Bayesian Nash equilibria and monetary policy
• Update beliefs: they update their inflation expectations based on the new information received, moderated by the transparency level. • Economic response: based on the updated expectations, they make decisions that can cause expectations traps, such as demanding higher wages. I have derived payoff functions that model the payoff (the value associated with the award given to a single player at the outcome of the game (Barkley, 2019)) at different levels of transparency for both players. US Federal Reserve data from 1998 to 2010 (figure 4) and Bank of England data from 1999 to 2010 (figure 5) will be used to simulate the models. The data highlights how increasing transparency stabilize s inflation expectations around the CB’s target rates due to their increased transparency. However, the datasets also highlight the issue of too much transparency, with little change being made on expectations after a rise by the Fed in 2004 from a transparency level of 10 to 11, unlike the change from 8.5 to 10.
Figures 4 & 5 (Federal Reserve Bank of Cleveland, 2024), (Trading Economics, 2019), (Dincer and Eichengreen, 2014)
The CB’s payoff function is as follows:
2 + 𝜅 ( 𝛼 − 0.65) 2 )
Π 𝐶𝐵 = − (( 𝜃 − 𝜋 )
(4)
Where: •
Π 𝐶𝐵 = payoff for the central bank.
• θ = MPs’ updated beliefs about inflation from. • π = actual inflation rate. • α = normalized transparency level (0 to 1). • κ = a scaling factor for the cost of transparency to ensure it is comparable to the variance term. • 0.65 = the theoretical midpoint of the transparency scale, where the cost is minimized, based on empirical evidence from the datasets (figure 4 & 5). The CB’s goal is to minim ize the difference between the MPs’ inflation expectations and the current inflation rate, while managing the costs associated with transparency. ( 𝜃 − 𝜋 ) 2 represents the variance between the expected and actual inflation, indicating how well the CB has managed expectations. 𝜅 ( 𝛼 − 0.65) 2 is the quadratic cost of transparency, representing deviations from the optimal transparency level. Variance equations are a common method of economic modelling, used in numerous papers, for example Park’s (2019) analysis of market friction.
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