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How linkages do, and don't, spread economic distortions

The sectoral spread of economic distortions is overestimated if input complementarity is ignored

May 14, 2020


Douglas Clement Managing Editor (former)
How linkages do, and don't, spread economic distortions key image
Cara Ewing/Minneapolis Fed

Article Highlights

  • Much research on sectoral linkages overestimates effect of distortions on productivity

  • Accounting for elasticity of input substitution permits accurate estimates

  • If a particular input is essential, input price distortions won’t spread widely

How linkages do, and don't, spread economic distortions

Will a ripple in one pond affect a nearby pond, a connected lake, or the neighboring ocean?

The degree to which disturbances in a single firm will disrupt any other firm, or industry, or even the entire economy is a matter of great consequence—and not just to economists. The Great Recession, many would argue, was sparked by the collapse of the U.S. housing market. A single sector brought the global economy to the brink of depression. (Indeed, the likelihood of contagion within the financial sector was the primary argument for government bailouts of “systemically important financial institutions.”) And as scholars gauge the coronavirus pandemic’s economic impact, understanding intersectoral linkages is crucial.

Disturbances that are unrelated to the firms’ productivity do not spread in the same way as productivity shocks.

The ability of networks, or linkages, to propagate shocks far beyond their initial source has been a focus of economists for at least a decade. Most of that research suggests that such networks amplify the consequences of shocks to specific firms or sectors, fanning a spark into flame. A 2012 paper by MIT economist Daron Acemoglu and co-authors refers to “cascade effects” and argues that “in the presence of intersectoral … linkages, microeconomic idiosyncratic shocks may lead to aggregate fluctuations. … The effects of microeconomic shocks may not remain confined to where they originate. Rather, microeconomic shocks may propagate throughout the economy, affect the output of other sectors, and generate sizable aggregate effects.”

But in "Misallocation and Sectoral Linkages” (Institute Working Paper 30), a recent study from the Opportunity & Inclusive Growth Institute, visiting scholar Sophie Osotimehin of the University of Québec at Montreal, with Latchezar Popov from Texas Tech University, argues that the mechanism is more nuanced. Not all disturbances are amplified by sectoral linkages. Disturbances that are unrelated to the firms’ productivity do not spread in the same way as the productivity shocks studied by Acemoglu. Under the right conditions, linkages can actually dampen the effects of such distortions. The ultimate outcomes, say the authors, “depend crucially on how substitutable inputs are.”

No substitutes

If a boutique soap company’s formula requires an exact blend of oil and fragrance, there may be no satisfactory replacement for either input. A price spike for one or the other won’t change the company’s purchasing decisions because substitutes aren’t acceptable. A distortion in the fragrance market will therefore have minimal impact on the input mix of the soap sector.

At a broader level, neglecting the role of low input substitutability (low substitutability means high complementarity—left shoes can’t substitute for right shoes, but they’re perfect complements for them) tends to overstate the power of linkages to propagate distortions from one sector to another. If a firm is highly dependent on a particular input and nothing else will do, distortions of that input’s price will have little impact on the firm’s decision to use it.

Under the right conditions, linkages can actually dampen the effects of distortions. The ultimate outcomes depend crucially on how substitutable inputs are.

“Firms respond less to the (distortion-induced) change in the relative prices when the elasticity of substitution is low,” explain Osotimehin and Popov, referring to how responsive demand for a product is to a change in price. If elasticity is low, an increase in an input price will barely change demand for it.

The insight is reminiscent, they observe, of the principle of optimal taxation, developed nearly a century ago by economist Frank Ramsey. The British wunderkind showed that optimal taxation depends entirely on the elasticity of demand for the goods being taxed. “Taxes should be such as to diminish in the same proportion the production of each commodity taxed,” he wrote.

That central finding is followed by a second: Sectoral linkages do not always amplify the impact of distortions. In fact, under the right conditions, linkages can soften the impact of distortions. This is particularly true when the elasticity of substitution is less than one. That bit of jargon simply means that the relative use of an input will fall proportionately less than its price rises. A 10 percent price hike, for instance, will decrease an input’s purchases relative to other inputs by less than 10 percent.

Their third finding is that the elasticity of substitution also determines the relative impact of any given sector. If inputs are not easily substitutable, buyers won’t decrease their purchases by as much as the price rises—then distortions to the sectors that are more upstream have less force; distortions in downstream sectors become relatively more important.

Modeling distortions

The economists arrive at these conclusions by building and analyzing a model with production linkages between sectors that combine primary inputs with intermediate inputs. The category of distortions they consider can result from frictions in financial or labor markets, contract enforcement, or market competition.

“Firms respond less to the (distortion-induced) change in the relative prices when the elasticity of substitution is low.”

Distortions can cause misallocations at several stages: (a) inefficient mix of intermediate inputs, (b) inefficient use of that mix, and (c) inefficient consumption. A more concrete example: A company’s inability to get a bank loan for an input purchase might force it to buy less-desirable inputs, to combine current inputs in less efficient ratios, or to raise its finished product price, thereby decreasing sales to customers who would buy more at the nondistorted price.

From theory to reality

The economists complement their three theoretical findings with an empirical analysis that quantifies the role played by input substitutability in the context of market distortion.

The analysis looks at a specific distortion: market power—the ability of monopolies to raise prices above what would be charged in a competitive economy. The economists estimate price-cost margins resulting from market power in a range of sectors for 35 countries. Some sectors, like agriculture and real estate, have very low, even negative, margins. Others, such as wholesale trade and finance, enjoy high markups.

Markups tend to be higher in low-income nations such as Mexico, Turkey, and Indonesia, and lower in rich nations like Belgium (though they’re higher in the United States and Canada than in Europe). The scholars say that because of weak tax enforcement in low-income nations, their measure may actually underestimate markups in those markets.

To measure the empirical importance of their theoretical results, they compute aggregate productivity gains in each country if monopoly markups were removed. Then they analyze how these estimated gains change as they vary the figure for elasticity of substitution.

Eliminating product markups would increase aggregate productivity, according to their analysis—reflecting the high cost of economic distortion from monopoly power. Most important: Productivity gain is greater when they use higher estimates of elasticity, validating their theoretical finding that a “higher elasticity leads to a larger cost of distortions.”

“Abstracting from input complementarity leads to overestimating the effects of distortions and the strength of amplification from sectoral linkages.”

Their benchmark result, using the median level for the 35 countries, is that productivity would increase by 1.3 percent, implying measurable but modest loss caused by monopoly power. But this quantification “hinges crucially” on the elasticity used in the analysis. Most research on sectoral linkages uses the Cobb-Douglas model, which assumes “unit elasticity”—a simple one-to-one proportional relationship between price increase and quantity decrease. That estimate of elasticity, the economists find, would multiply the productivity loss figure by a factor of 1.8, nearly twice the estimated loss caused by sectoral linkage of market distortions.

Their quantitative analysis also looks at how the results would differ if the distortions did not directly distort the firms’ intermediate-input decision. In that case, they find, there would be no amplification effect from linkages. In fact, productivity “loss is actually a fifth lower relative to the otherwise identical economy without sectoral linkages.”


The economists thus illustrate that to truly understand the role of intersectoral linkages in spreading distortionary effects, it is essential to account for complementarity among inputs and therefore for their elasticities of substitution. “Our results indicate that abstracting from input complementarity leads to overestimating the effects of distortions and the strength of amplification from sectoral linkages,” they write. And pinpointing a flaw of much research on the topic, Osotimehin and Popov note: “A central message … is that the Cobb-Douglas specification, ubiquitous in the literature on sectoral linkages of production, leads to greatly overestimating the effects of distortions on aggregate productivity as well as the role of sectoral linkages.”