REVIEW 2 major objections 4 minor 9 references
Philip G. Wright, directed acyclic graphs, and instrumental variables
T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read This editorial argues that Philip Wright's 1928 appendix to The Tariff on Animal and Vegetable Oils already contained the key ingredients of modern causal inference—structural supply and demand equations, moment-based identification of…
desk verdict A transparent, useful editorial that modernizes Wright's 1928 Appendix B; the historical claim is slightly over-stated but not misleading, and the algebraic typo is trivial. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is Wright's structural model of demand and supply, $D(p) = \alpha_1 p + U^d$ and $S(p) = \beta_1 p + U^s$, together with the orthogonality assumptions that identify the elasticities; the paper shows these imply moment conditions such as $E[(Y - \alpha_1 P) Z^s] = 0$ and hence the IV formulas $\alpha_1 = E(Y Z^s)/E(P Z^s)$ and $\beta_1 = E(Y Z^d)/E(P Z^d)$. The companion mechanism is Wright's Figure 10, a causal path diagram (now called a DAG) with nodes for the demand and supply functions, their shifters, the equilibrium price, and the traded quantity; the modernized version adds latent nodes for common causes of the shifters and of the demand and supply functions, which make the encoding of conditional exogeneity explicit. Together these let the authors translate Wright's verbal and graphical argument into a GMM estimation framework with weak-instrument inference.
What would settle it
Compare Wright's original 1928 Figure 10 with the reproduction: if the added latent nodes change which variables are conditionally independent, or if the four corrected formulas originally implied a different ratio than $E(Y Z^s)/E(P Z^s)$, then the appendix was not doing the modern IV argument. A direct check of the original text and data would settle whether the 'corrections' were cosmetic or substantive.
Extended reading notes
Core claim
The paper maintains that Wright's Appendix B simultaneously introduced the structural simultaneous equations framework for demand and supply, solved the identification problem by requiring that demand and supply shocks be orthogonal to the appropriate shifters, and derived the IV ratio $\alpha_1 = E(Y Z^s)/E(P Z^s)$ for the demand elasticity from the induced moment conditions. It further credits Wright with drawing a causal path diagram—reproduced and modernized here as a DAG with observed and latent nodes—to justify the exclusion restrictions, and with using the fitted model to compute the welfare consequences of a tariff. The reproduction presents Wright's text with four corrected mathematical typos and a modernized figure that adds two latent variables to make dependence between shifters and between demand and supply shocks explicit. In the authors' reading, the appendix contains a method-of-moments identification proof, an indirect least squares derivation, and an early counterfactual policy analysis, all taken to actual data on oils and butter.
Load-bearing premise
The historical attribution depends on the reproduction being faithful: the editors corrected four errors in the original mathematical expressions and added two latent variables to Wright's Figure 10, and if those changes alter the identification argument, the claim that Wright's appendix anticipated modern IV and DAG methods is weakened.
Editorial extensions
If this is right
- The history of econometrics should credit Wright's 1928 appendix, not later works, with the first complete IV estimation of a structural model.
- Wright's Figure 10 shows that a simultaneous equations model can be represented as an acyclic causal diagram once latent demand and supply functions are included, not as a cycle.
- The reproduced appendix can serve as a primary teaching text for IV, GMM, and DAG-based identification.
- Wright's tariff counterfactual provides an early template for structural policy evaluation: estimate elasticities from instruments, then simulate a policy shift.
Reading between the lines
- The same reattribution logic could be applied to other early econometric texts, checking whether later textbook derivations of IV formulas were anticipated by earlier path-diagram arguments.
- One could re-estimate Wright's oil and butter elasticities from historical data to see whether his empirical numbers are reproducible, which would test the quality of the original application.
- The acyclical DAG representation of equilibrium suggests a general recipe for drawing simultaneous systems with latent constructs, which may extend beyond supply and demand to any market equilibrium model.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript is an editorial introducing a special issue on Philip G. Wright's 1928 Appendix B to The Tariff on Animal and Vegetable Oils. It claims that Wright made foundational contributions to causal inference: a structural simultaneous-equations model of supply and demand, identification of elasticities via method-of-moments and path-diagram (DAG) reasoning, instrumental-variables estimation using weather shifters, and counterfactual welfare analysis of tariffs. The editorial reconstructs these ideas in modern notation, develops a GMM framework for the demand-and-supply model, discusses weak identification, partialling-out with high-dimensional controls, and connects the material to Pearl's DAG methodology and modern nonparametric IV. Section 6 describes a companion reproduction of Wright's Appendix B and summarizes the other articles in the special issue.
Significance. If the historical claims hold, the paper substantially reframes the origins of IV and DAG-based causal inference, crediting Wright with anticipating modern developments by decades. The editorial's own technical content is clean: the moment-condition derivation of the IV estimator in Section 2, the graphical indirect-least-squares argument, the GMM treatment in Section 4, and the d-separation check in Section 5.1 are all mathematically sound and presented in a way that is useful for teaching. The paper is also transparent about its own editorial choices, explicitly labeling Figure 3 as a generalized version of Wright's Figure 10 and flagging the added latent nodes K1 and K2. The main risk is calibration of the historical attribution: the strongest claims rest on the companion reproduction of Appendix B, which is not part of this arXiv posting, and the modern d-separation reasoning is an editorial extension rather than demonstrably Wright's own argument.
major comments (2)
- [Section 3, displayed tariff revenue equation] The equation following the consumer-surplus expression is algebraically incorrect. With ΔP = cτ and ΔY = α1ΔP, the display τ + (ΔY + ΔP + ΔY ΔP)τ = τ + c(1+α1)τ² + c³α1²τ³ is wrong: the cubic term should be α1 c² τ³, not c³ α1² τ³. Moreover, the supporting approximation (Rev*−Rev)/Rev ≈ ΔP + ΔY + ΔP ΔY does not follow from the exponential expansion e^{ΔP+ΔY}−1; to second order in τ the correct coefficient of τ² is c²(1+α1)²/2. This error propagates into the approximate optimal-tariff calculation that follows. Please correct the algebra and state explicitly the order of the approximation used in the welfare analysis.
- [Abstract and Section 1; Section 5.1] The abstract and Section 1 state that Wright 'established the identification of supply and demand elasticities via the method of moments and directed acyclical graphs.' The evidence for this attribution is the companion reproduction of Appendix B and the editorial's Figure 4, which is described as 'a version' of Wright's Figure 10. However, the d-separation argument in Section 5.1 is run on Figure 3, which explicitly adds latent nodes K1 and K2 that are not present in Wright's original figure. Consequently, the conditional exogeneity condition (5.1) is a property of the editorial's generalization, not of Wright's original graph. To avoid over-attribution, please state clearly that the modern d-separation analysis is an editorial reconstruction, and identify which specific equations or figures in the companion reproduction support the claim that Wright himself established identification via path diagrams.
minor comments (4)
- [Section 5.1, factorization display] The factorization includes the term f(w,k1). If the augmented DAG is intended to have the edge K1→W as suggested in the note to Figure 3, the factorization should write f(w|k1)f(k1); as written, the joint term is ambiguous about the assumed directed relationship between K1 and W.
- [Section 1, opening paragraphs] There are several stray spaces in the typeset text, for example 'W right' in the first paragraph and in the Wright (1915) citation. Please run a proofreading pass for these typographical artifacts.
- [Section 6] The editorial states that four 'obvious and potentially confusing errors' in Wright's Appendix B were corrected, but it does not list them. Since the companion reproduction's title page may not be available to all readers of the editorial, summarizing the corrections in a footnote would improve transparency.
- [Figure 4 note] The note to Figure 4 describes path coefficients such as -α1/(β1-α1) and β2/(β1-α1) in words, but the figure itself apparently does not display these labels. Please either label the coefficients in the figure or state explicitly that these labels appear in Wright's original Figure 10.
Circularity Check
No circularity: the editorial's historical claims rest on the reproduced primary source and standard econometric exposition, not on fitted inputs or on load-bearing self-citation.
full rationale
The paper does not present a new empirical or statistical derivation whose output is built into its own inputs. Section 2 states Wright's moment conditions directly from his orthogonality assumptions and algebraically solves for the IV formulas; these are reproductions of Wright's identification argument, not fitted parameters renamed as predictions. Section 4's GMM analysis is standard estimator algebra applied to the same moment conditions, and Section 5.1's d-separation discussion is an interpretive gloss on Wright's graph, not a claim that the graph proves something beyond its stated assumptions. The paper's central assertion is historical: that Wright's Appendix B anticipated IV and DAG-based identification. That assertion is supported by the reproduced appendix and by external historical scholarship; it is not supported by a self-citation chain. The few self-citations (e.g., Chernozhukov et al. 2015a,b; 2018; Chen et al. 2014) appear in Sections 4.3 and 5.2 as standard references for machine-learning and nonparametric methods, and none bears the load of the historical attribution. The editorial's own disclosure in Section 6 that it 'corrected four obvious and potentially confusing errors' and added latent nodes in Figure 3 is a transparency note that could weaken the historical claim, but it is a verification concern rather than circular reasoning. The derivation chain is therefore self-contained with respect to the paper's own contributions, and the appropriate score is 0.
Assumptions & free parameters
assumptions (4)
- ad hoc to paper The source text and figures of Wright's (1928) Appendix B are reproduced faithfully, apart from the four stated corrections and minor typographical changes.
- domain assumption Philip G. Wright, not Sewall Wright, authored Appendix B.
- ad hoc to paper The DAG modernization in Figure 3, with latent function nodes for demand and supply and latent factors K1 and K2, preserves the identification content of Wright's Figure 10.
- standard math Standard GMM asymptotic theory, regularity conditions, and d-separation criteria are invoked without proof.
invented entities (1)
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Latent factors K1 and K2 in Figure 3
Cite this review
Pith. "Pith review of Philip G. Wright, directed acyclic graphs, and instrumental variables." pith.science (2026). https://pith.science/paper/WB5PYWEL
@misc{pith2026250116395,
author = {Pith},
title = {Pith review of: Philip G. Wright, directed acyclic graphs, and instrumental variables},
year = {2026},
howpublished = {\url{https://pith.science/paper/WB5PYWEL}},
note = {Machine review of arXiv:2501.16395}
}
read the original abstract
Wright (1928) deals with demand and supply of oils and butter. In Appendix B of this book, Philip Wright made several fundamental contributions to causal inference. He introduced a structural equation model of supply and demand, established the identification of supply and demand elasticities via the method of moments and directed acyclical graphs, developed empirical methods for estimating demand elasticities using weather conditions as instruments, and proposed methods for counterfactual analysis of the welfare effect of imposing tariffs and taxes. Moreover, he took all of these methods to data. These ideas were far ahead, and much more profound than, any contemporary theoretical and empirical developments on causal inference in statistics or econometrics. This editorial aims to present P. Wright's work in a more modern framework, in a lecture note format that can be useful for teaching and linking to contemporary research.
Figures
Reference graph
Works this paper leans on
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[1]
WRIGHT’S SYSTEM OF DEMAND AND SUPPLY EQUATIONS We begin with a stochastic model of demand and supply for a given com modity. Consider the system D(p) := α1p + U d and S(p) := β1p + U s, (1.1) where D(p) denotes the (log) quantity demanded at the (log) price level p, S(p) denotes the (log) quantity supplied at the (log) price level p, and the random variab...
work page Pith review arXiv 1915
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[2]
WRIGHT’S IDENTIFICATION ARGUMENTS Here we simplify the arguments to get back to the original formulatio n of Wright. We assume that there is no W (or that it has been partialed out, as we do in the next section), and that Z d and Z s are scalar random variables. The crux of Wright’s method lies in the realization that the following moment conditions hold ...
work page 1928
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[3]
Here, we consider a simplified setting where all producers are foreign and consumers ar e domestic
COUNTERF ACTUALS UNDER TAX INTER VENTIONS Wright motivated the importance of the structural model (1.1) wit h an analysis of hy- pothetical policies such as the imposition of a tariff on imports. Here, we consider a simplified setting where all producers are foreign and consumers ar e domestic. 11 We also work with a log-linear system, whereas Wright used a...
work page 2009
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[4]
ANALYSIS OF WRIGHT’S MODEL VIA THE GENERALIZED METHOD OF MOMENTS In what follows it will be convenient to partial out some variables. To s et this up, we define a partialing-out operator that acts on any square integrab le variable V subtracting the best linear predictor L(V | M ) := M ′(EM M′)−EM V of V on M , and creating the population residual: 17 ˜V1 ...
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[5]
Set k = 1 , ˆA = ˆΩ −1, for block diagonal ˆΩ with top-left block En ˜Z s 1 ˜Z s′ 1 and bottom- right block En ˜Z d 2 ˜Z d′ 2 , and obtain ˆθ0 using (4.6)
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[6]
Set ˆA = ˆΩ −1, for ˆΩ = ˆVar(√nˆg(θ))|θ= ˆθk− 1 , and obtain ˆθk using (4.6)
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[7]
Repeat the previous step for k = 2, . . . , K. Report ˆθK as the estimator of θ0. Editorial 13 Note that Step 1 returns the conventional two-stage least squa res estimators. In step 2, we need to specify an estimator of Ω; under i.i.d. sampling we can use ˆVar(√nˆg(θ)) = Vng(Xi, θ) := Eng(Xi, θ)g(Xi, θ)′− Eng(Xi, θ)Eng(Xi, θ)′. For dependent data, we can ...
work page 1996
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[8]
SOME CONNECTIONS TO CONTEMPORARY WORK 5.1. Structural causal models and DAGs Judea Pearl’s work on causal DAGs and structural causal models is quintessential in modern causal inference. He has made several fundamental con tributions. One key con- tribution is to formally define causal DAGs as Markov networks repr esenting the joint distribution of variable...
work page 2009
Show all 9 references
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[9]
We have newly typeset the text, including its graphs and table
OUTLINE OF THE SPECIAL ISSUE The first article following this editorial is our reproduction of Wright’s (1928) Appendix B. We have newly typeset the text, including its graphs and table. Alo ng the way, we have corrected four obvious and potentially confusing errors in its math...
1928 arXiv
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