قوانین استهلاک و تغییر ناپذیری ارزش با شرکت های استخراجی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|7036||2002||18 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Economic Dynamics and Control, Volume 26, Issue 1, January 2002, Pages 99–116
The application of Samuelson's theorem on value invariance to the case of intertemporally optimizing firms is shown to require a judiciously chosen economic depreciation formula which depends on both current stock and current flow variables, in order to prevent the firms from changing their actions in the face of the tax regime. We illustrate by deriving depreciation rules which achieve non-distortingness of actions and value-invariance for resource-extracting firms.
Samuelson (1964) proved the following fundamental theorem of value invariance:1 ‘if, and only if, true loss of economic value is permitted as a tax-deductible depreciation expense will the present discounted value of a cash–receipt stream be independent of the rate of tax’ (p. 604). Value invariance is important because it is efficiency-enhancing: it is a sufficient condition for neutral business taxation, under the assumption (which we maintain throughout this paper) that the tax does not cause the rate of interest to change.2 In particular, in the case of natural resources, ownership of a resource deposit should not be dependent on one's marginal tax rate, but on one's comparative advantage of managing it. In general, however, neutrality with respect to investment does not require value invariance: it only requires that the sign of net present value of all investment projects remain unchanged when the tax is imposed.3 Value invariance is a strong form of neutrality. Many authors have sought weaker (i.e., less demanding) forms of neutrality.4 In this paper, we pursue the issue of value invariance in the context of taxation of natural resource firms because this strong form of neutrality does imply extraction path invariance, which is desirable in the sense that distortions are avoided. Admittedly, we are abstracting from the more important but more difficult question: what is the best set of biases (distortions) to have, given that some sort of distortions is unavoidable? We restrict our attention to the following question: can we be sure that the Samuelsonian economic depreciation will ensure value invariance and extraction path invariance, if firms try to reduce the tax burden by contemplating deviation from the extraction path which would be optimal under the no-tax scenario? In the analysis of resource extraction firms, each with a given resource stock (we abstract from capital equipment for simplicity), resource economists are often interested in the effects of taxation on the time path of extraction, which may be regarded as disinvestment, since extraction reduces the resource stock. (See, for example, Dasgupta and Heal, 1979; Gaudet and Lasserre, 1986). The purpose of this paper is to explore the invariance issue in the context of extractive firms. As will be seen below, in this context, value invariance goes hand-in-hand with extraction path invariance to the tax rate. If one interprets each feasible extraction path as an investment project (or, rather, disinvestment project), then the invariance of the firm's optimal extraction path to the tax rate is a sufficient condition for tax neutrality within the resource sector. It is conceivable that there are tax schemes that ensure value invariance without extraction path invariance, and vice versa. However, in this paper we restrict attention to tax schemes that ensure both sorts of invariance. Dasgupta and Heal (1979, pp. 370–371) show that if depreciation allowance is based on the observed change in the market value of the firm, then extraction path invariance is obtained. They did not however address the question of the behavior of the extractive firm seeking to reduce its tax burden. Samuelson's theorem has been shown to apply also to the case of uncertainty (see Richter, 1986; Fane, 1987) and to the case of a time-dependent tax rate (see Lyon, 1990). As in Samuelson's original paper, in these articles it is assumed that the cash-flow stream is exogenous or remains unperturbed by the tax regime. It might seem at first sight that Samuelson's value invariance theorem can be easily applied to the case of an intertemporally optimizing firm. Consider first the no-tax scenario. Take any feasible time path of production and investment, denoted by q(.); the corresponding time path of the value of the firm (given that it is committed to this production–investment path) can be computed, and hence the corresponding economic depreciation at each date along that path is known. Samuelson's result implies that the introduction of an income tax which permits economic depreciation to be tax-deductible will not change the value of the firm, if the production–investment path q(.) is kept unchanged. It follows that the best (i.e., value-maximizing) production–investment path under the no-tax scenario, say q∗(.), remains the best one under the Samuelsonian tax. This argument relies on the assumptions that market value of a firm can be observed at any given point, and that such value is independent of possible attempts by the firm to reduce its tax liability. In this paper, we show, with the firm running its known stock via extraction taking into account the impact of its chosen paths on its tax liability, that it is not a trivial problem to get the firm to reproduce, under the Samuelsonian tax scheme, its no-tax paths of control variable and state variable. In other words, value invariance is difficult to implement because the firm tends to deviate from its no-tax paths in the face of the tax and the depreciation allowance. We set out a scheme, inspired by the analysis of taxing a resource monopolist by Karp and Livernois (1992) — who did not consider the issue of depreciation allowance and value invariance — which leads to value (and path) invariance. Our result indicates that the scheme is informationally demanding. The authorities need a large amount of knowledge about the firm in order to set out an appropriate depreciation allowance of the (true) Samuelson form.5 We work in a partial equilibrium framework and focus on the response of the firm to the taxation scheme, as in a game between the taxation authority striving for neutrality with respect to extraction path, and the firm, striving for maximum after-tax profit. The interest rate is taken as given, as would be the case for a small open economy, or for an economy with constant marginal product of capital over a relevant range.6 Depreciation allowances are a central topic in mineral economics (Heaps and Helliwell, 1985), and we are dealing with the theoretically ideal depletion allowance for extractive firms with non-durable outputs (as in oil, coal, etc., as distinct from copper, gold, etc.). For an extractive firm, the decision at each date is one of optimal disinvestment from its current stock of reserves. Though formally optimal investment and disinvestment can be analyzed the same way under Samuelson taxation, the latter turns out to be simpler because the firm has no incentive to borrow and its single-state variable (its remaining stock) moves in a simple fashion with respect to its single control variable (its current extraction). In an optimal production–investment problem, the possibility of borrowing makes the link between the current production decision (the control), and the state variable (the capital stock of the firm) complicated because current investment is another control variable for the firm. Hence our analysis, based on the purely extractive firm, is in a sense prior to that of the producing-investing firm.7 We show that a Markovian depreciation rule would provide the incentive for a firm not to deviate from its best extraction (disinvestment) path for the no-tax scenario and has the subgame perfectness property: even if a firm has deviated (say accidentally) at some time, it will not have an incentive to deviate in the future from its best path achievable given the current state. Our invariance procedure can be described as follows: have the tax authority work out the firm's optimal extraction path under the no-tax scenario and, given this path, have the authority obtain the time path of true economic depreciation, contingent on the state of the firm. The tax authority then assigns this depreciation allowance to the firm for its optimization under the Samuelson tax-depreciation allowance scenario. Value of the firm invariance and extraction path invariance obtain. The invariance depreciation formula must be tied to the state variable in order to prevent the firm from reacting to the formula and, roughly speaking, the invariance formula must be derived in the no-tax environment in order that the firm assigns the correct shadow price to the state variable under the tax regime. We add two new bits to the Samuelson tax invariance literature: (a) we demonstrate that the ‘true economic depreciation’ in the tax depreciation scheme must be derived in the no-tax scenario, and (b) we demonstrate that the depreciation allowance must be ‘state-based’ in order to rule out deviations by the taxed firm. We also provide a rigorous economic analysis of the concept of a ‘depletion allowance’ for mining economics. Several authors have paid attention to economic depreciation in the context of intertemporal optimization; but they have not dealt with the examination of alternative tax rules that supposedly represent Samuelsonian true economic depreciation, and the possibility of deviation by the firm. In fact, some authors have chosen to work with a different concept of economic depreciation. Sandmo (1974) defined the ‘true’ rates of depreciation as the true rate of physical wear-and-tear rate plus the interest rate, minus the rate of increase in the price of the investment good. Atkinson and Stiglitz (1980, p. 142) seemed to equate Samuelsonian true economic depreciation with the replacement cost of physical wear-and-tear. Howitt and Sinn (1989), by abstracting from natural resources and pure profit, dealt with a model with much simplified economic depreciation, as invariance was not a central concern of their paper. None of these papers contemplates the possibility that the firm may deviate from a path in order to reduce its tax burden. In contrast, we focus precisely on the issue of the firm trying to reduce its tax burden, given a depreciation allowance rule. We emphasize the possibility that a tax rule which would ensure value invariance if the firm would commit to a given path may not work if the firm can deviate. In this respect, our paper is in the same spirit as that of Karp and Livernois (1992), but that paper did not deal with Samuelsonian economic depreciation: the authors were addressing the question of regulating a monopolist so as to achieve the extraction path that a social planner would choose. They reported on alternative taxing procedures, in the case of monopoly, which would lighten the information required by the tax setting authorities. Implementing the Samuelson tax scheme is information intensive. The firm must file its cost structure with the tax authorities at time zero. Contingent on its stock, s(t), of remaining reserves, the government calculates a depreciation allowance rate α(s(t)) which will result in the firm extracting the optimal quantity q(t). The rate α(s(t)) will change in general as the stock size shrinks. Samuelson (1964) was not explicit about how this tax scheme was to be implemented but the implicit rate in the depreciation allowance would also vary in his model. The analysis in Samuelson (1964) is very short and leaves one with the impression that value invariance and its associated path invariance is easy to implement. Clearly, neutrality is an obvious desideratum of a tax scheme. Our analysis suggests that neutrality is not easy to be achieved via legislated ‘true economic depreciation’. Like many results in optimal taxation, Samuelsonian invariance (value and path) is hard to implement because the tax authority must fine tune its ‘rules’ for each firm. The rest of this paper is organized as followed. Section 2 investigates, in a context of a very simple model of a resource extracting firm, the incentive for the firm to respond to the various depreciation allowance rules by deviating from its best production–investment path in the no-tax scenario. The correct economic depreciation rule is then derived, and is shown to have the Markovian property. Section 3 generalizes the result. Section 4 offers several additional examples.
نتیجه گیری انگلیسی
We have shown that when the application Samuelson's value invariance theorem to the case where firms optimize intertemporally requires a judicious representation of economic depreciation so that the firm would not deviate from the production–investment path that it would choose in the no-tax scenario. While a given path of economic depreciation can be represented in several different ways, only the Markovian representation does not distort incentives. This representation ensures ‘subgame perfectness’. In this paper, we have restricted attention to the polar cases where the firm is either a monopolist or a perfectly competitive firm. An extension to the case of oligopoly would not be trivial, because under oligopoly, each firm's value depends not only on its stock level, but also on the stock levels of its rivals. In that case, a firm's true economic depreciation would seem to depend on its rivals’ actions. This is a challenging research topic that is part of our future research agenda.