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Demand and the skill-premium puzzle

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Demand and the skill-premium puzzle

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Several areas of theoretical and applied microeconomics focus on explaining empirical phenomena from the production side of general equilibrium. International trade concentrates on explaining diverse questions such as trade volumes and relative wages, based on trade costs, differences in factor endowments, and differences in technologies across countries. Both trade and labour economists look to factors such as skill-biased technical change and trade liberalisation to explain changes in skill premia (i.e. the ratio of skilled to unskilled wages). 

But problems and puzzles remain. Focusing on production makes it hard for trade economists to explain puzzles such as the apparent home bias, small volumes of North-South trade, and the ‘missing trade’ puzzle (i.e. the lack of factor content of trade relative to predictions from standard Heckscher-Ohlin models). Standard trade models in the Heckscher-Ohlin tradition also predict that falling tariffs and trade costs should lead to a relative increase in the return to a country’s abundant factor, which implies that the skill premium should fall in low-income countries where less-skilled labour is the abundant factor. Yet this prediction is rejected by the data, which show relative skilled wage increases in low-income countries have been as large as those in high-income countries.  Labour economists have advocated skill-biased technical change as an explanation for rising skill premia, but evidence for this (such as shifting occupational demand) is not always conclusive.1

Our work turns to the demand side of general equilibrium in search of alternative, or rather complementary, mechanisms that help explain these gaps and inconsistencies. Some precedents go back as far as the Swedish economist Linder (1961), who noted that trade in manufactured goods (as opposed to primary products) is larger when countries have similar, and high, per-capita incomes. But this approach soon disappeared from almost all of international trade analysis in favour of the analytically tractable but counter-empirical assumption that consumers have homothetic preferences. This implies expenditure shares across goods and services depend only on relative prices, not on income. This assumption became so dominant that we simply assumed that it was true, and that consumption demand had little to contribute to our understanding of trade and wages.

Over the last decades,  several authors have relaxed the assumption, allowing for preferences to be non-homothetic so that demand is systematically related to per-capita income. These include Markusen (1986, 2013), Matsuyama (2000,2019), Fieler (2011), and Caron et al. (2014). All six papers mostly focus on trade volumes and trade partners (i.e. who trades a lot/little with whom). The empirical results in Fieler (2011) and Caron et al. (2014) confirm that deviations from homotheticity are considerable. But non-homotheticity alone does not solve the empirical puzzles nor explain changes in skill premia. Why does it matter if rising incomes mean that households shift spending toward smart phones and away from rice and potatoes?

The second step in the search was therefore to consider how the characteristics of goods and services in consumption, specifically their income elasticity of demand, might be correlated to their characteristics in production. For the latter, the principal suspect was the factor intensity. What if goods with high income elasticity of demand (i.e. ‘luxuries’) are skilled-labour intensive in production, and conversely, low income elasticity of demand sectors (i.e. ‘necessities’) are unskilled-labour intensive? The possibility and implications of such a correlation between demand and production characteristics was first explored theoretically by Markusen (1986), with respect to trade volume and trade partner questions, then tested and quantified in a richer theoretical framework in Caron et al. (2014).2

Per-capita income and the skill premium

Examining the consequences of the income elasticity / skill intensity correlation is at the heart of Caron et al. (2014, 2020). In both papers, we exploit the Global Trade Analysis Project (GTAP) data set, which includes harmonised data on consumption, production, and trade for a large range of countries. The data include full input-output structures and distinguish five primary factors of production including skilled and unskilled labour. Preferences are estimated in a two-step procedure. First, gravity equations are estimated to back out relative productivity and construct price indices for all the countries. Then, demand functions are estimated controlling for price differences across countries, providing income elasticities for each sector.

On the production side, we calculate factor intensities across sectors including indirect use from the input-output matrices. We then compute the correlation between income elasticities of demand and factor intensities. In both papers, the correlation with skill labour intensity is highly significant and varies between about 0.40 and 0.70. This correlation is robust to the inclusion of capital and natural resource intensities and the exclusion of services.

Our first paper (Caron et al. 2014) investigates the implications of this correlation for trade patterns. As discussed, the standard Heckscher-Ohlin model with homothetic preferences over-predicts trade volumes. With our non-homothetic demand system, countries are relatively specialised in consuming the same goods they are producing. Skilled-labour abundant countries are specialised in producing skilled-labour intensive goods as in Heckscher-Ohlin, but they are also high-income countries and hence are specialised in consuming those same skilled-labour intensive goods and services. We show that non-homothetic preferences reduce the Heckscher-Ohlin model’s over-prediction of the net factor content of trade by about 60%. The increased similarity between countries’ specialisation in production and consumption also explains why countries trade relatively more with countries of similar income level than what standard Heckscher-Ohlin forces would suggest.

The second paper (Caron et al. 2020) turns to the skill premium question. This is a topic that has generated a lot of controversy and for which the empirical regularities described above have important implications. We quantify these implications by counter-factual simulations using the same model and data set, though estimated at different points in time. In our main ‘unified’ experiment, we adjust total factor productivity and trade costs to match historical rates of real income growth and trade openness over the 1995-2010 period. Specifically, we back out the amount of Hicks-neutral (sector-neutral) productivity growth in each country that generates observed growth in that country’s income over the period. We simultaneously adjust trade costs to match the historical rates of trade openness. Then we compute a new world general equilibrium.

The results from our counterfactual are shown in Figure 1. The vertical axis is the percentage change in the skill premium and the horizontal axis lines up countries by their initial log per-capita expenditure. The red dots give the effect on each country with our estimated non-homothetic preferences while the blue triangles give results assuming homothetic preferences. For readability, we do not label the blue triangles, but each one corresponds to the country with the red dot directly above it. The solid red line is a linear fit for the non-homothetic case, while the dashed blue line is the linear fit for the homothetic case. 

Figure 1 Simulated changes in the skill premium

Demand and the skill-premium puzzle 2

Notes: Simulated changes in the skill premium caused by 1995-2010 changes in real per capita income and openness to trade (general equilibrium simulations).

With homothetic preferences, we find that the combined effect of observed changes in trade costs and observed growth in per-capita income (if neutral in terms of productivity changes across sectors and endowment changes across factors) would have had virtually no effect on the skill premium on average. But under our estimated non-homothetic preferences, we show that these changes had the potential to significantly increase the skill premium. This is especially true in developing countries: we find a 17% increase in the skill premium in China, a 30% increase in in India, and a 21% increase in Vietnam. Low-income countries see an average increase of 9%. Changes are positive but much more modest in developed countries. On average, our simulated changes are correlated with observed changes in the skill premium over the same period.

 Both the productivity and trade-cost channels contribute to these results (we also simulate these two changes separately in the paper). The productivity channel is a simple implication of the correlation between income elasticity and skill intensity across sectors: real-income growth shifts consumption toward skill-intensive goods and services, raising the skill premium in general equilibrium. An analysis of why this is significantly stronger in developing countries is elaborated in our paper.

Trade costs were generally falling significantly over this period. Under homothetic preferences, this should lead to a fall in the skill premium in the developing countries, consistent with the Stolper-Samuelson theorem – each country sees an increase in the relative price of its abundant factor. Indeed, this does happen for many low-income countries in our counter-factual simulation. Under our estimated non-homothetic preferences, the change in the skill premium is significantly more positive (meaning in some cases the change is less negative). Two forces are at work. The first is a direct implication of the reduction in the (initial) factor content of trade under non-homothetic demand – changes in trade costs imply smaller changes to the skill premium. The second is that real income growth due to falling trade costs is especially large for the poorer countries, which then see larger shifts in consumption toward skilled-labour intensive goods and services.

Summary

We have argued in our work that the attempt to address a range of empirical puzzles only from the production side of general equilibrium has been inadequate. Our position is that the demand side of general equilibrium interacted with supply contributes an important additional explanation. We emphasise that we are not proposing an alternative to Heckscher-Ohlin structures or skill-biased technical change, but rather an additional mechanism. These are not mutually exclusive and can all be contributing to things like a rising skill premium in various measures.

What we have shown is that consumer preferences differ significantly from homotheticity, and that goods and services with high income elasticities of demand are skilled-labour intensive in production. These in turn have important implications for empirical puzzles such as trade-volume and skill-premium findings that do not always fit well with production-side explanations. We hope to contribute to a resolution to the puzzle that the rising skill premia in developing countries seems inconsistent with standard trade theories.

 

References

Autor, D, D Dorn and G Hanson (2015), “Untangling trade and technology: evidence from local labour markets”, Economic Journal 125(584): 621-646.

Buera, F and J Kaboski (2012), “The rise of the service economy”, American Economic Review 102(6): 2540-2569.

Caron, J, T Fally and J Markusen (2014), “International trade puzzles: a solution linking production and preference”, Quarterly Journal of Economics 129(3): 1501-1552.

Caron, J, T Fally and J Markusen (2020), “Per-capita income and the demand for skills”, Journal of International Economics 123, article 103306.

Fieler, A C (2011), “Non-homotheticity and bilateral trade: evidence and a quantitative explanation”, Econometrica 79(4): 1069-1101.

Johnson, M and M Keen (2013), “A dynamic equilibrium model of the US wage structure, 1968-1996”, Journal of Labor Economics 31(1): 1-49.

Katz, L and K Murphy, “Changes in relative wages, 1963-1987: supply and demand factors”, Quarterly Journal of Economics 107(1): 35-78.

Linder, S B (1961), An Essay on Trade and Transformation, Stockholm: Almqvist and Wiksell.

Markusen, J R (1986), “Explaining the volume of trade: an eclectic approach”, American Economic Review 76: 1002-1011.

Markusen, J R (2013), “Putting per capita income back into trade theory”, Journal of International Economics 90(2): 255-265.

Matsuyama, K (2000), “A Ricardian model with a continuum of goods under non-homothetic preferences: demand complementarities, income distribution, and north-south trade”, Journal of Political Economy 108: 1093-2000.

Matsuyama, K (2019), “Engle’s Law in the global Economy: Demand-Induced Patterns of Structural Change, Innovation, and Trade”, Econometrica 87(2): 497-528.

Endnotes

1 While a detailed literature review is well beyond the scope of this article, some well-known papers in this literature are Autor et al. (2015), Johnson and Keane (2013), and Katz and Murphy (1992).

2 Buera and Kaboski (2012) document the large and persistent shift to services over time, and then show that within services, it is the skilled-labour intensive services that are expanding. Though they do not explore this, their findings have qualitatively similar consequences for the skill premium as in our framework.

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