seem to be a relatively straightforward exercise, it is actually challenging to verify the properties of TFP growth in sectoral value added production functions in a cross–country setting. The main reason is that calculating sectoral TFPs requires data on real value added, capital and labor inputs, and the factor shares at the sector level. Unfortunately, these data are unavailable for most countries. One of the many issues is that in order to compute real value added one must have data on the real quantity of intermediate inputs, not just the value of intermediate inputs. One data set that has the necessary information for a set of countries is EU KLEMS. 32 We begin, therefore, by using the EU KLEMS data starting in 1970 to compute TFP in the produc- tion of value added in agriculture, manufacturing, and services for the same set of countries as in Section 2: Australia, Canada, Japan, Korea and the US as well as the aggregate of 10 EU countries. 33 Figure 10 plots the sectoral TFPs for these countries. Given that we are interested in growth rates of TFP, we normalize TFP in 1990 for all sectors in all countries to be one. 32 See Timmer et al. (2010), particularly the chapter on structural change, for further discussion of the details of the EU KLEMS data on multifactor productivity. See also Duarte and Restuccia (2010) who document similar facts about TFP as we do here. 33 The 10 EU countries are the EU member states for which EU KLEMS performs growth accounting: Austria, Belgium, Denmark, Spain, Finland, France, Germany, Italy, the Netherlands, and the United Kingdom. 59
One message that emerges from Figure 10 is that there are indeed substantial di ff erences in the growth rates of TFP across sectors. Moreover, we can see that the conditions of Ngai and Pis- sarides (2007) broadly hold for Australia, Canada, the EU 10, and the United States: averaging over the time period 1970–2007, TFP in agriculture shows the strongest growth while TFP in services shows the weakest growth. This is exactly what is needed for the observed reallocation of employment out of agriculture and manufacturing into the service sector in the model of Ngai and Pissarides (2007). While data limitations make it di ffi cult to obtain long time series evidence on sectoral TFP for a large sample of countries, our theory suggests an alternative method which requires fewer data. Specifically, in the analysis of our benchmark model we highlighted the fact that if sec- toral production functions are Cobb–Douglas with equal capital shares then there is a direct inverse relationship in equilibrium between changes in relative prices and changes in relative productivities. Given appropriate data on prices, one could use this relationship to infer changes in relative productivity. Since long time series of price data is much more readily available that the data needed to measure TFP directly, this is an appealing alternative. However, in addition to requiring the assumption of Cobb–Douglas production functions with equal capital shares, there are two limitations to be noted. First, in our model we assumed that technological change
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