The Wit and Wisdom of Trygve Haavelmo

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.

  1. In the World Economics Association newsletter here, here, here, here, here,  here, and here. At present the series doesn’t seem to be collected in one place, tho I understand Knibbe is writing a book based on it.
  2. Quoted by Slobodian. Hayek of course was less sanguine than Haavelmo about the usefulness of economic data, but on this specific point there’s a parallel.
  3. In a conference presentation a few years ago,  Christian Schoder made a very forceful critique of the common practice of include control variables in empirical work that play no role in the theory the empirics are supposed to be evaluating. Unfortunately I don’t know if he’s published it.
  4. It might seem like medicine often gives knowledge of the second kind. I would say that’s only in areas where research is still at a preliminary stage; areas where medicine still doesn’t really work. If your give your kids the mumps vaccine, they won’t get mumps — you don’t need a statistical test to see if the effect is significant. In Haavelmo’s terms, we have useful knowledge because we can safely exclude the part of the probability distribution where the kid is vaccinated and gets mumps anyway.
  5. To see what I mean, just click over to, say, the latest NBER working papers. Most of the papers you see will have titles like, “Intertemporal Labor Supply Substitution? Evidence from the Swiss Income Tax Holidays,” where whatever concrete historical question they are actually studying is presented as just “evidence” for a general law.

12 thoughts on “The Wit and Wisdom of Trygve Haavelmo”

  1. Tweet-length reply cause we miss you over there:

    >economic theories have content only insofar as they’re associated with specific procedures for measurement

    So true. And so sad that it rules out supply and demand.

    1. Shortage and surplus do exist as psychological perceptions which translate into rising or falling transaction prices in a unique context. When this psychology expresses itself in a financial or money-culture it is called the law of supply and demand. However supply and demand are like gravity – it is invisible – we only see the change in momentum which is observable and we define methods to specify the ratio of mass say of the Earth and moon. When prices move up we think there is a shortage and when prices move down we think there is a surplus by using the mind to create a market model of other agents in so-called markets. Galileo postulated how motion would be observed by three or four observers in different locations: in each case he replicated the mental properties of one observer and used his mind to imagine all the possible perceptions at different locations. When physical scientists speak of laws of physics they only mean human observers have not witnessed a violation of those statements based on commonly accepted definitions that link conceptual models with perceptions.

    1. Thanks for this thoughtful response. I can imagine a reply to it laying out why I think you are wrong, and also one agreeing with almost all of it.

      I think this passage may get at the key point where we differ:

      To me the purpose of an economic model is to define a vocabulary that we can use to discuss economic phenomena. So the inherent value of a variable in an economic model is the way that the economic model gives the variable a very specific concrete meaning. “Consumer demand” means something very specific and clear in the context of a neoclassical model, and the fact that we can agree on this — separate and apart from economic data — is useful for the purposes of economic discourse.

      The perspective I’m ventriloquizing from Haavelmo here says that it doesn’t make sense to talk about the “meaning” of a variable within a model; meaning is an attribute of a model plus some procedure for confronting the external world. (Just like one can only talk about the meaning of a bit of language in the context of some specific communication.) But I say differ rather than dsiagree for a reason;l I don’t think this is so much a disagreement about what is the case as about what we think economics is supposed to be doing. Insofar as the property of some formal models is the ultimate object of inquiry, you are certainly right. As it happens I don’t think that’s what we’re interested in, but as you say, that may be the difference between a theorist and whatever I am.

      1. I can imagine a reply to it laying out why I think you are wrong, and also one agreeing with almost all of it.

        Incidentally, the fact that this is so often my response to disagreement is one reason I found twitter so uncongenial.

        1. That sentiment underlies my post/critique. I don’t think we actually have a disagreement over how economics should be done — which is what’s most important. I suspect we would agree on what constitutes a good economic paper. The disagreement lies only in how we talk about economics.

  2. A real response:

    Having come to the study of economics (and any understanding I may have achieved) sort of back-asswards — by delving into the national accounts and trying to explain/understand what I saw, rather than starting with theory — this post rings deeply true for me. But from a kind of reverse perspective.

    What I discovered was that for many/most measures, I had to go deep into their measurement/estimation methods, and in many cases into the implicit theory underlying their measurement and estimation. I found it hard to understand what the measures meant, absent an understanding of that theory.

    Some measures are pretty close to the ground. Adding up total wages and salaries is a fairly straightforward survey operation, based on actual account transactions/transfers between entities. This fits well in the category of “You can ignore this [methodology], most of the time.”

    But employee compensation — which also includes benefit payment money transfers that don’t actually go to employees — less so. And total income, including eg owner-imputed rent, even less so.

    Related: flow “measures” that aren’t actually measuring transaction flows. Personal/household saving is a great example: the residual of two actual transaction flows — income and expenditures. Actually (explicitly) a measure of non-flow. As soon as we look at saving, we’ve already begun to “choose our models from … the field of [very simple, arithmetic] mathematics.”

    So yes: “the ‘design of experiments’ means, in the first instance, the design of the national accounts.” Every different presentation of those accounts, choices of named and defined measures and the display of their identity relationships, is an economic model, and economic theory underpins and lurks within and behind it — invisibly, absent an explicit effort to understand what’s implicit therein.

    1. Yes, that all seems right. I like to think of a hierarchy running from concrete activity tomoney payments to privat accounts to national accounts to macroeconomic theory. But obviously it’s not a one way relationship. The accounting categories – national and even private – are shaped in all kinds of ways by economic theory. And not just one body of theory, but a palimpsest of theory of different vintages. Given the continuing pressure on the accounts to conform to modern theory, I half expect GDP to eventually be redefined as “net gain in consumer welfare from exogenous shocks in this period.”

      1. >“net gain in consumer welfare from exogenous shocks in this period.”

        😉

        I like the metaphor of vision. The retina starts modeling — selecting plus much processing — at the instant photons hit. Much more modeling in the optic nerve, and of course the brain’s vision centers.

        Without all this modeling (all “invisible” to us), we quite literally can’t see anything.

  3. “In other words, ceteris paribus knowledge isn’t knowledge at all.”

    I’d frame it in a different way. If your explanatory variables are strictly controlled in concept and number, then you are still in ceteris paribus territory on the residual. That’s a fact, and it becomes quite inconvenient when “black swans” fly in. Moving from the number 1 to the number n>1 does not banish ceteris paribus.

    Moreover, there is a difference between the utility of ceteris paribus in logic and its utility in prediction. I would say the first is more important to macroeconomics. Keynes’ great ideas are saturated with ceteris paribus thinking – it’s found throughout the General Theory. The paradox of thrift and the way he reconstructed his definition of saving are examples, as is most everything about accounting when applied at the macroeconomic level (which is what he did).

  4. Mainstream economics seems unware that accounting thought processes are the type of mathematics that is most relevant to its subject matter.

    It’s like watching Trump trying to be president.

  5. I usually think of any dynamic process as a transition system using the general balance equation:

    Accumulation = Generation – Consumption + Input – Output

    where we define a system along with methods to assign numbers and units. If the states are certain and the transition rules are certain the model is called deterministic. If states or transition rules are uncertain we may recognize and attempt to describe the nature of such uncertainty.

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