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I would like to thank Michele Boldrin, Eric Clifton, Andrew Feltenstein, Alex Mourmouras, and participants at the 59th European Meeting of the Econometric Society and at the IMF Institute Seminar for useful comments and suggestions.
Of course, the mapping of manufactured goods into tradables and services into nontradables is less than perfect, given the presence of other sectors in the economy and the fact that some services may be tradable while some manufactured goods may be rendered nontradable by policy measures. For that reason, empirical support for the Balassa-Samuelson effect is not as strong as for the Baumol-Bowen effect (Froot and Rogoff, 1995; Harberger, 2003).
Canzoneri et al. (1999) present empirical evidence of this link. Other possible reasons – such as a shift of consumer demand from goods to services – appear to play a relatively minor role.
A different, but not unrelated issue is a finding by Bernard and Jones (1996) that convergence among OECD economies both in terms of labor productivity and in terms of TFP can be found in services but not in manufacturing.
Since the “hat” variables are obtained by scaling their “no-hat” counterparts by the same factor, it is clear that kG > kS implies
We ignore capital depreciation for notational simplicity.
To be precise, the slope is guaranteed to be positive to the left of the line
Of course, the assumption of perfect factor mobility across sectors is important as well, but the models that rely on the TFP growth differential to explain changes in the relative price also make that assumption.
This relies on the determinant being negative and the trace being positive, as is the case here.
For the Cobb-Douglas function, the left-hand-side expression equals simply the capital share.