The fundamental econometric dilemma

27 May, 2017 at 10:20 | Posted in Statistics & Econometrics | Leave a comment

fraud-kit

Many thanks for sending me your article. I enjoyed it very much. I am sure these matters need discussing in that sort of way. There is one point, to which in practice I attach a great importance, you do not allude to. In many of these statistical researches, in order to get enough observations they have to be scattered over a lengthy period of time; and for a lengthy period of time it very seldom remains true that the environment is sufficiently stable. That is the dilemma of many of these enquiries, which they do not seem to me to face. Either they are dependent on too few observations, or they cannot rely on the stability of the environment. It is only rarely that this dilemma can be avoided.

Letter from J. M. Keynes to T. Koopmans, May 29, 1941

 

Econometric patterns should never be seen as anything else than possible clues to follow. Behind observable data there are real structures and mechanisms operating, things that are  — if we really want to understand, explain and (possibly) predict things in the real world — more important to get hold of than to simply correlate and regress observable variables.

Math cannot establish the truth value of a fact. Never has. Never will.

Paul Romer

Modern economics — pseudo-science based on FWUTV

25 May, 2017 at 14:39 | Posted in Statistics & Econometrics | Leave a comment

The use of FWUTV — facts with unknown truth values — is, as Paul Romeer noticed in last year’s perhaps most interesting insider critique of mainstream economics, all to often used in macroeconomic modelling. But there are other parts of ‘modern’ economics than New Classical RBC economics that also have succumbed to this questionable practice:

CnGyMOeWAAEQVaHStatistical significance is not the same as real-world significance — all it offers is an indication of whether you’re seeing an effect where there is none. Even this narrow technical meaning, though, depends on where you set the threshold at which you are willing to discard the ‘null hypothesis’ — that is, in the above case, the possibility that there is no effect. I would argue that there’s no good reason to always set it at 5 percent. Rather, it should depend on what is being studied, and on the risks involved in acting — or failing to act — on the conclusions …

This example illustrates three lessons. First, researchers shouldn’t blindly follow convention in picking an appropriate p-value cutoff. Second, in order to choose the right p-value threshold, they need to know how the threshold affects the probability of a Type II error. Finally, they should consider, as best they can, the costs associated with the two kinds of errors.

Statistics is a powerful tool. But, like any powerful tool, it can’t be used the same way in all situations.

Narayana Kocherlakota

Good lessons indeed — underlining how important it is not to equate science with statistical calculation. All science entail human judgement, and using statistical models doesn’t relieve us of that necessity. Working with misspecified models, the scientific value of significance testing is actually zero – even though you’re making valid statistical inferences! Statistical models and concomitant significance tests are no substitutes for doing science.

In its standard form, a significance test is not the kind of ‘severe test’ that we are looking for in our search for being able to confirm or disconfirm empirical scientific hypotheses. This is problematic for many reasons, one being that there is a strong tendency to accept the null hypothesis since they can’t be rejected at the standard 5% significance level. In their standard form, significance tests bias against new hypotheses by making it hard to disconfirm the null hypothesis.

And as shown over and over again when it is applied, people have a tendency to read “not disconfirmed” as ‘probably confirmed.’ Standard scientific methodology tells us that when there is only say a 10 % probability that pure sampling error could account for the observed difference between the data and the null hypothesis, it would be more ‘reasonable’ to conclude that we have a case of disconfirmation. Especially if we perform many independent tests of our hypothesis and they all give about the same 10 % result as our reported one, I guess most researchers would count the hypothesis as even more disconfirmed.

We should never forget that the underlying parameters we use when performing significance tests are model constructions. Our p-values mean next to nothing if the model is wrong. And most importantly — statistical significance tests DO NOT validate models!

411-y9smopl-_sx346_bo1204203200_In journal articles a typical regression equation will have an intercept and several explanatory variables. The regression output will usually include an F-test, with p – 1 degrees of freedom in the numerator and n – p in the denominator. The null hypothesis will not be stated. The missing null hypothesis is that all the coefficients vanish, except the intercept.

If F is significant, that is often thought to validate the model. Mistake. The F-test takes the model as given. Significance only means this: if the model is right and the coefficients are 0, it is very unlikely to get such a big F-statistic. Logically, there are three possibilities on the table:
i) An unlikely event occurred.
ii) Or the model is right and some of the coefficients differ from 0.
iii) Or the model is wrong.

Yes, indeed. Forgetting — or at least pretending to forget — that third possibility, turns much of ‘modern’ economics and econometrics into post-real blah blah blah pseudo-science.

‘Modern’ economics — blah blah blah

23 May, 2017 at 16:37 | Posted in Statistics & Econometrics | 2 Comments

A key part of the solution to the identification problem that Lucas and Sargent (1979) seemed to offer was that mathematical deduction could pin down some parameters in a simultaneous system. But solving the identification problem means feeding facts with truth values that can be assessed, yet math cannot establish the truth value of a fact. Never has. Never will.

blah_blahIn practice, what math does is let macro-economists locate the FWUTVs [facts with unknown truth values] farther away from the discussion of identification … Relying on a micro-foundation lets an author say, “Assume A, assume B, …  blah blah blah …. And so we have proven that P is true. Then the model is identified.” …

Distributional assumptions about error terms are a good place to bury things because hardly anyone pays attention to them. Moreover, if a critic does see that this is the identifying assumption, how can she win an argument about the true expected value the level of aether? If the author can make up an imaginary variable, “because I say so” seems like a pretty convincing answer to any question about its properties.

Paul Romer

Yes, indeed, modern mainstream economics — and especially its mathematical-statistical operationalization in the form of econometrics — fails miserably over and over again. One reason why it does, is that the error term in the regression models used are thought of as representing the effect of the variables that were omitted from the models. The error term is somehow thought to be a ‘cover-all’ term representing omitted content in the model and necessary to include to ‘save’ the assumed deterministic relation between the other random variables included in the model. Error terms are usually assumed to be orthogonal (uncorrelated) to the explanatory variables. But since they are unobservable, they are also impossible to empirically test. And without justification of the orthogonality assumption, there is as a rule nothing to ensure identifiability.

In mainstream econometrics the error term is usually portrayed as representing the combined effect of the variables that are omitted from the model. What one does not say — in a way bordering on intellectual dishonesty — is that this assumption only works when (1) the combined effect is independent of each and every variable included in the model, and (2) the expectational value of the combined effect equals zero. And that is something almost never fulfilled in real world settings!

‘Modern’ mainstream economics is based on the belief that deductive-axiomatic modelling  is a sufficient guide to truth. That belief is, however, totally unfounded as long as no proofs are supplied for us to believe in the assumptions on which the model-based deductions and conclusions  build. ‘Mathiness’ masquerading as science is often used by mainstream economists to hide the problematic character of the assumptions used in their theories and models. But — without showing the model assumptions to be realistic and relevant, that kind of economics indeed, as Romer puts it, produces nothing but “blah blah blah.”

The most beautiful identity in mathematics

21 May, 2017 at 20:09 | Posted in Statistics & Econometrics | Comments Off on The most beautiful identity in mathematics

 

On the fundamental difference between ergodic and non-ergodic processes in economics

19 May, 2017 at 19:43 | Posted in Statistics & Econometrics | 2 Comments

Yours truly has tried to explain the fundamental difference between time averages and ensemble averages repeatedly on this blog. Still people obviously seem to have problems grasping it. Maybe this video will help …

Structural econometrics

14 May, 2017 at 18:43 | Posted in Statistics & Econometrics | 2 Comments

In a blog post the other day, Noah Smith returned again to the discussion about the ’empirical revolution’ in economics and how to — if it really does exist — evaluate it. Counter those who think quasi-experiments and RCTs are the true solutions to finding causal parameters, Noah argues that without structural models

empirical results are only locally valid. And you don’t really know how local “local” is. If you find that raising the minimum wage from $10 to $12 doesn’t reduce employment much in Seattle, what does that really tell you about what would happen if you raised it from $10 to $15 in Baltimore?

That’s a good reason to want a good structural model. With a good structural model, you can predict the effects of policies far away from the current state of the world.

If only that were true! But it’s not.

Structural econometrics — essentially going back to the Cowles programme — more or less takes for granted the possibility of a priori postulating relations that describe economic behaviours as invariant within a Walrasian general equilibrium system. In practice that means the structural model is based on a straightjacket delivered by economic theory. Causal inferences in those models are — by assumption — made possible since the econometrician is supposed to know the true structure of the economy. And, of course, those exact assumptions are the crux of the matter. If the assumptions don’t hold, there is no reason whatsoever  to have any faith in the conclusions drawn, since they do not follow from the statistical machinery used!

Structural econometrics aims to infer causes from probabilities, inferred from sample data generated in non-experimental settings. Arguably, it is the most ambitious part of econometrics. It aims to identify economic structures, robust parts of the economy to which interventions can be made to bring about desirable events. This part of econometrics is distinguished from forecasting econometrics in its attempt to capture something of the ‘real’ economy in the hope of allowing policy makers to act on and control events …

LierBy making many strong background assumptions, the deductivist [the conventional logic of structural econometrics] reading of the regression model allows one — in principle — to support a structural reading of the equations and to support many rich causal claims as a result. Here, however, the difficulty is that of finding good evidence for many of the assumptions on which the approach rests. It seems difficult to believe, even in cases where we have good background economic knowledge, that the background information will be sufficiently to do the job that the deductivist asks of it. As a result, the deductivist approach may be difficult to sustain, at least in economics.

The difficulties in providing an evidence base for the deductive approach show just how difficult it is to warrant such strong causal claims. In short, as might be expected there is a trade-off between the strength of causal claims we would like to make from non-experimental data and the possibility of grounding these in evidence. If this conclusion is correct — and an appropriate elaboration were done to take into account the greater sophistication of actual structural econometric methods — then it suggests that if we want to do evidence-based structural econometrics, then we may need to be more modest in the causal knowledge we aim for. Or failing this, we should not act as if our causal claims — those that result from structural econometrics — are fully warranted by the evidence and we should acknowledge that they rest on contingent, conditional assumptions about the economy and the nature of causality.

Damien Fennell

Maintaining that economics is a science in the ‘true knowledge’ business, yours truly remains a skeptic of the pretences and aspirations of — both structural and non-structural — econometrics. So far, I cannot see that it has yielded much in terms of relevant, interesting economic knowledge. Over all the results have been bleak indeed.

Firmly stuck in an empiricist tradition, econometrics is only concerned with the measurable aspects of reality. But there is always the possibility that there are other variables — of vital importance and although perhaps unobservable and non-additive, not necessarily epistemologically inaccessible — that were not considered for the econometric modeling.

Most econometricians still concentrate on fixed parameter models and the structuralist belief/hope that parameter-values estimated in specific spatio-temporal contexts are 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.

Most of the assumptions that econometric modeling presupposes  are not only unrealistic — they are plainly wrong.

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-existant. Unfortunately that also makes most of the achievements of both structural and non-structural econometric forecasting and ‘causal explanation’ rather useless.

41svIj0RdVLInvariance assumptions need to be made in order to draw causal conclusions from non-experimental data: parameters are invariant to interventions, and so are errors or their distributions. Exogeneity is another concern. In a real example, as opposed to a hypothetical, real questions would have to be asked about these assumptions. Why are the equations “structural,” in the sense that the required invariance assumptions hold true? Applied papers seldom address such assumptions, or the narrower statistical assumptions: for instance, why are errors IID?

The tension here is worth considering. We want to use regression to draw causal inferences from non-experimental data. To do that, we need to know that certain parameters and certain distributions would remain invariant if we were to intervene. Invariance can seldom be demonstrated experimentally. If it could, we probably wouldn’t be discussing invariance assumptions. What then is the source of the knowledge?

“Economic theory” seems like a natural answer, but an incomplete one. Theory has to be anchored in reality. Sooner or later, invariance needs empirical demonstration, which is easier said than done.

The statistical crisis in social science

7 May, 2017 at 16:28 | Posted in Statistics & Econometrics | 3 Comments

 

Trig trick (student stuff)

7 May, 2017 at 13:01 | Posted in Statistics & Econometrics | Comments Off on Trig trick (student stuff)

 

Don’t trust summary statistics alone

6 May, 2017 at 08:49 | Posted in Statistics & Econometrics | 1 Comment

AllDinosGrey_1

When teaching statistics and econometrics yours truly always stress the importance of data visualization. The thirteen datasets shown above is a great illustration of why one should always plot data. They all have the same summary statistics — mean, standard deviation, correlation coefficient — but some are dinosaurs and others are stars …

Conclusion: never trust summary statistics alone!

drunk

The spectacular failure of DSGE models

1 May, 2017 at 11:34 | Posted in Statistics & Econometrics | 3 Comments

In most aspects of their lives humans must plan forwards. They take decisions today that affect their future in complex interactions with the decisions of others. When taking such decisions, the available information is only ever a subset of the universe of past and present information, as no individual or group of individuals can be aware of all the relevant information. Hence, views or expectations about the future, relevant for their decisions, use a partial information set, formally expressed as a conditional expectation given the available information.

macroeconomics-14-638 Moreover, all such views are predicated on there being no un-anticipated future changes in the environment pertinent to the decision. This is formally captured in the concept of ‘stationarity’. Without stationarity, good outcomes based on conditional expectations could not be achieved consistently. Fortunately, there are periods of stability when insights into the way that past events unfolded can assist in planning for the future.

The world, however, is far from completely stationary. Unanticipated events occur, and they cannot be dealt with using standard data-transformation techniques such as differencing, or by taking linear combinations, or ratios. In particular, ‘extrinsic unpredictability’ – unpredicted shifts of the distributions of economic variables at unanticipated times – is common. As we shall illustrate, extrinsic unpredictability has dramatic consequences for the standard macroeconomic forecasting models used by governments around the world – models known as ‘dynamic stochastic general equilibrium’ models – or DSGE models …

Many of the theoretical equations in DSGE models take a form in which a variable today, say incomes (denoted as yt) depends inter alia on its ‘expected future value’… For example, yt may be the log-difference between a de-trended level and its steady-state value. Implicitly, such a formulation assumes some form of stationarity is achieved by de-trending.

Unfortunately, in most economies, the underlying distributions can shift unexpectedly. This vitiates any assumption of stationarity. The consequences for DSGEs are profound. As we explain below, the mathematical basis of a DSGE model fails when distributions shift … This would be like a fire station automatically burning down at every outbreak of a fire. Economic agents are affected by, and notice such shifts. They consequently change their plans, and perhaps the way they form their expectations. When they do so, they violate the key assumptions on which DSGEs are built.

David Hendry & Grayham Mizon

A great article, not only showing on what shaky mathematical basis DSGE models are built, but also underlining that to understand real world ‘non-routine’ decisions and unforeseeable changes in behaviour, stationary probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not those that will rule the future.

Advocates of DSGE modeling want to have deductively automated answers to fundamental causal questions. But to apply ‘thin’ methods we have to have ‘thick’ background knowledge of what’s going on in the real world, and not in idealized models. Conclusions can only be as certain as their premises — and that also applies to the quest for causality and forecasting predictability in DSGE models.

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