We show an equivalence result in the standard representative agent New Keynesian model after demand, wage markup and correlated price markup and TFP shocks: assuming sticky prices and flexible wages yields identical allocations for GDP, consumption, labor, inflation and interest rates to the opposite case- flexible prices and sticky wages. This equivalence result arises if the price and wage Phillips curves' slopes are identical and generalizes to any pair of price and wage Phillips curve slopes such that their sum and product are identical. Nevertheless, the cyclical implications for profits and wages are substantially different. We discuss how the equivalence breaks when these factor-distributional implications matter for aggregate allocations, e.g. in New Keynesian models with heterogeneous agents, endogenous firm entry, and non-constant returns to scale in production. Lastly, we point to an econometric identification problem raised by our equivalence result and discuss possible solutions thereof.

We propose a macroeconomic model with a nonlinear Phillips curve that has a flat slope when inflationary pressures are subdued and steepens when inflationary pressures are elevated. The nonlinear Phillips curve in our model arises due to a quasi-kinked demand schedule for goods produced by firms. Our model can jointly account for the modest decline in inflation during the Great Recession and the surge in inflation during the post-COVID period. Because our model implies a stronger transmission of shocks when inflation is high, it generates conditional heteroskedasticity in inflation and inflation risk. Hence, our model can generate more sizeable inflation surges due to cost-push and demand shocks than a standard linearized model. Finally, our model implies that the central bank faces a more severe trade-off between inflation and output stabilization when inflation is elevated.

Early-warning models most commonly optimize signaling thresholds on crisis probabilities. The expost threshold optimization is based upon a loss function accounting for preferences between forecast errors, but comes with two crucial drawbacks: unstable thresholds in recursive estimations and an in-sample overfit at the expense of out-of-sample performance. We propose two alternatives for threshold setting: (i) including preferences in the estimation itself and (ii) setting thresholds ex-ante according to preferences only. Given probabilistic model output, it is intuitive that a decision rule is independent of the data or model specification, as thresholds on probabilities represent a willingness to issue a false alarm vis-à-vis missing a crisis. We provide simulated and real-world evidence that this simplification results in stable thresholds and improves out-of-sample performance. Our solution is not restricted to binary-choice models, but directly transferable to the signaling approach and all probabilistic early-warning models.

Early-warning models most commonly optimize signaling thresholds on crisis probabilities. The ex-post threshold optimization is based upon a loss function accounting for preferences between forecast errors, but comes with two crucial drawbacks: unstable thresholds in recursive estimations and an in-sample overfit at the expense of out-of-sample performance. We propose two alternatives for threshold setting: (i) including preferences in the estimation itself and (ii) setting thresholds ex-ante according to preferences only. We provide simulated and real-world evidence that this simplification results in stable thresholds and improves out-of-sample performance. Our solution is not restricted to binary-choice models, but directly transferable to the signaling approach and all probabilistic early-warning models.