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.


  1. I was going to write this in a comment, but I don't think the model fits into the comments section, so here's a blog post:

    tl;dr: The corporate tax rate cut isn't supposed to improve the incentive of the firm to invest, it's supposed to improve the incentive of consumers to save. If the real interest rate is constant forever, then this effect goes out of the window and corporate tax rate changes have no effect.

    1. If the reduction in tax revenues implies a lump-sum reduction in transfers to the representative consumer, then the increase in dividends for the consumer should exactly offset the reduction in transfers, and it shouldn't make any difference for the consumer's decisions. And it makes no difference for the firm's decisions. All the effects will have to do with redistribution, if you write down a model with heterogeneous households.

    2. It makes no difference to add lump-sum subsidies from the government to the model, which is why I omitted it (the lump-sum subsidies are there now, I edited the post). The household makes its saving decisions by assuming that lump-sum transfers remains fixed, since there's a continuum of households and a single household's decisions have no effect on the lump-sum transfers it gets from the government. It's essentially the same logic as in Dixit-Stiglitz, where a monopolist sets his price assuming that the aggregate price index remains fixed. In other words, if you're a household, you take the lump-sum transfers from the government as fixed when making your investment decisions, since your decisions alone have no impact on the size of the transfers.

      If the government gives a subsidy to share purchases, then it can exactly offset the disincentive created by the corporate income tax, but then it won't raise any revenue.

    3. This comment has been removed by the author.

  2. What you conclude from your maximization problem is only true if the capital stock is fixed if investment is fully deductible from profits (in present value), or if aggregate savings is not affected by tax policy. Your model essentially states that given a fixed capital stock, a firm will seek to maximize the present value of its after-tax profits, which given a constant tax rate is equivalent to maximizing the present value of its pre-tax profits, and thus taxation does not affect firm behavior.

    In any model that includes the determination of the firm's optimal capital stock, firms typically invest until the marginal product of capital is equal to the marginal cost of capital (the rental price or user cost of capital). Unless the present value of the deductions on a marginal investment (from the capital cost recovery through depreciation/expensing plus the interest paid deduction) is equal to 1, the marginal cost of capital is affected by the statutory tax rate.

    There is also a tendency among some economists to completely dismiss the impact of changing the statutory tax rate on international investment with supernormal returns (extensive margin, the location decision studied by Devereux and Griffith). It's perfectly reasonable to assume that other countries will lower their tax rates in response to the US reducing its rate. But unless they reduce it enough to completely offset the 15pp reduction in the US rate, there will be a change in the relative incentive to locate investments with supernormal returns abroad. Krugman dismisses the evidence on this in the literature as irrelevant to the US because we are larger than most countries. But even using lower bound estimates from the literature (which is usually estimated on OECD countries in general, not just the tax havens), the international investment impact is comparable in magnitude to the marginal investment impact from the literature.

    I'm not arguing with the redistributive aspect of the bill, which is fairly evident. But your analysis of taxation and investment is very lacking, and it is completely inconsistent with the existing theory and empirical evidence on the subject.

    1. To be more realistic about the tax code, as Cochrane points out, I shouldn't be deducting investment as an expense. But I should be deducting interest on the firm's debt outstanding, and depreciation. There's a way to do this so that you get the same result. More later.

  3. I think the "no uncertainty" bit is driving your result here. There's significant uncertainty and nontrivial risk aversion with common equity.

    Per-period profits can be negative. Can be large negative numbers, in fact. And when they are negative, they're usually not cushioned by negative taxes. So profits in a period are more like

    min{ (1-t) * P, P }


    P * 1[ P<0 ] + (1-t) * P * 1[P>0]

    Same amount of loss risk is compensated by less upside. I would expect that to reduce the appetite for taking downside risk, and therefore reduce how much resources the firm ties up in machines etc with uncertain payout down the line.