Climate Policies, Macroprudential Regulation, and the Welfare Cost of Business Cycles

Q1. What is the model structure and how does the environmental policy sector integrate with financial frictions?

The model is an E-DSGE built on the Christiano, Motto, and Rostagno (2014) financial accelerator framework, extended to include a carbon price instrument and heterogeneous firms that face both standard borrowing constraints and carbon compliance costs. There is a representative household and three firm sectors: a continuum of capital-producing entrepreneurs, retailers, and a goods sector. Banks extend loans to entrepreneurs at a spread over the risk-free rate; the external finance premium is endogenous because bank monitoring is costly and borrowers face costly state verification (as in Bernanke, Gertler, and Gilchrist, 1999). Environmental policy is introduced through a carbon permit or tax that enters firms’ marginal cost, so the carbon price affects both production decisions and the entrepreneur’s net worth, which in turn feeds back into the spread through the financial accelerator. Calibration uses US quarterly data (Table 1 in the paper), and the model is solved by log-linearizing around a deterministic steady state.

Q2. Why do financial frictions create a welfare advantage for cap-and-trade over carbon taxes?

Under a carbon tax, the tax rate is fixed by the regulator regardless of macroeconomic conditions; when a TFP or risk shock contracts output and reduces firm net worth, the fixed carbon cost amplifies the contraction by reducing the entrepreneur’s retained earnings, worsening the external finance premium, and deepening the financial accelerator loop. Under a CAT scheme, the equilibrium permit price is endogenous: it falls when aggregate activity and emissions decline, automatically lowering the compliance cost burden for firms at exactly the moment when balance sheets are most constrained. This procyclicality of permit prices functions as an automatic stabilizer, partially offsetting the financial accelerator’s amplification. The paper shows this via impulse response functions (Figures 1 and 2 in the paper) to TFP and risk shocks: under CAT, the responses of investment, bankruptcy, spread, and output are systematically more muted than under a carbon tax. Quantitatively, the baseline welfare cost of business cycles is 0.6178 percent of consumption under CAT versus 1.5231 percent under a carbon tax — a gap of nearly 0.91 percentage points of consumption.

Q3. How do optimal environmental policy rules affect welfare costs, and do they close the gap between regimes?

An optimal flexible CAT rule that allows permit prices to respond countercyclically to a macroeconomic indicator (net output) reduces welfare costs from 0.6178 to 0.4528 percent; an optimal flexible carbon tax rule reduces costs from 1.5231 to 1.1811 percent. In both cases, the optimal rule specifies vigorous countercyclical response: the optimal sensitivity parameter for the carbon tax rule is τ = 52.2245, meaning the tax rate must decrease sharply in recessions to mimic the automatic procyclicality of permit prices under CAT. Despite these improvements, the welfare gap between the two regimes persists even under optimal environmental rules: the optimized CAT still generates roughly 0.73 percentage points lower welfare costs than the optimized carbon tax. The paper concludes that countercyclical environmental policy can reduce but not eliminate the inherent stabilization advantage of CAT in the presence of financial frictions — because the fundamental mechanism (endogenous permit prices vs. fixed tax rate) cannot be fully replicated by a tax rule with a single output-gap indicator.

Q4. How do reserve requirement macroprudential regulations interact with the carbon pricing choice?

Introducing a static 2 percent reserve requirement (banks can loan out only 98 percent of deposits) already strongly reduces welfare costs and partially aligns the two regimes: CAT welfare costs fall from 0.6178 to 0.1957, and carbon tax costs fall from 1.5231 to 0.3863 (Table 5 in the paper). The mechanism is that reserve requirements limit bank credit expansion, lowering equilibrium leverage and reducing the severity of the financial accelerator — when firms’ balance sheets are less leveraged, adverse shocks cause smaller spirals in net worth and spreads. Dynamic reserve requirement rules — keyed to credit growth (optimal ψ_B ≈ 1.047) or asset price growth (optimal ψ_Q ≈ 0.722) — reduce welfare costs further, to 0.1207 under CAT and 0.2300 under a carbon tax with a credit-growth rule, effectively narrowing the gap to around 0.10 percentage points. The optimal policy mix (jointly optimizing both the macroprudential and environmental rules) achieves minimal additional improvement beyond the macroprudential optimum alone, suggesting the dominant stabilizing role is played by financial regulation rather than the choice of carbon pricing instrument when both are available and optimally calibrated.

Q5. How does macroprudential regulation affect the volatility of emissions and permit prices under each regime?

Table 6 in the paper reports coefficients of variation (CVE for emissions volatility, CVP_E for permit price volatility) across policy combinations. Under baseline CAT with no macroprudential regulation, CVE = 0 (the cap fixes aggregate emissions by construction) and CVP_E = 8.3578 — permit prices are very volatile. Adding a static reserve requirement reduces CVP_E to 2.5125; an optimal credit-growth rule reduces it to 1.0935, a reduction of nearly 87 percent from baseline. Under baseline carbon tax, CVP_E = 0 (the tax price is fixed by regulation) but CVE = 0.0574 — emissions are volatile. Adding a static reserve requirement reduces CVE to 0.0273; an optimal credit-growth rule reduces it to 0.0153. The paper interprets this as macroprudential regulation fostering convergence between the two instruments in their business cycle properties: it substantially stabilizes permit prices under CAT and substantially stabilizes emissions under a carbon tax, reducing the distinguishing uncertainty of each pricing approach. The optimal policy mix under a carbon tax with a dynamic subsidy achieves CVE = 0.0090 and CVP_E = 0.4956, showing that well-designed financial regulation can make a carbon tax nearly as emissions-stable as a CAT while also reducing permit price volatility.

Q6. What happens under an interest rate subsidy to depositors as an alternative macroprudential tool?

A static deposit interest rate subsidy of the welfare-maximizing level (1 percent) worsens welfare costs of business cycles — from 0.6178 to 1.1028 under CAT and from 1.5231 to 3.5597 under a carbon tax — because the subsidy moves the economy to a higher-leverage steady state, around which financial amplification is more severe (Table 7 in the paper). The intuition is that the subsidy encourages saving by raising the return on deposits, which raises equilibrium loan supply, which raises leverage; a more leveraged economy is more sensitive to adverse shocks. A dynamic subsidy rule that responds countercyclically to credit growth (optimal κ ≈ 1.319) mitigates this problem: it discourages saving when credit is expanding and encourages it when credit is contracting, partially stabilizing leverage dynamics. The dynamic subsidy reduces welfare costs substantially — to 0.2506 under CAT and 0.4706 under a carbon tax — and a joint optimization of the subsidy and the carbon pricing rule achieves 0.1926 under CAT and 0.4366 under a carbon tax with a dynamic subsidy. The authors note that the static subsidy result illustrates a general principle: macroprudential policies that move the steady state toward higher leverage can amplify cycle costs even while achieving efficiency gains around the steady state, and that distinguishing between steady-state and fluctuation welfare effects is essential when comparing such policies.

Q7. What are the main welfare and policy conclusions?

The paper establishes three conclusions. First, climate policy instrument choice has macroeconomic stabilization consequences in financially frictionous economies: CAT dominates a carbon tax for welfare when financial frictions are operative and macroprudential policy is absent or limited. Second, macroprudential regulation — particularly dynamic reserve requirement rules — is the more powerful tool for reducing the welfare cost of business cycles under both carbon pricing regimes, and can largely align the two regimes, making the instrument choice less consequential when macroprudential policy is well-calibrated. Third, the interaction between financial regulation and carbon pricing is non-trivial: the optimal sensitivity parameters for macroprudential rules differ depending on whether the economy uses CAT or a carbon tax, because the endogenous procyclicality of permit prices changes how financial shocks propagate through the economy.

Key concepts

financial accelerator: the mechanism by which adverse shocks to entrepreneurial net worth raise the external finance premium (the spread between the loan rate and the risk-free rate), reduce investment and output, further depress net worth, and generate amplified cycles; the core friction in the E-DSGE model and the channel through which carbon pricing affects welfare costs.

procyclical permit prices: the endogenous tendency of permit prices under a CAT scheme to fall when aggregate economic activity and emissions decline; the paper’s central mechanism through which CAT acts as an automatic stabilizer for the financial accelerator — permit prices fall precisely when firms’ balance sheets are most stressed, reducing compliance costs and partially offsetting amplification.

welfare cost of business cycles (Lucas measure): the percentage of consumption that a representative household would be willing to give up to move from a world with business cycle fluctuations to one without, evaluated relative to the deterministic steady state; in the paper’s baseline calibration, this is 0.6178 percent under CAT and 1.5231 percent under a carbon tax.

reserve requirement macroprudential regulation: a regulatory constraint requiring banks to hold a fraction of deposits in reserves, limiting loan supply; implemented in the model as Φ_t ∈ (0,1] where lower Φ_t requires banks to hold more reserves; a static 2 percent reserve requirement already substantially narrows the welfare gap between carbon pricing regimes, and an optimal dynamic rule nearly closes it.

E-DSGE (Environmental DSGE): the paper’s model class — a DSGE with financial frictions (Christiano-Motto-Rostagno financial accelerator) and a carbon pricing sector; used to analyze the interaction between environmental policy instruments and macroprudential regulation in an economy with both climate and financial externalities.

coefficient of variation of emissions (CVE) / permit prices (CVP_E): volatility measures used to assess how macroprudential regulation affects the business-cycle properties of each carbon pricing instrument; macroprudential regulation substantially reduces CVP_E under CAT and CVE under a carbon tax, making each instrument’s uncertainty properties more symmetric.