Unlocking Economic Secrets: A Fresh Look at Equilibrium, the Lucas Critique, and Keynesian Economics

Stochastic Equilibrium represents a state where the probability of future economic events aligns with their long-run average, grounded in ergodic theory. This contrasts with previous models by explicitly constructing this equilibrium, enabling extensive comparative statics and deeper insight into economic dynamics. It challenges the concept of multiple equilibria, suggesting some models may have no solutions, which were previously believed to have multiple solutions. Further research can explore the full potential of this framework, especially in analyzing models with capital and labor accumulation and models describing financial markets.

This new framework disproves the observational equivalence idea of the Lucas Critique. The framework shows that the bifurcation results from the breakdown of the constraints implied by lagged nominal rigidity, which is associated with cross-equation cancellation only possible at ZINSS (Zero Inflation Non-Stochastic Steady State). This is significant because it suggests that economic policies can be effective even when agents anticipate them, contrary to the Lucas Critique's assertion that expectations render traditional policy analysis ineffective. This is due to the fact that traditional policy analysis are rendered ineffective.

Econometric Duality, in this context, refers to the equivalence between constraints on the re-optimization of firms and statistical restrictions imposed on econometricians. This duality creates new avenues for identification in econometric models. This means that restrictions on how firms make decisions directly translate into statistical restrictions that econometricians can use to estimate and test their models, providing a more robust and theoretically grounded approach to empirical analysis. Further research is needed to explore these new avenues.

The Taylor Principle is reversed in this framework, suggesting that inactive settings are necessary and pointing toward inertial policy. This challenges the conventional view that central banks must aggressively adjust interest rates in response to inflation to maintain price stability. The findings imply that a more gradual and predictable approach to monetary policy, or inertial policy, may be more effective, contradicting what was previously understood about monetary policy. Central Banks should adopt this more inertial approach.

The new Phillips curve, derived from this framework, contains a large lagged inflation coefficient and a small response to expected inflation, aligning with empirical evidence. This contrasts with the traditional approach of linearizing the Calvo model at the Zero Inflation Non-Stochastic Steady State (ZINSS), which fails to capture the true dynamics of the underlying stochastic system. The implications are that inflation dynamics are more heavily influenced by past inflation than by expectations of future inflation, suggesting that policies aimed at managing inflation expectations may be less effective than policies that address the underlying drivers of past inflation.