Per Krusell | Macro Paper Warehouse

Distributional Consequences of Becoming Climate-Neutral

Thu, 01 Jan 2026 00:00:00 +0000

This paper investigates how the EU’s Fit-for-55 climate package will affect aggregate output and distribute its costs across the income distribution. The question matters because energy is a necessity good — poorer households devote a larger share of spending to energy — so policies that raise energy prices are regressive in their first-order incidence. Despite a large literature on the aggregate macroeconomics of the green transition, distributional consequences have received limited attention.

Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative

This paper proposes a new way to compute the equilibrium of heterogeneous-agent models with aggregate uncertainty: rather than building a recursive, linearized law of motion for a high-dimensional state such as the cross-sectional wealth distribution – the strategy behind existing linearization methods including Reiter (2009, 2010), Childers (2017), and Ahn, Kaplan, Moll, Winberry, and Wolf (2017) – the authors solve, using entirely standard nonlinear methods, a single deterministic perfect-foresight transition path that follows a one-time, unexpected (“MIT”) shock away from the model’s non-stochastic steady state. Under the working assumption that the true stochastic equilibrium is well approximated by a linear system, that one nonlinear transition path is literally the model’s numerical derivative at each future time horizon, so the response to any sequence of aggregate shocks – and to any number of independent shocks, with computation time rising only linearly in the number of shocks – can be recovered by scaling and summing copies of this single impulse response, with no analytical differentiation and no explicit treatment of the distribution as a linearized state. The only nontrivial numerical tool the method requires is value-function iteration: once to solve the model’s non-stochastic steady state, and again, backward over a finite horizon, to solve for the transition path, with the passage of calendar time serving as the sole state variable added along the way. Applied to a standard Aiyagari-style economy with valued leisure and two aggregate technology shocks, the method reproduces conditional-moment results close to Dynare’s linearization- and second-order-perturbation-based solutions in a representative-agent benchmark, delivers accurate impulse responses (including for distributional statistics like the Gini coefficient and the hand-to-mouth share) in the heterogeneous-agent case, and, in an extension with a consumption externality and deficit-financed transfers, shows that Ricardian equivalence breaks down and fiscal transfers have real stabilizing effects – all without added numerical difficulty. The paper reports that its own scalability and additivity checks are satisfied “with flying colors” in this application, but is explicit that the whole approach rests on the assumption that linearization is in fact a good approximation for the model at hand, offers no formal stability or determinacy characterization of the transition path it computes, and, unlike recursive methods, provides no separate goodness-of-fit metric for that assumption.

Income and Wealth Heterogeneity in the Macroeconomy

In a calibrated stochastic growth model where a continuum of infinitely lived households face partially uninsurable employment risk and can self-insure only by holding aggregate capital, the macroeconomic aggregates turn out to be almost perfectly described by just two numbers — the mean of the wealth distribution and the aggregate productivity shock. The paper calls this approximate aggregation and states it carefully: “all aggregate variables — consumption, the capital stock, and relative prices — can be almost perfectly described as a function of two simple statistics,” so that “the distribution of aggregate wealth is almost completely irrelevant for how the aggregates behave in the equilibrium.” With a log-linear law of motion in the mean alone, the fitted rules are log k’ = 0.095 + 0.962 log k in good times and 0.085 + 0.965 log k in bad, both with R² = 0.999998 and regression-error standard deviations of 0.0028% and 0.0036%; price forecasts 25 years ahead have maximum errors under 0.1 percent. The mechanism is not that the distribution is stable — its standard deviation, skewness and kurtosis all “display substantial variation” — but that the marginal propensity to save is nearly independent of wealth except at the very bottom, and the agents whose propensities differ hold a negligible share of capital. The paper is equally clear that this benchmark fails as a model of inequality: the poorest 20 percent hold 9 percent of wealth against roughly zero in the data, the richest 5 percent hold 11 percent against roughly half, and the Gini is 0.25 against 0.79. The fix is a stochastic discount factor taking three values 0.9858, 0.9894 and 0.9930 with 50-year average duration at the extremes, read as imperfectly inherited patience; that model reproduces the data’s Gini (0.82 against 0.79) and its 11 percent of households with negative wealth, though it still understates the extreme upper tail. Approximate aggregation survives — R² = 0.999991 and 0.999985, with errors roughly twice as large. What does not survive is permanent-income behaviour: because impatient households face a large wedge between their discount rate and the market return, they consume hand-to-mouth, and while they “matter little for what happens to the evolution of economywide wealth,” their consumption is a large share of the total, pushing the aggregate consumption-output correlation to 0.825 against 0.691 in the complete-markets benchmark. Precautionary saving is small in the benchmark (0.6 percent of the capital stock) but rises to 6.7 percent with risk aversion of five. The methodological claim is stated as an enabling one — this “opens the possibility of characterizing a large class of new macroeconomic models in which heterogeneity in income and wealth plays a key role” — and the robustness claim is stated as an empirical regularity of their experiments, not a theorem: “it is extremely difficult to find exceptions to the approximate aggregation result,” while “like most numerical procedures, the present one does not provide bounds on how far the approximate equilibrium deviates from an exact equilibrium.”

Staffing agencies and in-house bargaining

This paper asks whether a labor market with search-and-matching frictions and firms producing under decreasing returns to labor is better characterized by in-house hiring with intra-firm wage bargaining (Stole-Zwiebel) or by an alternative arrangement in which intermediaries — “staffing agencies” — search for and employ workers and then rent them to producing firms on a frictionless, perfectly competitive market. The paper’s second and central question is what happens when firms can choose their optimal combination of the two arrangements simultaneously.

The New Keynesian Transmission Mechanism: A Heterogeneous-Agent Perspective

This paper studies how the simplest possible form of household heterogeneity – splitting the representative agent of the textbook New Keynesian model into a “worker,” who receives only labor income, and a “capitalist,” who receives only firm profits – changes the model’s monetary transmission mechanism. Under the standard assumption that only goods prices are sticky and wages are flexible, the authors show that this 2-agent model behaves very differently from its representative-agent counterpart: the real interest rate, inflation, real wages, and profits all respond similarly to a monetary policy shock, but output and employment do not respond at all in the worker-capitalist model, whereas they fall sharply in the standard model. The reason is that with the balanced-growth (King-Plosser-Rebelo) preferences standard in macroeconomics, income and substitution effects on labor supply exactly cancel; once profit income is removed from a worker’s budget (because a worker earns only wages), this cancellation makes hours completely unresponsive to wage movements, so monetary policy only redistributes consumption between workers and capitalists – it does not move aggregate output. The authors then show that the representative-agent model’s own ability to generate an output response rests on an empirically fragile mechanism: profits move countercyclically with the policy rate, making the representative household poorer and inducing it, via a wealth effect, to work more – a channel undermined both by household balance-sheet data showing few households hold much non-labor income, and by the fact that profits are procyclical, not countercyclical, in the data. When wage stickiness is introduced instead of (or alongside) price stickiness, however, workers are pushed off their static labor-supply curve and simply supply whatever hours are demanded; in this case the worker-capitalist model’s impulse responses become nearly indistinguishable from the representative-agent model’s, and the authors show this equivalence strengthens as the degree of wage rigidity increases. The authors confirm these results are robust to allowing limited financial trade between workers and capitalists via a bond market with adjustment costs.