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2019 | OriginalPaper | Buchkapitel

8. Aggregation

verfasst von : Thorsten Hens, Sabine Elmiger

Erschienen in: Economic Foundations for Finance

Verlag: Springer International Publishing

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Abstract

In this book, we assume that the entire consumption (production) sector can be represented by a single household (firm). This seems to be an odd assumption given that those sectors consist of millions of heterogeneous agents: each household has different preferences and faces another budget constraint, whereas each firm produces goods in its own way and can be more or less profitable.

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Fußnoten
1
In our book, we only consider risk arising from uncertainty in capital productivity and technological progress. This type of risk is subject to many financial products. In contrast, uncertainty in the labor supply might not be tradeable because of moral hazard problems. Insuring against a decrease in labor supply (e.g., through unemployment insurance) may not be optimal for society because this could reduce the incentive to work.
 
2
Prices are normalized to one, and we suppress the subscript z 0. In addition, we use that dividends equal profits in equilibrium.
 
3
Since we only want to argue that Pareto-efficiency can be used to aggregate the consumers into one representative consumer, we fix the production decision at the equilibrium values.
 
4
As in earlier chapters we drop the subscript z t and normalize prices to one in order to shorten notation.
 
5
Note that the weights depend on the realized state prices. Therefore the aggregate utility function depends on the realization of past states \(U_t(\cdot )=U_{t,z^{t-1}}(\cdot )\).
 
6
The envelope theorem is explained in Sect. A.11>.
 
7
For an explanation of the envelope theorem see Sect. A.11.
 
8
The conditions on individual biases can be weakened. It suffices for example if the correlations are non-positive.
 
9
This is true since the positively weighted sum of concave functions is concave.
 
10
See e.g. Hens and Reichlin (2013) for this point. Moreover, the time preference of the aggregated individuals is typically no simple arithmetic averages of the individual time preferences (see e.g. Lengwiler 2005 and Gollier and Zeckhauser 2005).
 
11
For a review on the equity premium puzzle see Mehra (2006).
 
Literatur
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Zurück zum Zitat Gollier, C., & Zeckhauser, R. (2005). Aggregation of heterogeneous time preferences. Journal of Political Economy, 113 (4), 878–896.CrossRef Gollier, C., & Zeckhauser, R. (2005). Aggregation of heterogeneous time preferences. Journal of Political Economy, 113 (4), 878–896.CrossRef
Zurück zum Zitat Hens, T., & Reichlin, C. (2013). Three solutions to the pricing kernel puzzle. Review of Finance, 17 (3), 1065–1098.CrossRef Hens, T., & Reichlin, C. (2013). Three solutions to the pricing kernel puzzle. Review of Finance, 17 (3), 1065–1098.CrossRef
Zurück zum Zitat Hens, T., & Rieger, M. O. (2010). Financial economics: A consice introduction to classical and behavioral finance. Heidelberg: Springer.CrossRef Hens, T., & Rieger, M. O. (2010). Financial economics: A consice introduction to classical and behavioral finance. Heidelberg: Springer.CrossRef
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Zurück zum Zitat Lengwiler, Y. (2005). Heterogenous patience and the term structure of real interest rates. The American Economic Review, 95 (3), 890–896.CrossRef Lengwiler, Y. (2005). Heterogenous patience and the term structure of real interest rates. The American Economic Review, 95 (3), 890–896.CrossRef
Zurück zum Zitat Magill, M., & Quinzii, M. (1996). Theory of incomplete markets. Cambridge: MIT Press. Magill, M., & Quinzii, M. (1996). Theory of incomplete markets. Cambridge: MIT Press.
Zurück zum Zitat Mehra, R. (2006). The equity premium puzzle: A review. Foundations and Trends ® in Finance, 2 (1), 1–81. Mehra, R. (2006). The equity premium puzzle: A review. Foundations and Trends ® in Finance, 2 (1), 1–81.
Zurück zum Zitat Negishi, T. (1960). Welfare economics and existence of an equilibrium for a competitive economy. Metroeconomica, 12 (2–3), 92–97.CrossRef Negishi, T. (1960). Welfare economics and existence of an equilibrium for a competitive economy. Metroeconomica, 12 (2–3), 92–97.CrossRef
Metadaten
Titel
Aggregation
verfasst von
Thorsten Hens
Sabine Elmiger
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-05427-4_8