The price puzzle is the finding, standard in recursive vector autoregressive (VAR) estimates of monetary policy shocks, that a policy tightening is followed by higher rather than lower inflation. Castelnuovo (2012) estimated new-Keynesian DSGE models with the cost channel — the supply-side effect whereby cash-constrained firms borrow their wage bill, so the policy rate enters marginal costs — and rejected the structural interpretation of the puzzle, while leaving open a research agenda whose core is the sharp econometric identification and quantification of the cost-channel pass-through parameter and the design of welfare-optimal policy under uncertainty about it. This agenda remains open: identification-robust, shock-based macro estimates still cannot pin the channel down and find only weak support for it, and welfare-optimal policy under cost-channel uncertainty remains unsettled; post-2012 firm-level evidence finding a quantitatively large working-capital pass-through sharpens, without closing, the identification challenge.

Background

Vector autoregressions (VARs) regress a small set of macroeconomic time series on their own lags; to read off the causal effect of monetary policy, practitioners typically impose recursive (Cholesky) zero restrictions that let the policy rate respond contemporaneously to the macro variables but not vice versa. With US data this routinely delivers the "price puzzle": after an identified contractionary policy shock, the price level rises (Eichenbaum, 1992; Sims, 1992) — the opposite of textbook predictions. The leading structural (supply-side) candidate explanation is the cost channel of monetary transmission, also called the working-capital channel: firms must finance their wage bill and input purchases before revenues arrive, so the interest rate paid on borrowings is a component of marginal cost, and the policy rate therefore enters the new-Keynesian Phillips curve (NKPC — the forward-looking aggregate supply relation linking inflation to expected inflation, lagged inflation, the output gap, and marginal costs). In the model of Castelnuovo (2012) the NKPC reads πt=β1+αβEtπt+1+α1+αβπt−1+κ[(σ+η)xt+ψRt]+εtπ\pi_t=\frac{\beta}{1+\alpha\beta}E_t\pi_{t+1}+\frac{\alpha}{1+\alpha\beta}\pi_{t-1}+\kappa[(\sigma+\eta)x_t+\psi R_t]+\varepsilon^\pi_t, where πt\pi_t is inflation, xtx_t the output gap, RtR_t the nominal policy rate, and ψ\psi the cost-channel parameter measuring the pass-through from the policy rate to firms' marginal costs. If ψ\psi is large, a tightening can raise inflation through supply costs and rationalize the VAR fact; earlier single-equation and calibrated studies (Barth and Ramey, 2001; Ravenna and Walsh, 2006; Chowdhury, Hoffmann, and Schabert, 2006) found evidence for the channel but with magnitudes varying across countries, samples, and methods. Castelnuovo (2012) estimated small-scale new-Keynesian DSGE models (dynamic stochastic general equilibrium models solved and fitted by Bayesian likelihood methods) with this cost channel on US data, distinguishing an ordinary policy-rate shock from a shock to trend inflation (the time-varying inflation target the Federal Reserve is inferred to pursue). His estimated models fit better with the cost channel but predict a negative inflation response to tightening — rejecting the structural interpretation of the puzzle — and the posterior for ψ\psi varied across specifications, in the enriched specification being pushed to the prior zero lower bound and fixed there, leaving its magnitude unidentified in practice. The paper's conclusions therefore pose an explicit agenda of three strands: quantify and sharply identify the true structural pass-through ψ\psi; derive optimal monetary policy when the cost channel is present but its size uncertain (a Brainard-type problem — Brainard's principle being that parameter uncertainty makes optimal policy attenuated and cautious), an issue tackled by Tillmann (2009); and study determinacy (uniqueness of the rational-expectations equilibrium) and learnability (whether adaptive agents can converge to that equilibrium) of equilibria with supply effects, following Llosa and Tuesta (2009). Two further specification choices were robustness checks the paper carried out and concluded, not open agenda items: alternative stochastic specifications for the cost-push, policy, and trend-inflation processes (the paper reports its findings robust to model specifications and to specifications of the monetary policy shocks), and the choice of the observable output-gap indicator in the policy rule — unit-labor-cost-based versus Congressional Budget Office (CBO)-type measures — which the paper judges of limited empirical relevance for estimating the policy shock, with the evidence pointing toward the CBO gap. This agenda serves one objective: establishing whether, and by how much, the supply-side cost channel matters for monetary transmission and for policy design.

Problem Statement

As posed by Castelnuovo (2012, Oxford Bulletin of Economics and Statistics 74(3):425–452), whose estimated new-Keynesian DSGE models reject the structural interpretation of the price puzzle while leaving the channel's quantitative importance unidentified, the task is to answer all four of the following sub-questions: (i) establish, with sharp econometric identification, the true structural pass-through ψ\psi from policy rates to firms' marginal costs, where sharp econometric identification means pinning ψ\psi down to the sharp identified set that the estimated model and data imply — the tightest set of values they cannot rule out, collapsing to a point estimate when the model's restrictions deliver one; (ii) taking that pass-through as given, determine whether a cost channel of that magnitude can rationalize the positive inflation response to monetary tightenings found in recursively identified VARs; (iii) on that quantitative foundation, and given the uncertainty surrounding ψ\psi, derive the welfare-optimal monetary policy, including whether Brainard-style attenuation is warranted both when the cost channel is present but its size is uncertain and, as a separate scenario, when trend-inflation shocks dominate the variance of shocks; and (iv) separately from the preceding parts, determine whether equilibrium remains determinate and learnable in the presence of supply effects that the source flags as part of the same agenda.

References

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