Making the central bank more conservative
The parameter (5g is the weight that the central bank places on inflation. If (3g is large, then the central banker is, in Rogoff’s (1985b) terminology, conservative (it is more conservative than the population when f3g > of course). Alternatively, the size of pg could be interpreted as an indicator of central bank independence, with more independent monetary authorities having a larger f3g. In the limit as f3g —> oc, the central banker cares only about inflation. Since we know that in this case no time inconsistency issues can arise (technically, the precommitment and discretion solutions coincide), then the case of (3g —► oo can be thought of as capturing the case of perfect central bank precommitment and therefore perfect independence. We will stick to the interpretation of 0 as an index of Central Bank conservatism, but the reader should keep in mind that (at least in the limit) it also captures the degree of Central Bank independence.
How do employment, output and inflation levels depend on how conservative or populist the central bank is? We explore these questions holding the number n of unions constant.
Notice first that if j3g is zero (inflation is not costly for the government), ф —> 1 and the employment and output levels converge on the first best, namely log Lt (i) = ^ and logFt = y. The reason is that in this case the government will implement any rate of inflation necessary to take output to its first best level, regardless of what nominal wage increases unions have obtained. Understanding this, unions realize that nominal wage gains provide no benefit, and simply place the nominal wage at a level such that the first best aggregate real wage can be attained with no inflationary costs. Hence, in equilibrium, inflation is zero. Finally, it is easy to check that if pg is zero we have U (i) = (1 — <5)_1, which is its first best level. We therefore have: Result 2: For a fixed number n of unions, a radical-populist central banker, who cares not at all about the costs of inflation, maximizes the welfare of the population by delivering zero inflation and optimal employment and output levels. As /3 rises, output and employment fall, since they are both increasing in ф, and < 0 unambiguously. The intuition, as before, is that unions understand that a central bank that is concerned about inflation will not necessarily erode their wage gains, and hence have an incentive to seek higher wages. In equilibrium their conjecture turns out to be true, real wages are higher, and employment and output are lower. Hence, Result 3: For a fixed number n of unions, employment and output fall as the central bank becomes more conservative. instant loan
The behavior of equilibrium inflation as j3g rises is very interesting. As we just saw, output falls with /3 , and this creates an incentive for the central bank to try to raise it via higher inflation (algebraically, this is reflected in the denominator of 3.6, which is decreasing in >, and hence increasing in (3 ). At the same time, a higher pg makes inflation costlier for the authorities, which pushes inflation down (this is reflected in the denominator of 3.6, which is increasing in /3 ).