The P1-TT-EE-P2 Schema in Model Development

Hello! Welcome to your seventh and final lesson in the first module of our course on Popperian realism, tradition, and rationalism.

In our previous lesson, we unpacked Popper's dynamic model of knowledge growth: the evolutionary schema $P_{1} \to TT \to EE \to P_{2}$ . We saw how knowledge advances through an endless cycle of confronting problems with creative, conjectural theories, which are then subjected to rigorous attempts at refutation, leading to new, deeper problems.

Today, we will ground this abstract schema in a field you know intimately. We'll see how this framework isn't just a philosopher's theory but a precise and practical description of the work you've done throughout your academic and professional life.

Lesson 7: The Econometrician as a Critical Rationalist

Introduction

Today's lesson directly addresses our final learning outcome for this module: Relate the $P_{1} \to TT \to EE \to P_{2}$ schema to the process of model development in econometrics and statistics.

Your background in economics and statistical science, particularly your MSc work, provides the perfect foundation for this topic. You have spent years building, testing, and refining statistical models. My goal today is not to teach you any new econometrics, but to provide a new philosophical lens through which to view that familiar process. We will re-frame the workflow of econometric modeling—from forming a research question to running diagnostic tests—as a real-world application of Popper's evolutionary epistemology.

This lesson should take you approximately 45 minutes.

The Modeling Workflow: An Unconscious Application of Popper

Most practicing econometricians don't think of themselves as applying a specific philosophy of science, yet the best practices of the discipline align almost perfectly with the principles of critical rationalism. The "specify-estimate-test" cycle that forms the core of applied econometrics is a direct implementation of Popper's schema.

Let's break it down, stage by stage.

1. The Starting Point: An Economic Problem ( $P_{1}$ )

Where does an econometric study begin? Not with a dataset. It begins with a problem ( $P_{1}$ ). This is usually a question derived from economic theory or a puzzle presented by the world. It's a gap in our knowledge that needs filling.

"What is the causal effect of an additional year of schooling on an individual's wages?"
"Does a change in the central bank's interest rate have a measurable impact on inflation and unemployment?"
"Why did our new FX trading algorithm underperform its backtest?" (A problem you may have encountered!)

In each case, the problem is a conflict between ideas: the state of the world as we currently understand it, and the more detailed or accurate understanding we wish to have. This desire for resolution drives the entire inquiry.

2. The Creative Leap: Model Specification as a Tentative Theory ( $TT$ )

How do we answer the economic question? We make a guess. We propose a specific, formal relationship that we believe might describe the underlying reality. This is our Tentative Theory ( $TT$ ), and in econometrics, this takes the form of a model specification.

Consider the classic Mincer equation to answer the question about education and wages. A first attempt might be:

lo g (wage_{i}) = β_{0} + β_{1} educ_{i} + u_{i}

This equation is a bold conjecture. It hypothesizes that:

The relationship is log-linear.
The only relevant variable for explaining wage variance (besides the constant) is education.
The relationship is the same for all individuals $i$ .
All other myriad factors are relegated to a well-behaved, random error term $u_{i}$ .

This is not a statement of fact derived from data; it's a creative and falsifiable theory proposed as a potential solution to $P_{1}$ . You might quickly decide, based on economic theory, that this model is too simple. You propose a more sophisticated one:

lo g (wage_{i}) = β_{0} + β_{1} educ_{i} + β_{2} exper_{i} + β_{3} exper_{i}^{2} + u_{i}

This is simply a new Tentative Theory ( $T T_{2}$ ). It makes different conjectures (e.g., about the non-linear effect of experience) but it is still fundamentally a guess to be tested, not a truth to be verified.

3. The Crucible: Diagnostics as Error Elimination ( $EE$ )

This is the heart of the connection. Once we have our Tentative Theory (the model), we subject it to severe criticism. In econometrics, this is the Error Elimination ( $EE$ ) stage, and it comprises estimation and, most importantly, a battery of diagnostic tests.

Estimation: We use a method like Ordinary Least Squares (OLS) to get specific values for our parameters ( $\hat{β}_{0}, \hat{β}_{1}, ...$ ). This makes our general theory a specific, pointed claim about the world.
Criticism (Diagnostic Testing): The core of error elimination is trying to refute the model. Every diagnostic test is a potential falsifier designed to check if the assumptions required for our estimation to be valid (i.e., for our theory to be a good explanation) hold up.

Think about the standard Gauss-Markov assumptions for OLS. The diagnostic tests are all attempts to see if your theory ( $TT$ ) is contradicted by the evidence:

Hypothesis Testing (t-tests, F-tests): The most basic form of criticism. If economic theory says $β_{1}$ should be positive, but our t-test yields a large p-value, this is a partial refutation. Our conjecture that "education matters in this specific way" has failed the test.
Ramsey's RESET Test: This is a direct attack on the assumption of correct functional form. If this test fails, it's a strong piece of evidence that our linear (or log-linear) conjecture is wrong. We have falsified a core part of our $TT$ .
Breusch-Pagan/White Tests: These test for heteroskedasticity. A significant result refutes the model's assumption of constant error variance, telling us our theory about the error structure is flawed.
Durbin-Watson/Breusch-Godfrey Tests: These test for autocorrelation, attacking the assumption of independent errors. Again, a failure is a refutation of a key part of our model's structure.
Omitted Variable Bias: This is perhaps the most Popperian aspect. A good econometrician is constantly thinking, "What alternative theory could explain this result?" The fear that an unobserved variable (e.g., 'innate ability') is correlated with both education and wages is a conceptual criticism of the simple Mincer model. It's the conjecture of a flaw.

In a Popperian sense, a "good" econometric model is not one that is "proven true," but one that has been subjected to and has survived this barrage of severe and varied attempts at falsification.

4. The Next Frontier: Respecification as the New Problem ( $P_{2}$ )

What happens after error elimination?

Case 1: The Theory is Refuted. Our model fails a key diagnostic test (e.g., we find significant heteroskedasticity). We now have a New Problem ( $P_{2}$ ): "How do I build a model that accounts for this non-constant variance?" This problem drives the next stage of research. The solution might be a new Tentative Theory ( $T T_{n e w}$ ), such as using robust standard errors or specifying a model with Weighted Least Squares (WLS). The cycle $P_{2} \to T T_{n e w} \to E E_{n e w} \to ...$ begins again.
Case 2: The Theory Survives. Our model passes all the tests we can think of. It solves $P_{1}$ . But does the process end? No. A good model always reveals deeper puzzles, a new set of problems ( $P_{2}$ ). For instance, your robust Mincer model might show a statistically significant, but surprisingly small, return to education. Your new problem becomes: "Why is the return to schooling lower than economic theory suggests?" Or perhaps your model gives you a precise estimate, but the new problem is one of external validity: "Does this relationship, estimated on US data from the 1980s, still hold today? Does it hold in a different country?"

The goal of econometrics is not to find the "true" model and stop. It is an endless process of problem-solving, where each well-tested model serves as a stepping stone to a more refined question.

Conclusion

Today we have mapped the familiar workflow of econometric modeling onto Popper's evolutionary schema. This exercise reveals that the principles of critical rationalism are not confined to the history books of philosophy; they are the implicit, practical logic underpinning modern empirical inquiry.

Key Takeaways:

Economic Question as $P_{1}$ : All empirical research begins with a problem, a gap in our theoretical or practical knowledge.
Model Specification as $TT$ : The econometric model is a creative, falsifiable conjecture about the structure of reality, proposed to solve the problem.
Diagnostic Testing as $EE$ : The array of statistical tests we run are not for verifying the model, but for subjecting it to harsh criticism and attempting to refute its underlying assumptions. A "good" model is one that has survived this process.
Respecification as $P_{2}$ : Both refutation (a failed test) and survival (a surprising result from a robust model) lead to new, deeper problems, ensuring that the process of inquiry is a dynamic and unending cycle of progress.

Looking Ahead

In this first module, we have built the foundations of Popper's philosophy of science. In the next module, "The Open Society: Popper, Tradition, and Humility," we will take a significant turn. We will see how Popper applies this very same critical rationalist framework—this preference for bold but testable conjectures, this emphasis on error elimination, and this suspicion of claims to certainty—to the far messier worlds of politics and social organization.

Our first lesson in Module 2 will explore Popper's powerful critique of 'historicism'—the belief, held by thinkers like Marx, that history unfolds according to discoverable laws. We will see that for Popper, such grand theories are not just wrong, but profoundly dangerous.

The P1-TT-EE-P2 Schema in Model Development

Lesson 7: The Econometrician as a Critical Rationalist

The Modeling Workflow: An Unconscious Application of Popper

1. The Starting Point: An Economic Problem (P1​)

2. The Creative Leap: Model Specification as a Tentative Theory (TT)

3. The Crucible: Diagnostics as Error Elimination (EE)

4. The Next Frontier: Respecification as the New Problem (P2​)

Conclusion

1. The Starting Point: An Economic Problem ( $P_{1}$ )

2. The Creative Leap: Model Specification as a Tentative Theory ( $TT$ )

3. The Crucible: Diagnostics as Error Elimination ( $EE$ )

4. The Next Frontier: Respecification as the New Problem ( $P_{2}$ )