Handbook of Computable General Equilibrium Modeling SET, Vols. 1A and 1B

Dale W. Jorgenson , ... Peter J. Wilcoxen , in Handbook of Computable General Equilibrium Modeling, 2013

17.9 Intertemporal Allocation of Full Consumption

In this section we describe the intertemporal allocation of full consumption. Equation (17.21) serves as the basis for the estimation of the curvature parameter σ and the subjective rate of time preference δ. However, because we do not have longitudinal data on full consumption, we create synthetic panels from the CEX as described by Blundell et al. (1994) and Attanasio and Weber (1995). The estimating equation for this stage of the consumer model is:

(17.23) Δ ln F c , t + 1 = ( 1 − σ ) Δ ln V c , t + 1 + Δ ln ( − D ( ρ c , t + 1 ) ) + ln ( 1 + r t + 1 ) − ln ( 1 + δ ) + v c t ,

where:

Δ ln F c , t + 1 = ∑ k ε c ln F k , t + 1 n c , t + 1 − ∑ k ε c ln F k , t n c , t

Δ ln V c , t + 1 = ∑ k ε c ln V k , t + 1 n c , t + 1 − ∑ k ε c ln V k , t n c , t

Δ ln ( − D ( ρ c , t + 1 ) ) = ∑ k ε c ( − D ( ρ k , t + 1 ) ) n c , t + 1 − ∑ k ε c ( − D ( ρ k , t ) ) n c , t

where the summations are over all households in cohort c at time t.

To create the cohorts, we partition the sample of households in the CEX into birth cohorts defined over five year age bands on the basis of the age of the head of the household. In 1982 and 1983 the BLS did not include rural households in the survey and, to maintain continuity in our sample, we use data from 1984 through 2006. The characteristics of the resulting panel are described in Table 17.7. The oldest cohort was born between 1900 and 1904 and the youngest cohort was born between 1980 and 1984. The cell sizes for most of the cohorts were typically several hundred households, although the range is substantial.

Table 17.7. Characteristics of cohorts

Cohort Cohort birth year Average no. of observations Range of no. of observations Years covered
1 1900–1904 108 52–169 1980–1989
2 1905–1909 158 78–229 1980–1994
3 1910–1914 195 92–305 1980–2000
4 1915–1919 261 176–347 1980–2000
5 1920–1924 284 53–415 1980–2005
6 1925–1929 337 234–417 1980–2006
7 1930–1934 337 272–469 1980–2006
8 1935–1939 354 289–446 1980–2006
9 1940–1944 437 341–554 1980–2006
10 1945–1949 546 432–705 1980–2006
11 1950–1954 622 457–817 1980–2006
12 1955–1959 650 382–910 1980–2006
13 1960–1964 580 120–870 1980–2006
14 1965–1969 484 103–768 1985–2006
15 1970–1974 464 83–742 1990–2006
16 1975–1979 397 71–594 1995–2006
17 1980–1984 331 45–473 2000–2006

The age profiles of full consumption per capita, consumption per capita, and household leisure per capita are presented in Figure 17.27(a–c) for the cohorts in the sample. Not surprisingly, the profile of per capita full consumption is largely determined by the age profile of household leisure. Per capita full expenditure remains relatively constant until age 35, increases until age 60 and then decreases. Figure 17.28 shows the age profile of the average within period utility levels (lnVk ), which plays a critical role in the estimation of Equation (17.23).

Figure 17.27. Age profile of (a) per capita full consumption, (b) per capita consumption and (c) per capita leisure.

Figure 17.28. Age profile of the average within period utility levels (lnVk ).

The statistical properties of the disturbances vct in Equation (17.23) that are used with synthetic panels are described in detail by Attanasio and Weber (1995). They note that the error term is the sum of expectational error as well as measurement error associated with the use of averages tabulated for each cohort. We present estimates of δ and σ using ordinary least squares, least squares weighted by the cell sizes of each cohort in each year, and a random effects estimator that exploits the panel features of our synthetic cohort data. The first panel in Table 17.8 shows that estimates of δ are consistently around 0.015 while the estimates of σ are approximately 0.1.

Table 17.8. Parameter estimates

Least squares estimates
Variable OLS Weighted OLS Random effects
Estimate SE Estimate SE Estimate SE
δ 0.01471 0.0011 0.01185 0.0011 0.01460 0.0016
σ 0.08226 0.0194 0.11280 0.0218 0.10183 0.0202
Instrumental variables estimators
Variable IV1 IV2 IV3
Estimate SE Estimate SE Estimate SE
δ 0.01253 0.0012 0.01251 0.0012 0.01249 0.0011
σ 0.03414 0.0357 0.05521 0.0350 0.08150 0.0337

SE = Standard Error

We re-estimate Equation (17.23) using a variety of instruments to account for expectational and measurement error associated with synthetic cohorts. The results shown in the second panel of Table 17.8 are based on different sets of instruments. The first estimator (IV1) uses a constant, the average age of the cohort, a time trend, and the two period lagged average marginal tax rate on earnings as instruments. The second estimator (IV2) uses, in addition, the two period lags of wages, interest rates, and prices of capital services and consumer services. The third estimator (IV3) also includes the third period lags. Regardless of the instrument set, the point estimates of the subjective rate of time preference remains around 0.0125 while the estimates of σ are in the range between 0.0341 and 0.0815.

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RESOURCES

P. Gong , K.-G. Löfgren , in Encyclopedia of Energy, Natural Resource, and Environmental Economics, 2013

Introduction

This article presents an overview of the application of taxation as a policy instrument in forestry. Forests were traditionally regarded as a timber resource. Accordingly, a key issue in forest management was the intertemporal allocation of the resource, or the time path of harvest. With respect to old-growth natural forests, the harvest decision problem (i.e., the rate at which the forests should be harvested) is similar to the exploitation of nonrenewable resources. There is however, a fundamental difference between the two. For a nonrenewable resource, the exploitation ends at the time when the resource is depleted. In the case of old-growth natural forests, harvesting frees the land, which can be used to grow timber for future harvests. This possibility implies that timber harvesting can continue 'forever.'

When forests are regarded as a timber resource, examination of the forest management problem focus on the rate of harvest of the old-growth natural forests and the time interval of harvesting and regenerating the forest thereafter, in order to maximize the net present value of current and all future profits from timber production. A common assumption of such studies was that maximization of the net present value leads to socially optimal management and utilization of forests as a timber resource, though a rigorous proof was not available until the mid-1980s.

In addition to timber, forests produce a wide range of other products and ecological services, which are referred to here as nontimber goods. The quantity and/or quality of the nontimber goods produced in a forest depend on the state of the forest (age structure, tree species composition, etc.), which in turn are affected by silvicultural practices and timber harvest. This raises the question of how forests can be managed to optimize the joint production of timber and nontimber goods. With the rapid increase in the demand for nontimber goods that started after World War II, multiple use of forests became an important policy issue. Because many of the nontimber products and ecological services are freely accessible to the public, the free market solution would lead to underproduction of nontimber goods. It is reasonable to believe that investments in forestry, through the production of nontimber goods, yield benefits to large groups of individuals and have positive effects on other sectors of the economy. On the contrary, timber harvest may generate negative externalities as it reduces (sometimes temporarily stops) the production of nontimber goods in the harvested area.

Since the early 1990s, the aspiration for sustainable development and the threat of global warming have extended the objectives of forest management further to include biodiversity conservation, maintenance of the productivity of forest ecosystems, and carbon sequestration, as well. Sustainable forest management aims to meet the current demand for various forest products and services, while maintaining the potential to enhance the relevant ecological, economic, and social functions of the forests in the future. The shift from multiple use to sustainable forest management is not simply an extension of the benefits to be considered in forestry decisions. It also represents a profound change in the view of forest resources and the strategy of sustaining a high level of output of the various benefits. From a policy perspective, however, the fundamental question remains the same: how to motivate forest landowners/managers to achieve the socially optimal level of output of the various products and services over time.

Today, taxation is commonly regarded as an important element of forest policy. From natural resource and environmental economics, we know that taxes are an efficient means for correcting externalities. Theoretically, taxes can be used to internalize the negative externalities of timber production. Or, if one considers the production of nontimber goods as positive externalities of forestry investment, the output of nontimber goods can be stimulated through subsidies. In the past decades, many researchers have studied the optimal design of forest taxes in different contexts. To mention a few examples, Englin and Klan studied the taxation design that induces socially optimal management of forests for both timber production and amenity values; Koskela and Ollikainen examined the optimal design of forest taxes when used for collecting revenue for the government and for correcting the externalities. Koskela et al. focused on the optimal taxation policy for biodiversity conservation in commercial boreal forests. Upon reviewing the different approaches used in studying forest taxation design and the special features of forest taxation, Amacher identified a number of issues that remained to be examined. Amacher, Ollikainen, and Koskela provide a comprehensive treatment of the optimal design of forest taxes.

The purpose of this article is to discuss forest taxation as a policy instrument for improving the efficiency of forest management. The next section provides a brief review of the major forms of inefficiency in market solution of forest management problems. Section 'Forest Taxation as a Policy Instrument' summarizes and discusses the behavioral effects of the general types of taxes targeted at forest assets and forestry income. This is followed by an overview of the forest taxation systems in four selected countries. The final section provides some concluding remarks.

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Handbook of Social Choice and Welfare

William Thomson , in Handbook of Social Choice and Welfare, 2011

13 Other Domains and Issues

We began this survey by specifying its scope as being limited to resource allocation in concretely specified economic models. We conclude by tying it to literatures concern-ing other models.

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Arrovian model of extended sympathy. The no-envy concept has been studied in this context (Goldman and Sussangkarn 1978, Suzumura 1981a, 1981b, 1983, Denicolò 1999).

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Rights assignments. Here too, the no-envy concept has been the object of several studies (Austen-Smith 1979, Suzumura 1982).

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Quasi-linear model of social choice. This model is somewhat more structured, although physical resource constraints do not explicitly appear. A number of bounds on welfares have been defined, and relational fairness requirements investigated (Moulin 1987c, Chun 1986).

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Intertemporal allocation. Models of allocation across generations are usually formulated in utility space ( Diamond 1965 is a precursor; Svensson 1980 is the closest in spirit to the literature we reviewed).

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Choosing a point from an interval or a closed curve when agents have single-peaked preferences. Since all agents consume the same thing, punctual fairness requirements provide little help here, but relational requirements of monotonicity are still meaningful (Thomson 1993, Ching and Thomson 1992, Ehlers and Klaus 2006, Gordon 2007b). [Moulin 1980 is the classic reference for strategyproofness.]

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Strategic issues (the implementability of solutions, in particular strategyproofness) have been the object of a considerable literature, reviewed in Chapter 5. A number of authors have considered implementation in the special context of fairness (Crawford 1979, Demange 1984, van Damme 1986, 1992, Maniquet 1994, 2002, Thomson 2005).

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Cost sharing. This literature is reviewed in Chapter 6 (Moulin, and various coauthors).

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Queueing, scheduling, and sequencing. This is a very new literature (Crés and Moulin 2001, Maniquet 2003, Chun 2006a, 2006b).

•

Matching. A background reference here is Roth and Sotomayor (1990).

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Natural Resource use and the Environment

Charles D. Kolstad , Jeffrey A. Krautkraemer , in Handbook of Natural Resource and Energy Economics, 1993

4.2.1 Intertemporal efficiency

The basic static conditions implied by Pareto efficiency can be extended to an intertemporal setting in a straightforward fashion through the dating of commodities. That is, final goods and productive factors are distinguished by time as well as by the type of good. For private goods, distributional efficiency requires that each pair of individuals has the same marginal rate of substitution between any pair of commodities, including the same good consumed at different points in time. The common marginal rate of substitution must be equal to the economy's marginal rate of transformation between the pair of commodities. The necessary conditions for a Pareto-efficient allocation of a public good are somewhat more complicated. In particular, efficiency obtains when the marginal rate of transformation is equal to the summation of individual marginal rates of substitution over both time and individuals [Sandler and Smith (1976)].

As demonstrated in the previous section, the efficiency conditions for the use of long-lived assets require that the marginal value of the flow of services from the asset is equal to the marginal value of the asset, and that the marginal rate of return to each asset is the same. The basic condition of equal returns to each asset is independent of any ethical criterion. That is, given any social welfare function, if the intertemporal condition is not satisfied, then there exists a better path for the economy to follow, where better is defined in terms of the chosen social welfare criterion.

A market allocation will be intertemporally efficient given standard neoclassical conditions about the convexity of production and preference sets and a complete set of markets, including future markets for each dated commodity and a full set of contingent markets for each state of the world. Arbitrage activity by asset owners seeking to maximize the present value of their portfolio would ensure that the total return to each asset is equal. The future markets enable the economy to establish the proper initial price for each asset [Dasgupta and Heal (1979)]. In the absence of futures markets, it could be some time before an initial error is discovered and corrected. The absence of contingent markets would prevent the efficient allocation of risk. The exact impact on the pattern of natural resource use depends upon the source of uncertainty. For example, uncertainty about the timing of the development of a substitute for the resource can lead to more rapid depletion while uncertainty about the size of the resource stock can lead to less rapid depletion [Fisher (1981)].

The existence of a complete set of futures, risk, and capital markets is essential to the efficient allocation of any long-lived asset and is not specific to interactions between resource use and the environment. The open access to environmental assets and the public good characteristics of environmental amenities are important sources of intertemporal market inefficiencies derived from resource–environmental interactions. Because of the open-access and public-good aspects of the environment, the environmental costs of resource use are not fully internalized in private decision making. This market failure results in both direct intertemporal inefficiencies and static misallocations with indirect implications for intertemporal allocation. In general, one would expect that environmental assets would be undervalued and, therefore, over-exploited.

The static failure of the market to capture the current environmental costs of natural resource use induces greater extraction of natural resources than would occur if all costs were covered by the resource price. This static inefficiency also affects the entire time pattern of resource extraction. The intertemporal bias in the pattern of resource extraction created by market imperfections, including externalities, depends upon the rate of change in the market imperfection over time relative to the rate of discount [Sweeney 1977)]. A simple example is the case of a static environmental effect with a constant marginal cost so that the rate of change in the market imperfection is zero. In this case, if the rate of discount is positive and the environmental cost is external to the market, then the market depletes the resource more rapidly than socially desirable because the present value of the market imperfection is greater in the present than it is in the future.

In addition to the dynamic implications of static inefficiencies, there are several direct sources of intertemporal inefficiency that are associated with the interaction between natural resource use and the environment. Many of the environmental effects of resource use are long-lived and cumulative in nature – the climatic impact of carbon dioxide emissions will be felt long after the consumption of fossil fuels has ended. In the case of cumulative effects, there is a dynamic cost of the externality that captures the present value of any future environmental damage caused by current emissions. For example, if D(P(t)) denotes the value of the environmental damage of an accumulation of pollutant P at time t, then the shadow price of the resource should include the term

∫ t ∞ e − δ ( s − t ) D ′ ( P ( s ) ) d s ,

which represents the present value of the present and future marginal environmental damage caused by the use of the resource [Schulze (1974)].

This value is greater than the present value of the marginal damage of the current stock of pollution, D′(P(t))/δ, whenever the marginal damage of pollution increases with the level of pollution and the level of pollution is increasing over time. In the models of the previous section, this cumulative effect of natural resource use is captured in the shadow price of the resource – note the equivalence of this term with the second term on the right-hand side of eq. (25) above. Note also that the correct valuation of the environmental damage depends upon the entire future path of pollution. The persistence of pollutants can imply that economic incentive policies do not have an informational advantage over direct controls since it is not possible to determine the optimal tax (or number of tradeable permits) without solving for the optimal path for environmental quality [Griffin (1987)].

The open access to the environment means that the benefits of the regenerative capacity of the environment are not appropriable. Consequently, there are no market incentives for investment in the assimilative capacity of the environment nor for the development of technologies that use the environment less intensively. Commoner (1972) presents evidence that changes in production processes were the most significant factor in the increase in environmental degradation in the post-World War II period. For example, in the USA between 1949 and 1968, the use of fertilizer nitrogen increased by 648% while population increased by only 34% and per capita output increased by only 11%. Hence there has been a very significant increase in the use of nitrogen fertilizer per unit of output. Research and development efforts are guided by market forces and if environmental resources are undervalued, then R&D activities will be allocated inefficiently and technological progress will be oriented toward more extensive use of the environment and, in turn, the depletion of natural resources will be too rapid.

Other intertemporal inefficiencies may arise because future generations do not participate in the market. The general nature of these problems is the inability to conduct trades across generations. Future generations may prefer a different mix of capital, resource, and environmental assets than the mix of assets bequeathed to them by the present generation. It is possible that they may desire to exchange material wealth for environmental amenities. The present generation might be willing to accept the trade but cannot because of the temporal barrier. Such a situation arises when development is irreversible and there is uncertainty about future preferences [Fisher and Krutilla (1974)].

The public-good nature of an environmental asset over time raises questions about the effect of discounting on the intertemporal allocative efficiency. Sandler and Smith (1976) have argued that discounting can result in Pareto inefficiency in the intertemporal allocation of long-lived public goods such as environmental assets. Cabe (1982) establishes that the proper rate of discount on future services is the marginal rate of transformation for the numeraire good between the current period and the period in which the services are provided. He argues that the result obtained by Sandler and Smith is due to their implicit assumption of a numeraire with a marginal rate of transformation equal to unity and that this assumption is unrealistic in a growing economy. Sandler and Smith (1982) agree that the proper discount factor is the intertemporal marginal rate of transformation for the numeraire but argue that a value of unity is realistic for a commodity that serves as a standard of value. In any case, the market rate of discount is not necessarily the socially optimal rate of discount.

In summary, because of the open-access and public-good characteristics of environmental assets, the interaction between resource use and the environment poses significant problems for achieving an efficient intertemporal allocation even in the presence of a complete set of futures, risk and capital markets for privately owned commodities. While a variety of outcomes is possible, it is generally expected that a market allocation would deplete natural resource stocks too rapidly and that environmental degradation would be too great.

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Changing concepts of 'land' in economic theory: From single to multi-disciplinary approaches

Klaus Hubacek , Jeroen C.J.M. van den Bergh , in Ecological Economics, 2006

Even though Jevons had a theory of interest based on individual time preference – economic agents prefer consumption today to consumption tomorrow – it was only with Lewis C. Gray that the pattern of use of exhaustible resources over time was related to the interest rate (Martínez-Alier and Schlüpmann, 1987, p. 163). In his article The Economic Possibilities of Conservation Gray (1914) introduced the interest rate as an instrument for inter-temporal allocation of resources. He also identified external effects as responsible for the "lack of correlation in individual expense and social cost" (p. 514). Building on Gray, Ise (1925) discussed the effects of different prices and discount rates on quickly exhaustible resources. Hotelling (1931) developed an algorithm for optimal non-renewable resource depletion over time. His finding shows that an efficient allocation price is equated to marginal extraction cost plus the shadow price – also called the royalty or scarcity rent – of the resource in the ground. And, over time, this royalty grows at a rate equal to the rate of interest. Menger discussed the importance of raw materials and intermediate products in the production of goods of 'higher' and 'lower' orders, similar to consumption and inputs to production, respectively (Menger (1871), 1923, p. 21). He emphasized that the value of a good is derived from its importance for the user, a 'teleological connection', rather than from an inherent attribute. 10 He recognized the existence of fixed proportions between inputs. His theory of prices requires a theory of substitution in order to assess the difference made by the presence or absence of an individual factor. In his theory, input quantities can be varied: more land or more fertilizer can be employed to produce the same output (Christensen, 1989, p. 24).

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