Friday, December 29, 2017

The Corporate Tax Rate, Part 2

John Cochrane posted a reply to my previous post on how changes in the corporate tax rate might affect investment. The key issues seem to relate to the specifics of what the tax code will allow as an expense. In my analysis, I treated investment spending by the firm as fully-expensed, which is not correct. However, the tax code does permit businesses to deduct interest on their debt, and depreciation, which I didn't include. What I'll do here follows - I think - a comment by Francois Gourio (Chicago Fed) on Twitter.

So, let's write down the firm's problem again, assuming a constant real interest rate r, which the firm's shareholders face (an important assumption - I'm neglecting taxes affecting the sharelholders). We'll assume that dividends are paid period-by-period to the firm's shareholders, with the firm maximizing the present value of dividends:
Here, K is the capital stock, N is the labor input, w is the wage rate, b is the firm's debt, and d is the depreciation rate. The firm's debt comes due in one period. Net proceeds for the firm in the current period consist of output minus the wage bill plus new debt issued, minus interest and principal on the debt issued in the previous period, minus investment, minus corporate taxes. The corporate tax rate t applies to output minus the wage bill, minus the interest payments on the debt, minus depreciation.

If the firm were to fund investment out of retained earnings (provided this does not violate a nonnegativity constraint) then a reduction in the corporate tax rate will indeed raise the after-tax marginal net payoff to investing. Alternatively, suppose that the firm always funds new investment by issuing debt, then pays the interest on the debt, retires debt as capital depreciates, and otherwise rolls the debt over. This implies that the firm's outstanding debt is always backed one-for-one by the firm's capital, or
Then, we can rewrite the first equation as
So, the firm's choice of labor input in each period, and its choice of capital in periods 1,2,3,... (equivalent to choosing investment) is independent of the tax rate t. Essentially, debt financing of investment permits full expensing of the investment expenditure - indirectly, through expensing of interest on the debt and depreciation.


1. We need to worry about how the household is taxed, which in this formulation determines what the objective function is for the firm.
2. To do a proper job here, we need to determine the optimal financial structure for the firm.

This is potentially quite complicated (not blog material), though I'm sure someone has addressed related problems in the taxation literature. To do the problem justice, we need a complete general equilibrium model. That said,

1. There's no presumption that the corporate tax rate reduction is going to matter much for intensive-margin decisions of the firm - decisions about labor input and investment.
2. Where the change in the corporate tax rate should matter is for entry decisions - here we need to start worrying about nonconvexities - e.g. fixed costs of entry. But some entry, relating to the treatment of pass-throughs, would just be a renaming of the productive unit - call yourself a business and you can be taxed at a lower rate. As well, firms may choose to relocate from other countries to the U.S., though as I mentioned in my previous post, those other countries won't give up without at fight.
3. There's a clear redistributive effect, as I mentioned in my previous post. Owners of stocks will benefit, and they tend to be richer people. Long-term, government transfers and expenditures on goods and services have to fall, and the burden of those reductions will be borne by the relatively poor.
4. If the Republican Congress actually wanted to increase investment spending, there are straightforward ways to do this through the tax code - an investment tax credit, for example.

Wednesday, December 27, 2017

Where's the Fallacy?

Here's John Cochrane, writing about the "buyback fallacy:"
Many commenters on the tax bill repeat the worry that companies will just use tax savings to pay dividends or buy back shares rather than make new investments.
But, John concludes:
Investment will increase if the marginal, after-tax, return to investment increases. Lowering the corporate tax rate operates on that marginal incentive to new investments. It does not operate by "giving companies cash" which they may use, individually, to buy new forklifts, or to send to investors. Thinking about the cash, and not the marginal incentive, is a central mistake.
But, suppose that we use a simple model of firm behavior, along the lines of what we teach to undergraduates (see for example, Chapter 11, of this fine intermediate macro book). In each period i = 0,1,2,..., the firm hires labor and invests in new capital. Output is produced using labor and capital each period, using a constant-returns-to-scale technology. Each period the firm hires labor on a competitive market, produces output, and invests in new capital. The firm's profits (the return to capital, not economic profits) are P(i) in periods i = 0,1,2,..., and the firm maximizes the present value of profits. Suppose no uncertainty, and that the real interest rate is a constant r forever. Capital depreciates at a constant rate. The firm maximizes the after-tax present value of profits
Profits are ultimately distributed as dividends to the firm's shareholders, but the firm can borrow and lend freely at the interest rate r, so the timing of the dividend payments is irrelevant.

What happens if the corporate tax rate goes up permanently, with the tax rate constant forever, or t(i)=t? This has no effect on investment or on the firm's hiring decisions in any period. That is, if VB is before tax profits, then (1-t)VB = V, so maximizing VB is the same as maximizing V, and the tax rate is irrelevant, not only for investment decisions, but for the firm's hiring decision. In the aggregate, there is no effect on labor demand, and therefore no effect on wages.

Basically, investment is an intertemporal decision for the firm. But the corporate tax rate affects per-period after-tax profits in exactly the same way in every period, so there is no effect on the after tax rate of return on investment the firm is facing. Therefore, the firm won't invest more with a lower corporate tax rate - if it's permanent. How can a change in the corporate tax rate make investment go up in 2018? If the corporate tax rate were temporarily higher in 2018, returning to its former level permanently in 2019, that would do the trick.

I could be missing some subtlety in the tax code, for example in how the firm's financing decisions are affected by taxation, but I don't think so. Please fill me in if you think there's something important I've left out.

So, I don't think there's any fallacious thinking in the popular view of the effect of changes in corporate taxation included in the tax bill. The primary effect is redistributive. Ownership of stocks is concentrated among the relatively wealthy, and a permanently lower corporate tax rate will show up immediately in higher stock prices, as we've seen. Owners of stocks can hold them and receive their higher future dividends, or they can sell their stocks at any time and realize their capital gain. As more GDP doesn't magically come out of nothing, higher spending by these richer folks has to be offset by less spending by poorer folks.

If there are effects of changes in the corporate tax rate, these could come from two places. First, the change in the US rate relative to corporate tax rates elsewhere in the world matters. In some instances, this will have no implications for the location of production for the firm (e.g. management consulting done in various locations in the world), but will matter for the firm's choice of corporate tax home. The tax rate goes down, which reduces tax revenue, but more firms choose the US as a corporate tax home, which increases tax revenue. The net effect on tax revenue depends on how elastic corporate tax home is with respect to the US corporate tax rate. Also, some firms producing tangible goods may choose to relocate production to the US. This necessarily implies some increase in domestic investment expenditure, but the effect is temporary, and probably small, particularly as we can't take for granted that other countries will not provide inducements to prevent firms from moving production to the US.

Second, there is another effect on the extensive margin. Some economic activity that would formerly show up as labor income will now be classed as business income, so as to qualify for the lower tax rate. As I showed, there are no implications for investment expenditure. The effects are lower tax revenue and redistribution to the rich from the poor, who either can't do this, or can't afford to pay an accountant.

If the intent of the tax bill had been to increase investment spending, there are obvious ways to to that - an investment tax credit for example. But, the tax bill is not about investment. The primary effect is redistribution. In the short run, the tax bill makes the rich richer and the poor poorer, and it lowers tax revenue. Permanently lower tax revenue has to show up, in the long run, as permanently lower government transfers and lower spending on government-provided goods and services. This will hit the poor disproportionately. So, this isn't tax legislation that appears to work on marginal anything - it's just wealth redistribution.