A Heterogeneous Agent Model of Energy Consumption and Energy Conservation

Q1. What is energy conservation capital, how is it modeled, and why does it matter for the monetary policy transmission channel?

Energy conservation capital (abatement capital) is a durable investment good held by households that reduces raw energy required to produce a unit of energy service; because unemployed workers cannot afford it and its return competes with nominal savings, it creates a novel interaction between labor market outcomes and monetary policy. Households derive utility from a CES composite of non-energy consumption and energy services, where energy services are produced from raw energy multiplied by an efficiency factor that is increasing and concave in abatement capital: $E^s = f(K^e_{t-1}) E^r$, with $f(K^e) = \varphi_{1,e} (K^e)^{\varphi_{2,e}}$ and $\varphi_{2,e} = 2$. The elasticity of substitution between energy and non-energy goods is set to $\lambda_e = 0.3$, reflecting limited short-run substitutability. Abatement capital depreciates at 1% per quarter (equivalent to 4% annually, matching housing and heating systems lifetimes of ~25 years). Crucially, workers lose their abatement capital when they become unemployed (they move to a communal stock at the steady-state unemployed level $\bar{K}^e_u$), so abatement capital is not a precautionary savings vehicle and unemployed workers have no incentive to invest in it. Employed workers who optimally invest must account for the probability of becoming unemployed and therefore losing their capital. This structure means that monetary policy tightening — by raising unemployment and raising the return on nominal bonds — simultaneously pushes more workers into the non-investing unemployed pool and reduces the relative attractiveness of abatement investment for employed workers, raising the energy intensity of consumption.

Q2. What are the four agent types, and how do their asset positions differ?

The model compresses the household distribution into four types — employed workers, first-period unemployed, long-term unemployed, and capitalists — each with sharply different asset positions that determine how they are affected by monetary policy. Employed workers hold positive nominal bonds ($B’{e,t-1} > 0$) and invest in abatement capital ($K^e{e,t-1}$); they are the only group making active portfolio and investment decisions. First-period unemployed workers consume all their precautionary savings in a single period (their IMRS × R < 1) and receive 75% of unemployment benefits; they hold $B_{e,t-1} > 0$ (inherited from their last employed period) but make no new saving or abatement decisions. Long-term unemployed workers hold zero assets, receive full unemployment benefits indexed to the real wage, and maintain abatement capital at the fixed communal level $\bar{K}^e_u$. Capitalists ($\xi = 12%$ of population) own all firms, invest in productive capital and abatement capital, and are net borrowers in the steady state (rich hand-to-mouth in the Kaplan–Moll–Violante sense); they are subject to an endogenous discount factor that stabilizes the capital stock. Risk-sharing among employed workers — all employed household members pool their nominal bonds — enables tractability while preserving precautionary saving motives.

Q3. How does a monetary policy shock propagate through energy conservation decisions?

A 0.25 percentage-point positive monetary policy shock reduces abatement capital and raises energy intensity, operating through two reinforcing channels: the labor market channel (more unemployment, fewer households able to invest) and the intertemporal substitution channel (higher returns on nominal bonds reduce the relative attractiveness of abatement investment). Following the shock, the policy rate rise suppresses output and raises unemployment (Figure 3 of the paper). The increase in the job-destruction-net-of-finding probability $\omega(1-\eta_t)$ shifts more workers into the first-period unemployed pool, which carries no abatement investment. Among employed workers, the higher nominal bond return means that saving in bonds is relatively more attractive than investing in illiquid abatement capital, so their abatement holdings fall. The result is a rise in raw energy per unit of consumption, meaning the economy becomes more energy-intensive precisely when energy prices may also be elevated — a double vulnerability.

Q4. What are the welfare effects of different policy rules in response to a persistent energy price shock, and what are the magnitudes?

After a persistent hump-shaped energy price shock, welfare losses (measured as discounted infinite-horizon utility) are smaller for all agent groups under the weak-reaction policy (φ_π = 1.1, φ_y = 0) than under the baseline (φ_π = 2, φ_y = 0), even though inflation is higher under the weaker rule; the welfare gap is largest for employed workers and capitalists, and broadly preserved under alternative calibrations. Policies that react more weakly to inflation result in a smaller output recession and lower unemployment (Figures 7–9 of the paper). In the welfare simulation (Figure 9), all four agent types — capitalists, employed workers, newly unemployed, and long-term unemployed — show smaller welfare declines under the weak-reaction rule compared with baseline. Capitalists benefit because lower interest rates reduce their debt service and higher output raises firm profits. Employed and unemployed workers benefit primarily because of the higher job-finding rate, which lowers the probability of falling into the HtM state. Additionally, accommodative policy supports more investment in abatement capital, which reduces all agents’ long-run exposure to energy price fluctuations, further boosting welfare. The welfare ranking is robust to: (i) benefits fixed in nominal terms (narrower but preserved gap), (ii) more flexible wages (narrower gap; welfare ranking of capitalists reverses under flexible wages), and (iii) larger steady-state household savings (wider gap).

Q5. Why does the “looking-through” policy fail, and how does it differ from the weak-reaction policy?

The looking-through policy (φ_π = 2 on core inflation, ignoring energy-price CPI inflation) does not deliver welfare gains because it creates an asymmetric response profile: it is too accommodative during the energy price surge and too restrictive once energy prices start to fall, generating a welfare trajectory that is inferior to a consistently weaker policy. When energy prices are rising, CPI inflation exceeds core inflation; reacting only to core means the central bank does not raise rates as much as under the baseline, so the policy is more stimulative in the short term and supports output and abatement investment in the near term. However, once energy prices start declining, CPI inflation reverts to the steady state faster than core inflation (which is still elevated due to nominal rigidities), meaning the looking-through policy becomes more restrictive relative to the baseline at precisely the time when agents need support. The result is that long-run welfare, which discounts the entire future path, does not improve under looking-through relative to either the baseline or the weak-reaction rule. This finding provides an important caution against the standard “look through supply shocks” recommendation in a HANK environment with abatement capital.

Q6. What does Ramsey-optimal policy look like, and why does it differ from Taylor-type rules?

Ramsey-optimal policy — which minimizes the volatility of population-share-weighted aggregate utility — features a sharper and faster initial rate spike than the baseline Taylor rule, followed by a more rapid decline; it results in the highest abatement capital investment and lowest energy intensity of all policies considered. The Ramsey planner’s first-order conditions (solved with Dynare’s Ramsey tool, taking private-sector FOCs as constraints) imply that the policy rate peaks before the energy price shock itself peaks, reflecting the planner’s desire to front-load inflation stabilization while ensuring that rates fall quickly enough to not suppress abatement investment in the medium term. The Ramsey rate path is lower than the baseline Taylor rule after the shock peak. Compared with all Taylor-type rules, Ramsey policy results in the largest negative deviation in consumption energy intensity and the largest positive deviation in abatement capital (Figure 8). Ramsey policy also delivers the highest welfare for all agent groups (Figure 9), validating the intuition that protecting abatement investment is an important channel for central bank welfare optimization in this setting.

Q7. What is the role of heterogeneity in shaping these results, and what would be missed by a representative-agent model?

The distributional effects are essential to the paper’s core conclusions: a representative-agent model would miss the asymmetric impact of unemployment risk on energy conservation investment and would fail to generate the welfare reversal whereby a weaker inflation response dominates. Figure 6 of the paper shows the distributional responses to an energy price shock: capitalists reduce energy intensity the most because they can invest in abatement capital and their consumption is less constrained; employed workers also reduce energy intensity but less so; poor HtM households (unemployed workers) cannot adjust abatement capital and their energy intensity rises because the raw energy share in their limited consumption basket increases. The welfare comparison across agent types in Figure 9 shows that even newly unemployed workers — who lose their abatement investment and consume their precautionary savings — are better off under accommodative policy because the higher job-finding rate reduces the expected duration of unemployment. The key heterogeneity-driven mechanism absent from representative-agent models is the labor market channel: changes in unemployment risk affect who can and cannot invest in energy conservation, generating an indirect channel from monetary policy to aggregate energy intensity.

Q8. What are the model’s main limitations and scope conditions?

The paper abstracts from variable policy rule coefficients, wage-price spirals, unanchoring of inflation expectations, and open-economy dimensions beyond energy-price pass-through; the welfare ranking is conditional on the persistent energy price shock used for calibration and should not be extrapolated to short-lived or demand-driven inflation episodes. The authors explicitly note that the model operates under full-information rational expectations, which rules out the possibility that accommodation generates self-fulfilling inflation or credibility loss. Wage rigidity plays an important role: with more flexible wages, the welfare benefit of accommodative policy narrows and the capitalist welfare ranking reverses (baseline strict inflation targeting is preferred by capitalists). The “looking-through” and weak-reaction findings are specific to the persistent, hump-shaped energy price shock analyzed; for short-lived shocks the standard result (no reaction) would reassert itself. The model is also calibrated to the Czech Republic as a small open economy with above-average energy intensity; the qualitative conclusions extend to other European small open economies with similar energy share profiles, but quantitative magnitudes may differ.

Key Concepts

energy conservation capital (abatement capital) : a durable household investment good that converts raw energy into energy services more efficiently; modeled as $E^s = f(K^e_{t-1}) E^r$ with a quadratic abatement function; the level determines the energy intensity of consumption and is chosen optimally only by employed workers and capitalists.

energy intensity of consumption : the ratio of raw energy used to final consumption $E^r / C$; the paper’s key outcome variable for tracking how efficiently households use energy; a rise signals less efficient usage, a fall signals improved conservation.

looking-through policy : a monetary policy rule that reacts to core inflation (excluding energy) rather than CPI inflation, intended to avoid responding to transient supply shocks; the paper finds this does not improve welfare in a HANK setting because it creates an asymmetric response profile that is too accommodative when energy prices rise and too restrictive when they fall.

Ramsey-optimal policy : the interest-rate path that minimizes the volatility of population-share-weighted aggregate utility subject to the full set of private-sector equilibrium conditions; in this model it features a sharper front-loaded rate spike than Taylor-type rules followed by a rapid decline, and delivers the highest welfare for all agent groups by protecting abatement investment.

hand-to-mouth (HtM) households : households that are highly sensitive to income shocks but do not respond to interest rate changes as predicted by the Euler equation; in this model, poor HtM are both types of unemployed workers (zero savings, zero abatement investment), and rich HtM are capitalists (large debt, no labor income); their presence is central to the distributional welfare results.

search-and-matching frictions : the Challe–Ravn–Sterk labor market structure in which the job-finding rate $\eta_t$ is determined endogenously by the vacancy-unemployment ratio (Cobb-Douglas matching function) and job destruction is exogenous at rate $\omega$; this structure makes unemployment risk stochastic and endogenous to monetary policy, creating the key link between policy rates and energy conservation decisions.

Summary of a forthcoming paper, AI-assisted and pending human review. See the linked original for the authoritative claims and full conditions.