The Empirical Pivot: From Laws to Stochastic Models
Beyond Logic: The Birth of Econometric Ambition
Logical positivism promised an austere purity. Scientific statements would be either analytic truths, secured by logic alone, or empirical claims, answerable to observation. When that program fractured under its own internal difficulties, economics did not simply abandon the aspiration to be scientific. It redirected the aspiration toward a different conception of what scientific warrant could look like in a non-experimental domain.
The question that remained was sharper than the verifiability slogan, and more practical than any philosophical manifesto:
If universal economic “laws” cannot be verified in the strong sense, what does it mean to justify an economic mechanism empirically?
The twentieth-century response was not a single demarcation criterion. It was an institutionalized craft, econometrics, that attempted to fuse three methodological demands into a single research workflow:
- Theoretical structure capable of sustaining counterfactual reasoning, not merely summarizing correlations.
- Measurement conventions that make theoretical terms operational without trivializing them.
- Statistical inference that disciplines belief under uncertainty, acknowledging that evidence is always finite, noisy, and historically contingent.
Econometrics, on this view, is not “applied statistics.” It is a normative proposal for how a social science should earn the right to make claims about mechanisms. It is a framework for turning the economy’s refusal to become a laboratory into a problem of explicit assumptions, rather than an excuse for intellectual laxity.
The Keynes–Tinbergen Controversy: When the Economy Refuses to Be a Laboratory
The first public stress test of this ambition was the Keynes–Tinbergen controversy. Tinbergen’s project was bold: quantify macroeconomic relationships and treat estimation as a way to adjudicate among rival theories and policy proposals. Keynes’s reply has often been reduced to a posture of skepticism, but the enduring content is methodological, and it remains contemporary.
In an experimental science, a causal claim is often protected by design. The experiment separates mechanisms by controlling the environment. In macroeconomics, where “other things equal” is almost never guaranteed, a theory does not meet the data directly. It reaches the data through a chain of auxiliary commitments:
- how variables are chosen, defined, and aggregated,
- how proxies stand in for theoretical constructs,
- which omitted forces are treated as negligible,
- whether the institutional regime is stable,
- whether the policy environment is passive or reflexive,
- whether expectations adapt in response to the policy itself.
Keynes was pressing the epistemic vulnerability that haunts non-experimental inference: statistical fit cannot by itself certify causal structure. A regression may be numerically elegant and scientifically empty if its interpretive bridge cannot be defended.
The debate left modern applied work with a question that remains unavoidable:
When evidence contradicts an economic model, what exactly has failed: the mechanism, the measurement, the environment, or the inference?
The difference between careful and careless econometrics is not that the careful economist “has the right answer.” It is that the careful economist tries to make the structure of possible failure explicit, and then designs the empirical argument to constrain the most plausible escape routes.
Haavelmo’s Probability Turn: What Makes a Model Empirically Meaningful
Trygve Haavelmo’s probability approach is often described as the moment economics acquired modern statistical sophistication. That description is too small. Haavelmo’s contribution was methodological and philosophical at once. He did not merely add probability theory to economics. He redefined what an economic model is, and therefore what empirical testing could possibly mean.
A model, in Haavelmo’s framing, is not a deterministic sentence written onto the world. It is a stochastic data-generating system. The model proposes not only relationships among variables, but also a probabilistic structure that could have generated the data we observe.
A compact template is:
\[ Y = g(X,\theta,U), \qquad U \sim F_U, \qquad (Y,X)\sim P_\theta. \]
The scientific content of the model is the set of admissible probability laws \(\{P_\theta\}_{\theta\in\Theta}\). A model with genuine empirical content does not merely accommodate the data. It excludes many data patterns. In doing so, it becomes vulnerable, and vulnerability is precisely what a scientific theory must accept if it is to be more than rhetoric.
Seen this way, empirical economics becomes a discipline of explicit mapping:
- from theoretical primitives to probabilistic implications,
- from probabilistic implications to estimable objects,
- from estimable objects to tests that can genuinely embarrass the model.
This framing also clarifies why econometrics is not reducible to computational competence. A procedure can be technically flawless and yet epistemically irrelevant if it estimates an object that the model does not identify, or if it tests a prediction the model never truly put at risk.
Identification as the Logical Hinge
Haavelmo’s deeper message is that “more data” cannot rescue a model that is not identified. Identification is not a statistical nicety. It is a logical precondition for learning from evidence.
Identification as Non-Observational Equivalence.
Let the population distribution of observables be \(P\), and let the model imply the set \(\{P_\theta:\theta\in\Theta\}\). The parameter \(\theta\) is (point) identified if
\[ P_\theta = P_{\theta'} \ \Rightarrow\ \theta = \theta'. \]
If distinct parameter values generate the same observable distribution, they are observationally equivalent, and no amount of data can logically distinguish them.
This definition is deliberately austere. It strips away estimation methods and focuses on what must be true before estimation even becomes meaningful. If the mapping \(\theta \mapsto P_\theta\) is not injective, then the enterprise is not “hard.” It is ill-posed.
A subtlety that matters in practice is that identification can be local rather than global. A model may be identified “near the truth” yet admit multiple observationally equivalent explanations elsewhere in parameter space. This is not an esoteric worry. It is precisely the sort of fragility that makes some structural claims persuasive in a narrow domain and fragile outside it.
Identification is therefore not simply a property of a dataset. It is a property of a model relative to a data environment. It is the place where theoretical restrictions meet empirical reality, and where scientific ambition becomes either coherent or performative.
A Minimal Identification Parable: Why Equilibrium Data Do Not Reveal a Demand Curve
Consider the textbook market system:
\[ Q^d = \alpha - \beta P + u_d, \qquad \beta>0, \]
\[ Q^s = \gamma + \delta P + u_s, \qquad \delta>0, \]
\[ Q^d = Q^s = Q. \]
Solving for equilibrium price yields:
\[ P = \frac{\alpha-\gamma + (u_d-u_s)}{\beta+\delta}. \]
If you observe only equilibrium outcomes \((P,Q)\), variation in price is not an exogenous movement along a demand curve. It is a composite movement driven by both demand and supply shocks. The naive regression of \(Q\) on \(P\) does not identify \(-\beta\). It estimates a reduced-form mixture determined by the joint distribution of \((u_d,u_s)\) and the system’s structural parameters.
The deeper lesson is not merely that “price is endogenous.” It is that equilibrium collapses multiple mechanisms into a single observational object. Without a defended source of variation that isolates one structural margin, the model cannot tell you which parameter you are learning.
Identification arrives only when you can defend variation that shifts one equation while leaving the other unchanged. Suppose you have a cost shifter \(Z\) that enters supply but not demand:
\[ Q^s = \gamma + \delta P + \pi Z + u_s, \qquad \pi\neq 0. \]
Then \(Z\) induces price movements through supply, while holding demand fixed. Under an exclusion restriction and an exogeneity claim, the demand slope becomes an identifiable object.
This is why instrumental variables is best understood not as a “bias correction trick,” but as a logical device for restoring distinctness between structural objects that equilibrium data entangle.
The methodological point is general:
A model becomes empirically meaningful only when it implies an identifiable mapping from theoretical parameters to observable distributions.
From Identification to Information Content: Why Restrictions Matter
Haavelmo’s framework also clarifies a connection that applied work often leaves implicit: restrictions are information.
A restriction is informative because it rules out data patterns. Exclusion restrictions, functional-form commitments, monotonicity conditions, independence assumptions, timing assumptions, and invariance claims each carve away parts of the space of possible joint distributions.
Some restrictions are partially testable. Overidentifying restrictions, when multiple instruments exist, can generate coherence conditions that are at least probeable. Other restrictions are not directly testable in finite samples, but they still have empirical consequences, and those consequences can sometimes be challenged indirectly through falsification tests, sensitivity analyses, and external validation.
The deeper methodological point is that scientific seriousness is not a matter of how many assumptions a model contains. It is a matter of whether the assumptions generate nontrivial implications and whether the economist is willing to expose those implications to criticism.
Structural Versus Reduced Form: What Econometrics Is Really Choosing Between
Haavelmo’s probability turn also clarifies a fork that later defines econometric practice.
A structural model targets parameters with mechanistic interpretation, intended to travel into counterfactual worlds. It buys counterfactual reach by paying upfront in assumptions, often assumptions about preferences, technology, information, and equilibrium behavior.
A reduced-form relation targets stable predictive regularities. It typically avoids deep commitments about the mechanism and pays instead in scope. Reduced-form results often come with an implicit modesty: the estimate is local to a design, a population, and a regime.
Neither approach is philosophically pure. Both can be rigorous. The difference is where the burden of justification lies.
- Structural work must defend invariance under intervention.
- Reduced-form work must defend stability over the intended domain of use.
This difference becomes decisive in policy evaluation, especially when the policy itself changes behavior, constraints, or expectations. It is precisely here that later critiques, most famously the Lucas critique, sharpened the methodological stakes.
Measurement Without Theory, and Theory Without Measurement
The next methodological conflict was internal to empirical work itself.
On one side stood the NBER tradition: careful measurement, patient documentation of regularities, and a certain empiricist humility. On the other side stood the Cowles tradition: structural modeling, simultaneous equations, and inference guided by explicit theory.
Koopmans’s complaint, often summarized as “measurement without theory,” was fundamentally about scientific cumulation. Without theoretical scaffolding, measurement risks becoming archival. It can describe with exquisite care and still fail to explain.
Yet the counter-complaint is equally severe. Theory without credible measurement risks becoming a closed symbolic enterprise. It may be internally impeccable and still fail to encounter the world in a way that could falsify its commitments.
Modern economics still lives inside this tension. The best work treats it not as an embarrassment but as a productive dialectic: description motivates mechanism, mechanism generates risky implications, and those implications force measurement to become sharper.
Friedman’s “As If” Defense: A Re-Ranking of Scientific Virtues
Milton Friedman’s methodological essay redirected the discipline’s attention from the realism of assumptions to the performance of a model’s testable implications. It is often caricatured as “assumptions can be false.” A more disciplined reading is that Friedman proposed a re-ranking of scientific virtues.
Models are not evaluated as literal descriptions of cognition. They are evaluated by whether their implications survive discriminating confrontation with data, especially in comparison to rival models.
A natural way to strengthen Friedman’s position is to connect “as if” to the notion of information content. A serious model compresses an unruly world into a small set of assumptions. The question is not whether those assumptions photograph reality. The question is whether the compression preserves the structure that matters for prediction within the model’s intended domain.
Under this reading, Friedman is not licensing laziness. He is proposing competition under empirical discipline: theories are selected not by metaphysical realism but by their ability to generate nontrivial, resilient implications.
Untwisting the F-twist
Later philosophy of economics sharpened the debate by refusing to treat “unrealistic assumptions” as a single category. Some assumptions are:
- negligibility assumptions, setting small forces to zero,
- domain assumptions, restricting scope rather than describing the world,
- heuristic assumptions, scaffolding that supports exploration and is later replaced.
Distinguishing these categories makes methodological criticism precise. It also clarifies why economists can rationally keep some stylizations while rejecting others. The relevant question becomes: does the assumption merely simplify, or does it do substantive work that is empirically consequential?
The Boundary Problem Returns: What Prevents Curve Fitting?
If a model is a stochastic generator, and if assumptions are not literal descriptions, why is econometrics not merely curve fitting?
The most serious answer is procedural. It is a practice: increase the difficulty of survival.
- defend identification, not just statistical significance,
- separate exploration from evaluation when possible,
- use out-of-sample validation when prediction is the goal,
- run placebo tests and falsification checks when causal interpretation is the goal,
- demand robustness that targets plausible failure modes rather than cosmetic variations.
This is a methodological pivot away from treating empirical work as a search for definitive verification and toward treating it as a disciplined practice of criticism. The aspiration is not certainty. It is resilience: claims that survive serious, intelligently designed attempts to break them.
To make that ideal explicit, we need the next philosophical move. We need a logic of risk.
That is where Popper enters.
References
- Haavelmo, T. (1944). The Probability Approach in Econometrics (Cowles Foundation Paper No. 4).
- Keynes, J. M. (1939). “Professor Tinbergen’s Method.”
- Koopmans, T. C. (1947). “Measurement Without Theory.”
- Friedman, M. (1953). “The Methodology of Positive Economics,” in Essays in Positive Economics.
- Rothenberg, T. J. (1971). “Identification in Parametric Models.”
- Mäki, U. (2000). “Kinds of Assumptions and Their Truth: Shaking an Untwisted F-Twist.”
- Lucas, R. E. Jr. (1976). “Econometric Policy Evaluation: A Critique.”