Mathematical Modelling of the Gross Domestic Product of the Philippines

Betty T. Bulayo

Saint Mary’s University – Bayombong, DOST – SEI (CBPSME)

ABSTRACT: Gross Domestic Product (GDP) reflects a country’s economy. The higher the Gross Domestic Product (GDP), the healthier is the economy. Th objective of this study is to determine the best fit model to forecast the Gross Domestic Product (GDP) of the Philippines for the next five years (2022 – 2026). Using simple linear regression and multiple linear regression, the researcher found that there is significant linear relationship between the Gross Domestic Product (GDP) and unemployment rate, population, household expenditure, and government expenditure. Multiple linear regression also showed that the only significant predictors are population, household expenditure, and government expenditure. By the results of graphing and using formulas available in the Microsoft excel, the researcher determined that the best fit model is sextic. This study can be considered by the government of the Philippines in making decisions in implementing policies for economic growth and stability.

KEYWORDS: Mathematical Modelling, Best Fit Model, GDP, Regression

INTRODUCTION

Gross Domestic Product (GDP) says the most about the health of a country’s economy. A country with large GDP has great amount of goods and services generated within them, and also has a high standard of living (Fernando, 2023). It is important to track GDP as it provides a general assessment of a country’s economic state. When GDP is growing, it generally implies that companies are expanding and that there are more available jobs (Asian Development Bank, 2017).

Philippine Statistics Authority (2017) stated during its 28^th National Statistics Month that the country transitioned from being an economic laggard of Asia to one of the region’s best performing economies. The Philippines was one of the prosperous countries in the world in terms of economy. It finally shed its “sick man of Asia” reputation. However, the country’s economy falter during the COVID-19 pandemic. Philippine’s economic model is vulnerable to disease outbreak. It’s because it relies on mobility of people, thus tourism, services, and remittances were affected during the lockdown and consumer confidence declined as well (Mendoza, 2021). The Philippines had its worst GDP in 2020 as it shrank to 9.5%. (Venzon, 2021).

Looking back at the Philippines’ past economic performance, the country’s economy was flourishing since 2010, as it was growing over 6% on average per year. The country’s real GDP was more than doubled between 2001 and 2018, growing 5.6% per year on average. The Philippines was one of the top performers in the East Asia Pacific region. However, it still has over 20% of the population living below national and international poverty line (Qian, 2018). Also, in the late 1980s and early 1990s, Philippines began to undertake political and economic reforms. The GDP growth has increased to about 5 percent a year since 1994. With this, the number of Filipinos that were below the poverty line were decreasing. However, agricultural reform and the rise in investment in human assets would have made a more drastic reduction in the poverty rate (International Monetary Fund, 1998).

The Philippines has this long-term vision and aspirations called the Ambisyon 2040. It tells the way people want to live and the state of the country by 2040. In particular, government must use its tools of fiscal, monetary, and regulatory policies to guide the development path in facilitating Filipinos in attaining their Ambisyon, be it economic, human and physical capital, institutional and social and cultural. No one will be poor by 2040, instead, the country will be a prosperous middle-class society. The Philippines’ economic growth must be relevant, inclusive, and sustainable. The per capita income must increase by at least three-fold. It is also envisioned that more than the increase in income, economic growth must continuously improve the standard of living of the majority of the citizens (National Economic and Development Authority (NEDA), 2016).

Socioeconomic Planning Secretary Arsenio Balisacan said that Philippines expects a delay in achieving the Ambisyon 2040 due to the impact of COVID-19 pandemic. In 2022, Philippines aimed to 6.5 to 7.5 percent GDP growth and for the year 2023 to 2028, it is targeting 6.5 to 8 percent GDP growth. Balisacan stated that the prime concern for the medium term 2023 to 2028 are revitalizing job creation, prompt rapid poverty reduction and accelerate economic transformation. He concluded that the obstacles we face are not too great to overcome (The Philippine Star, 2022). With regards to this, the researcher aims to determine the best fit model to predict the GDP of the country that may serve as basis of the government in constructing a plan to acheive its goal by 2040.

STATEMENT OF THE PROBLEM

This study aimed to determine the best fit model to predict the main variable. Specifically, this aimed to:

1. Determine the trend of the Gross Domestic Product (GDP) of the Philippines, unemployment rate, population, household expenditure, and government expenditure from 2007 – 2021.
2. Find if GDP has a significant linear relationship with the following variables:
3. Unemployment rate
4. Population
5. Household expenditures
6. Government expenditures
7. Unemployment rate, population, household expenditure, and government expenditure all together.
8. Construct a time series model of the GDP using the following models to predict its value for 2022 – 2026.
9. Linear
10. Quadratic
11. Exponential
12. Polynomial (cubic, quartic, quantic, sextic)
13. Power
14. Moving Average
15. Exponential Smoothing
16. Autoregression
17. Determine the best fit models and predict the main variable for 2022 – 2026.

RESULTS

In this chapter, the researcher analyzed the data in order to find out the final results. The study was based on the time series data covering the period from 2007 to 2021.

(See in PDF File)

Figure 1. The trend of the GDP, Unemployment Rate, Population, Household Expenditure, and Government Expenditure from 2007 – 2021.

(See in PDF File)

Figure 2. Simple Linear Relationship of the GDP and Unemployment Rate

 The summary results showed that there is statistically significant linear relationship between the GDP of the Philippines and unemployment rate as significance F value is 0.002779254 which is less than at alpha of 0.05.

(See in PDF File)

Figure 3. Significant Linear Relationship of the GDP and Population

 The summary results showed that there is statistically significant linear relationship between the GDP of the Philippines and population as Significance F value of 0.0000000000712105 is less than at alpha of 0.05.

(See in PDF File)

Figure 4. Significant Linear Relationship of the GDP and Household Expenditure

Summary results showed that there is statistically significant linear relationship between the GDP of the Philippines and household expenditure as Significance F value of 0.0000000291638 is less than at alpha 0.05.

(See in PDF File)

Figure 5. Significant Linear Relationship of the GDP and Government Expenditure

 The summary results showed that there is statistically significant linear relationship between the GDP of the Philippines and government expenditure as Significance F value of 0.000000265522 is less than at alpha of 0.05.

(See in PDF File)

Figure 6. Significant Multiple Linear Relationship of the GDP, Unemployment Rate, Population, Household Expenditure and Government Expenditure

 The summary results showed that there is significant multiple linear relationship between the GDP of the Philippines and unemployment rate, population, household expenditure, and government expenditure as Significance F value of 0.0000000006857 is less than at alpha of 0.05. And as also shown by the p-values in each variable, the significant predictors of the main variable are population, household expenditure, and government expenditure as their p-values are less than at alpha 0.05.

SECTION 3: TIME SERIES MODEL

The following are the data collected from World Bank, Statistics Times, Bangko Sentral ng Pilipinas (BSP), and Philippine Statistics Authority (PSA).

Table 1. Data from World Bank, Statistics Times, BSP, and PSA from 2007 – 2021.

Based from table 1 and all the results shown in figures 2 to 6, below are the results of the equation of each model.

Table 2. Model Equation (See in PDF File)

Table 3. Best Fit Model Prediction

 As shown in Table 3, the best fit model is sextic. To determine the best fit model, the  must be closer to 1 and its Standard Error must be the lowest. Although sextic and moving average are both closest to 1, sextic model has lower Standard Error, thus it is the best fit model to predict the main variable.

Table 4. Forecasted Yearly GDP of the Philippines from 2022 to 2026.

DISCUSSION

There is an increasing trend among the GDP, unemployment rate, population, household expenditure, and government expenditure as shown in figure 1. It is also shown in figure 2 to figure 5 that there is a significant linear relationship between the GDP each independent variable. Figure 6 shows that there is a significant multiple linear relationship between the GDP and the dependent variables. It is also shown by the table that the significant predictors of GDP are population, household expenditure, and government expenditure.

Table 3 shows that the best fit model is sextic since its  value is closest to 1 other than the moving average but comparing the standard error of the two, sextic has lower standard error value, thus making it the best fit model.

The other time series models are linear with equation
, exponential with equation
, logarithmic with equation
, quadratic with equation
, cubic with equation
, quartic with equation

, quintic with equation
, power with equation
, moving average with equation
, exponential smoothing with equation
, and autoregression with equation

With sextic equation, , the researcher was able to predict the GDP of the Philippines from 2022 to 2026 as shown in table 4. The forecasted GDP of the Philippine from 2022 – 2026 will be 20980.7792, 25157.9163, 35078.7328, 55141.1087, and 91573.8 respectively. It is important to predict the GDP of a country as Roser (2021) stated that it reflects the quality and quantity of the goods and services that people need. Though they may seem unfelt or abstract, like the GDP per capita, we shouldn’t forget that they are actually a measure of people’s reality of material living condition.

 CONCLUSION

From the results, it is shown that all the variables: unemployment rate, population, household expenditure, and government expenditures have a significant linear relationship with GDP. However, multiple linear regression also showed that only population, household expenditure, and government expenditure are significant predictors of the GDP. The researcher compared the forecasting accuracy of the different models and it was found out that the best fit model in forecasting the GDP was sextic. Using the best fit model, the values of GDP of the Philippines for the year 2022 – 2026 were obtained.

 ACKNOWLEDGMENTS

The researcher would like to thank the Saint Mary’s University – Bayombong, Nueva Vizcaya and the scholarship given by the Department of Science and Technology – Science Education Institute (DOST – SEI) through its Capacity Building Program in Science and Mathematics Education (CBPSME).

 DISCLOSURE

The researcher declares no potential conflict of interests to disclose.

REFERENCES

1. Asian Development Bank (ADB) (2017). Gross domestic product (GDP): 12 things to know. https://www.adb.org/news/features/gross-domestic-product-gdp-12-things-know
2. Venzon C. (2021). Philippines GDP shrinks 9.5% in 2020, worst since 1947. https://asia.nikkei.com/Economy/Philippines-GDP-shrinks-9.5-in-2020-worst-since-1947
3. Fernando, J (2023). Gross domestic product (GDP): Formula and how to use it. https://www.investopedia.com/terms/g/gdp.asp
4. International Monetary Fund (1998). Poverty abd economic policy in the Philippines. https://www.imf.org/external/pubs/ft/fandd/1998/09/gerson.htm
5. Mandoza, R. (2021). The Philippine economy under the pandemic: From Asian tiger to sick man again? Brookings. https://www.brookings.edu/blog/order-from-chaos/2021/08/02/the-philippine-economy-under-the-pandemic-from-asian-tiger-to-sick-man-again/
6. National Economic and Development Authority (NEDA) (2016). About ambisyon natin 2040. https://2040.neda.gov.ph/about-ambisyon-natin-2040/
7. Philippine Statistics Authority (PSA) (2017). Facts and figures of the future. https://psa.gov.ph/nsm/theme-explanation/28th

8. Qian, R. (2018). How can the Philippines achieve its ambitious vision of becoming a country free of poverty? World Bank. https://blogs.worldbank.org/eastasiapacific/how-can-philippines-achieve-its-ambitious-vision-becoming-country-free-poverty
9. Roser, M. (2021). What is economic growth? And why is it so important? Our World Data. https://ourworldindata.org/what-is-economic-growth
10. The Philippine Star (2022). Philippines sets back target to reach high-income country status. https://www.philstar.com/business/2022/08/13/2202256/philippines-sets-back-target-reach-high-income-country-status