Optimal discretionary policy

Transcription

1 Advanced Monetary Theory and Policy EPOS 2012/13 Optimal discretionary policy Giovanni Di Bartolomeo

2 New Keynesian approach Most economists believe that short-run fluctuations in output and employment represent deviations from the natural rate, and that these deviations occur because wages and prices are sticky. New Keynesian research attempts to explain the stickiness of wages and prices by examining the microeconomics of price adjustment. 2

3 The New Keynesian approach 3 It starts from the RBC approach (taking its methodology) Additions Imperfect markets (e.g. imperfect competition) Price/Wage nominal rigidities Small menu cost Adjustment cost on other cost variables (quality) Nominal contracts Implicit contracts Price/quality relationship effect Price effects (9.99 ) Main implication money counts (in the short run), fluctuations are not efficient

4 4 Empirical evidence

5 Coordination problems An example Firm 1 cuts price Firm 1 does not cut price Firm 2 cuts price Profit(1) 30 Profit(2) 30 Profit(1) 15 Profit(2) 5 Firm 2 does not cut price Profit(1) 5 Profit(2) 15 Profit(1) 15 Profit(2) 15

6 Coordination problems An example Firm 1 cuts price Firm 1 does not cut price Firm 2 cuts price First best Profit(1) 30 Profit(2) 30 Profit(1) 15 Profit(2) 5 Firm 2 does not cut price Profit(1) 5 Profit(2) 15 Profit(1) 15 Profit(2) 15

7 Coordination problems A firm cuts its price only if the other will do (otherwise it is not convenient). Thus no one cuts price and they remain trapped in an inefficient equilibrium. Firm 1 cuts price Firm 1 does not cut price Firm 2 cuts price Profit(1) 30 Profit(2) 30 Profit(1) 15 Profit(2) 5 Firm 2 does not cut price Profit(1) 5 Profit(2) 15 Profit(1) 15 Profit(2) 15 7

8 A simple New Keynesian model The model (IS curve, Forward Phillips curve) x = - s (i - p e ) + x e + e D p = b p e + g x + e S x = C - C N = output/consumption gap w.r.t natural, e D e e S demand and supply shock. Note that I=0, G=0, C=Y In the long run e D = e S, x e = p e = 0, thus x = p = i = 0 (C = C N, Y = Y N )

9 How does it work? The model x = - s (i - p e ) + x e + e D p = b p e + g x + e S A change (increase) in i reduces the output (shifting the IS), the output change has a negative effect on the inflation rate (Phillips curve) Summarizing: i x p (or i x p)

10 Inefficiency Recall that that x = C - C N is not efficient. Under monopolistic competition, price are set as a markup on the marginal cost P=(1+m)CMA, but efficiency requires m=0. Monopolistic competition (Y N ) P>CMA=RMA Perfect competition (Y P ) P=CMA=RMA The output under monopolistic competition is thus too low (and price too high). 10

11 Phillips curve in the long run inflation Long run Phillips curve p = b p e + g x O output gap Recall that, in the long run (Friedman), p e is zero and there are no shocks

12 Supply shock Phillips curve after the supply shock p = b p e + g x + e S inflation Long run Phillips curve p = b p e + g x B C D Supply shock O output gap For the sake of simplicity we assume that p e is zero in the short run (true under some conditions, i.e. no shock persistence), thus the curve shift is exactly e S

13 Policy options after the shock Phillips curve after the supply shock p = b p e + g x + e S inflation E 1) Do nothing p=e D e x=0 B C Policy options D A O output gap 2) Fix i so that x is A and p is C 3) Fix i iso that x is D IS: x = - s (i - p e ) + x e

14 Central bank preferences inflation Central bank preferences O 1 2 output gap 3

15 Alternative preferences a = 1 a > 1 a < 1 Period loss: L = - (p) 2 - a(x) 2

16 Policy options and welfare inflation E B D O 2 output gap 3

17 Optimal choice inflation Optimality B C D A O output gap IS: x = - s (i - p e ) + x e

18 Optimal policy rule Policy rule: the central bank optimal reaction to the shocks Policy rule p = -a/gx inflation Positive shock Negative shock O output gap

19 Optimal policy and optimal rule Phillips curve after the supply shock p = b p e + g x + e S Policy rule p = -a/gx inflation Long run Phillips curve p = b p e + g x B C A O 2 output gap IS: x = - s (i - p e ) + x e

20 Demand shock What does the central bank implement if there is a demand shock (e D )? x = - s (i - p e ) + x e + e D p = b p e + g x Try i = e D /s, what does it occur? x = p e + x e p = b p e + g x Solution x = x e = p = p e = 0!! Shock is fully stabilized. 20

21 Transmission and policy: A summary The model x = - s (i - p e ) + x e + e D p = b p e + g x + e S In the short run ( Di sdx sgdp) e D x e p e S p Monetary policy e D x ( p) i x ( p) e S p i x p stabilization trade-off 21

22 Discretionary policy: A formal derivation The central bank minimize L = - (p) 2 - a(x) 2 - Future (taken as given) wrt i subject to x = - s (i - p e ) + x e + e D p = b p e + g x + e S However, note that the transmission mechanism implies i x IS x p AS (Phillips) Solve the problem in two steps 1.Find x that given the AS (i.e. p=f(x)) mimimizes the loss 2.Find the i by the IS that implement the optimal x.

23 The two steps problem; Step 1 The central bank minimize L = - (p) 2 - a(x) 2 - Future (taken as given) wrt x subject to p = b p e + g x + e S p e =0 As result we find (optimal policy) p = -a/g x That together with the Phillips curve yields -a/g x = g x + e S x = - g/(a+g 2 ) e S < 0 p = a/(a+g 2 ) e S > 0 Now we use x = - g/(a+g 2 ) e S in the IS and find the policy implementing it

24 Given The two steps problem; Step 2 x = - g/(a+g 2 ) e S < 0 p = a/(a+g 2 ) e S > 0 Take the IS x = - s (i - p e ) + x e + e D Recall that p e = x e = 0, and use there x = - (g +a/g) -1 e S to find the policy that implements it. It follows - g/(a+g 2 ) e S = - s (i) + e D Optimal policy is i = g/s(a+g 2 ) e S + e D /s

25 Monetary policy Macroeconomic policies It is able to stabilize (at lest partially) shocks in the short run Long run neutrality, it is not able to reduce the gap between potential and natural output Fiscal policy Low efficacy = small multipliers (even less than one) Crowding out effects Barro-Ricardo equivalence 25

26 AD/AS model In the long run we assume Po=0, after changes in P, it implies that the new P is the inflation rate (p=p Po) P LRAS SRAS P 0 AD Y 26

27 Demand shock (e D ) P LRAS SRAS P S P 0 YS The demand is shifted By the shock AD S AD Y 7

28 Demand shock: Optimal policy The central bank implements a restrictive monetary policy, moving the demand back to the initial position. P LRAS SRAS P S P = P 1 0 E YS AD S Y AD=AD 1 28

29 Supply shock (e S ) P LRAS SRAS S SRAS P S The supply is shifted by the shock P 0 YS AD Y 29

30 Supply shock: Optimal policy The central bank faces a trade off between inflation and output and moves along it until point E. P LRAS SRAS S SRAS P S E P 0 YS AD 1 AD Y 0

31 (Optimal) Taylor rule Remember that the IS curve is x = - s (i - p e ) + x e + e D i.e. (as x e = p e = 0) Policy optimality requires p = -a/g x i = - x/s + e D /s i.e., x = -g/a p Combining the two relationships above, we obtain i = g/(as) p + e D /s We have obtained a sort of Taylor rule, which describe how (optimal) monetary policy is managed.