This paper examines if an energy price shock should be compensated by a reduction in energy taxes to mitigate its impact on consumer prices. It shows that the consumer price should not increase by as much as the producer price, implying a small reduction in the energy tax in dollars. The energy tax rate, on the other hand, decreases sharply. This decline is primarily due to an adjustment in the Pigouvian component: A constant marginal social damage being divided by a higher producer price. The redistributive component of the tax remains at about 10% of the social cost of energy.
As energy is heavily taxed in most industrialized countries, an “oil shock” (a sudden and significant increase in energy prices) often leads to various interest groups putting political pressure on their respective governments asking for tax reductions. The issue regularly comes up in US presidential election campaign as it did during the 2008 campaign. In 2012, Connecticut capped its tax on the wholesale price of gasoline and Iowa forsook a previously planned state gas tax increase. Overseas, the Israeli government cuts its gasoline taxes citing the price increases as the reason. There has also been a similar debate in France with many interest groups (truck and fishery industries, agriculture, etc.), asking for an energy tax relief to mitigate the impact of oil price increases. Reacting to the 2012 increases in energy prices, the then socialist presidential candidate François Hollande proposed a legal cap on consumer price of gasoline. Adoption of a price cap means that any future increases in world energy prices will be absorbed by a one-to-one reduction in energy taxes.
Among possible justifications for energy tax reductions is the idea that consumers have difficulties to adjust to strong and sudden price shocks. This is because existing technologies and equipment limit the substitution possibilities in the short run. However, this argument would at best lead to a temporary reduction to smooth the transition. Another argument is based on the regressive character of rising energy prices. The share of energy consumption in total spending tends to decrease with income so that low-income individuals are affected more heavily, relative to their income, than high-income individuals by an oil price shock. Redistributive concerns may then call for an energy tax reduction.
This paper studies the validity of this redistributive argument using the model of optimal emission taxation developed by Cremer, Gahvari, and Ladoux (1998, 2001, 2003 and 2010). In doing this, we build on the vast body of theoretical and empirical literatures that have been developed over the past four decades or so. On the theory side, the literature has typically followed, with few exceptions, a Ramsey approach to the optimal tax problem. This means, in particular, that tax instruments have been restricted to be linear and non-linear income taxes are ignored. See, among others, Sandmo (1975), Bovenberg and de Mooij (1994), Bovenberg and van der Ploeg (1994), Fullerton (1997), Parry (1997), Cremer, Gahvari, and Ladoux (2001) and particularly Bovenberg and Goulder’s (2002) survey. In consequence, what emerges in this literature as an “optimal tax” system may in fact suboptimal in that a “true” optimal tax system must implement a Pareto-efficient allocation constrained only by the information structure in the economy.
Most recently, however, this tendency has been corrected and a number of authors have studied the optimal tax design problem with externalities, and the structure of environmental taxes, in light of modern optimal tax theory à la Mirrlees (1971). This theory allows for heterogeneity among individuals and justifies the use of distortionary taxes on the basis of informational asymmetries between tax authorities and taxpayers. A hallmark of this literature is its inclusion of nonlinear tax instruments. See, among others, Kaplow (1996), Mayeres and Proost (1997), Pirttilä and Tuomala (1997) and Cremer, Gahvari, and Ladoux (1998, 2001).
Turning to the empirical studies of environmental taxes, they have remained squarely in the Ramsey tradition; see, e.g. Bovenberg and Goulder (1996) or Goulder (1994). Moreover, the applied literature has been mainly concerned with welfare implications of “piecemeal” tax reforms. This approach ignores the fact that the benefits of reforming any particular tax is fundamentally linked to the way the other taxes in the system are set. The “piecemeal” approach is thus problematic from a policy perspective. It undermines the role that income taxation can play in offsetting the possible “regressive bias” of environmental taxes. Poterba (1991) estimates that, with few exceptions, the expenditure shares of such polluting goods as gasoline, fuel oil, natural gas and electricity decrease at all income deciles as income increases.
In Cremer, Gahvari, and Ladoux (2003), we made an initial attempt to break loose from this piecemeal tradition and examine quantitatively the efficiency and redistributive properties of optimal environmental taxes for the French economy within the context of the modern optimal tax theory à la Mirrlees (1971). In Cremer, Gahvari, and Ladoux (2010), we further developed this approach. There, we considered not only polluting goods but also polluting inputs. There are indeed intermediate goods that are polluting; energy being an obvious example. This is an important addition; lumping final goods and inputs together inevitably leads to incorrect policy recommendations. Diamond and Mirrlees (1971) have taught us that the tax treatment of intermediate and final goods should in general be different. Applying their production efficiency result to economies with a consumption externality, leads to the conclusion that polluting intermediate goods should be taxed only in so far as they correct externalities – a result proved by Cremer and Gahvari (2001). They also proved that, in contrast, polluting final goods is taxed for Pigouvian considerations as well as for redistributive concerns.
These two earlier empirical applications were concerned with a given state of the economy. However, their underlying models also provide a methodology that can be adapted to study the incidence of various shocks and their implications for policy design and environmental taxation. In the current paper, as in Cremer, Gahvari, and Ladoux (2010), energy is used as a consumption good by households and as an input by the firms. We calibrate a modified version of this model on US data. Subsequently, we simulate the optimal energy taxes for different shocks in the before-tax price of energy assuming a concomitant adjustment in optimal income taxes. We show that redistributive concerns call for a subsidy on energy goods equal to about 10% of its social cost (producer price plus the associated marginal social damage of emissions). Interestingly, simulations indicate that variations in the world market price of energy have an almost negligible effect on this percentage. On the other hand, the total tax rate on energy (redistributive plus Pigouvian) decreases sharply as the world price of energy increases. This arises purely as an arithmetic adjustment: A constant marginal social damage is divided by a rising producer price leading to a decline in the Pigouvian tax rate. Nevertheless, it is also true that the consumer price does not increase dollar by dollar with the producer price. As the world price of energy increases, the dollar amount of the subsidy increases too – albeit by small amounts.
Consider an open economy wherein people consume two produced goods: a composite consumption good and “energy.” The composite consumption good is produced domestically using “energy inputs,” capital and labor. Energy, whether used as a consumption good or as a factor input, is imported from overseas. Capital services are also rented from outside. Labor is the only factor of production which is supplied domestically. All imports are financed through exports of the portion of the general output that is not consumed domestically. Energy, both as a consumption good and a factor input, is polluting; the composite consumption good is not.
Labor is heterogeneous with different groups of individuals having different productivity levels and different tastes. There are four types of individuals. Denote a person’s type by j, his productivity factor by and the proportion of people of type j in the economy by (where the population size is normalized at 1). Preferences of a j-type person depend on his consumption of non-polluting goods, consumption of polluting goods, , labor supply, , and the total level of emissions in the atmosphere, E. This construct is based on Cremer, Gahvari, and Ladoux’s (2010) model. To make this paper self-contained, we first review its main features.
Consumers’ preferences are represented by nested constant elasticity of substitution (CES) utility functions, first in goods and labor supply and then in the two categories of consumer goods. All consumer types have identical elasticities of substitution between leisure and non-leisure goods, , and between polluting and non-polluting goods, . Differences in tastes are captured by differences in other parameter values of the posited utility function ( and in eqs  and ). Assume further that emissions enter the utility function linearly. The preferences for a person of type j can then be represented by
The production process, for the composite consumption good, uses three inputs: capital K, labor L and energy D. The technology of production is represented by a nested CES,
Capital services and energy inputs are imported at constant world market prices of r and where the units of D is chosen such that initially . Assume that there are no producer taxes on labor and capital. Let w denote the price of one unit of effective labor and denote the per-unit tax on energy input. The first-order conditions for the firms’ input-hiring decisions are assuming competitive markets,
As different types of people have different productivities, labor is a heterogeneous factor of production. When a j-type person with productivity works for hours, his effective labor is resulting in aggregate effective labor supply . Equating this with aggregate demand gives,
The optimal tax policy maximizes an isoelastic social welfare function
The feasibility of tax instruments depends on information available to the tax administration. Generally, this information allows for linear commodity taxes and non-linear income taxation. This is why we restrict our analysis to this case even if other possibilities could be considered. Under linear commodity taxation, all consumers face the same commodity prices.
With prices to be determined endogenously and optimally, the social welfare function , and thus the j-type’s utility function , must be rewritten as a function of prices. Denote the after-tax income (outlay) of a j-type household by . Maximizing the utility function  with respect to the budget constraint
The optimal tax structure is derived as the solution to
Mirrleesian optimal tax systems too may imply tax distortions but only if they lead to a better screening (relaxing an otherwise binding self-selection constraint). Thus, as long as emissions per se cannot be used for screening, taxation of polluting intermediate goods will have no direct effect on the incentive constraints. They should not then be taxed because that will entail no benefits; only costs that arise due to the induced inefficiencies in production. Now the structure of preferences in our model is such that it renders emissions useless as a screening device. It is the absence of nonlinear income taxes that makes taxation of polluting inputs non-Pigouvian for this preference structure.
To solve our model numerically, one must know the values of the parameters of the utility functions ( , , , , ) and the values of the parameters of the production function ( , , , , A, B). The data sources are the PSID (Panel Study of Income Dynamics), US Bureau of Labor Statistics (BLS) and the US Bureau of Economic Analysis. The first two gives data on households’ consumption, income and labor. The latter reports macroeconomic data from the EUKLEMS database on capital, labor and energy. The calibration process follows the one we have used in our previous paper (see Cremer et al. 1998). The data allow us to identify four types of households, “managers and professionals” (type 1), “technical sales and clerical workers” (type 2), “service workers, operators, fabricators and laborers” (type 3) and “construction workers and mechanics” (type 4). Table 1 provides a summary of the data and parameter values. Finally, observe that our optimal tax calculations are based on the assumption that the government’s external revenue requirement (share in GDP of expenditures on non-transfer payments) remains unchanged. The details of the calibration method are summarized in Appendix B (B1 and B2).
|Managers and professionals (type 1)||Technical sales and clerical workers (type 2)||Service workers, operators, fabricators and laborers (type 3)||Construction workers and mechanics (type 4)|
|p = 1.00000||q = 1.00000||= 0.8||= 0.42141|
|= 0.66490||= 0.26892||= 0.98662||= 0.54242|
|A = 1.28395||B = 0.74215|
Optimal energy taxes/subsidies are determined by solving the calibrated version of our model. The forces at work in their determination are twofold. One is Pigouvian in nature. To correct for the marginal social damage of emissions, one wants to impose a correcting tax on energy. In case of energy inputs, this is the only force at work. Another force comes into play in case of energy consumption goods. This arises because of the distributional considerations. Now because the share of energy expenditures tends to decrease with one’s income, one may want to subsidize energy consumption goods to offset this regressive bias. It is true that an optimally designed income tax mitigates this regressive bias, but in a world of asymmetric information (where first best lump-sum taxes are unavailable), it cannot eliminate it completely (as long as the Atkinson and Stiglitz Theorem does not apply so that Pareto-efficient tax structures include commodity taxes). There still remains a role for energy subsidies; see Cremer, Gahvari, and Ladoux (1998, 2001, 2003, 2010).
|World price of energy ( )||Optimal price of energy input ( )||Optimal price of energy consumption goods (q)||Optimal tax on energy input ( ).||Optimal tax on energy consumption goods ( )|
The optimal tax calculations reveal that while the optimal tax on energy input remains basically invariant to the world price of energy, the optimal tax on energy goods decreases as the world price of energy increases. That the tax on energy input does not change reflects the fact that the tax corrects for the externality caused by emissions – a cost that is basically independent of the producer price of energy. On the other hand, the decrease in the taxes on energy goods indicate that the tax should indeed be used to mitigate the impact of the increasing world energy prices on consumers.
The above observations concerning the behavior of optimal energy taxes are in terms of specific taxes. To the extent that these taxes may be levied on an ad valorem basis, the tax rates will show a different pattern. Specifically, with the producer prices increasing, one would expect the tax rates to be decreasing. This is indeed the case as shown in columns 2 and 3 of Table 3. Both tax rates show sharp declines.
The behavior of energy input tax rates warrant no further discussion. However, in the case of energy goods, it will be instructive to look into its different components separately. In this way, one will be able to discern how each of these components responds to the rise in the world price of energy. To this end, we first define the concept of a “Pigouvian price” to reflect the “social opportunity cost” of energy. Using Cremer, Gahvari, and Ladoux s (1998) definition of the Pigouvian tax, this is defined by
More specifically, consider Table 2 again. Initially, when the world price of energy is one dollar and the external emission damage is $0.4823, the Pigouvian price $1.4823. Under this circumstance, redistributive concerns call for a subsidy of $0.1464 resulting in a consumer price of energy equal to $1.3359. As the price of energy doubles, the Pigouvian tax changes only slightly (from $0.4823 to $0.4380). The redistributive subsidy, on the other hand, changes substantially (from $0.1464 to $0.2420 or an increase of 65%). Translating these changes into relative terms in Table 3, one observes that it is the Pigouvian tax rate which changes dramatically (from 48.23% of the energy price to 21.90% in column 4). On the other hand, the redistributive subsidy does not change much (decreasing from 14.64% to 12.10% in column 5).
|World price of energy||Optimal tax rate on energy inputs||Optimal tax rate on energy goods||Pigouvian tax component||Redistributive tax component||Redistributive component as a % of social price|
To summarize these findings, the rise in the world price of energy does not affect the Pigouvian tax but increases the required redistributive subsidy measured in dollars. In percentage terms, on the other hand, the rise in the world price of energy lowers the Pigouvian tax drastically but does not affect the subsidy rate by much. Of these latter two changes, that the Pigouvian tax rate decreases is basically an arithmetic artifact: a constant marginal social damage is divided by a higher world price.
In contrast, the behavior of the redistributive subsidy reflects a fundamental point: the subsidy rates, as a percentage of the “social price,” are constant. This finding is borne out by the calculations reported in the last column in Table 4. They show the subsidy rate on energy goods as a percentage of the Pigouvian price or the social price – reflecting both the producer price of energy as well as the social damage of emissions – as the producer price of energy doubles (increases from one to two). Similarly, Figure 1 depicts the Pigouvian price, the optimal price and the implicit subsidy in dollars as the world price of energy doubles.
Finally, it is interesting to note that the constancy of the tax/subsidy rate as a percentage of the social price of energy holds regardless of the emission costs and even if there are no such costs. Table 4 and Figure 2 depict the results in the absence of externality ( ). Under this circumstance, the world price of energy, reflects the social cost of a unit of energy and the consumer price, q, differs from the energy price by the redistributive subsidy ( ). The subsidy rate is then equal to
This paper examines if an energy price shock should be compensated by a reduction in energy taxes to mitigate its impact on consumer prices. Such an adjustment is often debated and advocated for redistributive reasons. Our investigation is based on a modified version of the model for optimal environmental taxation developed by Cremer, Gahvari, and Ladoux (1998, 2001, 2003, 2010) and Cremer and Gahvari (2001). This model allows us to characterize second-best optimal taxes in the presence of externalities generated by the use of energy in consumption and in production. The current paper has calibrated a version of this model on the US data and has run simulations on the calibrated model to examine how one may want, in light of redistributive concerns, to alter energy tax rates as world oil prices increase. Quite importantly, these calculations account for the government’s ability to also use the income tax schedule for effecting its redistributive goals.
The paper has shown that optimal energy taxes on consumption goods, as opposed to inputs, are affected by redistributive consideration and that the optimal energy tax is less than the Pigouvian tax (marginal social damage). The difference is a subsidy representing roughly 10% of the Pigouvian price of energy (its true social cost). Assuming that energy prices are subject to an exogenous shock, we have calculated the optimal tax mix, including income, commodity and energy taxes, for different levels of this shock. Simulations show that variation in the energy price has an almost negligible effect on the subsidy rate as a percentage of the Pigouvian price. On the other hand, the Pigouvian tax rate decreases substantially as the price of energy increases. This latter effect is simply a purely arithmetic adjustment due to the fact that the marginal social damage does not change. Nevertheless, it is also true that the dollar subsidy to the consumer price of energy increases by a small amount so that, in dollars, the consumer price should not increase by as much as world energy prices.
The Lagrangian for the second-best problem is (where p is set equal to 1),
Proposition A1The optimal tax on the polluting good is non-Pigouvian.
Second, we prove that the input tax is Pigouvian regardless of individuals’ tastes. The proof is facilitated through the following lemma.
Lemma A1In the optimal income tax problem ) and characterized by the first-order conditions –, the Lagrange multiplier associated with the constraint , is equal to zero.
Proof. Multiply eq.  through by , sum over and simplify to get
Observe that Lemma A1 is in fact an application of the production efficiency result as it tells us that imposes no constraint on our second-best problem. Using this lemma, we can easily show:
Proposition A2The optimal tax on energy input is Pigouvian.
Proof. Using the result that in the first-order conditions –, simplifies them to
The data used from EUKLEMS include:
gross value added,
intermediate energy compensation,
gross value added at current basic prices,
capital services, volume indices, 1995 = 100,
total hours worked by persons engaged (millions),
number of persons engaged (thousands),
intermediate energy inputs, volume indices, 1995 = 100,
gross value added, volume indices, 1995 = 100,
capital-labor elasticity (from the literature).
The parameters , , A and B are then the solution to the following system of equations
We combine data from the BLS and the PSID. We need those two sources because the BLS does not give any information on labor supply. The data from the BLS are given for different categories of households while the data from the PSID are individual data about 7,407 households. Consequently we must allocate the 7,407 households of the PSID to the different categories of households found in the BLS nomenclature. This is performed by considering the PSID information about the main occupation of the family head. We consider four categories of households:
Managers and professionals
Technical sales and clerical workers
Service workers, operators, fabricators and laborers
Construction workers and mechanics
Family interview ID number
Labor income of the head
Labor income of the wife
Main occupation of the head
Main occupation of the wife
Work weeks by the head
Work hours by the head
Wage rate by the head
Work weeks by the wife
Work hours by the wife
Wage rate by the wife
Number of consumer units
Income before and after taxes
Wages and salaries
Personal taxes (federal income taxes, state and local income taxes, other taxes)
Average number of persons, of child under 18, of persons 65 and over, of earners, of vehicle in the consumer unit (sex of reference, person, age, etc.)
Average annual expenditures
We use those data to build the small data set we need to calibrate the parameters of the utility functions of the different categories of households listed above. This data set includes the following variables:
Labor supply (L)
Before and after tax wage (respectively w and )
Non-energy consumption and energy consumption (respectively, x and y)
The authors would like to thank two anonymous referees and the editor for their helpful comments.
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