The effects of population size and age structure on innovative output: an empirical note

ABSTRACT

This note examines the effects of population size and age structure on innovative output. Employing panel data for 22 countries over the period from 1996 to 2015, it is found that population size has no statistically significant effect on innovative output. In contrast, changes in the age structure of the population are significantly associated with changes in innovative activity.

KEYWORDS:

• Population size
• population age structure
• innovative output
• Schumpeterian growth models
• Semi-endogenous growth models

JEL CLASSIFICATION:

• O30
• O40
• J10

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ To see this, consider the equation $\mathrm{l}\mathrm{n}(\mathrm{A})=\lambda \mathrm{l}\mathrm{n}(L_{R\text{amp}D})+\gamma ln\left(N\right)$, where $\mathrm{l}\mathrm{n}(\mathrm{A})$ stands for the log of innovative output,$\mathrm{l}\mathrm{n}({\mathrm{L}}_{\mathrm{R}\text{amp}\mathrm{D}})$ denotes the log of the number of workers engaged in the production of innovations, and $\mathrm{l}\mathrm{n}\left(N\right)$is the log of population size. Denoting the proportion of innovators in the population by s_R&D, the above equation can be written as $ln(A)=\lambda ln(s_{R\text{amp}D})+\rho ln\left(N\right)$, where $\rho$ ≡ $\lambda$ + $\gamma$. It follows that in the case $\gamma$ < 0 and $\lambda$ > 0 $\rho$ is positive if │$\lambda$│>│$\gamma$│.

² While some of their regressions include country (and year) fixed effects, the authors do not use fixed effects in their regressions of innovative output on population size.

³ First-generation endogenous growth models (see e.g. Romer 1990) assume $\beta =0$ and $\varphi$ = 1 (and λ = 1).

⁴ To see this, write the ratio of the number of researchers aged x to y to the total number of researchers as $r_{x\mathrm{\_}y}=\frac{N_{x\mathrm{\_}y}\frac{R_{x\mathrm{\_}y}}{N_{x\mathrm{\_}y}}}{N\frac{R}{N}}$ where N_{x_y} is the population aged x to y. If the ratio of the number of researchers aged x to y to the population aged x to y is proportional to s, $\frac{R}{N}=\frac{1}{\tau }\frac{R_{x\mathrm{\_}y}}{N_{x\mathrm{\_}y}}$, then r_{x_y} is equal to τn_{x_y} (where $n_{x\mathrm{\_}y}\equiv$ N_{x_y}/N).

⁵ The stock data were constructed using the perpetual inventory method with a depreciation rate of $\delta$ = 15%. Consistent with the literature, we set the initial value of the patent stock equal to $A_{i0}={\dot{A}}_{i0}/(g+\delta )$, where ${\dot{A}}_{i0}$ is the number of patent applications in the first year it is available, and g is average growth rate of the patent series between the first year with available data and the last year with available data.

⁶ The data used to construct s are only available from 1996 onwards from the WDI.

⁷ As shown by Kao (1999), the tendency for spuriously indicating a relationship may even be stronger in panel data regressions than in pure time-series regressions.

⁸ Although the conventional fixed-effects estimator is (super-)consistent under panel cointegration, it suffers from a second-order asymptotic bias arising from serial correlation and endogeneity, and its t-ratio is not asymptotically standard normal.

⁹ This procedure is equivalent to using the residuals from regressions of each variable on time dummies.