Bayesian Nash equilibria and monetary policy
participants expect or put the economy through recession. In this case, the central bank will validate the original rise in inflation expectations, thus deviating from their strategy and target.
The working-capital expectations trap relies on the assumption that firms borrow funds to finance the inputs needed for production. The central bank adopting a high interest rate will have a negative impact on economic activity because it raises the cost of borrowing and working capital. As inflation expectations increase, people anticipate lower real interest rates believing the central bank is afraid of the negative output effects of high interest rates. This makes them save less and take out more loans, which puts upwards pressure on interest rates for loanable funds. If the central bank keeps the money supply unchanged, the expected inflation would be avoided. However, this would be associated with high interest rates that slow the economy. The central bank will choose to prevent hiking interest rates by injecting money into the economy (creating more loans), thereby validating the jump in inflation expectations by increasing inflation.
Proof
Taylor (1993, 1999b) put forward that the Fed pursues an interest rate target, which varies with current economic indicators. Using data from the 1970s to adapt Taylor’s model, Clarida et al . (1999) estimated the federal funds rate (R t ) to be determined by:
R t = ρR t-1 + (1 − ρ ) R ∗ t
(1)
Where:
- R t : the interest rate set by the central bank at time t.
- ρ: the degree of interest rate smoothing, an indication of how much weight the central bank puts on the previous period’s interest rate (Sack et al, 1999). It lies between 0 and 1, with 1 being a high degree of smoothing, and 0 being a drastic shift towards its target R ∗ t , where R t = R ∗ t.
- R t-1 : the interest rate from the previous period.
- (1- ρ): determines the weight given to the target rate R* t when setting the current interest rate. (This is the inverse of ρ).
R ∗ t : the target interest rate.
-
The central bank’s target interest rate R ∗
t is determined as follows:
R ∗ t = A + α E t log( π t+1 ) + γ y t , π t+1 = P P t+ t 1
(2)
Where:
- A: a fixed component in the target interest rate, e.g the bank’s baseline interest rate.
- α : a coefficient of how strongly the central bank reacts to changes in inflation expectations.
- E t log( π t+1 ): the expectation of inflation at time t for the next period t + 1, where 𝜋 𝑡 +1 is the expected inflation rate and E t denotes the expectations based on information available at t. - γ : a coefficient that measures the central bank’s response to output gaps (deviations of the economy’s output from its potential level).
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