Until the end of 2008, the US dollar had been steadily depreciating against most world currencies, most prominently the euro. In effective terms, however, the magnitude of the depreciation was small – 10% to 15%.1 Over the same period, the US current account deficit shrank substantially – from a high of 6% of GDP in 2005 to 3.3% in the third quarter of 2008. Of course, this has many potential explanations – not least the ongoing crisis and its impact on trade. But on the face of it, such a large reversal implies a large response of traded quantities to changes in relative prices. It means that a reallocation is ongoing, whereby US consumers have been shifting away from imported goods as they have become relatively more expensive. Ultimately, it implies that US consumers are willing to substitute domestic for foreign goods, even in the face of a relatively modest shift in overall relative prices. In modelling terms, the episode suggests that a representative US consumer displays a relatively high elasticity of substitution between bundles of domestic and foreign goods.
The implication is surprising because most of the vast empirical research on the topic has identified low values for the elasticity parameter, at least on the basis of aggregated, country-level data. In historical data, aggregate traded quantities respond little to changes in prices, so that the implied elasticity of substitution must be low. Orcutt (1950) labelled this a cause for “elasticity pessimism”, because calibrated models using such low estimates would translate large movements in prices into relatively small changes in quantities. For example, a low elasticity means large exchange rate movements are necessary to substantially affect traded quantities. Thus, Obstfeld and Rogoff (2007) found a rebalancing of the US current account would require a 30% dollar depreciation, quite a considerable change.
Interestingly, a second robust conclusion has emerged from the literature. Estimated elasticities vary enormously across sectors, with an average that tends to take higher values in disaggregated data than at the country level. The result is intuitive. Some goods are much easier to substitute than others – commodities, for instance, are close substitutes, whereas branded goods, cars, and gourmet food are not. But the two facts taken together seem a contradiction. Why would the aggregate elasticity of substitution be a systematically lower number than the good-by-good estimates? After all, the former is supposed to be a weighted average of the latter.
Reconciling the evidence
There is a simple way to reconcile the evidence. Estimating the response of aggregate quantities to changes in aggregate prices is, by construction, forcing all elasticities to be the same. This ignores the intuitive, tried-and-tested fact that different goods are not substitutable to the same extent and thereby creates a pure econometric bias. Furthermore, an estimate based on aggregate data gives equal weight to all goods, when in reality some are more prominent in traded aggregated quantities. Suppose, for instance, highly substitutable goods constitute a large fraction of imports. These are goods for which small changes in price will have large effects on imported quantities. But imposing equal weights across all imported goods will act to minimise their importance, and aggregate quantities will appear to be less responsive to prices – a composition effect.
Both effects suggest estimates based on aggregate data can substantially differ from an average elasticity of substitution accounting for the fact different goods are not equally substitutable. In fact, both effects illustrate the possibility that the estimated response of aggregate traded quantities is actually silent about the average aggregate elasticity of substitution between a bundle of domestic goods and its foreign counterpart. To address both concerns, we ought to obtain disaggregated estimates of the elasticity parameter and then aggregate to the country level, using weights reflective of goods’ relative importance in overall quantities.
A striking result
Implementing that procedure gives striking results. An appropriately weighted average of good-specific elasticities is more than twice the estimate implied by aggregate data. Interestingly, constraining good specific estimates to homogeneity – i.e. simulating the procedure imposed on the data in an estimation based on aggregates – does reproduce the low estimates that were the cause for elasticity pessimism in the first place. In other words, using disaggregated data continues to pinpoint the elasticity of substitution – but imposing homogeneity has dramatic effects on the magnitude of the parameter (Imbs and Méjean, 2009).
Does it matter that the “true” elasticity of substitution is more than twice the elasticity implied by aggregate data? Surely, it will matter for the calibrated models seeking to evaluate the depreciation required to alleviate global imbalances. For instance, doubling the value of the parameter in Obstfeld and Rogoff (2007) implies the dollar depreciation required to bring the US current account back to balance drops below 20%, a number closer to what we have witnessed over the past few months.
But the correction has far-ranging implications beyond the resolution of external balances. For example, the value of the elasticity of substitution determines how much a monetary authority should care about exchange rate movements. If domestic and foreign goods are close substitutes, a central bank should not care very much about the exchange rate. And if they are close substitutes, shocks to the domestic economy will not affect much international trade, since domestic varieties are readily available. Then protectionist defences against the international diffusion of recessions seem out of order. In general, the magnitude of the elasticity of substitution will substantially affect the policy implications of most models in international economics – beyond monetary or trade policy.
Footnotes
1 As per the January 2nd 2009 Federal Reserve Statistical Release, the Broad indicator of the international value of the dollar went from 110.71 in 2005 to 99.83 in 2008.
References
Guy Orcutt (1950), Measurement of Price Elasticities in International Trade, The Review of Economics and Statistics, 32(2): 117-132.
Maurice Obstfeld and Kenneth Rogoff (2007), The Unsustainable US Current Account Position Revisited, in Richard Clarida (ed.), G7 Current Account Imbalances: Sustainability and Adjustment, University of Chicago Press.
Imbs and Méjean (2009), Elasticity Optimism, CEPR Discussion Paper No 7177
