This is also at odds with the data since as shown in Herrendorf et al 2013 the

This is also at odds with the data since as shown in

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value added to the other sectors using constant shares. This is also at odds with the data, since as shown in Herrendorf et al. (2013), the increasing importance of software as a component of investment has led to an increase in the share of investment value added occurring in the service sector. Nonetheless, since it serves to facilitate transparency, we will adopt this alternative as a benchmark in the next section when we discuss the qualitative features of balanced growth paths in di ff erent special cases of the model. However, it should be kept in mind that movements in the sectoral distribution of investment value added shares could a ff ect the predictions that we highlight. As a practical matter, while this e ff ect can matter, it is probably not so relevant at the quantitative level because total investment is a relatively small share of GDP. The second issue concerns how to connect the model with production value added data ver- sus consumption expenditure data. Specifically, assuming that the sector production functions are interpreted as value added production functions leads to a di ffi culty when trying to connect the model with data on consumption expenditure shares. Because equilibrium requires that c it = k θ it ( A it n it ) 1 - θ , it would seem natural to identify p it c it / j p jt c jt as the model’s measure of the nominal consumption share of sector i in period t . However, this share is not the appro- priate measure for the nominal consumption expenditure share of sector i as measured in the data. To see why, let us return to the example discussed earlier of the purchase of a cotton shirt. To measure the contribution of this shirt to manufactured final consumption expenditure, we need to aggregate all value added that goes into the production of the shirt through the use of intermediate inputs from each of the three sectors. This requires us to take into account the input–output relationships about how value added is aggregated into final consumption expen- 36
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diture. In contrast, the above definition of consumption shares includes only the value added that came from the manufacturing sector itself, and so it does not reflect how final consumption expenditure is measured in a world in which each sector uses intermediate inputs from the other sectors. To avoid this problem, one could alternatively assume that p it c it / p jt c jt in the model does correspond to the nominal consumption expenditure share of sector i in period t as measured in the data. But since in equilibrium c it = k θ it ( A it n it ) 1 - θ , it would then follow that p it k θ it ( A it n it ) 1 - θ is not an appropriate measure of value added from sector i in period t as measured in the data. Returning to the shirt example, this piece of c mt now reflects the value added components from each of the three sectors that went into producing the final product, and so it cannot be the value added from one particular sector. In order to maintain consistency, it must be that the production functions summarize the labor and capital from the various stages of production that are used to produce final consumption expenditure. In order to obtain value added shares
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