Research on the Relationship between Population Size and Expenditure-Side Real GDP: A Comparative Analysis of 20 Countries from 1999 to 2019

Abstract

Solow model has long been a subject that has attracted researchers from diverse range of fields including economics, finance, and political. The convergence effect of Solow model is also an important measurement and the predict method to global long-term economy development. In the past, some researchers raised the academic-practice gap of the Solow model, and side proved the conditional convergence is more realistic. This paper will investigate the usage of Solow model in reality and analyze the impact of policies of different contemporary economies on GDP growth in different regions.

1. Introduction

This paper will examine the link between population (in millions) and expenditure-side real GDP at chained PPPs (in millions of US dollars) for 20 countries between 1999 and 2019. Egypt, Morocco, Sudan, China, Singapore, India, Philippines, Qatar, South Korea, France, Italy, Switzerland, Ukraine, United Kingdom, Canada, Mexico, the United States, Australia, Brazil, and Colombia are among the 20 nations. Singapore, France, Italy, Switzerland, the United Kingdom, Canada, the United States, and Australia are developed countries in the countries under observation; the others are developing countries. Between these countries, there are significant disparities in GDP and population, which will be covered in more detail in the next sections. The remainder of the research will examine these nations’ GDP, GDP per capita, populations, and GDP growth while utilizing a comparison with the Solow model to see whether any fresh insights, particularly in convergence theory, have been made.

This section will use data from PWT version 10.0 to determine the GDP per capita per year and the population growth rate per year, as well as expenditure-side real GDP at chained PPPs (in mil. US$) and population (in million) [1].

Formula:

$$GDPper\text{capita}=GDP/\text{population}$$

$$\text{Population growth}=\left[\left(\text{population this year}/\text{population last year}\right)-1\right]\ast 100\%$$

$$\text{Population growth in}\text{a}\text{period}\text{t}=\left[\left(1/\text{t}\right)\ast \text{lnXt}/\text{X}0\right]\ast 100\%$$

According to Desai and Potter [2], GDP per capita can measure the living standards of people in a country, allowing these countries to be characterized as “richer” or “poorer” on page 40 of the companion to development studies. Figure 1 demonstrates that Qatar, Singapore, Switzerland, the United States, Australia, Canada, the United Kingdom, and Italy had greater GDP per capita levels than the rest of the observed countries from 1999 to 2019. In Figure 2, almost all of these “richer” nations have lower population growth rates over the same time period, with the notable exception of Qatar and Ukraine. Qatar which has really high immigration growth rates from 2000 to 2010 that range from 79.5 to 125.44%, in contrast to the UK, which has immigration growth rates of only 25.28 to 28.26% [3]. Since the 1990s, Ukraine’s population has been declining due to a combination of high emigration, high death, and low birth rates. Since 1993, the population has dwindled by an average of more than 300,000 per year. In 2007, the country had the fourth highest rate of population decline in the world, and the war will only exacerbate this problem. Many young women have left the country since the invasion, and a decline in the proportion of fertile women may result in a falling birth rate and a “demographic decline spiral” [4]. Moreover, as shown in Figures 1 and 3, there is a period of decline from 2008 to 2011 for the majority of countries, which corresponds to the “financial crisis;” the reasons why it affected the expenditure-side GDP per capita are that individuals had less disposable income, government expenditure decreased, unemployment rose, etc. For instance, in order to reduce their budget deficits, a number of European nations, including Italy, Spain, and Greece, have proposed austerity measures such as wage cutbacks and price freezes that will result in a decline in GDP per capita [5].

Figure 1.

GDP per capita 1999–2019.

Figure 2.

Population growth rate in total (%).

Figure 3.

Population growth rate (%) from 2000 to 2019.

This section will establish, with the use of the data presented previously, whether or not the connection between rising population and rising living standards conforms to the Solow model. The Solow Model is an exogenous model of economic growth that investigates the impact that changes in the rate of population growth, the rate at which savings are accrued, and the rate at which technological progress is made have on the level of production that an economy maintains over the course of time. The only variables in this research model are GDP and population. As a result, the equation for the Solow model is (s–saving rate, f(k) = y–GDP per capita, k–capital, n–population growth rate, δ −depreciation rate, and k dot represents the change in capital per worker over time; here use Cobb Douglas production function that looks like this in intensive form:)

$$\begin{array}{c}\dot{k}=sf\left(k\right)-\left(n+\delta \right)k\\ k={\left(s+\left(\delta +n\right)\right)}^{1/\left(1-\alpha \right)}\\ y={\left(s+\left(\delta +n\right)\right)}^{\alpha /\left(1-\alpha \right)}\end{array}$$

The calculation results that the population growth rate and GDP per capita have a negative connection, meaning that as the population growth rate rises, GDP per capita falls, and vice versa.

Figure 4 uses a scatter point diagram to investigate the relationship between the population growth rate in the total period and GDP per capita in 2019, where it results in the opposite direction with the calculation results, and the trend line is upwards flowing, which shows that there is a positive relationship between the population growth rate and the GDP. There is a very special point in the right upside of Figure 4, which is the scatter of Qatar, and the reasons have been explained in the previous section already, which not only because of the immigration rate is much higher than other countries but also because of high capital due to petroleum and natural gas are the pillars of Qatar’s economy, accounting for over 70% of total government income, over 60% of gross domestic product, and around 85% of export profits [6]. Qatar is the second-largest exporter of natural gas and has the third-largest known natural gas resource in the world.

Figure 4.

GDP per capita in 2019. Source: [1].

Figure 5 examines the relationship between GDP per capita and population growth rate using data excluding Qatar; the figure reveals that the association is negative because the trend line slopes downward, but the trend is very weak because the line is fairly flat. In conclusion, in these 20 nations, there is insufficient evidence of a negative association between GDP per capita and population growth rate; thus, the Solow model’s predictions regarding the impacts of GDP per capita, standards of living, and population growth cannot be supported in this research.

Figure 5.

GDP per capita in 2019. Source: [1].

The last section will use the scatter diagram of GDP per capita in 1999 and the growth rate of GDP to discuss that if there is convergence taking place in the research data.

There are two types of convergence — absolute convergence and conditional convergence. Absolute convergence is a condition in which poor countries grow faster than affluent ones and ultimately catch up to the per capita GDP of industrialized nations. Conditional convergence indicates that nations converge to their own steady states, which are defined by saving, population growth, and other external factors indicated by the growth theory that the Solow model really implies. In conclusion, conditional convergence suggests that a nation or territory is converging to its own steady state, while absolute convergence implies that all countries or regions are converging to a shared steady-state potential income level [7].

Formula:

$$GDP\text{growth in}\text{a}\text{period}\text{t}=\left[\left(1/\text{t}\right)\ast \text{lnXt}/\text{X}0\right]\ast 100\%$$

$$GDPper\text{capita}=\text{total}GDP/\text{population}$$

Figure 6 is the Solow model of different capital countries and directly shows the growth rate by the angel degree, which leads to the theory the country has higher GDP per capita, and capital has lower growth rate, which is the meaning of convergence. Population growth rate, depreciation rate, and saving rate are exogenous variables, hence they are treated as constants and represented by a horizontal line in the 7.2. f(k)/k = APK — the average production of capital decreases as a country’s wealth increases, hence the line is sloping downward (Figure 7).

Figure 6.

Solow model of different capital country. Source: [8].

Figure 7.

Convergence explanation. Source: [8].

Since the convergence theory predicts the link between initial capital and future growth rate, Figure 8 utilizes the GDP per capita in 1999 and the GDP growth rate from 1999 to 2019.

Figure 8.

GDP growth rate in total %. Source: [1].

Figure 8 suggests that there is a negative link between the GDP per capita in 1999 and the GDP growth rate from 1999 to 2019, consistent with the convergence theory that “poor” countries have a faster capital growth rate than “rich” countries. However, the trend line is extremely flat, indicating that the theory is not perfectly supported by the research data. If Figure 8‘s data from Qatar are omitted.

Figure 9‘s trend line indicates a considerably larger negative association between the GDP per capita in 1999 and the GDP growth rate for the entire period from 1999 to 2019, which better explains the convergence in the study data. Qatar’s high capital and growth rate are attributable not only to the country’s vast petroleum and natural gas reserves but also to the fact that the scarcity of natural energy in other parts of the world raises the country’s net export, hence boosting the GDP growth rate in Qatar.

Figure 9.

GDP growth rate in total % without Qatar. Source: [1].

The downward-sloping trend line in Figure 10 indicates that the 5-year GDP growth rate per capita and the GDP per capita have a weakly negative connection, as seen by the figure. And Figure 11 demonstrates that substantial convergence indicates in Qatar, where the slope of the trend line is extremely negative and downward sloping so that in the data of this research, there is convergence in these 20 countries, but the “levels” of convergence vary per country. Figure 12 illustrates other reasons why the data cannot match the convergence theory exactly. The “richer” country may have a higher GDP growth rate than the “poorer” country due to differences in its technology capabilities, which are not included in this paper’s study data but exist in the whole Solow model and population growth rate, as seen in the top figure. Or, their distinct stable states, as depicted in the bottom picture, can potentially result in opposing convergence.

Figure 10.

Five year GDP growth (%). Source: [1].

Figure 11.

Qatar convergence relationship. Source: [1].

Figure 12.

Other reason of convergence. Source: [8].

2. Conclusion

In conclusion, the study findings presented in this paper cannot absolutely imply the accuracy and convergence of the Solow model such as the immigration policy in Dubai leads to the population growth but has not decreased the GDP growth. Nonetheless, it has provided a few hints as to how the Solow model and convergence can occur in the real world. And the reason why the data do not exactly fit the theory may be because there are too few observations or too many factors to consider. In future researches, researchers may need to find more observation data and put behavior economy in consideration.