Bayesian Nash equilibria and monetary policy
also incorporates a level of noise to the MPs’ decisions, which may represent external factors such as prejudice or supply shocks.
Figure 6 In the simulation, the BoE and Fed data initialize market participants' prior beliefs about inflation (from the 'Expectations' column) and provide actual inflation outcomes (from the 'Inflation' column) for each period covered by the dataset. These data points are essential inputs for the Bayesian updating process, where prior beliefs are adjusted in response to actual inflation based on the level of transparency set by the central bank, quantified, and normalized in the model. The transparency influences the precision of the updating mechanism, directly affecting how beliefs are adjusted. Each cycle of the simulation calculates the variance between updated beliefs and actual inflation, with this variance serving as a measure of the performance of different levels of transparency in aligning expectations with reality, thereby determining the effectiveness of communication strategies in terms of economic stability.
Resulting Bayesian Nash Equilibria
By finding the total payoff for every transparency level, an equilibrium is returned where neither player has an incentive to deviate from their strategy which is where the total payoff is at its highest. The simulation of both data sets returns a slightly different Bayesian Nash equilibrium and transparency value for each cycle due to varying noise (all within 8.8 – 10.2 out of 15). The average of 10 equilibria’s optimal transparency returns 9.675 (0.645) for the Federal Reserve and 9.795 (0.653) for the Bank of England on the Eijffinger-Geraats transparency index of 0 to 15 (2002). These can be seen plotted in
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