The New Keynesian Transmission Mechanism: A Heterogeneous-Agent Perspective

The paper asks how income inequality affects the monetary transmission mechanism, noting that “traditional New Keynesian (NK) models rely on a setting with a representative agent (RA) and thus by definition do not allow this topic to be analyzed” (Introduction, p. 2). Motivated by the extreme concentration of wealth relative to labor income in the data, the authors deliberately choose “the very simplest extension of a NK model, namely, a model with two consumers aimed to represent ‘workers’ and ‘capitalists,’ hence capturing what is arguably the key element of inequality in the data” (Introduction, p. 3), explicitly framing it as a tractable shortcut for a richer Aiyagari/Huggett-style economy in which a small group of agents lives mostly off capital income (footnote 9).

“There is no response at all in these variables” to a monetary policy shock, in sharp contrast to the standard model’s substantial negative output and employment response to a rate increase (Section 3.1, p. 12). The real interest rate, inflation, real wages, and profits all respond in qualitatively similar ways across the two models, but hours worked in the worker-capitalist model stay exactly at zero deviation regardless of the shock, so “although aggregate consumption is unaffected by monetary policy, its distribution is: in response to a higher interest rate, the consumption of workers falls and that of capitalists increases” (Section 3.1, p. 13).

Combining the market-clearing condition (worker consumption equals labor income, c-hat_wt = omega-hat_t + n-hat_t) with the intratemporal optimality condition under King-Plosser-Rebelo preferences (phi n-hat_t + c-hat_wt = omega-hat_t) yields phi n-hat_t + omega-hat_t + n-hat_t = omega-hat_t, which reduces to n-hat_t = 0 “regardless of the Frisch elasticity” (Section 3.1, p. 13). Because KPR preferences are constructed so that income and substitution effects on labor supply exactly cancel for a household living solely off its own labor income, removing profit income from the worker’s budget makes this cancellation exact and hours completely invariant to the wage; the entire adjustment instead falls on the real wage, which moves one-for-one with worker consumption.

Inserting the analogous market-clearing condition for the standard model (which includes profit income) into the labor-supply optimality condition yields n-hat_t = [(1-S-bar)/(phi+S-bar)](omega-hat_t - d-hat_t), where S-bar is the steady-state labor share (equation 23, Section 3.1, p. 14) – so hours respond only to the extent that profits (d-hat_t) deviate from wages, and this term is zero exactly when the labor share is 100%. The authors explain the economic logic: “the increase in profits makes the representative household choose to work less: an income (wealth) effect,” so a monetary loosening that lowers real wages and raises profits makes the representative agent poorer via lost profit income, inducing it to supply more labor – an effect that scales with the steady-state profit share (about 17% in their calibration).

First, using Survey of Consumer Finances data (Table 2, from Gornemann, Kuester, and Nakajima 2016), the paper shows that even households in the 80th-95th wealth percentile derive 81% of income from labor and only 14% from financial sources, so “few households have substantial non-labor income,” undermining the premise that ordinary workers’ labor supply should respond much to profit movements (Section 3.1, p. 14). Second, “profits are strongly procyclical, not countercyclical, in the data,” and the available evidence is that they fall after a monetary tightening (citing Christiano and Eichenbaum 1992/2005) – the opposite sign from what the representative-agent transmission channel requires (Section 3.1, p. 15). The authors conclude that although the textbook 3-equation model produces intuitive reduced-form responses, “the transmission mechanism whereby this is achieved is very hard to justify empirically.”

With wages sticky (theta_w = 3/4, an average four-quarter wage-reset duration) and prices sticky as before, “the responses to the monetary shock are almost indistinguishable” between the textbook and worker-capitalist models (Section 3.2, p. 16). The mechanism: workers become constrained to supply whatever labor is demanded (equation 7) rather than choosing hours from their now largely inoperative labor-supply first-order condition, so labor demand follows directly from consumption demand, and since profits are now a small (about 17%) and procyclical share of income, aggregate consumption demand in the worker-capitalist model tracks the textbook model closely. The authors show “the difference between the textbook and the worker-capitalist model is decreasing in theta_w,” so the robustness of the transmission mechanism strengthens continuously with the degree of wage rigidity.

Yes – with rigid wages, nominal wages barely respond to the shock, so nominal marginal costs and hence inflation respond only modestly, which “almost completely close[s] the real wage gap”; since profit movements are then determined almost solely by the movement in output, “profits respond procyclically” rather than countercyclically (Section 3.2, p. 15) – bringing the model’s profit dynamics closer in line with the empirical procyclicality the flexible-wage version could not match.

No – the paper’s robustness check allows the capitalist to trade a risk-free bond with workers subject to quadratic portfolio-adjustment costs (to preserve stationarity), and shows the resulting impulse responses are very similar to the no-trade baseline under both flexible and rigid wages (Section 4, pp. 17-19). At their chosen intermediate adjustment-cost calibration (zeta = 4), the debt-to-GDP ratio peaks at only about 0.1 percent of GDP in response to the shock and mean-reverts within about three years, so “worker consumption is still close to labor income every period,” leaving the determination of labor supply essentially as in the no-trade model (Section 4, pp. 18-19). The paper notes that a fully unconstrained bond market instead makes the model non-stationary, since flexible-wage dynamics would otherwise imply permanently growing worker indebtedness to the capitalist (Section 4, p. 17).

"(i) the benchmark textbook NK model is not robust to the introduction of stark and real world-like inequality; but (ii) the textbook NK model with added wage rigidity does show robustness" (Section 5, p. 20). The authors frame this as also exposing an under-appreciated feature of the standard sticky-price-only RANK model itself: its transmission mechanism “relies on a transmission mechanism that is implausible: in response to a lowering of the policy rate, profits fall, making workers poorer and hence enticing them to work harder” – a mechanism that, once profit and labor income are separated across distinct agents as in the data, simply is not available to move output.

The paper is explicit that its conclusions rest on standard King-Plosser-Rebelo balanced-growth preferences with exactly offsetting income and substitution effects; a footnote notes that with the slightly more general preference class of Boppart and Krusell (2016), where income effects slightly outweigh substitution effects, “we would see hours rise in response to a drop in wages,” making the wedge between the two models under flexible wages “even more different,” i.e., strengthening rather than overturning the paper’s qualitative conclusion (Introduction, footnote 4; Section 3.1, footnote 12). The authors also flag that whether real-world wage rigidity is empirically large enough at business-cycle frequency to deliver their solution “is an empirical question that we do not evaluate here,” while stressing that accurately measuring labor-market rigidity is therefore important for this class of models (Section 3.2, p. 16).