Q50 | Macro Paper Warehouse

A Heterogeneous Agent Model of Energy Consumption and Energy Conservation

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

Audzei and Sutóris ask whether inflation-targeting monetary policy affects households’ incentives to invest in energy conservation, and whether the standard central bank response to energy price shocks is welfare-optimal when agents are heterogeneous. They embed energy in both the consumption bundle and the production function of a tractable heterogeneous-agent New Keynesian (HANK) model that features Challe–Ravn–Sterk search-and-matching frictions in the labor market, nominal bond holdings, and — the paper’s central innovation — household-level energy conservation (abatement) capital that converts raw energy into energy services. The model is calibrated to the Czech Republic, with an energy share in household consumption of 10%, an energy share in production of 5%, a steady-state job-finding rate of 0.15 (targeting a poor hand-to-mouth share of 9%), and a capitalist share of 12%. The main quantitative findings are that a tighter monetary policy shock reduces abatement capital investment, increases the energy intensity of consumption, and depresses the job-finding rate, all of which fall disproportionately on lower-wealth households; conversely, a weaker policy response to a persistent energy price shock — one with a lower inflation coefficient (φ_π = 1.1 rather than the baseline φ_π = 2) — generates welfare gains for all agent groups (capitalists, employed workers, newly unemployed, long-term unemployed) despite higher measured inflation, because it preserves employment and stimulates abatement investment, reducing households’ long-run exposure to energy price shocks. The paper also shows that a “looking-through” policy (reacting to core rather than CPI inflation) does not deliver welfare benefits because it is too accommodative when energy prices rise but too restrictive once they start to fall; Ramsey-optimal policy instead features a sharp front-loaded rate spike followed by a rapid decline, minimizing aggregate consumption volatility through higher abatement capital.

In depth

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.

Energy Transitions in Regulated Markets

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks how rate-of-return (RoR) regulation in U.S. electricity markets affects the speed and efficiency of energy transitions, specifically the transition from coal to combined-cycle natural gas (CCNG) generation driven by fracking-induced cost declines. The authors build and estimate a structural model of regulated utility behavior in which utilities optimize investment, retirement, and hourly operations decisions against an incentive structure set by state Public Utility Commissions (PUCs).

The regulatory environment combines two instruments: (1) an allowable rate of return that is decreasing in consumer electricity rates (incentive regulation), parameterized as s = (r/r₀)^{-γ}, where higher γ penalizes high-cost outcomes more severely; and (2) a “used-and-useful” standard in which a coal plant’s contribution to the rate base depends on its capacity utilization via a logit function. These two instruments create a tension: utilities want to lower costs to earn a higher RoR, but also want to run existing coal plants—even when uneconomical—to prove they are “used and useful” and thus maximize their rate base and profits.

The authors estimate the model using publicly available EIA and EPA CEMS data spanning 2006–2017, covering 39 unique regulated utilities in the Eastern Interconnection across more than 4 million utility-hour observations (459 utility-years). Structural parameters are recovered via a nested fixed-point indirect inference approach that matches simulated regression coefficients to actual data; investment and retirement costs are estimated with a GMM nested fixed-point approach.

Key reduced-form findings confirm the model’s two core mechanisms. First, a 10% increase in total variable costs is associated with a 2.5% decrease in variable profits per MW of capacity (with utility fixed effects), consistent with incentive regulation. Second, regulated utilities reduce coal generation by only a statistically insignificant 4.2 percentage points when coal fuel costs exceed import prices, compared to 16.1 percentage points for restructured utilities—consistent with regulated utilities running coal out-of-dispatch order to preserve used-and-useful status.

In counterfactual simulations that impose 2018–20 natural gas prices ($2.01/MMBtu versus the 2006 price of $7.24/MMBtu) on utilities with their 2006 capital stocks, regulated utilities retire only 53% of coal capacity over 30 years and increase CCNG capacity by 296%, whereas a cost minimizer would retire most coal capacity while increasing CCNG by only 58%. The Averch-Johnson over-investment effect dominates: regulated utilities over-invest in CCNG while simultaneously over-using legacy coal.

Carbon taxes on regulated utilities reduce short-run coal generation only 48% as much as when imposed on a cost minimizer (because the used-and-useful incentive partially offsets the carbon price signal), but in the long run result in 68% lower coal capacity and 77% lower coal generation relative to baseline by year 30—larger effects than for the cost minimizer. Eliminating the coal usage incentive (μ₂ = 0) produces 82% lower coal capacity and 92% lower coal generation over 30 years but requires utility variable profits to fall by over $300 million, threatening reliability without compensating transfers.

Scope conditions: Results apply to regulated (non-restructured) utilities in the Eastern Interconnection, 2006–2017. The model estimates the coal-to-CCNG transition only; it explicitly does not model the ongoing transition to renewables and storage due to insufficient data variation.

In depth

Q1. What is the central research question?

The paper asks whether and how rate-of-return regulation in U.S. electricity markets slows energy transitions, and what alternative regulatory structures or carbon tax policies could accelerate the transition away from coal. It addresses this both theoretically—through a structural model of regulated utility behavior—and empirically, through estimation and counterfactual simulation using data on 39 regulated utilities over 2006–2017.

Q2. What are the two key regulatory instruments in the model, and what distortions do they create?

The first instrument is incentive regulation: the allowable rate of return declines as consumer electricity rates rise (s = (r/r₀)^{-γ}), so utilities have an incentive to lower costs. The second is the used-and-useful standard: a coal plant’s contribution to the rate base depends on its capacity utilization via a logit function, creating an incentive to run coal plants even when their fuel costs exceed import prices. Together, these instruments generate a tension between cost-reduction incentives and legacy-capacity-preservation incentives, causing the regulated utility to both over-invest in new CCNG capacity (Averch-Johnson effect) and over-use existing coal capacity relative to the cost-minimizing benchmark.

Q3. What does the reduced-form evidence show about uneconomical coal usage?

In a triple-difference specification, regulated utilities reduce coal generation by only 4.2 percentage points (statistically insignificant) when coal fuel costs exceed import prices, compared to a 16.1 percentage point reduction for restructured utilities. CCNG generation responds similarly under both regulatory regimes (21.1 vs. 19.7 percentage points), confirming that the distortion is specific to legacy coal under RoR regulation and not a general feature of high-cost generation. The six states with the largest responsiveness of coal usage to low market prices are all restructured states; out-of-dispatch-order coal generation also correlates strongly with utility ownership share across states.

Q4. What do the structural parameter estimates reveal about the rate base?

Each MW of CCNG capacity increases the rate base by $229,000. When fully utilized, each MW of coal capacity contributes 1.144 times as much as CCNG. When coal is not fully used, unused coal capacity contributes only 40% as much to the rate base as CCNG. NGT capacity contributes 79% more to the rate base than CCNG per MW. Operations cost estimates include O&M costs of $12.89/MWh for coal, $8.82/MWh for CCNG, and $44.63/MWh for NGT; a 100 MW coal ramp in one hour costs $4,770 versus $3,860 for CCNG.

Q5. What happens in the 30-year long-run counterfactual under the baseline regulated utility?

Facing a sudden drop to 2018–20 natural gas prices ($2.01/MMBtu vs. $7.24/MMBtu in 2006), regulated utilities retire 53% of coal capacity and increase CCNG capacity by 296% over 30 years. The Averch-Johnson over-investment effect dominates: utilities invest heavily in CCNG while retaining and using legacy coal far longer than a cost minimizer would. The social planner effectively eliminates coal generation immediately (99% reduction in the first period) and retires almost all coal capacity over the horizon.

Q6. How does a cost minimizer behave relative to the regulated utility in the same long-run counterfactual?

A cost minimizer immediately reduces coal generation by 50% in the first period and retires most coal capacity over 30 years while increasing CCNG capacity by only 58%—versus the regulated utility’s 296% CCNG increase. Thirty years after the shock, the cost minimizer has retired 71% more coal capacity than the regulated utility. The cost minimizer’s much smaller CCNG expansion reflects that it does not face Averch-Johnson incentives to over-invest in rate-base capital.

Q7. What is the short-run vs. long-run impact of carbon taxes on regulated utilities compared to cost minimizers?

In the short run, carbon taxes on regulated utilities reduce coal generation only 48% as much as when imposed on a cost minimizer (34% vs. ~100% in immediate generation drop), because the used-and-useful incentive counteracts the carbon price signal. In the long run (30-year horizon), however, carbon taxes on regulated utilities result in 68% lower coal capacity and 77% lower coal generation relative to baseline—larger percentage reductions than for a cost minimizer—because the regulatory structure amplifies the retirement incentive over time once carbon costs erode the economic rationale for keeping coal in the rate base.

Q8. What is the short-run operations counterfactual finding for carbon taxes in the sample period?

Using each utility-year in the analysis sample, imposing carbon taxes on regulated utilities reduces carbon costs by only about $500 million relative to baseline—41% of the $1.3 billion carbon cost savings from imposing the same carbon taxes on a cost minimizer. Despite this limited carbon reduction, electricity rates nearly triple from $77.58/MWh to $224.18/MWh under the regulated utility with carbon taxes, as the utility passes through most carbon costs to consumers; regulated utility variable profits also fall by over $500 million.

Q9. What happens when the coal usage incentive is eliminated (μ₂ = 0)?

Setting the coal usage incentive parameter μ₂ = 0 (eliminating the logit slope on capacity utilization) causes coal capacity to fall 82% and coal generation to fall 92% relative to baseline over 30 years—a slightly larger generation decline than for the cost minimizer. However, this comes at the cost of more than twice the CCNG capacity due to the Averch-Johnson effect, and requires utility variable profits to fall by over $300 million, raising reliability concerns unless accompanied by compensating transfers.

Q10. How does the paper’s mechanism relate to observed differences in coal exit rates between regulated and restructured states?

Between 2006 and 2018, 26.0% of coal capacity exited in restructured states versus only 17.2% in regulated states—a gap the authors attribute primarily to the used-and-useful incentive structure in RoR regulation. The structural model quantifies how this regulatory feature specifically distorts coal usage and retirement decisions; it is not explained by demand or cost differences across states, as confirmed by the triple-difference evidence showing the gap is specific to coal (not CCNG) and to regulated (not restructured) utilities.

Q11. Why does the paper argue that alternative regulatory adjustments are insufficient to replicate cost-minimizing transitions?

Changing regulatory parameters—such as increasing the coal usage incentive or adjusting the electricity rate penalty—does not come close to replicating the speed of the energy transition under a cost minimizer in the long-run simulations. Regulatory adjustments that do approach cost-minimizing outcomes (such as eliminating μ₂) require large reductions in utility variable profits sufficient to risk reliability, consistent with why the 2022 Inflation Reduction Act relied on substantial investment transfers rather than carbon taxes as its primary clean energy instrument.

Q12. What is the paper’s identification strategy?

Identification exploits the sharp, exogenous decline in natural gas fuel prices from fracking, which had heterogeneous implications across utilities depending on their initial capital mixes (coal-heavy vs. CCNG-heavy). By comparing investment, retirement, and operations decisions across utilities and over time—particularly between utilities that had CCNG exposure before the price decline and those that did not—the authors recover the structural regulatory and cost parameters. The IV specification for reduced-form evidence uses the current natural gas price interacted with the utility’s initial CCNG generation share as an instrument for fuel and import costs.

Q13. What are the paper’s explicit limitations?

The paper estimates the coal-to-CCNG transition only and cannot speak to the transition to renewables and storage, because there is insufficient variation in the data to identify how regulators would treat CCNG as a legacy technology subject to used-and-useful standards, or how renewables and storage would contribute to the rate base. The authors note that over-investment in CCNG capacity may create future stranded asset problems for ratepayers and that usage incentives for CCNG are likely to further hinder the transition to renewables—but these are conjectures rather than estimated findings.

Rate-of-return (RoR) regulation: A regulatory structure in which the PUC sets electricity rates so that utility revenues cover total variable costs plus an allowable return on the utility’s rate base (capital stock), with the allowable return parameterized as s = (r/r₀)^{-γ}, declining as consumer electricity rates rise.

Used-and-useful standard: A prudence criterion under which a capital asset’s contribution to the rate base depends on its capacity utilization, modeled as a logit function of the generation-to-capacity ratio; fully used coal capacity contributes 1.144 times as much as CCNG per MW, while unused coal contributes only 40% as much.

Rate base: The capital stock on which the PUC grants the utility its allowable rate of return; adjusted by prudence and used-and-useful assessments and described in the paper as “at best an arduous task” to quantify precisely.

Averch-Johnson (AJ) over-investment effect: The tendency of regulated utilities to over-invest in capital because profits are proportional to the rate base; in this paper’s setting, this causes regulated utilities to increase CCNG capacity by 296% over 30 years following the natural gas price shock, compared to 58% for a cost minimizer.

Incentive regulation: A modification of cost-plus RoR regulation in which the allowable rate of return declines as electricity rates rise; it provides efficiency incentives for cost reduction but does not achieve first-best outcomes and is insufficient to overcome the used-and-useful distortion for legacy coal.

Out-of-dispatch-order generation: Running a generation unit when its fuel costs exceed the market import price; regulated utilities engage in this behavior with coal plants to maintain used-and-useful status and rate base contribution, whereas restructured utilities do not face this incentive.

Nested fixed-point indirect inference: The estimation approach used to recover structural regulatory and operations parameters by minimizing the distance between regression coefficients from actual data and those from model-simulated data via a non-linear parameter search.