26 Hall and Jones 2007 also develop a framework that can give rise to

26 hall and jones 2007 also develop a framework that

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guidance for how to connect the model with data at the level of broad sectors. 26 Hall and Jones (2007) also develop a framework that can give rise to non–homothetic de- mand functions, though their focus is specifically on the rise of spending on health care, as opposed to the more general process of structural transformation. Nonetheless this is of interest in the current context since increases in health care account for a significant part of the overall increase in the size of the service sector. In the basic model of Hall and Jones, utility in the 26 Buera and Kaboski (2012a, 2012b) adopt a similar preference structure as Foellmi and Zweim¨uller (2008), except that they stress the introduction of new goods and adjustment along the extensive margin. Other aspects of their analysis are quite di ff erent, however. We discuss their model in more detail later in this section and again in Subsection 7.6. For now we simply note that Buera and Kaboski (2012a) derive an explicit mapping from their preferences to a reduced–from representation of preferences over goods and services. The interesting feature of this mapping is that it includes a term that is analogous to our term ¯ c s , but rather than being a constant, its value changes over time as technological progress occurs. 50
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current period is derived from a single good that represents all non–health consumption. The period utility function is homothetic and health consumption in period t provides no direct util- ity flow in period t but does influence the probability of survival to next period. Intuitively, this model has features akin to the model with intensive–extensive margins that we discussed above. Specifically, a household can adjust along the intensive margin by spending more on consump- tion, or along the extensive margin by spending more on health care and therefore increasing the expected number of periods in which consumption occurs. As the level of consumption increases, the marginal utility from additional consumption at the intensive margin decreases relative to the marginal utility of living an additional period. This can generate an increasing expenditure share for health consumption as incomes rise, and therefore look like a model that features a non–homothetic period utility function over health and non–health consumption. 27 4.2.2 Other Specifications Emphasizing Relative Price E ff ects In the Ngai–Pissarides model analyzed as Case 2 above, sectoral reallocation of factors of pro- duction and nominal value added shares occurred as a result of relative output price changes along the balanced growth path. Relative price changes were in turn generated by having di ff er- ential rates of technological progress across sectors. The literature has also noted that relative output price changes can result from changes in the relative prices of inputs if sectors vary in the intensity with which they use inputs and there are changes in the relative supply of fac- tors. In this case, one can generate structural transformation via relative price changes even if technological change is neutral.
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