Productivity, Trade, and Relative Prices in a Ricardian World

Abstract

In an extended Ricardian model of trade, we study the effects of improving trade deficits on relative prices, and the relation between productivity improvements and real exchange rates. An improvement in the trade balance induces relative wages to overshoot their long-run value, placing downward pressure on the terms of trade of the same order of magnitude found in Armington type models. Once the pattern of specialization changes, some of the decline is reversed with a smaller value of depreciation. We find that persistent productivity differentials do not cause distinct trends in the terms of trade. The result depends on the size of the non-tradable sector and the variability of industry-specific efficiencies. We also find that self-selection into export markets causes the relative price of non-tradable goods to respond to exogenous shift, giving birth to an endogenous Balassa-Samuelson effect. The model also suggests that in the long-run the variation of the real exchange rate is dominated by the volatility of the terms of trade.

Appendix: Increasing returns, productivity and the terms of trade

There are two countries, Home and Foreign. The number of goods produced in the world is endogenously determined. The representative agent in country k maximizes the utility function ${C}_k={\left({\displaystyle {\sum}_z}{c}_k^{\frac{\eta -1}{\eta }}(z)\right)}^{\frac{\eta }{\eta -1}}$. The domestic agent’s demand for a Home produced good i is c _h (i) = (p _h (i)/P _h )^− η C _h , while the demand for a Foreign produced good j is c _h (j) = (p _h (j)/P _h )^− η C _h . Similar demand equations are derived for the foreign agent.

There exists a pool of firms that can produce and export. To produce, a potential entrant must incur fixed costs. Output is produced using labor as the only input in production: y _k (z) = A _k (L _k (z) − α _k ). Under these assumptions, the monopolist charges a price that is marked-up over the marginal cost of production: p _k (z) = η(η − 1)^− 1 w _k A ^− 1 _k , where w and A denote wages and productivity respectively.

The zero-profit condition pins down output per firm, y _k (z) = α _k A _k (η − 1). Moreover, equilibrium in the labor market identifies the number of firms producing in domestic and foreign countries, n _k  = L _k (α _k η)^− 1. Finally, equilibrium in the goods market identifies relative wages, ω = (A _h /A _f )^1 − η(α _h /α _f )^− η. The terms of trade is then given by τ = ω(A _h /A _f )^− 1.

Higher productivity raises average output per firm, leaving the number of firms unaltered. Following a hike in domestic productivity, wages decline by more than the fall in the relative unit labour requirement. The composite effect is a decline in relative marginal costs, and a deterioration in the terms of trade.

If fixed costs take a form of output instead of labour (that is α _k  = β _k /A _k in the above), then higher domestic productivity increases the number of firms, leaving output per firm unaffected: y _k (z) = β _k (η − 1), n _k  = A _k L _k (ηβ _k )^− 1. Rising productivity increases relative wages by the same amount, ω = (A _h /A _f )(β _h /β _f )^− η. Furthermore, the unit labour requirement declines by the same magnitude. As a result, the terms of trade does not deteriorate: τ = (β _h /β _f )^− η.

The addition of a non-tradable sector will influence the results as inter-sectoral labor reallocation will also tend to affect relative wages.