Economic growth and the size of the ‘private sector’

26 Mar, 2020 at 17:52 | Posted in Statistics & Econometrics | 2 Comments

Economic growth has since long interested economists. Not least, the question of which factors are behind high growth rates has been in focus. The factors usually pointed at are mainly economic, social and political variables. In an interesting study from the University of  Helsinki, Tatu Westling expanded the potential causal variables to also include biological and sexual variables. In the report Male Organ and Economic Growth: Does Size Matter (2011), he was — based on the ‘cross-country’ data of Mankiw et al (1992), Summers and Heston (1988), Polity IV Project data of political regime types and a data set on average penis size in 76 non-oil producing countries (www.everyoneweb.com/worldpenissize) — able to show that the level and growth of GDP per capita between 1960 and 1985 varies with penis size. Replicating Westling’s study — yours truly has used his favourite program Gretl — we obtain the following two charts:


The Solow-based model estimates show that the maximum GDP is achieved with the penis of about 13.5 cm and that the male reproductive organ (OLS without control variables) are negatively correlated with — and able to ‘explain’ 20% of the variation in — GDP growth.

Even with the reservation for problems such as endogeneity and confounders one can not but agree with Westling’s final assessment that “the ‘male organ hypothesis’ is worth pursuing in future research” and that it “clearly seems that the ‘private sector’ deserves more credit for economic development than is typically acknowledged.” Or? …

Econometric modelling as junk science

20 Mar, 2020 at 12:09 | Posted in Statistics & Econometrics | Leave a comment

Do you believe that 10 to 20% of the decline in crime in the 1990s was caused by an increase in abortions in the 1970s? Or that the murder rate would have increased by 250% since 1974 if the United States had not built so many new prisons? Did you believe predictions that the welfare reform of the 1990s would force 1,100,000 children into poverty?

qs-econometrics-titleIf you were misled by any of these studies, you may have fallen for a pernicious form of junk science: the use of mathematical modeling to evaluate the impact of social policies. These studies are superficially impressive. Produced by reputable social scientists from prestigious institutions, they are often published in peer reviewed scientific journals. They are filled with statistical calculations too complex for anyone but another specialist to untangle. They give precise numerical “facts” that are often quoted in policy debates. But these “facts” turn out to be will o’ the wisps …

These predictions are based on a statistical technique called multiple regression that uses correlational analysis to make causal arguments … The problem with this, as anyone who has studied statistics knows, is that correlation is not causation. A correlation between two variables may be “spurious” if it is caused by some third variable. Multiple regression researchers try to overcome the spuriousness problem by including all the variables in analysis. The data available for this purpose simply is not up to this task, however, and the studies have consistently failed.

Ted Goertzel

Mainstream economists often hold the view that if you are critical of econometrics it can only be because you are a sadly misinformed and misguided person who dislike and do not understand much of it.

As Goertzel’s eminent article shows, this is, however, nothing but a gross misapprehension.

LierTo apply statistical and mathematical methods to the real-world economy, the econometrician has to make some quite strong, limiting, and unreal assumptions (completeness, homogeneity, stability, measurability, independence, linearity, additivity, etc., etc.)

Building econometric models can’t be a goal in itself. Good econometric models are means that make it possible for us to infer things about the real-world systems they ‘represent.’ If we can’t show that the mechanisms or causes that we isolate and handle in our econometric models are ‘exportable’ to the real world, they are of limited value to our understanding, explanations or predictions of real-world economic systems.

Real-world social systems are usually not governed by stable causal mechanisms or capacities. The kinds of ‘laws’ and relations that econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms and variables — and the relationship between them — being linear, additive, homogenous, stable, invariant and atomistic. But — when causal mechanisms operate in the real world they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. Since econometricians haven’t been able to convincingly warrant their assumptions of homogeneity, stability, invariance, independence, additivity as being ontologically isomorphic to real-world economic systems, I remain doubtful of the scientific aspirations of econometrics.

There are fundamental logical, epistemological and ontological problems of applying statistical methods to a basically unpredictable, uncertain, complex, unstable, interdependent, and ever-changing social reality. Methods designed to analyse repeated sampling in controlled experiments under fixed conditions are not easily extended to an organic and non-atomistic world where time and history play decisive roles.

Econometric modelling should never be a substitute for thinking. From that perspective, it is really depressing to see how much of Keynes’ critique of the pioneering econometrics in the 1930s-1940s is still relevant today. And that is also a reason why social scientists like Goertzl and yours truly keep on criticizing it.

The general line you take is interesting and useful. It is, of course, not exactly comparable with mine. I was raising the logical difficulties. You say in effect that, if one was to take these seriously, one would give up the ghost in the first lap, but that the method, used judiciously as an aid to more theoretical enquiries and as a means of suggesting possibilities and probabilities rather than anything else, taken with enough grains of salt and applied with superlative common sense, won’t do much harm. I should quite agree with that. That is how the method ought to be used.

Keynes, letter to E.J. Broster, December 19, 1939

Econometrics — the signal-to-noise problem

19 Mar, 2020 at 11:24 | Posted in Statistics & Econometrics | 3 Comments

communication-engineering-chapter-6-noise-28-638When we first encounter the term, “noisy data,” in econometrics, we are usually told that it refers to the problem of measurement error, or errors-in-variables—especially in the explanatory variables (x). Most textbooks contain a discussion of measurement error bias. In the case of a bivariate regression, y = a + bx + u, measurement error in x means the ordinary least squares (OLS) estimator is biased. The magnitude of the bias depends on the ratio of the measurement error variance to the variance of x. If that ratio is very small, then the bias is negligible; but if the ratio is large, that means the measurement error can “drown” the true variation in x, and the bias is large.

In principle, the extent of the bias can be assessed by a simple formula, but in practice, this is rarely done. This is partly because we need to know the variance of the measurement error and, in most cases, we simply don’t know that. But there is more to it than that. There is a common opinion among many econometricians that, relative to the other problems of econometrics, a little bit of measurement error really doesn’t matter very much. Unfortunately, this misses the point. It is not the absolute size of the measurement error that matters, but its size relative to the variation in x. Nevertheless, many econometricians just ignore the problem …

Kalman proposed to “adopt the contemporary—very wide—implications of the word “noise,” as used in physics and engineering: any causal or random factors that should not or cannot be modeled, about which further information is not available, which are not analyzable, which may not recur reproducibly, etc. Thus, “noise” = the “unexplained.” This is a much more comprehensive category.”

This means that “noise” should include not just measurement errors and ambiguities in our economic concepts, but also any idiosyncracies and peculiarities in individual observations, which are not explained by the economic relationship we are interested in, and indeed, which obscure that relationship. Noisy data becomes a problem when it dominates the signal we want to observe. For Kalman, moreover, noisy data cannot be ignored, because noisy data must imply a noisy model. More precisely: “When we have noisy data, the uncertainty in the data will be inherited by the model. This is a fundamental difficulty; it can be camouflaged by adopting some prejudice but it cannot be eliminated.”

Peter Swann

Econometric testing

18 Mar, 2020 at 15:43 | Posted in Statistics & Econometrics | Leave a comment

Debating econometrics and its short-comings yours truly often gets the response from econometricians that “ok, maybe econometrics isn’t perfect, but you have to admit that it is a great technique for empirical testing of economic hypotheses.”

But is econometrics — really — such a great testing instrument?

ecokEconometrics is supposed to be able to test economic theories but to serve as a testing device you have to make many assumptions, many of which themselves cannot be tested or verified. To make things worse, there are also only rarely strong and reliable ways of telling us which set of assumptions is to be preferred. Trying to test and infer causality from (non-experimental) data you have to rely on assumptions such as disturbance terms being ‘independent and identically distributed’; functions being additive, linear, and with constant coefficients; parameters being’ ‘invariant under intervention; variables being ‘exogenous’, ‘identifiable’, ‘structural and so on. Unfortunately, we are seldom or never informed of where that kind of ‘knowledge’ comes from, beyond referring to the economic theory that one is supposed to test. Performing technical tests is of course needed, but perhaps even more important is to know — as David Colander recently put it — “how to deal with situations where the assumptions of the tests do not fit the data.”

That leaves us in the awkward position of having to admit that if the assumptions made do not hold, the inferences, conclusions, and testing outcomes econometricians come up with simply do not follow from the data and statistics they use.

The central question is “how do we learn from empirical data?” Testing statistical/econometric models is one way, but we have to remember that the value of testing hinges on our ability to validate the — often unarticulated technical — basic assumptions on which the testing models build. If the model is wrong, the test apparatus simply gives us fictional values. There is always a strong risk that one puts a blind eye on some of those non-fulfilled technical assumptions that actually makes the testing results — and the inferences we build on them — unwarranted.

Haavelmo’s probabilistic revolution gave econometricians their basic framework for testing economic hypotheses. It still builds on the assumption that the hypotheses can be treated as hypotheses about (joint) probability distributions and that economic variables can be treated as if pulled out of an urn as a random sample. But as far as I can see economic variables are nothing of that kind.

I still do not find any hard evidence that econometric testing uniquely has been able to “exclude a theory”. As Renzo Orsi once put it: “If one judges the success of the discipline on the basis of its capability of eliminating invalid theories, econometrics has not been very successful.”

testMost econometricians today … believe that the main objective of applied econometrics is the confrontation of economic theories with observable phenomena. This involves theory testing, for example testing monetarism or rational consumer behaviour. The econometrician’s task would be to find out whether a particular economic theory is true or not, using economic data and statistical tools. Nobody would say that this is easy. But is it possible? This question is discussed in Keuzenkamp and Magnus 􏰄1995􏰀. At the end of our paper we invited the readers to name a published paper that contains a test which, in their opinion, significantly changed the way economists think about some economic proposition. Such a paper, if it existed, would be an example of a successful theory test. The most convincing contribution, we promised, would be awarded with a one week visit to CentER for Economic Research, all expenses paid. What happened? One 􏰄Dutch􏰀 colleague called me up and asked whether he could participate without having to accept the prize. I replied that he could, but he did not participate. Nobody else responded. Such is the state of current econometrics.

Jan Magnus

Ergodicity: a primer

15 Mar, 2020 at 17:12 | Posted in Statistics & Econometrics | 5 Comments

Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity of human ensembles. Many scientists agree that ergodicity is one of the most important concepts in statistics. So, what is it?

Suppose you are concerned with determining what the most visited parks in a city are. One idea is to take a momentary snapshot: to see how many people are this moment in park A, how many are in park B and so on. Another idea is to look at one individual (or few of them) and to follow him for a certain period of time, e.g. a year. Then, you observe how often the individual is going to park A, how often he is going to park B and so on.

slide_5Thus, you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people.

The idea is that an ensemble is ergodic if the two types of statistics give the same result. Many ensembles, like the human populations, are not ergodic.

The importance of ergodicity becomes manifest when you think about how we all infer various things, how we draw some conclusion about something while having information about something else. For example, one goes once to a restaurant and likes the fish and next time he goes to the same restaurant and orders chicken, confident that the chicken will be good. Why is he confident? Or one observes that a newspaper has printed some inaccurate information at one point in time and infers that the newspaper is going to publish inaccurate information in the future. Why are these inferences ok, while others such as “more crimes are committed by black persons than by white persons, therefore each individual black person is not to be trusted” are not ok?

The answer is that the ensemble of articles published in a newspaper is more or less ergodic, while the ensemble of black people is not at all ergodic. If one searches how many mistakes appear in an entire newspaper in one issue, and then searches how many mistakes one news editor does over time, one finds the two results almost identical (not exactly, but nonetheless approximately equal). However, if one takes the number of crimes committed by black people in a certain day divided by the total number of black people, and then follows one random-picked black individual over his life, one would not find that, e.g. each month, this individual commits crimes at the same rate as the crime rate determined over the entire ensemble. Thus, one cannot use ensemble statistics to properly infer what is and what is not probable that a certain individual will do.

Or take an even clearer example: In an election each party gets some percentage of votes, party A gets a%, party B gets b% and so on. However, this does not mean that over the course of their lives each individual votes with party A in a% of elections, with B in b% of elections and so on …

A similar problem is faced by scientists in general when they are trying to infer some general statement from various particular experiments. When is a generalization correct and when it isn’t? The answer concerns ergodicity. If the generalization is done towards an ergodic ensemble, then it has a good chance of being correct.

Vlad Tarko

Paul Samuelson once famously claimed that the “ergodic hypothesis” is essential for advancing economics from the realm of history to the realm of science. But is it really tenable to assume — as Samuelson and most other mainstream economists — that ergodicity is essential to economics?

In this video Ole Peters shows why ergodicity is such an important concept for understanding the deep fundamental flaws of mainstream economics:

Sometimes ergodicity is mistaken for stationarity. But although all ergodic processes are stationary, they are not equivalent.

Let’s say we have a stationary process. That does not guarantee that it is also ergodic. The long-run time average of a single output function of the stationary process may not converge to the expectation of the corresponding variables — and so the long-run time average may not equal the probabilistic (expectational) average. cointossingSay we have two coins, where coin A has a probability of 1/2 of coming up heads, and coin B has a probability of 1/4 of coming up heads. We pick either of these coins with a probability of 1/2 and then toss the chosen coin over and over again. Now let H1, H2, … be either one or zero as the coin comes up heads or tales. This process is obviously stationary, but the time averages — [H1 + … + Hn]/n — converges to 1/2 if coin A is chosen, and 1/4 if coin B is chosen. Both these time averages have a probability of 1/2 and so their expectational average is 1/2 x 1/2 + 1/2 x 1/4 = 3/8, which obviously is not equal to 1/2 or 1/4. The time averages depend on which coin you happen to choose, while the probabilistic (expectational) average is calculated for the whole “system” consisting of both coin A and coin B.

In an ergodic system time is irrelevant and has no direction. Nothing changes in any significant way; at most you will see some short-lived fluctuations. An ergodic system is indifferent to its initial conditions: if you re-start it, after a little while it always falls into the same equilibrium behavior.

arrow_of_time_1For example, say I gave 1,000 people one die each, had them roll their die once, added all the points rolled, and divided by 1,000. That would be a finite-sample average, approaching the ensemble average as I include more and more people.

Now say I rolled a die 1,000 times in a row, added all the points rolled and divided by 1,000. That would be a finite-time average, approaching the time average as I keep rolling that die.

One implication of ergodicity is that ensemble averages will be the same as time averages. In the first case, it is the size of the sample that eventually removes the randomness from the system. In the second case, it is the time that I’m devoting to rolling that removes randomness. But both methods give the same answer, within errors. In this sense, rolling dice is an ergodic system.

I say “in this sense” because if we bet on the results of rolling a die, wealth does not follow an ergodic process under typical betting rules. If I go bankrupt, I’ll stay bankrupt. So the time average of my wealth will approach zero as time passes, even though the ensemble average of my wealth may increase.

A precondition for ergodicity is stationarity, so there can be no growth in an ergodic system. Ergodic systems are zero-sum games: things slosh around from here to there and back, but nothing is ever added, invented, created or lost. No branching occurs in an ergodic system, no decision has any consequences because sooner or later we’ll end up in the same situation again and can reconsider. The key is that most systems of interest to us, including finance, are non-ergodic.

Ole Peters

Machine learning — puzzling ‘big data’ nonsense

14 Mar, 2020 at 09:00 | Posted in Statistics & Econometrics | 4 Comments

maIf we wanted highly probable claims, scientists would stick to​​ low-level observables and not seek generalizations, much less theories with high explanatory content. In this day​ of fascination with Big data’s ability to predict​ what book I’ll buy next, a healthy Popperian reminder is due: humans also want to understand and to explain. We want bold ‘improbable’ theories. I’m a little puzzled when I hear leading machine learners praise Popper, a realist, while proclaiming themselves fervid instrumentalists. That is, they hold the view that theories, rather than aiming at truth, are just instruments for organizing and predicting observable facts. It follows from the success of machine learning, Vladimir Cherkassy avers, that​ “realism is not possible.” This is very quick philosophy!

Quick indeed!

The central problem with the present ‘machine learning’ and ‘big data’ hype is that so many — falsely — think that they can get away with analysing real-world phenomena without any (commitment to) theory. But — data never speaks for itself. Without a prior statistical set-up, there actually are no data at all to process. And — using a machine learning algorithm will only produce what you are looking for.

Machine learning algorithms always express a view of what constitutes a pattern or regularity. They are never theory-neutral.

Clever data-mining tricks are not enough to answer important scientific questions. Theory matters.

Statistical models for causation — a critical review

12 Mar, 2020 at 11:37 | Posted in Statistics & Econometrics | Leave a comment

maxresdefCausal inferences can be drawn from nonexperimental data. However, no mechanical rules can be laid down for the activity. Since Hume, that is almost a truism. Instead, causal inference seems to require an enormous investment of skill, intelligence, and hard work. Many convergent lines of evidence must be developed. Natural variation needs to be identified and exploited. Data must be collected. Confounders need to be considered. Alternative explanations have to be exhaustively tested. Before anything else, the right question needs to be framed. Naturally, there is a desire to substitute intellectual capital for labor. That is why investigators try to base causal inference on statistical models. The technology is relatively easy to use, and promises to open a wide variety of ques- tions to the research effort. However, the appearance of methodological rigor can be deceptive. The models themselves demand critical scrutiny. Mathematical equations are used to adjust for confounding and other sources of bias. These equations may appear formidably precise, but they typically derive from many somewhat arbitrary choices. Which variables to enter in the regression? What functional form to use? What assumptions to make about parameters and error terms? These choices are seldom dictated either by data or prior scientific knowledge. That is why judgment is so critical, the opportunity for error so large, and the number of successful applications so limited.

David Freedman

Causality in social sciences — and economics — can never solely be a question of statistical inference. Causality entails more than predictability, and to really in depth explain social phenomena require theory. Analysis of variation — the foundation of all regression analysis and econometrics — can never in itself reveal how these variations are brought about. First, when we are able to tie actions, processes or structures to the statistical relations detected, can we say that we are getting at relevant explanations of causation.

Most facts have many different, possible, alternative explanations, but we want to find the best of all contrastive (since all real explanation takes place relative to a set of alternatives) explanations. So which is the best explanation? Many scientists, influenced by statistical reasoning, think that the likeliest explanation is the best explanation. But the likelihood of x is not in itself a strong argument for thinking it explains y. I would rather argue that what makes one explanation better than another are things like aiming for and finding powerful, deep, causal, features and mechanisms that we have warranted and justified reasons to believe in. Statistical — especially the variety based on a Bayesian epistemology — reasoning generally has no room for these kinds of explanatory considerations. The only thing that matters is the probabilistic relation between evidence and hypothesis. That is also one of the main reasons I find abduction — inference to the best explanation — a better description and account of what constitute actual scientific reasoning and inferences.

Some statisticians and data scientists think that algorithmic formalisms somehow give them access to causality. That is, however, simply not true. Assuming ‘convenient’ things like linearity, additivity,  faithfulness or stability is not to give proofs. It’s to assume what has to be proven. Deductive-axiomatic methods used in statistics do no produce evidence for causal inferences. The real causality we are searching for is the one existing in the real world around us. If there is no warranted connection between axiomatically derived theorems and the real world, well, then we haven’t really obtained the causation we are looking for.

Randomness and probability — a theoretical reexamination

10 Mar, 2020 at 15:51 | Posted in Statistics & Econometrics | 14 Comments

raModern probabilistic econometrics relies on the notion of probability. To at all be amenable to econometric analysis, economic observations allegedly have to be conceived as random events. But is it really necessary to model the economic system as a system where randomness can only be analyzed and understood when based on an a priori notion of probability?

In probabilistic econometrics, events and observations are as a rule interpreted as random variables as if generated by an underlying probability density function, and a fortiori – since probability density functions are only definable in a probability context – consistent with a probability. As Haavelmo (1944:iii) has it:

For no tool developed in the theory of statistics has any meaning – except , perhaps for descriptive purposes – without being referred to some stochastic scheme.

When attempting to convince us of the necessity of founding empirical economic analysis on probability models, Haavelmo – building largely on the earlier Fisherian paradigm – actually forces econometrics to (implicitly) interpret events as random variables generated by an underlying probability density function.

This is at odds with reality. Randomness obviously is a fact of the real world. Probability, on the other hand, attaches to the world via intellectually constructed models, and a fortiori is only a fact of a probability generating machine or a well constructed experimental arrangement or “chance set-up”.

Just as there is no such thing as a “free lunch,” there is no such thing as a “free probability.” To be able at all to talk about probabilities, you have to specify a model. If there is no chance set-up or model that generates the probabilistic outcomes or events – in statistics one refers to any process where you observe or measure as an experiment (rolling a die) and the results obtained as the outcomes or events (number of points rolled with the die, being e. g. 3 or 5) of the experiment –there strictly seen is no event at all.

Probability is a relational element. It always must come with a specification of the model from which it is calculated. And then to be of any empirical scientific value it has to be shown to coincide with (or at least converge to) real data generating processes or structures – something seldom or never done!

And this is the basic problem with economic data. If you have a fair roulette-wheel, you can arguably specify probabilities and probability density distributions. But how do you conceive of the analogous nomological machines for prices, gross domestic product, income distribution etc? Only by a leap of faith. And that does not suffice. You have to come up with some really good arguments if you want to persuade people into believing in the existence of socio-economic structures that generate data with characteristics conceivable as stochastic events portrayed by probabilistic density distributions!

Continue Reading Randomness and probability — a theoretical reexamination…

Econometrics — a critical realist critique

5 Mar, 2020 at 20:17 | Posted in Statistics & Econometrics | 1 Comment

Mainstream economists often hold the view that criticisms of econometrics are the conclusions of sadly misinformed and misguided people who dislike and do not understand much of it. This is really a gross misapprehension. To be careful and cautious is not the same as to dislike. keuzenkampAnd as any perusal of the mathematical-statistical and philosophical works of people like for example Nancy Cartwright, Chris Chatfield, Hugo Keuzenkamp, John Maynard Keynes, Tony Lawson, Asad Zaman, Aris Spanos, Duo Qin, and David Freedman, would show, the critique is put forward by respected authorities. I would argue, against “common knowledge”, that they do not misunderstand the crucial issues at stake in the development of econometrics. Quite the contrary. They — just as yours truly — know them all too well, and are not satisfied with the validity and philosophical underpinning of the assumptions made for applying its methods.

Let me try to do justice to the critical arguments on the logic of probabilistic induction and shortly elaborate — mostly from a philosophy of science vantage point — on some insights critical realism gives us on econometrics and its methodological foundations.

The methodological difference between an empiricist and a deductivist approach can also clearly be seen in econometrics. The ordinary deductivist “textbook approach” views the modelling process as foremost an estimation problem, since one (at least implicitly) assumes that the model provided by economic theory is a well-specified and “true” model. The more empiricist, general-to-specific-methodology (often identified as “the LSE approach”) on the other hand views models as theoretically and empirically adequate representations (approximations) of a data generating process (DGP). Diagnostics tests (mostly some variant of the F-test) are used to ensure that the models are “true” – or at least “congruent” – representations of the DGP. The modelling process is here more seen as a specification problem where poor diagnostics results may indicate possible misspecification requiring re-specification of the model. The objective is standardly to identify models that are structurally stable and valid across a large time-space horizon. The DGP is not seen as something we already know, but rather something we discover in the process of modelling it. Considerable effort is put into testing to what extent the models are structurally stable and generalizable over space and time.

Although I have sympathy for this approach in general, there are still some unsolved “problematics” with its epistemological and ontological presuppositions. There is, e. g., an implicit assumption that the DGP fundamentally has an invariant property and that models that are structurally unstable just have not been able to get hold of that invariance. But, as already Keynes maintained, one cannot just presuppose or take for granted that kind of invariance. It has to be argued and justified. Grounds have to be given for viewing reality as satisfying conditions of model-closure. It is as if the lack of closure that shows up in the form of structurally unstable models somehow could be solved by searching for more autonomous and invariable “atomic uniformity”. But if reality is “congruent” to this analytical prerequisite has to be argued for, and not simply taken for granted.

Even granted that closures come in degrees, we should not compromise on ontology. Some methods simply introduce improper closures, closures that make the disjuncture between models and real-world target systems inappropriately large. “Garbage in, garbage out.”

Underlying the search for these immutable “fundamentals” lays the implicit view of the world as consisting of material entities with their own separate and invariable effects. These entities are thought of as being able to be treated as separate and addible causes, thereby making it possible to infer complex interaction from knowledge of individual constituents with limited independent variety. But, again, if this is a justified analytical procedure cannot be answered without confronting it with the nature of the objects the models are supposed to describe, explain or predict. Keynes himself thought it generally inappropriate to apply the “atomic hypothesis” to such an open and “organic entity” as the real world. As far as I can see these are still appropriate strictures all econometric approaches have to face. Grounds for believing otherwise have to be provided by the econometricians.

haavelmoTrygve Haavelmo, the “father” of modern probabilistic econometrics, wrote that he and other econometricians could not “build a complete bridge between our models and reality” by logical operations alone, but finally had to make “a non-logical jump” [1943:15]. A part of that jump consisted in that econometricians “like to believe … that the various a priori possible sequences would somehow cluster around some typical time shapes, which if we knew them, could be used for prediction” [1943:16]. But since we do not know the true distribution, one has to look for the mechanisms (processes) that “might rule the data” and that hopefully persist so that predictions may be made. Of possible hypotheses, on different time sequences (“samples” in Haavelmo’s somewhat idiosyncratic vocabulary) most had to be ruled out a priori “by economic theory”, although “one shall always remain in doubt as to the possibility of some … outside hypothesis being the true one” [1943:18].

To Haavelmo and his modern followers, econometrics is not really in the truth business. The explanations we can give of economic relations and structures based on econometric models are “not hidden truths to be discovered” but rather our own “artificial inventions”. Models are consequently perceived not as true representations of DGP, but rather instrumentally conceived “as if”-constructs. Their “intrinsic closure” is realized by searching for parameters showing “a great degree of invariance” or relative autonomy and the “extrinsic closure” by hoping that the “practically decisive” explanatory variables are relatively few, so that one may proceed “as if … natural limitations of the number of relevant factors exist” [Haavelmo 1944:29].

Haavelmo seems to believe that persistence and autonomy can only be found at the level of the individual since individual agents are seen as the ultimate determinants of the variables in the economic system.

But why the “logically conceivable” really should turn out to be the case is difficult to see. At least if we are not satisfied with sheer hope. As we have already noted Keynes reacted against using unargued for and unjustified assumptions of complex structures in an open system being reducible to those of individuals. In real economies, it is unlikely that we find many “autonomous” relations and events. And one could of course, with Keynes and from a critical realist point of view, also raise the objection that to invoke a probabilistic approach to econometrics presupposes, e. g., that we have to be able to describe the world in terms of risk rather than genuine uncertainty.

Continue Reading Econometrics — a critical realist critique…

The history of econometrics

29 Feb, 2020 at 12:40 | Posted in Statistics & Econometrics | Comments Off on The history of econometrics

9780199679348There have been over four decades of econometric research on business cycles …

But the significance of the formalization becomes more difficult to identify when it is assessed from the applied perspective …

The wide conviction of the superiority of the methods of the science has converted the econometric community largely to a group of fundamentalist guards of mathematical rigour … So much so that the relevance of the research to business cycles is reduced to empirical illustrations. To that extent, probabilistic formalisation has trapped econometric business cycle research in the pursuit of means at the expense of ends.

The limits of econometric forecasting have, as noted by Qin, been critically pointed out many times before. Trygve Haavelmo assessed the role of econometrics — in an article from 1958 — and although mainly positive of the “repair work” and “clearing-up work” done, Haavelmo also found some grounds for despair:

Haavelmo-intro-2-125397_630x210There is the possibility that the more stringent methods we have been striving to develop have actually opened our eyes to recognize a plain fact: viz., that the “laws” of economics are not very accurate in the sense of a close fit, and that we have been living in a dream-world of large but somewhat superficial or spurious correlations.

Maintaining that economics is a science in the ‘true knowledge’ business, yours truly remains a sceptic of the pretences and aspirations of econometrics. The marginal return on its ever higher technical sophistication in no way makes up for the lack of serious under-labouring of its deeper philosophical and methodological foundations that already Keynes complained about. The rather one-sided emphasis of usefulness and its concomitant instrumentalist justification cannot hide that the legions of probabilistic econometricians who give supportive evidence for their considering it ‘fruitful to believe’ in the possibility of treating unique economic data as the observable results of random drawings from an imaginary sampling of an imaginary population, are skating on thin ice.

A rigorous application of econometric methods in economics presupposes that the phenomena of our real world economies are ruled by stable causal relations between variables. The endemic lack of predictive success of the econometric project indicates that this hope of finding fixed parameters is a hope for which there, really, is no other ground than hope itself.

Econometrics — the scientific illusion of an empirical failure

27 Feb, 2020 at 19:03 | Posted in Statistics & Econometrics | Comments Off on Econometrics — the scientific illusion of an empirical failure

Ed Leamer’s Tantalus on the Road to Asymptopia is one of yours truly’s favourite critiques of econometrics, and for the benefit of those who are not versed in the econometric jargon, this handy summary gives the gist of it in plain English:

noahtantalus

Most work in econometrics and regression analysis is made on the assumption that the researcher has a theoretical model that is ‘true.’ Based on this belief of having a correct specification for an econometric model or running a regression, one proceeds as if the only problem remaining to solve have to do with measurement and observation.

economWhen things sound to good to be true, they usually aren’t. And that goes for econometric wet dreams too. The snag is, as Leamer convincingly argues, that there is pretty little to support the perfect specification assumption. Looking around in social science and economics we don’t find a single regression or econometric model that lives up to the standards set by the ‘true’ theoretical model — and there is pretty little that gives us reason to believe things will be different in the future.

To think that we are being able to construct a model where all relevant variables are included and correctly specify the functional relationships that exist between them, is  not only a belief without support, but a belief impossible to support. The theories we work with when building our econometric models are insufficient. No matter what we study, there are always some variables missing, and we don’t know the correct way to functionally specify the relationships between the variables we choose to put into our models.

Every econometric model constructed is misspecified. There are always an endless list of possible variables to include, and endless possible ways to specify the relationships between them. So every applied econometrician comes up with his own specification and parameter estimates. The econometric Holy Grail of consistent and stable parameter-values is nothing but a dream.

A rigorous application of econometric methods presupposes that the phenomena of our real world economies are ruled by stable causal relations between variables.  Parameter-values estimated in specific spatio-temporal contexts are presupposed to be exportable to totally different contexts. To warrant this assumption one, however, has to convincingly establish that the targeted acting causes are stable and invariant so that they maintain their parametric status after the bridging. The endemic lack of predictive success of the econometric project indicates that this hope of finding fixed parameters is a hope for which there really is no other ground than hope itself.

The theoretical conditions that have to be fulfilled for regression analysis and econometrics to really work are nowhere even closely met in reality. Making outlandish statistical assumptions does not provide a solid ground for doing relevant social science and economics. Although regression analysis and econometrics have become the most used quantitative methods in social sciences and economics today, it’s still a fact that the inferences made from them are, strictly seen, invalid.

Econometrics is basically a deductive method. Given the assumptions (such as manipulability, transitivity, separability, additivity, linearity, etc) it delivers deductive inferences. The problem, of course, is that we will never completely know when the assumptions are right. Conclusions can only be as certain as their premises. That also applies to econometrics.

Why I am not a Bayesian

26 Feb, 2020 at 15:50 | Posted in Statistics & Econometrics | 1 Comment

Assume you’re a Bayesian turkey and hold a nonzero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule

P(H|e) = [P(e|H)P(H)]/P(e),

where evidence e stands for “not being eaten” and P(e|H) = 1. Given that there do exist other hypotheses than H, P(e) is less than 1 and so P(H|e) is greater than P(H). Every day you survive increases your probability belief that you will not be eaten. This is totally rational according to the Bayesian definition of rationality. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer …

Neoclassical economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules — that is, they maximize expected utility with respect to some subjective probability measure that is continually updated according to Bayes theorem. If not, they are supposed to be irrational.

bayes_dog_tshirtBayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs, but — even granted this questionable reductionism — do rational agents really have to be Bayesian?

The nodal point here is — of course — that although Bayes’ Rule is mathematically unquestionable, that doesn’t qualify it as indisputably applicable to scientific questions. As one of my favourite statistics bloggers —  Andrew Gelman — puts it:

The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this raises suspicion in anyone with applied experience, who realizes that different methods work well in different settings … Bayesians promote the idea that a multiplicity of parameters can be handled via hierarchical, typically exchangeable, models, but it seems implausible that this could really work automatically. In contrast, much of the work in modern non-Bayesian statistics is focused on developing methods that give reasonable answers using minimal assumptions.

The second objection to Bayes comes from the opposite direction and addresses the subjective strand of Bayesian inference: the idea that prior and posterior distributions represent subjective states of knowledge. Here the concern from outsiders is, first, that as scientists we should be concerned with objective knowledge rather than subjective belief, and second, that it’s not clear how to assess subjective knowledge in any case.

bayesfunBeyond these objections is a general impression of the shoddiness of some Bayesian analyses, combined with a feeling that Bayesian methods are being oversold as an all-purpose statistical solution to genuinely hard problems. Compared to classical inference, which focuses on how to extract the information available in data, Bayesian methods seem to quickly move to elaborate computation. It does not seem like a good thing for a generation of statistics to be ignorant of experimental design and analysis of variance, instead of becoming experts on the convergence of the Gibbs sampler. In the short term this represents a dead end, and in the long term it represents a withdrawal of statisticians from the deeper questions of inference and an invitation for econometricians, computer scientists, and others to move in and fill in the gap …

Bayesian inference is a coherent mathematical theory but I don’t trust it in scientific applications. Subjective prior distributions don’t transfer well from person to person, and there’s no good objective principle for choosing a noninformative prior (even if that concept were mathematically defined, which it’s not). Where do prior distributions come from, anyway? I don’t trust them and I see no reason to recommend that other people do, just so that I can have the warm feeling of philosophical coherence …

Econometrics — a crooked path from cause to effect

24 Feb, 2020 at 19:48 | Posted in Statistics & Econometrics | 1 Comment

 

In their book Mastering ‘Metrics: The Path from Cause to Effect Joshua Angrist and Jörn-Steffen Pischke write:

masteringOur first line of attack on the causality problem is a randomized experiment, often called a randomized trial. In a randomized trial, researchers change the causal variables of interest … for a group selected using something like a coin toss. By changing circumstances randomly, we make it highly likely that the variable of interest is unrelated to the many other factors determining the outcomes we want to study. Random assignment isn’t the same as holding everything else fixed, but it has the same effect. Random manipulation makes other things equal hold on average across the groups that did and did not experience manipulation. As we explain … ‘on average’ is usually good enough.

Angrist and Pischke may “dream of the trials we’d like to do” and consider “the notion of an ideal experiment” something that “disciplines our approach to econometric research,” but to maintain that ‘on average’ is “usually good enough” is an allegation that in my view is rather unwarranted, and for many reasons.

First of all, it amounts to nothing but hand waving to simpliciter assume, without argumentation, that it is tenable to treat social agents and relations as homogeneous and interchangeable entities.

notes7-2Randomization is used to basically allow the econometrician to treat the population as consisting of interchangeable and homogeneous groups (‘treatment’ and ‘control’). The regression models one arrives at by using randomized trials tell us the average effect that variations in variable X has on the outcome variable Y, without having to explicitly control for effects of other explanatory variables R, S, T, etc., etc. Everything is assumed to be essentially equal except the values taken by variable X.

In a usual regression context one would apply an ordinary least squares estimator (OLS) in trying to get an unbiased and consistent estimate:

Y = α + βX + ε,

where α is a constant intercept, β a constant “structural” causal effect and ε an error term.

The problem here is that although we may get an estimate of the “true” average causal effect, this may “mask” important heterogeneous effects of a causal nature. Although we get the right answer of the average causal effect being 0, those who are “treated”( X=1) may have causal effects equal to – 100 and those “not treated” (X=0) may have causal effects equal to 100. Contemplating being treated or not, most people would probably be interested in knowing about this underlying heterogeneity and would not consider the OLS average effect particularly enlightening.

Limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we “export” them to our “target systems”, we have to be able to show that they do not only hold under ceteris paribus conditions and a fortiori only are of limited value to our understanding, explanations or predictions of real economic systems.

Real-world social systems are not governed by stable causal mechanisms or capacities. The kinds of “laws” and relations that econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms being atomistic and additive. When causal mechanisms operate in real-world social target systems they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. If economic regularities obtain they do it (as a rule) only because we engineered them for that purpose. Outside man-made “nomological machines” they are rare, or even non-existent. Unfortunately, that also makes most of the achievements of econometrics – as most of the contemporary endeavours of mainstream economic theoretical modelling – rather useless.

Remember that a model is not the truth. It is a lie to help you get your point across. And in the case of modeling economic risk, your model is a lie about others, who are probably lying themselves. And what’s worse than a simple lie? A complicated lie.

Sam L. Savage The Flaw of Averages

When Joshua Angrist and Jörn-Steffen Pischke in an earlier article of theirs [“The Credibility Revolution in Empirical Economics: How Better Research Design Is Taking the Con out of Econometrics,” Journal of Economic Perspectives, 2010] say that

anyone who makes a living out of data analysis probably believes that heterogeneity is limited enough that the well-understood past can be informative about the future

I really think they underestimate the heterogeneity problem. It does not just turn up as an external validity problem when trying to “export” regression results to different times or different target populations. It is also often an internal problem to the millions of regression estimates that economists produce every year.

But when the randomization is purposeful, a whole new set of issues arises — experimental contamination — which is much more serious with human subjects in a social system than with chemicals mixed in beakers … Anyone who designs an experiment in economics would do well to anticipate the inevitable barrage of questions regarding the valid transference of things learned in the lab (one value of z) into the real world (a different value of z) …

randomizeAbsent observation of the interactive compounding effects z, what is estimated is some kind of average treatment effect which is called by Imbens and Angrist (1994) a “Local Average Treatment Effect,” which is a little like the lawyer who explained that when he was a young man he lost many cases he should have won but as he grew older he won many that he should have lost, so that on the average justice was done. In other words, if you act as if the treatment effect is a random variable by substituting βt for β0 + β′zt, the notation inappropriately relieves you of the heavy burden of considering what are the interactive confounders and finding some way to measure them …

If little thought has gone into identifying these possible confounders, it seems probable that little thought will be given to the limited applicability of the results in other settings.

Ed Leamer

Evidence-based theories and policies are highly valued nowadays. Randomization is supposed to control for bias from unknown confounders. The received opinion is that evidence-based on randomized experiments, therefore, is the best.

More and more economists have also lately come to advocate randomization as the principal method for ensuring being able to make valid causal inferences.

I would however rather argue that randomization, just as econometrics, promises more than it can deliver, basically because it requires assumptions that in practice are not possible to maintain.

Especially when it comes to questions of causality, randomization is nowadays considered some kind of “gold standard”. Everything has to be evidence-based, and the evidence has to come from randomized experiments.

But just as econometrics, randomization is basically a deductive method. Given the assumptions (such as manipulability, transitivity, separability, additivity, linearity, etc.) these methods deliver deductive inferences. The problem, of course, is that we will never completely know when the assumptions are right. And although randomization may contribute to controlling for confounding, it does not guarantee it, since genuine randomness presupposes infinite experimentation and we know all real experimentation is finite. And even if randomization may help to establish average causal effects, it says nothing of individual effects unless homogeneity is added to the list of assumptions. Real target systems are seldom epistemically isomorphic to our axiomatic-deductive models/systems, and even if they were, we still have to argue for the external validity of the conclusions reached from within these epistemically convenient models/systems. Causal evidence generated by randomization procedures may be valid in “closed” models, but what we usually are interested in, is causal evidence in the real target system we happen to live in.

When does a conclusion established in population X hold for target population Y? Only under very restrictive conditions!

Angrist’s and Pischke’s “ideally controlled experiments,” tell us with certainty what causes what effects — but only given the right “closures”. Making appropriate extrapolations from (ideal, accidental, natural or quasi) experiments to different settings, populations or target systems, is not easy. “It works there” is no evidence for “it will work here”. Causes deduced in an experimental setting still have to show that they come with an export-warrant to the target population/system. The causal background assumptions made have to be justified, and without licenses to export, the value of “rigorous” and “precise” methods — and ‘on-average-knowledge’ — is despairingly small.

On randomization and regression (wonkish)

21 Feb, 2020 at 09:21 | Posted in Statistics & Econometrics | Comments Off on On randomization and regression (wonkish)

Randomization does not justify the regression model, so that bias can be expected, and the usual formulas do not give the right variances. Moreover, regression need not improve precision …

linWhat is the source of the bias when regression models are applied to experimental data? In brief, the regression model assumes linear additive effects. Given the assignments, the response is taken to be a linear combina- tion of treatment dummies and covariates, with an additive random error; coefficients are assumed to be constant across subjects. The Neyman [potential outcome] model makes no assumptions about linearity and additivity. If we write the expected response given the assignments as a linear combination of treatment dummies, coefficients will vary across subjects. That is the source of the bias …

To put this more starkly, in the Neyman model, inferences are based on the random assignment to the several treatments. Indeed, the only stochastic element in the model is the randomization. With regression, inferences are made conditional on the assignments. The stochastic element is the error term, and the inferences depend on assumptions about that error term. Those assumptions are not justified by randomization. The breakdown in assumptions explains why regression comes up short when calibrated against the Neyman model …

Variances in the Neyman model are (necessarily) computed across the assignments, for it is the assignments that are the random elements in the model. With regression, variances are computed conditionally on the assignments, from an error term assumed to be IID across subjects, and independent of the assignment variables as well as the covariates. These assumptions do not follow from the randomization, explaining why the usual formulas break down.

David Freedman

Workshop on causal graphs (student stuff)

20 Feb, 2020 at 19:39 | Posted in Statistics & Econometrics | Comments Off on Workshop on causal graphs (student stuff)

 

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