Key Assumptions in Dynamic Scoring

March 18, 2015

A recent New York Times article by Josh Barro has questioned the Tax Foundation’s TAG model forecast of the economic gains to be expected for the Lee-Rubio tax reform plan. We show an eventual increase in the GDP of about 15 percent. We assume this would occur over about a decade, during which the yearly growth rate would average about 1.45 percent over the baseline. By the end of the period, we expect federal revenues to match what they would be under current law, and a little bit more. Not all of the features of the Lee-Rubio plan would add to the growth (such as he enhanced child credit), but the major reductions in the taxation of capital income would so. The results are comparable to those of several other models for major changes in the corporate tax rate, of a shift from taxing income to taxing consumption, allowing for the differences in the degree of the tax reduction in the different experiments.[1]

Barro questions the magnitude of the response, doubting that the “elasticity” (responsiveness) of the physical capital stock (the quantities of plant, equipment, residential and commercial real estate, etc.) to changes in the rate of return could be as high as our model assumes (an “infinite” supply elasticity in the long run). He also suggests that impediments to trade or capital flows in an “imperfectly” open economy would lead to incomplete adjustments that would fall short of the model’s predictions that returns would be driven back down to a long run “normal” rate. Further, he is concerned we may not be giving enough weight to the effects of tax and deficit changes on interest rates, and to the role of borrowing to finance investment. Some of the comments reported in the piece question whether the concept of an open economy can apply to a nation as large as the United States, whose actions may be large enough to alter world market conditions. On a slightly different topic, some of the sources he quotes seem to be questioning the availability of saving to finance the predicted expansion, and how long it might take.

These criticisms provide us with a great opportunity to discuss the assumptions in our model and their grounding in the historical evidence.

The Evidence behind the Assumptions in Our Taxes and Growth Model

Why does the Taxes and Growth model assume capital formation is so responsive to after-tax rates of return? We base that crucial assumption on a reading of the historical evidence regarding the flexibility of saving and investment and the stability of returns over time. Saving and investment have proven to be highly flexible over time. The tendency for investment to seek out above normal returns, and to expand until the returns on capital are driven back to their normal level, is a basic tenet of neoclassical analysis, and is a common trait of any neoclassical model of the economy. Professor John H. Cochrane of the University of Chicago Booth School of Business recently wrote us that “About the most basic conclusion of a neoclassical growth model is that in the end the after tax rate of return is the same. Sure, it happens faster if you’re open internationally, but the same mechanism happens through saving.”

The After-Tax Return Is Stable in the Long Run

The issue is how changes in taxation affect the returns on physical capital, and how that affects the growth of physical plant, equipment, and structures, and its location, here or abroad. Taxes affect capital formation because capital expands or contracts to keep the returns to capital within narrow bounds. Abnormal returns following a tax reduction or discovery of a new technology or the invention of a desirable new product are rapidly competed away. The stock of capital expands until its returns are driven back to normal levels. That requires only a finite and plausible expansion of the capital stock.[2] Data from the Commerce Department’s Bureau of Economic Affairs reveals great stability, decade-by-decade, in after-tax real returns on real capital in the United State over the better part of a century.[3] In most years, non-financial corporations have seen after-tax returns of between 4 percent and 8 percent since 1960. After subtracting shareholder taxes, the returns would be somewhat lower, primarily in the 2 percent to 5 percent range, centered a bit over 3 percent. When returns are in the upper portion of the ranges, capital expands unusually rapidly. When returns are lower, capital formation lags. These responses confine returns to a narrow band around this apparent “marginal rate of time preference” which is part of both human nature and economic theory.

The Economy Adjusts Fairly Quickly to Tax Changes

The return to a normal rate of return is not instantaneous. One cannot suddenly double the rate of construction, or place huge orders for new equipment that might strain the capacity of the machine tool industry, and expect a huge increase in the supply of buildings and machines overnight. Supply curves are somewhat inelastic in the short run. In the long run, however, the supply of physical capital is far more elastic. Over several years, buildings, infrastructure, and machinery can be ramped up without any significant increase in unit costs. Our model is a long run model, looking out to the ultimate adjustment in the capital stock after the economy has had time to respond to the additional demand for capital.

In fact, the adjustment periods are fairly short. The capital goods industries are fairly nimble, and imports can satisfy part of the demand. Proof is to be seen in the historical record. The bulge in returns after the 1962-63 Kennedy tax cuts wore off by 1969. The bulge in returns following the Reagan cuts, the Clinton capital gains rate reduction, and the 2003 Bush tax cut wore off within a few years. We have built this nimble response into our model, but adding a few years to the adjustment path would not change the ultimate gain in capital and wages. Other models that have nothing with which to anchor their predicted capital formation are at odds with history and economic theory, and are largely adrift.

The U.S. Has a Relatively Open Economy

Barriers to trade may mean that the economy is not “perfectly” open, but that would affect only the speed of the adjustment, not its ultimate outcome. A higher after-tax return to capital in the United States would still lead to more investment that would fully compete away the abnormally high earnings. The capital stock would grow, and returns would be driven down to normal due to competition among U.S. businesses, even if we were the only country in the world. Failure to achieve that outcome would require investors to leave ready money on the table forever. The adjustment is sped up because there are multiple possible sites for locating a plant, such that global growth can shift toward the U.S. It would be sped up more in the complete absence of trade barriers, but it is certainly not prevented by the modest remaining trade barriers in place today.

International Capital Flows Provide Money to Finance Public Deficits

Another attribute of an open economy is access to global saving and financial capital. This dampens concerns that a temporary budget deficit resulting from a tax reduction might affect interest rates and slow the increase in capital formation. Some economic models that are driven by spending flows instead of rates of return and adjustments to the stock of capital place too much importance on the effect of tax and deficit changes on interest rates, and on the role borrowing to finance investment.

Our model is open to international capital flows, including financial flows as well as those involving direct foreign investment in plant, equipment, and other property. All that means is that any adjustments to changes in the rate of return to investment in the United States can occur quickly by tapping into the global savings pool or by redirecting savings flows, instead of more slowly by relying only on changes in our own saving rates. The Barro piece quotes public finance figures asserting that the United States is so large that its budget affects world interest rates; that we are price setters in the credit markets instead of price takers, and that this restricts our access to world saving, discourages investment, and dampens any growth effects from better treatment of capital. The claim is that open markets and elastic capital flows only occur for small economies, but cannot work for an economy the size of the United States.

The international economy and how economists think about it have changed a great deal since the 1950s. Foremost among the changes in economic thinking has been the realization that capital flows, not exchange rates and trade in physical goods and services, dominate the scene. In that context, the U.S. is as dominated by the global market as are much smaller nations. We are no longer the colossus we once were—shortly after World War II and the Korean War—when we dwarfed the rest of the free world economy. The global economy is now much larger and more integrated than it was sixty years ago. We are much less dominant in these markets than we once were. The economic literature is clear on this point. U.S. deficits in the ranges seen since the end of WWII has had little effect on global or U.S. interest rates, a matter of a few basis points at most. Any effect they may have had has surely been swamped by changes in Federal Reserve policy.[4]

For example, following the housing bond collapse, about $2 trillion in federal government stimulus spending, resulting in massive deficits, was funded easily even as interest rates on U.S. government debt fell to ridiculously low levels. This was partly due to an activist Federal Reserve, and partly due to international capital flows into the safe haven of U.S. government debt. This was true even though the spending was largely wasteful and did little to enhance productive capacity in the United States. The lower interest rates and enhanced bank reserves had little impact on business investment, as businesses had little need or desire to borrow to fund additional private investment. There will be no problem financing the government tax and deficit changes in the ranges being discussed in connection with tax reform, especially if the reforms are focused on enhancing the productive capacity of the U.S. economy.

Money Is Available for Private Investment through Retained Earnings, Foreign Investment, and Increased Saving

As for financing additional private sector investment, even in the presence of transitory increases in the government deficit, history is clear. Financial market and saving constraints are not the issue for expanding private sector investment. The only obstacle to expanding the quantity of real plant, equipment, and buildings is the time needed to plan the investment, obtain permits, and then build the machines or structures.

Saving available to the United States can be increased five ways: by Americans consuming less and saving more; by individuals reducing leisure and working harder to earn additional money to save, by retaining more business income for reinvestment instead of paying larger dividends or other distributions to owners when new investment opportunities arise; by lending less U.S. saving abroad, including repatriating foreign U.S. holdings (smaller capital outflow); or by attracting more foreign savings (larger capital inflow).

Most business investment is funded by retained earnings, a business’s own money. That is the largest source of saving in the economy. Relatively little business financing comes from the credit markets. When business taxes are cut to lower the cost of machinery by, say, 3 percent, due to lower tax liabilities, then the tax savings alone are enough to increase the amount of capital employed by about 3 percent without any outside money. As the stock of capital expands, and the economy grows over the next several years as a result, additional earnings become available for further expansion of capital beyond the initial 3 percent. We do not need outside funding to pay for the added business investment.

Other saving, including outside money channeled through the credit markets, is needed to cover the near term rise in the government deficit. There is plenty of saving in the world to do that. The amount of new domestic and global saving is flexible, and accumulated past saving is highly mobile across borders. Leading economists of the last 50 years, such as Milton Friedman, Gary Becker, Robert Barro, Harry Johnson, and Robert Mundell (three of them Nobel laureates), have emphasized the flexibility of domestic saving and international capital flows in response to changes in taxation and returns on investment.

Capital Is Mobile

It is not the size of the economy that determines the openness of its credit markets and how much interest rates might move if borrowing rises; it is the size of the capital flows needed to accommodate borrowing requirements relative to the stock of world financial assets. Capital flows run in the trillions of dollars a year, and could go much higher. Even these flow amounts pale in comparison to the stock of financial assets, which run into the hundreds of trillions of dollars; they dwarf any remotely possible financing needs from U.S. tax reform, transitory budget deficits, recessions, or even a financial panic such as occurred in the 2008-2012 era. They are orders of magnitude larger than the amounts needed to facilitate the expansion subsequent to a corporate rate cut and the end to double taxation of saving in the United States.

Economic history tells us that it takes only minor changes in interest rates to trigger massive amounts of capital flows. Examples abound over the last two hundred years.

As one example, the U.S. reduced tax rates in 1981, and began to restore the stability of the U.S. dollar by ending the 1970s inflation. Annual lending by U.S. banks to foreign borrowers dropped by $100 billion (over 80 percent!) between 1982 and 1984, funding the tax cuts and a revival of U.S. business investment by keeping more of our saving at home, even as interest rates began a decade’s decline. Instead of lending as much to Latin America, Europe, and Asia as before, the banks lent more here at home. Later, increased foreign investment in the United States contributed further to the expansion.

For an earlier example, when the pound was the world currency, and the British Empire spanned a fourth of the planet, the Bank of England maintained the parity of the pound and the level of its gold and currency reserves with the tiniest of interest rate tweaks. That systems lasted a century from the end of the Napoleonic Wars until World War One.

Adam Smith eloquently described the mobility of capital in the Wealth of Nations in 1776. He noted that investors were citizens of the world and that they could take their activities anywhere if they were abused in their home country.[5]

Markets demonstrate every day that capital is highly mobile. Foreign exchange markets are well known to be the most responsive markets in the world, shifting trillions of dollars in value from one currency to another on the thinnest of price changes with the speed of electrons. The bond markets are not far behind. The government had no trouble issuing new bonds to fund its trillion-dollar-plus stimulus plan, even as interest rates on government debt plunged to record low post-WWII levels, abetted by a bond-buying spree by the Federal Reserve. But none of this has much to do with the rate at which computers, machine tools, buildings, airplanes, railroads, and harbors can be expanded.

Labor Responds Less than Capital

Barro states correctly that our model’s labor response to tax cuts and higher wages is at the top end of the range reported by the Congressional Budget Office. A CBO survey of the literature offers a range of 0.1 to 0.3 for the “labor supply substitution elasticity.”[6] The Joint Committee on Taxation’s MEG model assumed 0.15 to 0.2 in its work on the Congressman Dave Camp’s tax reform plan in 2014 (similar to the middle of the CBO’s range). Our assumption is reasonable and within the mainstream; it is less than half the response numbers found by means of cross-country comparisons by Nobel Laureate Ed Prescott. Moreover, using a labor supply elasticity of 0.2 would not materially change our results.[7] The bulk of the growth in our model comes from changes in capital formation. If we were to lower our labor response to 0.2, we would only reduce our 15 percent growth forecast for Lee-Rubio to 14.15 percent.

Constructive Criticism Is Welcome

Our model data are derived from the economic data supplied by the Department of Commerce, the public use tax sample from the Internal Revenue Service for the individual income tax, and the tax rates and depreciation schedules in current law. These furnish us with the quantities of capital and labor that determine GDP, and the resulting wages and other sources of income, by means of a typical textbook Cobb-Douglas production function, solved in the usual manner.[8] We have more detailed capital stock data and can generate a more detailed calculation of the cost of capital than most other models can manage. We believe our model offers a reasonable link between tax policy changes and the likely outcome for economic activity, based on historical observations. Its equations and approach are described with some considerable transparency in a number of our publications.[9] Constructive, informed criticism is always welcome.

[1] William McBride, Critics of Rubio-Lee Tax Reform Are Way Off the Mark, Real Clear Markets (Mar. 12, 2015),

[2] The term “infinite elasticity” merely means that the quantity increases with, ultimately, a zero change in the ultimate return. Dividing by zero makes the idea sound scary, but that is only semantics.

[3] See Chart 1 from Andrew W. Hodge, Robert J. Corea, Benjamin J. Hobbs, and Bonnie A. Retus, Returns for Domestic Nonfinancial Business, Survey of Current Business, Bureau of Economic Analysis (Jun. 2013),

[4] See note 1.

[5] According to Adam Smith, ‘The proprietor of stock is properly a citizen of the world, and is not necessarily attached to any particular country. He would be apt to abandon the country in which he was exposed to a vexatious inquisition, in order to be assessed to a burdensome tax, and would remove his stock to some other country where he could either carry on his business, or enjoy his fortune more at his ease. By removing his stock he would put an end to all the industry which it had maintained in the country which he left. Stock cultivates land; stock employs labor. A tax which tended to drive away stock from any particular country would so far tend to dry up every source of revenue both to the sovereign and to the society.” See Chapter 2 from Adam Smith, An Inquiry into the Nature And Causes of the Wealth of Nations (1776).

[6] See Robert McClelland and Shannon Mok, A Review of Recent Research on Labor Supply Elasticities, Congressional Budget Office (Oct. 2012),

[7] Our higher elasticity would dampen the labor response of higher income workers in the Lee-Rubio bill.

[8] Invented in part by professor, later Senator (D-IL), Paul Douglas.

[9] See Michael Schuyler, The Taxes and Growth Model—A Brief Overview, Tax Foundation Fiscal Fact No. 429 (May 6, 2014),; Tax Foundation, The Tax Foundation Small Comparative Statics Model of the U.S. Economy,



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