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2018 | OriginalPaper | Buchkapitel

2. Overlapping-Generations Model of Economic Growth

verfasst von : Sibabrata Das, Alex Mourmouras, Peter Rangazas

Erschienen in: Economic Growth and Development

Verlag: Springer International Publishing

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Abstract

This chapter introduces the one-sector neoclassical growth model with overlapping generations. The primary focus of the chapter is growth via private physical capital accumulation. We think of private physical capital as manmade durable inputs to the production process. For our purposes, private capital can be primarily thought of as plant and equipment that is produced in one period and then used in production in the following period. To model production, we introduce firms, economic institutions that combine physical capital and labor to produce goods and services. Later in the chapter, we introduce human capital, the knowledge and skills embodied in workers. Chapter 3 adds public capital, the economy’s infrastructure created by the government, such as roads, laws, and utilities.

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Fußnoten
1
Definitions of physical capital will vary depending on the purpose at hand. In some cases physical capital is defined to include inventories, software, land, and other inputs that extend beyond plant and equipment. Public capital is often lumped together with private capital as if they are close substitutes. Chapter 3 argues that it makes more sense to treat them as complementary inputs.
 
2
You can think of the value of rt as actually determined in period t−1. In that period households make their saving decision based on the firms’ commitments to rent capital in period t and pay the rental rate rt. In other words, rt is determined in period t−1 based on the savings behavior of households and the planned investment demands of firms.
 
3
The economy never literally reaches the steady state, although it will get arbitrarily close.
 
4
The weakening effect of the capital-labor ratio on wages, stems from the diminishing marginal product of capital. As capital accumulates relative to labor, the effect of further capital accumulation on output and wages gets smaller. Formally, note that the effect of an increase in k on the marginal product of labor is (1 − α)αAkα−1 = (1 − αmarginal product of capital.
 
5
There are differences of opinion about what qualifies as an appropriate target. Some believe that calibration should not involve previous econometric estimation. According to this view, all parameters within a model should be set to match particular data points or statistical moments of a data set (sample means, variances, and covariances), but not to match econometric estimates found in the literature. Others broaden the targets to include previous statistical estimates of the model’s parameters and behavioral responses, even if the model used in the estimation is not the same as the one used in the calibration. We are comfortable with either approach. The important point from our perspective is that all quantitative models, however calibrated, should be tested by comparing their predictions against observations or statistics not used in the calibration process. The fact that these “tests” or comparisons are not as formal and refined as traditional hypothesis testing in statistics does not particularly concern us. At this stage in the profession’s understanding of macroeconomics, models that even roughly approximate reality are difficult to find. Hopefully, as our approximations become more refined, we will need to worry about more formal testing procedure.
 
6
For a further discussion of the issues associated with quantifying overlapping generations models see Appendix B.
 
7
One can think of the financing of public school expenditures as coming from a tax on capital or capital income (similar to the property tax used to finance schooling in the U.S.). When σ = 1, as with our log preferences, a capital tax has no effect on saving and the transition equation.
 
8
Note that the acquisition of financial assets occurs in the first period of adulthood and the financial transfers are made in the second period of adulthood. Thus, the transfers are made when both generations are alive. Transfers of this type are called inter vivos transfers, as opposed to bequests that are transferred at death. In our model, where we assume (i) perfect certainty, (ii) perfect life-cycle credit markets, and (iii) no strategic interactions between generations, the timing of financial transfers is irrelevant. However, the timing of transfers can matter when these conditions are not met (see for example, Bernheim et al. (1985) and Cox 1987).
 
9
In microeconomics, the maximum attainable utility function is called an indirect utility function. In the pure life cycle version of our model, with no altruism, an indirect utility function is easily obtained. Take the optimal consumption choices of the household (5) and substitute them back into the CES utility function. For example, if we do this for the case of σ = 1, we get the very simple indirect utility function \( {U}_t^{\ast }=\beta \ln \beta +\left(1+\beta \right)\ln \frac{1}{1+\beta }+\left(1+\beta \right)\ln {w}_t+\beta \ln {R}_t \). With altruism, things are not nearly so simple. This is because generation-t’s utility depends on generation-t+1’s utility, which depends on generation-t + 2’s utility, and so on. As we shall see, in this case Vt cannot be found directly. Instead it is implicitly defined by a difference equation in the function Vt— what is known as a Bellman equation. In this case, Vt is called a value function and solving for this function is tricky business. Stokey and Lucas (1989) provide a general discussion of the conditions under which the value function exists, is unique, and is differentiable with respect to initial wealth.
 
10
Often, when the focus of the analysis is on intergenerational transfers, the life-cycle feature of the model is dropped. Households are modeled as living only a single period of adulthood in which they consume and make transfers to their children. We will see examples of these models in future chapters.
 
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Metadaten
Titel
Overlapping-Generations Model of Economic Growth
verfasst von
Sibabrata Das
Alex Mourmouras
Peter Rangazas
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-89755-4_2