## Abstract

Intergenerational transfers are a very important part of our daily economic activity. These transfers, whether familial or public, may influence our economic decisions to the same extent that financial markets do. In this paper, we seek to shed some light on the effects of transfers on capital accumulation in the face of demographic aging. In particular, a general equilibrium overlapping generations model with realistic public and familial transfers drawn from the National Transfer Accounts project is implemented to Spain. Given that, in this case, net familial transfers mainly go from parents to children while public transfers go from children to parents, it is shown that the Spanish baby boom and baby bust could lead to capital depletion and a reduction in consumption per capita.

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## Notes

The term demographic dividend has been used in economic demography literature, and it is full of economic meaning. The first dividend refers to the positive initial effect of a demographic transition on consumption per capita: the so called support ratio of workers to consumers increases in the first stages of the demographic transition (Bloom and Williamson 1998). This effect always occurs and is temporary—it disappears as those workers age. In contrast, the second demographic dividend, called capital deepening in economic terms, is not automatic and might be persistent.

National Transfer Account database (NTA), http://www.ntaccounts.org.

The calibration procedure is shown in Appendix A.1 in Supplementary material.

As detailed in the demography section in the online material, we deviate from many of the available large-scale OLG models for Spain and other countries (Börsch-Supan et al. 2006) in that our economy is in steady state in 1870 rather than in 1960, capturing most of the Spanish demographic transition features.

As NTA assumes the individual is the fundamental unit, net transfers received by firms from the government are also imputed to individuals.

In an open economy, the sum of all private transfers is equal to the value of net transfers with the rest of the world.

Current estimates of NTA profiles do not explicitly report bequests given. As a consequence, the ABR profile implicitly includes bequests received (

*h*). This fact implies that if the amount of bequests is sizable, ABR will be higher than expected at younger ages.Total wealth by an individual at age

*x*equals the present value, survival weighted, of the stream of public and private consumption less gross labor income. Let the present value of consumption and gross labor income be denoted by \(\tilde{c}\) and \(\tilde{H}_x\). Then, the intertemporal budget constraint is given by the following:$$ w_x=\tilde{c}_x-\tilde{H}_x=a_x+t_x\Rightarrow \tilde{c}_x=\tilde{H}_x+a_x+t_x. $$(8)Thus, for \(\tilde{c}_x>(<)\tilde{H}_x+a_x\) it is necessary that

*t*_{ x }> ( < )0.An alternative approach could be to maximize the expected utility of the adult in the household (Tobin 1967; Deaton and Muellbauer 1980; Ríos-Rull 2001). To illustrate this point, let us assume the following standard household problem:

$$ \begin{array}{rll} V_{x}(a_{x})&=&\max\limits_{c_{x}}\left\{u\left(c_{x}/\lambda_{x}\right)+\beta V_{x+1}(a_{x+1})\right\},\\ \text{s.t. }a_{x+1}&=&(1+r)a_{x}+{y_l}_{x}-c_{x}, \text{ for $x\in\{T_w,\dots,\Omega-1\}$}, \end{array} $$(9)where

*c*_{ x }is now the total household consumption with a household head of age*x*.Assuming a logarithmic instantaneous utility function and substituting the flow budget constraint into the Bellman equation

$$ V_{x}(a_{x})=\max\limits_{a_{x+1}}\left\{\log\left(\frac{(1+r)a_{x}-a_{x+1}+{y_l}_{x}}{\lambda_{x}}\right)+\beta V_{x+1}(a_{x+1})\right\}. $$(10)Differentiating with respect to

*a*_{ x + 1}and using the envelope theorem gives the Euler equation$$ c_{x+1}=c_x\beta(1+r). $$(11)Equation 11 implies that household saving does not change over the lifespan for a constant household labor income stream, even when the number of equivalent adult consumers in the household increases. However, a cross-country comparison of consumption profiles using NTA data suggests that adults smooth consumption at the individual level.

In particular, the effect of credit rationing on the probability of giving transfers is analyzed as a way to discriminate between altruistic and strategic motives for giving transfers and the constitutional model.

The specific formula applied to each transfer has been placed in Appendix A.1 in Supplementary material.

Although the increase in public debt with respect to GDP in 2009 is expected to have an important impact in the short and medium run in interest rates, it is likely that a misleading progressive income tax will have a stronger effect in the long run on the accumulation of capital.

This is a very interesting question that has been previously modeled for the Spanish case by Jimenez-Martin and Sanchez-Martin (2007) to analyze the effect that minimum pension benefits has on the optimal age of retirement or by Díaz-Giménez and Díaz-Saavedra (2009) to study how a change in the mandatory age of retirement affects the sustainability of the Spanish pension system.

In fact, the total dependency ratio in Spain from the year 2000 to 2010 was the lowest of the last century.

See Fig. A-7 in the Appendix of Supplementary material.

Assuming a Cobb–Douglas production function with a capital share of

*α*= .36, capital-to-output ratio values of 3.75 and 3.27 correspond to capital per effective units of labor values of 7.9 and 6.35, respectively, which are contained in the solid black line in Fig. 5.Assuming a Cobb–Douglas production function, the increase in labor productivity was calculated according to the formula:

$$\log \frac{\omega_{t+T}}{\omega_{t}}=\log \frac{A_{t+T}}{A_{t}} +\alpha\log\frac{k_{t+T}}{ k_{t}}.$$Assuming that at time

*t*+*T*, any variable*X*_{ t + T }can be expressed according to an initial value*X*_{ t }times a constant growth rate*g*_{ X }during*T*periods, then we find that the growth rate of salaries*g*_{ w }is equal to \(g_A+\alpha g_k\approx 1.26\mbox{\%}+0.36\cdot 0.93\mbox{\%}=1.59\mbox{\%}\), where the set {*g*_{ A },*g*_{ k }} correspond to the growth rate of the labor-augmenting technological progress and the growth rate of effective units of capital, respectively.We have assumed that the observed employment rates by age in 2010 linearly improve to the values projected by the European Policy Committee in 2009.

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## Acknowledgements

We are extremely thankful to Ronald D. Lee, Andrew Mason, Gretchen Donehower, David Reher, participants of various seminars/conferences, and two anonymous referees for giving us very useful comments, suggestions, and ideas. We have received helpful research assistance from Ignacio Moral and language editing from Miriam Hils Cosgrove. We are also grateful to the Center on Economics and Demography of Aging and the Department of Demography at UC Berkeley for their hospitality.

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*Responsible editor:* Alessandro Cigno

This work received institutional support from the Spanish Science and Technology System (Projects No ECO2009-10003 and ECO2008-04997/ECON), the Catalan Government Science Network (Projects No SGR2009-600 and SGR2009-359 as well as from XREPP- Xarxa de referència en Economia i Política Públiques), the Fulbright Commission (reference 2007-0445), the European Science Foundation (09-ECRP-021), and the Max Planck Society.

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Sánchez-Romero, M., Patxot, C., Rentería, E. *et al.* On the effects of public and private transfers on capital accumulation: some lessons from the NTA aggregates.
*J Popul Econ* **26**, 1409–1430 (2013). https://doi.org/10.1007/s00148-012-0422-z

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DOI: https://doi.org/10.1007/s00148-012-0422-z

### Keywords

- Second demographic dividend
- Transfers
- Computable general equilibrium

### JEL Classification

- D58
- J11
- H53