Saving, fertility and public policy in an overlapping generations small open economy☆
Introduction
In this paper we explore the fiscal policies needed for public debt management and their effects on both saving and fertility choices in an OLG small open economy. Although these issues are not new in economic research (as we shall see in Section 2), we believe that our attempt is relevant for at least three reasons.
First, for theoretical purposes. To the best of our knowledge the analysis of the relationship between fertility and saving, on one hand, and fiscal policies and public debt in a small open economy, on the other hand, has not been carried out so far. Hence, although based on simplistic assumptions, our insight may help to better understand the forces at work on saving and fertility in presence of public debt, which can extend to more complex models with endogenous prices and/or growth. Second, our work is potentially relevant for policy reasons, since the recent financial crisis has raised concern about the viability of sustained growth in presence of increasing levels of public debt. Therefore, it is natural to analyse the circumstances under which such debt increases (as well as any other possible debt change) can be associated with a stable long run pattern of steady growth and to assess the consequences of debt management effects on the economy. Finally, besides providing clear-cut policy implications, our analysis also offers possible testable implications concerning the pattern of fertility, taxes and public debt observed in many developed economies.
Our main results can be summarized as follows: the effects of a policy aimed at modifying the steady state value of per-capita public debt depend on the conditions of the economy (where per-capita is to be intended as per-worker in our context), in that the latter determine the direction and the intensity of the fiscal adjustments needed to achieve the desired level of debt. More precisely, under a low world-interest-rate regime, a per-capita public debt cut needs a fiscal adjustment that, at the equilibrium, will decrease both saving and fertility, while under a high world-interest-rate regime the same debt reduction needs a fiscal adjustment that operates in the opposite direction and finally will increase both saving and fertility. We also show that in both cases these fiscal adjustments require two periods: in the first one, taxes will be moved in such a way to allow next period per-capita debt to reach the desired new level. In the second period, taxes will be moved in the opposite direction, so as to stabilize the otherwise unstable level of debt. The economic rationale behind these results is the following: any tax change exerts a two-fold effect on per-capita debt: on one hand, higher tax revenues will decrease next period per-capita debt (direct or “tax revenues” effect); on the other hand, higher taxes will reduce fertility of current workers, so that each member of the next-period (smaller) generation of workers will bear a higher level of per-capita debt (indirect or “dilution” effect). In a low world-interest-rate regime the latter effect prevails, so that next period per-capita debt will be higher after a tax increase, while in a high world-interest-rate regime the opposite outcome occurs. However, any tax change from a previously level associated with a stable steady state will lead public debt to undertake an unstable trajectory, so that in the second period an extra tax adjustment, of opposite sign and larger extent than the one of the first-period, is needed in order to stabilize public debt at its new level. Furthermore, given that, in each period, such tax variations induce a corresponding change in disposable income, any of these policies will generate a two-period fluctuation of both saving and fertility in the same direction as disposable income. Fluctuations in fertility have been unveiled, among others, by Jones and Schoonbroodt (2016), showing procyclical behaviour along the business cycle. We provide here another possible explanation for fertility fluctuations which may complement the existing ones: a policy aiming at stabilizing the level of debt requires the implementation of a multi-period fiscal policy with tax variations that alternate in sign and hence affect fertility in opposite directions, through their effect on disposable income; we notice that this latter channel for fertility fluctuations represents an outcome that has clear empirical testable implications.
Our results have far reaching policy implications which may help to tackle some issues that are at the heart of the current political debate: for example, public debt cuts will be beneficial for the economy (i.e. for both fertility and saving and also in terms of welfare) under a high interest rate regime, while under a low interest rate regime (as the current one), reducing public debt will reduce welfare and exacerbate the dramatic drop of fertility and saving of many (small) Western countries.
The paper work is organized as follows: in section 2 we present the related literature, in section 3 we lay out the model and in section 4 we characterize the steady state equilibrium and the fiscal adjustment procedure for debt management and we carry out a welfare analysis; in section 5 we carry out comparative statics exercises by investigating the effects of some relevant parameters of the model on the long run levels of fertility and saving. Conclusions will end the paper.
Section snippets
Literature review
Although the analysis of the effects of debt management on individual choices, such as fertility and saving, is not new in economic research, most literature has focused on identifying and testing explicit links between those decisions and economic factors such as income/wage or the process of economic development.
In the first vein,1 some theories predict an inverse
The model
In this work we extend a standard OLG model (Diamond, 1965) in order to entail endogenous fertility.7 In doing this, we focus on the case of a small open economy, where both the interest rate and the wage are fixed. The basic actors of this economy are (i) a Government which can affect the levels of a lump sum taxation to achieve a target level of per-worker public debt
Characterization of the steady state
To characterize the steady state for this economy, we explicitly rule out exceptional cases and hence we assume
A: 1) , and , i.e. the economic parameters of the model are positive;
2) and , i.e. preferences are well defined and monotone;
3) , i.e. the target level of per-worker debt fixed by the Government is non-negative.12
Comparative statics on the steady state solutions
In this Section we extend the previous analysis and, fixed the objective in terms of per-worker debt, we analyse the effects on taxes and on individual decisions of a change in the underlying parameters of the model through comparative static exercises. We will focus on changes of the economic variables and and of the preference parameter . Throughout this Section we assume the validity of A) and that the system satisfies ).
Conclusions
In this paper, we characterize the steady state and the fiscal policy adjustments necessary for public debt management in an OLG small open economy.
We found that, in steady state positions, the public variables (i.e. taxes and public debt levels) display a different correlation depending on the parameters of the model defining two different regimes: high and low world interest rate. The reason for this finding is that any correction of the outstanding level of debt needs a corresponding tax
References (46)
- et al.
Stability periods between financial crises: the role of macroeconomic fundamentals and crises management policies
Econ. Modell.
(2014) - et al.
Mortality, fertility and saving in a malthusian economy
Rev. Econ. Dynam.
(2002) - et al.
Optimal government investment and public debt in an economic growth model
China Econ. Rev.
(2017) - et al.
Public debt and growth: heterogeneity and non-linearity
J. Int. Econ.
(2015) - et al.
Endogenous fertility and optimal population growth
J. Publ. Econ.
(1985) - et al.
Population and neoclassical economic growth: a new child policy perspective
Econ. Lett.
(2009) - et al.
On the relationship between fertility and public national debt
Econ. Modell.
(2013) - et al.
Limits to government debt sustainability in OECD countries
Econ. Modell.
(2017) - et al.
Child benefit and fiscal burden in the endogenous fertility setting
Econ. Modell.
(2015) - et al.
Fiscal and monetary policies in the BRICS: a panel VAR approach
Econ. Modell.
(2016)
Was an industrial revolution inevitable? Economic growth over the very long run
Adv. Macroecon.
Baby busts and baby booms: the fertility response to shocks in dynastic models
Rev. Econ. Dynam.
A model of economic growth with altruism between generations
J. Econ. Theor.
Does the design of a fiscal rule matter for welfare?
Econ. Modell.
Optimal taxation, critical-level utilitarianism and economic growth
J. Publ. Econ.
Demographic transition, stagnation, and demoeconomic cycles in a model for the less developed economy
J. Macroecon.
Social security and endogenous fertility: pensions and child allowances as Siamese twins
J. Publ. Econ.
Fiscal policy in the US: sustainable after all?
Econ. Modell.
Fertility choice in a model of economic growth
Econometrica
An economic analysis of fertility
A reformulation of the economic theory of fertility
Q. J. Econ.
Human capital, fertility and economic growth
J. Polit. Econ.
Child endowments and the quantity and quality of children
J. Polit. Econ.
Cited by (1)
Fertility, fiscal deficit and sustainability of public debt in an endogenous growth model
2023, Economics and Business Review
- ☆
The authors would like to thank three anonymous referees and the Editor (Sushanta Mallick) for their useful comments and insights. The usual disclaimer applies.