Now that the Republican-led US House of Representatives and Senate have each passed bills to overhaul the tax system, we can start to see what effect the coming changes will have on the US economy. By reducing the costs of investments and cutting the tax rate on corporate profits, the final plan that emerges will likely boost growth substantially.
In The Great US Tax Debate, Robert Barro makes the case for the GOP Tax Plan. Jason Furman & Lawrence H. Summers take issue in a seperate PS On Point, linked below.
CAMBRIDGE – With the US Senate and House of Representatives now reconciling their respective tax-reform bills, many in the United States and around the world are wondering what impact the legislation will have on the US economy. Most important, how will the legislation change the country’s long-term growth prospects? To address this question, I focus on three likely changes to the taxation of businesses.
The first change is the reduction of the main tax rate on profits of C-corporations from 35% to 20%. (A C‑corporation, unlike an S-corporation, is taxed separately from its owners.) The second change is the replacement of the current system of depreciation allowances for new equipment with immediate 100% expensing. Third, the recovery period for most non-residential business structures, such as office buildings, is to be shortened from 39 to 25 years.
In the final bill, the full expensing of equipment may expire after five years, although a future Congress can extend this provision. My analysis treats the three key changes in business taxation as permanent. If businesses instead regard the expensing provision as temporary, the effects on equipment investment would likely be accelerated in order to take advantage of the more favorable treatment offered over a five-year window.
A Two-Pronged Approach
I use two complementary approaches to estimate impacts on investment and economic growth. The first method starts by gauging the effects of the tax-law changes on the costs (referred to as user costs) that businesses attach to investment in equipment and structures. Then I estimate long-run responses of the capital-labor ratio to the changes in user costs. This approach was pioneered by Mervyn King, before his stint as Governor of the Bank of England, and Don Fullerton in their 1984 book The Taxation of Income from Capital: A Comparative Study of the United States, the United Kingdom, Sweden, and West Germany.
Once we know the change in the capital-labor ratio, it is straightforward to estimate the long-run change in real (inflation-adjusted) per capita GDP. The short-run effects can then be inferred by using previous estimates of convergence rates associated with economic growth. The results can be expressed as increases in average rates of real per capita GDP growth over the ten-year period emphasized in the legislation.
The second approach uses the framework developed in empirical analyses of the determinants of economic growth for a large number of countries observed since 1960. (A summary of this approach is in my June 2015 paper “Convergence and Modernization.”) The underlying data were extended to encompass information on tax rates on corporate profits dating back to 1980 (these data come from a project at the American Enterprise Institute). The empirical results provide estimates of effects of changes in corporate-tax rates on real per capita GDP growth over five-year intervals. These results turn out to accord with those obtained from the first method.
User Costs
For the user-cost approach, I assume that corporations discount all expected future cash flows in accordance with the net expected real rate of return on capital. To accord with the observed high average equity premium (the gap in returns between stocks and safe assets), this rate has to be well above the average risk-free real interest rate, now around 1% per year. My main analysis uses an expected real rate of return on capital of 8% per year (the average long-term real rate of return on stocks in the US and other rich countries), but allows for a rate of 6% as an alternative.
I assume that the expected real rate of return on capital is fixed in the long run, even when there is a change in business taxation. This condition obtains in economists’ most popular model of economic growth (the neoclassical growth model for a closed economy with an infinite planning horizon), owing to household saving behavior. And the result serves as an approximation even in modified versions of this model. For a small open economy (not the US), the condition holds even in the short run, given the availability of foreign borrowing and lending.
The key condition for business investment is the marginal product of capital – the amount of additional output per additional unit of capital input. This marginal product is equated to the user cost, which involves the expected rate of return on capital and features of the tax system. A key element in the user cost is the effective expensing rate for equipment and structures implied by the existing and proposed systems of business taxation. (See the technical note at the end of this article for details.)
The table shows my characterization of the old and new corporate tax systems with regard to effective expensing rates for equipment and structures. These calculations assume that the existing tax law entails double-declining balance depreciation for five- or seven-year equipment (ignoring the temporary bonus depreciation currently in effect).
The calculations assume straight-line depreciation for non-residential structures over 39 years in the current law and over 25 years in the new law. I assume that one-third of structures are financed by corporate bonds, that the nominal interest rate on corporate bonds is 4% per year, and that the inflation rate is 2% per year (relevant for capitalizing deductions for depreciation and interest payments). Finally, I focus on the case where the real rate of return on capital is 8% per year.
For equipment, the tax reform lowers user cost by 12%. For structures, the decrease is 16%. Surprisingly, although full expensing applies to equipment in the new law, the proportionate decrease in user cost is larger for structures, owing to the reduction in the recovery period from 39 to 25 years. My results accord with an open letter that eight other economists (Michael Boskin, John Cogan, Douglas Holtz-Eakin, Glenn Hubbard, Lawrence Lindsey, Harvey Rosen, George Shultz, and John Taylor) and I addressed to Treasury Secretary Steven Mnuchin in late November. That letter estimated that the corporate tax changes “would reduce the user cost by an average of 15%.”
From User-Cost Reductions to Growth
Converting the changes in user costs into long-run changes in capital-labor ratios requires an estimate of the relevant elasticity (the proportionate sensitivity of the capital-labor ratio to the user cost). Empirical estimates of these elasticities, summarized in a recent report from the US Council of Economic Advisers, are not far from unity. I focus on an elasticity of 1.25, which corresponds to a Cobb-Douglas production function (commonly used by economists) in which equipment and structures each have an income share of 20%. In this case, the tax changes raise long-run capital-labor ratios by 25% for non-residential corporate structures and 17% for corporate equipment.
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If we thought of C-corporations as corresponding to the whole economy, the changes in capital-labor ratios would imply a rise in long-run real per capita GDP by about 8.4%. Given that the overall corporate sector (which includes S-corporations) accounted for only 56% of national income in 2016, the effects on long-run GDP would be smaller than 8.4%. But not by much, because the changes related to depreciation apply generally to businesses, and the legislation also includes reductions in tax rates on pass-through businesses, such as S-corporations and partnerships. Moreover, the reduced tax burden on C-corporations will induce an efficient flow of resources toward this sector, including movements out of residential housing and conversions of pass-through enterprises to C-corporations.
To get estimates for GDP growth rates, I made a rough downward adjustment of the long-run level effect from 8.4% to 7%. Then I estimated the dynamics of real per capita GDP based on estimates of convergence rates – the rate at which a country adjusts toward its long-run position. In previous research, I estimated this rate of convergence to be 2-3% per year. Former US Secretary of the Treasury Lawrence H. Summers dubbed my estimate of 2% per year as the “iron law of convergence,” but more recent estimates are closer to 3%.
However, convergence rates in the range of 2-3% per year accord with the underlying neoclassical growth model only if one takes a broad view of capital, particularly to include human capital, so that the capital share of income is 75-80%. In that case, diminishing productivity of capital sets in slowly, and convergence rates are correspondingly low. This setting does not apply to the proposed changes in corporate taxation, because they affect physical capital but not human capital. In this context, a narrower concept of capital applies, and the convergence rate would be correspondingly higher. For example, if one assumes a capital share of income of 40%, the convergence rate in the neoclassical growth model would be around 5% per year.
If I apply a convergence rate of 5% per year to the long-run 7% change in real per capita GDP, the growth rate rises in the short run by 0.34% per year. After ten years, the level of real per capita GDP is higher by 2.8%, implying that the average growth rate is higher by around 0.28% per year over a ten-year span.
Cross-Country Growth Analysis
As I noted above, my second approach consists of entering the tax rate for corporate profits into a cross-country growth analysis. The available data refer to the top marginal tax rate on corporations and provide no information about effective expensing in the tax structure.
As usual in this type of analysis, there are issues concerning holding constant other determinants of economic growth and dealing with reverse causation from economic outcomes to the tax structure. (The latter consideration suggests that the estimated effect would understate the magnitude of the true impact of the tax rate on economic growth.) But this procedure also has important advantages – for example, there are 500 data points on five-year average growth rates of real per capita GDP, and one does not have to make a lot of modeling assumptions, as required by the user-cost framework.
The result from a cross-country regression for explaining five-year-average per capita GDP growth rates is a negative estimated coefficient on the corporate-tax rate. In other words, a higher tax rate means lower economic growth. However, the estimated value has a high standard error and is statistically significant only at a 15% critical value. The point estimate implies that a cut in the corporate-tax rate by 15 percentage points (as in the pending US legislation) would raise the growth rate of real per capita GDP over a five-year interval by about 0.4% per year. The interesting point is that this result accords with the results from the user-cost approach. Hence, the cross-country analysis supports the reasonableness of the user-cost findings.
The bottom line is that the pending corporate tax changes would produce a large long-run increase in real per capita GDP – by around 7%. The associated rise in growth rates over a ten-year horizon would be about 0.3% per year.
Technical note
The analysis of user costs is based on a formula derived from the 1984 book by King and Fullerton:
where τ is the proportionate tax rate on corporate earnings, computed by allowing for expensing at the effective rate λ on investment outlays, and δ is the true depreciation rate on capital. In calculating λ for the existing and proposed corporate tax systems, I estimate present values (using the real discount rate, rk) associated with depreciation allowances and deductibility of corporate interest payments. (I assume that bond financing applies fractionally to structures and not at all to equipment, and that proposed limitations on deductibility of bond interest would not be an effective constraint with regard to investment in structures.)
Note that user cost on the right side of the equation falls with the expensing rate, λ, if τ<1: more expensing encourages investment. If λ<1 (as in the current system), user cost rises with τ, so that a higher corporate-tax rate discourages investment. However, the effect of τ on user cost is nil if λ=1 (as with full expensing of equipment) and is negative if λ>1 (for example, if full expensing were combined with deductibility of interest payments). If λ=0, the equation gives the familiar result that the after-tax marginal product of capital, (1-τ)∙MPK, equals rk+δ. For given features of the tax system, user cost rises with rk+δ. However, because I treat rk+δ as fixed, all of the estimated effects on investment come directly from the tax term, (1‑τλ)/(1-τ), shown in the equation.
With the US Republicans’ tax plan nearing enactment, two of the most senior economists serving in recent Democratic presidential administrations examine the most rigorous professional defense of the plan.
They find that Robert Barro’s estimates are riddled by methodological flaws, measurement errors, and implausible assumptions.
raise fundamental objections to the economic model used to defend and promote the Republican tax plan.
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CAMBRIDGE – With the US Senate and House of Representatives now reconciling their respective tax-reform bills, many in the United States and around the world are wondering what impact the legislation will have on the US economy. Most important, how will the legislation change the country’s long-term growth prospects? To address this question, I focus on three likely changes to the taxation of businesses.
The first change is the reduction of the main tax rate on profits of C-corporations from 35% to 20%. (A C‑corporation, unlike an S-corporation, is taxed separately from its owners.) The second change is the replacement of the current system of depreciation allowances for new equipment with immediate 100% expensing. Third, the recovery period for most non-residential business structures, such as office buildings, is to be shortened from 39 to 25 years.
In the final bill, the full expensing of equipment may expire after five years, although a future Congress can extend this provision. My analysis treats the three key changes in business taxation as permanent. If businesses instead regard the expensing provision as temporary, the effects on equipment investment would likely be accelerated in order to take advantage of the more favorable treatment offered over a five-year window.
A Two-Pronged Approach
I use two complementary approaches to estimate impacts on investment and economic growth. The first method starts by gauging the effects of the tax-law changes on the costs (referred to as user costs) that businesses attach to investment in equipment and structures. Then I estimate long-run responses of the capital-labor ratio to the changes in user costs. This approach was pioneered by Mervyn King, before his stint as Governor of the Bank of England, and Don Fullerton in their 1984 book The Taxation of Income from Capital: A Comparative Study of the United States, the United Kingdom, Sweden, and West Germany.
Once we know the change in the capital-labor ratio, it is straightforward to estimate the long-run change in real (inflation-adjusted) per capita GDP. The short-run effects can then be inferred by using previous estimates of convergence rates associated with economic growth. The results can be expressed as increases in average rates of real per capita GDP growth over the ten-year period emphasized in the legislation.
The second approach uses the framework developed in empirical analyses of the determinants of economic growth for a large number of countries observed since 1960. (A summary of this approach is in my June 2015 paper “Convergence and Modernization.”) The underlying data were extended to encompass information on tax rates on corporate profits dating back to 1980 (these data come from a project at the American Enterprise Institute). The empirical results provide estimates of effects of changes in corporate-tax rates on real per capita GDP growth over five-year intervals. These results turn out to accord with those obtained from the first method.
User Costs
For the user-cost approach, I assume that corporations discount all expected future cash flows in accordance with the net expected real rate of return on capital. To accord with the observed high average equity premium (the gap in returns between stocks and safe assets), this rate has to be well above the average risk-free real interest rate, now around 1% per year. My main analysis uses an expected real rate of return on capital of 8% per year (the average long-term real rate of return on stocks in the US and other rich countries), but allows for a rate of 6% as an alternative.
I assume that the expected real rate of return on capital is fixed in the long run, even when there is a change in business taxation. This condition obtains in economists’ most popular model of economic growth (the neoclassical growth model for a closed economy with an infinite planning horizon), owing to household saving behavior. And the result serves as an approximation even in modified versions of this model. For a small open economy (not the US), the condition holds even in the short run, given the availability of foreign borrowing and lending.
The key condition for business investment is the marginal product of capital – the amount of additional output per additional unit of capital input. This marginal product is equated to the user cost, which involves the expected rate of return on capital and features of the tax system. A key element in the user cost is the effective expensing rate for equipment and structures implied by the existing and proposed systems of business taxation. (See the technical note at the end of this article for details.)
The table shows my characterization of the old and new corporate tax systems with regard to effective expensing rates for equipment and structures. These calculations assume that the existing tax law entails double-declining balance depreciation for five- or seven-year equipment (ignoring the temporary bonus depreciation currently in effect).
The calculations assume straight-line depreciation for non-residential structures over 39 years in the current law and over 25 years in the new law. I assume that one-third of structures are financed by corporate bonds, that the nominal interest rate on corporate bonds is 4% per year, and that the inflation rate is 2% per year (relevant for capitalizing deductions for depreciation and interest payments). Finally, I focus on the case where the real rate of return on capital is 8% per year.
For equipment, the tax reform lowers user cost by 12%. For structures, the decrease is 16%. Surprisingly, although full expensing applies to equipment in the new law, the proportionate decrease in user cost is larger for structures, owing to the reduction in the recovery period from 39 to 25 years. My results accord with an open letter that eight other economists (Michael Boskin, John Cogan, Douglas Holtz-Eakin, Glenn Hubbard, Lawrence Lindsey, Harvey Rosen, George Shultz, and John Taylor) and I addressed to Treasury Secretary Steven Mnuchin in late November. That letter estimated that the corporate tax changes “would reduce the user cost by an average of 15%.”
From User-Cost Reductions to Growth
Converting the changes in user costs into long-run changes in capital-labor ratios requires an estimate of the relevant elasticity (the proportionate sensitivity of the capital-labor ratio to the user cost). Empirical estimates of these elasticities, summarized in a recent report from the US Council of Economic Advisers, are not far from unity. I focus on an elasticity of 1.25, which corresponds to a Cobb-Douglas production function (commonly used by economists) in which equipment and structures each have an income share of 20%. In this case, the tax changes raise long-run capital-labor ratios by 25% for non-residential corporate structures and 17% for corporate equipment.
Secure your copy of PS Quarterly: The Climate Crucible
The newest issue of our magazine, PS Quarterly: The Climate Crucible, is here. To gain digital access to all of the magazine’s content, and receive your print copy, subscribe to PS Premium now.
Subscribe Now
If we thought of C-corporations as corresponding to the whole economy, the changes in capital-labor ratios would imply a rise in long-run real per capita GDP by about 8.4%. Given that the overall corporate sector (which includes S-corporations) accounted for only 56% of national income in 2016, the effects on long-run GDP would be smaller than 8.4%. But not by much, because the changes related to depreciation apply generally to businesses, and the legislation also includes reductions in tax rates on pass-through businesses, such as S-corporations and partnerships. Moreover, the reduced tax burden on C-corporations will induce an efficient flow of resources toward this sector, including movements out of residential housing and conversions of pass-through enterprises to C-corporations.
To get estimates for GDP growth rates, I made a rough downward adjustment of the long-run level effect from 8.4% to 7%. Then I estimated the dynamics of real per capita GDP based on estimates of convergence rates – the rate at which a country adjusts toward its long-run position. In previous research, I estimated this rate of convergence to be 2-3% per year. Former US Secretary of the Treasury Lawrence H. Summers dubbed my estimate of 2% per year as the “iron law of convergence,” but more recent estimates are closer to 3%.
However, convergence rates in the range of 2-3% per year accord with the underlying neoclassical growth model only if one takes a broad view of capital, particularly to include human capital, so that the capital share of income is 75-80%. In that case, diminishing productivity of capital sets in slowly, and convergence rates are correspondingly low. This setting does not apply to the proposed changes in corporate taxation, because they affect physical capital but not human capital. In this context, a narrower concept of capital applies, and the convergence rate would be correspondingly higher. For example, if one assumes a capital share of income of 40%, the convergence rate in the neoclassical growth model would be around 5% per year.
If I apply a convergence rate of 5% per year to the long-run 7% change in real per capita GDP, the growth rate rises in the short run by 0.34% per year. After ten years, the level of real per capita GDP is higher by 2.8%, implying that the average growth rate is higher by around 0.28% per year over a ten-year span.
Cross-Country Growth Analysis
As I noted above, my second approach consists of entering the tax rate for corporate profits into a cross-country growth analysis. The available data refer to the top marginal tax rate on corporations and provide no information about effective expensing in the tax structure.
As usual in this type of analysis, there are issues concerning holding constant other determinants of economic growth and dealing with reverse causation from economic outcomes to the tax structure. (The latter consideration suggests that the estimated effect would understate the magnitude of the true impact of the tax rate on economic growth.) But this procedure also has important advantages – for example, there are 500 data points on five-year average growth rates of real per capita GDP, and one does not have to make a lot of modeling assumptions, as required by the user-cost framework.
The result from a cross-country regression for explaining five-year-average per capita GDP growth rates is a negative estimated coefficient on the corporate-tax rate. In other words, a higher tax rate means lower economic growth. However, the estimated value has a high standard error and is statistically significant only at a 15% critical value. The point estimate implies that a cut in the corporate-tax rate by 15 percentage points (as in the pending US legislation) would raise the growth rate of real per capita GDP over a five-year interval by about 0.4% per year. The interesting point is that this result accords with the results from the user-cost approach. Hence, the cross-country analysis supports the reasonableness of the user-cost findings.
The bottom line is that the pending corporate tax changes would produce a large long-run increase in real per capita GDP – by around 7%. The associated rise in growth rates over a ten-year horizon would be about 0.3% per year.
Technical note
The analysis of user costs is based on a formula derived from the 1984 book by King and Fullerton:
where τ is the proportionate tax rate on corporate earnings, computed by allowing for expensing at the effective rate λ on investment outlays, and δ is the true depreciation rate on capital. In calculating λ for the existing and proposed corporate tax systems, I estimate present values (using the real discount rate, rk) associated with depreciation allowances and deductibility of corporate interest payments. (I assume that bond financing applies fractionally to structures and not at all to equipment, and that proposed limitations on deductibility of bond interest would not be an effective constraint with regard to investment in structures.)
Note that user cost on the right side of the equation falls with the expensing rate, λ, if τ<1: more expensing encourages investment. If λ<1 (as in the current system), user cost rises with τ, so that a higher corporate-tax rate discourages investment. However, the effect of τ on user cost is nil if λ=1 (as with full expensing of equipment) and is negative if λ>1 (for example, if full expensing were combined with deductibility of interest payments). If λ=0, the equation gives the familiar result that the after-tax marginal product of capital, (1-τ)∙MPK, equals rk+δ. For given features of the tax system, user cost rises with rk+δ. However, because I treat rk+δ as fixed, all of the estimated effects on investment come directly from the tax term, (1‑τλ)/(1-τ), shown in the equation.