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.

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