The trade off between central bank independence and conservativeness.(Special Issue on the Economics of Central Bank Independence)

1. Introduction

This paper deals with the following fundamental question. It tries to explain the optimal degree of central bank independence and conservativeness by four economic and political determinants (the natural rate of unemployment, society's preferences for unemployment stabilization relative to inflation stabilization, the variance of productivity shocks and the benefits of unanticipated inflation) both theoretically and empirically. The empirical results are only given for the (12) member states of the European Union.(1)

The paper is organized as follows. Central bank independence is included in the model of a conservative central banker and the trade off between independence and conservativeness is discussed in Section 2. In this Section, also the relationship between (independence and) conservativeness of the central banks and the four economic and political determinants is investigated with an extension of the Rogoff (1985) model. Furthermore, we test this relationship empirically using a latent variables approach (LISREL) for 19 industrial countries including the member states of the European Union in Section 3. Also, the optimal degree of conservativeness of the central banks is identified for 12 member states of the European Union. Finally, our conclusions are drawn in Section 4.

2. The Rogoff (1985) model

In the Rogoff (1985) model, society can make itself better off by appointing a conservative central banker who does not share the social objective function, but instead places too large a weight on inflation rate stabilization relative to output stabilization. In this simplified version, output is given by the Lucas supply function which is reformulated in terms of unemployment [u.sub.t]

[Mathematical Expression Omitted] (1)

where [Theta] [greater than] 0 denotes the slope of the Phillips curve, [[Pi].sub.t] is inflation, [[Pi].sup.e] is expected inflation, [Mathematical Expression Omitted] is the natural rate of unemployment, and [[Mu].sub.t] is a serially uncorrelated productivity shock with mean zero and variance [Mathematical Expression Omitted]. The timing of events is as follows: first [[Pi].sup.e] is set (nominal wage contracts are signed), then the shock [[Mu].sub.t] occurs and finally the central banker sets [[Pi].sub.t].

Society's loss function is given by

[Mathematical Expression Omitted] (2)

where the weight on output stabilization [Chi] [greater than] 0. The target level of inflation and the target level of unemployment are set to zero. Rogoff now shows that it is optimal for society to choose a conservative central banker who assigns too large a weight to inflation in his loss function

[Mathematical Expression Omitted] (3)

where [Epsilon], the additional weight on the inflation goal, lies between zero and infinity (0 [less than] [Epsilon] [less than] [infinity]).

Substituting (1) in (3), taking first order conditions with respect to [[Pi].sub.t] and solving for rational expectations, we obtain

[Mathematical Expression Omitted] (4)

[Mathematical Expression Omitted] (5)

[Mathematical Expression Omitted] (6)

Policy rule (4) shows that the introduction of a conservative central banker ([Epsilon] [greater than] 0) leads to a lower inflationary bias

[Mathematical Expression Omitted]

and a lower variance of inflation

[Mathematical Expression Omitted].

The variance of output

[Mathematical Expression Omitted],

however, is an increasing function of the conservativeness of the central banker. This is the trade off between credibility and flexibility that is already apparent in the Rogoff model. It can be shown that the optimal value for, in terms of social loss function (2), is positive but finite.(2) This implies that it is optimal for society to appoint a conservative central banker.

2.1 From conservativeness to independence

The independence of a central bank can be seen as the extent to which it determines monetary policy without interference of the government. In the Rogoff model, this can be incorporated in the loss function that determines monetary policy, [M.sub.t]. This function is a weighted average of the central bank's loss function [I.sub.t] and society's loss function Lt where the weight 0 [less than] [Gamma] [less than] 1 is the degree of central bank independence(3)

[M.sub.t] = [Gamma][I.sub.t] + (1 - [Gamma])[L.sub.t] (7)

Substituting society's loss function (2) and central bank's loss function (3) into (7) gives

[Mathematical Expression Omitted] (8)

So, what matters for monetary policy is [Gamma][Epsilon]: the product of independence and conservativeness of the central bank. There is an optimal degree of independence and conservativeness ([Gamma][[Epsilon].sup.*]) which minimizes society's loss [L.sub.t]. In practice, the degree of (legal) independence of a central bank is fixed as measured by the legal indices of independence which reflect the central bank laws in various countries. The level of conservativeness, however, can generally be chosen by the central bank. Hence, a lack of central bank independence can be compensated by choosing more conservative central bankers. On the basis of economic and political determinants, we determine the optimal degree of independence …