What’s Wrong With the Neoclassical Production Function

Posted on April 25, 2014 by Arnold Kling

The NPF makes sense in a simple context. Suppose you are an entrepreneur with a fruit orchard. You can pay to have fruit trees planted. That is your capital. After a while the fruit trees mature, and you hire workers to pick and sell the fruit. That is your labor. The function Y = f(K,L), which says that output is a function of capital and labor, is a reasonable model that can help to predict your decisions and the share of income that goes to your workers.

Economists from Ricardo to Piketty have wanted to describe the relationship between economic growth and income distribution in terms of simple laws. For the past fifty years or so, the NPF has been the go-to tool for economists trying to do this. Mathematically, it is very elegant for that purpose.

But thinking of the economy in terms of an aggregate NPF has many problems, including the following:

1. Capital aggregation. There is a huge, huge literature on this (see “Cambridge capital controversies”). The result was that the economists who claimed that you cannot construct a meaningful aggregate out of different types of capital equipment won the theoretical battle but lost the practical war. That is, those who use capital aggregation admit that it is bogus, but they go ahead and do it anyway. It’s a matter of “I need the eggs.”

2. Solow residual. The NPF can account for only a small fraction of changes in economic growth over time or differences in productivity across countries. The unexplained differences are known as the Solow residual. Again, there is a huge literature devoted to this issue.

3. Labor heterogeneity. In the NPF, there is one wage rate, which is what is needed to induce you to give up an hour of leisure. In the real world, there are many different salaries paid to different people.

4. Capital proliferation. Over the past fifty years, economists have conceptualized many types of capital. We now have human capital, social capital, organizational capital, institutional capital, environmental capital, network capital, consumer capital, cultural capital, knowledge capital, innovation capital, and so on. Some forms of capital help with understanding labor heterogeneity. Other types help with the Solow residual. But these multiple forms of capital mess with the simple NPF and with the correspondence between theoretical concepts and real world data.

5. Knightian uncertainty. Unlike our theoretical orchard-owner, real-world entrepreneurs must cope with the fact that the return on a particular investment is unknown ex ante. The distribution of income among capitalists is affected by differences in ex post returns. Moreover, since so much of “labor” income is an accrual to human capital, all of us are capitalists, and hence most “labor” income is subject to differences in ex post returns.

So, should we use the NPF to guide economic policy to try to achieve the best balance among growth and the distribution of income? Some possibilities:

(1) The criticisms of the aggregate NPF are not important, so that policy conclusions are still sound.

(2) Some of the criticisms are devastating, but we need some tool to guide policy, and until something better comes along our best choice is the aggregate NPF.

(3) Some criticisms are devastating, and as a result we should be very cautious and humble about making policy pronouncements based on our understanding of the NPF.

To me, (3) makes the most sense. But that is not a popular position at the moment.

Correlation, Signal, and Noise

Posted on March 12, 2014 by Arnold Kling

As a public service, I am going to offer two propositions about correlation.

1. Where there is correlation, there is signal.

2. Where there is noise, correlation is understated.

The other night, I met with a large group of people to discuss Gregory Clark’s new book. Many people made comments that were uninformed regarding these two propositions.

For example, I gather that people who are strongly into political correctness are wont to say that “There is no reason to believe that IQ measures anything.” I think that is untrue.

Measured IQ is correlated with other variables, including education and income. Any variable that is reliably correlated with other variables must have some signal. It must be measuring something. It may not be measuring what it purports to measure. It may not have a causal relationship with the variables to which it is correlated. But to deny that it measures anything at all moves you deeply into science-denier territory.

Other comments suggest that people believe that if the correlation between parents and children on some variable is, say, 0.4, then this represents a ceiling on heritability. In fact, if measurement of the variable in question is subject to noise, then true heritability could be higher. For example, if IQ tests are inexact (which I assume they are), then it could be that the heritability of “true IQ” could be 0.6, even though the heritability of measured IQ is only 0.4. The opposite is not the case–random noise will not cause the measured IQ to appear more correlated than it really is. The bias is only downward.

I have written a review (may appear next month) of Clark’s book, and in my view the main contribution of his multigenerational studies of social mobility is to give us a means for assessing the impact of noise on heritability estimates. The affect appears to be large, meaning that some characteristics are far more heritable than one-generation correlation studies suggest.

Velasquez-Manoff on Causal Density

Posted on March 9, 2014 by Arnold Kling

From An Epidemic of Absence.

The scientific method that had proven so useful in defeating infectious disease was, by definition, reductionist in its approach. Germ theory was predicated on certain microbes causing certain diseases. Scientists invariably tried to isolate one product, reproduce one result consistently in experiments, and then, based on this research, create one drug. But we’d evolved surrounded by almost incomprehensible microbial diversity, not just one, or even ten species. And the immune system had an array of inputs for communication with microbes. What if we required multiple stimuli acting on these sensors simultaneously? How would any of the purified substances mentioned above mimic that experience? “The reductionist approach is going to fail in this arena,” says Anthony Horner, who’d used a melange of microbes in his experiment. “There are just too many things we’re exposed to.”

In an essay over ten years ago, I wrote,

E.D. Hirsch, Jr., writes, “If just one factor such as class size is being analyzed, then its relative contribution to student outcomes (which might be co-dependent on many other real-world factors) may not be revealed by even the most careful analysis…And if a whole host of factors are simultaneously evaluated as in ‘whole-school reform,’ it is not just difficult but, despite the claims made for regression analysis, impossible to determine relative causality with confidence.”

In the essay, my own example of a complex process that is not amenable to reductionist scientific method is economic development and growth. In that essay, I also provide a little game, like the children’s game “mastermind,” to illustrate the difficulty of applying reductionism in a complex, nonlinear world. Try playing it (it shows up better in Internet Explorer than in Google Chrome).

The phrase “causal density” is, of course, from James Manzi and his book, Uncontrolled.

The Case Against VARs

Posted on February 10, 2014 by Arnold Kling

In a comment on this post, Noah Smith commended to me the work of George-Marios Angeletos of MIT. Unfortunately, Angeletos is fond of vector autoregressions (VARs), which I detest.

I got my start in macro working on structural macroeconometric models. I saw them close up, and I am keenly aware of the problems with them. Hence, I wrote Macroeconometrics: The Science of Hubris.

However, I will give the old-fashioned macroeconometricians credit for at least worrying about the details of the data they are using. If there are structural factors that are changing over time, such as trend productivity growth or labor force participation, the macroeconometrician will keep track of these trends. If there are special factors that change quarterly patterns, such as the “cash-for-clunkers” program that shifted automobile purchases around, the macroeconometrician will take these into account.

The VAR crowd cheerfully ignores all the details in macro data. The economist with a computer program that will churn out VARs is like a 25-year-old with a new immersion blender. He does not want to spend time cooking carefully-selected ingredients. He just wants to throw whatever is in the pantry into the blender to make a smoothie or soup. (Note that I am being unfair to people with immersion blenders. I am not being unfair to people who use VARs.)

The VAR appeared because economists became convinced that structural macroeconometric models are subject to the Lucas Critique, which says that as monetary policy attempts to manipulate demand, people will adjust their expectations. My reaction to this is

(a) the Lucas critique is a minor theoretical curiosity. There are much worse problems with macroeconometrics in practice.

(b) How the heck does running a VAR exempt you from the Lucas Critique? A VAR is no less subject to breakdown than is a structural model.

The macroeconometric project that I first worked with is doomed to fail. Implicitly, you are trying to make 1988 Q1 identical to 2006 Q3 except for the one causal factor with which you are concerned. This cannot be done. There is too much Manzian causal density.

The VAR just takes this doomed macroeconometric project and cavalierly ignores details. It is not an improvement over the macroeconometrics that I learned in the 1970s. On the contrary, it is inferior. And if the big names in modern macro all use it, that does not say that there is something right about VAR. It says that there is something wrong with all the big names in modern macro. On this point, Robert Solow and I still agree.

The Qualifications for Fed Chair

Posted on February 6, 2014 by Arnold Kling

Justin Fox writes,

So has an economics PhD basically become a prerequisite for running the Fed? “I think the answer is ‘probably yes’ these days,” former Fed vice chairman Alan Blinder — a Princeton economics professor — emailed when I asked him. “Otherwise, the Fed’s staff will run technical rings around you.”

Not if you have enough confidence in your own judgment. Paul Volcker could not have cared less about the macroeconomic models of the Fed staff. In fact, nowhere in academic economics do they teach how the central bank really operates on a day-to-day basis. For that, you have to read Marcia Stigum’s Money Market.

Pointer from Mark Thoma.

It does seem to be true that Ph.D economists are now in the saddle at the Fed. In fact, there is a non-trivial chance that Janet Yellen will be the last Fed Chair not to have Stan Fischer as part of her intellectual ancestry (she is roughly the same age as Fischer and did her dissertation under James Tobin).

Statistics vs. Calculus in High School

Posted on February 4, 2014 by Arnold Kling

From a podcast with Russ Roberts and Erik Brynjolfsson (the guest):

Guest: My pet little thing, I just wanted to mention, is I’m not as much of a fan of calculus as I once was, and I’m on a little push in my high school to replace calculus with statistics. In terms of what I think is practical for most people, with the possible exception of Ph.D. economists: calculus is just widely needed. But that’s sort of a tangent. Russ: Well, it’s interesting. My wife is a math teacher, and she is teaching a class of seniors this year, split between calculus and statistics, for one of the levels of the school. And statistics is–I agree with you. Statistics is in many ways much more useful for most students than calculus. The problem is, to teach it well is extraordinarily difficult. It’s very easy to teach a horrible statistics class where you spin back the definitions of mean and median. But you become dangerous because you think you know something about data when in fact it’s kind of subtle. Guest: Yeah. But you read newspapers saying–I just grimace because the journalists don’t understand basic statistics, and I don’t think the readers do either. And that’s something that appears almost daily in our lives. I’d love it if we upped our education in that area. As data and data science becomes more important, it’s going to be more important to do that.

Most of the discussion concerns the new book The Second Machine Age, or what I call “average is over and over.”

Over-rated in Economics

Posted on February 3, 2014 by Arnold Kling

Tyler Cowen writes,

at any point in time, the most overrated economists are the most highly rated young empirical economists at the top schools.

He says this is because empirical results do not hold up terribly well, and because what matters in empirical work is the overall body of work done by the profession, not so much the contributions of particular individuals.

I think that economists in policy-hot fields tend to be over-rated. Macro is one example. Health care is another. When I think of Jonathan Gruber or David Cutler, what comes to mind are their policy opinions, rather than any research discoveries. They are rated highly by economists who think that Gruber and Cutler know how to fix the health care system. Given that I do not believe this to be the case, I have to view them as dangerously over-rated.

I think that the fields of economic history and financial institutions are under-rated. Doug Diamond is known for his paper with Dybvig, but he has done other stuff that I like that has not received as much attention. Consequently, I think of him as under-rated. Gregory Clark may be under-rated. In my macro memoir, I end up saying that if I had it to do over again, I would pursue economic history and financial institutions as fields, rather than macro.

Many years ago Dick Startz wrote advice to economists on the job market. He said that the quality of professors at lower-institutions tends to be higher than you probably expect. Given that observation, it would be easier to find under-rated economists at lower-tier institutions and easier to find over-rated economists at top-tier institutions.

The Case Against Y = f(K,L)

Posted on January 25, 2014 by Arnold Kling

1. You want to use it to explain incomes. But you end up having to make up all sorts of alternative types of capital in order to do so.

2. It makes it seem as if you found a planet identical to earth and inhabited only by hunter-gatherers, that you could give them all the equipment that we use to make a brand-new Honda, combine this K with their L, and produce said Honda.

3. In general, it completely overlooks the path-dependency and context-dependency of the value of capital and of labor skills. Fischer Black’s theory of economic fluctuations is focused on the fact that people make investments in an uncertain environment, and sometimes a lot of those investments turn out sour. The way I would put it is that people start down paths expecting them to lead one way, and then the paths do not lead where they want.

In general, it might be better to think of production “paths” rather than production functions. The path enabling the hunter-gatherers to build a Honda would be long and complex. It would include general-purpose technologies, like language, writing, electric motors, the internal combustion engine, computer chips, and radio-frequency communication. It would include the accumulation of human skills, know-how, infrastructure of various kinds, business norms, and regulations.

Models as Traps

Posted on January 15, 2014 by Arnold Kling

Tyler Cowen writes,

Enter DSGE models. There are plenty of good arguments against them. Still, they provide a useful discipline and they pinpoint rather ruthlessly what it is they we still do not understand. We can and should devalue them in a variety of ways, and for a variety of reasons, but still we should not dismiss them.

Models are simplifications. Sometimes they seem useful. For example, the AS-AD model often seems useful for explaining economic fluctuations. The production function often seems useful for explaining the distribution of income.

The DSGE model was never adopted for its usefulness in that sense. It was adopted in order to satisfy a methodological principle. That may be why I am tempted to dismiss it.

Any model can be described as valuable if you say that it shows us what we do not understand. To me, that is a low bar.

I think that a model is a trap if factors outside of the model constantly have to be invoked, to the point where they overwhelm the factors that are in the model.

Take the neoclassical production function. Recently, it has occurred to me that this may be a trap. Economists seem to need to add all sorts of types of capital to the model: human capital, social capital, network capital, brand-name capital, etc. It is hard enough dealing with heterogeneity in physical capital–how many forklifts equal one blast furnace? But when physical capital does such a poor job of explaining differences in performance across firms, across economies, and over time, at what point do you say that the neoclassical production function is a trap?

DSGE and the Market Test

Posted on January 11, 2014 by Arnold Kling

Noah Smith writes,

In other words, DSGE models (not just “Freshwater” models, I mean the whole kit & caboodle) have failed a key test of usefulness. Their main selling point – satisfying the Lucas critique – should make them very valuable to industry. But industry shuns them.