3 Analytical framework
This section describes the Ramsey-Solow model of optimal saving, as modified to incorporate population ageing. Before giving a detailed description of the model, this section discusses two important issues for the application of the model: the existence of an endogenous interest rate premium, and labour productivity growth.
3.1 Endogenous interest rate premium
This study extends the analytical approach adopted in the seminal work by Cutler et al. (1990) and later by two of the same authors in Elmendorf and Sheiner (1999). They apply a Ramsey-Solow model, allowing for heterogeneous consumers and workers, to the case of both a closed economy and a small open economy. Yet neither the small open economy nor the closed economy is an entirely appropriate framework for an economy such as New Zealand. While it is both small and relatively open, New Zealand almost certainly does not face perfect capital mobility in that it does not face a perfectly elastic supply of foreign capital.
Indeed there is extensive evidence for many other countries that capital is not perfectly mobile and is in fact quite immobile.[4] The most important explanation according to Gordon and Bovenberg (1996) is asymmetric information between investors of different countries. In particular, foreign investors know less about the economic prospects of another country than do the residents of that country. Foreign investors therefore tend to earn a lower return on their investments than do domestic investors in the borrowing country. This drives a wedge between the equilibrium interest rate in borrowing and lending countries, where the size of the wedge depends on the amount of international capital flows. There is also evidence that small countries face a risk premium, the size of which depends on their level of foreign debt[5]. The result of each of these mechanisms – asymmetric information and a risk premium - is that the equilibrium interest rate in capital importing countries is higher than the interest rate in capital exporting countries.
The existence of an endogenous interest rate premium is potentially important in determining the effect of a demographic shock on optimal saving. With a constant world interest rate and a constant rate of time preference the rate of return to saving, following a demographic shock, is unaffected by the path of debt. This is not the case, however, if the interest rate is affected by the level of foreign debt for example. In that case the marginal cost of borrowing increases as debt increases and conversely falls as debt falls. Hence the rate of return to saving is a function of the path of debt and is therefore endogenous as it is in the closed economy case. The extent to which an interest rate premium matters for the path of optimal saving was investigated in Guest and McDonald (2002b) by simulations of the same model as that applied in this study. They found that the path of optimal saving in response to a demographic shock – in particular, a lower fertility rate – becomes close to that for the closed economy for quite small endogenous interest rate premia.
In representing an endogenous interest rate premium as an upward sloping supply price of foreign capital, we draw on Glenn (1997) who considers the impact of a rise in the price of an imported production input for an economy facing an interest rate that depends on its level of foreign liabilities.
3.2 Demographic change and labour productivity growth
An important question concerns the impact of demographic change on labour productivity growth. This could quite easily go either way, as discussed by Cutler et al. (1990: 38). On the one hand slower population growth makes innovation less profitable by reducing the gains from economies of scale through the spreading of fixed costs; and a smaller youth share of the population may reduce innovation through a loss of “dynamism”. Also, in endogenous growth models of the type in Steinman, Prskavetz, and Feichtinger (Steinman, Prskawetz and Feichtinger 1998), lower population growth results in less human capital accumulation and therefore a lower growth rate of labour productivity. On the other hand, in other endogenous growth models, slower labour force growth implies a higher relative price of labour and therefore greater incentive to innovate through capital investment or research and development (Romer 1990). Also, diseconomies of higher population growth, through congestion for example, can reduce labour productivity growth.
The empirical evidence on the effect of demographic change on labour productivity is relatively scarce. Galor et al. (1997), using panel data on 73 countries, find evidence that countries with smaller average family size attain higher labour productivity. They attribute this to the extra resources that parents with smaller families can provide to each of their children to finance their education. Similarly, Ahituv (2001), using panel data on 114 countries, concludes that lower population growth increases GDP per capita growth. The principal mechanism here seems to be the effect of the time required for child rearing on the labour input of their parents. Fewer children imply less time input from parents thereby freeing up labour time (although, properly measured, this would not amount to an effect on labour productivity but rather a change in labour input). On the other hand Hondroyiannis and Papapetrou (1999) find no long run relationship between the fertility rate and the output growth rate using time series data for the U.S. On the basis of this ambiguity in theory and evidence, Guest and McDonald (2002b) assume that demographic change has no net effect on labour productivity; that assumption is also adopted in this paper.
