l;t � � t � L l;t =R m t : Lenders are willing to sell secured loans for above market prices R m t � R L t � Households rely on money for purchases of consumption goods (for b and l ) P t c i;t � I i;t + I L i;t + M H i;t � 1 � L i;t =R L t :
13 THE MODEL Households III/III � Households maximize welfare taking all constraints into account – Borrowers’ loan demand satis…es (with the collateral constraint multiplier � i;t ) h i u 0 ( � i ; c i;t +1 ) =� t +1 E t � i;t 1 = � + R L u 0 ( � i ; c i;t ) u 0 ( � i ; c i;t ) t – Lenders’ loan supply satis…es h i u 0 ( � i ; c i;t +1 ) =� t +1 E t 1 1 � � t = � � R L 1 � � t R L t =R m u 0 ( � i ; c i;t ) t t 1 � � t exceeds one for R m t < R L � The wedge t and a positive fraction � t > 0 1 � � t R L t =R m t – It increases with a larger fraction � t and a larger price discount R L t =R m t .
14 THE MODEL Monetary policy � The central bank sets the price of money in terms of eligible assets R m t � 1 – decides how many assets are purchased � t 2 [0 ; 1] and � B t 2 (0 ; 1] – supplies money outright and temporarily, M R t = � t M H t , – and transfers its interest earnings leading to the balance sheet B c t = M H t : � CB can control both prices and money supply under money rationing (Schabert, 2015) R m t < R L t
15 THE MODEL Government � The government issues bonds and has access to lump-sum taxes/transfers � t – Supply of short-term government bonds is speci…ed in an ad-hoc way ( � > � ): B T t = � B T t � 1 – This policy does not support the implementation of …rst best, which satis…es u c ( � b ; c � b;t ) = u c ( � l ; c � l;t ) ; and h � b;t = h � l;t :
16 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION
17 WELFARE ENHANCING ASSET PURCHASES Simplifying assumptions � Assumptions 1. Instantaneous utility of households satis…es u ( � i ; c i;t ; h i;t ) = � i ( �c i;t � (1 = 2) c 2 i;t ) + ( �h i;t � (1 = 2) h 2 i;t ) , where @u=@c i;t = u 0 ( � i ; c i;t ) > 0 and @u=@h i;t = u 0 ( h i;t ) > 0 . 2. Agents will hold money equal to the amount of planned nominal consumption expenditures even when the multiplier on the cash-in-advance constraint equals zero. 3. The ratio ( � b � � l ) =z is su¢ciently large such that the borrowing constraint is binding for all agents drawing � b .
18 WELFARE ENHANCING ASSET PURCHASES Aggregation � Under Assumptions 1-3, a competitive equilibrium in terms of a representative bor- rower and a representative lender under a conventional monetary policy regime is a set of sequences f c b;t ; c l;t ; h b;t , q t , � t g 1 t =0 satisfying h n oi R L u c l ;t = �E t 0 : 5( u c l ;t +1 + u c b ;t +1 ) � t =� t +1 ; n o n o R L R L � (2 h b;t � h ) =z = u c b ;t � �E t [0 : 5( u c l ;t +1 + u c b ;t +1 ) � ] ; t =q t t =� t +1 n o n o q t =R L q t +1 =R L u c l ;t = u h l + �E t [ u c l ;t +1 � ] ; t t +1 n o q t =R L c b;t � c l;t = zh b;t 2 � ; t y t = c b;t + c l;t ; and R L t = R m t , for f y t g 1 t =0 and a sequence f R m t � 1 g 1 t =0 set by the central bank.
19 WELFARE ENHANCING ASSET PURCHASES Neutrality of conventional monetary policy � Under a binding borrowing constraint consumption and housing satis…es � � � b;t = [ u c b ;t � u c l ;t ] =R L t = 2 h b;t � h = ( zq t ) > 0 ; (1) Corollary 2 Under a conventional monetary policy regime, changes in the monetary policy rate do not a¤ect the equilibrium allocation, while the housing price and the in‡ation rate increase with the nominal interest rate .
20 WELFARE ENHANCING ASSET PURCHASES A pecuniary externality � When there is no aggregate risk, the relative price of collateral q=R L satis…es u h l ( h � h b ) q R L = (1 � � ) u c l ( y � c b ) – The relative price is increasing (decreasing) in borrowers’ housing (consumption). – A Pigouvian tax/subsidy on debt issuance can address the externality R L t =� t +1 1 � � L t Proposition 1 The implementation of a constrained e¢cient allocation of the rep- resentative agents economy without aggregate risk requires a subsidy on borrowing, � L < 0 , if but not only if z= (1 � � ) � 1 . Compared to the laissez-faire case ( � L = 0 ), the Pigouvian subsidy raises borrowers’ consumption and housing as well as the real interest rate R L =� , which is associated with a decline in lenders’ con- sumption and housing .
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