Monetary Policy: Rules versus discretion.. Huw David Dixon. March 17, 2008
1 Introduction Current view of monetary policy: NNS consensus. Basic ideas: Determinacy: monetary policy should be designed so as to provide a determinate solution. Eliminate extrinisic uncertainty. No sunspots etc. (no of unstable roots equals the number of forward looking variables). Commitment: discretion vs commitment. How to commit. Taylor rules.
2 Basic model. De ne x t = y t yt f. The output gap relative to the ex price output. We have two basic equations x t = E t x t+1 (i t E t t+1 ) + g t t = E t t+1 + x t + e t g t = preference/demand shock (U c is stochastic): g t = g t 1 + ^g t u t = in ation or cost shock (productivity shock...).u t = u t 1 + ^u t Objective function for government (see Walsh Chapter 11, appendix). E t 1 X i=1 i V 1 2 E t 1X i=1 i h 2 t+i + (x t+i x ) 2i
Woodford: this is a quadratic approximation. increases price dispersion (sticky prices). In ation is bad because it x > 0. The initial ex-price equilibrium is too low (imperfect competition). Some argue that should set it at 0 by tax policy (Dixit and Lambertini). Monetary policy: CB sets interest rate, money supply accommodates to hit rate.
3 Optimal Policy without commitment. "Discretion". The CB chooses i t each period to maximize utility from t onwards. Treats expectations as given. E ectively, chooses ( t ; x t ) to satisfy NKP C and given that i t to satisfy Euler and choice of ( t ; x t ). Period by period, solve max - 1 2 h x 2 t + 2 t i + Future Subject to t = x t + " future E t t+1 # + u t Solution x t = t
Lean into the wind: if in ation higher, output lower. Substitute constraint into objective function: FOC: 1 2 2 ( t E t t+1 u t ) 2 t + 2 t 2 ( t E t t+1 ) + t = 0 x t + t = 0 x t = t If private sector has RE : put optimal solution into NKP C and solve for
RE using undetermined coe cients: x t = qu t t = qu t E t t+1 = qu t where q = h 2 + (1 ) i 1 Put into Euler (IS) equation i t = E t t+1 + 1 g t (1 ) = 1 + Note: cost push makes the model interesting: if u t = 0 for all t, x t = t = 0, and interest rate exactly o sets any demand shock g t :
If u > 0, then there is a trade-o between the variance of output and the variance of in ation. if u > 0, optimal discretionary policy involves gradual convergence to target in ation. Lim E t t+i = E t t+1 Lim i!1 i!1 i = 0 can hit target t = 0; but not optimal unless = 0. Taylor Principle: > 1. If expected in ation rises, nominal interest rate rises by more (real interest rate rises). Interest rate o sets demand shocks 1 g t : g causes x and to move in the same direction, so no con ict. If g > 0, rising interest rates reduces both x and. "Demand management": in this model, perfect demand management is possible using interest rates.
u t : a rise in u t causes a rise in, but a fall in x: there is a trade-o - to cut in ation you need to move the output gap further away from target. In this model, so long as > 1, there is a dete3rminate solution. Automatically avoids "extrinsic uncertainty" problem. 4 Commitment. Two ways it can work: reducing or eliminating the in ationary bias; improving the trade-o between the variances of output and in ation (shifting the e cient frontier).
4.1 In ationary bias. Choose policy ex ante. Must do better: can always choose the discretionary policy, but have lots of others to choose from! In ationary bias. Suppose that the target output gap is x > 0 : optimal rule becomes x t = x The rational expectations solution is x t = qu t t t = qu t + x By trying to hit higher target, you fail but end up with more in ation. This is because agents have RE and they anticipate in ation. The only output consistent with RE is x = 0.
Delegate to as conservative central banker: B <, reduces in ationary bias. If there is only one output level consistent with fully anticipated in ation (the natural rate) then trying to target a higher output does not work and under RE will lead to in ationary bias. Delegation can overcome this. 4.2 E ciency gain from commitment. Even with no in ationary bias, can get a better policy through commitment. The monetary policy ties down expectations, and so can improve
the output/in ation short-run trade-o t = x t + " future E t t+1 # + u t the Bank can choose! where x c t =!u t Discretionary! d = q: Can choose this, or do even better... Under commitment, start from NKP C c t = x c t + E t c t+1 + u t solving forward to eliminate E t c t+1 c t = E t 1 X i=0 i h x c t+i + u t+i i
since x c t =!u t c t = E t 1 X i=0 i [u t+i (1!)] = (1!) = 1! 1 u t 1X i=0 i i u t Hence higher! means expectations come down E t c t+i = 1! 1 i u t
Hence 1 2 2 4 (!u t ) 2 + 1! 1 u t! 2 3 5 FOC with respect to!!u 2 t (1 )! 1! 1 u2 t = 0 re-arranging and using x c t =!u t and c t = 1! 1 u t x c t = x c t = (1 ) c t (1 ) c t Hence with commitment, the optimal policy is to be more aggressive against in ation than with discretion. This drives down in ationary
expectations. can manage expectations: makes the (short-run) in ation-output trade o better, so can improve welfare. Moves in "e ciency frontier" in ( ; x ) space. the commitment solution mimics the discretionary case with a lower a c (1 ). optimal Taylor rule i c t = c E t t+1 + 1 g t c = (1 ) 1 + ( (1 )) The coe cient c is bigger than in the discretionary case.
What if you have "unconstrained commitment", i.e. can have any function: gets into a mess! 5 Interest Rate or money supply? With certainty, no di erence. Choosing price or quantity simply picks out a point on the demand curve. With uncertainty Choose price i then quantity m uctuates.
Choose money supply m; then i uctuates. Poole (1970). Choosing interest rates probably best: i varies causes y to vary through Euler/IS equation. US, Volcker 1979-1982: monetarist experiment, abandoned because it caused very large uctuations in i. 6 Taylor Rules. Taylor (1993). Proposed simple rule of the following form i T t = r + + ( t ) + x x t
where > 1, x > 0; r =long-run real interest rate; = target in ation rate. Can estimate it: US data use i t = i t 1 + (1 ) i T t to capture serial correlation... Pre-Volcker (pre-1979) = 0:83; x = 0:27; = 0:68: Volcker-Greenspan: = 2:15; x ' 0; = 0:79: Note: this is not a structural equation: all variables are endogenous. To estimate the underlying monetary policy rule, would need to estimate structurally identi ed model.
Macroeconomic Analysis Topic 2. Module Code: 3565 Huw Dixon 20 28/01/08
Macroeconomic Analysis Topic 2. Module Code: 3565 Huw Dixon 21 28/01/08
Other rules: nominal national income, the price-level, speci c price index, asset prices (stock market, housing). 7 General comments. Private sector behaviour is in uenced by monetary policy: Monetary policy is a ected by private sector behaviour. Lucas critique: changes in monetary policy may induce changes in private sector behaviour.
Example: higher in ation implies less nominal rigidity. Less nominal rigidity implies a bigger e ect of x t on in ation. So, the short-run trade-o between in ation and output worsens. Empirical features of the economy will vary with di erent policy regimes: e.g.compare the 1970s with post 1980 (the great moderation since 1990). Output has become very stable in big economies in 90s, despite some big shocks (dot com bubble, oil prices, war etc.). Due to in ation targeting and central bank independence? many empirical and theoretical issues to pursue.