Bayesian Nash equilibria and monetary policy
- y t : the output gap at time t. - P t : the price level (inflation).
A central banker who is committed to low inflation would adopt a higher value of α (the strength of reaction to inflation expectations); however, analysis by Clarida et al. (1999) shows that this value is low in the 1970s and only picked up in the 1980s, a period characterized by a greater commitment to low inflation. This can be seen in figure 1, 2 and 3 from Christiano and Gust’s (2000) research.
Figures 1 and 2 focus on the real rate, the interest rate calculated with regards to the expected, or actual inflation that took place during that period. Figure 1 refers to the ex-ante real rate, calculated before the fact, considering the expected inflation that occurred over the period (nominal interest rate minus the expected inflation rate). Figure 2 refers to the ex-post real rate, which is calculated after the fact with the real inflation rate of the period. They both show that the real rate was noticeably higher during the 1980s. Figure 3 shows the difference between what the fund rate was and what it was predicted to be based on the estimated fund rate equation (1), being roughly 0 until it shifts up to the horizontal line in the 1980s. This line highlights that the actual funds rate in the period was higher than what policymakers would have been allowed in the previous decade. The ex-ante real interest rate is:
R real = R t − E t log(π t+1 )
(3)
The equation can be used to prove the working-capital inflation expectations trap as follows: to produce output, firms must borrow money from banks for investment. The central bank has the power to manage the scarcity or abundance of those funds by decreasing or increasing injections of liquidity. With scarce funds, firms cannot invest in their factors of production and therefore cannot produce as much, slowing down economic growth. An abundance of funds leads to a fall in the interest rate and more investment and economic growth. When there is an increase in expected inflation, E t log(π t+1 ) rises and, coupled with α < 1, the real interest rate (3) decreases. Households will now reduce their deposits with their banks, which in turn creates a scarcity of funds for lending. Upward pressure will then develop on the interest rate and the central bank, being committed to low inflation, must inject some liquidity into the banking system. This then produces a rise in prices, validating the original rise in inflation expectations and falling into the trap. As α > 0, the monetary authority will permit some change in the nominal rate of interest, which suppresses output, employment, consumption, and investment.
Looking at equations (2) and (3), a common factor is the expected level of inflation in the economy by consumers. Although economists such as Gust and Christiano (2000) state that ‘ exactly why their
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