Introduction Causality Models Identification Epistemological Concerns Debate Critique

Lecture 1

Economics 2123 – Section 81George Washington University

Instructor: Prof. Ben Williams

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Introduction

Consider a simple regression model:

Yi = β′Xi + εi , i = 1, . . . ,n

What does this “model” mean and where does it comefrom?Supposing the equation and other auxiliary assumptionsconstituting a model hold. When and in what sense can wecome to know β (more generally, the “structure”)?What purpose does knowledge of β (or more generally, the“structure”) serve?

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

What is causality?

That is, when can we say that X causes Y ?

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

In the simple regression model:

Yi = β1Xi1 + . . .+ βK XiK + εi , i = 1, . . . ,n

the causal effect of variable X1 on Y for individual i is

∂Yi/∂Xi1 = β1

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

More generally we do not need an explicit model.Potential outcomes: Yi(x1) – the outcome individual iwould experience if Xi1 were equal to x1.The (individual level) causal effect is then ∂Yi(x1)/∂x1 orYi(x ′

1)− Yi(x1)

The causal effect is the ceteris paribus effect (Marshall,1890).

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

One school of thought appeals to the “experimental ideal”:“...the rise of regression led to a focus on equations foroutcomes, rather than careful thinking about how the datain hand differ from what would have been generated by theideal experiments one might wish to have conducted.”(Morgan and Winship, 2007)“The description of an ideal experiment also helps youformulate causal questions precisely.” (MHE)Heckman (2008) summarizes Rubin (1978), Holland(1986), and Berk et al. (2005) as arguing that “if anexperiment cannot “in principle” be performed, a causaleffect cannot be defined.”

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

Another school of thought emphasizes the role of a model:“The econometric approach to policy evaluation ...emphasizes the provisional nature of causal knowledge. ...human knowledge advances by developing theoreticalmodels and testing them against data. The models usedare inevitably provisional and depend on a prioriassumptions.” (Heckman, 2008)“The crucial difference is that the relationship betweenrailways and poverty is not a model at all...there are manypossible mechanisms..." (Deaton, 2009) He goes on to saythat the role of the analysis is not to uncover a causalmodel but to create a possibly forced analogy to anexperimental ideal.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

Causality is in the mind“... the act of defining a causal effect (is) a purely mentalact..." (Heckman, 2008)“ a cause ... (is) a certain way of thinking, an intellectualtrick ... which has proved itself to be a useful weapon ...the scientific ... problem of causality is essentially aproblem regarding our way of thinking, not a problemregarding the nature of the exterior world.” (Frisch, 1930)

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

Consider the concept of force in physics.Does it “exist” in the world or is it merely a property ordisposition of certain objects in certain situations?I contend (as do some philosophers of science) that it ismerely a mental construct that allows us to understand howdifferent bodies interact in certain well-defined situations.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Causality

My best attempt to understand this is as follows:Are we seeking the “truth” when we ask causal questions?or are we seeking a convincing, reliable way ofunderstanding a particular phenomenon that is consistentwith how we have come to understand similar phenomena?This is controversial!

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

“Models are descriptions of hypothetical worlds.”(Heckman, 2008)“econometric models are metaphors providing differentwindows on a complex and bewildering reality.” (Pesaran,1988)A model is successful if it “fits the data” and “is useful”.(Kennedy, 2003)

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

Three parts of a model:An economic modelAn econometric modelA statistical model

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

Three steps of evaluation (Heckman, 2008):DefinitionIdentificationInference

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

Example: Mincer Model of education and earnings

ln(Y (s, x)) = α + ρs + β0x + β1x2

where Y (s, x) is the hypothetical earnings of an individualwho has completed s years of schooling and has x yearsof work experience.This model comes from an “accounting” model that statesthat an individual’s potential earnings are equal to theirpotential earnings in the previous year plus the return oninvestment in education or on-the-job training.The model makes simplifying assumptions about thenature of on the job training, makes functionalapproximations to get linearity, and several moreassumptions.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

The econometric modelWe observe experience, education and earnings.What constitutes earnings?We add a residual because of (a) heterogeneity and (b)incompleteness of the economic model.What is the relationship between this residual andexperience, schooling?

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Models

The statistical modelWe obtain a sample from, e.g., the Census.What is the sampling design?How large is the sample?Is there clustering?

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

A model is identified if there is only one example of thatmodel that is consistent with the data.More concretely, let θ ∈ Θ be a parameter of the model.Let Pθ denote the hypothetical population distribution of theobserved data. Let P0 denote the actual populationdistribution of the observed data.In this construction, the econometric model tells use howto get a distribution from θ. The model is identified if thereis only one θ ∈ Θ for which Pθ = P0.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

Identification of some parameters but not others.Identification of “features” of the model.Partial identification.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

Example 1:Y = β′X + ε; Y ,X observedThe “parameters” (θ) are the vector β and the conditionaldistribution function Fε|X .The population distribution can be decomposed asFX ,FY |X .

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

Example 1, continued:The model tells us that a hypothetical distribution for Y | Xcan be constructed from any potential pair β,Fε|X :Pr(Y ≤ y | X = x) = Pr(ε ≤ y − β′x | X = x).Assumption 1: E(ε | X ) = 0.This implies that E(Y | X = x) = β′x .If β1 6= β2 then β′1x 6= β′2x (for some values of the vector x).Hence β is identified.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

Example 2:Yt = β′Xt + γ′W + α + εt , Yt ,Xt ,W observed.This implies that Yt − Yt ′ = β′(Xt − X ′

t ) + εt − εt ′

If E(εt − εt ′ | Xt ,Xt ′) = 0 then β is identified, but not γ.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Identification

Identification of causal effects without a model?According to MHE, an identification strategy is the way inwhich the ideal experiment is approximated usingobservational data.The validity of the approximation requires a set ofassumptions that constitute a model.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Epistemological concerns

How do we come to “know” things? (How is scientificknowledge formed?)In a single regression, with respect to a single causalquestion, or generally within the scientific community.A relevant question regardless of how we think of causality,models, laws.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Epistemological concerns

The inductivist tradition uses repeated confirmations of ahypothesis to generalize a causal effect.Knowledge comes from facts; we don’t need theory.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Epistemological concerns

The Popperian tradition rejects a hypothesis when the datacontradicts it but never proves a theory.Definition of science as something that produces falsifiablehypotheses.Better if these hypotheses/predictions are novel.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Epistemological concerns

Auxiliary assumptions, description of experimental setup –when we get a rejection what is rejected?According to Kuhn (1962), scientists work within aparadigm with maintained assumptions. We only reject atheory once sufficient evidence has built up within thescientific community.“The paradigm sets the standards for legitimate work withinthe science it governs.”Crisis, rival paradigms, revolution.charge of relativism

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Structural vs. Program Evaluation

theoretical vs. atheoreticaleconometric vs. statisticalexperimental ideal vs. model-basedHeckman/Deaton vs. Imbens/Angrist

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Structural vs. Program Evaluation

MHE steps to empirical work:causal questionexperimental idealidentification strategyinference

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Structural vs. Program Evaluation

Structural methods require strong assumptions,complicated models/estimation techniques.Actual RCTs aren’t inherently superior in terms of internalvalidity either – they require assumptions too!Atheoretical approaches that use the experiment as ametaphor require strong assumptions as well.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

Structural vs. Program Evaluation

The strength and weakness of the nonstructural approachis that it bypasses the economic modeling step.Avoids bad assumptions such as normality or rationalityIdentification assumptions are harder to motivate.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

A critique of our whole enterprise

Bernard Harcourt, a political theorist, contends that usingprediction in conjunction with sentencing “distorts ourperception of just punishment".This is a criticism you will inevitably face as an empiricaleconomist...and it has some validity.

Economics 2123 – Section 81 George Washington University

Lecture 1

Introduction Causality Models Identification Epistemological Concerns Debate Critique

A critique of our whole enterprise

Ian Hacking (1990) claims that the revolution in datacollection and statistical methods (part of the IndustrialRevolution) fundamentally altered the way we think aboutourselves/the world.It brought about the end of determinism but at the sametime introduced the idea of the “normal” person (and thedeviant).statistical regularities.

Economics 2123 – Section 81 George Washington University

Lecture 1