LeatherSagiKnowledgebase

DSGE Model-Based Estimation of the New Keynesian Phillips Curve

5 min read

Problem

The New Keynesian Phillips Curve (NKPC) is a central building block of modern DSGE models, linking inflation to current and future expected real marginal costs. Its slope parameter lambda determines the output-inflation tradeoff faced by policymakers. Despite its importance, no consensus has emerged from the empirical literature on the value of this slope or the importance of lagged inflation. This review paper seeks to understand why different DSGE model-based estimation approaches produce such widely varying estimates.

Key idea

The identification of new-keynesian-phillips-curve parameters through DSGE model-based estimation is a “black box” that this paper opens. Three distinct sources of identifying information are characterized: (1) contemporaneous correlations between output, inflation, and interest rates imposed by the structural model, (2) impulse response dynamics to identified structural shocks (especially monetary policy shocks), and (3) reduced-form autocovariance restrictions that relate inflation forecasts to marginal cost forecasts. A key finding is that simple OLS regression of inflation on measures of expected marginal costs produces slope estimates very close to zero due to endogeneity bias, and much of the variation in published DSGE estimates is attributable to differences in the implicit endogeneity correction rather than to fundamental data features.

Method

  • Analytical characterization of identification in a simple three-equation NK model (IS curve, NKPC, Taylor rule) that can be solved in closed form.
  • Decomposition of the likelihood function into components that isolate the role of contemporaneous correlations, impulse responses, and autocovariance dynamics.
  • Least-squares regressions of U.S. inflation on various measures of discounted future expected marginal costs (1960:Q1-2005:Q4) using different detrending methods and marginal cost proxies (output gap, labor share).
  • Comprehensive survey of published DSGE model-based NKPC estimates from ~25 studies, classified by: (a) whether marginal costs are latent or observed, (b) whether the model includes capital and habit formation, (c) estimation method (Bayesian, MLE, IRF-MD, moment matching).

Results

  • OLS slope estimates of kappa (output coefficient in NKPC) range from 0 to 0.03; OLS slope estimates of lambda (marginal cost coefficient) range from 0 to 0.05. These are very small and robust to detrending methods.
  • Published DSGE model-based estimates of kappa range from <0.001 to 4.15 — variation far exceeding the OLS range, driven by differences in endogeneity correction.
  • When marginal costs are observed (labor share included in data): lambda estimates cluster in 0.005-0.135, much tighter than when marginal costs are latent.
  • Models in which shocks in the Euler equation and Phillips curve are correlated tend to produce larger kappa estimates.
  • No consensus on the backward-looking coefficient gamma_b: estimates range from 0 to 0.72 across studies. The backward-looking term is poorly identified separately from persistent mark-up shocks.
  • The output-inflation tradeoff (ratio of peak inflation to peak output response to monetary policy shock) ranges from 0.07 to 1.4 across studies.
  • Key estimates from testing-indeterminacy-application-monetary-policy are reported: kappa = 0.77 (pre-Volcker) and 0.58 (post-1982) under the Bayesian approach.

Limitations

  • Survey scope limited to models with Calvo/Rotemberg price setting and labor-share-based marginal costs. State-dependent pricing, menu costs, and information frictions are excluded.
  • The analytical identification results are derived in a simple model without capital, habit formation, or wage stickiness; the mapping to larger models is heuristic.
  • Published estimates use different samples, detrending methods, prior specifications, and model sizes, making exact apples-to-apples comparisons difficult.
  • The survey does not resolve which set of estimates is “correct” — it documents the sources of variation.

Open questions

  • Can the slope of the NKPC be identified more robustly by using microeconomic price-change data to discipline the Calvo probability parameter?
  • How sensitive are NKPC estimates to the specification of wage rigidity (an issue flagged but not deeply explored)?
  • Does the use of regime-switching models (which allow the NKPC parameters themselves to change over time) resolve the apparent instability in estimates across sub-samples?
  • What is the true importance of the backward-looking term gamma_b for inflation persistence and optimal monetary policy?

My take

This is an excellent review paper that clarifies why the empirical NKPC literature has struggled to converge. The core insight — that the endogeneity correction implicit in the DSGE likelihood is the main driver of estimate variation, not the raw data — is important for any structural estimation exercise. For the CRE project, the NKPC is embedded in the 3-equation NK macro block (the kappa parameter in the inflation equation), and this paper’s finding that kappa identification depends heavily on what else is in the model reinforces the importance of the full-system approach (RBPF with cap rate data) rather than equation-by-equation estimation. The wide range of published estimates (0.001 to 4.15 for kappa) also suggests that the prior specification in the CRE model’s Bayesian estimation matters more than might be assumed.

Graph View

Backlinks