Bayes correlated equilibrium and inflationary bias
To simulate the inflation, we employ a stochastic differential equation (SDE) model, specifically the Ornstein-Uhlenbeck (OU) process. This model allows us to simulate the behaviour of inflation as it reverts towards a target influenced by policy actions. The OU process is particularly effective in modelling inflation due to its mean-reverting property – it is consistent with the principle that inflation tends to revert to a target set by the CB, influenced by monetary policy expectations. The formula is given by 𝑑𝑋 t = 𝜃 ( 𝜇 – 𝑋 t ) 𝑑𝑡 + 𝜎𝑑𝑊 t ( 𝟏𝟔 ), where: • 𝑋 is the value of the process at the time 𝑡 • 𝜃 is the rate of mean reversion, which measures how quickly the process returns to its mean. Higher values of 𝜃 indicate a faster return to the mean. • 𝜇 is the long-term mean to which the process reverts. • 𝜎 is the volatility or standard deviation, representing the degree of variation around the mean driven by random fluctuations. • 𝑑𝑊 t represents the increments of a Wiener process which are random and normally distribution with mean 0 and variance 𝑑𝑡 . This term introduces the stochastic or random elements to the model. The formula above captures the dynamics where the inflation rate 𝑋 is pulled towards the target 𝜇 over time, but with fluctuations driven by random shocks 𝜎𝑑𝑊 . Results for this simulation process (100 trials) can be seen in Fig.2 , where it can be seen that both inflation and unemployment exhibit a degree of mean reversion, a behaviour well modelled by the OU process. The implications of this are profound: the CB’s and EA’ s strategies, while optimal in the short term, must also be resilient to vagaries of longer- term economic trends. We test for this implication by calculating and comparing the cumulative utility difference between BCE and other non-BCE strategies i.e. those that react randomly or do not adopt and react to CB’s signals regarding the state of the economy.
Fig.2 – Inflation dynamics and unemployment dynamics across 100 simulations
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