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Not a panacea for economic growth: the case of accelerated depreciation.

I. INTRODUCTION

Accelerated depreciation deductions have been a tenet of U.S. tax policy for the past fifty years. They are widely believed to promote economic growth. (1) In this paper, I argue that accelerated depreciation is based on a questionable economic growth theory and suggest switching to a depreciation method that is closer to economic depreciation. (2) This may allow lowering tax rates (3) or increasing tax incentives to research and development--the real engine of economic growth. (4)

Accelerated depreciation policy can be traced back to an influential 1953 paper by Evsey Domar. In The Case for Accelerated Depreciation, Domar argued that "[g]iven the choice between a lower tax rate with normal depreciation, or a higher rate with accelerated depreciation, I would, except in severe inflation, certainly recommend the latter." (5) Domar's policy advice was based on a theory he developed in a 1946 paper, known as the Harrod-Domar model, predicting that Gross Domestic Product (GDP) was proportional to the number of machines; namely, that investment is the key to growth. (6)

The theory that increasing investment in building and machinery is the fundamental determinant of growth was disproved by Nobel Laureate Robert Solow as early as 1956. (7) Moreover, Domar, complaining of an ever-guilty conscience, admitted in 1957 that his theory made no sense for long-run growth and instead endorsed Solow's growth theory. (8) Solow argued that technological change is the only source of sustained growth. He showed that as capital per worker increases, the marginal productivity of capital declines until the capital-labor ratio approaches a steady-state level. At that point, savings are just sufficient to replace worn out machines and equip new workers (assuming population growth), so productivity growth is zero. It is technological progress that increases the supply of "effective" labor, (9) thus keeping the capital-labor ratio going and preventing the decline of marginal returns to capital.

Nevertheless, the idea that capital investment was the key to growth remained popular among politicians in and outside the United States. According to a 2001 book written by Easterly, a former World Bank economist, "Domar's growth model became, and continues to be today, the most widely applied growth model in economic history." (10) More than a trillion dollars has been given to developing countries on the basis of a flawed theory known as the "financing gap," founded on the Harrod-Domar model. (11) According to the model, developing countries would invest the money in machines, experience economic growth, and repay the loans. (12) As Easterly put it: "With the benefit of hindsight, the use of Domar's model for determining aid requirements and growth projections was (and still is) a big mistake." (13)

The belief that investment was the key to growth affected not only international institutions and U.S. foreign policy, but domestic policy as well. Two major forms of government intervention inducing businesses to expand the level of their outlays for plant and machinery were added to the tax code: accelerated depreciation deductions were introduced in 1954 and significantly expanded in 1981; and the investment tax credit was added in 1962. The latter was repealed in the tax reform of 1986, but accelerated depreciation deductions are still considered important for economic growth and are very significant in terms of tax revenue forgone. (14)

More recently, The Job Creation and Worker Assistance Act of 2002 allowed taxpayers to deduct thirty percent of the cost of capital assets in their first year, (15) for investments acquired between September 10, 2001 and September 11, 2004 and placed into service before January 2005. (16) In his speech on the day he signed the act, President Bush said: "The terrorist attacks of September the 11th were also an attack on our economy.... [T]his new law will provide tax incentives for companies to expand and create jobs by investing in plant and equipment." (17)

In this paper, I argue that accelerated depreciation is based on a questionable economic growth theory and suggest switching to a depreciation method that is closer to economic depreciation. In Part II, I explain the meaning and importance of economic growth and briefly review the change in our understanding of the key determinants of growth, from mere reliance on investment in machines to the economics of ideas. In Part III, I define accelerated depreciation. In Part IV, I discuss the question whether tax incentives can induce investment in machines. In Part V, I follow a debate whether induced investment in machines could promote economic growth in the United States. Finally I conclude.

II. ECONOMIC GROWTH THEORIES

In his 1776 book, An Inquiry into the Nature and Causes of the Wealth of Nations, (18) Adam Smith was the first to suggest a theory of economic growth. Smith argued that national production was the basis of the wealth of a nation and that increases in production per worker would lead to a higher standard of living, as higher production allows greater consumption. Clearly, consumption is not the sole measure of well-being as there are other important factors such as life expectancy, infant mortality, freedom, health, and a clean environment. It is, however, a fundamental part, highly correlated with most other measures of quality of life, and is relatively easy to measure.

National production is measured by Gross Domestic Product (GDP). This is the market value of all goods and services produced by labor and property located in the country. Alternatively, national production could be measured by the Gross National Product (GNP), which is the value of goods and services that the country's citizens produced regardless of their location. The literature usually prefers to use GDP, simply because there is more reliable data regarding the GDP of various countries than data on GNP.

The size of GDP reflects the size of the economy. China, for example, had in 2005, $8.859 trillion measured on a purchasing power parity (PPP), (19) making it the second-largest economy in the world after the United States. Its standard of living, however, is much lower than that of countries in North America or Europe because its GDP per capita, that is, the average purchasing power per person was only $6800. (20)

China and India, until recently amongst the world's poorest nations, may become the world's wealthiest if they continue growing at the rates they have been experiencing for the last two decades. China has been growing at an astounding 9.5% a year and has tripled per capita income in a generation. (21) India has been experiencing an average growth rate of 6% over a similar period. (22) If this trend of growth rates continues, within three decades China will overtake the United States as the world's wealthiest nation and India will be in third place. (23)

As difficult as this must be to imagine, this huge expected reversal of fortunes is merely another example of the miracle of compound interest. (24) People are reasonably good at forming estimates based on addition, but for operations such as compounding that depend on repeated multiplication, we systematically underestimate how fast things grow. (25)

Nobel Prize winner Robert Lucas introduced a rule of thumb to development economics that is often used by investors. Lucas found that a country growing at g percent per year will double its per capita income every 70 / g years. (26) With the 1.8% per capita growth rate that has persisted in the United States over most of the last 200 years, we see that the average American is two or three times richer than his or her grandparents. A few other countries, including Japan, Singapore, Hong-Kong, South Korea, and Taiwan experienced high growth rates beginning in the 1950s and continuing well into the 1990s. Per capita income in Singapore, Hong-Kong, South Korea, and Taiwan increased from 18% of the developed countries' average in 1965 to 66% in 1995. (27) After World War II, Japan's GDP per capita was about one-sixth that of the United States. Now it is about three-quarters that of the United States. The average citizen in those countries is twenty times as rich as her grandparents.

A. Harrod-Domar and Solow

So, now that we have emphasized the importance of achieving sustained growth, let us try to explain what determines it. The first post-Keynesian growth theory is known as the Harrod-Domar model. (28) According to this model, all that the government has to do to secure growth is to invest in machines. More machines meant greater output and thus greater GDP. The model excludes labor and assumes an unlimited supply of workers because high unemployment rates are taken as a given.

A later model, developed by Noble Laureate Robert Solow between 1956-57, points out that the Harrod-Domar model cannot explain sustained growth. Solow showed that as capital per worker increases, the marginal productivity of capital declines until the capital-labor ratio approaches a steady-state level. At that point, savings (assumed in the model to be a constant fraction of income) are just sufficient to replace worn out machines and equip new workers (assuming population growth), so productivity growth is zero. (29)

The production function that Solow used assumed constant returns to scale; namely, output increases exactly in proportion to inputs. (30) For example, if all inputs are doubled, the output will exactly double. Firms hire labor until the marginal product of labor is equal to the wage, and rent capital until the marginal product of capital is equal to the rental price. With more capital per worker, firms produce more output per worker. However, there are diminishing returns to capital per worker as each additional unit of capital given to a single worker increases the output of that worker by less and less. Under Solow's model, saving equals investment, as the only use of investment in this economy is to accumulate capital. Solow further assumed depreciation to be a constant fraction of the capital stock. Lastly, he assumed fixed population growth. In each period, there are new workers around who were not there during the last period. Both depreciation and the growing workforce reduce the amount of capital per person in the economy. This calls for investment in capital until a steady state is reached.

According to Solow's model, in the steady state there is no per capita growth. Output itself is growing, but only at the rate of population growth. To explain the long-run sustained growth of the U.S. economy, Solow added a term called "technological progress." Solow assumed that technology was exogenous; that is, the technology available to firms in this simple world is unaffected by the actions of the firms, including research and development. Under Solow's formulation, technology is a pure public good that is freely accessible to all. Technological progress increases the supply of "effective labor" (31) and sustains the capital-labor ratio, preventing the decline of marginal returns to capital.

Sustained economic growth occurs only in the presence of technological progress. Without technological progress, capital accumulation runs into diminishing returns. With technological progress, however, improvements in technology continually offset the diminishing returns to capital accumulation. Labor productivity grows as a result, both directly because of improvements in technology and indirectly because of the additional capital accumulation these improvements make possible.

B. The New Growth Theories

Unlike neoclassical theories, which assume that policy cannot affect technological progress (which is exogenous to the model), the new theories recognize that policies like promoting research and development can increase the rate of technological progress. (32) In other words, policy can increase the production of ideas. New ideas, in turn, allow a given bundle of inputs to produce more or better output. There are plenty of examples of growth-promoting ideas: Henry Ford's assembly lines and mass production techniques, software, drive-through windows at fast-food restaurants, and the double-entry method in bookkeeping are only a few. The reason that ideas are the engine of growth is their non-rivalrous character. The use of an idea by one person does not preclude its use by another.

Think, for example, of software. It may take a lot of money and effort in the research and development stage, but once the software is written, the cost of manufacturing the final product is negligible. The developer can do it, but so can anyone else with access to the Internet or a disc burner. (33)

Physical capital, that is, machines, do not have this trait. The machine can be used by a limited number of workers and produce fixed output. Ideas, on the other hand, can be used simultaneously by an unlimited number of producers.

The problem, however, is that without government intervention, people will have no incentive to innovate, because unless an idea can be made excludable, no one will want to incur the research and development costs. Sometimes government intervention takes the form of research grants, as in the case of basic research at universities or prizes offered to people who manage to solve important problems. (34) Intellectual property rights are an important form of government intervention aimed at making ideas at least partially excludable, to provide people with an incentive to innovate. By giving innovators monopoly power, intellectual property rights allow them to charge prices above marginal cost, as otherwise they would have no incentive to innovate. The development of intellectual property rights, a cumulative process that occurred over centuries, probably played a critical role in sparking the Industrial Revolution and is largely responsible for modern economic growth. (35)

Intellectual property rights usually cannot provide innovators with full excludability. Ideas, therefore, are only partially excludable. The same is true for grants and prizes. Inventors do not capture the full value of their inventions while society benefits from positive externalities, also known as spillover effects. In other words, the social rate of return far exceeds the private returns to the investor. (36)

A classic example is the solving of the longitude problem. Up until the middle of the eighteenth century, sea travelers could not determine the longitude of their location. A generous prize of [pounds sterling]20,000 offered by the British Board of Longitude encouraged a clockmaker named John Harrison to spend many years building a chronometer that solved this problem of navigation. (37) To earn the prize, Harrison had to hand over the clock and a written description of how to make one, so that others could replicate it. (38) The prize money clearly did not reflect the huge benefit realized by society from the ability to navigate accurately.

Positive spillovers are especially large because innovation has a positive externality that increases the productivity of all subsequent innovative activity. A classic example is Isaac Newton's famously modest saying: "If I have been able to see further, it was only because I stood on the shoulders of giants," referring to the work done by previous scientists such as Copernicus, Galileo and Kepler. This externality offsets the tendency toward decreasing productivity of new investments in innovative activity, allowing innovation production--and growth--to continue.

High growth also implies high growth in physical capital. However, contrary to the old models in which physical capital was a cause of technological progress, here, it is a result. Even though innovation activity is risky and only a small percentage of R & D projects succeed, actual success is not an exogenous event. The more time and money firms invest to achieve technological progress, the more technological progress occurs. To sum up, ideas are very different from other economic goods. Ideas are non-rivalrous. The non-rivalry of ideas implies that production is characterized by increasing returns to scale over a relatively long period of time, before they start decreasing. It also implies that ideas, like all other goods with positive spillovers, tend to be under-produced by the markets, providing a classic opportunity for government to intervene to improve welfare. Machines, on the other hand, are rivalrous; that is, they have decreasing marginal returns.

There is no robust economic theory that shows market failures that cause under-investment in machines and justify government intervention in the allocation of resources.

III. DEPRECIATION DEDUCTIONS

A. Economic Depreciation

Income taxation is used as a proxy for the taxpayer's ability to consume. (39) The relevant tax base should therefore be net income. A taxpayer generating $100,000 while incurring $90,000 in costs should be taxed on $10,000, not on $100,000. Deducting costs incurred in generating income is essential if we are to tax net income. (40) It is, however, complicated to match income and cost on an annual basis, when the costs take the form of investment in assets that produce income (that is, have "useful lives") for periods that extend beyond the tax year. If, for example, a taxpayer purchases a machine for $10,000, with a useful life of five years, it is necessary to determine the actual wear and tear of the machine in each of its five years of operation in order to calculate the taxable income on an annual basis. (41) It should be noted that the amount that the taxpayer is allowed to deduct is the amount invested in purchasing or creating the asset, rather than the cost of replacing the asset in the future when it wears out. Current income should be matched to expenses incurred in generating this income. The cost of replacement should be matched to income generated by the new machine.

Economic analysis views investment in depreciable assets, such as machines, like any other investment. The value of the asset is the present value of the future expected revenue to be generated by it. The annual depreciation is the difference between the present value of expected cash flow from the asset at the start of each year and the present value of the expected cash flow at the end of each year.

For example, if a machine with a useful life of five years is purchased for $1000 and the annual discount rate is five percent, the machine is expected to generate a stream of cash flow with a present value of $1000. If we assume that the amount of income generated by the machine each year is fixed, then under the assumption of a five percent discount rate, the annual cash flow that is expected to be generated by the machine is $231. After one year, the present value of the assets, based on the same expected cash flow and discount rate, but with only four years of expected useful life, is $819. The economic loss in value is therefore the $181 difference between the value at the beginning and at the end of the year. Table 1 shows the economic value and economic depreciation in the above example.

As shown in Table 1, the economic depreciation, also known as the sinking fund, increases each year. Depreciation was $181 dollars in the first year and gradually increased to $220 in the fifth year. In reality, the income generated by most assets is not fixed and it is plausible to assume that machines produce more output in the first years of operation than in later years. Hence, a more equal depreciation method may be appropriate. It should be noted that the argument against sinking fund depreciation cannot be based on the premise that machines tend to lose significant market value in the first year--that is, once they become "used." Such loss in value is due to asymmetric information in the market for used machines. Buyers fear that the used machine will be a "lemon." (42) This reduction in value is irrelevant for the calculation of the depreciation deduction because it has to do with the machine's replacement value, not with its wear and tear in the production of income. Only the latter is relevant to the matching of income and expenses that is necessary for an accurate measurement of taxable income. The wear and tear is not limited to physical depreciation.

B. Accelerated Depreciation

Accounting for depreciation is also required for financial reporting purposes. Generally accepted accounting principles (GAAP) require the depreciation of the (depreciable) cost of income generating assets, usually, tangible assets. (43) The cost has to be allocated among accounting periods on a systematic and rational basis that reflects the use of the asset in the revenue generating process over the asset's operational life. (44)

The vast majority of U.S. corporations use a depreciation method called "straight-line" for financial reporting purposes. (45) According to the straight-line depreciation method, annual depreciation is calculated by subtracting the salvage value of the asset from the purchase price (46) and dividing this number by the estimated useful life of the asset. The outcome is equal periodical deductions throughout the asset's useful life. If the asset in the above example is depreciated under the straight-line method, its $1000 cost is allocated uniformly over its useful life period of five years, resulting in $200 of depreciation deduction each year.

For tax reporting purposes, the Code allows the use of much more accelerated depreciation methods than the straight-line method. (47) Straight-line was the only depreciation method allowed until 1954. In that year, firms were granted the opportunity to accelerate depreciation through the use of declining balance (48) and sum-of-digits (49) depreciation methods. (50) In 1962, guidelines for "useful lives" of assets for tax purposes were promulgated. The guidelines reduced the lifetimes used for calculating depreciation on equipment and machinery prior to 1962. (51) In 1971, the Department of Treasury adopted the Asset Depreciation Range System (ADR) that allowed firms to depreciate their assets over a period that was twenty percent shorter than the 1962 guidelines. (52) In 1981, Congress, under the Reagan Administration's Economic Recovery Act, adopted the Accelerated Cost Recovery System (ACRS), which was replaced by the Modified Accelerated Recovery System (MACRS) in 1982. (53) The favorable treatment of equipment survived the tax reform of 1986. (54) Under MACRS, which is still in effect today, (55) acceleration is achieved by four means: (a) the deductions are calculated on the basis that is often shorter than actual useful lives--thus, machinery and equipment are now depreciable over periods of three to ten years, even though actual service lives are typically longer; (b) salvage value is assumed to be zero; (c) using the half-year convention, taxpayers can take one-half of the total depreciation allowance for the year of purchase even if the depreciable asset was purchased late in the year; (56) and (d) the annual depreciation is calculated on the basis of a double declining balance under which a straight-line percentage is increased by a factor of 200% for assets with short useful lives or 150% for assets with longer useful lives. To understand how the factor works, assume, for example, an asset that costs $1000 and has five years of useful life. The straight-line percentage is 20%; namely, the taxpayer may deduct $200 in calculating her annual taxable income. Under a double declining balance method, the straight-line deduction is multiplied by a factor of 200%. In the first year, the depreciation deduction is computed as: $1000 * 20% * 200% = $400. (57) In the second year, the depreciation deduction is calculated as the original cost minus the depreciated sum of the previous year, multiplied by the original straight-line percentage and the increasing factor: $600 * 20% * 200% = $240. This method is implemented until the first year in which the straight-line depreciation of the not-yet-depreciated cost exceeds the depreciation under the declining balance method. In this example, the first year in which the straight-line depreciation exceeds the declining balance depreciation is the fourth year. Therefore, the depreciation deduction in the fourth and fifth year is calculated according to the straight-line method. Table 2 shows the depreciation of the asset in this example over five years.

In the above example, the present value of the depreciation deductions, assuming a five percent discount rate, is $897 under the declining balance method, $866 under the straight-line method, and $862 under the economic depreciation. The difference between the present value of the double declining method of depreciation and that of the economic depreciation or the straight-line method of depreciation, multiplied by the tax rate, is the tax advantage of the declining balance method. Table 3 shows a comparison between the methods in the above example.

C. Congressional Intent in Accelerating Depreciation Deductions

In times of inflation, recovery of the nominal cost of investment is not sufficient to match income and expenses. Because of inflation, the income generated by the asset is expressed in a larger number of dollars though it has the same purchasing power. There is a need to express the costs incurred in generating that income in current dollars. In order to account for the wear and tear of the asset in each year, the annual amount must be expressed in dollars that represent the purchasing power in the year in which the deduction is allowed. This requires adjusting the historic cost of the asset for inflation. Assume, for example, that a machine with five years of useful life is purchased for $1000 at the beginning of year one. Further assume that the machine generates $231 per year. Under the straight-line depreciation method, $200 is allowed as a depreciation deduction, so that the net income is $31. At a thirty-five percent tax rate, the tax liability is $10.85. Assuming inflation during the second year, allowing only $200 deduction in the second year ignores reality in the sense that $200 dollars in year two is less than $200 in year one. To see this clearly, assume that prices suddenly doubled at the beginning of year two and the income generated by the machine in that year was $462. A $200, instead of $400, depreciation deduction results in taxable income of $262 dollars instead of $62. The true income amount is $62, because this is equivalent to $31 in year one. The tax liability in year two should be $21.70--the equivalent of $10.85 in year one dollars. By not adjusting the depreciation deduction for inflation, the taxpayer will have to pay thirty-five percent of $262, or $91.70; that is, more than four times her real tax liability and close to 150% tax on her real income. Inflation rates were never that high in the United States, but even low inflation rates may significantly erode the value of depreciation deductions. To sum up, if income generated by a depreciable asset increased due to inflation, it should be offset against inflation-adjusted deductions, not nominal ones. (58)

Instead of adjusting the tax-basis of assets for inflation, Congress allowed the use of accelerated deprecation as a rough measure to overcome the erosion of straight-line depreciation deductions by inflation. This, however, was not the main reason for allowing accelerated depreciation deductions. The rate of acceleration was faster than what was required to overcome the effect of inflation, and it is certainly so today, as inflation rates were higher in the 1980s than they are today. (59) The main reason, explicitly stated, was to stimulate investment.

According to Cary Brown, stimulating investment was the Congressional intent when accelerated depreciation deductions were introduced into the Code in 1954 and when the 1962 guidelines were promulgated:
 Especially following World War II, a movement toward manipulating
 depreciation or tax reduction to induce variations in capital
 formation is evident. In this country the Eisenhower Administration
 modified depreciation charges in 1954, and the Kennedy Administration

 recommended this year a tax credit to stimulate investment in plant
 and equipment and is now moving in the direction of further
 liberalization of depreciation. (60)


This was also the explicit intention of Congress in enacting the ACRS, which later became the MACRS--the current depreciation system. In enacting the ACRS, "Congress' stated aim was to stimulate investment in plant and equipment, and with this overriding goal in view it simply discarded accuracy of measurement as an objective for tax law to pursue." (61)

IV. DOES IT STIMULATE INVESTMENT?

Before addressing the question of whether accelerated depreciation promotes economic growth, we have to address a preliminary question: does accelerated depreciation encourage investment? If tax incentives did not induce investment, there could be no effect on economic growth.

Intuitively, one would expect tax incentives to influence the investment decisions of firms, because tax incentives reduce the price of capital goods and firms are expected to find the purchase of capital goods more attractive if they cost less. This is what one would expect based on the theory that the marginal user cost of capital should be the primary determinant of investment demand. (62) Hall and Jorgenson formulated an investment model based on this neo-classical econometric theory and found significant effects of accelerated depreciation on firms' investment decisions. (63)

Surprisingly, later empirical studies commonly found tax incentives to have very little effect on real investment. The calculations by Hall and Jorgenson were based on the assumption that the elasticity of capital stock with respect to the cost of capital is unity, whereas under most empirical studies, it was found to be between 0.2 and 0.4. (64)

The precise explanation of these empirical findings is unclear. One possible explanation is that a firm's liquidity is an important factor in firms' decisions regarding investment. According to this explanation, the availability of cash and other measures of firm liquidity determine firms' investment decisions, and not the marginal cost of assets. (65) Another possible explanation, within the neo-classical framework, is that firms expect policies to change over time. The investment decision is therefore taken on the basis of some weighted average of current and expected user cost of capital. (66) The primary explanation is that of adjustment costs. (67) Decisions cannot be implemented instantaneously. Adjustment costs must be very significant to explain the lack of tax stimulus effect found in the empirical studies. (68) In order to explain the small response to tax incentives, the adjustment costs need to be between one and five dollars per dollar of investment, (69) which is quite implausible. For example, one major form of adjustment cost is known as the risk of irreversibility. A firm contemplating the purchase of a machine wants to know that if the output market turns bad, it will be able to sell the machine and recoup some of its investment. In order for this to take place there has to be an efficient secondary market for capital. In the absence of resale markets, or in the case of asymmetric information between buyers and sellers, such an efficient market may not exist. (70) This adjustment cost could explain why the elasticity of demand is far from unity. However, there is no existing evidence that secondary markets for equipment goods are inefficient.

Some recent literature has argued that measurement error is at the root of the relatively weak empirical performance of traditional investment models. (71) Measurement errors were already identified in earlier literature, such as Cummins, Hassett, and Hubbard in 1994, that used tax reforms as a natural experiment in order to estimate the responsiveness of business fixed investment to tax induced changes in the cost of capital. (72) However, they did not offer a theory to support their findings: that long-lasting tax policy changes could have a significant effect on the level of business fixed investment. As, Ricardo Caballero, one of the commentators in the discussion that followed their paper's presentation at the Brookings Institute said, "There is no precise statement as to which of the ingredients in their complex medicine has cured the patient and as to whether the cure has left the patient with a life worth living." (73)

Normally, adjustment costs are thought of as internal to the firm. When analyzing the impact of tax policy, however, it may be important to consider the impact of external adjustment costs as well. A paper by Austan Goolsbee presented evidence for an alternative explanation of the low estimated response of real investment to changes in the cost of capital, highlighting external adjustment costs. (74) He argued that the supply of capital goods is upward sloping in the short run so that the value of tax subsidies is capitalized into prices. This is a standard tax incidence analysis. Paying a tax and bearing the burden of a tax are not the same. It is possible that the taxpayer who is paying the tax is shifting all or part of the tax economic burden to others. This holds equally for tax subsidies. A large part of the subsidy's reduction of the effective purchase price of equipment is simply shifted to the capital suppliers, through a price increase. Goolsbee found the approximate incidence of investment subsidies to be sixty percent to buyers of capital goods, thirty percent to capital suppliers and ten percent to their workers (through wage increases). These findings are especially important for short-term tax policies, meant to smooth business cycle fluctuations. Such policies may not work because in the short run the supply of capital goods is upward-sloping and investment tax subsidies may give large, unintended rents to capital suppliers without increasing real investment until several years later.

In the case of accelerated depreciation--a long-standing tax policy--supply may well be highly elastic in the long run, especially if the world market for capital goods is open. Using data for the United States and ten other countries, Hassett and Hubbard found that local investment tax credits have a negligible effect on prices paid for capital goods; indeed, they found that the capital goods prices for most countries are very highly correlated and that the movements of these over time are consistent with "the law of one price." (75)

To sum up, tax incentives are likely to stimulate investment, but their effect is not straightforward. (76) Adjustment costs weaken the firms' demand and delay their response. The upward-sloping supply curve may increase prices instead of quantities in the short run. Therefore, the effect of tax incentives on investment is weaker than intuitively expected and comes after a lag. This means that tax incentives are probably not recommended as a tool to smooth business cycle fluctuations. On the other hand, supply may well be highly elastic in the long run, especially if the world market for capital goods is open. Hence, permanent tax policies, such as accelerated depreciation in the United States, are likely to have a long-term effect on capital formation; that is, they will increase investment in depreciable assets, albeit less dramatically than what one may intuitively expect.

V. THE NEXUS BETWEEN INVESTMENT IN EQUIPMENT AND GROWTH

Bradford De Long and Lawrence Summers have argued that investment in equipment has positive externalities; that is, social returns that exceed the private returns. If that is true, government intervention is warranted because the free market equilibrium is likely to reach under-investment. De Long and Summers based their theory on the existence of a strong link between equipment investment and economic growth for a broad cross-section of nations. (77)

Some commentators, such as Auerbach, Hassett, and Oliner, disputed the validity of the evidence for lack of robustness and for relying too much on outliers. (78) Some of these weaknesses were pointed out by De Long and Summers themselves in the form of qualifications to their model. (79) Others, such as Mancur Olson and Robert Hall, questioned whether the association was causal. (80) They suggested that "[H]igher equipment investment may simply be associated with other growth-inducing factors.... There must be a reason why some countries invest in more or less equipment than others, and whatever these reasons are, they themselves may be the reasons for differences in growth." (81) Olson noted "[F]or example, that Argentina, with terrible general economic policy, had low growth and, perhaps incidentally, had low investment in equipment." (82) Robert Hall suggested that "policies that encouraged investment in equipment are often part of a package of standard free-market economic policies." (83) According to Hall, "Equipment investment is therefore a proxy for the pro-trade and pro-growth policies that in fact are responsible for high growth." (84)

De Long and Summers argued that they found that fast growth goes with high quantities and low prices of equipment investment. They saw the association of growth with high quantities and low prices of equipment as strong evidence that equipment investment drives growth. If high rates of investment were a consequence rather than a cause of growth, one would expect that due to strong demand, the price of equipment would be high in rapidly growing countries.

In his criticism of the paper, Olson assumed that all countries have the same access to equipment at similar prices (excluding transport costs). (85) This assumption seems plausible but is in contrast with the findings of the paper. This factual question was not discussed in the exchange and the issue of causality was therefore left unresolved.

As for theory, De Long and Summers found very attractive the idea that the high social product of equipment investment reflects technology transfer mediated through capital goods and thus that the social product is higher for poor countries with a larger technology gap to bridge. (86) This may mean that such effects are important only for developing countries that are moving toward the production frontier, but not relevant for countries like the United States, Germany, or Japan that are near the frontier, as claimed by Auerbach, Hassett, and Oliner. (87) If that is so, then tax distortions in favor of equipment investment are unlikely to aid U.S. productivity growth and could even hinder it by directing investment away from areas where its marginal productivity is the highest.

Another possible explanation for the nexus between investment in machines and growth is that newer vintages of capital have higher levels of productivity built in and add to the productivity of workers who learn how to operate them, so that higher rates of equipment investment raise productivity more than envisioned by standard growth accounting. (88) However, De Long and Summers did not provide any empirical evidence to support this thesis, and according to Clark and Sichel, "the times-series evidence for the United States does not indicate a disproportionate role of capital equipment in productivity growth." (89) Clark and Sichel therefore argued that "[g]iven the lack of empirical evidence that equipment investment improves productivity growth in the United States more than investment in other assets, moves to shift the business tax burden away from equipment are likely to hinder, rather than enhance, long-term productivity growth." (90)

To sum up, the important question of causality was left unanswered because it was not clear whether equipment prices measured in purchasing power parity differ across countries. The various points regarding the quality of the data are probably well taken; De Long and Summers admitted that their "work is vulnerable because our data are of poorer quality than we might wish, and because the direction of causation and the isolation of other possible influences is extremely difficult." (91) Lastly, De Long and Summers admitted that the "jury is still out" regarding the question of whether the results apply to the United States, which is still the world's technological leader, and hence is the only country that cannot appropriate more productive and advanced technologies by importing the capital goods that embody such technologies. (92)

Scaling back the acceleration of depreciation deductions will increase tax revenues. This may allow lowering the corporate tax rate. Using cross-country data during the period from 1970 to 1997, Lee and Gordon recently predicted that cutting "the corporate tax rate by ten percentage points will raise the annual growth rate by one to two percentage points." (93) In an attempt to provide some indirect evidence for the mechanism by which corporate tax rates affect economic growth, they measured the responses of personal tax payments to cuts in corporate tax rates. They presumed that if a lower corporate tax rate generates added investment, then it should generate extra personal tax payments on the resulting income from capital. If instead, it generates added entrepreneurial activity, then it should reduce personal tax payments, due to the drop in wage and salary income, and due to the reporting of business losses but not of large business profits under the personal tax. (94) They found that lower corporate tax rates lead to lower personal tax revenue, a result consistent with a lower corporate tax rate encouraging more entrepreneurial activity, and concluded that these growth effects plausibly reflect a correction for the positive externalities arising from innovative activity. (95)

VI. CONCLUSION

U.S. tax policy in the past fifty years has closely followed Evsey Domar's advice in a 1953 paper: "Given the choice between a lower tax rate with normal depreciation, or a higher rate with accelerated depreciation, I would, except in severe inflation, certainly recommend the latter." (96) In this paper, I beg to differ. I argue that much like another influential paper by Domar, promoting investment as a panacea for economic growth (97)--a paper that is now generally acknowledged to have misguided the World Bank and the IMF in their aid policy for the past fifty years--so has his 1953 paper misguided U.S. domestic tax policy, though to a smaller degree.

The key to U.S. economic growth is not additional capital investment. Having more machines and structures will increase output level, but machines have diminishing marginal returns and the additional tax-induced investment comes at the cost of forgone current consumption (that is, reduced welfare) or at the cost of diversion from other forms of investment or growth promoting policies, such as reducing the corporate tax rate.

Government intervention is necessary in the economics of ideas as the social rate of return on the marginal investment in innovation is much higher than the private rate of return. Such intervention allows innovators to charge fees above marginal cost, in order to recoup their fixed investment during the R & D phase and to make a profit.

Assuming markets are competitive, efficient investment in machinery will take place with no government intervention because the private return equals the social return. There seems to be no robust economic theory supported by strong evidence to justify U.S. government intervention in the market for capital goods. Nevertheless, accelerated depreciation is the foundation of U.S. tax policy. It is time to give it a closer look.

Yoram Margalioth*

* Tel Aviv University Law School. The author would like to thank Steve Bank, Oren Bar-Gil, David Cameron, Charlotte Grane, Michal Gal, David Gilo, Hanoch Dagan, Tsilly Dagan, Ofer Grosskopf, Sharon Hannes, Al Harberger, Elhanan Helpman, Doron Herman, Assaf Likhovski, Ariel Porat, Philip Postlewaite, Sharon Rabin-Margalioth, Eli Salzberger, Dan Shaviro, Kirk Stark, Eric Zolt, and participants in the Northwestern Tax Series forum, UCLA Tax Policy and Public Finance Colloquium, Tel Aviv University Law and Economics Workshop, University of Haifa Law and Economics Workshop, and Tel Aviv University Law Faculty seminar, for fruitful discussions and comments; Noam Noked for research assistance; and the Cegla Center for Interdisciplinary Research of Law for financial support.

(1) There are numerous acknowledgements of such policy in the literature. See, e.g., MARVIN A. CHIRELSTEIN, FEDERAL INCOME TAXATION 163 (9th ed. 2002) ("Most would agree, I think, that at least since the enactment of the 1954 Code, the depreciation allowance ... has reflected a Congressional policy of encouraging growth and expansion."); MICHAEL J. GRAETZ & DEBORAH H. SCHENK, FEDERAL INCOME TAXATION: PRINCIPLES AND POLICIES 343 (rev. 4th ed. 2002) ("Depreciation allowances often have been used not to just measure income, but also as a subsidy to affect the overall investment in plant and equipment for fiscal and economic policy reasons."); WILLIAM A. KLEIN, JOSEPH BANKMAN & DANIEL N. SHAVIRO, FEDERAL INCOME TAXATION 613 (12th ed. 2000) ("Congress has deliberately provided taxpayers with a deduction that is generally in excess of the anticipated decline in value of the asset, in the hope of thereby stimulating investment."); Michael J. Graetz & Alvin C. Warren, Jr., Income Tax Discrimination and the Political and Economic Integration of Europe, 115 YALE L.J. 1186, 1225 (2006) ("One standard method for combating recessions, for example, is to increase depreciation allowances or to provide tax credits for new investments in plant and equipment. The United States often has used these techniques in efforts to stimulate its economy.").

(2) An inflation adjusted straight-line depreciation is one such method. See discussion infra Part III.C.

(3) See Young Lee & Roger H. Gordon, Tax Structure and Economic Growth, 89 J. PUB. ECON. 1027, 1041 (2005) (suggesting that a cut in the corporate tax rate by 10 percentage points will raise the annual growth rate by 1.1-1.8 percentage points and that this outcome should be attributed to the inducement of entrepreneurial activity and not to an increase in investment).

(4) See, e.g., Bronwyn H. Hall, The Private and Social Returns to Research and Development, in TECHNOLOGY, R & D, AND THE ECONOMY 140 (Bruce L.R. Smith & Claude E. Barfield eds., The Brookings Institution 1995) (providing evidence that the social return to R & D is much above the private return).

(5) Evsey D. Domar, The Case for Accelerated Depreciation, 67 Q. J. ECON. 493, 509 (1953).

(6) Evsey D. Domar, Capital Expansion, Rate of Growth, and Employment, 14 ECONOMETRICA 137 (1946); see also Roy F. Harrod, An Essay in Dynamic Theory, 49 ECON. J. 14 (1939) (presenting a similar theory, suggested independently by a British economist).

(7) See Robert M. Solow, A Contribution to the Theory of Economic Growth, 70 Q. J. ECON. 65 (1956); see also Robert M. Solow, Technical Change and the Aggregate Production Function, 39 REV. ECON. & STAT. 312 (1957).

(8) WILLIAM EASTERLY, THE ELUSIVE QUEST FOR GROWTH 28 (MIT Press 2001).

(9) The number of workers does not increase because labor is a fixed factor, but technology makes each worker more effective. This gives the same result as an increase in the number of workers.

(10) See EASTERLY, supra note 8, at 28.

(11) Id. at 29.

(12) Id. at 33.

(13) Id. at 29.

(14) The approximate value of the tax benefit of the accelerated depreciation in 2004, measured as the present value of government revenue loss due to this tax benefit, was $45 billion dollars (consisting of $39.3 billion in depreciation of machinery and equipment and $5.7 billion in depreciation of buildings). See Analytical Perspectives, Budget of the United States Government, Fiscal Year 2006, 326, available at http://www.whitehouse.gov/omb/budget/fy2006/(follow hyperlink to "Analytical Perspectives, Budget of the United States")

(15) Thirty percent of the investment was immediately expensed. The remaining seventy percent was depreciated according to the normal depreciation schedule. The fraction of investment that could be deducted in the year of purchase was increased in 2003 to fifty percent. See I.R.C. [section] 168(k)(4)(B).

(16) STAFF OF JOINT COMM. ON TAXATION, 107TH CONG., SUMMARY OF P. L. 107-147, THE "JOB CREATION AND WORKER ASSISTANCE ACT OF 2002" (Joint Comm. Print 2002), available at http://www.house.gov/jct/x-22-02.pdf.

(17) Press Release, Office of the Press Secr'y, President Signs Stimulus Bill During Live Radio Address (Mar. 9, 2002), available at http://www.whitehouse.gov/news/releases/2002/03/20020309-2.html.

(18) ADAM SMITH, AN INQUIRY INTO THE NATURE AND CAUSES OF THE WEALTH OF NATIONS (1776), available at http://www.adamsmith.org/smith/won-index.htm.

(19) See THE CIA FACT BOOK, available at https://www.cia.gov/cia/publications/factbook/geos/ch.html#Econ (search "China").

(20) Id.

(21) Id.

(22) See THE CIA FACT BOOK, available at https://www.cia.gov/cia/publications/factbook/geos/ch.html#Econ (search "India").

(23) See, e.g., A New World Economy, Bus. WK. ONLINE (Aug. 22, 2005), available at http://www.businessweek.com/magazine/content/05_34/b3948401.htm; see also Laurence J. Kotlikoff, Hans Fehr & Sabine Jokisch, Will China Eat Our Lunch or Take Us to Dinner? Simulating the Transition Paths of the U.S., E.U., Japan, and China, (Nat'l Bureau of Econ. Research, Working Paper No. 11668, Sept. 2005).

(24) Albert Einstein is said to have called compound interest "the greatest mathematical discovery of all time." See JOHN BOGLE, BOGLE ON MUTUAL FUNDS: NEW PERSPECTIVES FOR THE INTELLIGENT INVESTOR 1(Dell, reprint ed. 1994).

(25) Paul M. Romer, Economic Growth, in THE CONCISE ENCYCLOPEDIA OF ECONOMICS (David R. Henderson, ed. Liberty Fund)(forthcoming 2007), available at http://www.stanford.edu/~promer/EconomicGrowth.pdf.

(26) Robert E. Lucas, Jr., On the Mechanics of Economic Development, 22 J. MONETARY ECON. 3,4 (1988).

(27) TATYANA P. SOUBBOTINA & KATHERINE SHERAM, BEYOND ECONOMIC GROWTH 25 (2000).

(28) See supra note 6.

(29) See supra note 7.

(30) Id.

(31) The number of workers does not increase because labor is a fixed factor, but technology makes each worker more effective. This gives the same result as an increase in the number of workers.

(32) For short reviews of the basics of the new growth theories by three of their pioneers, see Gene M. Grossman & Elhanan Helpman, Endogenous Innovation in the Theory of Growth, 8 J. ECON. PERSP. 23 (1994); Paul M. Romer, The Origins of Endogenous Growth, 8 J. ECON. PERSP. 3 (1994).

(33) For a detailed explanation on how ideas promote growth, see Charles I. Jones, Growth and Ideas, in HANDBOOK OF ECONOMIC GROWTH 1063 (P. Aghion & S. Durlauf eds., Elsevier 2005).

(34) For a discussion and comparison of the various forms of intervention, see SUZANNE SCOTCHMER, INNOVATION AND INCENTIVES (MIT Press 2004).

(35) DOUGLASS C. NORTH, STRUCTURE AND CHANGE IN ECONOMIC HISTORY 164-67 (W.W. Norton & Co. 1981).

(36) See Zvi Griliches, The Search for R & D Spillovers, 94 SCAND. J. ECON. 29 (Supp. 1992) (evaluating calculations of the social rates of return for research and development); see also Hall, supra note 4.

(37) The clocks are on display at the National Maritime Greenwich Museum, London.

(38) See SCOTCHMER, supra note 34, at 33.

(39) See Daniel Shaviro, Endowment and Inequality, in TAX JUSTICE RECONSIDERED: THE MORAL AND ETHICAL BASES OF TAXATION (Joseph J. Thorndike & Dennis J. Ventry Jr. eds., Urban Institute Press 2002).

(40) See, e.g., U.S.C. [section] 162 (allowing a deduction for "all the ordinary and necessary expenses paid or incurred during the taxable year in carrying on any trade or business.").

(41) The wear and tear is not limited to physical depreciation. Machines may become less productive due to obsolescence. For example, computers may become obsolete when new software requires more powerful hardware.

(42) George Akerlof, The Market for Lemons: Quality Uncertainty and the Market Mechanism, 84 Q. J. ECON. 488, 489-90 (1970).

(43) EMERGENCY FACILITIES: DEPRECIATION, AMORTIZATION, AND INCOME TAXES, Accounting Research Bulletin No. 43, ch. 9C, para. 5 (Am. Inst. of Certified Pub. Accountants 1953).

(44) Id.

(45) Henry McFarland, Alternative Methods of Depreciation and the Reliability of Accounting Measures of Economic Profits, 72 REV. ECON. & STAT. 521, 521 (1990).

(46) The salvage value is the value of the asset at the end of its useful life. It is usually assumed to be zero.

(47) The present discounted value of the accelerated depreciation deductions exceeds the present discounted value of depreciation allowances under the straight-line method.

(48) In declining balance depreciation, each year's depreciation is based on the previous year's net book value, namely the historic cost minus depreciation deducted in previous years. A percentage rate is applied to the un-depreciated balance, rather than to the original cost.

(49) Under the declining sum-of-digits depreciation method, the percentage of the annual depreciation is the remaining useful life from the beginning of the current year, divided by the sum of digits of the total useful life of the asset. For example, an asset with a useful life of five years, is depreciated 5 / (1 + 2 + 3 + 4 + 5) = 0.33 of its value in the first year.

(50) Robert M. Coen, Effects of Tax Policy on Investment in Manufacturing, 58 AM. ECON. REV. 200,202-03 (1968).

(51) See Robert E. Hall & Dale W. Jorgenson, Tax Policy and Investment Behavior, 57 AM. ECON. REV. 391,404 (1967).

(52) Gerard B. Brannon, Tax Policy and Depreciation: The Case for ADR, 27 J. FIN. 525,525 (1971).

(53) The Tax Equity and Fiscal Responsibility Act of 1982, Pub. L. 324, [section] 206, 96 Stat. 324, 431 (1982). The useful lives of structures were shortened, but those of machines remained intact.

(54) See Jane G. Gravelle, Whither Tax Depreciation?, 54 NAT'L TAX J. 513 (arguing that 1986 tax reform brought the depreciation of structures and equipment closer together and describing the reasons why structures are currently treated less favorably than equipment, calling to bring them together again).

(55) See 26 U.S.C. [section] 168.

(56) See 26 U.S.C. [section] 168(d)(1). Where the taxpayer purchases a significant amount of depreciable property in the last quarter, a mid-quarter convention applies. 26 U.S.C. [section] 168(d)(3). For real property, a mid-month convention is used. 26 U.S.C. [section] 168(d)(2).

(57) For the sake of simplicity, in the example of the declining balance method, the depreciation in the first year of the asset is full, not half of the depreciation as it should be, in the first year under MACRS.

(58) There are, however, offsetting distortions if the asset is debt financed, because the taxpayer can deduct the full nominal interest rate, which includes the inflationary charge. Yoram Margalioth, The Case for Tax Indexation of Debt, 15 AM. J. TAX POL'Y 205, 257-60 (1998).

(59) See InflationData.com, Historical US Inflation Rate 1914-Present, available at http://inflationdata.com/inflation/Inflation_Rate/HistoricalInflation.aspx?dsInflation_currentPage=0.

(60) Cary E. Brown, Tax Incentives for Investments, 52 AM. ECON. REV. 335, 335 (1962); see also Hall & Jorgenson, supra note 51, at 404 ("The effectiveness of tax policy in altering investment behavior is an article of faith among both policymakers and economists. Whatever the grounds for this belief, its influence on postwar tax policy in the United States has been enormous.").

(61) See CHIRELSTEIN, supra note 1, at 162; see also S. REP. NO. 97-144, at 39-63 (1981) ("The committee agrees with numerous witnesses who testified that a substantial restructuring of depreciation and the [investment] credit will be an effective way of stimulating capital formation, increasing productivity, and improving the nation's competitiveness in international trade."); CONG. BUDGET OFFICE, THE PRODUCTIVITY PROBLEM: ALTERNATIVES FOR ACTION 36-44 (1981), available at http://www.cbo.gov/ftpdocs/51xx/doc5169/doc04-Entire.pdf.

(62) The user cost of capital is an expression coined by Jorgenson in 1963 and is a function of prices, tax provisions, financing costs, and actual depreciation. See Dale W. Jorgenson, Capital Theory and Investment Behavior, 53 AM. ECON. REV. 247, 248-51 (1963).

(63) See Hall & Jorgenson, supra note 51, at 404.

(64) See, e.g., Alan J. Auerbach & Kevin A. Hassett, Tax Policy and Business Fixed Investment in the United States, 47 J. PUB. ECON. 141 (1992); R. M. Coen, Tax Depreciation Reform: Discussion, 27 J. FIN. 534, 537 (1972); Robert Eisner, Tax Policy and Investment Behavior: Comment, 59 AM. ECON. REV. 379, 382 (1969).

(65) See, e.g., Steven M. Fazzari et al., Financing Constraints and Corporate Investment, 19 BROOKINGS PAPERS ON ECON. ACTIVITY 141, 143 (1988) (finding that cash flow was an important determinant of investment even when other factors were controlled for, especially for low-payout firms likely to be cash-constrained).

(66) See Alan J. Auerbach, Tax Reform and Adjustment Costs: The Impact on Investment and Market Value, 30 INT'L ECON. REV. 939, 939 (1989); see also Alan J. Auerbach & Kevin Hassett, Tax Policy and Business Fixed Investment in the United States, 47 J. PUB. ECON. 141 (1992).

(67) See Darrel S. Cohen et al., The Effects of Temporary Partial Expensing on Investment Incentives in the United States, 55 NAT'L TAX J. 457, 461 (2002) ("The fact that firms do not instantaneously change their capital stocks in response to changes in the incentives to invest suggests that the costs of adjustment are empirically important.").

(68) See, e.g., Lawrence H. Summers, Taxation and Investment: A Q Theory Approach, 12 BROOKINGS PAPERS ON ECON. ACTIVITY 67 (1981).

(69) See Jason G. Cummins et al., A Reconsideration of Investment Behavior Using Tax Reforms and Natural Experiments, 35 BROOKINGS PAPERS ON ECON. ACTIVITY 28, 30 (1994).

(70) Akerlof, supra note 42, at 490-91.

(71) See, e.g., Mihir A. Desai & Austan D. Goolsbee, Investment, Overhang, and Tax Policy, 35 BROOKINGS PAPERS ON ECON. ACTIVITY 285, 313 (2004); Austan D. Goolsbee, The Importance of Measurement Error in the Cost of Capital, 53 NAT'L TAX J. 215, 215 (2001).

(72) See Cummins et al., supra note 69, at 30.

(73) Id. at 63.

(74) Austan D. Goolsbee, Investment Tax Incentives, Prices, and the Supply of Capital Goods, 113 Q.J. ECON. 121 (1998).

(75) Kevin A. Hassett & Glenn R. Hubbard, Tax Policy and Investment at 33 (Nat'l Bureau of Econ. Research, Working Paper No. 5683,1998).

(76) See Cohen et al., supra note 67; see also Darrel Cohen & Jason Cummins, A Retrospective Evaluation of the Effects of Temporary Partial Expensing, (Fin. & Econ. Discussion Series, Div. of Research & Statistics & Monetary Affairs Fed. Reserve Bd., Working Paper No. 2006-19, 2006) (examining how business investment responded to temporary partial expensing, first enacted in 2002 and expanded in 2003, and finding that that partial expensing did not boost the incentives to invest by all that much).

(77) Bradford J. De Long & Lawrence Summers, Equipment Investment and Economic Growth, 106 Q. J. ECON. 445,446 (1991); Bradford J. De Long & Lawrence Summers, Equipment Investment and Economic Growth: How Strong Is the Nexus? 2 BROOKINGS PAPERS ON ECON. ACTIVITY 157 (1992) [hereinafter De Long & Summers, Nexus].

(78) Alan J. Auerbach et al., Reassessing the Social Returns to Equipment Investment, 109 Q. J. ECON. 789, 790 (1994).

(79) Bradford J. De Long & Lawrence Summers, Equipment Investment and Economic Growth: Reply, 109 Q. J. ECON. 803 (1994).

(80) See De Long & Summers, Nexus, supra note 77, at 206.

(81) Id.

(82) Id.

(83) Id.

(84) Id.

(85) Id.; see also Hassett & Hubbard, supra note 75, at 33 ("[C]apital goods prices for most countries are very highly correlated, and that the movements of these over time are consistent with 'the law of one price.'").

(86) De Long & Summers, Nexus, supra note 77, at 206-07.

(87) Id.; see also Auerbach et al., supra note 78; Hassett & Hubbard, supra note 87.

(88) But see Gravelle, supra note 54. Gravell states:
 One is the notion that if technological advance is embodied in
 equipment productivity will increase if more of such investment is
 made. But this reasoning is faulty economic reasoning: the most
 productive investment is that which is chosen in a competitive market,
 and older equipment should only be replaced when the gain from doing
 so is worthwhile.


Id. at 520.

(89) Peter K. Clark & Daniel E. Sichel, Tax Incentive and Equipment Investment, 1 BROOKINGS PAPERS ON ECON. ACTIVITY 317, 335 (1993).

(90) Id. at 339.

(91) De Long & Summers, supra note 79, at 806-07.

(92) Id. at 806.

(93) See Lee & Gordon, supra note 3.

(94) Id.

(95) Id.

(96) See Domar, supra note 5.

(97) See Domar, supra note 6.
TABLE 1.

Year Value Economic Depreciation

0 1000 --
1 819 181
2 629 190
3 429 200
4 220 209
5 0 229
 1000

TABLE 2.

 Asset's Tax Basis Declining Balance
Year at Year End Depreciation

0 1000 --
1 600 400
2 360 240
3 216 144
4 108 108
5 0 108
 1000

TABLE 3.

 Declining
Year Balance Economic Straight-line

1 400 181 200
2 240 190 200
3 144 200 200
4 108 209 200
5 108 220 200
 1000 1000 1000
Present Value 897 862 866
 (5%)
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