INDUSTRIAL POLICIES IN PRODUCTION NETWORKS& · Many developing economies adopt industrial policies to se-lectively promote economic sectors: Japan from the 1950s to the 1970s, South

INDUSTRIAL POLICIES IN PRODUCTION NETWORKS∗

ERNEST LIU

Many developing economies adopt industrial policies favoring selected sec-tors. Is there an economic logic to this type of intervention? I analyze industrialpolicy when economic sectors form a production network via input-output linkages.Market imperfections generate distortionary effects that compound through back-ward demand linkages, causing upstream sectors to become the sink for imperfec-tions and have the greatest size distortions. My key finding is that the distortionin sectoral size is a sufficient statistic for the social value of promoting that sector;thus, there is an incentive for a well-meaning government to subsidize upstreamsectors. Furthermore, sectoral interventions’ aggregate effects can be simply sum-marized, to first order, by the cross-sector covariance between my sufficient statis-tic and subsidy spending. My sufficient statistic predicts sectoral policies in SouthKorea in the 1970s and modern-day China, suggesting that sectoral interventionsmight have generated positive aggregate effects in these economies. JEL Codes:C67, O11, O25, O47.

I. INTRODUCTION

Many developing economies adopt industrial policies to se-lectively promote economic sectors: Japan from the 1950s to the1970s, South Korea and Taiwan from the 1960s to the 1980s,and modern-day China. One of the oldest problems in economicsis understanding how industrial policies can facilitate economicdevelopment (Hirschman 1958).

In this article, I provide the first formal analysis of the eco-nomic rationale behind industrial policies in the presence of cross-sector linkages and market imperfections. My key finding is thatthe effects of market imperfections accumulate through what I callbackward demand linkages, causing certain sectors to become thesinks for market imperfections and thereby creating an incentivefor well-meaning governments to subsidize those sectors. Within

∗Previously circulated under the title “Industrial Policies and Economic De-velopment.” I am indebted to Daron Acemoglu and Abhijit Banerjee for their con-tinuous guidance and support, and I thank Chad Jones, Daniel Green, NathanielLane, Atif Mian, Ezra Oberfield, Michael Peters, Nancy Qian, Dani Rodrik, RichardRogerson, Jesse Shapiro, and Aleh Tsyvinski for detailed feedback. I also thankmany seminar participants for their insights and Nathaniel Lane for graciouslysharing the input-output table of South Korea.C© The Author(s) 2019. Published by Oxford University Press on behalf of Presidentand Fellows of Harvard College. All rights reserved. For Permissions, please email:[email protected] Quarterly Journal of Economics (2019), 1883–1948. doi:10.1093/qje/qjz024.

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1884 THE QUARTERLY JOURNAL OF ECONOMICS

the networks literature, the sectors in which imperfections ac-cumulate are typically designated as “upstream,” meaning theysupply to many other sectors and use few inputs from other sec-tors. In the data, the sectors considered upstream correspond withthe same sectors policy makers seem to view as important tar-gets for intervention in historical South Korea and modern-dayChina,1 and my analysis suggests that industrial policies in theseeconomies may have generated positive aggregate effects.

To develop my results, I embed a generic formulation of mar-ket imperfections into a canonical model of production networks.Market imperfections represent inefficient, nonpolicy features ofthe market allocation, such as financial and contracting frictions.These features generate deadweight losses with input use, rais-ing effective input prices and production costs. The distortionaryeffects lead to misallocation of resources across sectors, therebycreating room for welfare-improving policy interventions.

Consider the problem faced by a government with limitedfiscal capacity, one that cannot directly remove all imperfectionsbut can only selectively intervene and subsidize sectoral produc-tion. Which sector should be promoted first? This is not easy toanswer, either conceptually or empirically. First, distortionary ef-fects of imperfections compound through input-output linkages;consequently, subsidizing the most distorted sectors might notimprove efficiency, and policy prescriptions need to incorporatenetwork effects. Second, because input-output structures are notnecessarily invariant to interventions, policy prescriptions couldbe sensitive to structural assumptions on aggregate productiontechnologies. Finally, policy prescriptions might depend on theseverity of market imperfections, which are difficult to measure.

My analysis tackles these difficulties. My first result showsthat starting from a decentralized, no-intervention economy, poli-cies can be guided by a simple measure I call “distortion central-ity.” This measure integrates all distortionary effects of marketimperfections in the production network and is a nonparametricsufficient statistic for the marginal social value of policy subsidiesin each sector. A well-meaning government should prioritize fundstoward sectors with high distortion centrality.

1. Public documents from interventionist governments often explicitly statethat “network linkages” are a criterion for choosing sectors to promote; see Li andYu (1982), Kuo (1983), and Yang (1993) for Taiwan; Kim (1997) for Korea; StateDevelopment Planning Commission of China (1995) for China.

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INDUSTRIAL POLICIES IN PRODUCTION NETWORKS 1885

Formally, distortion centrality is the ratio between sectoralinfluence and the Domar weight. Influence is a local notion ofimportance and optimal sectoral size; it captures the aggregateeffect of marginally expanding sectoral resources. The Domarweight, on the other hand, captures equilibrium sectoral size andis thus the cost of proportionally promoting a sector. Subsidizinginfluential sectors brings great benefits, and subsidizing large sec-tors is costly; hence, the ratio—distortion centrality—captures themarginal social value of policy expenditure. Distortion centralityis a nonparametric sufficient statistic—additional features of pro-duction technologies are irrelevant—because, starting from theno-intervention economy, policy-induced network changes haveonly second-order effects on the aggregate economy.

Sectors with the highest distortion centrality are not neces-sarily the most distorted ones, nor are they the largest or mostinfluential. Instead, they tend to be upstream sectors that sup-ply inputs, directly or indirectly, to many distorted downstreamsectors. This is because the distortionary effects of imperfectionsaccumulate through backward demand linkages. Imperfectionscause less-than-optimal input use, thereby depressing the re-sources used by the input suppliers, which in turn purchase lessfrom their own input suppliers. The effects keep transmitting up-stream through intermediate demand, and, as a result, the mostupstream sector becomes the sink for all market imperfectionsand thus has the highest distortion centrality. The distinctionsbetween distortion centrality and other notions of importance aresubstantive, as promoting large, influential, or very distorted sec-tors can indeed amplify—rather than attenuate—market imper-fections and therefore lead to aggregate losses.

In an efficient economy, distortion centrality is identically 1,and there is no role for intervention. With market imperfections,as I show, distortion centrality averages to 1 across sectors; thus,uniformly promoting all sectors generates no aggregate gains. Ef-fective interventions must disproportionally allocate policy fundsto sectors with high distortion centrality. My second result showsthat, to first order, the aggregate general equilibrium effect ofselective interventions can be succinctly captured by the covari-ance between each sector’s distortion centrality and governmentspending on sectoral subsidies. This simple formula enables non-parametric evaluation of sectoral interventions’ aggregate effectsusing cross-sector variation in policy spending.

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In a general production network, distortion centrality de-pends on market imperfections, which are challenging to esti-mate. Indeed, a leading criticism of industrial policies is that gov-ernments have difficulty identifying market imperfections (Packand Saggi 2006). Yet precisely because imperfections accumulatethrough backward linkages, I show that if the network follows a“hierarchical” structure—one where sectors follow a pecking or-der so that upstream sectors supply a disproportionate fraction ofoutput to other relatively upstream sectors—then distortion cen-trality is insensitive to underlying imperfections. In hierarchicalnetworks, distortion centrality tends to align with the “upstream-ness” measure proposed by Antras et al. (2012).

I apply my theoretical results and empirically examine theinput-output structures of South Korea during the 1970s andmodern-day China, because these are two of the most salienteconomies with interventionist governments that actively imple-ment industrial policies. I first show that in these economies, pro-ductive sectors closely follow a hierarchical structure, and mytheory suggests that distortion centrality should be insensitiveto underlying market imperfections. To empirically verify this, Iestimate market imperfections using a variety of strategies basedon distinct assumptions, pushing available data in as many direc-tions as possible. To complement the estimation strategies, I ran-domly simulate imperfections from a wide range of distributions.My results show that distortion centrality is almost perfectly cor-related across all specifications, and correlates strongly with themeasure of Antras et al. (2012), thereby validating that distor-tion centrality is largely driven by variations in these economies’hierarchical network structure and is insensitive to underlyingimperfections.

I then evaluate sectoral interventions in these economies. Ishow that the heavy and chemical manufacturing sectors pro-moted by South Korea in the 1970s are upstream and have signif-icantly higher distortion centrality than nontargeted sectors. Inmodern-day China, non-state-owned firms in sectors with higherdistortion centrality have significantly better access to loans, re-ceive more favorable interest rates, and pay lower taxes; thesesectors also tend to have more state-owned enterprises, to whichthe government directly extends credit and subsidies. These pat-terns survive even after controlling for a host of other potential,nonnetwork motives for state intervention. My sufficient statis-tics reveal that, to first order, differential sectoral interest rates,

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tax incentives, and funds given to state-owned firms have all gen-erated positive aggregate effects in China. Using estimates basedon firm-level data, these policies together improve aggregate effi-ciency by 6.7%. I also perform various policy counterfactuals.

To be clear, my findings by no means suggest that these gov-ernments’ economic policies were optimal, as my main resultscapture only the first-order effects of interventions. Furthermore,my analysis does not address the decision process behind thesepolicies, as the model abstracts away from various political econ-omy factors that affect policy choices in these economies (Krueger1990; Rodrik 2008; Lane 2017). Nevertheless, the predominantview is that industrial policies tend to generate resource misallo-cations and harm developing economies (e.g., see Krueger 1990;Lal 2000; Williamson 1990, 2000; and the survey by Rodrik andWorld Bank 2006). Yet, my findings challenge this view by show-ing there may be an economic rationale behind certain aspectsof the Korean and Chinese industrial strategy, and these policiesmight have generated positive network effects.

The literature on industrial policies reaches back toRosenstein-Rodan (1943) and Hirschman (1958). More recently,Song, Storesletten, and Zilibotti (2011) study resource reallocationbetween state-owned enterprises and private firms during China’srecent economic transition. Itskhoki and Moll (2019) study opti-mal Ramsey policies in a multisector growth model with financialfrictions. Also related is Aghion et al. (2015), who show that Chi-nese industrial policy increases productivity growth by fosteringcompetition. These papers do not consider input-output linkages,which are the focus of my study. In contemporaneous work, Lane(2017) empirically studies South Korea’s industrial policies dur-ing the 1970s through the lens of a production network and findsthat sectors downstream of promoted ones experienced positivespillovers. Rather than focusing on cross-sector spillovers, I theo-retically and empirically analyze the general equilibrium effectsof interventions on the aggregate economy. The first-order na-ture of my policy analysis relates to an older body of literature,including Hatta (1977), Ahmad and Stern (1984, 1991), Deaton(1987), and Dixit (1985), regarding marginal policy reforms in thedifferent context of commodity taxation. More broadly, my arti-cle contributes to a large literature on the aggregate implicationsof micro imperfections, including seminal work by Restuccia andRogerson (2008), Hsieh and Klenow (2009), and other important

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studies, such as Banerjee and Duflo (2005), Banerjee and Moll(2010), Buera, Kaboski, and Shin (2011, 2015), Midrigan and Xu(2014), Rotemberg (2018), and Cheremukhin et al. (2015, 2016)among many others.

Methodologically, my article builds on the production net-works literature. Papers on efficient networks include Hulten(1978), Acemoglu et al. (2012), Acemoglu, Akcigit, and Kerr(2016), Acemoglu, Ozdaglar, and Tahbaz-Salehi (2017), andBaqaee and Farhi (2019); on inefficient networks, see Bartelmeand Gorodnichenko (2015), Caliendo, Parro, and Tsyvinski (2017),Grassi (2017), Altinoglu (2018), Baqaee (2018), Boehm (2018),and Boehm and Oberfield (2019), among others.2 Particularlyrelated to my theoretical results are works that study propertiesof inefficient networks with generic “wedges,” including Jones(2011, 2013), and Bigio and La’O (2019), who study Cobb-Douglasnetworks, and, more recently, Baqaee and Farhi (forthcoming),who study nonparametric and CES networks. Unlike thesepapers, I separate “wedges” into market imperfections and policysubsidies, and I study the impact of subsidies taking preexistingimperfections as given. My theoretical contribution starts withthe novel discovery that, by modeling payments associated withimperfections as quasi-rents, the ratio between influence andDomar weights—what I call “distortion centrality”—is an ex ante,nonparametric sufficient statistic that predicts the aggregateimpact of introducing subsidies to the decentralized economy.This sufficient statistic provides an empirically feasible way toevaluate, ex ante, the aggregate impact of sectoral interventionsin production networks. By contrast, the nonparametric results inBaqaee and Farhi (forthcoming) are ex post in nature, requiringallocations to be measured from both the pre- and postshockeconomies. Those results are therefore useful for ex post account-ing but cannot be used for policy evaluation and prescription.

II. MODEL

There is a composite production factor L in fixed supply anda numeraire consumption good that is endogenously produced.

2. Also see Long and Plosser (1983), Horvath (1998, 2000), Dupor (1999), Shea(2002), Atalay (2017), and Oberfield (2018). For the active literature on input-output linkages and international trade, see di Giovanni and Levchenko (2010),Antras et al. (2012), Chaney (2014), Caliendo and Parro (2014), Carvalho et al.(2016), Antras and de Gortari (2017), Kikkawa, Magerman, and Dhyne (2017),Redding and Rossi-Hansberg (2017), and Auer, Levchenko, and Saure (2019).

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There are N intermediate goods; each is used as a production inputfor both the consumption good and other intermediate goods. Theaggregator for the consumption good is

(1) Y G = F (Y1, · · · , YN),

where Y1 is the intermediate good i used for consumption. Inter-mediate good i is produced by

(2) Qi = zi Fi

(Li,

{Mij

}Nj=1

),

where Li is the factor used by sector i, zi is the Hicks-neutralsectoral productivity, and Mij is the amount of intermediate goodj used by sector i. I assume production functions {Fi} and F arecontinuously differentiable, increasing and concave in arguments,and exhibit constant returns to scale.

II.A. Market Imperfections and Policy Interventions

I introduce market imperfections into the economy, and Istudy how policy interventions can affect aggregate efficiency, tak-ing imperfections as given.

Market imperfections represent inefficient and nonpolicy fea-tures that affect the market allocation, including transactioncosts, financial frictions, and contracting frictions; they can alsoarise from production externalities and monopoly markups. Suchimperfections are modeled as reduced-form “wedges” χ and havetwo properties. First, market imperfections raise input prices: forevery dollar of good j that producer i buys, he must make an ad-ditional payment that is χ ij � 0 fraction of the transaction value.Second, these payments represent “quasi-rents,” meaning they arecompeted away and can be seen as deadweight losses that leavethe economy in terms of the consumption good.

Importantly, market imperfections do not represent govern-ment interventions, which are separately modeled as productionsubsidies represented by τ . My goal is to analyze how policy inter-ventions τ affect aggregate efficiency, taking market imperfectionsχ as given.

In what follows, I use financial frictions as a runningnarrative for market imperfections, motivated by financialfrictions’ well-documented importance in developing countries(Banerjee and Munshi 2004; Banerjee and Duflo 2005; Banerjeeand Moll 2010; Buera, Kaboski, and Shin 2011). A more elaborated

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microfoundation is provided in Online Appendix A.2, where I alsoshow that imperfection wedges χ with the aforementioned twofeatures can be microfounded by various other imperfections, in-cluding monopoly markups (with profits dissipated by entry), con-tracting frictions, and externalities.

1. Producer Problem. Suppose market imperfections arisebecause seller j requires each buyer i to pay a fraction δij of trans-action value up front. Buyers can achieve this by borrowing work-ing capital, which carries an interest rate λ. Effectively, for everydollar producer i spends on input j, he must pay χ ij ≡ λδij dollarsto a lender. These interest payments raise producer i’s productioncosts. On the other hand, producer i also receives governmentsubsidies τ ij and τ iL proportional to input expenditures. Produc-ers otherwise behave competitively, and equilibrium prices solvethe following cost-minimization problem:

Pi ≡ min�i ,{mij}N

j=1

⎛⎝

N∑j=1

(1 − τi j + χi j

)Pjmij + (1 − τiL) W�i

⎞⎠

s.t. zi Fi

(�i,

{mij

}Nj=1

)� 1,(3)

where Pi is the market price of good i and W is the factor price.

2. Imperfections Generate Deadweight Losses. Lenders re-ceive interest payments in proportion to loan size but incur thedisutility cost of financial monitoring to ensure loan repayment.Interest rates are competitive, and lenders’ interest income ex-actly compensates disutility costs; hence, after spending incomeon consumption, lenders earn zero net utility. The interest pay-ments can thus be seen as deadweight losses that leave the econ-omy via the consumption good. Payments made by producer i are∑N

j=1 χi j Pj Mij , and the total deadweight losses in the economy are

(4) � ≡N∑

i=1

N∑j=1

χi j Pj Mij .

For accounting purposes, I assume these payments are alwaysincurred by intermediate buyers and that using factor inputsdoes not generate deadweight losses, so that factor endowment Laccurately represents the total resources in the economy.

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Misallocation over factor inputs can always be modeled by eitherrelabeling or adding fictitious producers to the economy.

3. Price Normalization. To focus on imperfections and in-terventions in the intermediate goods network, I assume the con-sumption good is produced without any wedges. Price normaliza-tion implies

(5) 1 ≡ min{Yj}N

j=1

N∑j=1

PjYj s.t. F (Y1, · · · , YN) = 1.

II.B. Government Interventions

Policy interventions are modeled as sector-input-specific pro-duction subsidies

{τi j, τiL

}Ni, j=1 paid by the government. Let Si de-

note the total policy expenditure in sector i:

(6) Si ≡N∑

j=1

τi j Pj Mij + τiLW Li.

Besides policy interventions, the government also has real ex-penditure G, which represents public consumption. To balanceits budget, the government charges lump-sum taxes T from theconsumer:

G +N∑

i=1

Si = T . (Government Budget Constraint)(7)

1. Consumer. The representative consumer spends posttaxfactor income on consumption C:

C = W L − T . (Consumer Budget Constraint)(8)

II.C. Aggregation

The expenditure accounting identity follows:

Y G − � ≡ Y = C + G. (expenditure accounting identity)(9)

The identity states that YG, the gross output of the consump-tion good, is equal to the sum of private, public, and lenders’consumption (C, G, and �). Since lenders earn zero utility and

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their consumption � is seen as deadweight loss, I refer to thesum of private and public consumption Y = C + G as “aggregateconsumption” or, simply, “output.” Y is the aggregate variable ofinterest in my analysis.

The income accounting identity is obtained by substitutingbudget constraints (7) and (8) into equation (9):

Y = W L −N∑

i=1

Si. (income accounting identity)(10)

The identity states that the output Y is equal to total factor incomenet of policy expenditures.

DEFINITION 1. Given productivities zi, market imperfections χ ij �0, subsidies {τ ij, τ iL}, and public consumption G, an equi-librium is the collection of prices {Pi, W}, allocations {Qi,Li, Mij, Yi, YG, Y, C}, lump-sum taxes T, and quasi-rents�, such that (i) producers choose allocations to solve cost-minimization problems (3) and (5), setting prices to produc-tion costs; (ii) government and consumer budget constraints(7) and (8) are satisfied; (iii) the income accounting identity(10) holds; and (iv) markets for the factor and intermediategoods clear: L = ∑N

i=1 Li and Qj = Yj + ∑Ni Mij for all j.

1. Model Summary. This is a canonical model of a constant-returns-to-scale, nonparametric production network augmentedby two types of wedges: market imperfections χ and subsidies τ .The goal of my theory is to derive a set of empirically measur-able objects to capture how changes in subsidies τ affect outputY, holding imperfections χ constant. In the model, both wedgesaffect prices but differ in that subsidies redistribute—and neitherdestroy nor generate—resources, whereas imperfections destroyresources through deadweight losses � in the form of the con-sumption good.3 Note that the size of deadweight losses dependson the value of intermediate transactions and relative prices. Thisis a source of pecuniary externalities and allocative inefficiency

3. The treatment of wedges varies in the literature. Caliendo, Parro, andTsyvinski (2017) also use factor income as the aggregate variable and discard �

as deadweight losses. By contrast, Jones (2013), Bigio and La’O (2019), and morerecently, Baqaee and Farhi (forthcoming), rebate � back to the consumer; the“aggregate output” in these papers corresponds to the “gross output” (YG ≡ Y +�) in my model. The role of this deadweight-loss assumption will be discussed inSection III.D.

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(Greenwald and Stiglitz 1986). In Online Appendix A.2, I provideadditional microfoundations for market imperfections, includingmonopoly markups (with profits dissipated by entry), contractingfrictions, and externalities.

2. Notations for the Rest of the Article. Throughout the arti-cle, I refer to the economy with neither imperfections nor subsi-dies (χ = τ = 0) as “efficient.” In this economy, the First Wel-fare Theorem holds, and sectoral allocations {Li, Mij, Qi}, aswell as output Y, clearly coincide with those chosen by a socialplanner.

I refer to the economy with market imperfections but with-out any government interventions (τ = 0) as “decentralized.” Thedecentralized economy serves as an important benchmark: mymain theoretical results will characterize the first-order impact ofintroducing subsidies to this benchmark.

I now introduce notations to capture several objects that de-scribe local features of an equilibrium. These objects are “reducedform,” meaning they are defined with respect to equilibrium allo-cations and are not necessarily policy invariant.

Let � ≡ [σ ij] be the N × N matrix of equilibrium intermediateproduction elasticities:

σi j =∂ ln Fi

(Li,

{Mij

}Nj=1

)

∂ ln Mij.

Let � ≡ [ωi j

] ≡[

Pj Mij

Pi Qi

]be the N × N matrix of equilibrium inter-

mediate expenditure shares. I similarly define σL ≡ [σ iL] and ωL≡ [ωiL] as the elasticity and expenditure share vector of the factorinput. Expenditure shares relate to elasticities by market imper-fections and subsidies: (1 + χ i − τ ij)ωij = σ ij for intermediate inputj and (1 − τ iL)ωiL = σ iL for the factor.

Let β be the N × 1 expenditure share for producing the con-sumption good, β j ≡ PjYj∑

i PiYi.

Let μ be the N × 1 vector of sectoral influence μ′ ≡ β ′(I −�)−1. Influence is an elasticity-based centrality measure of sec-toral importance. The Leontief inverse in the expression (i.e., (I −�)−1 ≡ I + � + �2 + ···) captures the infinite rounds of networkeffects, that is, how productivity shocks to one sector affect pricesin another, taking all higher-order effects into account (Acemogluet al. 2012).

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Let γi ≡ Pi QiW L be sector i’s Domar weight, which is an

expenditure-based centrality measure of equilibrium sectoral size.The Domar weight captures the value of production resources ineach sector relative to total factor income. The measure can also beexpressed in vector form as γ ′ = β ′(I−�)−1

β ′(I−�)−1ωL

.4 In efficient economies,γ i’s are used as sectoral weights for growth accounting (Domar1961).

The ratio between influence μ and Domar weight γ is the keyobject of this article.

DEFINITION 2. The distortion centrality ξ i of sector i is defined asξi ≡ μi

γi.

Influence and Domar weights coincide in an efficient econ-omy (μ = γ ) but differ in distorted economies; influence canthus be seen as a local measure of potential sectoral sizeunder optimal production. ξ i is therefore the local ratio be-tween a sector’s potential and actual size. The name “dis-tortion centrality” reflects the fact that this measure inte-grates all distortionary effects through input-output linkagesand summarizes the aggregate degree of misallocation in eachsector.

Distortion centrality is not policy invariant and depends onboth market imperfections and policy subsidies. It is identicallyequal to 1 across all sectors in an efficient economy. In the decen-tralized economy, distortion centrality differs from 1 because ofmarket imperfections.

The rest of the article revolves around distortion centrality ξ .Section III shows its economic significance: policy makers shouldfirst subsidize sectors with higher ξ , and the cross-sector covari-ance between ξ and policy spending on subsidies reveals the ag-gregate effect of interventions. Section IV analyzes how ξ dependson network structures and shows why ξ tends to be higher inupstream sectors. In Section V, I measure distortion centrality,show that it predicts sectoral interventions in South Korea andChina, and quantify the aggregate impact of interventions in theseeconomies. All proofs are in Online Appendix B.

4. The expression follows from market clearing (see Online Appendix B). Thedenominator equals 1 in an efficient economy.

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III. THEORY: DISTORTION CENTRALITY AND SECTORAL

INTERVENTIONS

This section provides several results that highlight distor-tion centrality’s importance for policy design. Proposition 1 showsthat, starting from the decentralized economy, sectors with highdistortion centrality should be promoted first, because the mea-sure is a sufficient statistic for the marginal social value ofpolicy expenditure and captures the “bang for the buck” of sub-sidies. Proposition 2 presents a simple formula for policy eval-uations and counterfactuals, indicating that, to first order, theaggregate impact of sectoral interventions can be nonparametri-cally assessed by the covariance between subsidy spending anddistortion centrality across sectors. Proposition 3 shows that un-der Cobb-Douglas, distortion centrality is a sufficient statistic forconstrained-optimal subsidies to the factor input. Through an ex-ample in Section III.B, I demonstrate that distortion centralitydiffers substantively from other notions of sectoral importance.I discuss various interpretation and robustness issues inSection III.D.

To begin, note that the income accounting identity (equa-tion (10); reproduced below) maps aggregate consumption Y intototal factor income net of policy expenditures:

(10) Y = W L −N∑

i=1

Si.

The identity enables one to analyze the policy impact on Y by firstanalyzing the policy impact on prices. This transformation is use-ful because even with full knowledge of market imperfections, onegenerically cannot predict the policy response of allocations usingempirical objects measured from the preintervention economy;how allocations respond is governed by production technologies’structural features, which are not directly observable. This high-lights a key conceptual difficulty in industrial policy design: policyprescriptions are generically sensitive to ex ante parametric as-sumptions on production technologies.

By contrast, the policy response of prices can always be sum-marized by reduced-form objects measured from the equilibriumbefore the policy change. This is because producers engage incost-minimization, and, according to the envelope theorem, policy-induced changes in production elasticities have only second-order

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effects on prices even in the presence of imperfections and sub-sidies. I exploit this fact and separately analyze the effects ofsubsidies on factor income and policy expenditures and thenapply the income accounting identity to obtain net effects onoutput Y.

First, note that subsidies’ effect on factor income is similar tothat of input-augmenting productivity shocks; hence, the follow-ing lemma is useful for finding dW L

dτi j.

LEMMA 1. d ln W Ld ln zi

= μi.

Influence is a sufficient statistic for how factor income re-sponds to TFP shocks. This is because production elasticities cap-ture how changes in one price affect another, and μ′ summarizesTFP’s general equilibrium effects on the factor price W throughthe Leontief-inverse of the elasticity matrix, (I − �)−1 (recall L isexogenous, thus d ln W = d ln WL).

As a technical note, Lemma 1 relates to Hulten’s (1978)theorem, which only holds in efficient economies and statesthat Domar weight summarizes how output responds to TFPshocks ( d ln Y

d ln zi= γi). By contrast, Lemma 1 shows that the dual of

Hulten’s theorem holds even in inefficient economies: influence al-ways summarizes how the factor price W responds to TFP shocks.The lemma also reveals that Hulten’s theorem fails in inefficienteconomies for two distinct reasons: (i) influence differs from Do-mar weights, and (ii) output is decoupled from factor income. In ageneric inefficient economy, neither influence nor Domar weightis a sufficient statistic for how output responds to TFP.5

The next lemma establishes sufficient statistics that predictsubsidies’ impact on Y in the decentralized economy.

LEMMA 2. In the decentralized economy, the effect of subsidies onoutput Y is

(11)d ln Ydτi j

∣∣∣∣τ=0

= ωi j (μi − γi) for j = 1, · · · , N, L.

5. Jones (2013) and Bigio and La’O (2019) analyze Cobb-Douglas networks,rebating quasi-rents � to the consumer. Aggregate output in these papers isequivalent to gross output in mine (YG = Y + �). These publications showd ln Y G

d ln zi= μi �= γi , but their equality sign relies crucially on the Cobb-Douglas as-

sumption. Generically, d ln Y G

d ln zi�= d ln Y

d ln zi�= d ln W L

d ln zi= μi �= γi .

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By the income accounting identity, the aggregate impact ofsubsidies on Y is the net effect on factor income and policy ex-penditures. On the one hand, subsidies raise factor income WLin ways similar to input-augmenting productivity shocks, and theeffect scales with the influence μi of the targeted sector i. On theother hand, subsidies cost the government resources, and, startingfrom the decentralized economy, subsidies’ first-order impact onthe government budget (

∑Ni=1 Si) is proportional to total resources

in the targeted sector, captured by Domar weight γ i. The aggre-gate impact of subsidies is therefore proportional to the distancebetween the targeted sector’s influence and its Domar weight.The effect in equation (11) is scaled by intermediate expenditureshare, ωij, because the subsidy τ ij only targets a single input j inthe sector.

The sufficient statistics in Lemma 2 are nonparametric in thesense that, in order to predict the left-hand side, one does not needto specify structural properties of production technologies on theright-hand side: intermediate expenditure shares (ωij), influence(μi), and Domar weights (γ i) are all reduced-form objects in thelocal equilibrium and are, in principle, observable. The formulaholds in the decentralized economy. As noted already, nonpara-metric characterizations of allocations are generically not possibleaway from this benchmark.6 To understand why the decentralizedeconomy is special, consider the impact of subsidies on the gov-ernment budget, that is, the second term in equation (10):

d(∑N

i=1 Si

)

dτi j= Pj Mij︸︷︷︸

direct impact from targeted input

+N∑

k,n=1

τknd (PnMkn)

dτi j+

N∑k=1

τkLdW Lk

dτi j.

︸︷︷︸indirect effects due to endogenous changes in network structure

6. Baqaee and Farhi (forthcoming) provide ex ante but parametric formulasfor how YG responds to shocks under CES assumptions. To apply these formulas,one needs to know elasticities of substitutions, productivities, as well as the CESweights and distortions on every intermediate input in every sector. The paper alsoprovides nonparametric but ex post accounting formulas, requiring both ex antelevel and ex post changes in elasticities and expenditure shares to be observed.By contrast, my results are nonparametric and ex ante, enabling one to performpolicy evaluation and counterfactuals on Y only using reduced-form objects fromthe preintervention economy.

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Subsidy τ ij expands the use of targeted input Mij and directlyraises policy expenditure in proportion to the equilibrium valueof the input (PjMij). The intervention also induces reallocations,which causes producers in other sectors to adjust inputs, andgenerates endogenous changes in production elasticities and thenetwork structure. Such reallocations interact with existing sub-sidies and have indirect but first-order effects on total policyexpenditures (the second term). These indirect effects are thesource of difficulty in industrial-policy design: short of makingdifficult-to-verify, parametric assumptions about production tech-nologies, policy interventions’ aggregate impact cannot be ex antepredicted. In the decentralized economy, however, existing sub-sidies are zero, and the indirect effects are second order—henceLemma 2.

My main propositions, which I now introduce, leverage thisspecial property of the decentralized economy and highlight theeconomic implications of Lemma 2.

III.A. Social Value of Policy Expenditures and Counterfactuals

My first proposition directly interprets influence and theDomar weight as the marginal social benefit and social cost of pol-icy subsidies, respectively, thereby highlighting the role of theirratio, that is, distortion centrality, as a first-order sufficient statis-tic that guides interventions.

Aggregate consumption Y is the sum of private and publicconsumption, C and G, which satisfy the consumer and govern-ment budget constraints, respectively:

C = W L − T ,︸︷︷︸consumer budget constraint

G +N∑

i=1

Si = T .

︸︷︷︸government budget constraint

Now consider the trade-off between private and public consump-tion as subsidies, holding constant the lump-sum tax T. In thiscase, subsidies raise factor income, thereby raising private con-sumption ( dC

dτi j= dW L

dτi j). To finance the subsidy, the government cuts

back public consumption to balance its budget ( dGdτi j

= −d∑N

i=1 Si

dτi j).

The following result shows that distortion centrality captures themarginal rate of transformation between private and public con-sumption through policy subsidies.

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PROPOSITION 1. In the decentralized economy, the social value ofpolicy expenditure on τ ij is

SVij ≡ −dC/dτi j

dG/dτi j

∣∣∣∣τ=0, T constant

= ξi for j = 1, · · · , N, L.

The social value of policy expenditure captures the gains inprivate consumption per unit reduction of public consumption(“bang for the buck”) that is spent on subsidy τ ij. This measureis informative for policy design because it is a general equilib-rium spending multiplier. Proposition 1 shows that SVij is sector-specific, that is, distortion centrality ξ i is a sufficient statistic forthe social value of policy expenditure on subsidies to any input inthe sector. A benevolent government that trades off private andpublic consumption should therefore prioritize subsidies to sectorswith high distortion centrality.

Intuitively, while influence captures the marginal benefit ofsubsidies accrued to the consumer through higher factor income,the marginal costs of subsidies—the impact on a government’sbudget and thus the reduction in public consumption—is capturedby the Domar weight. Their ratio, that is, distortion centrality,captures the social value of policy spending by integrating alldistortionary effects of market imperfections in the network andsummarizing the aggregate degree of misallocation in each sector.Note that this result holds only in the decentralized economy (asdoes Lemma 2), in which the indirect effects of policy-inducednetwork changes on government budget are only second order.

According to the government budget constraint, subsidies canalso be financed by raising lump-sum taxes while holding publicconsumption G constant. In this case, Proposition 1 can be recast.

COROLLARY 1. dY/dτi j

dT/dτi j

∣∣∣τ=0, G constant

= ξi − 1.

(ξ i − 1) captures the net effect on output for every unit of policyspending on subsidies. Industrial policy raises output if and onlyif the promoted sector has distortion centrality above 1.

In an efficient economy, distortion centrality is always 1, andinterventions generate one-to-one transfers between public andprivate consumption, leaving no first-order aggregate effects. Un-der market imperfections, distortion centrality differs from 1, andpolicy interventions do have first-order effects starting from thedecentralized economy. Nevertheless, interventions can improve

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aggregate efficiency only through effective targeting. As I shownext, uniformly promoting all sectors is guaranteed to be ineffec-tive, and poor sectoral targeting could in fact lead to aggregatelosses.

Consider multiple and simultaneously adopted subsidies{τi j, τiL

}Ni, j=1, and let si ≡ Si

W Lidenote policy spending per value

added in each sector.

PROPOSITION 2. (i) In the decentralized economy, distortion cen-trality averages to 1 (E [ξ ] = 1). (ii) The proportional outputgains from policy interventions, as a first-order approxima-tion around the decentralized economy, is the covariance be-tween distortion centrality and sectoral policy spending pervalue added:7

� ln Y ≈ Cov (ξ, si).

The expectation and covariance are taken across sectors usingrelative sectoral value added as the distribution, for example,E [ξ ] ≡ ∑

i

(ξi · Li

L

).

Part (i) of the result shows that distortion centrality aver-ages to 1 in the decentralized economy; hence, promoting sectorsuniformly—with si equalized across sectors—does not have ag-gregate effects. This is because subsidies affect allocations onlyby redistributing resources; uniform intervention does not redis-tribute resources and is equivalent to a lump-sum transfer fromthe government to the consumer, generating zero net effect.

Even though distortion centrality always averages to 1, itsrange and cross-sector variance depend on the magnitude of un-derlying imperfections. Intuitively, when imperfections are smallin the economy, allocations are close to the first best, and distor-tion centrality is close to 1 in all sectors. Conversely, severe im-perfections lead to significant cross-sector dispersion in distortioncentrality.

Part (ii) of Proposition 2 provides a succinct covariance for-mula that nonparametrically summarizes the first-order, generalequilibrium impact of sectoral interventions. For a policy programto be effective in aggregate, subsidy expenditures must be posi-tively selected toward sectors with high distortion centrality, and

7. Formally, � ln Y ≡ Y |{τi j ,τiL}−Y |τ=0

Y |τ=0.

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sectors with low distortion centrality should be taxed. To applythe formula, distortion centrality and policy spending si can beevaluated using prices and allocations from either the pre- orpostintervention economy, as the differences therein have onlysecond-order impact on the covariance term.

Proposition 2 enables econometricians and policy makers toconduct nonparametric policy evaluations and perform counter-factuals to compare alternative interventions. The result is useful,because it is usually difficult for empirical before-after studies thatcompare across sectors (the difference-in-differences approach) toshed light on interventions’ aggregate effect. That promoted in-dustries use more resources and pay lower prices or interest ratesis evidence of interventions at work—that is, that funds are notentirely siphoned off into bureaucrats’ pockets—and does not in-dicate policy failure; conversely, expanded production in promotedsectors is not evidence of policy success. To evaluate policies, it isimportant to ask the counterfactual, “What would have happenedin aggregate, absent these interventions?” The answer inevitablyhinges on general equilibrium reallocative effects, about whichbefore-after studies are silent.

In Section V, I apply Proposition 2 to evaluate industrial poli-cies in South Korea and China.

III.B. Distortion Centrality �= Other Notions of Importance: AnExample

Standard intuitions might suggest that to improve efficiency,subsidies should be given to the most distorted sectors. However,this intuition is incomplete because it ignores input-output link-ages, along which market imperfections’ distortionary effects ac-cumulate. Alternatively, one might also believe, based on Lemma1 and Hulten (1978), that governments should first subsidize in-fluential or large sectors. My results show that these intuitionsare also incomplete. Although influence captures the effect of sub-sidies on factor income, it misses the fiscal costs. Unlike productiv-ity shocks, which do not cost resources, subsidies affect allocationsby redistributing resources. Therefore, it is crucially important toinclude the cost of subsidies into policy calculations. Targetingsectors by influence only considers benefits, whereas targeting bysize only considers costs, and neither intuition is complete.

The distinctions between distortion centrality and these othernotions of “importance” are substantive, as promoting large,

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FIGURE I

A Vertical Production Network with Three Intermediate Sectors

influential, or very distorted sectors can indeed amplify—ratherthan attenuate—misallocations and lead to aggregate losses. Inow turn to a simple example to illustrate how distortion central-ity relates to these other measures. In Section V, I also empiricallydemonstrate that distortion centrality differs substantially fromthese other measures in real-world networks.

1. Example Setup: A Vertical Production Network with ThreeIntermediate Sectors. Upstream good 1 is produced linearly fromthe factor input; midstream good 2 is produced from the factor andgood 1; downstream good 3 is produced from the factor and good 2.The downstream good directly transforms into the consumptiongood. Producers i = 2, 3 face imperfections χ i > 0 when purchas-ing intermediate good (i − 1). The network is demonstrated inFigure I, omitting the final sector.

In the decentralized economy, sectoral influence, Domarweights, and distortion centrality follow

Upstream Midstream Downstream

(Influence)(μ1, μ2, μ3

)∝

(σ2σ3, σ3, 1

),

(Domar weights)(

γ1, γ2, γ3

)∝

(σ2

(1+χ2) · σ3(1+χ3) ,

σ31+χ3

, 1),

(Distortion centrality)(ξ1, ξ2, ξ3

)∝

((1 + χ2) (1 + χ3), (1 + χ3), 1

).

For notational simplicity, these objects are expressed in pro-portional terms. The term σ i < 1 is the production elasticityof intermediate input in sector i. Derivations are in OnlineAppendix A.7.

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2. Downstream Is Large and Influential, But Upstream HasHigh Distortion Centrality. I want to highlight two observations.First, influence and Domar weights are highest in downstreamsector 3 and lowest in upstream sector 1. Influence is a measureof sectoral importance and the Domar weight is a measure ofsize; the two coincide absent market imperfections. Downstreamis influential because its productivity raises the value not onlyfor factor inputs in the downstream sector but also for those inmidstream and upstream sectors through production linkages.Likewise, the downstream sector is large because it provides ad-ditional value added over midstream (and, indirectly, upstream)production. Conversely, upstream sector 1 has low influence andis small because its productivity only benefits its own factor in-put and because its output constitutes only a fractional value ofmidstream and downstream production.

Second, observe that the sectoral rankings by distortion cen-trality are unambiguously the inverse of the rankings by influenceor by size: upstream sector 1 has the highest distortion central-ity and downstream has the lowest (ξ1 > ξ2 > ξ3), irrespectiveof the magnitude of imperfections in midstream and downstreamsectors. This is because the distortionary effects of market imper-fections accumulate into distortion centrality through backwarddemand linkages. Market imperfections in downstream sector 3depress intermediate demand and lower midstream sector’s sizerelative to its influence; midstream imperfections further depressdemand for upstream goods, generating compounding effects andleaving upstream with the highest distortion centrality. In otherwords, it is not the imperfections within a sector that contributeto its distortion centrality, but imperfections in sectors it supplies,directly and indirectly. The further upstream a sector is and themore layers of distorted linkages its output must travel throughbefore reaching the final consumer, the higher the sector’s distor-tion centrality.

2. Promoting Upstream Mitigates Misallocations. Becauseupstream sector 1 has the highest distortion centrality, my re-sults show that subsidizing upstream improves aggregate effi-ciency and conversely, because distortion centrality averages to 1,subsidizing the large, influential, and potentially most-distorteddownstream sector 3 leads to aggregate losses. This is becausemarket imperfections generate resource misallocations, causingtoo few inputs in the upstream sector and too many inputs in the

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downstream. Promoting downstream production therefore exacer-bates the misallocation. To see this more explicitly, consider factorallocations, which can be solved in closed form in this example be-cause of the Cobb-Douglas assumption:

Upstream Midstream Downstream(L∗

1, L∗2, L∗

3

)∝

(σ2σ3, σ3 (1 − σ2), (1 − σ3)

),(

L1, L2, L3

)∝

(σ2

(1+χ2) · σ3(1+χ3) ,

σ31+χ3

(1 − σ2), (1 − σ3)),

where L∗i ’s represent efficient factor allocations and Li’s are those

in the inefficient decentralized economy. Relative to efficient allo-cations, the inefficient economy allocates too few factor inputs up-stream and too many downstream. Policy interventions improveefficiency only if they counteract misallocations, redirecting thefactor input to the upstream sector.

Here is a roadmap for the remaining theoretical results. NextI characterize nonmarginal interventions in Cobb-Douglas net-works and further elaborate on the allocative inefficiency of dis-torted economies. I discuss a few conceptual issues and exten-sions in Section III.D. Section IV analyzes how network structuregenerally shapes distortion centrality, formalizing the intuitionthat distortionary effects accumulate through backward demandlinkages.

III.C. Cobb-Douglas Case: Optimal Subsidies and Misallocations

Now consider constrained optimal (as opposed to marginal)interventions, which, given constraints P over policy instru-ments, is the solution to {arg maxτ∈P Y }. Away from thedecentralized economy, dY

dτi jgenerically depends on production

technologies’ parametric structures because the network changesendogenously in response to policy. I now analyze a knife-edgecase: Cobb-Douglas production functions, with policy instrumentsconstrained to be sector-specific subsidies to value-added factorinputs, P = {τiL}N

i=1. The solution to this case is particularly sim-ple and provides additional insights into the role of distortioncentrality.

PROPOSITION 3. Under Cobb-Douglas, the solution{τ ∗

iL

}Ni=1 to the

problem{arg max{τiL}N

i=1Y

}satisfies

{1

1−τ ∗iL

= ξi

}N

i=1. Moreover,

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{τ ∗

iL

}Ni=1 is also the solution to maximizing gross output,{

arg max{τiL} Y G}.

Distortion centrality is a sufficient statistic for optimal value-added subsidies under Cobb-Douglas. This result holds underarbitrary outstanding subsidies to intermediate inputs (τi j /∈{τiL}N

i=1), the levels of which are implicitly reflected in sectoralDomar weights and hence in distortion centrality.

To understand the result, note that factor allocations in effi-cient and distorted economies follow

(12) (first best) L∗i = μiσiLL, (distorted) Li = γi

1 − τiLσiLL.

Optimal subsidies therefore align distorted allocations with effi-cient ones, setting γi

1−τ ∗iL

= μi. Another interpretation is to considera fictitious sector that buys the factor and sells to sector i, withμiσ iL and γiσiL

1−τiLrepresenting the influence and the Domar weight,

respectively, of this fictitious sector. Proposition 3 states that sub-sidies to the fictitious sector should be chosen to align the sector’sinfluence with its Domar weight.

The intuition that nonmarginal interventions should alignwith distortion centrality ignores the indirect budgetary effectscaused by endogenous network changes. These indirect effectsare shut down in this case because (i) elasticities are constantunder Cobb-Douglas and (ii) value-added subsidies do not affectexpenditure shares on intermediate inputs.

As a technical note, the assumption that imperfectionsgenerate quasi-rents, as opposed to real economic rents, isinconsequential in the case analyzed in Proposition 3, asconstrained-optimal policies that maximize net and gross output(Y and YG ≡ Y + �) coincide. This is because under Cobb-Douglas,the network structure is policy invariant, and Y always moves pro-portionally to YG in response to value-added subsidies.

III.D. Discussions and Extensions

In the next section, I analyze how general network struc-ture shapes distortion centrality. Before moving on, I brieflydiscuss some conceptual issues within my results. I also ad-dress many additional theoretical issues and extensions in OnlineAppendix A.

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1. Within-Sector Heterogeneity. In the real world, firmswithin a narrowly defined industry classification may produce dif-ferentiated goods and are subject to distinct market imperfections.Ideally, to apply my theory, one would compute distortion central-ity for each “variety,” which is the level of differentiation at whichheterogeneity is defined. Nevertheless, I show in Online AppendixA.1 that ξ remains sector-specific under the following condition:there exist sectoral aggregators that combine within-sector vari-eties into sectoral bundles so that cross-sector transactions takeplace using these bundles. Intuitively, this condition implies thateach firm is subject to one common imperfection wedge when buy-ing different varieties produced by a common sector. When thiscondition holds, government interventions’ first-order aggregateeffects depend on the net—not gross—subsidy spending withineach sector, as subsidizing one variety while taxing another in thesame sector generates exactly zero aggregate effect.

2. Policy Instruments. Propositions 1 and 2 are formulatedusing input-specific subsidies, but they also apply more broadlyto other practical and real-world policy instruments that affectproduction input use. For instance, a policy that promotes over-all sectoral production is isomorphic to a uniform subsidy to allinputs; likewise, under financial frictions, credit market interven-tions can also be represented by subsidies to inputs under workingcapital constraints. To see the latter, suppose the government sub-sidizes sectoral interest rates to (λ − ui), paying the difference ui tothe lender out of the government budget. The profit-maximizationproblem of producer i becomes

max�i Qi ,Li ,{Mij}S

j=1

Pi Qi −⎛⎝

N∑j=1

Pj Mij + W Li + (λ − ui) �i

⎞⎠

s.t. (2) and∑N

j=1δi j Pj Mij � �i.

Credit subsidy ui generates production decisions and policy ex-penditures that are identical to those induced by the set of simul-taneous input subsidies {τ ij ≡ uiδij}; thus, Propositions 1 and 2apply.

3. Subsidies Redistribute Resources But Do Not Counter-act Market Imperfections. The social value of policy expenditure

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(SVij) depends on the distortion centrality of sector i and not onthe targeted input j. This is because imperfection χ ij generatesdeadweight losses χ ijPjMij instead of χ ij(1 − τ ij)PjMij: the formerscales with transactions’ market value, whereas the latter scaleswith the subsidized value. I adopt the former specification becauseit subjects policy instruments to the same imperfections faced bymarket-based transactions, thereby isolating only the reallocativeeffects of policy interventions. This distinction is elaborated on inOnline Appendix A.5.

4. Market Imperfections Generate Deadweight Losses. In mymodel, market imperfections generate quasi-rents that are com-peted away as deadweight losses. The assumption is used tomotivate net output Y ≡ YG − � as the aggregate outcome vari-able of interest instead of the gross output YG. The mathemati-cal statements in Propositions 1 and 2 nonparametrically predictthe policy response of Y; by contrast, parametric assumptions arealways necessary to predict how gross output YG responds to pol-icy shocks. When imperfections generate real economic rents, mypropositions are policy relevant insofar as net output Y is pol-icy relevant. Finally, as Proposition 3 shows, the assumption isinconsequential under Cobb-Douglas for the constrained-optimalsubsidies to value added.

5. Market Imperfections �= Iceberg Costs. Despite the quasi-rent assumption, market imperfections are not isomorphic toiceberg trade costs, under which a fraction of inputs are lost dur-ing transactions. An iceberg economy is constrained efficient—allocations coincide with the planner’s solution—whereas adecentralized economy with market imperfections is not. Ineffi-ciency arises because, under market imperfections, quasi-rentsare proportional to the transaction value and depend on relativeprices; hence, pecuniary externalities do not “net out” (Greenwaldand Stiglitz 1986). In other words, under market imperfections(and unlike under iceberg costs), input demand is distorted forgiven input prices; hence, by affecting prices, subsidies can havefirst-order aggregate effects.8 I elaborate on this issue in OnlineAppendix A.4, where I demonstrate (i) allocations in my economydo not coincide with allocations under the first-best economy, and

8. Contracting frictions in Boehm and Oberfield (2019) feature pecuniary ex-ternalities of the same nature.

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by redistributing resources, policy interventions can raise outputY; (ii) factor allocations under an iceberg economy coincide withthose under the first best; and (iii) distortion centrality is alwaysequal to 1 in an iceberg economy, so policy interventions have nofirst-order effects.

IV. THEORY: DISTORTION CENTRALITY AND NETWORK STRUCTURE

How does distortion centrality relate to network structure?The vertical-network example in Section III.B shows that marketimperfections accumulate through backward demand linkages,and consequently, sectors with high distortion centrality are up-stream and directly or indirectly supply to many other sectors.I generalize this intuition in Proposition 4, which provides aclosed-form formula for distortion centrality in arbitrary net-works. I then analyze a class of hierarchical networks, in whichsectors follow a pecking order, and relatively upstream sectorssupply a disproportionate fraction of their output to other rela-tively upstream sectors. Proposition 5 shows that in hierarchicalnetworks, the ranking of distortion centrality is insensitive to un-derlying imperfections. This last result is useful for my empiricalanalysis later.

To proceed, let θi j ≡ Mij

Qjbe the fraction of good j sold to sec-

tor i. This object captures the importance of sector i as a buyerof good j. Likewise, let θ F

j = Yj

Qjcapture the importance of con-

sumer demand for intermediate good j. The market-clearing con-dition for good j implies that θ F

j + ∑Ni=1 θi j = 1. Note that θ ij is

different from intermediate expenditure share ωij: the latter cap-tures the importance of sector j as a supplier to i, and the twoobjects relate by θi j = Pj Mij

Pi Qi

Pi QiPj Qj

= ωi jγiγ j

. I refer to � ≡ [θ ij] as theinput-output (IO) demand matrix. Even though the IO expendi-ture share matrix � ≡ [ωij] is a more common representation ofinput-output relationships in the literature, the demand matrix �

is the relevant representation for computing distortion centrality.

PROPOSITION 4. In the decentralized economy, the distortion cen-trality of sector j can be written as

(13) ξ j = θ Fj · δ +

N∑i=1

ξi · (1 + χi j

) · θi j

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for scalar δ = W LY G . In matrix form,

ξ ′ = δ · (θ F)′(I − (� + D ◦ �))−1

,

where D ≡ [χi j

]is the matrix of sectoral imperfections and ◦

denotes the Hadamard product.

The formula expresses distortion centrality in terms of net-work structure and underlying imperfections; it formalizes theintuition that imperfections accumulate through backward de-mand linkages. A sector has high distortion centrality if it sellsa disproportionate share of its output to other sectors with highdistortion centrality and large imperfections. To see this, considersector j which supplies to sectors indexed by i. Imperfections ininput-using sectors (1 + χ ij) depress demand for good j and con-tribute to sector j’s distortion centrality ξ j; the effect is magnifiedby ξ i and weighted by the importance of the demand relationshipθ ij. The distortion centrality of sector j then travels through j’sinput demand and contributes to the distortion centrality of j’ssuppliers further upstream. The proportionality scalar δ ensuresdistortion centrality averages to 1 across sectors.

IV.A. Distortion Centrality and the “Upstreamness” Measure

The “upstreamness” measure by Antras et al. (2012) (“up-streamness” henceforth) is

(14) U ′ = 1′ (I − �)−1.

The formulation in equation (14) was first proposed by Jones(1976) as a measure of “forward linkages.” It captures the no-tion that sectors selling a disproportionate share of their outputto relatively upstream sectors should themselves be relativelyupstream. Distortion centrality is related to the upstreamnessmeasure but instead captures the idea that high distortion cen-trality sectors sell a disproportionate share of their output toother sectors with high distortion centrality and large imperfec-tions. In an efficient economy, distortion centrality can be writtenas ξ ′ = (

θ F)′

(I − �)−1, which always collapses to the identityvector 1′.

1. Distortion Centrality Aligns with Upstreamness in Hierar-chical Networks. In an arbitrary production network, distortion

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centrality may depend strongly on the underlying market imper-fections and thus correlate poorly with the upstreamness mea-sure. On the other hand, there is a class of networks—what Icall “hierarchical” networks—in which distortion centrality tendsto be stable across varying distributions of market imperfectionsand tends to correlate strongly with the upstreamness measure.

DEFINITION 3. (Hierarchical Networks) A production network ishierarchical if its N × N input-output demand matrix � hasnonincreasing partial column sums:

(15)K∑

k=1

θki �K∑

k=1

θkj for all i < j and K � N.

LEMMA 3. Let Ui denote “upstreamness” as in equation (14). In ahierarchical network, Ui � Uj ⇔ i � j.

Intuitively, a production network is hierarchical if a sectoralordering exists, so that higher-ranked sectors supply a dispro-portionate share of their output to other higher-ranked sectors.9

Figure II visualizes the IO demand matrix � of a hierarchicalnetwork, with entry size drawn in proportion to the strength ofthe demand linkages θ ij. The condition that partial column sumsare nonincreasing is evident from sparse entries in the bottom leftand dense entries just below the diagonal.

In vertical networks, upstream sectors always have higherdistortion centrality, as seen in Section III.B. Hierarchical net-works are generalizations of vertical networks. In hierarchicalnetworks, upstream sectors tend to have higher distortion central-ity because imperfections accumulate through backward linkages.To formalize this, I first provide two sufficient conditions underwhich distortion centrality aligns perfectly with upstreamness inrank order. I then turn to an example.

PROPOSITION 5. Consider a hierarchical production network withinput-output demand matrix �.

9. A sufficient (but unnecessary) condition for an IO demand matrix � to sat-isfy the hierarchical property is for its entries θ im to exhibit log-supermodularityin (i, m), that is, θ imθ jn � θ inθ jm for i � j, m � n.

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Inpu

t-U

sing

Indu

strie

s

Input-Supplying Industries

FIGURE II

An Illustrative Input-Output Demand Matrix of a Hierarchical Network

CASE 1. (Deterministic imperfections) If D ◦ � satisfies the hierar-chical property, then

ξi � ξ j for all i < j in the decentralized economy.

CASE 2. (Random imperfections) Suppose � is lower-triangular.If cross-sector imperfections {χ ij} are i.i.d. and E

χ[χi j

]� 0,

then

Eχ [ξi] � E

χ[ξ j

]for all i < j in the decentralized economy,

where the expectation is taken with respect to the distributionof χ ij’s.

Case 1 shows that distortion centrality aligns with upstream-ness if D ◦ � is hierarchical. This condition is satisfied when, forinstance, upstream sectors are more financially constrained andmore working capital is required for sourcing upstream goods asinputs (χ im > χ jn for all i � j and m � n). This condition is rea-sonable because, as I show later, upstream sectors in real-world

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economies tend to be heavy manufacturing sectors, which usemore intermediate inputs and produce capital goods such as in-dustrial equipment and machinery, the purchase of which is morelikely to be subject to financial and contracting frictions. Case 2of the proposition takes the equilibrium IO demand relationship� as fixed and imposes stochasticity on market imperfections.The result shows that if cross-sector imperfections are i.i.d. ina lower-triangular hierarchical network, then upstreamness anddistortion centrality are aligned in expectation.

Note that these are sufficient but unnecessary conditions fordistortion centrality and upstreamness to align perfectly acrossall sectors. Even if these conditions do not hold perfectly, the twomeasures still tend to align across most sectors. Intuitively, tobreak the alignment between distortion centrality and upstream-ness in a hierarchical network, producers in the economy mustface few imperfections when purchasing upstream goods (eventhough they use upstream inputs heavily) and face enormousimperfections when purchasing downstream goods (even thoughthey use few downstream inputs in equilibrium). Moreover, thecounterintuitive pattern of imperfections must be sufficientlystrong—perhaps implausibly so—to counteract the networkeffects.

Consider the following numerical illustration. Sector 1 is up-stream, supplying 90% of its output to sector 2 and 10% to sector 3;sector 2 supplies its entire output to sector 3; good 3 is transformedlinearly into the consumption good. Producers face imperfectionsx when buying good 1 (χ31 = χ21 = x) and y when buying good 2(χ32 = y). The economy can be summarized by

� =⎡⎣ 0 0 0

0.9 0 00.1 1 0

⎤⎦ , θ F = (0, 0, 1) , D =

⎡⎣0 0 0

x 0 0x y 0

⎤⎦ ;

ξ ′ ∝ (((1 + y) × 0.9 + 0.1) × (1 + x) , (1 + y), 1

).

In this hierarchical (but nonvertical) network, downstream (sector3) unambiguously has the lowest distortion centrality, but therelative distortion centrality of sectors 1 and 2 depends on the sizeof market imperfections x and y. To break the monotone ranking(ξ1 � ξ2 � ξ3), a necessary condition is y > 10x

1−0.9x , that is, marketimperfections over input 2 (y) have to be at least 10 times higher

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than those over input 1 (x); furthermore, the condition becomesdisproportionally more stringent as x, the imperfection wedge ofusing input 1, increases. When x = 5%, y has to be over 18 timeshigher than x; when x > 11.2%, monotonicity is always maintainedregardless of how high y is.

The stability of distortion centrality in hierarchical networksplays an important role in my empirical analysis in the nextsection.

Finally, it is worth emphasizing that despite similarities, up-streamness differs from distortion centrality in terms of bothscale and interpretation, and only the latter is suitable for policyanalysis. Upstreamness is an accounting measure and is con-structed wholly from the input-output structure; it always liesabove 1. By contrast, distortion centrality also depends on marketimperfections (the D matrix), as the measure captures the degreeto which distortionary effects in the network accumulate to eachsector. Distortion centrality always averages to 1.

V. APPLICATION: EVALUATING INDUSTRIAL POLICY EPISODES

In this section, I apply my theoretical results to evaluate sec-toral interventions adopted by South Korea during the 1970s andby modern-day China. These are two of the most salient economieswith active industrial policies: from 1973 to 1979, South Korea hada state-led industrial policy program that selectively promotedheavy and chemical industries; likewise, the interventionist gov-ernment of modern-day China implements a variety of sectoralpolicies.

I discuss how to measure distortion centrality in Section V.A,and I conduct policy evaluations and counterfactuals in SectionV.B. I conduct extensive robustness tests in Section V.C and OnlineAppendix D.

V.A. Recovering Distortion Centrality

To measure distortion centrality, I apply the formula in Propo-sition 4, which expresses ξ as a function of (i) the network struc-ture and (ii) underlying imperfections.

I use national IO tables to measure network structures. Apotential concern is that real-world production data are endoge-nous to policy interventions; however, because such endogeneityhas second-order aggregate effects in the decentralized economy,

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it can be ignored when applying my first-order formula for policyevaluation. I first suppress this issue and proceed as if real-worldproduction data are not contaminated by sectoral interventions.Later, in Section V.C and Online Appendix D, I present exten-sive arguments and evidence on the robustness of my empiricalapproach.

Another empirical challenge is to recover underlying marketimperfections. In principle, these can be estimated from rich pro-duction data, for instance, if all transactions and payments canbe observed. In practice, credibly identifying all market imperfec-tions in the entire economy, with sufficient degrees of precisionand certainty, is a demanding task. Ultimately, no strategy canperfectly recover all imperfections, and this is a key argumentagainst industrial policies (Pack and Saggi 2006; also see refer-ences in Rodrik 2008). Indeed, one should be uncomfortable inapplying my theory if policy evaluations turn out to be very sen-sitive to how imperfections are specified.

In addressing this difficulty, the discussion on hierarchicalnetworks proves to be especially useful, and I proceed in twosteps to recover distortion centrality. First, I establish that the IOtables of South Korea and China are hierarchical: sectors in theseeconomies exhibit a clear pecking order, with unambiguouslydefined upstream and downstream sectors. Second, I empiricallyshow that distortion centrality is not only rank stable in theseeconomies, as my theory suggests, but also quantitatively stablewith respect to underlying imperfections. Specifically, I recovermarket imperfections using a range of strategies from the liter-ature. These strategies come with various pros and cons, requiredistinct assumptions, and push against data constraints indifferent ways. I show that distortion centrality almost perfectlycorrelates across all specifications and correlates strongly withthe upstreamness measure, indicating that it is the networkstructure—not underlying imperfections—that generates themost variations in distortion centrality. This finding lendscredence to using distortion centrality for subsequent policyevaluations.

In what follows, I first treat these as closed economies. I dis-cuss how to incorporate international trade into my analysis to-ward the end of this subsection.

1. Production Networks in South Korea and China AreHierarchical. The starting point for measurement is a na-tional input-output table, entries in which capture the value of

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cross-sector flow of intermediate goods (PjMij) exclusive of imper-fection and subsidy payments.10 I work with IO tables from SouthKorea in 1970 and China in 2007, disaggregated at 148 and 135three-digit sectors, respectively. For each country, I construct theinput-output demand matrix � ≡

[Mij

Qj

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[Yj

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]from

the IO table by dividing appropriate entries by the total output ofinput-supplying sectors.

To illustrate the hierarchical property, I need to reorder sec-tors, as the property is defined using a sectoral ordering thatmaps into upstreamness, which does not align well with standardindustrial classification codes. To this end, I construct a simplebenchmark distortion centrality measure, ξ10%

i , by assuming im-perfections to be 10% across all sectors and all inputs, and I re-order sectors to descend in ξ10%

i . By construction, all variations inthis benchmark measure originate from the input-output struc-ture. As I show later, this benchmark measure is almost perfectlycorrelated with distortion centrality based on imperfections esti-mated from data.

Figure III visualizes the input-output demand matrices � ofSouth Korea and China, with sectors arranged to descend in thebenchmark distortion centrality ξ10%

i . For ease of visualization,entries are drawn in proportion to the strength of demand linkagesθ ij and are truncated below at 5%, so that only important linkagesare shown.

This figure shows a striking pattern of cross-sector linkagestructures in these economies. Once sectors are arranged by ξ10%

i ,both matrices bear remarkable resemblance to the hierarchi-cal network depicted in Figure II. Intermediate sectors in botheconomies exhibit a clear pecking order and have highly asymmet-ric input-output relationships. The downstream sectors purchaseheavily from upstream ones but the reverse is not true, as bothmatrices have dense entries below the diagonal and are sparseabove. The lower-triangular entries are, on average, an order of

10. Entries exclude imperfections and subsidies because, by construction, IOtables respect the market-clearing conditions of intermediate goods: total value ofgood j supplied to all other industries (inclusive of net exports) should be equal tosector j’s total output, as recorded in the table (see United Nations Department ofEconomic and Social Affairs 1999).

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FIGURE III

The IO Demand Matrices of South Korea (Left) and China (Right) AreHierarchical

magnitude larger than the upper-triangular ones.11 More impor-tant, the matrices are hierarchical: the bottom-left area is sparsebut gets denser toward the diagonal, indicating that upstream in-puts are used more heavily by relatively upstream producers thanby downstream producers. These patterns are entirely obfuscatedwhen sectors are arranged by standard industrial codes (OnlineAppendix Figure D.2).

To formally assess the hierarchical property in these net-works, I follow Definition 3 and exhaustively compare upstreamsectors’ partial-column-sums with those of downstream sectors.These comparisons correspondingly generate over one million in-equalities to be tested for each economy, 85.0% of which hold truefor South Korea and 86.0% for China, as shown in Table I. This isstrong evidence that the production networks in these economiesare hierarchical, as only 50% of the inequalities would have heldtrue if demand linkages were randomly generated. Moreover,among the partial-sum comparisons that fail to hold, inequalityviolations are minuscule and thus unlikely to have large effectson distortion centrality: close to 90% of partial-sum comparisonshold true in both economies if the test tolerates violations smallerthan 0.5% of the supplying sector’s total output.

11. For South Korea and China, respectively, entries below the diagonal aver-age to 0.81% and 0.83%, whereas entries above the diagonal average to 0.13% and0.33%.

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TABLE ITESTING THE HIERARCHICAL PROPERTY OF INPUT-OUTPUT DEMAND MATRICES IN

SOUTH KOREA AND CHINA

Fraction of partial-column-sum comparisons(in Definition 3) that hold true

Relax inequalities by ε South Korea China(∑Kk=1 θik � ∑K

k=1 θ jk − ε)

0 85.0% 86.0%0.001 87.0% 87.4%0.005 89.0% 88.9%

2. Recovering Market Imperfections. Because these net-works are hierarchical, their sectoral distortion centrality rank-ings tend to align with upstreamness and are insensitive tounderlying market imperfections, as the results in Section IV sug-gest. To verify this, I specify imperfections using multiple strate-gies from the literature. The goal at this point is not to argue thatany particular estimates exhaustively represent all imperfectionsin these economies; instead, this exercise is meant to push avail-able data in as many directions as possible and show that distor-tion centrality stays extremely stable across all specifications.

The production networks literature has adopted both sim-ulation (e.g., Jones 2013) and estimation (e.g., Bigio and La’O2019; Baqaee and Farhi forthcoming) approaches to specify im-perfections. I use a variety of specifications based on both of theseapproaches. For every specification, I overlay the input-output de-mand matrix � with simulated or estimated imperfections andcompute distortion centrality based on Proposition 4. I show thatdistortion centrality is stable across all strategies.

For the simulation approach, I draw imperfections χ ij inde-pendently across ij from a wide range of distributions, as listed inTable II and Online Appendix Table D.9. I later show that non-i.i.d. imperfections are unlikely to overturn my findings.

The estimation approach uses sectoral observables to proxyfor imperfections and is therefore more reliant on data. Formodern-day China, I estimate imperfections using four alterna-tive strategies (B1, B2, B3, and B4, described below), exploitingsectoral data from national accounts as well as the firm-level An-nual Survey of Manufacturers, a comprehensive survey of Chi-nese manufacturing firms. For South Korea, only two strategies

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(B3 and B4) can be implemented due to the lack of firm-level datafrom the historical period. Because my contribution does not liein these estimation strategies, I briefly describe them here andinclude further details in Online Appendix C.2.

Strategies B1 and B2 use firm-level data to estimate produc-tion elasticities and recover wedges from expenditure shares. B1nonparametrically estimates elasticities using the methodologyof De Loecker and Warzynski (2012). B2 uses input shares byforeign-owned firms in China to estimate production elasticities,following Gandhi, Navarro, and Rivers (2017), under the assump-tion that foreign firms face fewer imperfections than domesticproducers. B3 uses the measure of external financial dependenceby Rajan and Zingales (1998), interacted with the average interestrate in the respective economies. Because this measure intends tocapture financial frictions in the United States, it is likely to be alower bound for financial frictions in the two developing economiesI study. Last, B4 assumes imperfections arise from noncompeti-tive conduct (see Online Appendix A.2 for microfoundation) anduses sectoral profit shares to proxy for imperfection wedges.12

For specifications that recover firm-level imperfections, I com-pute sectoral averages according to the within-sector heterogene-ity analysis in Online Appendix A.1, so that every specificationresults in one wedge per sector. My baseline analysis assumesthat all intermediate inputs within each sector are equally dis-torted by the common sectoral wedge. This generates potentialmisspecification if market imperfections are input specific; mis-specification can also arise for strategies B1 and B2 because theyrecover generic wedges and might confound subsidies as part ofmarket imperfections. I suppress these issues for now and willreturn to them in Section V.C, where I address policy endogeneity

12. Another potential approach is to use cross-country differences in input-output tables to proxy for imperfections (e.g., Bartelme and Gorodnichenko 2015).I do not use this approach because doing so requires matching cross-country IOtables, and, because industrial codes differ significantly across countries, the ap-proach unavoidably generates very coarse industrial partitions, eliminating manyof the cross-sector variations necessary for my analysis. For instance, the standardWIOD database of cross-country IO tables contains only 33 sectors for China, only13 of which are manufacturing sectors. Careful hand-matching of country-pairIO tables is not significantly better: the finest common coarsening of 135 Chi-nese sectors and 389 U.S. sectors contain only 52 sectors, 25 of which belong tomanufacturing.

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and conduct extensive sensitivity analysis to specification errorsin imperfection wedges.

Online Appendix C.2 provides further details on the variousprocedures as well as robustness and summary statistics for theimperfection wedges. As Online Appendix Table C.1 shows, almostall of the estimated sectoral wedges are positive across all strate-gies, thereby lending credence to my modeling assumption thatχ � 0.

3. Distortion Centrality Is Highly Correlated across Speci-fications. For each specification described above, I compute thecorresponding distortion centrality measure using Proposition 4. Ithen examine both Pearson’s correlation (r) and Spearman’s rankcorrelation (ρ) between these alternative measures and the bench-mark measure ξ10%

i . The results are reported in Table II. PanelA shows simulated specifications, where the reported numbersare correlations averaged over 10,000 simulations. Panel B showscorrelations based on estimation strategies.

Strikingly, for both South Korea and China, sectoral distor-tion centrality is close to being perfectly correlated across all sim-ulated and estimated specifications and correlates strongly withthe upstreamness measure by Antras et al. (2012) (first row). Thisfinding is notable because the simulation strategies draw imper-fections independently, and the estimation strategies rely on dis-tinct assumptions and data moments and yield imperfection es-timates of varying magnitudes. Yet the corresponding distortioncentrality measures are rank stable (ρ ≈ 1) and quantitatively sta-ble, and the near-perfect Pearson correlations (r ≈ 1) indicate thatthese various measures are almost affine transformations of oneanother. The stability of distortion centrality suggests that mostvariations therein come from the hierarchical network structure.In fact, if the networks were randomly generated and nonhier-archical, the correlation between simulated distortion centralityand the benchmark measure would have been precisely 0 by con-struction.

The finding in Table II suggests that interventions in theseeconomies should always start with a set of upstream sectors,the selection of which is insensitive to how market imperfectionsare specified. Note, however, that even though they are highlycorrelated and all average to 1, various distortion centrality mea-sures differ in ranges and scales (as reported in Online AppendixTable C.2). This is because different specifications produce

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imperfection estimates of varying magnitudes. Intuitively, if mar-ket imperfections are small in the economy, distortion centralityis close to 1 in all sectors; conversely, severe imperfections lead tosignificant distortion centrality dispersion across sectors.

4. Choosing Specifications for Inference. The reduced-formanalysis below is scale-invariant and is robust to using any spec-ification of distortion centrality; for simplicity, I report resultsusing the benchmark measure ξ10%

i . For the scale-dependent wel-fare analysis, I report a range of specifications and discuss theirdifferences.

Note that even though distortion centrality highly correlateswith upstreamness, the two measures are defined over differ-ent scales, and only the former measure is appropriate for policyevaluation.

5. Open-Economy Adjustments. Because both South Koreaand China engage in international trade, I adjust my empiricaldistortion centrality measures as follows. Intuitively, a countrysells exports abroad in exchange for imports; thus imports canbe seen as “produced” from exports. Under this view, an export-intensive sector might appear downstream in a closed economybut can in fact be very upstream if the country exchanges ex-ports for imported inputs that are used heavily by other upstreamproducers.

To this end, I extend my model to open economies by addinga fictitious “trade intermediary” sector, which buys exports (as itsproduction inputs) from other domestic sectors and sells imports(as its output) to other sectors. I assume the fictitious producer fea-tures constant returns: when exports double, imports also double.Trade imbalance is treated as an exogenous lump-sum transfer.It is easy to see that my theory applies to this extended economy.

Guided by this extension, I map the fictitious “intermediary”sector into IO tables and rerun my estimations. Table III reportscorrelations for the various distortion centrality measures beforeand after open-economy adjustments, showing that all specifica-tions remain quantitatively stable as a whole. Interestingly, thedistortion centrality of the fictitious “trade intermediary” sectorsits consistently above median in both economies and approxi-mately compares with the third quartile in modern-day China.This pattern indicates that imported inputs are quite upstreamin these economies, and promoting export-intensive sectors—in

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TABLE IIIDISTORTION CENTRALITY AFTER OPEN-ECONOMY ADJUSTMENTS

Correlation (Pearson’s r)before and after

open-economy adjustments

Fraction of sectors with distortioncentrality below the fictitious

trade intermediary sector

ξ specification South Korea China South Korea China

Benchmark 0.95 0.98 63% 77%B1 – 0.98 – 76%B2 – 0.98 – 79%B3 0.95 0.98 64% 79%B4 0.97 0.98 56% 73%

exchange for more imports—can potentially generate aggregategains. As a result, even though distortion centrality as a wholeremains largely unchanged, open-economy adjustments do raisethe relative distortion centrality of various textile-related sectors,the output of which both economies tend to export.

Open-economy adjustments are made for all empirical resultsunless noted.

6. Distortion Centrality Weakly Correlates with OtherSectoral Measures. Table IV reports correlations between thebenchmark distortion centrality and various other sectoral mea-sures. Results show that promoting large sectors (high Domarweights or value-added) and those that produce consumptiongoods (high consumer expenditure share β) will likely exacerbatemisallocations and lead to aggregate losses. Across the varioussectoral measures, only export intensity and expenditure shareon intermediates correlate positively with distortion centrality.I later compute welfare counterfactuals using these alternativemeasures as policy targets.

7. Which Sectors Have High Distortion Centrality? In SouthKorea and China, manufacturing sectors with high distortioncentrality tend to supply intermediate inputs such as metals,machines, chemicals, and transportation equipment. Conversely,light industries that supply more heavily to consumers—sectorsthat sell food and household products, for example—tend to havelow distortion centrality. Tables V and VI list the top 10 and thebottom 10 manufacturing sectors ranked by the benchmark mea-sure in these economies.

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TABLE VSOUTH KOREAN MANUFACTURING SECTORS WITH HIGH AND LOW DISTORTION

CENTRALITY

Top 10 ξ10%i Bottom 10 ξ10%

i

Pig iron 1.43 Tobacco 0.91Crude steel 1.38 Condiments 0.91Iron alloy 1.35 Bread and pastry 0.92Steel forging 1.26 Cosmetics and toothpaste 0.92Explosives 1.26 Slaughter, meat, and dairy products 0.93Acyclic intermediates 1.25 Leather goods 0.93Construction clay products 1.25 Furniture 0.93Carbides 1.25 Soaps 0.95Nonferrous metals 1.24 Other miscellaneous food products 0.95Machine tools 1.23 Drugs 0.96

TABLE VICHINESE MANUFACTURING SECTORS WITH HIGH AND LOW DISTORTION CENTRALITY

Top 10 ξ10%i Bottom 10 ξ10%

i

Coke making 1.36 Canned food products 0.62Nonferrous metals and alloys 1.35 Dairy products 0.65Ironmaking 1.35 Other miscellaneous food

products0.68

Ferrous alloy 1.33 Condiments 0.69Steelmaking 1.33 Drugs 0.77Metal cutting machinery 1.32 Meat products 0.77Chemical fibers 1.31 Grain mill products 0.78Electronic components 1.30 Liquor and alcoholic drinks 0.81Specialized industrial

equipments1.30 Vegetable oil products 0.82

Basic chemicals 1.29 Tobacco 0.83

V.B. Industrial Policies in South Korea and in China

In this section, I evaluate sectoral interventions adopted bySouth Korea during the 1970s and by modern-day China, and Iperform policy counterfactuals on these economies.

1. South Korea in the 1970s. Between 1973 and 1979,South Korea implemented a government-led industrializationprogram, officially called the “Heavy-Chemical Industry” (HCI)drive. This program promoted six broad sectors, including thoseproducing metal products, machinery, electronics, petrochemicals,automobiles, and ships. Firms that operated in the promoted

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FIGURE IV

South Korea’s IO Demand Matrix, with HCI Sectors Darkened

sectors received very favorable policy incentives (see, e.g., Lane2017), and some of today’s largest South Korean manufacturingconglomerates originated in this era.13 Online AppendixTable D.10 shows the full list of 38 targeted three-digit industries.

2. HCI Sectors Are Upstream and Have High DistortionCentrality. That HCI sectors are upstream can be clearly vi-sualized. In Figure IV, I reproduce South Korea’s IO demandmatrix with sectors ranked by the benchmark measure, as inFigure II, but with one small change: cells are now darkened if thecorresponding input-using sectors were promoted by the HCIdrive. Note the ith row and column in the figure correspond tothe same sector.

The input-output data strikingly demonstrate that HCI sec-tors are upstream. All darkened cells appear at the top left ofthe figure, indicating that promoted sectors rank highly accord-ing to the benchmark measure ξ10%

i . The targeted sectors supplystrongly to nontargeted sectors (i.e., the area below the darkenedcells is dense) and demand few inputs in return (i.e., the top rightarea is sparse). In manufacturing, all top 10 high-ξ sectors in

13. For instance, POSCO (the world’s fourth-largest steelmaker as of 2015)and Hyundai Heavy Industries (the world’s largest shipbuilder as of 2012) werefounded during this time.

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TABLE VIIHCI SECTORS HAVE HIGHER DISTORTION CENTRALITY THAN NONTARGETED ONES

ξ i of HCI sectorsShare of sectors with

ξ i > 1

ξ Specification sd(ξ ) HCI Non-HCI

Benchmark 0.09 1.16 100% 47.8%B3 Rajan and Zingales 0.06 1.12 100% 47.0%B4 Sectoral profit share 0.16 1.28 100% 45.1%A3 N(0.1, 0.1) 0.09 1.17 100% 47.7%A7 U[0, 0.2] 0.09 1.16 100% 47.7%A8 Exp(0.1) 0.10 1.17 100% 47.7%

Notes. For the simulated specifications, the reported distortion centrality is averaged across 10,000 simu-lations draws.

Table V were promoted by the HCI program, and none of thebottom 10 sectors were targeted.

HCI sectors’ upstreamness translates into high distortioncentrality, as shown in Table VII. Because results are quanti-tatively similar across all specifications, I omit some simulatedspecifications to avoid redundancy. Results show that every HCIsector has distortion centrality consistently above 1 across allspecifications, indicating that promoting HCI sectors likely leadsto aggregate gains. Conversely, promoting non-HCI sectors tendsto be ineffective and can generate negative value on net. Take thebenchmark measure, for instance: the HCI sectors have ξ10%

i av-eraging to 1.16, meaning that every dollar of public expenditureon subsidies to these sectors translates into aggregate gains of16 cents. The last two columns show that, across all specifica-tions, 100% of HCI sectors have distortion centrality above 1, ascompared to 48% of non-HCI sectors. Note that the total valueadded from HCI sectors constituted only a small fraction (5.6%)of the South Korean economy in 1970.

I conduct extensive robustness tests in Section V.C and OnlineAppendix D.

3. Counterfactuals. In Table VIII, I compute counterfactualsunder which different sectors were promoted. The rows separatelyselect sectors that rank highly according to Domar weights, sec-toral share in the consumption bundle (β), export intensity, sec-toral value added, and intermediate expenditure shares. For eachscenario, I maintain the HCI drive’s number (38) of promoted

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three-digit sectors. Column (1) reports the average benchmarkdistortion centrality among selected sectors for the correspondingcounterfactual; these numbers reflect the gains in private con-sumption per dollar of public spending, if public funds were al-located equally per value added across sectors selected by thesealternative measures.14 Net gains in aggregate consumption areequal to the reported numbers minus 1. Columns (2) and (3) repeatthe exercise using distortion centrality specifications B3 (Rajan-Zingales wedge) and B4 (profit share). On the right panel, I re-port how net gains in aggregate consumption under each coun-terfactual compare to the gains under the HCI drive. Note thateven though columns (1)–(3) are not scale-free and depend on thedistortion centrality specification, the relative gains reported incolumns (4)–(6) are scale-free and quite robust across all distor-tion centrality measures. For completeness, the counterfactual inrow CF6 promotes the top 38 sectors ranked by distortion cen-trality, and the last counterfactual (row CF7) promotes all sectorsof the economy equally. By construction, this last counterfactualresults in zero gains on net.

Results show that the HCI drive selected sectors withhigher distortion centrality—across various specifications forξ—than those that would have been chosen by various sec-toral observable measures. Promoting sectors by Domar weights,consumption share, or sectoral value added would all result inaggregate losses, as sectors that rank highly according to thesemeasures have distortion centrality below 1, on average. Promot-ing export-intensive sectors (row CF3) and those that rely signifi-cantly on intermediate inputs (row CF5) could result in aggregategains, but these gains would be lower than those produced by theHCI drive. For instance, under the benchmark distortion central-ity specification, counterfactuals CF3 and CF5 generate net gainsthat are 46% and 41%, respectively, relative to gains under theHCI drive. Row CF6 shows that promoting the 38 sectors with thehighest distortion centrality only generates moderate additionalgains (between 9% and 37%) over those generated under the HCIdrive.

4. Modern-Day China. State intervention has a long tradi-tion in China and remains alive and well today, as the government

14. Reliable data on sectoral policy spending are unavailable for this historicalperiod; see Lane (2017).

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employs a wide range of policy levers and instruments to exertinfluence over sectoral production. First, the credit market is pre-dominantly state controlled: interest rates are heavily regulated,and banks often receive policy directives on lending prioritiesacross sectors. Second, corporate income tax laws feature a na-tional standard tax rate with a menu of policy incentives thatare “predominantly industry-oriented” (Ministry of Finance, P. R.China 2008) and provide tax breaks to selected sectors. Third,the state directly engages in production through state-owned en-terprises (SOEs), which receive subsidies from the governmentand easy access to credit; Song, Storesletten, and Zilibotti (2011)explicitly model modern-day Chinese SOEs as financially uncon-strained market participants. I refer interested readers to Du,Harrison, and Jefferson (2014) and Aghion et al. (2015) for de-tailed discussions of modern industrial policies in China, andto Boyreau-Debray and Wei (2005), Dollar and Wei (2007), andRiedel, Jin, and Gao (2007) for China’s credit market policies per-taining to SOEs.

I construct several quantitative measures of sectoral inter-ventions in China based on private firms’ interest payments,debt obligations, corporate income taxes, and subsidies receivedfrom the government.15 I also measure SOEs’ sectoral presence.Information on corporate taxes comes from the administrativeenterprise income tax records for 2008, which contain detailedfirm-level records of tax payments and tax incentives. The dataare collected by the State Administration of Taxation, which isChina’s counterpart to the IRS and is responsible for tax collection,auditing, and supervision of various tax incentive programs. Allother variables are extracted from the 2007 edition of the ChineseAnnual Survey of Manufacturing, a well-studied, comprehensivesurvey that contains balance sheets and production data for man-ufacturing firms.16 Online Appendix C.1 provides details on thesedata sets and variable construction.

I exploit cross-sector variations in policy interventions andexamine how they covary with distortion centrality. Interventionmeasures are constructed for 79 three-digit manufacturing sec-tors, the finest partition that concords with both national IO table

15. “Private firms” refers to non-SOEs.16. That these two data sets are misaligned by one year should not lead to

systemic biases because I exploit cross-sector variations.

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and firm-level data sets.17 Tables IX and X provide some descrip-tive statistics, from which I highlight two features.

First, industrial policies in China vary substantially acrosssectors. The first row of Table IX shows sectoral means for effectiveinterest rates paid by private manufacturing firms. Interest ratesfor producers in the median sector are 4.12%, whereas producersin sectors with the highest and lowest interest rates pay as muchas 12.33% and as little as 1.85% on average. The second row showsthat firms in the most-indebted sector have an average debt-to-asset ratio that is over 1.5 times that of firms in the least-indebtedsector. Likewise, rows 3 through 6 show considerable variationsin the fraction of firms that receive tax incentives from the taxauthority, effective corporate income tax rates, the fraction of firmsreceiving subsidies from the government, and the average amountof subsidies (as a share of revenue) conditioned on having receivedany. All variables in rows 1 through 6 are based on the sample ofdomestic, privately owned firms. The seventh row shows ChineseSOEs account for sectoral value-added that ranges from 0.66% to74.5%, highlighting their heterogeneous presence across sectors.

Second, SOEs receive significantly more-favorable policiesthan private firms, as shown in Table X. On average, the effec-tive interest rate paid by SOEs is half that paid by private firms,despite the former’s debt ratios being 9 percentage points (17%)higher than the latter’s. SOEs are also twice as likely to receiveproduction subsidies from the government, and conditional onhaving received any, SOEs receive more subsidies (as a share ofrevenue) than private firms.

5. Reduced-Form Evidence. I now show that distortion cen-trality predicts sectoral interventions in China. I examine sectoralpolicy outcomes for the sample of private firms, performing cross-sector regressions of the form

Outcomei = a + b × ξ10%i + controlsi + εi.

Each observation i is a sector, and Outcomei is the sectoralmean for the corresponding policy variable for non-SOEs, mea-sured in percentage points. In accordance with my later appli-cation of Proposition 2, each observation is weighted by sectoral

17. I exclude the tobacco sector from the policy analysis because it is heavilyregulated and entirely state-owned in China.

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TABLE XDESCRIPTIVE STATISTICS: SOES RECEIVE MORE FAVORABLE POLICIES

Variable means by ownership Private firms SOEs

Effective interest rate 4.63 2.23Debt ratio 54.38 63.49Fraction of firms with tax incentives 31.93 31.48Effective corporate income tax rate 17.29 14.98Fraction of firms receiving subsidies 11.46 22.41Subsidies/revenue 1.56 2.78

value-added. ξ10%i is the benchmark distortion centrality stan-

dardized to unit variance. Note that because of standardization,the regression results are insensitive to the choice of distortioncentrality measures. The results should be read as, for instance,“1 standard deviation higher in distortion centrality above themean is associated with b percentage points higher in the policyoutcome.” I control for several sectoral characteristics to partialout nonnetwork reasons for state interventions, and I also stan-dardize these control variables.

Regression results (Table XI) show that private firms in highdistortion centrality sectors receive more-favorable policies. Basedon columns (2), (4), (6), and (8), a 1 standard deviation highersectoral distortion centrality is associated with having a 0.99 per-centage point lower effective interest rate for firms, a 2.73 percent-age points higher debt-to-capital ratio, a 2.91 percentage pointshigher likelihood of receiving tax incentives, and a 1.59 percentagepoints lower effective corporate income tax rate. These variationsin the policy variables are economically significant: 1 standard de-viation in distortion centrality translates into policy differencesof between 0.30 and 0.59 standard deviations of the respectivepolicy variables (see the last column in Table IX). These specifi-cations control for a variety of sectoral characteristics, includingcapital intensity (fixed asset over output), Lerner index (operatingprofits over output), average log–fixed capital of firms during thefirst year of operation (a proxy for the minimum scale of opera-tion), and export intensity (exports over output). Together, thesevariables serve to partial out other, nonnetwork predictors forstate interventions. Some of these control variables do have pre-dictive power over certain intervention measures, although noneis as consistently predictive as the distortion centrality measure.Also note that coefficients on distortion centrality remain almost

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unaffected after including the controls. Online Appendix Table D.8shows that coefficients remain quantitatively robust after control-ling for various estimates of sectoral wedges. The only policy vari-ables for which distortion centrality lacks predictive power relateto direct subsidies from the government. As shown in Table X, pri-vate firms tend to receive few subsidies to begin with, comparedwith SOEs.

Chinese manufacturing sectors were predominantly state-owned in the 1990s. Through several subsequent waves of marketreform, small and unproductive SOEs were privatized or closed,and large and relatively successful SOEs were corporatized asmarket participants (Hsieh and Song (2015)). Consequently, to-day SOEs are large and perhaps overly profitable corporations (Li,Liu, and Wang 2015; Bai, Hsieh, and Song 2019). The predomi-nant view in the literature is that these SOEs are overcapitalized,and their existence impedes the efficient allocation of resourceswithin sectors (Song, Storesletten, and Zilibotti 2011). I do notdispute this view, but I highlight that in a world with many policyconstraints, SOEs might serve as a means to implement sectoralpolicies, and strategically placing SOEs in selected sectors mightexpand sectoral production. This latter view is not new to eco-nomic historians, especially in the context of East Asian economiessuch as Taiwan and Singapore (see Hernandez 2004; Chang 2007,2009 for overviews).

Table XII shows that distortion centrality predicts the sec-toral presence of SOEs. In 2007, in sectors with distortion central-ity 1 standard deviation above the mean, SOEs had a 7.81 per-centage points (0.46 standard deviations) higher share of sectoralvalue added. Moreover, this correlation is not driven by histori-cal legacy: columns (3) through (6) examine sectoral value-addedshares of SOEs that were established after 2000, and the correla-tions remain significant.

6. Policy Evaluations. The reduced-form evidence suggeststhat Chinese sectors with high distortion centrality—that is, theupstream sectors—tend to receive favorable policies. I now applyProposition 2 and compute the covariance between policy expen-diture si and distortion centrality ξ i to quantitatively evaluatethese sectoral policies’ aggregate impact. Note the covariancecan be calculated using a bivariate regression: let ξi ≡ ξi

sd(ξ )denote distortion centrality standardized to unit variance; then

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Cov(si, ξ i) = b · sd(ξ ), where b is the slope coefficient fromregressing si on ξi. Higher coefficient b indicates better sectoraltargeting, meaning that sectors with high distortion centralityare more heavily subsidized. Higher dispersion in distortioncentrality, sd(ξ ), implies more misallocations and thus more roomfor welfare-improving policies. The residual variation in si, afterpartialing out ξi, has no first-order impact on output Y.

To proceed, I compute policy spending {si} separately for (i)subsidized credit, (ii) tax incentives based on the sample of privatefirms, and (iii) policy incentives to SOEs. For subsidized credit, Iproxy the market interest rate r by the highest sectoral averageinterest rate, and I calculate policy spending in each sector as thedifference between private firms’ total interest payments and thenominal payments implied by debt obligations and the marketrate ((r − ri) × debti). The choice of market rate r is an unim-portant normalization because uniform cross-sector spending hasno aggregate effect. I compute policy spending on tax incentivesusing the difference between the statutory corporate income taxrate and the effective tax rate at the sector level (25% × Profitsi− TaxesPaidi). Finally, I compute policy spending on SOEs as thesum of credit subsidies, tax incentives, and direct government sub-sidies received by SOEs in each sector. Because intervention mea-sures are available only for manufacturing sectors, the reportedgains can be seen as extrapolations that project in-sample poli-cies onto sectors outside manufacturing, while maintaining thesame covariances between distortion centrality and policy spend-ing. Alternatively, the reported numbers can be interpreted as theproportional gains in net manufacturing output.

As Table XIII shows, sectoral interventions in all three cate-gories generate positive aggregate effects in China. The gains inoutput across these categories are on the same order of magni-tude, with credit subsidies playing a somewhat stronger role thanfunds given to SOEs, which are in turn more effective than tax in-centives. For instance, under specification B1, differential sectoralinterest rates lead to 3.1% aggregate gains, while tax incentivesand funds to SOEs generate 1.2% and 2.4% gains, respectively.The pattern is qualitatively robust across various specificationsof distortion centrality.

Quantitatively, the magnitude of output gains depends onthe standard deviation of the corresponding distortion central-ity measure (reported in the first column). Specification B1,which follows De Loecker and Warzynski (2012) and structurally

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estimates generic wedges based on firm-level data, is my preferredspecification for policy evaluation. Results show that in China,industrial policies together generate 6.7% first-order gains in out-put. These gains are sizable given the scale of the interventions:policy expenditures are, on average, only 6% of sectoral revenueand 23% of sectoral value added (see Online Appendix Table D.3);this means that every dollar of subsidies generates 29 cents of out-put gains. These gains are entirely due to the positive selectionof policy expenditures in sectors with high distortion centrality;gains would have been precisely 0 if subsidies were uncorrelatedwith distortion centrality.

The output gains are smaller under the other specifications(B2–B4) because these strategies recover smaller imperfectionwedges (see Online Appendix Table C.1). This is unsurprising:by construction, strategy B2 recovers imperfections faced by pri-vate firms relative to those faced by foreign firms operating inChina; to the extent that foreign firms are also subject to im-perfections, the strategy leads to underestimates. Likewise, spec-ifications B3 and B4 each capture only a single source of mar-ket imperfections—financial frictions and profits that arise fromnoncompetitive conduct, respectively—and therefore miss othersources of imperfections. Smaller wedges imply a lesser degreeof cross-sectoral misallocations; output gains are thus smallerunder these specifications and should be seen as conservativelower bounds for the aggregate policy impact. Online AppendixTable C.5 computes an additional specification that captures bothfinancial frictions and markups, with sectoral wedges computedas the sum of wedges from B3 and B4. Interestingly, based on thisspecification, sectoral policies in China generate 5.01% aggregategains, which is of comparable magnitude to estimates based onB1.

7. Policy Counterfactuals. I now conduct policy counterfac-tuals for China. Each policy experiment evaluates the aggregateimpact of a hypothetical vector of sectoral subsidies. To keep theexercise tractable and transparent, I proceed as follows. Recallb is the slope coefficient from regressing actual subsidy expen-diture si on ξi, the distortion centrality measure standardized tounit variance. I first answer questions of the type, “if a regressionof counterfactual subsidy expenditure si on [a sectoral character-istic] has coefficient b, what would the aggregate effects be?”

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For instance, consider the Domar weight (standardized to unitvariance, γi ≡ γi

sd(γ ) ) as a counterfactual policy target. Instead ofspecifying subsidies sector by sector, I specify that counterfactualpolicy spending si projects linearly onto the Domar weight witha slope coefficient b, and that the residual ui is independent ofboth the Domar weight and the distortion centrality (i.e., si = a +b · γi + ui and u ⊥ ξ , γ ). The coefficient b captures the sensitivityof subsidies {si} to the policy target. To first order, the generalequilibrium impact of counterfactual policy spending {si} is

� ln Y ({si}) ≈ Cov (si, ξi) = ρξ,γ × bb

× � ln Y ({si}),

where ρξ ,γ is the correlation between distortion centrality ξ andthe Domar weight γ . Intuitively, subsidizing sectors with high Do-mar weights can raise output Y only to the extent that γ correlatespositively with ξ ; hence, by construction, the counterfactual {si}is always less effective than the actual policy spending {si} whenb = b. Policy makers can achieve different aggregate impacts byvarying the policy sensitivity b.

Following this procedure, I conduct policy experiments us-ing various alternative measures as policy targets, and I repeateach counterfactual across various specifications of distortion cen-trality. For each specification and counterfactual scenario, I stan-dardize the policy target to unit variance, and I normalize policysensitivity to b = b. Counterfactuals under alternative policy sen-sitivity b can be obtained by proportionally rescaling the numbersreported in Table XIV.

Table XIV shows that using Domar weights (CF1), consump-tion share (CF2), or sectoral value added (CF4) as policy targetsleads to aggregate losses. Among observable sectoral measures,only two would be good policy targets: export intensity (CF3) andintermediate expenditure shares (CF5). Interestingly, these mea-sures also work well for South Korea. Promoting sectors withhigh intermediate shares using policy sensitivity b = b, for in-stance, generates between 29% and 39% of the gains relative toreal-world interventions across different specifications of distor-tion centrality. Put another way, for policy target CF5 to be aseffective as real-world interventions, the policy sensitivity (b) hasto be two or three times as large as b, the sensitivity of si onξi. This means higher cross-sector dispersions in policy spend-ing: sectors with high intermediate shares need to receive two or

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three times higher subsidies under the counterfactual, relativeto funds spent in high-distortion-centrality sectors under real-world policies. Overall, for each counterfactual and across distor-tion centrality specifications, welfare numbers on the left panelare qualitatively robust, and the relative gains on the right panelare quantitatively stable; the stability reflects high correlationsacross various distortion centrality measures.

How much better could China have done? My theory con-cerns the first-order impact of interventions and does not addresspolicy optimality; nevertheless, the last row of Table XIV (CFO)computes the counterfactual output gains under the optimal re-assignment of subsidies across sectors while holding fixed thevector of policy expenditures as measured from real-world data.18

Results show that sectoral interventions in China could have beenmore effective by 48–67% if the same vector of policy expenditureswas reassigned optimally across sectors.

V.C. Robustness of Empirical Findings

Online Appendix D conducts extensive empirical robustnesstests, and I provide a brief summary here.

1. Data Aggregation. In Section III.D, I discussed a condi-tion under which distortion centrality is sector specific and infer-ence based on sectoral data is appropriate. Nevertheless, therecould still be a mismatch between the level of aggregation in IOtables and the level of product differentiation at which my theoryapplies, either because a sectoral aggregator over varieties doesnot exist or because data are mismeasured due to firms’ operatingacross industries and conducting multistage production in-house.Although I cannot conclusively verify empirical robustness whenthe underlying product differentiation is finer than the data avail-able, I can indeed conduct the robustness check in reverse, testingdistortion centrality’s stability when I use even coarser data thanthose available. This is done in Online Appendix D.1, where Imerge sectors and progressively create coarser sectoral partitionsover several iterations, and I recompute distortion centrality us-ing the collapsed IO tables at each iteration. Online AppendixTable D.1 shows that at all levels of aggregation for both

18. Specifically, row (CFO) of Table XIV shows the covariance between s(i),the ith highest sectoral policy spending per value added, and ξ (i), the ith highestdistortion centrality.

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economies, the benchmark distortion centrality computed fromthe collapsed IO tables almost perfectly correlates with the bench-mark measure computed from the original, disaggregated tables.The stability is once again due to the hierarchical property of thecollapsed IO tables, as shown in Online Appendix Figure D.1.

2. Policy Endogeneity and Systematic Specification Errors.In the main text, I construct distortion centrality using real-worlddata, yet both the IO demand matrix � and market imperfectionsχ could be contaminated by existing policy interventions and othererrors. Here I demonstrate that my empirical findings are quan-titatively robust and discuss the underlying intuitions.

Policy endogeneity in � could arise from either (i) endoge-nous changes in production elasticities or (ii) failing to account forsubsidies in observed input-output structure. As Lemma 2 shows,both sources of error are second order; hence, it is conceptuallyappropriate to ignore them in my first-order analysis. In OnlineAppendix D.2, I show that correctly accounting for subsidies inobserved input-output structures does not quantitatively affectany of my findings (Table D.2) and that policy spending accountsfor only a small fraction—about 6% (Table D.3)—of sectoral rev-enue, thereby providing empirical support for conducting policyevaluations as first-order approximations.

Policy-induced measurement errors in χ can arise becausesome estimated specifications (B1 and B2) misattribute imperfec-tions net of subsidies (χ − τ ) as true imperfections χ . These errorsare also second order; more important, they bias ξ against myfindings. Intuitively, because imperfections accumulate throughbackward demand linkages, systematic underspecification of χ ’sin promoted sectors, which tend to have high ξ , compresscross-sector ξ ’s towards the mean, causing upstream (down-stream) distortion centrality to be biased downward (upward).These errors in χ therefore weaken any positive correlationsbetween subsidies and ξ , and correcting for the errors shouldstrengthen my findings. Online Appendix D.2 conducts error cor-rections and shows that my findings remain quantitatively un-changed and, if anything, become slightly stronger.

Indeed, for my findings to be spurious, the systematic er-rors in χ must be perverse. Intuitively, false positives arisewhen ξ is biased negatively for downstream sectors, meaningχ must be underspecified for buying downstream goods as pro-duction inputs and, conversely, overspecified for buying upstreamgoods. In practice, the scope for false positives is very limited in

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hierarchical networks. Consider the “shoemaking” sector, whichhas low estimated ξ because it appears downstream and is not animportant supplier to upstream sectors. In order for “shoemaking”to have high actual ξ , it is necessary for shoes to be an importantinput for producing upstream goods, such as machinery and chem-icals, and for “shoemaking” to appear downstream only because ofthe enormous market imperfections that upstream producers facewhen buying shoes. As implausible as it is, the condition may stillbe insufficient, because imperfections over buying shoes eventu-ally also accumulate into upstream sectors’ distortion centrality.Online Appendix D.3 verifies these intuitions by showing that myfindings are robust even with substantial specification errors ofthe most perverse kind.

Online Appendix D.4 contains additional robustness testsfor my analysis of China. Table D.6 shows that endogeneity-corrected distortion centrality measures remain almost per-fectly correlated with the respective uncorrected measures.Table D.7 reproduces the reduced-form regressions in Tables XIand XII, using the upstreamness measure from Antras et al.(2012) as an instrumental variable for the benchmark distor-tion centrality measure. The instrumental variable should purgespecification errors in distortions insofar as upstreamness cap-tures nonpolicy features of the input-output relationship; re-sults show that coefficients remain quantitatively unchanged.Table D.8 shows that my reduced-form findings are also ro-bust after including estimated market imperfections as controlvariables.

VI. CONCLUSION

I do not wish to imply that South Korea and China adoptedoptimal policies. My nonparametric sufficient statistics capturewelfare effects to the first order but do not address optimality.Furthermore, my analysis does not address the decision processbehind policy adoption, as my model abstracts away from vari-ous political economy factors that affect policy choices in theseeconomies.

The key takeaways from my analysis and findings are asfollows:

First, interventions should begin with sectors that have highdistortion centrality. Well-meaning interventions need not tar-get the most distorted sectors, and promoting undistorted sectorsneed not exacerbate misallocation. Qualitatively, these findings

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echo the theory of the second best; yet distortion centrality suc-cinctly and quantitatively summarizes how misallocative effectsof imperfections accumulate through input-output linkages in aproduction network.

Second, Proposition 2 provides a simple formula for policyevaluations and counterfactuals. To the first order, economic gainsare higher if more subsidies are given to high-distortion-centralitysectors, and the aggregate effect can be summarized by the covari-ance between sectoral policy spending and distortion centrality. Itis usually difficult for empirical studies to shed light on sectoralinterventions’ aggregate effects, as the answer inevitably hingeson general equilibrium reallocative effects. My results overcomethis difficulty.

Third, the misallocative effects of imperfections accumulatethrough backward demand linkages and, as a result, upstreamsectors—those that supply directly or indirectly to many sectors—become sinks for imperfections and tend to have higher distortioncentrality. Moreover, in South Korea and China, sectors followa hierarchical production structure. In these economies, sectorswith high distortion centrality tend to be the upstream heavyindustries and chemical sectors; conversely, light manufacturingsectors tend to have low distortion centrality. This conclusion isinsensitive to underlying imperfections because of the hierarchicalstructure of sectoral production.

Fourth and finally, distortion centrality predicts sectoral in-terventions in these economies. According to market imperfec-tions recovered from firm-level data, sectoral variations in creditavailability, tax incentives, and policy funds to SOEs raise aggre-gate consumption in China by 3.5–6.7%; in South Korea, policyspending in sectors targeted by the HCI drive also generated pos-itive net effects.

There are several important caveats: my results concernmarginal interventions and do not address when are subsidiesbecoming too high; I analyze the economic effects of reallocationand omit political economy aspects of policy implementation; Iassume market imperfections are policy invariant, though theformer could be directly influenced by the latter; I study staticeffects of interventions and omit dynamic considerations. I leavethese areas for future research.

PRINCETON UNIVERSITY

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SUPPLEMENTARY MATERIAL

An Online Appendix for this article can be found at TheQuarterly Journal of Economics online. Data and code replicatingtables and figures in this article can be found in Liu (2019), inthe Harvard Dataverse, doi: 10.7910/DVN/MIWUVM.

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