Central banks (CB) or monetary authority all over the world have the power to exercise, with their own judgement, policies for their own economies. These policies are essentially instruments for the CB to prevent recessions or promote booms by controlling either the interest rate or the money supply for example. With that being said, a monetary policymaker's failure to respond to certain shocks which could then lead to a crisis begs the question; are the policies implemented now, optimal choice for the economy in the future? Essentially, the macroeconomic equilibrium depends on both current and future monetary policy (MP). Most CBs work under a systematic policy rule which is used to determine rational expectations of future MP. The rule here is nothing more than the objective function of a CB maximized. Firms and workers set nominal wages and prices based on the fact that the MP would be set in a particular manner following the rule. However, as we will see, CBs may have an incentive to abandon such a rule in favour of an expansionary MP for example.
A policy is time-consistent if what has been planned for the economy at time t for t+1 is still optimal to be implemented once it is t+1. This means that the policies set out for the next period must take into account whatever new information and shocks that the economy might endure and still be optimal once t+1 arrives. Time-inconsistency of policies arises if at time t+1 the CB decides to respond differently as it is no longer optimal to stick to the original policy. Departures from optimal policy do not appear to be random (Romer, 2012). There are more cases where money growth and inflation are too high compared to when they are too low. Therefore, there are many possible sources of inflationary bias (tendency of a CB to have higher than the optimal level of inflation) in MP.
Using the work of Kydland and Prescott (1977), we are able to build a model to illustrate this time-inconsistency of MP. They argue that if CBs fail to commit themselves to a low inflation policy, this would lead to excessive inflation. The idea is - if the expected inflation is low, the marginal cost of additional inflation is also low. CBs would then pursue expansionary policies to put output above its normal level to reduce unemployment for example. However, the public's knowledge of this would mean they would not expect low inflation. The end result is higher inflation without any increase in output. We can show this formally by first considering the Lucas supply curve: where is the log output and is the natural level of output. can be thought of as the inflation surprise as it is the amount of inflation exceeding the expected level. At time t wages are set according to expected inflation, . If at time t+1, the CB increases money supply so that, output is now higher. Intuitively, firms and workers set their wage according to future inflation. The real wage is defined as where w is the wage and pe is the expected price level at t+1. However, at time t+1, inflation is now higher than the expected level. Consequently, . This means that the real wages is now lower than expected and labour now is cheaper. Firms react to this by expanding production and therefore increasing output in the economy. The magnitude of this increase is determined by the b parameter in the supply curve. This is theoretically sound but unfortunately not realistic. In the next section, we will see why output will not be able to increase and the economy will actually end up with a higher inflation rate.
The other component of conducting an optimal MP is the CB minimizing the loss function which is defined as: where the first term is defined as the output gap [1] and the latter term is the inflation gap (i.e. deviations from their optimal levels). reflects the weight a CB puts on inflation. By minimizing both deviations, the CB increases the utility of households by having a more stable economy. [2] With these equations, we can learn why a time-inconsistent policy would not work to expand output. There are two ways of conducting a MP, commitment and discretion. Under commitment, the CB makes a binding commitment to have and and there is no problems. The CB would then set inflation to the optimal inflation, . The problem with binding commitments is the CB cannot account for completely unexpected circumstances. Also, we can observe many countries such as Germany where policies are not binding but the average inflation is low. Thus, there must be other ways of alleviating this time-inconsistency problem without binding commitments. Discretionary MP is when the CB chooses taking as given. [3] Solving for the CBs maximization problem for we have ). [4] As you can see, inflation is higher in the absence of commitment by this distortion k.1 Also, if the public expects the CB to choose , the marginal cost of higher inflation is 0 white the marginal benefit of higher output it positive. The assumption made here - no uncertainty, allows us to impose and solve for the equation above where We now have: where ). If exceeds , then actual inflation is less than what people expect and vice versa, and thus the economy is not in equilibrium. The only equilibrium is for and to equal to and . Therefore, the equilibrium when the CB acts with discretion implies a higher inflation rate but there is no effect of output. Intuitively, the CB wants a higher output, to further reduce unemployment possibly motivated by political reasons. They know that wages and prices have been set in this period and the public do not expect any rise in inflation. As a result, the "surprise" increase in inflation raises output by making labour cheaper and firms producing more as discussed earlier. However, in reality, since the public knows that the CB acts with discretion, they will anticipate these actions by the CB and will negotiate their wages/prices at a higher rate in the previous period. As a result, in the next period with higher inflation and there is no effect on output. The source of the problem is the knowledge that the CB acts with discretion rather than the discretion itself.
Next, we will look at ways to address this time-inconsistency and inefficiently high inflation problem. The first approach is known as reputation; the idea behind this to deal with the time-inconsistency problem is that the public is unsure of the CB's characteristics and modus-operandi. Through observing inflation, the public learns about the CB's preferences between output and inflation and essentially their policy rules. The CB's actions reveals information about their characteristics and thus affects the public's expectation of inflation in subsequent periods. Since the CB has better output-inflation choices when the expected inflation is low, this provides them with an incentive to pursue low-inflation policies. This idea is realistic as we can see many CB's around the world (i.e. Bundesbank in the 1980s) who have maintained long periods of low inflation and being trustworthy. The second approach is known as delegation; the idea is - the output-inflation trade off would be more favourable if the CB in charge strongly opposed inflation (Rogoff, 1985). To see this, we use the model above once more: where > . This means that the CB's tolerance towards inflation is now lower since there is a greater weight on . Similar to before, the public knows how the inflation is determined and in equilibrium The equilibrium interest now is also lower with). Inflation is now much lower than it was in the discretion case. As for social welfare, determined by the minimization of the loss function, is now higher as the loss function is lower cause by Intuitively, when the CB clamps down hard on inflation, the public realize this and realizes that the CB has no plans to implement an expansionary monetary policy. Therefore, their expectation of inflation in subsequent periods will be lower. However, when Rogoff extended this model to study an economy that was hit by contemporaneous shocks, he found that it does not react optimally to the disturbances. There is a trade-off for the CB. A no-nonsense approach towards inflation produces stabilizes the average inflation, but is not optimal when reacting to shocks. Essentially, there needs to be some level of conservatism by the CB to decide between the options. This argument is also very realistic as many CB's worldwide have clear inflation targets to state out their objectives to the public. The other 2 solutions to this are punishment equilibria and incentive contracts. For the former, the CBs have multiple equilibria including ones that stays below . Low inflation is sustained on the notion that, if the CB chooses high inflation, the public would "punish" them by expecting higher inflation now and subsequent periods. Incentive contracts are agreements that the CB would be penalized (financially or through reputation) for high inflation.
Conclusively, average inflation has been high for a lot of countries for a long period of time. These rates sometimes exceed what is estimated to be the socially optimal level of inflation. Time-inconsistency of MP is an attempt to understand this anomaly. The CB's preference for inflation, the short-run real effects of inflation, the rate which CB discounts the futures, the effect of political influences on the CB are among the factors that could contribute to this (Walsh, 2009). The theoretical framework used in analysing this has helped us think formally of the possible incentives the CBs face and how the public's expectation about how the CB would react is crucial. CBs should be clear and transparent about their policies and objectives. The public should be aware of the costs involved but mostly of the benefits that would be gained by the economy should a policy be implemented. The combination of a credible CB to anchor down expectations of the public and follow through on their policies is pivotal. Furthermore, CBs should try to be rid of government interventions when designing policies so that there are no distortions/bias and the need to implement a new policy should there be a shock in the next period.
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