## Abstract

Computable general equilibrium (CGE) models and “convergence models” differ in their assessment of the extent to which demography influences economic growth. Here, I show that CGE models produce results similar to those of convergence models when more detailed demographic information is used. To do so, I implement a CGE model to explain Taiwan’s economic miracle during the period 1965–2005. I find that Taiwan’s demographic transition accounts for 22 % of per capita output growth and 17.7 % of investment rate for the period 1965–2005. Moreover, this paper confirms most of the literature written on the role of demography on per capita output growth and saving rates since the seminar article by Coale and Hoover (1958).

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## Notes

Since the demographic transition is happening in all populations, this result can be extended to other countries that have already face, or will face, the first demographic dividend. The reason for focusing on Taiwan, rather than on Japan, is because Taiwan started the demographic transition in the twentieth century.

Taiwan’s demographic transition started in the 1920s, 40 years before the economic boom. In 1944, the constitution of the Republic of China established 6 years of compulsory education, and this period was extended to 9 years in 1968. As a result, the proportion of illiterate and self-educated people changed from 40 % in 1940 to almost 0 % in 1970 (Huang 2001).

All requirements for a steady-state equilibrium will then be satisfied.

The population of Taiwan was reconstructed using historical data from 1906 to 2010. During the first half of the twentieth century, Taiwan experienced massive in- and out-migration flows, which are explained in Section 3.1. I have run simulations under both closed and open populations. However, similar to Lee et al. (2000), I use a closed population because the results do not change significantly and are less noisy.

This assumption does not affect the results during the period 1965–2005, and it is assumed for comparability to Braun et al. (2009). However, additional simulations with borrowing constraints, which are not presented here, suggest that results might depend on this assumption from year 2020 onwards.

Applying the same methodology used by Costa (1998), the average retirement age in Taiwan decreased from 61 to 59 during the period 1978–2010.

Taiwan experienced a dramatic increase in human capital accumulation for cohorts born between the 1940s and the 1970s (Huang 2001). In order to capture the effect that human capital heterogeneity has on economic growth, I have included six different educational levels \(\mathcal{E}=\){illiterate and self-educated, elementary school, junior middle school, senior high school, vocational school, and college and above}, where \(j\in \mathcal{E}\). The age-specific labor productivity indexes by educational attainment are calculated based on Table 11.3 Huang (2001).

Let

*E*_{ t }(*j*) be the cumulative distribution function of the educational attainment of an individual born in year*t*. Thus, for any \(j\in\mathcal{E}\),*E*_{ t }(*j*) is defined as \(\Pr\) (education of an individual born in year*t*is equal to or less than*j*).Since the economic model does not distinguish between gender, parity, region, etc., I use a simplified version of a GIP model that matches the specific characteristics of this economic model. The objective function used to solve the problem is

$$ \begin{array}{lll} \min\limits_{\{\{\alpha_t^i,\gamma_t^i\}_{i=0}^2\}_{t=t_0}^{T}}\sum\limits_{t\in\mathbb{D}}\left(\frac{D_t-\hat{D}_t}{D_t}\right)^2 &+&\sum\limits_{t\in\mathbb{B}}\left(\frac{B_t-\hat{B}_t}{B_t}\right)^2+\sum\limits_{t\in\mathbb{N}}\left(\frac{N_t-\hat{N}_t}{N_t}\right)^2 +\sum\limits_{t\in\mathbb{E}}\left(\frac{e_t-\hat{e}_t}{e_t}\right)^2+\sum\limits_{t\in\mathbb{T}}\left(\frac{tfr_t-\hat{tfr}_t}{tfr_t}\right)^2 \\ &+&\sum\limits_{t\in\mathbb{C}}\sum\limits_{a=0}^{\Omega-1}\left(\frac{N_{a,t}-\hat{N}_{a,t}}{N_{t}}\right)^2 +\sum\limits_{t=t_0}^{T}\sum\limits_{i=0}^2\left(\alpha_{t+1}^i-\alpha_t^i\right)^2+\left(\gamma_{t+1}^i-\gamma_t^i\right)^2, \end{array} $$(24)subject to Eqs. 3 and 4 and to

$${f}_{t,x}=\sum\limits_{i}\alpha_t^if_{x}^{(i)}, \quad (1-{\pi}_{t,x})=\sum\limits_{i}\gamma_t^i(1-\pi_{x}^{(i)}),\quad\sum\limits_{i}\alpha_t^i=1,\quad \sum\limits_{i}\gamma_t^i=1, $$(25)where \(\{\{\alpha_t^i,\gamma_t^i\}_{i=0}^2\}_{t=t_0}^{T}\) are the set of parameters for mortality and fertility, respectively; \(f_{x}^{(i)}\) and \(\pi_{x}^{(i)}\) are the actual age-specific fertility rates and conditional survival probability by age for specific years; and \(\mathbb{I}\equiv\{\mathbb{D, B, N, E, T, C}\)} are the sets of deaths, births, total population, life expectancy, total fertility rates, and censuses used in the calculation. Crude migration rates are obtained using

*inverse population projection*and are exogenous to the GIP model.Based on Taiwanese data, Lee et al. (2000) observed an annual population growth rate of 1.1 %, a life expectancy at birth of 28.3 years, and a total fertility rate of six births per woman.

In order to assume an open population, the common approach in the economic literature is to sum all migrants and introduce them at age 0. This approach can be problematic when the net migrants-to-population ratio in any given year is high, which is the case of Taiwan during the period analyzed (see Fig. 1, panel a).

I calculate the household size as follows:

$$ \lambda_{t,x}=1+\sum_{s=T_{\rm w}}^{x}\frac{S_{t-x+s,s}f_{t-x+s,s}}{S_{t,x}}S_{t,x-s}\theta_{x-s}\cdot I_{x-s}, $$(26)where

*θ*_{ x }is the continuous scale that equals 0.4 from ages 0 to 4 and rises with age until reaching 1 at the age of 18 (Mueller 1976).*I*_{ x − s }is the index function that takes the value of 1 when*x*−*s*is lower than*T*_{w}and 0 otherwise.The relative risk aversion coefficient and the Frisch elasticity on labor supply are given as 1 −

*ϕλ*(1 −*σ*) and \(\frac{1-l}{l}\frac{1-\phi\lambda(1-\sigma)}{\sigma}\), respectively.The difference between the estimated and actual CFC gives an average error of 1 % from 1965 to 2009. Since the capital stock derived is almost insensitive to the method used after 15 years, I focus my analysis on the economic performance of Taiwan from 1965 to 2005.

This assumption does not change the results for the period analyzed: 1965–2005.

The values of TFP chosen correspond to those obtained using the primal approach.

Indeed, net factor income from abroad represents around 2 % annually of the output in Taiwan since the 1980s.

It should be noted that a higher elasticity of substitution yields not only a lower interest rate but also the finding that Taiwanese households are net investors in foreign capital markets, which is not supported by SNA data.

The same analysis has been done with migration. However, the contribution of this demographic process during the period analyzed (i.e., 1965–2005) is negligible. Thus, I opted to not report the results in the paper for the sake of space.

Assuming a Cobb–Douglas production function, net investment rates are given by

$$ \frac{K_{t+1}-K_t}{Y_t-\delta K_t}=\frac{1}{\kappa_t^{\alpha-1}-\delta}\left(\frac{\kappa_{t+1}}{\kappa_t}\frac{\Gamma_{t+1}}{\Gamma_{t}}\frac{H_{t+1}}{H_{t}}-1\right),\label{eq:invrate} $$(29)where

*κ*_{ t }is the capital in effective units of labor in year*t*. It should be noted that, in a small-open economy, capital in effective units of labor is determined exogenously by competitive international capital markets, and Γ_{ t }is exogenously given in the model.In a closed economy, one cohort can influence the saving rate throughout their life span. However, the cohort members do not have a strong effect on the capital (in units of effective labor) until they enter the labor market.

The same results are obtained running similar counterfactual simulations starting in 1925 and in 1950.

Simulation results not presented here show that the impact of mortality is greater at the first and last stages of the demographic transition. This result is consistent with Braun et al. (2009) for Japan.

Notice that, using Eq. 5 and taking into account public expenditures and the depreciation of capital, it is easy to show that in the steady-state equilibrium,

$$ s(\kappa^*) (\kappa^*)^{\alpha}(1-G/Y-\delta (\kappa^*)^{1-\alpha})=\kappa^* (n+\dot{F}/F), $$(31)where

*s*(*κ*^{*}) is the saving rate,*G*/*Y*is the ratio public expenditures to output,*δ*is the depreciation rate,*n*is the population growth rate, and \(\dot{F}/F\) denotes the labor-augmenting technological progress. The results are based on the information collected for the last reference year, i.e.,*G*/*Y*= 13 %,*δ*= 5 %, and \(\dot{F}/F=3\) %.

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## Acknowledgements

I am extremely thankful to Ronald D. Lee, Andrew Mason, David Canning, Paul Lau, Bernardo Queiros, Cyrus Chu, P. C. Roger Cheng, Ester González Prieto, Fanny Kluge, Gustav Oeberg, two anonymous referees, and seminar participants at CEDEPLAR, SAEe11, and PAA for giving me very useful comments, suggestions, and ideas. I am also grateful to the Max Planck Society, the Center on Economics and Demography of Aging, and the Department of Demography at UC Berkeley for their support and hospitality.

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*Responsible editor:* Alessandro Cigno

This work received institutional support in its earliest stage from the Fulbright Commission (reference number 2007-0445).

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Sánchez-Romero, M. The role of demography on per capita output growth and saving rates.
*J Popul Econ* **26**, 1347–1377 (2013). https://doi.org/10.1007/s00148-012-0447-3

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DOI: https://doi.org/10.1007/s00148-012-0447-3

### Keywords

- Demography
- Saving rates
- Investment rates
- Income growth
- Overlapping generations

### JEL Classification

- D58
- E21
- J11