metadata: authors: 0: author: Sinha,Rishabh
count: World
docna: 0: docna: Input Substitutability and Cross-Country
            Variation in Sectoral Linkages
docty: Policy Research Working Paper
subtopic: Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Textiles, Apparel & Leather Industry,Plastics & Rubber Industry,Business Cycles and Stabilization Policies,Food Security,Transport Services,International Trade and Trade Rules,Mining & Extractive Industry (Non-Energy)
teratopic: Macroeconomics and Economic Growth,Agriculture,Transport,International Economics and Trade,Industry
abstracts: cdata!: Using panel data on input-output
            intensities and expenditure prices from 28 countries, this
            paper finds the elasticity of substitution across sectoral
            inputs to be less than one in each of the three broad
            sectors of the economy. Intermediates are most complementary
            in the production of services while it is easiest to
            substitute across intermediates in the production of
            agricultural goods. Differences in relative prices alone
            account for a non-trivial fraction of the cross-country
            variation in sectoral linkages. Abstracting from the price
            channel that allows for substitution across inputs in
            response to changes in relative prices delivers biased
            aggregate implications of changes in productivity and distortions.
repnme: repnme: Input Substitutability and Cross-Country
            Variation in Sectoral Linkages
display_title: Input Substitutability and
            Cross-Country Variation in Sectoral Linkages
listing_relative_url: /research/2019/03/30892631/input-substitutability-cross-country-variation-sectoral-linkages
topicv3: Agriculture and Food Security m1326205 435,Mining Services m1326410 1701,Manufacturing Sectors m1326521 1281,Transport m1326661 135,Trade m1326924 698
publishtoextweb_dt: 2019-03-11T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Agriculture,Transport,International Economics and Trade,Industry
no_of_pages: 16
author_keys: 0: author_key: 1411342
model_extractions: Policy Research Working Paper 8770 Input Substitutability and Cross-Country Variation in Sectoral Linkages _Rishabh Sinha_ Development Economics Development Research Group March 2019
Policy Research Working Paper 8770

# **Abstract**

Using panel data on input-output intensities and expenditure prices from 28 countries, this paper finds the elasticity of substitution across sectoral inputs to be less than one in each of the three broad sectors of the economy. Intermediates are most complementary in the production of services while it is easiest to substitute across intermediates in the production of agricultural goods. Differences in relative prices alone account for a non-trivial fraction of the cross-country variation in sectoral linkages. Abstracting from the price channel that allows for substitution across inputs in response to changes in relative prices delivers biased aggregate implications of changes in productivity and distortions.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The author may be contacted at rishabhsinha@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Input Substitutability and Cross-Country Variation in Sectoral Linkages<sup>1</sup> Rishabh Sinha The World Bank Keywords: Sectoral Linkages, Input Substitutability, Distortions in Intermediate Markets JEL Classification: O11, O47 1 Contact: 1818 H St NW, Washington, DC 20433, USA (rishabhsinha@worldbank.org). The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
# **1   Introduction**

Sectoral linkages – the extent to which goods from different sectors are utilized as intermediates in the production of sectoral goods, bear a systematic relationship with GDP per capita. The share of services in intermediate expenditure is higher in the developed countries. While this holds in the production of all sectoral goods, the gap in the services share across countries is starker in the production of services itself (Sposi, 2018). An interpretation that helps reconcile the cross-country variation is that distortions exist in the intermediate markets.

Nevertheless, such analyses typically employ a production technology with a CobbDouglas (CD) association across sectoral inputs. Hence, linkages do not respond to changes in relative prices. On the other hand, a well-documented fact in the development literature is that the relative price of services rises with GDP per capita.<sup>2</sup> If intermediates from different sectors enter production as complements, then the higher relative price of services in developed countries will lead to the sector commanding a larger share of the aggregate intermediate expenditure seen in the data.<sup>3</sup> The objective of this note is to examine if the elasticity of substitution across sectoral inputs differs from unity, making the price channel a factor in accounting for the cross-country variation in linkages. Using panel data on input-output intensities and expenditure prices from 28 countries, I find the elasticity to be less than one in each of the three sectors. Intermediates are most complementary in the production of services, while it is easiest to substitute across intermediates in the production of agricultural goods.

**2   Theoretical Framework and Data** The gross output of a sector is produced using the intermediate bundle and a composite aggregated from all other factors. The production technology is CD in and . In jj jj QQ jj XX addition to price-effects, I also allow for scale-effects in production technology, i.e., the jj jj jj ZZ XX ZZ intermediate expenditure shares react to changes in . The scale-effect establishes an additional link between incomes and linkages as the size of the intermediate bundle rises with income. jj XX Borrowing from Comin et al. (2018), is a scaled CES aggregate of intermediates from all sectors implicitly defined as jj XX

> 2 Balassa (1964) is an early example that documents this relationship. More recently, Duarte & Restuccia (2010) provide the within-country evidence.

> 3 The idea of complimentary in sectoral linkages goes way back (Leontief (1936), Hirschman (1958)) and is more recently investigated in Jones (2011).

2
~~OH~~ ; i ~~n(—)~~ =( - ~~—)+~~ (1-0)e - 1)I ~~n(—)~~ + € —-DInfy )+In(v_ ) (3)
featuring 28 countries over the period 1995–2011. The panel includes countries with very high incomes but lacks the representation of low-income countries. Latvia, Lithuania and South Africa are the countries with the lowest incomes in the sample. Even so, there is a substantial variation in income. GDP per capita in the richest country is seven times larger than that of the poorest. The appendix contains more details on the data.

# **3   Results**

<u>Figure 1</u> plots the point estimates of the substitution elasticity and the accompanying 95 percent confidence intervals (CIs). The squares represent the baseline estimates in which both price- and scale-effects operate together. The baseline specification overwhelmingly rejects the assumption of a unit elasticity. Moreover, this result is not sensitive to the introduction of scaleeffects. The estimates in circles correspond to a standard CES specification so that only the priceeffect endures. All the point estimates are lower than one, though the assumption of a CD relationship for the industrial sector is not rejected owing to a lower precision. The baseline estimates show that the elasticity is highest in agriculture followed closely by industry. The substitutability drops considerably in the production of services.

Next, I consider if there exists a systematic link between elasticity of input substitution and development. It is possible that the nature of production becomes more complex as countries grow richer making inputs less substitutable as they start serving special functions. For example, farm machinery, fertilizers and agronomical know-how are more easily substitutable when the organic content of agricultural produce is not a primary concern. Substitutability diminishes if the organic content becomes critical. To this end, I divide the sample into two equal sub-samples of low- (LI) and high-income (HI) countries based on mean GDP per capita.<sup>6</sup> <u>Table 1</u> lists the estimates. The elasticities for the two groups are very similar for agriculture and industry, with the difference in estimates not being significant in the latter case. The point estimates suggest that the substitutability between inputs in services production is considerably lower for the HI group. Still, the estimate of elasticity for the HI group is noisy with the upper end of its CI lying close to the lower end of the estimate of the LI group.

How effective are the price- and scale-effects in explaining the cross-country variation in linkages? Panel A of <u>Table 2 presents the explained variation</u><sup>7</sup> in intermediate shares. Column (1) corresponds to the baseline specification. Irrespective of the production sector, the two effects jointly explain more than 70 percent of the variation in the intermediate shares of agriculture. The explained variation is even higher when considering the shares of industry and services. Columns (2) and (3) shed light on the relative importance of the two effects. The former relates to the case when only the scale-effect is active while the latter holds the sole operation of the

> 6 The composition of sub-samples is stable over time –  the 14 countries with the highest incomes in 2003 (the earliest when all 28 countries feature in the sample) also have the highest incomes in 2011.

> 7 j ��, where � is the predicted share. ȷȷjj ȷȷjj var�ln�γγ���/var�ln�γγ γγ 4
price-effect. On their own, the two effects come close to explaining what is explained considering their joint action. The scale-effect dominates the baseline specification in industrial production while the price-effect comes on top in accounting for the intermediate share of agriculture in agricultural and services production. The figures in columns (1)–(3) hide the importance of country-specific sector weights. Column (4) lists the explained variation when sector-weights are invariant across countries and only price differences drive the cross-country variation. The explained variation drops appreciably. The loss is most severe in agricultural production, with the substitution elasticity being nearer to unity. The relevance of sector-weights in explaining the variation suggests the influence of other country-specific factors including distortions. Nonetheless, the price-effect still accounts for a meaningful variation for industrial and services production. The channel is especially effective in explaining the shares of the sectors themselves where it accounts for 40–70 percent of the total variation.

Lastly, I compare the absolute fit of the specifications by reporting the root mean square errors (RMSE) in Panel B. Unsurprisingly, the RMSEs are highest when sector-weights are invariant. Comparing columns (6) and (7) reveals that the price channel does a better job at fitting the data for agriculture and industry. The scale channel dominates when it comes to services production, surpassing even the fit achieved in the presence of both channels. Introducing both effects taxes the absolute fit even though the substitution elasticity in services lies notably below one.

# **4   Conclusion**

There exists a massive cross-country variation in how sectors interact with each other. The allocation of resources depends critically on these linkages and hence has implications for efficiency and growth. The analysis finds the elasticity of substitution across intermediates from the three broad sectors to be less than one.<sup>8</sup> A non-trivial fraction of the variation in intermediate shares is accounted for by nothing but the variation in prices across countries.<sup>9</sup> A ramification is that models of sectoral linkages must allow for an effective price channel to operate so that shares respond to changes in relative prices. The aggregate implications of changes in productivity and distortions derived in absence of the price channel will be biased.<sup>10</sup>

> 8 Peter and Ruane (2018) (PR) examine input substitutability using data on Indian firms. Their point estimate of elasticity for inputs aggregated at a broad level is less than one. However, they cannot rule out the CD association. The estimates in figure 1 and table 1 lie in the CI of the estimates in PR. Their analysis also highlights the relevance of aggregation as they conclusively find the elasticity to be greater than one when inputs are disaggregated to withinsector levels.

> 9 From a development accounting perspective, the price channel owing to complementarity in inputs implies that sectoral linkages constrict income differences as richer countries allocate more resources into the sector with a higher relative price. Fadinger et al. (2018) also report the same effect, though they take variations in linkages to be exogenous.

> 10 Jones (2011) discusses the relationship between aggregate output and input substitutability. Peter and Ruane (2018) quantitatively investigate the issue using data on Indian firms.

5
Furthermore, the estimates of distortions themselves are biased if they are inferred using a model with no price-effects.

# **References**

Balassa, Bela. 1964. The Purchasing-Power Parity Doctrine: A Reappraisal. Journal of Political Economy, 72(6), 584–596.

Comin, Diego A, Lashkari, Danial, & Mestieri, Marti. 2018. Structural Change with Long-Run Income and Price Effects. Working Paper: Dartmouth College, Yale University & Northwestern University.

Duarte, Margarida, & Restuccia, Diego. 2010. The Role of the Structural Transformation in Aggregate Productivity. Quarterly Journal of Economics, 125(1), 129–173.

Fadinger, Harald, Ghiglino, Christian, & Teteryatnikova, Mariya. 2018. Income Differences and Input-Output Structure. Working Paper: University of Mannheim, University of London and European University Institute.

Feenstra, Robert C., Inklaar, Robert, & Timmer, Marcel P. 2015. The Next Generation of the Penn World Table. American Economic Review, 105(10), 3150–3182.

Greene, William H. 2011. Econometric Analysis. Seventh Edition, Upper Saddle River, NJ: Prentice Hall.

Hirschman, Albert O. 1958. The Strategy of Economic Development. New Haven, CT: Yale University Press.

Inklaar, Robert, & Timmer, Marcel P. 2014. The Relative Price of Services. Review of Income and Wealth, 60(4), 727–746.

ISIC Rev. 3.1. 2002. International Standard Industrial Classification of All Economic Activities. Statistics Division, United Nations Statistical Commission, New York.

Jones, Charles. 2011. Intermediate Goods and Weak Links in the Theory of Economic Development. American Economic Journal: Macroeconomics, 3(2), 1–28.

Leontief, Wassily W. 1936. Quantitative Input and Output Relations in the Economic Systems of the United States. Review of Economic Statistics, 105–125.

OECD. 2017a. Final Consumption Expenditure of Households (Table 5), National Accounts. OECD Publishing, Paris.

OECD. 2017b. Input-Output Tables. OECD Publishing, Paris.

6
Peter, Alessandra, & Ruane, Cian. 2018. The Aggregate Importance of Intermediate Input Substitutability. Working Paper: Stanford University & IMF.

Sposi, Michael J. 2018. Evolving Comparative Advantage, Sectoral Linkages, and Structural Change. Journal of Monetary Economics, forthcoming.

7
<!-- Start of picture text --> Agriculture<br>oO<br>oO<br>-N Industry<br>2<br>x)<br>8<br>Ww<br>0 | Services<br>wo .<br>N<br><!-- End of picture text -->
||θa<br>(1)|θm<br>(2)|θs<br>(3)|
|---|---|---|---|
|**All Countries**|0.839|0.780|0.357|
||(0.004)|(0.005)|(0.051)|
|Low-Income Group|0.872|0.781|0.575|
||(0.002)|(0.005)|(0.011)|
|High-Income Group|0.861|0.777|0.375|
||(0.001)|(0.003)|(0.081)|

Table 1: Estimates of Substitution Elasticity by Income Groups 1Standard errors in parentheses. All estimates significant at 1 percent. 2Estimation corresponds to the specification in which both price- and scale-channels are active.

9
||Pa<br>|nel A: Expla<br>|ined Variati<br>|on<br>|Pane<br>|l B: Root M<br>|ean Square<br>|Error<br>|
|---|---|---|---|---|---|---|---|---|
|Channels|Price &|Scale|Price|Only|Price &|Scale|Price|Only|
||Scale|Only|||Scale|Only|||
||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|
|γa <br> <br>|0.718|0.711|0.861|0.059|0.044|0.064|0.047|0.096|
|γam<br>|0.859|0.714|0.796|0.037|0.022|0.058|0.039|0.090|
|<br>γas <br><br>|0.805|0.741|0.734|0.268|0.032|0.031|0.029|0.053|
|γma<br><br>|0.740|0.865|0.714|0.207|0.012|0.020|0.014|0.020|
|γm<br>|0.844|0.911|0.825|0.392|0.019|0.039|0.022|0.047|
|γms<br><br>|0.860|0.857|0.854|0.490|0.019|0.027|0.020|0.039|
|γsa<br><br>|0.705|0.823|0.726|0.227|0.005|0.005|0.005|0.006|
|γsm<br>|0.941|0.897|0.917|0.578|0.022|0.015|0.021|0.045|
|γs|0.898|0.836|0.856|0.689|0.024|0.014|0.023|0.045|
|CountrySpecific Sector-Weights|Yes|Yes|Yes|No|Yes|Yes|Yes|No|

Table 2: Explained Variation and Root Mean Square Error 10