Handout 2 (Time Inconsistency)

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1.1
A Simple Model
= ( − ) (1)
• We assume an aggregate supply function of the (1) as (which will sometimes be convenient) − = −1 (2)
• In particular, central bank wants to stabilise output around and inflation around 0 Why does the bank want to stabilise output gap around instead of zero (zero corresponds to what is called the natural level of output i.e. the level of output if wages and prices are fully flexible). Possible reasons for 0 are presence of monopolisitic competition and labour market distortions (a wage tax) which cause the natural rate of output to be inefficiently low. There might also be political pressures on the central bank- economic expansions (high output) increase the probability of re-election for politicians. We will demonstrate three different methods to solve the policy problem of the central bank. 1.2.1 Method 1: Economic/Intuitive argument
1
- Unexpected monetary expansions reflected in unexpected inflation leads to increases in output - (Lucas) aggregate supply curve or expectational Philips curve. - Governmental revenue. Real value of government bonds decreases which lowers the government’s future real expenditures for interest and repayment of principal.
1.2
Loss function of Central Bank
Assume that the central bank wants to minimise fluctuations of inflation and output gap around some target levels i.e. they try to minimise = 2 ( − )2 + 2 2 (3)
EC5605 Monetary Policy HANDOUT 2
1
Time Inconsistency of Monetary Policy
Empirical evidence for the OECD countries in the post-war period suggests the following stylised facts: 1. Inflation rates vary greatly across countries and time. But there is a common time pattern: in most countries inflation was low in the 1960s, but very high in the 1970s; it came down in the 1980s and 1990s in all countries. 2. Inflation rates are correlated with real variables, such as growth and unemployment, in the short run. But there is little evidence of systematic correlation over longer periods. 3. Inflation increases shortly after elections and there is some evidence that monetary policy is more expansionary before elections- suggests that political factors may be important for successful positive models of inflation and macroeconomic policy. 4. Average inflation rates and measures of central bank independence are negatively correlated- suggests that institutional features of the monetary regime-like statutes regulating the central bank are potentially important for delivering low inflation. The general idea in the economics literature was that the actions of central banks may have been responsible for bad (i.e. high inflation) outcomes of the 1970s since they might have believed in a long-run trade-off between inflation and unemployment depicted by the so-called Phillips curve. • Discretionary monetary policy where policymakers select the best action, given the current situation, will not typically result in the social objective function being maximised. On the contrary, reliance on policy rules may give a better outcome since expectations about future policy actions matter- Argument for rules over discretion. • A policy is time consistent if an action planned at time for time + remains optimal to implement when time + actually arrives. Otherwise the policy is time inconsistent. • If inflation is costly, why are inflation rates consistently positive? • A low inflation rate, though optimal, is not time consistent. If the public expects low inflation, then the central bank has an incentive to inflate at a higher rate. Understanding this incentive and believing that the policy maker will succumb to it, the public correctly anticipates a higher inflation rate. • Benefits of surprise inflation are two fold:
• is the output (gap) (i.e. difference between actual output and natural rate of output with flexible prices and wages), is the inflation rate (change in the price level) and is what the producers (private sector) expect the inflation rate to be (mathematically this is the conditional expectation of the inflation rate). (1) is an aggregate supply function (also called a Phillips curve): if producers of goods observe a higher price then they want to produce more given their expectations of the price level (or change in prices i.e. the inflation rate). One motivation is the presence of one period nominal wage contracts which are fixed at the beginning of each period based on the private sector’s (worker’s) expectations of inflation (workers may demand a stable real (i.e. in terms of purchasing power) wage rate so that they are not hurt by price increases which take place until the next time the nominal wage rate (in pounds) is changed). However, once the wage rate is fixed, if actual inflation turns out to be higher than what was expected, then real wages fall i.e. labour becomes relatively cheap and firms find it profitable to expand employment/output: this explains the positive relationship between inflation and output in (1). • Sequence of events: -Private sector forms its inflation expectations first so as to aim for a stable real wage when nominal wages are set on this basis. -Central bank then chooses a given inflation rate taking inflation expectations of the private sector, as given This is also called discretionary policy by the central bank. - Actual inflation then in turn determines (private sector has perfect foresight i.e. can accurately predict the actual inflation rate) and this finally determines output. • Justification for timing of events: Wage setting process is laborious whereas monetary policy decisions are taken relatively easily. Policymaker could also have an information advantage. 2