Policy Biases in a Model with Labor‐Market Frictions

Layer 1 — Overview

Research Question

Dennis and Kirsanova ask whether shocks to labor-market matching efficiency and worker bargaining power pose a significant problem for monetary policy, and whether the inability to commit (discretion versus commitment) generates important stabilization bias in a model with labor-market matching frictions. They also examine how several popular simple monetary policy rules perform in response to these and other shocks.

Model and Methodology

The paper develops a fully nonlinear DSGE model featuring: (1) a goods market characterized by monopolistic competition and Rotemberg-style quadratic price-adjustment costs; and (2) a labor market characterized by a constant-returns-to-scale matching function (Mortensen-Pissarides) and Nash bargaining over wages and hours worked. Because the flex-price equilibrium is inefficient — owing to both monopolistic competition and the matching friction — a linear-quadratic approximation is not valid for the discretionary policy problem, and the authors solve the model using Smolyak sparse-grid methods with Chebyshev polynomial basis functions.

The model is calibrated to quarterly U.S. data. Key parameter values include: discount factor β = 0.99 (annualized real interest rate ≈ 4 percent), elasticity of substitution across goods ε = 11 (steady-state markup of 10 percent), price-adjustment cost φ = 80, quarterly separation rate δ = 0.12, job-finding rate f = 0.65 (delivering an employment rate close to 0.94 and an unemployment rate near 5.95 percent in steady state), elasticity of matching function with respect to unemployment ξ = 0.72, and workers’ mean bargaining power equal to ξ = 0.72 (satisfying the Hosios condition at steady state). Five AR(1) shocks are included: aggregate technology (persistence 0.95, standard deviation 0.008), matching efficiency (persistence 0.80, standard deviation 0.032), bargaining power (persistence 0.80, standard deviation 0.028), consumption preference (persistence 0.70, standard deviation 0.006), and elasticity of substitution (persistence 0.85, standard deviation 0.12).

Main Findings

The central finding is that optimal monetary policy — whether conducted under commitment (Ramsey) or discretion — is highly efficient at responding to labor-market shocks, producing impulse responses that closely replicate the flex-price equilibrium for real variables. Specifically, in response to matching efficiency shocks and bargaining power shocks, the commitment and discretionary equilibria both track the flex-price equilibrium closely for output, consumption, employment, tightness, and the real wage.

Discretion generates a pronounced inflation bias of approximately 1.82 percent per annum — large but not implausible — but does not generate a meaningful stabilization bias for the class of shocks studied (technology, matching efficiency, bargaining power, and consumption preference). The one exception is the elasticity of substitution shock (analogous to a markup shock in linearized models): for this shock, the impulse responses under discretion diverge noticeably from those under commitment, revealing a discretionary stabilization bias — consistent with conventional New Keynesian results.

Regarding simple rules, strict inflation targeting (SIT) performs closely in line with commitment and discretion for all shocks. The two Taylor-type rules — one responding to inflation and output growth, the other to inflation and the unemployment rate — generate substantially greater volatility in inflation and the nominal interest rate relative to optimal policy. The unemployment-gap Taylor rule is the worst performer among the three simple rules; nevertheless, all three simple rules produce household welfare outcomes close to those under optimal monetary policy. The suboptimality of the simple rules is most evident in nominal variables, particularly inflation and the nominal interest rate, and less evident in real variables — though labor-market inefficiencies under the Taylor-type rules do emerge in response to matching efficiency and bargaining power shocks, with hours worked and the real wage deviating noticeably from flex-price outcomes.

The probability of encountering the zero lower bound is, for all policies considered, considerably less than 0.5 percent across one million simulated observations, suggesting that ZLB concerns are not material for the shocks under study.

Scope Conditions

These results hold within the context of a model with a fixed labor force (no participation margin), balanced-budget fiscal authority, no capital accumulation, and Nash bargaining over both wages and hours. The Hosios condition is satisfied at steady state (though the authors report that relaxing it has little effect on results). The analysis abstracts from the zero lower bound constraint when solving the model.

Layer 2 — Q&A

Q1: What is the Hosios condition and what role does it play in this model?

The Hosios condition requires that workers’ bargaining power equal the elasticity of matches with respect to unemployment in the matching function (ξ = 0.72). When the condition holds, bargaining is efficient in the sense that the decentralized search equilibrium replicates the social planner’s allocation. The authors impose it at steady state (mean bargaining power & = ξ = 0.72) so that the flex-price equilibrium is distorted only by monopolistic competition, not by inefficient search. The authors state they also analyzed versions where the Hosios condition does not hold and found it had little effect on results.

Q2: How are matching efficiency shocks transmitted through the economy, and how does optimal policy respond?

An improvement in matching efficiency raises the rate at which vacancies are filled and the unemployed find jobs, increasing employment from existing vacancy and unemployment levels. Employment rises, unemployment falls, labor market tightness increases, and the real wage rises. Firms substitute toward more workers (extensive margin) and away from hours-per-worker (intensive margin), so hours worked per employee decline even as aggregate hours rise. Both commitment and discretion track the flex-price equilibrium closely for all these real variables. Some difference is visible in inflation: under discretion the real wage rises by more than under commitment, pushing real marginal costs and inflation higher in the short run.

Q3: How does a bargaining power shock affect the economy under optimal monetary policy?

An increase in worker bargaining power shifts the match surplus toward workers, raising real wages and hours worked per employee. Firms, receiving a smaller surplus share, post fewer vacancies and hire fewer workers, leading to a decline in employment, a fall in labor market tightness, and a rise in unemployment. The employment decline is large enough to lower household income, goods production, and aggregate consumption. Under both commitment and discretion, the real economy tracks the flex-price equilibrium closely. Notable differences between commitment and discretion appear in inflation: under discretion, the inflation response on impact is larger and more persistent than under commitment, and monetary policy tightens more aggressively (higher nominal rate) under discretion.

Q4: What is the key difference between the commitment and discretionary equilibria, and why is stabilization bias mostly absent?

Commitment (Ramsey) policy differs from discretionary policy primarily in the level of inflation, not in the dynamics of the real economy. Discretion generates an inflation bias of approximately 1.82 percent per annum. However, the impulse responses for real variables (output, consumption, employment, tightness, real wage) under commitment and discretion are very similar to each other and to the flex-price equilibrium for four of the five shocks. This indicates that forward guidance — which commitment provides and discretion does not — is not an important factor in this model’s response to these shocks. The intuition is that the economy’s fluctuations in response to matching efficiency and bargaining power shocks are largely efficient, so the central bank needs only to avoid creating additional distortions, which both commitment and discretion achieve.

Q5: What distinguishes the elasticity of substitution shock from the other shocks in terms of policy performance?

The elasticity of substitution shock behaves similarly to a markup shock in linearized models: an increase in substitutability reduces firms’ monopolistic power, lowers the price markup, raises output and consumption, increases hours worked, posted vacancies, employment, and the real wage. For this shock, the impulse responses under discretion diverge noticeably from those under commitment — the decline in inflation is larger and more persistent under discretion than under commitment, and the nominal interest rate response differs in sign across policies. This is the only shock in the model for which a meaningful discretionary stabilization bias is evident, consistent with conventional wisdom from linearized New Keynesian models that markup shocks generate stabilization bias.

Q6: How do the three simple rules compare with optimal policy for labor-market shocks?

Strict inflation targeting (SIT) behaves similarly to commitment and discretion and hence closely replicates the flex-price equilibrium for all five shocks. The two Taylor-type rules — one responding to inflation and output growth (parameterized with φ_π = 2.5, φ_y = 0.5/4) and one responding to inflation and the unemployment rate (φ_π = 2.5, φ_u = 1.5/4) — both generate substantially more volatility in inflation and the nominal interest rate relative to optimal policy. The unemployment-gap Taylor rule generally results in inflation moving more in response to shocks and in the economy returning more slowly to baseline, making it the worst-performing simple rule. However, all three simple rules produce welfare outcomes close to those under optimal policy; the suboptimality of the Taylor-type rules is most evident in nominal rather than real variables.

Q7: Does the zero lower bound (ZLB) pose a concern under any of the policies studied?

Based on simulating one million observations from each model, the unconditional probability of encountering the ZLB is very small — well below 0.5 percent — for all policies considered. The commitment policy has a ZLB probability of approximately 0.077 percent, reflecting its near-zero average inflation. Discretion’s positive inflation bias of 1.82 percent reduces the ZLB probability to approximately 0.001 percent. The Taylor-type rules — especially the unemployment-gap rule (ZLB probability approximately 0.296 percent) — have higher probabilities than discretion, though these remain very small. These results suggest that for the shocks analyzed, violations of the ZLB are extremely unlikely.

Q8: What are the steady-state and stochastic simulation mean outcomes, and how do they compare across regimes?

The deterministic steady-state unemployment rate is approximately 5.95 percent, rising slightly to a mean of 6.04 percent in the stochastic flex-price economy. The stochastic means for output, consumption, employment, and the real wage are all slightly below their deterministic steady states across all regimes, because in the absence of capital households respond to increased volatility by substituting away from labor toward leisure (precautionary leisure) rather than precautionary saving. Mean outcomes for real variables under discretion (e.g., output mean ≈ 0.3730, unemployment mean ≈ 6.025 percent) and commitment (output mean ≈ 0.3729, unemployment mean ≈ 6.028 percent) are very similar to each other and to the flex-price means (output mean ≈ 0.3728, unemployment mean ≈ 6.038 percent). The key difference is in inflation: commitment delivers near-zero mean inflation (≈ 0.00043 percent annually) while discretion delivers ≈ 1.82 percent annually.

Q9: Why is a nonlinear solution method used, and what does this allow the paper to capture that log-linearized approaches cannot?

The nonlinear solution is required because the flex-price equilibrium is not efficient (monopolistic competition and the matching friction both create distortions), so the discretionary policy problem cannot be formulated as a linear-quadratic problem. The nonlinear approach allows the paper to analyze both level biases (the steady-state inflation bias) and stabilization biases (the dynamic response to shocks) in a unified framework — something that log-linearization around the efficient steady state would preclude. Related papers by Furlanetto and Groshenny (2016) and Zhang (2017) focus on log-linearized models and the natural rate of unemployment; this paper focuses instead on optimal policy and policy biases.

Q10: What role does the consumption preference shock play, and how does it differ from the other shocks?

The consumption preference shock is the only shock in the model that acts somewhat like a demand shock. A one standard deviation increase raises the utility obtained from consumption, leading households to increase consumption and hours worked (at a slightly lower real wage), which induces firms to post more vacancies and raise employment. Most of the labor market response comes through higher hours rather than higher employment. Both commitment and discretionary policy cope well with this shock — the real economy closely tracks the flex-price equilibrium — because the shock has relatively little impact on inflation (inflation declines slightly due to lower real marginal costs from the lower real wage). The nominal interest rate rises because the increase in the real interest rate (driven by households’ desire to borrow) more than offsets the decline in inflation.

Key Concepts

Matching efficiency shock: A stochastic shock to the parameter mt in the constant-returns-to-scale matching function Mt = mt * u_t^xi * v_t^(1-xi), which governs the overall rate at which unemployed workers and posted vacancies are matched. A decline in mt reduces the number of matches formed at any given levels of unemployment and vacancies, raising unemployment and reducing employment. The paper treats this as an empirically relevant shock motivated by evidence of a sustained decline in aggregate matching efficiency during the Great Recession.

Discretionary inflation bias: The tendency for a central bank conducting policy without the ability to commit to produce systematically higher inflation than would occur under a commitment (Ramsey) regime. In this model, discretion generates an annualized inflation rate of approximately 1.82 percent, while commitment produces near-zero average inflation. This reflects the time-inconsistency problem (Kydland and Prescott, 1977; Barro and Gordon, 1983) arising from the interaction of monopolistic competition and price stickiness.

Stabilization bias: A distortion that arises under discretionary policy, in which the central bank’s inability to commit leads it to respond to shocks in a manner that departs from optimal commitment responses, producing suboptimal dynamics for real variables in addition to the inflation bias. In this paper, stabilization bias is found to be largely absent for matching efficiency, bargaining power, technology, and consumption preference shocks, but is present for the elasticity of substitution shock.

Hosios condition: The condition, derived in Hosios (1990), that efficient decentralized search-and-matching equilibrium requires workers’ bargaining power to equal the elasticity of matches with respect to the unemployment rate (ξ). In the paper’s notation: & = ξ. When the condition holds, the flex-price equilibrium replicates the social planner’s allocation in the labor market; deviations cause either excessive or insufficient vacancy posting.

Labor market tightness (θ): Defined as the ratio of vacancies to unemployed searchers, θt = vt/ut. When tightness is high, the labor market is tight and firms have difficulty filling vacancies (low job-filling rate q(θ)) while workers find jobs easily (high job-finding rate f(θ)). Tightness is the key state variable linking vacancy posting decisions by firms to employment dynamics and wage bargaining outcomes.

Bargaining power shock: A stochastic shock to the worker’s share of the Nash bargaining surplus (&t), which follows an AR(1) process. The Hosios condition holds at steady state but is violated when the shock is realized. A positive shock shifts surplus from firms to workers, raising real wages, depressing vacancy posting, and reducing employment, while a negative shock has the reverse effect.

Rotemberg price-adjustment cost: A quadratic cost φ/2 * (π_t)^2 * y_t paid by firms when they change prices, creating price stickiness without the “menu cost” lumpiness of Calvo pricing. This creates a role for monetary policy and generates a nonlinear Phillips curve. The coefficient φ is set to 80, based on the estimate in Ireland (2001).

Flex-price equilibrium: The benchmark equilibrium in which prices are fully flexible and bargaining is efficient (Hosios condition satisfied exactly). In this equilibrium there is no role for monetary policy over the price-adjustment margin, and the economy responds to shocks in a manner that is efficient conditional on the remaining frictions (monopolistic competition and the matching friction). The paper uses deviations of commitment and discretionary outcomes from this benchmark to measure the efficiency of optimal monetary policy.