The Real Test of the December 2017 Tax Reform Will Be Its Long-Run Effect

                                        Link to the article above

                                     Link to the article above

The Solow Growth Model is a mainstay of intermediate macroeconomics classes. A key lesson of the Solow Growth Model is that if the net marginal product of capital is above the growth rate of the economy, increasing the share of output devoted to investment can raise the long-run quantity of goods available for consumption. 

As a cut in corporate taxes, the recent tax reform is intended (among other things) as a cut in the effective rate of taxation of capital formation through investment. (As examples of capital formation through investment, think of building factories or writing software.) Thus, it is hoped that it will raise the share of GDP devoted to investment now, leading to a higher capital stock later than what the path of the capital stock would otherwise be. 

It is important to realize how slow this process is. In "The Medium-Run Natural Interest Rate and the Short-Run Natural Interest Rate" I wrote:


Introductory macroeconomics classes make heavy use of the concepts of the "short run” and the “long run.” To think clearly about economic fluctuations at a somewhat more advanced level, I find I need to use these four different time scales:

  • The Ultra Short Run: the period of about 9 months during which investment plans adjust–primarily as existing investment projects finish and new projects are started–to gradually bring the economy to short-run equilibrium. 
  • The Short Run: the period of about 3 years during which prices (and wages) adjust gradually bring the economy to medium-run equilibrium.
  • The Medium Run: the period of about 12 years during which the capital stock adjusts gradually to bring the economy to long-run equilibrium. 
  • The Long Run: what the economy looks like after investment, prices and wages, and capital have all adjusted. In the long run, the economy is still evolving as technology changes and the population grows or shrinks.  

Obviously, this hierarchy of different time scales reflects my own views in many ways. And it is missing some crucial pieces of the puzzle. Most notably, I have left out entry and exit of firms from the adjustment processes I listed. I don’t know have fast that process takes place. It could be an important short-run adjustment process, or it could be primarily a medium-run adjustment process. Or it could be somewhere in between.


Suppose that after a cut in capital taxation the adjustment process brings the economy 10% of the way toward its new steady state each year. Then, after whatever the impact effect is, the gradual adjustment in the capital stock thereafter has on average only 37% percent of the effect in the first ten years that it will have in the new steady state. You can see some details of the calculation in my wonky Christmas Twitter thread here, but you can also see it visually in the blue graph near the top of this post. The area below the upside-down exponential curve for the convergence to the new steady state is obviously less than half the area beneath the line for the full steady state effect. Personally, I learned something I hadn't realized from doing this calculation. 

Note that, among the effects tied to the increase in the capital stock are a large share of the dynamic tax revenue effects of the tax reform. The dynamic benefits for tax revenue should be more than two and a half times as big (1/.37 times) in the new steady state as they are in the first ten years, which is the bureaucratic window over which such things are often evaluated. 

Now, what about the impact effect? Let's consider the impact effect on GDP first, then the impact effect on interest rates. Most of the supply-side improvement from the tax reform, if it has one, should only occur when additional capital formation has actually taken place. So aggregate supply shouldn't be that different in the short run. So if the Fed keeps output at the natural level, GDP also shoulnd't be affected all that much in the short run by the tax reform, even though it could be raised quite a bit in the long run if it works as claimed. 

As for interest rates, remember that this tax reform changed the taxation of interest rates. One reason the Fed doesn't need to raise interest rates all that much to keep GDP at the natural level is that the tax reform itself raises after-tax interest rates. For example, in addition to some direct limitations on deducting mortgage interest, the standard deduction is so much bigger that many people won't want to deduct mortgage interest. That means that the same before-tax interest rate corresponds to a larger after-tax interest rate for many people. The Fed's interest rate is a before-tax interest rate. So if the Fed looks like it is standing pat, after-tax interest rates are going up.

For business investment, the after-tax rental rate on capital also goes up because it got a big tax cut. (The rental rate is the more general concept that in very simple models is equal to the marginal product of capital.) Investment per the Q-theory depends on the gap between the after-tax rental rate and the after tax interest rate. So given a large corporate tax cut and a reduction in interest deductibility and no reaction by the Fed, business investment can go up while housing investment goes down.  

Contrary to the headline of Pedro da Costa's Business Insider article above, the bottom line is that the Fed not needing to react to the recent tax reform in a big way doesn't mean that the tax reform isn't working as intended to increase capital formation through investment. The real test of the tax reform is what it does in the long run, not what it does in the next few years.

                                               Link to the article shown just above

                                            Link to the article shown just above