## 1. Introduction

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### Model purpose and key features
- Constructs and solves a dynamic stochastic general equilibrium (DSGE) model with nominal rigidities and an energy market that includes exhaustible (fossil fuel) and renewable resources.
- Government implements tax policies to discourage fossil fuel usage.
- Distinctive feature: explicit fossil fuel storage facility operated by forward-looking, risk-neutral, profit-maximizing speculative storers who form rational expectations about future fossil fuel prices.
- Storage modeled as a way of transferring fossil fuel from current to future periods and follows the modeling approach of Wright and Williams (1982, 1984, 1991) and Deaton and Laroque (1992, 1996).
- Commodity futures market is not explicitly modeled; competitive storage implies an arbitrage condition linking futures and spot markets (cited Hamilton (2009), Alquist and Kilian (2010), Kilian and Murphy (2014)); simplification focuses on spot-market speculation without loss of generality.

### Role of speculative storage and monetary policy transmission
- Speculative storage introduces a dynamic link among fossil fuel inventories, storers’ expectations of fossil fuel price, and the spot price.
- Storage generates a new transmission channel for monetary policy: changes in the real interest rate directly affect storage demand.
- Investigating speculative storage motives within a short-run general equilibrium model is motivated by its suitability for monetary policy analysis.

### Empirical motivation and existing literature
- Energy Information Agency data: ending stocks of crude oil as a percentage of quarterly total oil usage increased to 83 percent in 2010 from 62 percent in 2000 in the US.
- Prior DSGE work incorporating storage: Unalmis, Unalmis, and Unsal (2012) (UUU) show accounting for oil storage improves model fit and that storage demand can amplify or mitigate fossil fuel price dynamics depending on shock origins.
- Gap identified: no prior work (to the authors’ knowledge) investigates the role of speculative storage in amplifying short-term fluctuations caused by environmental taxes; this paper attempts to fill that gap.

### Model extensions and structure relative to prior work
- Four main extensions relative to UUU:
  - Fossil fuel supply partly endogenous: fossil fuel production split into exogenous OPEC component and endogenous non-OPEC component (following Backus and Crucini (2000) and Nakov and Pescatori (2010)).
  - Introduces renewable energy as an alternative endogenous energy source consumed by households and used in production.
  - More detailed treatment of fiscal policy: government taxes consumption and/or production of fossil fuels to promote substitution to renewable energy.
  - Focuses on dynamics following a fossil fuel tax shock.
- Agents and sectors: households, three types of production firms (differentiated core consumption good producers; renewable energy producers; fossil fuel producers), a government, a monetary authority, and fossil fuel storers.
- Fossil fuel is storable; renewable energy is not.

### Households and preferences (model specifics)
- Continuum of infinitely-lived households indexed j ∈ [0,1].
- Representative household maximizes expected discounted utility:
  - E_0 ∑_{t=0}^∞ β^t ((C_t(j) − H_t)^{1−σ}/(1−σ) − N_t(j)^{1+φ}/(1+φ)), where H_t = h C_{t−1} with h ∈ [0,1], 0< β <1, σ >0, φ >0.
- Aggregate consumption:
  - C_t = (∫_0^1 C_t(j)^{(ε−1)/ε} dj)^{ε/(ε−1)}, where ε is elasticity of substitution across varieties.
- Individual consumption C_t(j) is a CES aggregate of core consumption Z_t(j) and energy consumption E_{c,t}(j):
  - C_t(j) = [ (1−ω_{ec})^{1/ρ_c} Z_t(j)^{(ρ_c−1)/ρ_c} + ω_{ec}^{1/ρ_c} E_{c,t}(j)^{(ρ_c−1)/ρ_c} ]^{ρ_c/(ρ_c−1)}, with ρ_c intratemporal elasticity and 0< ω_{ec} <1 the energy expenditure share.
- Energy consumption E_{c,t}(j) is a CES aggregate of renewable energy RE_{c,t}(j) and fossil fuel FF_{c,t}(j):
  - E_{c,t}(j) = [ (1−ω_{ff,c})^{1/ρ_e} RE_{c,t}(j)^{(ρ_e−1)/ρ_e} + ω_{ff,c}^{1/ρ_e} FF_{c,t}(j)^{(ρ_e−1)/ρ_e} ]^{ρ_e/(ρ_e−1)}, with ρ_e intratemporal elasticity and 0< ω_{ff,c} <1 fossil-fuel share in household energy basket.
- Price indexes:
  - P_t = [ (1−ω_{ec}) P_{z,t}^{1−ρ_c} + ω_{ec} P_{e,t}^{1−ρ_c} ]^{1/(1−ρ_c)}.
  - P_{e,t} = [ (1−ω_{ff,c}) {(1−s_{re,c,t}) P_{re,t}}^{1−ρ_e} + ω_{ff,c} {(1+τ_{ff,c,t}) P_{ff,t}}^{1−ρ_e} ]^{1/(1−ρ_e)}, where s_{re,c,t} is subsidy on P_{re,t} and τ_{ff,c,t} is tax on P_{ff,t}.
- Demand functions (examples):
  - RE_{c,t}(j) = (1−ω_{ff,c}) [ (1−s_{re,c,t}) P_{re,t} / P_{e,t} ]^{−ρ_e} E_{c,t}(j).
  - FF_{c,t}(j) = ω_{ff,c} [ (1+τ_{ff,c,t}) P_{ff,t} / P_{e,t} ]^{−ρ_e} E_{c,t}(j).
- Households hold portfolios D_t(j), supply labor N_t(j), rent capital K_{1,t}(j), K_{2,t}(j), K_{3,t}(j), earn wage W_t(j), rental returns R^K_{ι,t}, and profits Π_t(j).
- Budget constraint (aggregated terms):
  - P_t C_t(j) + P_{z,t} I_{1,t}(j) + P_{z,t} I_{2,t}(j) + P_{z,t} I_{3,t}(j) + R_t^{-1} D_{t+1}(j) ≤ D_t(j) + W_t N_t(j) + R^K_{1,t} K_{1,t}(j) + R^K_{2,t} K_{2,t}(j) + R^K_{3,t} K_{3,t}(j) + Π_t(j).
- Capital accumulation for ι = 1,2,3:
  - K_{ι,t+1}(j) = (1−δ) K_{ι,t}(j) + Φ( I_{ι,t}(j) / K_{ι,t}(j) ) K_{ι,t}(j), with 0< δ <1, and steady-state properties Φ_ss = δ, Φ'_ss = 1, Φ''_ss = ξ <0, and δ ξ = −1.
- Under complete markets and perfect risk-sharing, consumption equal across households and R_t denotes risk-free nominal interest rate.
- First-order conditions (examples preserved as in text):
  - β E_t [ ( (C_{t+1} − H_{t+1}) / (C_t − H_t) )^{−σ} (P_t / P_{t+1}) ] = 1 / R_t.  (Equation (2.12))
  - (C_t − H_t)^σ N_t^φ = W_t / P_t.  (Equation (2.13))
  - P_{z,t} Λ_{ι,t} = β E_t { ( (C_{t+1} − H_{t+1}) / (C_t − H_t) )^{−σ} (P_t / P_{t+1}) ( R^K_{ι,t+1} + P_{z,t+1} Λ_{ι,t+1} ̃Φ_{ι} ) }, with definitions for ̃Φ_{ι} and Λ_{ι,t}.  (Equation (2.14))

### Main findings (summary)
- Speculative storage motives crucially affect:
  1. The effectiveness of fossil fuel taxes (consumer-only, producer-only, or both).
  2. The impact of these taxes on macroeconomic aggregates.
- Mechanism: Taxes on fossil fuel usage raise expected returns to speculation, increasing storage demand; higher storage demand reduces market-available fossil fuel supply, raises fossil fuel price, and further decreases fossil fuel usage — thereby enhancing policy effectiveness in reducing carbon emissions.
- Ignoring storage leads to substantial underestimation of the effect of fossil fuel taxes on overall fossil fuel consumption.
- Taxing fossil fuels under speculative storage increases volatility in macroeconomic variables including inflation and output.
- Monetary policy implications:
  - Without storage: responding to CPI inflation (rather than core inflation) along with output reduces macroeconomic fluctuations after a fossil fuel tax shock.
  - With speculative storage: responding to output in the monetary rule becomes less desirable; policymakers can further limit welfare loss by responding solely to CPI inflation due to significantly higher CPI inflation volatility in response to a tax shock under storage.

### Paper plan
- Section 2 introduces the model in detail.
- Section 3 presents results with calibration, impulse responses, and policy implications.
- Section 4 concludes.

*Source: _wp14228 - 1. Introduction (PDF chapter).*

### 1.   Introduction.................................................................................      4

### 1. Introduction

### Model purpose and key features
- Constructs and solves a dynamic stochastic general equilibrium (DSGE) model with nominal rigidities and an energy market that includes exhaustible (fossil fuel) and renewable resources.
- Government implements tax policies to discourage fossil fuel usage.
- Distinctive feature: explicit fossil fuel storage facility operated by forward-looking, risk-neutral, profit-maximizing speculative storers who form rational expectations about future fossil fuel prices.
- Storage modeled as a way of transferring fossil fuel from current to future periods and follows the modeling approach of Wright and Williams (1982, 1984, 1991) and Deaton and Laroque (1992, 1996).
- Commodity futures market is not explicitly modeled; competitive storage implies an arbitrage condition linking futures and spot markets (cited Hamilton (2009), Alquist and Kilian (2010), Kilian and Murphy (2014)); simplification focuses on spot-market speculation without loss of generality.

### Role of speculative storage and monetary policy transmission
- Speculative storage introduces a dynamic link among fossil fuel inventories, storers’ expectations of fossil fuel price, and the spot price.
- Storage generates a new transmission channel for monetary policy: changes in the real interest rate directly affect storage demand.
- Investigating speculative storage motives within a short-run general equilibrium model is motivated by its suitability for monetary policy analysis.

### Empirical motivation and existing literature
- Financialization and increased speculative oil storage in the 2000s motivate inclusion of storage: Energy Information Agency data indicate ending stocks of crude oil as a percentage of quarterly total oil usage increased to 83 percent in 2010 from 62 percent in 2000 in the US.
- Literature on environmental taxes and macroeconomic effects includes Ganelli and Tervala (2011), Sinn (2008), de Miguel and Manzano (2011), Golosov et al. (2014), de Mooij, Keen, and Parry (2012), and others.
- Prior DSGE work incorporating storage includes Unalmis, Unalmis, and Unsal (2012) (UUU), who show accounting for oil storage improves model fit and that storage demand can amplify or mitigate fossil fuel price dynamics depending on shock origins.
- Gap identified: no prior work (to the authors’ knowledge) investigates the role of speculative storage in amplifying short-term fluctuations caused by environmental taxes; this paper attempts to fill that gap.

### Model extensions and structure relative to prior work
- Builds on UUU with four main extensions:
  - Fossil fuel supply is partly endogenous (fossil fuel production split into exogenous OPEC component and endogenous non-OPEC component, following Backus and Crucini (2000) and Nakov and Pescatori (2010)).
  - Introduces renewable energy as an alternative endogenous energy source consumed by households and used in production.
  - Includes a more detailed treatment of fiscal policy: government taxes consumption and/or production of fossil fuels to promote substitution to renewable energy.
  - Focuses on dynamics following a fossil fuel tax shock.
- Economy populated by households, three types of production firms, a government, a monetary authority, and fossil fuel storers.
- Three firm types:
  - Differentiated core consumption good producers: use capital, labor, and energy; set prices in staggered fashion (sticky prices).
  - Renewable energy producers: use only capital.
  - Fossil fuel producers: use only capital; fossil fuel production has OPEC (exogenous) and non-OPEC (endogenous) components.
- Fossil fuel is storable; renewable energy is not.

### Households and preferences (model specifics)
- Continuum of infinitely-lived households indexed j ∈ [0,1].
- Representative household maximizes expected discounted utility:
  - Utility specified as E_0 ∑_{t=0}^∞ β^t ((C_t(j) − H_t)^{1−σ}/(1−σ) − N_t(j)^{1+φ}/(1+φ)), where H_t = h C_{t−1} captures external habit formation with h ∈ [0,1], 0< β <1, σ >0, φ >0.
- Aggregate consumption C_t = (∫_0^1 C_t(j)^{(ε−1)/ε} dj)^{ε/(ε−1)}, where ε is elasticity of substitution between varieties.
- Individual consumption C_t(j) is a CES aggregate of core consumption Z_t(j) and energy consumption E_{c,t}(j):
  - C_t(j) = [ (1−ω_{ec})^{1/ρ_c} Z_t(j)^{(ρ_c−1)/ρ_c} + ω_{ec}^{1/ρ_c} E_{c,t}(j)^{(ρ_c−1)/ρ_c} ]^{ρ_c/(ρ_c−1)}, with ρ_c intratemporal elasticity and 0< ω_{ec} <1 the energy expenditure share.
- Energy consumption E_{c,t}(j) is a CES aggregate of renewable energy RE_{c,t}(j) and fossil fuel FF_{c,t}(j):
  - E_{c,t}(j) = [ (1−ω_{ff,c})^{1/ρ_e} RE_{c,t}(j)^{(ρ_e−1)/ρ_e} + ω_{ff,c}^{1/ρ_e} FF_{c,t}(j)^{(ρ_e−1)/ρ_e} ]^{ρ_e/(ρ_e−1)}, with ρ_e intratemporal elasticity and 0< ω_{ff,c} <1 fossil-fuel share in household energy basket.
- Consumer price index P_t and energy price index P_{e,t} defined as:
  - P_t = [ (1−ω_{ec}) P_{z,t}^{1−ρ_c} + ω_{ec} P_{e,t}^{1−ρ_c} ]^{1/(1−ρ_c)}.
  - P_{e,t} = [ (1−ω_{ff,c}) {(1−s_{re,c,t}) P_{re,t}}^{1−ρ_e} + ω_{ff,c} {(1+τ_{ff,c,t}) P_{ff,t}}^{1−ρ_e} ]^{1/(1−ρ_e)}, where s_{re,c,t} is percentage subsidy on P_{re,t} and τ_{ff,c,t} is percentage tax on P_{ff,t}.
- Demand functions:
  - RE_{c,t}(j) = (1−ω_{ff,c}) [ (1−s_{re,c,t}) P_{re,t} / P_{e,t} ]^{−ρ_e} E_{c,t}(j).
  - FF_{c,t}(j) = ω_{ff,c} [ (1+τ_{ff,c,t}) P_{ff,t} / P_{e,t} ]^{−ρ_e} E_{c,t}(j).
  - Z_t(j) = (1−ω_{ec}) [ P_{z,t} / P_t ]^{−ρ_c} C_t(j).
- Households hold portfolios D_t(j), supply labor N_t(j), rent capital K_{1,t}(j), K_{2,t}(j), K_{3,t}(j), earn wage W_t(j), rental returns R^K_{ι,t}, and profits Π_t(j).
- Budget constraint:
  - P_t C_t(j) + P_{z,t} I_{1,t}(j) + P_{z,t} I_{2,t}(j) + P_{z,t} I_{3,t}(j) + R_t^{-1} D_{t+1}(j) ≤ D_t(j) + W_t N_t(j) + R^K_{1,t} K_{1,t}(j) + R^K_{2,t} K_{2,t}(j) + R^K_{3,t} K_{3,t}(j) + Π_t(j).
- Capital accumulation laws for types ι = 1,2,3:
  - K_{ι,t+1}(j) = (1−δ) K_{ι,t}(j) + Φ( I_{ι,t}(j) / K_{ι,t}(j) ) K_{ι,t}(j), with 0< δ <1, steady-state assumptions for Φ: Φ_ss = δ, Φ'_ss = 1, Φ''_ss = ξ <0, and δ ξ = −1.
- Under complete markets and perfect risk-sharing, consumption equal across households and R_t denotes risk-free nominal interest rate.
- Equilibrium conditions for households (first-order conditions):
  - β E_t [ ( (C_{t+1} − H_{t+1}) / (C_t − H_t) )^{−σ} (P_t / P_{t+1}) ] = 1 / R_t.  (Equation (2.12))
  - (C_t − H_t)^σ N_t^φ = W_t / P_t.  (Equation (2.13))
  - P_{z,t} Λ_{ι,t} = β E_t { ( (C_{t+1} − H_{t+1}) / (C_t − H_t) )^{−σ} (P_t / P_{t+1}) ( R^K_{ι,t+1} + P_{z,t+1} Λ_{ι,t+1} ̃Φ_{ι} ) }, where ̃Φ_{ι} = (1−δ) + Φ_{ι}( I_{ι,t+1} / K_{ι,t+1} ) − Φ'_{ι}( I_{ι,t+1} / K_{ι,t+1} ) ( I_{ι,t+1} / K_{ι,t+1} ) and Λ_{ι,t} = 1 / Φ'_{ι}( I_{ι,t+1} / K_{ι,t+1} ).  (Equation (2.14))

### Main findings (summary of results stated in Introduction)
- Speculative storage motives crucially affect:
  1. The effectiveness of fossil fuel taxes (consumer-only, producer-only, or both).
  2. The impact of these taxes on macroeconomic aggregates.
- Mechanism: Taxes on fossil fuel usage raise expected returns to speculation, increasing storage demand; higher storage demand reduces market-available fossil fuel supply, raises fossil fuel price, and further decreases fossil fuel usage — thereby enhancing policy effectiveness in reducing carbon emissions.
- Ignoring storage leads to substantial underestimation of the effect of fossil fuel taxes on overall fossil fuel consumption.
- Taxing fossil fuels under speculative storage increases volatility in macroeconomic variables including inflation and output.
- Monetary policy implications:
  - Without storage: responding to CPI inflation (rather than core inflation) along with output reduces macroeconomic fluctuations after a fossil fuel tax shock — responding to immediate and second-round inflation effects is justified.
  - With speculative storage: responding to output in the monetary rule becomes less desirable; policymakers can further limit welfare loss by responding solely to CPI inflation due to significantly higher CPI inflation volatility in response to a tax shock under storage.

### Paper plan
- Section 2 introduces the model in detail.
- Section 3 presents results with calibration, impulse responses, and policy implications.
- Section 4 concludes.

*Source: _wp14228 - 1. Introduction (PDF chapter).*

### 2.2  Firms Producing Core Goods

### 2.2  Firms Producing Core Goods

### Production technology for core (non-energy) goods
- Continuum of monopolistically competitive firms indexed by i ∈ [0,1].
- Core good production function (Equation (2.15)):
  - Y_{z,t}(i) = A_{1t} [ (1−ω_{ey})^{1/ρ_y} V_{t}(i)^{(ρ_y−1)/ρ_y} + ω_{ey}^{1/ρ_y} E_{y,t}(i)^{(ρ_y−1)/ρ_y} ]^{ρ_y/(ρ_y−1)}
  - Definitions/parameters appearing:
    - E_{y,t}(i): fossil fuel used by firm i
    - ρ_y: elasticity of substitution between fossil fuel and value added inputs
    - 0< ω_{ey} <1: share of energy in production
    - A_{1t}: stationary total factor productivity shock in the goods sector (common to all firms)

### Value-added input (CES between capital and labor)
- Value added input V_{t}(i) (Equation (2.16)):
  - V_{t}(i) = [ (1−ω_{ny})^{1/ρ_v} K_{1,t}(i)^{(ρ_v−1)/ρ_v} + ω_{ny}^{1/ρ_v} N_{t}(i)^{(ρ_v−1)/ρ_v} ]^{ρ_v/(ρ_v−1)}
  - Definitions/parameters:
    - ρ_v: elasticity of substitution between capital and labor inputs
    - 0< ω_{ny} <1: share of labor in production

### Energy input (CES between renewable energy and fossil fuel)
- Energy input E_{y,t}(i) (Equation (2.17)):
  - E_{y,t}(i) = [ (1−ω_{ff,y})^{1/ρ_e} (A_{2t} RE_{y,t}(i))^{(ρ_e−1)/ρ_e} + ω_{ff,y}^{1/ρ_e} (A_{3t} FF_{y,t}(i))^{(ρ_e−1)/ρ_e} ]^{ρ_e/(ρ_e−1)}
  - Definitions/parameters:
    - ρ_e: elasticity of substitution between renewable energy and fossil fuel
    - 0< ω_{ff,y} <1: share of fossil fuel in production
    - A_{2t}, A_{3t}: efficiency terms multiplying RE and FF inputs respectively

### Cost minimization and first-order conditions (price-taking firms)
- Firms take input prices as given. Cost-minimization implies (holding for each firm i):
  - Labor–capital relative condition (Equation (2.18)):
    - W_{t} N_{t}(i)^{1/ρ_v} ω_{ny}^{1/ρ_v} = R_{K1t} K_{1,t}(i)^{1/ρ_v} (1−ω_{ny})^{1/ρ_v}
  - Renewable–fossil relative condition (Equation (2.19)):
    - (1 + τ_{ff,y,t}) P_{ff,t} FF_{y,t}(i)^{1/ρ_e} ω_{ff,y}^{1/ρ_e} A_{2t}^{(ρ_e−1)/ρ_e}
      = (1−s_{re,y,t}) P_{re,t} RE_{y,t}(i)^{1/ρ_e} (1−ω_{ff,y})^{1/ρ_e} A_{3t}^{(ρ_e−1)/ρ_e}
  - Note: P_{re,t} and P_{ff,t} are determined endogenously elsewhere in the model.

### Nominal marginal cost and component unit costs
- Nominal marginal cost (same across firms) (Equation (2.20)):
  - MC_{n,t} = 1/A_{1t} [ (1−ω_{ey}) C_{v,t}^{1−ρ_y} + ω_{ey} C_{e,t}^{1−ρ_y} ]^{1/(1−ρ_y)}
- Component unit costs:
  - C_{v,t} (Equation (2.21)):
    - C_{v,t} = [ (1−ω_{ny}) (R_{K1t})^{1−ρ_v} + ω_{ny} (W_{t})^{1−ρ_v} ]^{1/(1−ρ_v)}
  - C_{e,t} (Equation (2.22)):
    - C_{e,t} = [ (1−ω_{ff,y}) ( (1−s_{re,y,t}) P_{re,t} A_{2t} )^{1−ρ_e} + ω_{ff,y} ( (1 + τ_{ff,y,t}) P_{ff,t} A_{3t} )^{1−ρ_e} ]^{1/(1−ρ_e)}

### Price setting and Phillips curve
- Firms follow Calvo (1983) pricing: only a fraction (1−θ) can optimally adjust prices each period; partial indexation parameter ς captures degree of inflation indexation.
- Log-linear marginal cost–based Phillips curve (Equation (2.23)):
  - π_{z,t} = β/(1 + βς) E_{t}{π_{z,t+1}} + ς/(1 + βς) π_{z,t−1} + (1−θ)(1−βθ)/[θ(1 + βς)] mc_{t}
  - π_{z,t} = p_{z,t} − p_{z,t−1}: non-energy CPI inflation between t−1 and t

### Aggregate CPI inflation composition
- CPI inflation (Equation (2.24)):
  - π_{t} = (1−ω_{ec}) π_{z,t} + ω_{ec} π_{e,t}
  - π_{e,t} = p_{e,t} − p_{e,t−1}: energy price inflation

*Source: _wp14228 - 2.2  Firms Producing Core Goods*

### 3.2  Impulse Responses

### 3.2  Impulse Responses

### Taxing households
- A percentage point increase in taxes on households’ fossil fuel consumption:
  - Raises the real price of fossil fuel faced by consumers and reduces households’ fossil fuel consumption.
  - Lowers the real price of fossil fuel faced by producers (producers are exempt from the tax), which increases fossil fuel used in production and limits the overall decline in total fossil fuel usage.
  - Induces substitution by households toward relatively cheaper renewable energy, increasing households’ consumption of renewable energy and stimulating renewable energy investment while reducing fossil fuel sector investment.
  - Initially lowers GDP due to reduced capital investment and consumption, but GDP rebounds quickly as capital investment revives.
  - Lowers firms’ marginal cost (because the real price of fossil fuel faced by producers declines), but taxes and rising renewable energy prices increase the real cost of the energy basket, raising CPI and prompting the central bank to raise the policy interest rate.

- Effect of speculative fossil fuel storers (storage turned on, responses shown in solid lines in figures):
  - Storers face a lower fossil fuel price and increase fossil fuel holdings in response to higher household taxes, adding demand and limiting the fall in fossil fuel prices.
  - Total fossil fuel usage drops more when storage is present because income declines further with the storage facility active.
  - Conclusion: speculative fossil fuel storers improve the effectiveness of fossil fuel taxation policies on reducing fossil fuel consumption.

### Taxing firms
- A percentage point increase in taxes on firms’ fossil fuel use:
  - Without speculative storers:
    - Reduces fossil fuel usage in production and increases fossil fuel usage in consumption.
    - The real price of fossil fuel declines in almost the same amount as in the household-tax case.
    - GDP increases initially, then declines and remains below steady state for a prolonged period.
    - Household consumption rises above steady state due to falling interest rates and lower real energy prices.
  - With speculative storers:
    - The decline in the real price of fossil fuel faced by consumers and storers is smaller.
    - Consumer fossil fuel usage increases less while producer fossil fuel usage declines more, producing a much larger contraction in GDP.
    - At the end, the fall in total fossil fuel consumption is almost 50 percent higher compared to the no-storage case.
  - Conclusion: taxing producers is more effective in lowering fossil fuel usage than taxing consumers.

### Taxing both households and firms
- A percentage point increase in taxes on both households’ and firms’ fossil fuel usage:
  - Without storage:
    - The real price of fossil fuel faced by storers falls by almost 1 percent.
    - The real price of fossil fuel faced by consumers and producers shows a minimal increase; renewable energy prices increase only slightly.
    - The real cost of the energy basket rises only marginally, so general price level and interest rate effects are limited.
    - Fossil fuel usage responses in consumption and production do not change significantly; overall effect on fossil fuel usage is very small.
  - With speculative storers:
    - Effects on the real price of the energy basket are amplified: the real price of renewable energy declines but the real price of fossil fuel faced by consumers and producers rises sufficiently that the cost of the energy basket goes up.
    - Household and firm fossil fuel consumption both fall by almost the same amount.
    - The decline in fossil fuel usage is the highest among the three taxation scenarios.
    - Higher marginal cost for firms raises CPI, prompting monetary tightening and higher policy interest rates; higher interest rates reduce consumption and investment and GDP declines (contrary to the no-storage case).

- Five-year cumulative responses to tax shocks on both production and consumption (Table 2):
  - No Storage vs Storage
    - GDP: -0.055, -0.107
    - Real Price of FF: 0.299, 4.441
    - Real Price of RE: 0.220, 2.677
    - Total FF Usage: -0.128, -0.673
    - Total RE Usage: 0.024, 0.020

- Comparisons with other studies:
  - Golosov et al. (2014): an optimal tax decreasing fossil fuel use by about 5 percent would bring a decline in output by about 1 percent in the short run. In this framework with storage, a tax bringing down overall fossil fuel consumption by the same amount would result in slightly lower, but comparable, output losses (about 0.6).
  - de Miguel and Manzano (2011): about a 30 percent rise in a fossil fuel tax on households’ consumption (firms’ use) would bring about 8 percent (11 percent) decline in fossil fuel consumption (used by firms). In our simulations, the same type of shock in the same magnitude would bring a comparable decline in fossil fuel use of about 9 percent (10 percent).
  - Ganelli and Tervala (2011): one percent tax shock brings an immediate decline in output and in consumption by about 0.03 – 0.04 percent and 0.005 – 0.015 percent, respectively.

### 3.2.1 Impulse Responses with Subsidy Policy
- Policy experiment: use receipts from additional fossil fuel taxation as a subsidy to renewable energy users (instead of lump-sum transfers).
  - A rise in fossil fuel taxation combined with renewable energy subsidies:
    - Increases renewable energy investments and decreases fossil fuel investments.
    - With storage, usage of renewable energy in both production and consumption increases when the government subsidizes renewable energy usage.
    - Finding: unless the government subsidizes renewable energy, it is difficult to increase renewable energy usage (in production and consumption) by fossil fuel taxation policies alone.
  - Policy implication: to increase renewable energy consumption, governments may need to support renewable energy consumption through subsidies.

### 3.2.2 Policy Analysis (monetary policy responses)
- Objective: assess how a central bank can reduce fluctuations in macroeconomic variables following tax shocks.
- Policy experiments I — Taylor Rule with either core (non-energy) inflation target or CPI inflation target; compare Storage vs No Storage (Table 3).
  - Standard deviations (first five rows) calculated from impulse response series to a percentage point increase in taxes on fossil fuel use of consumers and producers.
  - Table 3 — Standard Errors and Welfare Losses (Ω):
    - Columns: Taylor Rule with Core Inflation (Storage, No Storage); Taylor Rule with CPI Inflation (Storage, No Storage)
    - Standard Errors
      - Consumption: 0.0205, 0.0457, 0.0235, 0.0528
      - Output: 0.0357, 0.0247, 0.0320, 0.0240
      - Investment: 0.0445, 0.0385, 0.0458, 0.0572
      - Hours: 0.0059, 0.0070, 0.0058, 0.0090
      - CPI: 0.0377, 0.0635, 0.0309, 0.0471
    - Welfare Losses (Ω)
      - $π=$y= 0.5: 0.1349, 0.2322, 0.0989, 0.1398
      - $π=1,$y= 0.5: 0.2058, 0.4339, 0.1466, 0.2508
  - Key findings:
    - Without storage, targeting core inflation reduces volatility in consumption, investment, and labor hours, but not necessarily output and inflation (compare columns 2 and 4).
    - With speculative storers, volatilities of consumption and investment improve when the central bank targets CPI (compare columns 1 and 3).

- Policy experiments II — Simple rule reacting only to inflation (core inflation or CPI) (Table 4).
  - Table 4 — Standard Errors and Welfare Losses (Ω):
    - Columns: Core Inflation (Storage, No Storage); CPI Inflation (Storage, No Storage)
    - Standard Errors
      - Consumption: 0.0188, 0.0405, 0.0187, 0.0497
      - Output: 0.0477, 0.0318, 0.0404, 0.0270
      - Investment: 0.0603, 0.0444, 0.0531, 0.0575
      - Hours: 0.0074, 0.0064, 0.0066, 0.0086
      - CPI: 0.0266, 0.0623, 0.0174, 0.0471
    - Welfare Losses (Ω)
      - $π=$y= 0.5: 0.1492, 0.2448, 0.0967, 0.1475
      - $π=1,$y= 0.5: 0.1847, 0.4389, 0.1118, 0.2585
  - Key findings:
    - Macroeconomic stabilization from consumption and inflation perspectives is better served when the central bank focuses solely on inflation (core inflation or CPI), regardless of whether speculative storage is accounted for.
    - Without storage, responding to core inflation brings lower volatility in consumption, investment, and labor hours than responding to CPI inflation.
    - Policy ranking via welfare criterion (Ω = $π Var(πt) + $y Var(yz,t)):
      - A lower Ω implies lower welfare loss and better stabilization.
      - If storage is not considered, responding to CPI inflation along with output yields lower welfare losses following the environmental tax policy.
      - With storage, responding to output could bring higher welfare losses depending on the relative weights on inflation and output in the welfare function, and thus responding to output could be undesirable.

### Concluding Remarks (selected findings)
- Incorporating speculative storage into a New Keynesian general equilibrium model highlights the role of forward-looking storers in transmitting environmental tax policy into macroeconomic aggregates.
- Key conclusions:
  - The storable nature of fossil fuels and speculative profit motives must be accounted for when designing environmental tax policies.
  - In a model without storage, short-term impacts of environmental tax policies are less pronounced.
  - The existence of forward-looking speculators improves the effectiveness of environmental taxes by amplifying fossil fuel price responses and decreasing overall fossil fuel consumption further.
  - When subsidies to renewable energy usage are implemented, total fossil fuel consumption declines by almost the same amount regardless of whether speculative storage is included.
  - Fossil fuel taxes can decrease output and increase core and CPI inflation, calling for a monetary policy response for macroeconomic stabilization.
  - Monetary policy that responds to output impacts of the tax shock becomes less desirable when speculative storage is present.

- Extensions and limitations noted by the authors:
  - The paper does not take a position on whether environmental taxes can be justified in economic terms; it assumes policymakers may choose to implement them.
  - Fiscal implications and longer-term effects of environmental policies are not considered.
  - Below-ground inventory storage and endogenous responses of non-US fossil fuel supply are neglected; these could be addressed in extensions for longer-term analysis.
  - The model assumes US fossil fuel production is endogenous but non-US supply is exogenous, justified by the short-run focus and empirical tendencies of oil-producing countries.

*Source: _wp14228 - 3.2  Impulse Responses*

### References

### _wp14228 - References

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*Reference list extracted from _wp14228 - References*

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