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1. The Balassa-Samuelson effect: intuition and standard formalisation
The intuition underlying the Balassa-Samuelson effect (BSE) is as follows: consider a country producing two goods: tradables and nontradables. Suppose the wage rate in either sector equals the marginal labour product. Assume that labour is mobile and homogenous; also assume that both sectors pay the same wage rate. Now imagine an increase in the (physical) labour productivity in the tradable sector for instance, on account of technological change. Then there is a rise in the wage rate in the sector. Due to the 'law of one wage' that is assumed, the wage rate in the non-tradable sector rises as well. This raises costs and hence prices in the latter sector. In effect, a rise in the relative (non-tradable/tradable) price ratio follows.
Equation 8 is interpreted as the BSE:3 dA/A is identified with the rate of growth of productivity in the tradable sector; dB/B with the rate of growth of productivity in the non-tradable sector. The relative price of the non-tradable good increases with rising dA/A (and decreases with rising dB/B). If the sectors' labour elasticities are the same (α = β), the relative price of the non-tradable good rises when dA/A > dB/B (and in particular when dA/A > 0 and dB/B = 0). If α < β (the tradable sector is more capital-intensive), the relative price of the non-tradable good will rise - even at the same rates of productivity growth (dA/A = dB/B).
The second, and more consequential, problem pertinent to interpreting equation 8 - as well as equation 9 - arises with respect to the treatment of the production-elasticity parameters α and β. Hitherto, these have been assumed to be constant over time. Thus, equations 8 and 9 apply only when technical progress is neutral. When technical progress is non-neutral, α and β will vary over time, possibly together with A and B. In this case neither equation 8 nor equation 9 can capture the associated change in the relative price of the non-tradable good.
The proper analytical formula for determining Δp/p as a function of all varying parameters, which can be derived from equation 6, appears rather difficult to handle in analytical terms; however, some properties of Δp/p as a function of...