## Estimating the Long Run Growth Effects of Tax Cuts: An Example

Does this belong in the next edition of Martha Olney's and my Macroeconomics textbook?

Box 4.4.6: Estimating the Effects of Policy Changes: An Example

In late 2017 and early 2018 the Trump administration and the Republican congressional caucuses pushed through a combined tax cut and a relaxation of spending caps to the tune of increasing the federal government budget deficit by about 1.4% of GDP. These policy changes were intended to be permanent.

Not the consensus but the center-of-gravity analysis by informed opinion in the economics profession of the effects on long-run growth of such a permanent change in fiscal policy would have made the following points:

1. The U.S. economy at the start of 2018 was roughly at full employment, or at least the Federal Reserve believed that it was at full employment and was taking active steps to keep spending from rising faster than their estimate of the trend growth of the economy, so a long-run Solow growth model analysis would be appropriate.

2. The economy's savings-investment effort rate, s, has two parts: private and government saving: $s = s_p + s_g$.

3. The private savings rate $s_p$ is very hard to move by changes in economic policy. Policy changes that raise rates of return on capital—interest and profit rates—both make it more profitable to save and invest more but also make us richer in the future, and so diminish the need to save and invest more. These two roughly offset.

4. Therefore, when the economy is at full employment, changes in overall savings are driven by changes in the government contribution: ${\Delta}s = {\Delta}s_g$.

5. And an increase in the deficit is a reduction in the government savings rate.

The standard center-of-gravity analysis would thus start by assuming that the economy was on its balanced growth path, and investigate the consequences of a reduction in s by 1.4% points in order to get an estimate of the effect of this policy shift if it were to be a permanent change.

Set up the Solow growth model, with the Labor force growth rate n = 1.0% per year, the labor efficiency growth rate g = 1.5% per year, the depreciation rate $\delta$ = 3% per year, the production function diminishing returns to investment parameter $\alpha$ = 1/3, and the initial efficiency of labor $E_0$ = 65000. That produces an initial state of the economy's balanced growth path of:

$\left(\frac{K}{Y}\right)^*_{ini} = 4$

${\left(\frac{Y}{L}\right)^_{ini} = {\left(\frac{K}{Y}\right)^{ini}} ^{\left(\frac{\alpha}{1-\alpha}\right)} E0 = 4^{(1/2)}(65000) = 130000}$

Along the alternative balanced growth path, the same variables are:

$\left(\frac{K}{Y}\right)^*_{alt} = \left(\frac{0.22-0.014}{0.01 + 0.015 + 0.03}\right)^{\left(\frac{1/3}{1-1/3}\right)} = 3.745$

$\left(\frac{Y}{L}\right)^_{alt} =$ ${\left(\frac{K}{Y}\right)^{alt}}$ $^{\left(\frac{\alpha}{1-\alpha}\right)}$ $E0 =$ $\left(\frac{0.22-0.014}{0.01 + 0.015 + 0.03}\right)^{\left(\frac{1/3}{1-1/3}\right)}(65000) =$ $3.745^{(1/2)}(65000) = 130000$

That is, the alternative balanced growth path has an output per worker level 3.3 percent below the initial path The policy is expensive for the economy in the long run.

How fast does this growth retardation make itself felt? We know that the velocity of convergence $v_c$ in the Solow growth model is:

$v_c = -(1-\alpha)(n+g+\delta)$

In this case:

$v_c = -(1-\alpha)(n+g+\delta) = -(1-1/3)(0.01+0.015+0.035) = -0.0329$

The economy closes about 1/30 of the gap between its initial and its alternative balanced growth path every year. The first-year effect is thus about (-0.033)(0.33) = -0.001: a drop in the growth rate of 0.1% point, and a drop in the level of 0.1% point after one year. After 10 years, the economy will have closed about 28 percent of the 3.3 percentage point gap—a total effect on the level of real GDP ten years out of 0.9%: nine-tenths of a percentage point.

# CODE
#
# a "what if"—if the tax "reform" and the spending increase were
# to become permanent changes in policy, and were to reduce the
# savings rate by 1.4% points...

# ----

alpha = 1/3

n = 0.01
g = 0.015
delta = 0.03
s = 0.22

Delta_s = -0.014

E0 = 65000

KoYstar_ini = s/(n + g + delta)
YoLstar_ini = (KoYstar_ini)**(alpha/(1-alpha))*E0
KoYstar_alt = (s + Delta_s)/(n + g + delta)
YoLstar_alt = (KoYstar_alt)**(alpha/(1-alpha))*E0
conv_speed = (1-alpha)*(n+g+delta)

print(KoYstar_ini, "= Initial BGP Capital-Output Ratio")
print(YoLstar_ini, "= Initial BGP Output per Worker")
print(KoYstar_alt, "= Alternative BGP Capital-Output Ratio")
print(YoLstar_alt, "= Alternative BGP Output per Worker")
print(conv_speed, "= speed of convergence")
print(np.log(YoLstar_alt/YoLstar_ini), "= long-run growth effect in percentage points")


4.0 = Initial BGP Capital-Output Ratio
129999.99999999999 = Initial BGP Output per Worker
3.745454545454545 = Alternative BGP Capital-Output Ratio
125795.64958513252 = Alternative BGP Output per Worker
0.036666666666666674 = speed of convergence
-0.0328756887814 = long-run growth effect in percentage points

Box 4.4.7: Speed of Convergence and Estimating the Effects of Policy Changes: An Alternative

It is worth noting an alternative calculation of the likely effects of the Trump administration's economic policies, carried out by four Stanford economists and five others. The most important thing to know to understand and evaluate this calculation is that all nine of these economists are strong Republicans. They wrote http://delong.typepad.com/2017-11-26-nine-unprofessional-republican-economists.pdf, in a piece that was notionally a letter to U.S. Treasury Secretary Steven Mnuchin but that was in actuality primarily intended to be published in the Wall Street Journal to influence the debate, that Trump administration fiscal policy—the tax cut—would:

increase... the capital stock... raise the level of GDP in the long run by just over 4%. If achieved over a decade, the associated increase in the annual rate of GDP growth would be about 0.4% per year.... [In] the House and Senate bills... the increase in capital accumulation would be less, and the gain in the long-run level of GDP would be just over 3%, or 0.3% per year for a decade...

The four Stanford University economists are:

• Michael J. Boskin, Tully M. Friedman Professor of Economics, Stanford University; Chairman of the Council of Economic Advisers under President George H.W. Bush

• John Cogan, Leonard and Shirley Ely Senior Fellow, Hoover Institution, Stanford University; Deputy Director of the Office of Management and Budget under President Ronald Reagan

• George P. Shultz, Thomas W. and Susan B. Ford Distinguished Fellow, Hoover Institution, Stanford University; Secretary of State under President Ronald Reagan; Secretary of the Treasury under President Richard Nixon

• John. B. Taylor, Mary and Robert Raymond Professor of Economics, Stanford University; Undersecretary of the Treasury for International Affairs under President George W. Bush

The five others are:

• Robert J. Barro, Paul M. Warburg Professor of Economics, Harvard University

• Douglas Holtz-Eakin, President, American Action Forum, former director of the Congressional Budget Office

• Glenn Hubbard, Dean and Russell L. Carson Professor of Finance and Economics (Graduate School of Business) and Professor of Economics (Arts and Sciences), Columbia University; Chairman of the Council of Economic Advisers under President George W. Bush

• Lawrence B. Lindsey, President and Chief Executive Officer, The Lindsey Group; Director of the National Economic Council under President George W. Bush

• Harvey S. Rosen, John L. Weinberg Professor of Economics and Business Policy, Princeton University; Chairman of the Council of Economic Advisers under President George W. Bush

Their conclusions—"the gain in the long-run level of GDP would be just over 3%, or 0.3% per year for a decade..."—look in their effects on levels of output per worker like the calculation in box 4.4.6, with one crucial difference: the sign is reversed. In 4.4.6, the first order effect of the policy changes was to reduce national savings and investment and thus make America a less capital intensive and poorer economy. And this calculation, the first order effect is to raise national savings and investment and us make America a more capital intensive and richer economy. Moreover, the effect on the growth rate is not only of the wrong sign, but three times the magnitude: instead of a slowdown in annual growth of 0.1% point, there is a speedup of

Why the difference?

Why does not the increased government deficit and thus government anti-saving reduce the national savings investment rate s? The authors do not say.

Where is the analysis stating that increased after tax rates of return on savings and investment have offsetting substitution and income effects, with the substitution effect raising saving and the income effect lowering it? That analysis, also, is absent.

What, then, is present? This:

Fundamental tax reform... [is] a set of tax changes that reduces tax distortions on productive activities (for example, business investment and work) and broadens the tax base to reduce tax differences among similarly situated businesses and individuals. Fundamental tax reform should also advance the objectives of fairness and simplification.... The proposals emerging from the House, Senate, and President Trump’s administration, fall squarely within this tradition.... There is some uncertainty about just how much additional investment is induced by reductions in the cost of capital, but... many economists believe that a 10% reduction in the cost of capital would lead to a 10% increase in the amount of investment. Simultaneously reducing the corporate tax rate to 20% and moving to immediate expensing of equipment and intangible investment would reduce the user cost by an average of 15%, which would increase the demand for capital by 15%.... Such an increase in the capital stock would raise the level of GDP... just over 3%, or 0.3% per year for a decade...

That's all she writes. And note: "many" economists—not "most economists", not "nearly all economists", not "the center of gravity of informed economic opinion".

And the claims about "the proposals emerging from the House, Senate, and President Trump’s administration" being "within this tradition" of "broaden[ing] the tax base to reduce tax differences among similarly situated businesses and individuals... advanc[ing] the objectives of fairness and simplification..." are simply false.

Even more alarming than the reversal-of-sign of the effect, is the estimate of the growth rate: a jump of + 0.3 percentage points per year. It comes from the nine economists' observation that:

increase... [would] raise the level of GDP in the long run by just over 4%. If achieved over a decade, the associated increase in the annual rate of GDP growth would be about 0.4% per year.... [In] the House and Senate bills... the increase in capital accumulation would be less, and the gain in the long-run level of GDP would be just over 3%, or 0.3% per year for a decade...

But the nine economists know just as well as you do that only 28 percent of the total gain accrues in the first decades, not all of it.

When challenged by former U.S. Treasury Secretary Lawrence Summers and former Council of Economic Advisers Chair Jason Furman https://www.washingtonpost.com/news/wonk/wp/2017/11/28/lawrence-summers-dear-colleagues-please-explain-your-letter-to-steven-mnuchin/?utm_term=.9d690352f4b3:

Since you are explicitly talking about 10-year growth rates in your letter, would it not be better to... show that the effect in the 10th year is less than one-third of the long-run effect, translating into an annual growth rate of less than 0.1 percentage point?...

The nine economists denied that they had made claims about the speed of adjustment to the post policy change blaanced growth path and so offered a prediction that real GDP growth would be boosted by not 0.1% (or -0.1%) but rather 0.3% points per year over the next decade https://www.washingtonpost.com/news/wonk/wp/2017/11/29/economists-respond-to-summers-furman-over-mnuchin-letter/?utm_term=.8d4d8991717a:

First point you raised: Our letter addresses the impact of corporate tax reform on GDP; we did not offer claims about the speed of adjustment to a long-run result...

We believe that Stanford (and Harvard, and Columbia, and Princeton, and the American Action Forum, and the Lindsey Group) have a serious problem here: As Berkeley medieval history professor Ernst Kantorowicz wrote http://www.lib.berkeley.edu/uchistory/archives_exhibits/loyaltyoath/symposium/kantorowicz.html back in the 1940s, shortly before being fired for refusing to take a loyalty oath demanded by the Regents of the University of California, academic freedom is a grave and serious thing:

Professions... entitled to wear a gown: the judge, the priest, the scholar. This garment stands for its bearer's maturity of mind, his independence of judgment, and his direct responsibility to his conscience and to his God.... They should be the very last to allow themselves to act under duress and yield to pressure. It is... shameful and undignified... an affront and a violation of both human sovereignty and professional dignity... to bully... under... economic coercion... compell[ing] either giv[ing] up... tenure or... his freedom of judgment, his human dignity and his responsible sovereignty as a scholar...

Those possessing academic freedom are given great latitude so that they can speak what they, after great and considered research and reflection, believe sincerely to be the truth. But this freedom to be responsible solely to one's conscience and God requires that one be responsible to one's conscience and God. But what if bearers of academic freedom fear not God nor their own consciences? What then?

One possibility is to inquire and point out that something has gone wrong, as Summers and Furman did, politely, with:

Since you are explicitly talking about 10-year growth rates in your letter, would it not be better to... show that the effect in the 10th year is less than one-third of the long-run effect, translating into an annual growth rate of less than 0.1 percentage point?...

inviting the response: "yes, it would have been better; we have made an error; we will correct it".

But that is not the reply Summers and Furman got.

A second possibility is to teach young people the basics of macroeconomics. I hope everybody who read the nine economists letter who had ever taken a macroeconomics course read that "the gain in the long-run level of GDP would be just over 3%, or 0.3% per year for a decade..." and immediately thought: "that is not how the effects of an increase in the economy's capital intensity from a higher savings-investement effort work—these authors, prestigious as their academic appointments may be, are not doing economic analysis but rather playing political Three-Card Monte". I hope everybody who reads this textbook remembers enough of it that they are able to do the work of reading with a jaundiced eye that is clearly needed here.

There was, I should say, a further oblique reply by one of the four Stanford economists, Michael Boskin https://www.project-syndicate.org/commentary/republican-tax-plan-growth-effects-by-michael-boskin-2017-12. In it he made points:

1. "Robert Barro..." published a deeper elaboration of the tax plan’s growth effects..." (which saiclaimedd that the long-run balanced growth path boost to the level of output per worker would be not 3 percent but 7 percent).

2. "The current tax bill could... have been better.... But such a bill would not pass Congress."

3. "The question is whether a viable final bill will be better than the status quo."

4. "Barro and I have clearly come to a different conclusion.... While I certainly respect Summers and Furman’s right to their views, I am not about to cede my professional judgment to others, in or out of government."

5. "There are legitimate differences of opinion on how much and how quickly the tax plan will affect investment decisions."

6. "Summers... and DeLong... have made the strongest case I know that equipment investment can have a large impact... much larger than in the conventional models."

7. "I believe that the current reform may well have deviated further from the ideal had we not offered our analysis and advice.... Many factors other than economists’ textbook policy proposals affect the final product."

8. "The actual tax provisions people and businesses will be required to use have yet to be written, and will be determined partly by technical interpretations and regulations in the coming months."

Point (6) seems to me to be a red herring, at least as far as the policy change's effects on the growth rate are concerned. We—DeLong and Summers—believe that $\alpha$ is higher than the 1/3 assumed in the center-of-gravity of informed economic opinion analyses. A higher value of $\alpha$ both stretches out the time it takes for the economy to converge and magnifies the ultimate differential, and these effects roughly cancel out, leaving the near term growth rate effect unchanged. And a higher $\alpha$ magnifies both the boost from higher savings and the drag from those savings being diverted to finance larger government deficits.

The overwhelming impression I get from Boskin's piece is one of extraordinary cognitive dissonance. If I sincerely believed that a policy change was likely to boost America's productivity and wealth by 7 percent, I would not be apologizing for it. I would be crowing from the rooftops. I would not be agreeing that "the current tax bill could... have been better". I would not be saying that the bar is the very low "better than the status quo". I would not be defending my participation in the process on the grounds that the bill would have been worse if I had washed my hands of it. I would not be saying that we need to work hard now to improve it because "the actual tax provisions people and businesses will be required to use have yet to be written". I would not be saying that there are legitimate differences of opinion and that I respect the judgemtns of those who think differently.

I thus read Boskin's piece as, in large part, and perhaps not completely of his intention, a sotto voce argument that:

1. We nine economists said in public what we needed to say so that we could get into the room where the decisions were really being made.

2. We nine economists made the bill better than it would have been otherwise.

3. We nine economists will continue to make the implementation of the bill better.