I was talking some time ago with my friend Enno about Merijn Knibbe’s series of articles on the disconnect between the variables used in economic models and the corresponding variables in the national accounts.1 Enno mentioned Trygve Haavelmo’s 1944 article The Probability Approach in Econometrics; he thought Haavelmo’s distinction between “theroetical variables,” “true variables,” and “observable variables” could be a useful way of thinking about the slippages between economic reality, economic data and economic theory.
I finally picked up the Haavelmo article, and it turns out to be a deep and insightful piece — for the reason Enno mentioned, but also more broadly on how to think about empirical economics. It’s especially interesting coming from soeone who won the Nobel Prize for his foundational work in econometrics. Another piece of evidence that orthodox economists in the mid-20th century thought more deeply and critically about the nature of their project than their successors do today.
It’s a long piece, with a lot of mathematical illustrations that someone reading it today can safely skip. The central argument comes down to three overlapping points. First, economic models are tools, developed to solve specific problems. Second, economic theories have content only insofar as they’re associated with specific procedures for measurement. Third, we have positive economic knowledge only insofar as we can make unconditional predictions about the distribution of observable variables.
The first point: We study economics in order to “become master of the happenings of real life.” This is on some level obvious, or vacuous, but it'[s important; it functions as a kind of “he who has ears, let him hear.” It marks the line between those who come to economics as a means to some other end — a political commitment, for many of us; but it could just as well come from a role in business or policy — and those for whom economic theory is an end in itself. Economics education must, obviously, be organized on the latter principle. As soon as you walk into an economics classroom, the purpose of your being there is to learn economics. But you can’t, from within the classroom, make any judgement about what is useful or interesting for the world outside. Or as Hayek put it, “One who is only an economist, cannot be a good economist.”2
Here is what Haavelmo says:
Theoretical models are necessary tools in our attempts to understand and explain events in real life. … Whatever be the “explanations” we prefer, it is not to be forgotten that they are all our own artificial inventions in a search for an understanding of real life; they are not hidden truths to be “discovered.”
It’s an interesting question, which we don’t have to answer here, whether or to what extent this applies to the physical sciences as well. Haavelmo thinks this pragmatic view of scientific laws applies across the board:
The phrase “In the natural sciences we have laws” means not much more and not much less than this: The natural sciences have chosen fruitful ways of looking upon physical reality.
We don’t need to decide here whether we want to apply this pragmatic view to the physical sciences. It is certainly the right way to look at economic models, in particular the models we construct in econometrics. The “data generating process” is not an object existing out in the world. It is a construct you have created for one or both of these reasons: It is an efficient description of the structure of a specific matrix of observed data; it allows you to make predictions about some specific yet-to-be-observed outcome. The idea of a data-generating process is obviously very useful in thinking about the logic of different statistical techniques. It may be useful to do econometrics as if there were a certain data generating process. It is dangerously wrong to believe there really is one.
Speaking of observation brings us to Haavelmo’s second theme: the meaningless of economic theory except in the context of a specific procedure for observation. It might naively seem, he says, that
since the facts we want to study present themselves in the form of numerical measurement, we shall have to choose our models from … the field of mathematics. But the concepts of mathematics obtain their quantitative meaning implicitly through the system of logical operations we impose. In pure mathematics there really is no such problem as quantitative definition of a concept per se …
When economists talk about the problem of quantitative definitions of economic variables, they must have something in mind which has to do with real economic phenomena. More precisely, they want to give exact rules how to measure certain phenomena of real life.
Anyone who got a B+ in real analysis will have no problem with the first part of this statement. For the rest, this is the point: economic quantities come into existence only through some concrete human activity that involves someone writing down a number. You can ignore this, most of the time; but you should not ignore it all of the time. Because without that concrete activity there’s no link between economic theory and the social reality it hopes to help us master or make sense of.
Haavelmo has some sharp observations on the kind of economics that ignores the concrete activity that generates its data, which seem just as relevant to economic practice today:
Does a system of questions become less mathematical and more economic in character just by calling x “consumption,” y “price,” etc.? There are certainly many examples of studies to be found that do not go very much further than this, as far as economic significance is concerned.
There certainly are!
An equation, Haavelmo continues,
does not become an economic theory just by using economic terminology to name the variables invovled. It becomes an economic theory when associated with the rule of actual measurement of economic variables.
I’ve seen plenty of papers where the thought process seems to have been somthing like, “I think this phenomenaon is cyclical. Here is a set of difference equations that produce a cycle. I’ll label the variables with names of parts of the phenomenon. Now I have a theory of it!” With no discussion of how to measure the variables or in what sense the objects they describe exist in the external world.
What makes a piece of mathematical economics not only mathematics but also economics is this: When we set up a system of theoretical relationships and use economic names for the otherwise purely theoretical variables involved, we have in mind some actual experiment, or some design of an experiment, which we could at least imagine arranging, in order to measure those quantities in real economic life that we think might obey the laws imposed on their theoretical namesakes.
Right. A model has positive content only insofar as we can describe the concrete set of procedures that gets us from the directly accessible evidence of our senses. In my experience this comes through very clearly if you talk to someone who actually works in the physical sciences. A large part of their time is spent close to the interface with concrete reality — capturing that lizard, calibrating that laser. The practice of science isn’t simply constructing a formal analog of physical reality, a model trainset. It’s actively pushing against unknown reality and seeing how it pushes back.
Haavelmo:
When considering a theoretical setup … it is common to ask about the actual meaning of this or that variable. But this question has no sense within the theoretical model. And if the question applies to reality it has no precise answer … we will always need some willingness among our fellow research workers to agree “for practical purposes” on questions of definitions and measurement …A design of experiments … is an essential appendix to any quantitative theory.
With respect to macroeconomics, the “design of experiments” means, in the first instance, the design of the national accounts. Needless to say, national accounting concepts cannot be treated as direct observations of the corresponding terms in economic theory, even if they have been reconstructed with that theory in mind. Cynamon and Fazzari’s paper on the measurement of household spending gives some perfect examples of this. There can’t be many contexts in which Medicare payments to hospitals, for example, are what people have in mind when they construct models of household consumption. But nonetheless that’s what they’re measuring, when they use consumption data from the national accounts.
I think there’s an important sense in which the actual question of any empirical macroeconomics work has to be: What concrete social process led the people working at the statistics office to enter these particular values in the accounts?
Or as Haavelmo puts it:
There is hardly an economist who feels really happy about identifying the current series of “national income, “consumptions,” etc. with the variables by those names in his theories. Or, conversely, he would think it too complicated or perhaps uninteresting to try to build models … [whose] variables would correspond to those actually given by current economic statistics. … The practical conclusion… is the advice that economists hardly ever fail to give, but that few actually follow, that one should study very carefully the actual series considered and the conditions under which they were produced, before identifying them with the variables of a particular theoretical model.
Good advice! And, as he says, hardly ever followed.
I want to go back to the question of the “meaning” of a variable, because this point is so easy to miss. Within a model, the variables have no meaning, we simply have a set of mathematical relationships that are either tautologous, arbitrary, or false. The variables only acquire meaning insofar as we can connect them to concrete social phenomena. It may be unclear to you, as a blog reader, why I’m banging on this point so insistently. Go to an economics conference and you’ll see.
The third central point of the piece is that meaningful explanation requires being able to identify a few causal links as decisive, so that all the other possible ones can be ignored.
Think back to that Paul Romer piece on what’s wrong with modern macroeconomics. One of the most interesting parts of it, to me, was its insistent Humean skepticism about the possibility of a purely inductive economics, or for that matter science of any kind. Paraphrasing Romer: suppose we have n variables, any of which may potentially influence the others. Well then, we have n equations, one for each variable, and n2 parameters (counting intercepts). In general, we are not going to be able to estimate this system based on data alone. We have to restrict the possible parameter space either on the basis of theory, or by “experiments” (natural or otherwise) that let us set most of the parameters to zero on the grounds that there is no independent variation in those variables between observations. I’m not sure that Romer fully engages with this point, whose implications go well beyond the failings of real business cycle theory. But it’s a central concern for Haavelmo:
A theoretical model may be said to be simply a restriction upon the joint variations of a system of quantities … which otherwise might have any value. … Our hope in economic theory and research is that it may be possible to establish contant and relatively simple relations between dependent variables … and a realtively small number of independent variables. … We hope that for each variable y to be explained, there is a realtively small number of explaining factors the variations of which are practically decisive in determining the variations of y. … If we are trying to explain a certain observable varaible, y, by a system of causal factors, there is, in general, no limit to the number of such factors that might have a potential influence upon y. But Nature may limit the number of fctors that have a nonneglible factual influence to a relatively small number. Our hope for simple laws in economics rests upon the assumption that we may proceed as if such natural limitations of the number of relevant factors exist.
One way or another, to do empirical economic, we have to ignore mst of the logically possible relationships between our variables. Our goal, after all, is to explain variation in the dependent variable. Meaningful explanation is possible only if the number of relevant causal factors is small. If someone asks “why is unemployment high”, a meaningful answer is going to involve at most two or three causes. If you say, “I have no idea, but all else equal wage regulations are making it higher,” then you haven’t given an answer at all. To be masters of the hapennings of real life, we need to focus on causes of effects, not effects of causes.
In other words, ceteris paribus knowledge isn’t knowledge at all. Only unconditional claims count — but they don’t have to be predictions of a single variable, they can be claims about the joint distribution of several. But in any case we have positive knowledge only to the extent we can unconditionally say that future observations will fall entirely in a certain part of the state space. This fails if we have a ceteris paribus condition, or if our empirical works “corrects” for factors whose distribution and the nature of whose influence we have not invstigated.3 Applied science is useful because it gives us knowledge of the kind, “If I don’t turn the key, the car will not start, if I do turn the key, it will — or if it doesn’t there is a short list of possible reasons why not.” It doesn’t give us knowledge like “All else equal, the car is more likely to start when the key is turned than when it isn’t.”4
If probability distributions are simply tools for making unconditional claims about specific events, then it doesn’t make sense to think of them as existing out in the world. They are, as Keynes also emphasized, simply ways of describing our own subjective state of belief:
We might interpret “probability” simply as a measure of our a priori confidence in the occurrence of a certain event. Then the theoretical notion of a probability distribution serves us chiefly as a tool for deriving statements that have a very high probability of being true.
Another way of looking at this. Research in economics is generally framed in terms of uncovering universal laws, for which the particular phenomenon being studied merely serves as a case study.5 But in the real world, it’s more oftne the other way: We are interested in some specific case, often the outcome of some specific action we are considering. Or as Haavelmo puts it,
As a rule we are not particularly interested in making statements about a large number of observations. Usually, we are interested in a relatively small number of observations points; or perhaps even more frequently, we are interested in a practical statement about just one single new observation.
We want economics to answer questions like, “what will happen if US imposes tariffs on China”? The question of what effects tariffs have on trade in the abstract is, itself, uninteresting and unanswerable.
What do we take from this? How, according to Haavelmo, should empirical economics be?
First, the goal of empirical work is to explain concrete phenomena — what happened, or will happen, in some particular case.
Second, the content of a theory is inseparable from the procedures for measuring the variables in it.
Third, empirical work requires restrictions on the logically possible space of parameters, some of which have to be imposed a priori.
Finally, prediction (the goal) means making unconditional claims about the joint distribution of one or more variables. “Everything else equal” means “I don’t know.”
All of this based on the idea that we study economics not as an end in itself, but in response to the problems forced on us by the world.
A big question about corporate income taxes is their effects on investment. Is it reasonable to expect that lower taxes on profits will lead to greater investment, or will the tax cuts simply be paid out to shareholders? When the tax bill was being finalized late last year, John Cochrane made a typically uncompromising case for the former, arguing that it doesn’t make sense even in principle to pose investment and shareholder payouts as alternatives. In press interviews he madethe same argument even more emphatically: “If you lower the price of something, you get more of it. That’s pretty basic.” The same argument that there’s a direct link between taxes investment, regardless of what individual firms do with the money, has been made by plenty of others, such as Justin Wolfers in a recent NYT piece.
I have written somethings arguing the other side. But I don’t want to jump into polemic here. Instead I want to lay out as systematically as I can the kind of considerations that would lead one to one view or the other — the questions you need to ask before asking the question.
* * *
There are two sets of issues to consider. The micro issue is how tax cuts affect the choices facing an individual business. The macro is what outcomes one can consistently describe for the economy as a whole. In this post I will focus on the micro side. On the macro side, for now I just want to say that, contrary to what Cochrane and Wolfers seems to suggest, there is no logical reason why a corporate tax cut cannot simply result in greater cash holdings by corporations and/or shareholders. One might or might not see a reasonable story in which people would choose to behave this way, but there’s nothing nonsensical or incoherent about it in principle.
So what about the corporate investment decision? The natural way to think about this, as an economist, is in terms of two curves – one the expected return on each incremental dollar of investment, the other the cost of each incremental dollar of financing. 6 If the firm is maximizing profits, they will pick the level of investment at which these two values are equal. Even if they are not strictly maximizing (expected) profits, the analysis doesn’t change in any fundamental way – we can just think of a region around the intersection instead of a precise point. Investment is still more likely to proceed when the expected return is high relative to the cost of funds as perceived by the decisionmaker.
The basic situation is as shown in Figure 1. If the cost of funds rises with each additional dollar of investment, the cost-of-funds curve will slope upward. In particular, Minsky’s hierarchy of finance suggests that internal funds are cheaper than external funds, and the cost of external funds rises with the amount raised. Meanwhile, if the firm for whatever reason has limited investment opportunities and chooses the best ones first, then the return on investment curve will slop downward, since each additional unit of investment will be expected to yield less than the last one.
Figure 1
We see here that four kinds of development can change the desired level of investment. First, cheaper finance (lower interest rates, for example) shifts the cost of funds curve downward — the same level of investment costs less. Greater resources available to the firm — i.e. increased retained earnings or equivalent — shift the cost-of-funds curve to the right, since the firm can carry out more investment before cheaper funds are exhausted. Increased profitability (lower taxes, but also lower wages or other costs) shift the expected-returns curve up — the same level of investment generates a greater expected return. And increased demand for the firm’s output shifts the expected-returns curve to the right.
In this framework, vertical movements in the curves represent price changes – the price of additional funds (measured as an interest rate or equivalent), and the price the firm expects to produce for incremental output less the price of producing it. (Or if we imagine the investment to be raising productivity rather than increasing capacity, the price of the labor and other inputs saved per unit of output, less the cost of operation of the new capital goods.) Horizontal movements in the curves represent quantity changes – changes in the quantity of internal funds available to the firm in the case of the supply-of-funds curve, and in the quantity of output the the firm expects to sell (and the amount of new capital equipment it needs to buy this period to maintain its existing operations) in the case of the expected-returns curve.
With generic upward and downward sloping curves as in Figure 1, the price-quantity distinction doesn’t matter. Downward and outward shifts of the cost-of-funds curve are equivalent, as are upward and outward shifts of the expected-returns curve. And all four of these result in greater investment. Nonetheless it’s important to keep the four kinds of changes distinct. First, because the economic logic is different in each case. And second, because changes in the slopes of the curves will have the opposite effect in the first and third cases than in the second and fourth. It seems to me that a good deal of the differences in views on this issue can be interpreted in terms of different beliefs about the normal shapes of these curves. So let’s think through some alternatives.
The first case is that both curves are flat. This is the case for a firm that faces perfectly competitive markets both for its output and for funds. It can sell as much as it wants to at the going price, and borrow as much as it wants at the going interest rate (which is also the opportunity cost for internal funds). In the extreme case, the two curves are identical horizontal lines.
Obviously, this extreme case doesn’t make sense. Firms don’t grow without limit, so they must face either a declining return on investment, or an increasing cost of funds, or both. But there is case close to this one which is useful to think about, at least as a baseline. We can imagine a Modigliani-Miller world in which external and internal finance are perfect substitutes and the firm can borrow without limit at the market interest rate. This is represented by a horizontal supply of funds line. The return on investment curve slopes downward, but gently — this corresponds to a case where the firm expects it can sell additional output at very close to the price it gets now, and/or where the investment opportunities open to the firm do not depend very much on its current operations. The larger the universe from which the firm can pick investment projects, the smaller the gap between the best one and the second-best one. This is the kind of world that Cochrane and Wolfers have in mind.
Figure 2
(Why does the expected-return curve slope down at all? If the firm is small relative to the market, why doesn’t the next unit of investment have exactly the same return as the last one? You might say, technology. But that doesn’t work — it tells us at best the size of the establishment, not the firm — new investment can simply reproduce an existing establishment, with the same output and costs. A better argument for declining returns is some kind of non-purchaseable factor, often glossed as entrepreneurship.)
In this world, because internal and external funds are perfect substitutes, it makes no difference if a firm uses its profits for its own investment spending, lends them to another firm, or pays them out to shareholders. There is one economy-wide cost of capital that all investment projects are evaluated against, regardless of the details of how they are financed. (That’s the horizontal line in Figure 2.) Meanwhile, because the expected-return curve is nearly flat, any change in the expected return should lead to a large change in the volume of investment. If the expected return on the next project is only a little lower than the return on the last one, then a fall in the cost of capital should lead to a large number of projects moving from the not-profitable to the profitable column. So if Figure 2 is a good description of the investment decision, then Cochrane should be right, at least at the micro level: A fall in capital taxation should lead to higher investment regardless of whether the newly untaxed profits are invested by the same firms that receive them.
Wolfers states this clearly: “Companies with profitable investment opportunities can usually find ways to finance them.” Cochrane is even blunter: “Real decisions are … independent of financial decisions.”7
I’m quite sympathetic to Wolfers view that, for large corproations expecially, what is scarce is profitable outlets for investment, not funds to pay for them. But in its strong form, this view faces some problems. Clearly some businesses are financially constrained, as Wolfers acknowledges – but small businesses aren’t responsible for much investment and presumably don’t face pressure from shareholders. A more serious puzzle is the existence of a vast industry for getting around the financial constraints that Wolfers and Cochrane dismiss. If finance isn’t a problem, what is the purpose of venture capital? Why do even larger corporations worry about their credit rating? Why do we have so many different instruments for finance, many with costs substantially above “the” interest rate? What are banks for, if not deciding what gets financed and what does not? What is finance for in general? If, as Wolfers says, finance is not scarce, why is there so much money to be made selling it?8
There’s also the question of how monetary policy works in a world of abundant finance — thoughtful central bankers have long argued that quantitative limits on lending, and not just the interest rate, are important to the transmission of policy. And of course there is a vast empirical literature exploring the importance of credit constraints for investment. No doubt there are cases where the Wolfers-Cochrane position is a reasonable first approximation. But it doesn’t seem like something one can state as an unproblematic matter of fact.
Let’s move on to the other possible cases.
A second possibility is where the cost-of-funds curve is still flat or close to it, but the expected-return curve is steep. This is shown in Figure 3a. The steep downward slope means that the expected return on the next investment project might be much lower than the expected return on the last one. Why might this be the case? First, it can’t be easy to substitute capital for labor or other factors of production. (This is the intensive margin.) Second, the return on new capacity must be well below the return on existing capacity, at least past some threshold. (This is the extensive margin.) This latter might be the case either because the firm enjoys significant market power, or because it faces significant demand constraints. In the case of market power, increased capacity is not worthwhile since higher sales will reduce the margin on existing sales; in the case of demand constraints, higher capacity is not worthwhile because it’s not feasible to increase sales at all. (In some contexts these might be just two ways of describing the same phenomenon, but I think they are worth distinguishing at least conceptually.) Either way, you can have a firm whose current operations are quite profitable but nonetheless expects only a very low return on new investment.
Figure 3a
In this case, reducing the cost of capital has only a modest effect on investment (or none at all in the extreme case where the expected-returns curve is vertical). But it does still increase the firm’s profits. Those profits can be either held as cash or investments, or paid out to shareholders. If only some firms are in the position of Figure 3a, then the paid-out or lent-out cashflow will eventually make its way to the firms that face a flatter expected-returns curve. But if market power and/or demand constraints are ubiquitous, then the cash will simply circulate until it is held by someone who wants a more liquid balance sheet. (This includes paying down debt – the old law of reflux revived by Richard Koo under the name balance-sheet recession.) In this story, shareholder payouts aren’t the reason for the failure of investment to respond to tax changes (or interest rate cuts). But, along with increased corporate cash holdings, they are an important symptom.
Before moving on to the next case, it’s worth considering an alternative representation of the demand-constraints case, as in Figure 3b.
Figure 3b
Here, the firm has some guess about the sales it can achieve in the relevant future period. If this requires more capacity than it will have (taking into account depreciation) then the return on new investment will be high. But once it has raised capacity enough to meet expected demand at a reasonable level of utilization, the return gets steeply lower. In this case, it makes a big difference whether the cost-of-funds curve crosses the expected-return curve in its horizontal or its vertical segment. In the former case, the firm is genuinely credit-constrained — it believes it could sell more output at current prices, but financing increased capacity is too expensive (or simply not possible). In this case, investment will be responsive to changes in the cost of capital, or the supply of credit on other dimensions. But where the cost-of-funds curve crosses the expected-return curve on its vertical segment, we will be in the situation of the previous paragraph, where investment responds mostly or entirely to shifts in demand and little if at all to changes in the cost of capital. To me, this is a useful framework, since it captures what seems to be a genuine feature of modern economies — financing is more likely to matter when demand is strong, or for fast-growing firms, than when demand is weak or for mature firms.
The third case is where the expected-return curve is relatively flat, but the supply-of-funds curve slopes steeply upward. This case is discussed at length by Minsky. 9 The essence of this view is that finance is not frictionless. Because of various risks, information asymmetries, or other reasons, firms cannot borrow at “the” interest rate but only at some premium above it. And the costs of borrowing are not merely the interest rate. Both borrowers and lenders face risks from debt, and for the borrower there are also the various legal restrictions (covenants, etc.) that taking on debt implies. So for the lender the effective interest rate is below the market rate, and for the borrower it is above it; and both these wedges widen as the level of debt increases. The implication is that internal funds are cheaper than external funds, that the next dollar of borrowing will be more costly than the last, and that past a certain point further funds may not be available at all.
This perspective is captured in the supply-of-funds curve in Figures 4a and 4b.10 The critical thing about this case is that while financing matters, the important shifts are horizontal movements in the supply-of-funds curve rather than vertical ones. In other words, for financially constrained firms the issue is not the price at which they can borrow so much as how much they are able to borrow. (This is even more true if we add the realistic detail that the firms’ profitability will also affect the terms on which it can borrow.) With respect to monetary policy, this corresponds to what Bernanke and Gertler call the bank-lending channel — changes in policy work not so much through moving the whole curve up or down, as in conventional models, but moving the steep portion of it left or right.
Figure 4a
In the extreme case here, the cost of funds makes no difference to investment. But taxes and interest rates can still be quite important, because they affect the internal funds available to the firm. If external funds are not a good substitute for internal funds, then anything that allows a firm to retain more of its own funds will tend to raise investment. In a superb empirical article, Brown, Hubbard and Fazzari claim that the 1990s tech boom got a major boost from earlier tax cuts — but for this was because lower taxes left corporations with more internal funds, not anything to do with incentives.
Figure 4b
It’s in this setting that shareholder payouts become important not just a symptom but as a problem in their own right. If shareholders exercise a first claim on the firm’s earnings, then they are no longer available as a low-cost form of finance. This case is shown in Figure 5 (adapted from my Disgorge the Cash paper) where the new dotted line shows the minimum return acceptable to shareholders – what I call the rentier constraint. In a world in which dividends are relatively constant — the assumption of Minsky’s framework — they are essentially a fixed cost; each additional dollar of earnings is a dollar available to the firm. But if, thanks to some set of legal and institutional changes, shareholders are really able to exercise their notional claim on every dollar of profits, then new investment projects will need to show a high enough expected return to justify retaining the money for them rather than paying it out. Now, investment takes place only ewhere the expected-return curve is above the cost-of-funds curve and the rentier constraint. In the situation shown, you can see that higher earnings — a rightward shift in the supply of funds curve — do not imply a greater supply of cheap internal finance, but rather higher payouts to shareholders.
Figure 5
It’s worth emphasizing that there are two key assumptions here. First, that internal funds are perceived as a less costly source of investment finance than external funds; and second, that shareholder payouts have shifted from relatively fixed to an effective claim on each incremental dollar of earnings. Many discussions of investment power and shareholder power, it seems to me, don’t make these points clearly enough, ignoring or leaving unstated the first, and blurring the second with the fact of higher payouts. Higher fixed payouts, in a world where internal finance is cheaper than external, will indeed reduce investment; but they won’t change the functional relationship between cashflow and investment.
On the other hand, people who want to argue that payouts are irrelevant need to explicitly challenge the assumption that internal funds are preferable to external — that they’re perceived as lower cost by corporate decisionmakers. This assumption may or may not be a good description of the investment decision at a typical American firm. But one has to actually make the argument; one can’t simply ignore it, as Cochrane and Wolfers do, and claim that payout critics are making a simple logical error.
Finally, there’s the case where both the supply-of-funds and expected-return curves are steep. At the level of the individual firm, this doesn’t introduce anything new, since the firm will only be on the steep/vertical segment of one or the other of the two curves. If it’s on the steep part of the expected-returns curve, the situation will be in the same as in the second case; if it’s on the steep part of the supply-of-funds curve, the situation will be the same as in the third case. Nonetheless, it’s worth thinking about this case if we think that, in general, there are two groups of firms. There are smaller, more rapidly growing firms whose investment is financially constrained; and there are established firms whose investment is demand-constrained. Neither group will be especially sensitive to the cost of capital. Of course, there logically might be a third group constrained by neither; but this would have to be a business without significant market power that was small relative to its market, but that nonetheless was considered a very safe risk by lenders. Probably there are some such. But it doesn’t seem unreasonable to suppose that by the time a business is big enough to face a flat cost-of-funds curve, it is normally also big enough to face a steep expected-return curve.
So we now have four cases. Case one is the Cochrane-Wolfers world of a horizontal cost-of-funds curve and a shallow expected-return curve. Case two is a market-power or demand-constraints world where the expected return curve is steep and the cost-of-funds curve is relatively flat. (It doesn’t matter in this case whether the cost-of-funds curve is perfectly flat as in the first case or slopes upward, as long as it is much flatter than the expected-return curve.) Case three is the Minsky world where the cost of external funds rises as the firm borrows more. And case four is case three, but with shareholders exercising an effective claim on each dollar of incremental funds. What is the effect of tax cuts on investment in each of these cases?
We can think of a tax cut as having two effects: it shifts the expected-return curve upward, since the firm now keeps more of the sales dollars generated by additional capacity; and it shifts the cost-of-funds curve to the right, since the firm also keeps more of the sales dollars generated by its existing capacity. The exact mix of these two effects will of course depend on the specifics of the tax cut; in the extreme case of revenue-neutral tax reform, only the expected-returns curve moves. Using the figures above, we can see the effects of these changes.
In the first case, the rise in expected returns has a large effect on the volume of investment; the flat slope of the expected-return curve means that lowering the required pre-tax return on investment even slightly means a large number of additional projects qualify. The rightward shift of the cost-of-funds curve has no effect. Since internal and external funds are perfect substitutes in this world, there is no benefit to increasing firms’ retained earnings.
In the second case, neither shift will have much effect on the volume of investment. If a firm faces highly inelastic demand for its output there is no reason to increase investment in response to a higher profit margin on sales or cheaper financing. Only increased demand — a rightward shift in the expected-return curve — will lead to significantly more investment. Without that, a tax cut will lead only to some mix of less borrowing, increased financial asset holdings, and increased payouts.
In the third case, the effect of the tax cut depends where the firm is on the supply-of-funds curve. If it can already finance all of its desired investment out of internal funds, then the horizontal shift in the cost-of-funds curve will have no effect; the vertical movement of the expected-return curve may or may not have a significant effect, depending on how steep it is. Most likely, for mature firms generating substantial profits, the expected-returns curve is steep, so this effect will be small. For firms that rely on borrowing to finance investment, on the other hand, the rightward shift in the cost-of-funds curve may lead to a large increase in investment, as it allows them to substitute cheap internal funds for more costly external funds. In this case, a across-the-board tax cut will be more effective than one that only reduces taxes on earnings from new investment.
The fourth case is similar to the third case except now the horizontal movement of the cost-of-funds curve has no effect on investment, because internal funds are no longer a source of cheap financing. Instead, empowered shareholders impose a minimum return on new investment that lies above the cost-of-funds curve some distance into the borrowing segment. In this case, again, changes in the cost of funds are not going to affect investment, since the economy-wide interest rate or equivalent is no longer the relevant opportunity cost for the corporation.
So in two cases tax cuts are likely to increase investment; in two cases they are not. But the pairs are not the same. In one case of investment-boosting tax cuts, a cut targeted at new investment will be more effective than an across-the-board cut, in the other the “badly targeted” cut is actually more effective. And in one case of ineffective tax cuts, shareholder payouts are just an incidental symptom; in the other case they are the root of the problem.
So far, I think, there is nothing here that John Cochrane would disagree with. My goal up to here is not to argue for or against any of these perspectives, but simply to clarify the key assumptions that drive different views about tax cuts and investment. I think all of us, on all sides, would do better to be more explicit about the logic of our arguments. People who think that the level of investment depends varies in a straightforward way with changes in the cost of funds and/or expected return (as from interest rate and tax changes) need to recognize that doubters are not just economically illiterate, but probably have a vision of the investment decision something like cases two, three or four here. To convince people that a fall in the cost of capital should, in general, lead to higher investment, you need to make an affirmative case that there is a large population of firms that face neither demand constraints nor credit constraints. On the other side, for people who are skeptical of these links, it’s not enough to point to econometric evidence that investment isn’t sensitive to taxes or interest rates. We need coherent stories about investment that rationalize this insensitivity, and are consistent with what else we know about the investment process. And it probably is stories, plural!11
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If the world looks like Figure 5b, then most firms will be on the vertical segments of one of the two curves. Large, established firms will normally be on the vertical part of the expected-returns curve; they don’t care much about changes in expected returns or the cost of capital because they don’t expect to be able to sell additional output, or at least not without unacceptably large price reductions. Smaller, newer firms don’t care much either, because they can’t borrow more at anything like the market interest rate, or at all, so they require more internal funds (or a more tolerant attitude from lenders) to undertake even very high-return investments. One thing to note: the effect of greater market power is ambivalent here. For the first group of firms, it will limit desired investment, but in the second case it will allow more investment to be financed. It seems to me that the history of, for instance, 19th century US railroads illustrates the way in which both too much and too little competition can be inimical to high levels of investment. But again, this is only if the world does in fact look like Figure 5b.
But now I want to bring up a reason to doubt that the Cochrane-Wolfers story works even if the world looks like Figure 2, the most favorable case for it. Does a tax cut really move the curves in the required way? At first glance, the answer might seem obvious: If the tax on corporate profits is cut from, say, 50 percent to 40 percent, then the after-tax return on any project with positive earnings has now increased by 20 percent. This would be a reasonable way to think about it if we were imagining a representative wealth owner considering whether to consume their income or to invest it in some some project – if investment normally took the form of free-standing, one-off projects, that were dissolved at completion, like a long-distance merchant voyage in the 15th century.
The problem is, investment today is carried out by ongoing enterprises. It is financed not directly by contributions from wealthy households, but either by incurring new liabilities — normally debt — or else by spending down assets. And the tax cut also affects the terms of that financing. Suppose that a firm would finance additional investment by issuing debt. The interest payments on that debt are deducted from the firm’s income for tax purposes. So a tax cut raises the after-tax cost of debt payments by exactly the same proportion as it raises the after-tax return on new investment. Of course, if the expected return on the investment is higher than the interest rate faced by the firm, the effects will not exactly cancel out. But by hypothesis in the Cochrane-Wolfers world, these two rates must be very close, so the net effect must be very small. On the other hand, suppose that the firm pays for additional fund out of retained earnings. In this case, the opportunity cost is whatever earnings it would get on those funds if it held them in financial form. And these earnings are also benefiting from the tax cut, so again there the opportunity cost rises by just as much as the after-tax return on new investment does. And Cochrane’s money-flows-to-returns assumption implies that firms’ earnings on cash should not be much lower than the marginal return on new investment. In which case, again, the tax cut effectively shifts the cost-of-funds curve up by nearly as much as the expected-return curve, meaning there is no reason for investment to respond either way.
It’s easy to come up with reasons why these counteracting effects won’t apply. If the subjective cost of borrowing to corporate management includes substantial elements beyond the interest rate itself (because of the danger it creates of loss of control, because of covenants and other legal restrictions, etc.) these other elements will not be affected by the tax cut, so the effective cost of funds will rise by less than the expected return. Or, if the firm holds cash at returns substantially below the expected returns on new investment, then the tax cut will raise the opportunity cost of spending cash by less than it raises the expected return. Both these claims probably have an important element of truth. The problem is, you have to believe them consistently. If you think a firm’s cost of borrowing may be much higher than the market interest rate, or that firms hold large amounts of cash at less than the market interest rate, then you’ve landed squarely in Minsky world. Here pervasive financial frictions mean that the investment decision is no longer a straightforward matter of comparing a smoothly declining expected-return curve to an economy-wide cost of capital.
Another way to think of this: The Cochrane-Wolfers vision is a set of investment projects with smoothly declining expected returns, with the firm picking every investment project with expected earnings above the economy-wide cost of capital. In this framework the investment decision is not going to be affected by taxes on income from projects that earn above the cost of capital, which is what a corporate income tax does. The marginal project will be exactly the same whether the firm keeps 100 percent of the income from infra-marginal projects or only 10 percent of it.
This might seem obvious. I think one reason it’s not as obvious as you think, is the ambiguous meaning of “profit” in economics. In both everyday and business usage, profits are income in excess of all costs of production, including costs incurred for the use of capital goods — interest and depreciation. But in economic theory, profit is used to mean the payments to capital, just as wages are the payments to labor. Models are set up in terms of the rental price of capital. The vision is of a world in which the current services of capital are paid for in each period just as the current services are paid for with a wage. The payments to capital are normally labeled profit. This leads to various (hopelessly confused, in my opinion) efforts to separate out the rental payments in this notional market for capital services from the profits we observe in the data. More to the current point, it leads economists to think of a tax on profits as a tax on capital. If there really was a market for capital services, and the corporate income tax really was a tax on purchases in that market, then the link between corporate taxation and investment would be as straightforward as Cochrane suggests. But in the real world there is no such market, and the corporate income tax is not a tax on purchases in that nonexistent market. This is one of many cases where what economists justify as a convenient simplification gives rise to very misleading intuitions.
So it seems to me that if you want to make an argument for the investment-boosting effects of tax cuts, the strongest one would be based on the exact opposite of Cochrane’s premise: Tax cuts work not because capital freely flows to wherever the return is highest, but precisely because it does not do so. Higher investment may require higher cashflow for the firms that themselves will be doing the investing. This a corporate tax cut could deliver.
I think this argument would also be more consistent with the evidence. In this post I’m just trying to lay out an analytic framework. But for what it’s worth, my read of the empirical literature is that it is very hard to find evidence that investment responds much, or at all, to shifts in returns or the cost of capital. There is more support for the idea that some firms — including younger and rapidly-growing firms whose investment is plausibly especially socially valuable — do sometimes face credit constraints. Implying you can raise investment not by changing incentives, but just by handing the constrained firms money.
UPDATE: I had thought I’d based these figures on Minsky and was a bit puzzled that I couldn’t find them in the obvious places. But it turns out I actually got them from Hubbard, Fazzari and Petersen (1988).
