Robot adoption and inflation dynamics

Robot Adoption and Inflation Dynamics

Research Question

Basso and Rachedi investigate how robot adoption influences inflation dynamics — specifically, whether the surge in automation during the 2000s and 2010s can explain the muted sensitivity of inflation to unemployment (the “flat Phillips curve”) observed in advanced economies prior to the Covid pandemic, and whether the same framework can account for the subsequent resurgence of steep inflation-unemployment co-movement.

Data and Methodology

The empirical analysis uses an annual panel covering 384 U.S. metropolitan statistical areas (MSAs) from 2008 to 2018. The dependent variables are non-tradable goods inflation (log-difference of services prices excluding rents and utilities, from BEA regional price parities) and wage inflation (log-difference of average compensation per job). Robot adoption at the MSA-year level is constructed following Acemoglu and Restrepo (2020a): industry-level robots per employee at the U.S. national level are weighted by industry employment shares in each MSA, yielding an MSA-year robot-per-employee ratio.

The regression specification extends Hazell et al. (2022) by adding an interaction term between the lagged unemployment rate and the (demeaned) robot-per-employee ratio, along with MSA and year fixed effects. Year fixed effects absorb common inflation expectations and the endogenous response of monetary policy to aggregate demand shocks. To address endogeneity, unemployment is instrumented with a Bartik shift-share variable of tradable demand spillovers, and robot adoption is instrumented with average industry-level robot penetration in the five largest European economies — under the identifying assumption that robot demand shocks are weakly correlated across advanced countries.

The theoretical framework is a New Keynesian model augmented with (i) directed search frictions in the labor market, and (ii) producer-level automation decisions in the spirit of Acemoglu and Restrepo (2020a). Producers pay a fixed entry cost, draw idiosyncratic efficiency for employing labor, and then choose between a robot technology (certain output at low efficiency) and a labor technology (uncertain hiring, higher potential efficiency). This generates an automation threshold: low-efficiency producers install robots, displacing low-wage jobs. A Taylor rule closes the model. Quantitative exercises compare two steady states calibrated to robot-per-employee ratios of 0.2% (low automation, targeting the U.S. in the early 2000s) and 0.6% (high automation, calibrated to one standard deviation of robot penetration variation across MSAs).

Main Findings

Empirical. In the baseline IV regression, a one standard deviation increase in robot adoption reduces the sensitivity of price inflation to unemployment by 17%, and the sensitivity of wage inflation to unemployment by 9%, relative to a MSA with the average robot penetration. The larger flattening effect on price inflation than on wage inflation implies that robot adoption also diminishes the pass-through from wages to prices. All three effects are statistically significant at the 5% level, and are robust to controls for demographic structure (age composition, gender/race/education participation rates, MPC heterogeneity), occupational structure (abstract, routine, manual, and offshorable occupations), and import competition exposure (Chinese and Mexican import shares).

Model quantification. Comparing the high-automation to the low-automation steady state, the model generates a 14% reduction in the slope of the price Phillips curve and a 13% reduction in the slope of the wage Phillips curve, conditional on the same-sized demand shocks in both economies. The price Phillips curve result accounts for 82% of the empirical estimate (17%). The model overstates the flattening of the wage Phillips curve (13% vs. 9% in the data), and therefore understates the reduction in the wage-to-price pass-through.

Mechanisms. Automation flattens the Phillips curve through two primary channels. First, the outside option of automating production reduces workers’ bargaining power and dampens the elasticity of wages to unemployment (the “Wage Setting Effect”). Second, a higher share of robot firms reduces the aggregate labor share, muting the pass-through from wages into prices (the “Steady State Effect”). A third channel — firms cyclically substituting workers for machines in response to a shock (the “Cyclical Effect”) — operates during the transition but the Wage Setting Effect accounts for the bulk of the flattening.

Non-linearity and the post-Covid resurgence. When robot-production is subject to convex adjustment costs, the threat of automation that underlies the Wage Setting Effect becomes inoperative during large expansionary shocks. When investment in machines surges, the marginal cost of producing robots rises sharply, raising the price of machines and pushing the automation threshold downward — more firms must use labor. Workers then negotiate higher wages, which pass into prices. Conditional on small demand shocks, the high-automation economy still exhibits a flatter Phillips curve than the low-automation economy. Conditional on large demand shocks (simulated as a 2 percentage point drop in unemployment), there is no difference in the inflation response between the low- and high-automation economies, so the Phillips curve reverts to steep.

Q&A

Q1: What is the exact empirical specification and how does it map to a structural object?

The regression is: non-tradable goods inflation = β × lagged unemployment + γ × (lagged unemployment × demeaned robot adoption) + ζ × lagged robot adoption + χ × relative non-tradable price + MSA fixed effects + year fixed effects + error. In a multi-region model without automation, Hazell et al. (2022) show that the coefficient β identifies the aggregate slope of the Phillips curve because year fixed effects absorb both common inflation expectations and the endogenous monetary policy response to aggregate demand shocks. Adding the interaction term extends this logic: γ identifies how robot adoption causally shifts the slope of the local Phillips curve, which maps into changes in the aggregate slope.

Q2: What are the first-stage instruments and why are they valid?

Unemployment is instrumented with local tradable demand spillovers — a Bartik variable weighting national industry value-added growth (excluding each MSA’s own contribution) by each MSA’s average industry value-added shares, so national supply disturbances uncorrelated with MSA-level heterogeneity generate plausibly exogenous unemployment variation. Robot adoption is instrumented with the implied robot-per-employee ratio obtained by replacing U.S. industry robot installations with the average across the five largest European economies, weighted by U.S. industry employment shares; this isolates the supply-side efficiency improvements in robot technology that drove global adoption, conditional on robot demand shocks being weakly correlated across countries. The correlation between the two instruments in the sample is 0.2, ensuring they do not strongly co-move.

Q3: What are the point estimates and their magnitudes in the baseline IV regression?

For price inflation (Panel A, Column 4), the base sensitivity β = −0.5069 (SE 0.1381, significant at 1%), and the interaction coefficient γ = 0.0066 (SE 0.0030, significant at 5%). For wage inflation (Panel B, Column 4), β = −0.9580 (SE 0.2450, significant at 1%), and γ = 0.0049 (SE 0.0024, significant at 5%). A one standard deviation increase in robot adoption reduces price inflation sensitivity by 17% and wage inflation sensitivity by 9% relative to the average-automation MSA.

Q4: What does the difference in flattening magnitudes (17% for prices vs. 9% for wages) imply about the wage-price pass-through?

Because automation reduces the price Phillips curve slope by proportionally more than the wage Phillips curve slope, each percentage-point change in wages translates into a smaller percentage-point change in prices in higher-automation areas. This indicates that robot adoption diminishes the influence of wage changes on price changes — i.e., it reduces the wage-to-price pass-through. In the model, this operates through the Steady State Effect: a larger share of production carried out by robot firms means that a given change in average wages applies to a smaller portion of total marginal costs, weakening the price response.

Q5: How is the automation threshold determined in the theoretical model, and what economic forces govern it?

A producer opts for the labor technology if and only if the expected value of a labor firm (= job-filling probability × (producer price × labor efficiency − posted wage) − entry cost) exceeds the value of a robot firm (= producer price × robot efficiency − machine price − entry cost). Since the value of a labor firm increases in labor efficiency, there is a unique cut-off efficiency level γ* at which a producer is indifferent. Producers with labor efficiency above γ* post vacancies; those below γ* install robots. The cut-off rises (more automation) when wages rise relative to machine prices, and falls (less automation) when machine prices rise due to costly robot production during large expansionary shocks.

Q6: How does the wage-posting equilibrium under directed search generate the Wage Setting Effect of automation?

Under directed search, each labor firm posts a wage to maximize its expected value, and workers sort into sub-markets offering higher wages but lower job-finding probabilities. The equilibrium posted wage for a firm with labor efficiency γj is Wγj,t = PP,t × γj × (1 − η), where η is the elasticity of matches to vacancies. The option to install a robot — available at any time — limits how much any individual firm needs to offer workers. When automation increases, the outside option becomes more attractive to more firms, which constrains wage offers industry-wide, reducing the elasticity of average wages to unemployment fluctuations.

Q7: How is the slope of the price Phillips curve characterized analytically?

Log-linearizing the model around the steady state and substituting labor market and wholesaler equilibrium conditions into the pricing equation yields: inflation = −[(ε−1)/φ] × Ψ(γ*; Θ) × unemployment gap + β × expected future inflation, where Ψ(γ*; Θ) is a function of the automation cut-off γ*, the elasticity of substitution ε, the matching function elasticity η, the efficiency bounds γM and γH, and the distribution shape parameter α. In contrast to standard New Keynesian models where the slope depends only on markup and nominal rigidity parameters, this expression depends directly on the degree of automation through the steady-state threshold γ*.

Q8: Across different structural parameter configurations, does automation always flatten the Phillips curve?

Yes. Numerical analysis of the closed-form Phillips curve expression (Figure 1) shows that robot adoption unambiguously decreases the slope of the price Phillips curve across all combinations of the key structural parameters — the distribution shape parameter α, the matching elasticity η, the upper bound of labor efficiency γH, and the steady-state unemployment rate ū. The flattening effect is more pronounced when η is low, when α implies a larger fraction of low-efficiency producers, and when the steady-state unemployment rate is low.

Q9: How do the three mechanism channels (Cyclical, Wage Setting, Steady State) compare quantitatively?

The paper isolates channels by comparing alternative model specifications: (i) Baseline directed search with endogenous automation, (ii) Directed search with fixed automation (removing Cyclical and Wage Setting Effects, leaving only the Steady State Effect), (iii) Random search with τ = 0.5 (efficient bargaining, retaining both the Cyclical and Wage Setting Effects), (iv) Random search with τ = 0.01 (near-zero worker bargaining power, removing the Wage Setting Effect but retaining the Cyclical Effect). Figure 5 shows that the Steady State Effect alone accounts for only a small portion of the total inflation differential between low- and high-automation economies. The Wage Setting Effect — isolated by comparing τ = 0.01 and τ = 0.5 economies with endogenous automation — accounts for the bulk of the flattening. The Cyclical Effect (isolated by comparing fixed and endogenous automation with τ = 0.01) contributes an intermediate amount.

Q10: What is the quantitative exercise comparing low- and high-automation steady states?

The low-automation economy targets the U.S. robot-per-employee ratio of 0.2% in the early 2000s (Acemoglu and Restrepo, 2020a), calibrated with robot-specific technological change ζ = 2. The high-automation economy features a 200% higher robot-per-employee ratio of 0.6%, calibrated to replicate one standard deviation of cross-MSA dispersion in robot penetration in the data. Both economies are simulated with 10,000 realizations of preference shocks, and the slopes of the price and wage Phillips curves are estimated from simulated inflation and unemployment outcomes. The price Phillips curve flattens by 14% and the wage Phillips curve by 13% moving from low to high automation, conditional on the same-sized shock in both economies.

Q11: How does the model account for the Covid-era resurgence of high inflation despite high automation?

The paper extends the machine manufacturer’s production function to include an asymmetric convex adjustment cost that activates when investment deviates more than 5% from its steady-state level (parameterized with δ = 0.0015 and ϱ = 100). Under a small expansionary shock (0.25 percentage point decrease in unemployment), inflation rises less in the high-automation economy, consistent with a flat Phillips curve. Under a large expansionary shock (2 percentage point decrease in unemployment), the surge in robot investment triggers sharply rising machine prices, eliminating the automation outside option for marginal producers and fully restoring workers’ bargaining power — so the inflation response is identical in the low- and high-automation economies, consistent with a steep Phillips curve. The paper interprets this as a proof-of-concept consistent with post-Covid wage compression evidence for low-wage workers documented by Autor, Dube, and McGrew (2023).

Q12: What do the robustness checks establish regarding alternative explanations?

The interaction of unemployment and robot adoption remains statistically significant at the 5% level across all the robustness checks (Appendix A). These include controlling for: (i) demographic heterogeneity — shares of young (below 30) and old (above 60) individuals, female/Black/Asian labor market participation, low-education attainment shares, overall participation, and MSA-level average marginal propensity to consume (MPC); (ii) occupational structure — shares of abstract, routine, manual, and offshorable occupations; and (iii) import competition — MSA exposure to Chinese and Mexican import competition. The coefficient on the robot-unemployment interaction term is stable across specifications, with the magnitude remaining close to that in the baseline (approximately 0.0140 across all demographic robustness columns in Table A.1).

Key Concepts

Automation threshold (γ):* The paper-specific level of idiosyncratic labor efficiency at which a producer is indifferent between installing a robot and posting a vacancy. Producers with labor efficiency below γ* choose the machine technology; those above choose the labor technology. The threshold is determined by the relative profitability of the two technologies, and it shifts endogenously with wages, machine prices, and job-filling probabilities. A higher γ* means more of the production sector is automated.

Wage Setting Effect of automation: The channel through which the existence of the outside option to install robots reduces workers’ bargaining power and dampens the elasticity of wages to unemployment fluctuations. Under directed search, firms’ ability to substitute machines for labor at a lower cost constrains the wage offers they need to post, so that a given decline in unemployment generates a smaller increase in average wages in higher-automation economies.

Steady State Effect of automation: The channel through which a larger steady-state fraction of robot firms reduces the aggregate labor share, so that even a given change in wages translates into a smaller change in aggregate marginal costs and prices. This channel operates even when automation cannot change upon a shock (fixed automation baseline).

Cyclical Effect of automation: The channel through which firms actively replace workers with machines in response to expansionary shocks that raise wages, generating an endogenous dampening of labor demand and putting downward pressure on the wage increase itself. This channel requires endogenous automation choices at business-cycle frequencies.

Robot-specific technological change (ζ): In the paper’s model, the parameter governing the efficiency with which machine manufacturers transform final goods into robots. A higher ζ reduces the relative price of machines (PM/P = 1/ζ), making automation more attractive to lower-efficiency producers and raising the automation threshold γ*. In quantitative exercises, variation in ζ across steady states drives differences in the degree of automation.

Price Phillips curve slope (Ψ): In the paper’s log-linearized model, the structural coefficient linking inflation to the unemployment gap. Unlike in standard New Keynesian models — where the slope depends only on the markup and nominal rigidity — Ψ is a function of the automation threshold γ*, the matching elasticity η, the efficiency distribution parameters (γM, γH, α), and the elasticity of substitution ε. Robot adoption shifts γ* and thereby changes Ψ.

Asymmetric investment adjustment cost: An extension of the machine manufacturer’s production function that imposes convex costs when robot investment deviates above 5% from its steady-state level (parameterized by δ and ϱ). This specification makes it increasingly costly to rapidly scale up automation in response to large demand shocks, causing the machine price to spike and the automation outside option to cease being effective for marginal producers, thereby restoring workers’ bargaining power and steepening the Phillips curve during large expansionary episodes.