Charles Engel University of Wisconsin

Transcription

1 Policy Cooperation, Incomplete Markets and Risk Sharing Charles Engel University of Wisconsin Tenth Annual Workshop on Macroeconomics of Global Interdependence, Trinity College, Dublin, 6-7 March

2 Motivation What are the obectives of monetary policymakers when they do not cooperate? How do these strategic obectives compare with cooperation? How are spillovers influenced under cooperative policymaking? There has been a lot of attention to strategic monetary policymaking recently: 2010: Guido Mantega, the Brazilian finance minister, we are in the middle of a currency war 2014: Raghuram Raan, governor of the Central Bank of India, I propose that large country central banks internalize more of the spillovers from their policies in their mandates 2

3 Targeting Rules The New Keynesian literature on optimal monetary policy has been very successful. In part because in simple cases, the optimal policy can be expressed in terms of a targeting rule. Targeting rules quantify the tradeoffs of the obectives of policymakers (inflation, output gap) In contrast to an instrument rule that, for example, expresses how the interest rate or money supply should react to the state of the economy. Targeting rules are expressed in terms of tradeoffs between deviations of actual outcomes and desired outcomes: Output gap, deviation of inflation from the target, deviation of exchange rate from PPP, etc. My obective is to derive targeting rules under non-cooperation 3

4 The Model Simplest model I could come up with: Static model 2-countries Flexible prices and wages Preferences CRRA utility over aggregate consumption Cobb-Douglas over H and F goods, with home bias Linear disutility of work Production linear in labor, with productivity shocks Competitive markets in each country, specialization Law of one price holds Isomorphic to a particular PCP sticky-price model 4

5 The Model: Home households is to maximize: 1 U = π C π N 1 1 σ. σ ( ) C = C C ν, ν > 1 ν /2 2 /2 H, F, Home firms: Y = AN Home profits: P, Y (1 τ ) WY / A H Analogous equations hold in Foreign country. 5

6 Balanced Trade vs. Complete Markets Will compare model under distortion no asset trade to undistorted case of complete markets Balanced trade is restricted case of complete markets, where there are no state-contingent payoffs Policymaker commits to policy for each state, asset markets open, then state is realized. Why look at this distortion? - Important - Simple - pricing-to-market distortion is similar (Corsetti et. al. 2012) 6

7 Equilibrium Balanced trade: PC = P C Complete markets: ZPC = ZEPC Sometimes complete markets equilibrium (with symmetric countries) is represented as: C / P = C / P σ σ PC = P C σ σ but there is missing something. We can see there is no way balanced trade is a restricted case. Also, steady states are different 7

8 Equilibrium continued We want instead that C / λp = C / λ P, σ σ where λ / λ is relative marginal utility of wealth. A key obective of strategic policy is to affect (by influencing terms of trade in every state) λ / λ We can derive ( 1 σ / C ) / ( C 1 σ λ λ ) C / Ε C P = C / Ε C P σ 1 σ σ 1 σ =Ε Ε, and write equilibrium as: Note that steady state is same as incomplete markets 8

9 Strategies What do policymakers choose? It may be natural to have Home choose τ taking τ as given Literature has Home choosing Y taking Y as given. I have it as Home choosing C taking C as given. That is, Home chooses C taking C as given. Why? - Motivated by analogy to monetary policy - Leaves obective unconstrained, which is simpler Markets then determine C H,, C F,, C, H, C, N, F, N, Y, Y. The prices that do this allocation are S, W, W. 9

10 Obectives of Home Policymaker Complete Markets: 1 1 σ Ε( C ) 1 σ ν ( [ σ( 2 ν) + 2( ν 1 )]/2( ν 1 ) σ( 2 ν) /2( ν 1) 1 ) 1 σ 1 σ Ε C C A C ( C ) 2 Ε Ε 2 ν ( /2( 1) [ σν 2( ν 1 )]/2( ν 1) ) ν ( ν ) ν ν σν ν 1 1 σ 1 σ Ε C C A Ε( C ) Ε( C ) 2 Incomplete Markets: 1 1 σ 1 Ε C Ε A C C 1 σ ν/2( ν 1 ) ( 2 ν) /2( ν 1) 2 ν /2 ν 1 2 ν /2 ν 1 /2 1 /2 1 10

11 Discussion Utility takes the form ( ) E f C E g C. More generally, when utility not linear in leisure, E f CE, gc That is, utility is not separable across states: π ( ) f C π g( C). Intuitively, choice of C affects ex ante wealth, so utility in all states. 11

12 1 st -Order Conditions σ ν 1 ( ν 2( ν 1 ))/2( ν 1 ) ( 2 ν) /2( ν 1) Balanced trade: C A C C = 2( ν 1) Complete markets: 0 ( 1 ) ( 2 ) + 2( 1) ( ν ) ν σ ν ν σ ν ν σ ν ν σ σ π C C A πic i πic i π ( 2 )/2( 1 ) ( 2 )/2( 1) 1 1 ( 2 ν) /2( ν 1) 1 ( 2 ν) /2( ν 1) 2 ν ν σ 1 σ ( 2 ν) 2( ν 1 ) /2( ν 1) 1 σ ( 2 ν) /2( ν 1) σ C πici πici 2( ν 1) 2 σ( 2 ν) + 2( ν 1) /2( ν 1 ) σ( 2 ν) /2( ν 1) 1 π i( Ci Ci Ai ) 2 ν σν σν 2ν 1 /2ν 1 σν 2ν 1 /2ν σ 1 σ π C C A πic i πic i 2 2( ν 1) ν/2( ν 1 ) ν/2( ν 1) ν 2 ν σ 1 σ ν 2( ν 1 ) /2( ν 1 ) 1 σ ν/2( ν 1) ( 1 σ) C πic i π 2( ν 1) 2 π ic i σ + π C = 0 σν 2( 1 ) /2( 1) /2 ν 1 σν ν ν π 1 i Ci Ci Ai 12

13 Discussion on Approximations Usually we want to approximate something like U C = Eu C = π u C, around a non-stochastic steady state. We only need to approximate a regular function, and then take π vc treating the π as constants. as our approximation of uc. by say vc ( ) U C. We are Here, in each state, we need to approximate something like, U C = π f C, E g C. ( ) f ( C ) E g C. That is, ( ) Does this mean we have to approximate E g C instead of ust approximating a regular function? Not really. Same principle applies. π f C, π g C π as ( i i ) and treat We are ust approximating constants. 13

14 Approximations to FOCs Incomplete markets: ( σν ν) ( ν) ( ν ) c + 2 c a = 0 Complete markets: (overbar means under complete markets) ( 2σν ( 1) 2 ν) ( 2 ν) 2( ν 1) ( σ 1)( 2 ν) 1 σ( 2ν 1) c Ec + c + c + a ( ) ( 2 )( σ ν c ) Ec σ( ν)( ν )( a Ea) = 0 14

15 Rewrite these in intuitive way Incomplete markets: ( σ 1)( 2 ν) σ y s a = 2 0 Complete markets: ( σ 1)( 2 ν) σy s a + σ 1 2 ν τ Eτ = 0 2 Discuss goods-market distortion in undistorted economy Discuss meaning of the FOC 15

16 Targeting rule ( σ 1)( 2 ν) σy s σ 1 2 ν τ Eτ = 0 2 (Another approach: derive FOC under truly undistorted economy where a tariff is used to influence the terms of trade.) The policymaker under incomplete markets wants to drive output toward the complete markets output and the terms of trade toward the complete markets terms of trade (ignoring goods market distortion term.) In a sense, nothing new here!! But the efficient output and terms of trade depend on how policy is set under complete markets. E.g., how do we measure output gap? 16

17 Under Cooperation For any variable x, define FOCs under incomplete markets R x = ( x x )/2 and 2 σν 1 c R + ν 2 ν c R ν 1 a R = 0 W x = ( x+ x )/2. σ c a = W W 0 FOCs under complete markets R R W W σc ν 1 a = 0 and σ c a = 0 Targeting rules R ( σ 1)( ν 1) ν( 2 ν) σ y + m = 0 and y W = 0 2 where m ln ( M ) =, with M C / P C / P = C C S σ σ σ σ ν 1 17

18 Equilibrium and Spillovers Under cooperation (and complete markets) we find: ν 1 c = a = ba σ R R C R Under non-cooperation (and complete markets) we find: ( ν 1) 1+ ( σ 1)( 2 ν) σ 1+ ( σ 1) ν( 2 ν) c = a = b a R R N R Spillovers are smaller under non-cooperation. Why? Relative consumption responds to terms of trade, but under non-cooperation, policymakers reduce fluctuations in terms of trade. Analysis is the same under incomplete markets. 18

19 Next Steps Get a better characterization of targeting rule Write out the loss function Try different strategies Other forms of market incompleteness (trade in equities, e.g.) Price stickiness Dynamic model! 19