The impact of digital economy factors on gdp of southeast asia countries from 2008 to 2017

ECONOMETRICS REPORT KTEE218.1 Group 9 Teacher in charge: PhD Nguyễn Thúy Quỳnh Department/ Faculty: International Economics Keywords: Digital economy, GDP, Southeast Asia, fixed broadba

General theory of GDP (gross domestic produc†) . căn 3 "h1 v ha Ô (‹dj 3 hs: co na a

Roles of GDP Hddáại1 didddi1Ănố ỀêẼ 4 1.2 General theory of digital @COnOTy c nh HH KH 4 "vn rn 7ô 4dđaa

GDP is a crucial indicator that reflects the size and overall performance of an economy The growth rate of real GDP is widely used to assess the economic health and stability of a country Generally, an increase in real GDP signifies a thriving economy, indicating positive economic growth and prosperity.

- GDP is an important tool reflecting the changing development situation of the national economy

- GDP is the core basis of economic development strategic goals and macroeconomic policies

- GDP is an important indicator of international economic relations

1.2 General theory of digital economy

The digital economy represents the transformation of traditional economic activities, products, and services into digital formats, driven by the internet and electronic technologies It leverages information technology to create, market, and consume goods and services more efficiently Key innovations in the digital economy include digital banking, e-commerce, virtual education, smartphone applications, and collaboration platforms, revolutionizing the way businesses and consumers interact in the modern marketplace.

The digital economy marks the transition from the third to the fourth industrial revolution, reflecting significant technological advancements The third industrial revolution, also known as the digital revolution, involved the shift from analog electronic and mechanical devices to digital technologies in the late 20th century Building on this foundation, the fourth industrial revolution integrates cutting-edge technologies that seamlessly connect the physical and cyber worlds This ongoing evolution continues to drive innovation and transform industries worldwide.

Thomas Mesenbourghg, an American statistician, and economist have identified three key components of the digital economy They are:

- E-Business Infrastructure: This refers to the electronic systems that businesses use to conduct their operations This includes the hardware, software, networks, and data storage systems

E-Business involves conducting commercial activities through electronic systems, encompassing online buying, selling, and digital marketing It also includes the production and delivery of goods and services via digital platforms, transforming traditional business operations into efficient digital processes.

- E-Commerce: This is the buying and selling of goods and services through electronic systems This includes exchanging money, goods, and services between businesses and consumers

In this research, our team uses five factors belonging to the three components above:

Fixed broadband subscriptions provide high-speed internet access through wired connections, including cable modem, DSL, fiber-to-the-home or building, satellite broadband, and terrestrial fixed wireless broadband These subscriptions offer downstream speeds of at least 256 kbit/s, ensuring reliable and fast connectivity for users.

Internet users are individuals who have engaged with the Internet from any location within the past three months They access online content through various devices such as computers, mobile phones, personal digital assistants, gaming consoles, and digital TVs Staying connected across multiple devices is essential for understanding modern internet usage trends and online behavior.

- High-technology exports are products with high R&D intensity, such aS aerospace, computers, pharmaceuticals, scientific instruments, and electrical machinery

A mobile cellular subscription is a service that provides access to the Public Switched Telephone Network (PSTN) using cellular technology It encompasses both postpaid and prepaid plans, supporting various systems such as analog and digital cellular networks This subscription enables users to make calls and communicate through mobile devices, ensuring connectivity across GSM, LTE, 5G, and other cellular standards.

Secure internet servers, commonly known as SSL servers, utilize the Secure Sockets Layer (SSL) protocol to safeguard communication from unauthorized access These servers facilitate encrypted communication between web servers and browsers, ensuring data privacy and security through cryptography Implementing SSL on web servers is essential for protecting sensitive information and establishing trust with users during online transactions.

1.2.3 Roles of the digital economy

The digital economy surpasses traditional economic limitations across all areas, including production, marketing, and commerce It has become the primary driver of innovation, growth, and job creation worldwide By transforming business operations, the digital economy opens up new opportunities for companies while empowering consumers with greater influence over market trends and purchase decisions.

Aghion and Howitt (1992) propose that technology is endogenous, emphasizing that technological development drives economic growth While both traditional and endogenous growth models identify technological progress as a key source of economic expansion, endogenous growth models specifically explain the mechanisms through which technological innovation occurs within countries and how it fosters sustainable economic development (Ozcelik et al., 2018).

Compensation Theory, as outlined by Vivarelli and Pianta (1995, 2000, 2004), explains how various market compensation mechanisms respond to technological changes, offsetting the impact of trade on innovation processes This theory emphasizes that process innovations, such as the introduction of new machines, can replace workers in the consumer industry while simultaneously creating new employment opportunities in sectors where capital is generated through advanced machinery These mechanisms highlight the dynamic nature of technological progress in shifting employment and fostering innovation across different industries.

Neoclassical Growth Theory explains how substantial economic growth is attainable through key drivers such as labor, capital, and technology It emphasizes that adjusting the levels of labor and capital in the production process can help achieve economic balance and growth The theory highlights the critical role of technological innovation, asserting that ongoing technological progress is essential for sustained economic development Overall, technological advancements are fundamental to maintaining long-term growth in the economy.

Qiang, Rossotto & Kimura (2009) have suggested that for each additional percentage point of broadband penetration results show an increase in the GDP growth rate

Research by Bloom, Draca, Kretschmer, and Sadun (2010) demonstrates a strong positive correlation between Internet adoption and GDP growth The study highlights that increases in Internet usage typically occur before and contribute to subsequent economic growth This evidence underscores the significant impact of digital connectivity on boosting national economies and emphasizes the importance of expanding Internet infrastructure for economic development.

Tracy Lum (2011) found out that the mobile cellular subscription rate had a positive and significant impact on countries’ level of real per capita GDP

James Manyika and Charles Roxburgh, 2011 from McKinsey Global Institute showed that the Internet exerts a strong influence on economic growth rates

Research by Vicente and Lopez (2011) highlights that while information technology and internet adoption are not the sole drivers of economic efficiency, they serve as significant catalysts contributing to increased economic productivity Their findings suggest that integrating IT and online capabilities can positively impact GDP growth, underscoring the importance of technological advancements for fostering sustainable economic development.

Since research has been ongoing since 2011, the update remains relatively outdated, particularly given the rapid pace of technological advancements and internet developments in the modern era Staying current is essential, as information technology evolves swiftly each year, making recent data crucial for accuracy and relevance.

MODEL SPECIFICATION AND DATA eo 9 ÊN 2i(2c9 92 n0 (43

Methodology used to collect da†a ch nhện 9 2.1.2 Methodology used to analyze dal†a ng ke 9 2.2 Theoretical model specificatiOn - nh Hành 9 2.2.1 Model specificatiOr' ch nh” kh kh Hy 9 2.2.2 Variables explanafion ch kh 10 2.3 Theoretical relatioònships between variables - che 11 2.3.1 Relationship between Broadband Subscriptions and GDP

This study analyzes the influence of digital infrastructure on the overall GDP of Southeast Asian countries, utilizing secondary data from 11 nations—including Malaysia, Indonesia, Thailand, Cambodia, Laos, Singapore, Brunei, Vietnam, Myanmar, East Timor, and the Philippines—covering a ten-year period from 2008 to 2017.

This article utilizes data from the World Development Indicators of the World Bank to analyze key digital and economic metrics It highlights the importance of Gross Domestic Product (GDP) alongside variables such as Fixed Broadband Subscriptions, Internet Users, High-Technology Exports, Mobile Cellular Subscriptions, and Secure Internet Servers These indicators collectively provide a comprehensive overview of a country's technological infrastructure and economic development Analyzing these data points helps understand the digital landscape's role in economic growth and global connectivity.

2.1.2 Methodology used to analyze data

This article investigates the impact of digital infrastructure on GDP through comprehensive analysis It employs descriptive analysis to highlight the fundamental characteristics of the data, ensuring a clear understanding of the variables involved Additionally, Ordinary Least Squares (OLS) regression is used to estimate the parameters of a linear regression model, providing minimum-variance, mean-unbiased estimates This approach offers valuable insights into the relationship between digital infrastructure and economic growth, strengthening the validity of the findings.

This study analyzes the impact of digital infrastructure variables on the total GDP of Southeast Asian countries using a multiple linear regression model Key factors such as broadband connectivity, internet user rates, e-commerce activity, mobile subscription levels, and server infrastructure are examined for their influence on economic growth The regression model estimates the relationship as GDP = BBROAD + £,USER + B3[ECH + B,MOBILE + B-SERVER +72;, incorporating residuals (ui) to account for unexplained variability Understanding these digital infrastructure components is crucial for fostering economic development in Southeast Asia.

ECONOMETRICS REPORT KTEE218.1 Group 9 2.2.2 Variables explanation

Variable Index Symbol Definition Unit

A monetary measure of the market value of all

Dependent | Gross Domestit the final goods and

Variable Product services produced and sold in a specific perioc by countries

Fixed broadband Fixed subscriptions to high- | Broadband | BROAD Subscriptions speed access to the Subscriptions public Internet

The number of people Internet Users accessing the internet percentage of | USER | expressed as a % the population proportion of the

High- Products with high R&L technology TECH | intensity US$ exports

Mobile cellular public mobile cellular bn

MOBILE subscriptions service that provides | Subscriptions access to the Public

Switched Telephone Network using cellular technology

The number of distinc publicly trusted SERVER] TLS/SSL _ certificatey Servers found in the Netcraf

2.3.1 Relationship between Broadband Subscriptions and GDP

Some findings from previous studies suggest the positive relationship between Broadband Subscriptions and GDP as follows:

Findings from the Background paper prepared for the World Development Report

(2016) Digital Dividends of Michael Minges showed a positive relationship between Broadband Subscription and GDP

Qiang, Rossotto & Kimura (2009) have suggested that for each additional percentage point of broadband penetration results show an increase in the GDP growth rate

Crandall et al (2007) highlight the indirect economic effects of broadband, noting that these benefits may not be immediately observable They emphasize that such impacts can take time to disperse throughout the economy, indicating a delayed but significant influence of broadband expansion on economic growth.

Cardona, Kretschmer & Strobel (2013) also summarized the impact of broadband on individual productivity, which leads to the growth in the economy.

Relationship between Internet Users and GDP cc eeceeeeeeeeestteeeeeeee 11 2.3.3 Relationship between High-technology exports and GDP

Some findings from previous studies suggest the positive relationship between Internet users and GDP:

According to Vicente & Lopez (2011), ICT and Internet adoption are important factors contributing to economic growth, but they are not the sole drivers Instead, these technologies serve as key root causes that have led to increased benefits and significant GDP growth.

Research by Bloom, Draca, Kretschmer, and Sadun (2010) demonstrates a strong correlation between increasing Internet adoption and GDP growth Their findings also reveal that growth in Internet usage typically occurs before noticeable increases in GDP, suggesting that expanding Internet connectivity can serve as a catalyst for economic development This highlights the importance of fostering Internet infrastructure to boost overall economic performance.

2.3.3 Relationship between High-technology exports and GDP

Some findings from previous models and studies suggest a positive relationship between High-technology exports and GDP:

In the Neoclassical Growth Model, Solow (1956) showed that technological development is the source of economic growth

Research by Deniz Dilara Dereli (2019), published in Press Academia, highlights a causal relationship between high-technology exports and economic growth Similarly, Konak (2018) emphasizes that advances in technology enhance the efficient utilization of production factors, ultimately accelerating economic development These findings underscore the crucial role of technological progress in fostering sustainable economic growth.

Relationship between Mobile cellular subscriptions and GDP

Some findings from previous studies suggest a positive relationship between High-technology exports and GDP:

Tracy Lum (2011) found out that the mobile cellular subscription rate had a positive and significant impact on countries’ level of real per capita GDP

Pantelimon et al (2020) argued that the rapid increase in mobile cellular use, such as mobile commerce, correlated with the gross domestic product (GDP)

Haftu (2019) study showed that mobile phone penetration was associated with GDP significantly.

Relationship between Secure Internet servers and GDP 12 2.4 Descriptive AnalWSẽS ch KHE khi 13 2.4.1 Descriptive s†a†iS[ẽCS nh HH kh kh kiệt 13 2.4.1.1 Source of statistical da†a cc- Tnhh nh key 13

Some findings from previous studies showed a positive relationship between High-technology exports and GDP:

James Manyika and Charles Roxburgh, 2011 from McKinsey Global Institute showed that the Internet exerts a strong influence on economic growth rates

The data & information are collected from World Development Indicators of the World Bank covering 11 Southeast Asia Countries during 10 years from

GDP: GDP (current US$) | Data

Fixed Broadband Subscriptions: Fixed broadband subscriptions | Data

Internet Users percentage of population: Individuals using the Internet (% of the population) | Data

High-technology exports at current US$: High-technology exports (current US$)

Mobile cellular subscriptions: Mobile cellular subscriptions | Data

Secure Internet servers: Secure Internet servers | Data

2.4.1.2 Descriptive statistics and interpretation for each variable

The Descriptive Analysis Results provide a comprehensive overview of the data, including the overall mean, standard deviation, as well as the minimum and maximum values for all variables examined This summary offers valuable insights into the distribution and variability of the data, supporting a clearer understanding of the dataset's characteristics.

Variables} Number of | Mean Standard Minimum | Maximum observation! Deviation

Table 2: Descriptive Analysis Result ô GDP

Mean _ | Standard Deviatio) Minimum} Maximum 213150.1 243080.5 648.4927] 1015620

Table 3: GDP data description The result shows that the GDP of 11 South East Asia countries from 2008

— 2017 varies from 648.4927 to 1015620, with a standard deviation is 243080.5 and a mean is 213150.1

Mean | Standard Deviatio} Minimum | Maximurr

Table 4: BROAD data description The result shows that the BOARD of 11 South East Asia countries from

2008 - 2017 varies from 71 to 1.13e+07, with a standard deviation is 2292582 and a mean is 1833873 ô USER

Mean _ | Standard Deviatio} Minimum | Maximum 32.57329 26.64087 22 94.86669

Table 5: USER data description The result shows that the USER of 11 South East Asia countries from 2008

— 2017 varies from 22 to 94.86669, with a standard deviation is 26.64087 anda mean is 32.57329

ECONOMETRICS REPORT KTEE218.1 Group 9 ô HIGH

Mean | Standard Deviatio) Minimum} Maximum 2.66e+10 4.02e+10 23749 | 1.47e+11

The result shows that the HIGH of 11 South East Asia countries from 2008

— 2017 varies from 23749 to 1.47e+11, with a standard deviation is 4.02e+10 and a mean is 2.66e+10

Mean _ | Standard Deviatio| Minimum | Maximum 6.14e+07 8.71e+07 125002 | 4.35e+08

The result shows that the MOBILE of 11 South East Asia countries from

2008 — 2017 varies from 125002 to 4.35e+08, with a standard deviation is 8.71e+07 and a mean is 6.14e+07 ằ SERVER

Mean | Standard Deviatio} Minimum | Maximum 12672.83 49554.77 0 338925

The result shows that the SERVER of 11 South East Asia countries from

2008 — 2017 varies from 0 to 338925, with a standard deviation is 49554.77 and a mean is 12672.85.

Correlation Matrix between variables che 15

Using STATA, choosing the correlate command will display the correlation matrix as follows:

GDP | BOARD] USER} HIGH | MOBILE | SERVER

Table 9: The correlation matrix table

The correlation matrix table shows that:

All of the correlation coefficients between the independent variables and the dependent variable GDP are different from 0 so they all have an impact on the dependent variable

The analysis reveals that the correlation between MOBILE and GDP is the strongest, with a coefficient of 0.8912, indicating a substantial positive relationship In contrast, the correlation between USER and GDP is the weakest, at only 0.0800, suggesting minimal association These findings highlight the significant impact of mobile technology on economic growth compared to user numbers alone.

The correlation coefficients between the independent variables and the dependent variable are all positive, which shows the positive relationship between the independent variables and the dependent variable GDP

The correlation coefficients between the independent variables are not high, except for the case between USER and HIGH with a 0.7022 correlation

ESTIMATION LH HH iu 18 3.1 Estimated model .-‹‹ - k** SH Tnhh tệp 18 3.2 Sample regression funcfẽO' - nh HH HH HH Hrket 18

Statistical significance of individual coefficiens c.ằ 19 3.3.2 Fixed Broadband Subscrip†ions ch He 19 3.3.3 Internet US@FS ch KHE kg kkt 19

To test the significance of estimated coefficients of estimators we construct the following hypothesis testing, considering a significance level of 5%

1-sided test: Are the Fixed Broadband Subscriptions of each country negatively related to its GDP?

At 5% of significance, Fixed Broadband Subscriptions in each country have a negative effect on its GDP

1-sided test: Are the Internet Users of each country negatively related to its GDP?

Ho: B2>0 Hy: B20.05 => do not reject Ho

P-value is smaller than a, showing that there is not enough evidence to reject the null hypothesis

2-sided test: Do the Fixed Broadband Subscriptions of each country have an impact on its GDP?

Ho: B1 =0 Hy: B1 40 The test statistic: ts =-0.78

P-value=0.878>0.05 => do not reject Ho

1-sided test: Are the High-technology exports of each country positively related to its GDP?

Ho: B3>0 Hy: B30 Hy: B50.05 => do not reject Ho

2-sided test: Do the Secure Internet servers of each country have an impact on its GDP?

P-value=0.166>0.05 => do not reject Ho

Due to insufficient evidence supporting the inclusion of the Internet Users and Secure Internet Servers indexes as independent variables, it is essential to test their joint effect to determine their significance in the model Confirming whether these indices should be incorporated will enhance the accuracy and robustness of the analysis This approach ensures that only relevant predictors are considered, optimizing model performance and aligning with best SEO practices for data-driven decision making.

3.4 Overall significance of the multiple regression

Hypothesis: Do all factors jointly explain the variation in the gross domestic product?

At a 5% level of significance, the model is statistically significant

3.5 Joint significance of the Internet Users and Secure Internet servers

GDPi = B1BROADi + B2USERi + B3TECHi + B4MOBILE: + B5SERVERi + ui

Hypothesis: Do the Internet Users and Secure Internet servers of each country have a joint effect on its GDP?

Fs< Fa(m, n- k) => do not reject Ho

Current evidence does not support a significant joint effect of Internet users and secure internet servers on a country's GDP Therefore, it is advisable not to include these two factors as independent variables in the model.

GDPi = 61BROADi + 3TECHi + B4MOBILE:/ + ui

3.6 Consistency of the regression results with the theories

The regression analysis confirms that the estimators are consistent with our economic theory outlined in section I of this essay The positive signs of the third and fourth estimated coefficients indicate that high-technology exports and mobile cellular subscriptions are positively correlated with GDP These findings align with the Neoclassical Growth Theory discussed earlier, supporting the role of technological advancement and mobile infrastructure in driving economic growth.

However, the signs of the 3 remaining independent variables are negative 3.7 The model’s coefficient of determination:

The coefficient of determination (R-squared) is 0.9179, indicating that 91.79% of the variation in GDP is explained by five independent variables in this sample However, R-squared tends to increase as more variables are added, which can be misleading due to overfitting To address this, the adjusted R-squared, a modified version that accounts for the number of predictors, provides a more accurate measure of model fit.

ECONOMETRICS REPORT KTEE218.1 Group 9 to yield a more honest value to estimate the R2 for the population, and measured the corrected goodness of fit of 91.39% of the model

3.8.1 Meaning of the estimated coefficients

Result Meaning of the coefficients

B, = -.0146694 When all independent variables remain unchanged, the

GDP will decrease by 0146694 units if the Fixed

Broadband Subscriptions increase by 1 unit

8; = -288.639 When all independent variables remain unchanged, the

GDP will decrease by 288.639 units if the Internet User: increase by 1 unit

B3= 2.55e-06 When all independent variables remain unchanged, the

GDP will increase by 2.55e-06 units if the High-technolô export increases by 1 unit

By = 0028511 When all independent variables remain unchanged, the

GDP will increase by 0.0028511 units if the Mobile cellu subscription increases by 1 unit

Bc = -.2170239 When all independent variables remain unchanged, the

GDP will decrease by 2170239 units if the Secure Inte server increases by 1 unit

Table 12: Meaning of the estimated coefficients

These findings highlight the crucial role of developing the digital economy to boost GDP growth in Southeast Asia Governments should implement targeted policies to reduce broadband, internet, and mobile cellular costs, thereby increasing subscription rates and fostering digital adoption Prioritizing affordable digital infrastructure is essential for accelerating economic development and ensuring inclusive growth across the region.

ECONOMETRICS REPORT KTEE218.1 Group 9 enhance the achievement of economic development and increase the number of Base Transceiver Stations to foster access to mobile cellular subscriptions to promote economic growth

Our research examines the influence of key digital economy factors—including fixed broadband subscriptions, internet users, high-technology exports, mobile cellular subscriptions, and secure Internet servers—on Southeast Asia's GDP from 2008 to 2017 The findings highlight that expanding digital infrastructure and internet adoption significantly boost economic growth in the region Specifically, increased internet connectivity and high-tech exports are positively correlated with higher GDP, underscoring the crucial role of digital development in Southeast Asia’s economic progress.

- The model does not omit variables with a Significance level œ = 5%

- The model does not have defects such as multicollinearity, and there is no phenomenon of variable variance

- The research model is consistent with economic theory

Our research confirms that there is a negative correlation between GDP and fixed broadband subscriptions, internet users, and secure internet servers, indicating that higher economic growth may be associated with reduced reliance on these technologies Conversely, we found a positive relationship between GDP and high-technology exports as well as mobile cellular subscriptions, suggesting that economic development tends to boost high-tech export activities and mobile technology adoption These findings support our research hypothesis and provide valuable insights into the digital economy dynamics across different regions.

Research on the digital economy faces limitations due to its novelty and the limited number of variables considered There is a scarcity of relevant economic theories and prior studies examining the relationship between the digital economy and GDP, resulting in few research gaps to build upon During data collection, the team aimed to use numerous observations for more robust regression analysis but found insufficient data on the Southeast Asia General Statistics Office website Ultimately, they sourced the necessary data from the World Bank website to ensure comprehensive analysis.

Based on comprehensive research, the group has proposed several solutions aimed at promoting the country's economic growth These recommendations are rooted in their extensive study of the digital economy's evolving landscape As digital transformation advances, its impact on GDP will vary, highlighting the need for adaptive strategies Future development of the digital economy requires targeted policies and innovative approaches to maximize positive effects on national economic indicators.

The digital revolution signifies a seismic shift in our daily lives and workplaces, presenting a compelling long-term investment opportunity This econometrics report, Group 9's continually updated project, reflects our collective effort and dedication We express our gratitude to Ms Nguyen Thuy Quynh for her invaluable guidance, which enhanced our understanding of econometrics and enabled us to apply critical knowledge in this analysis.

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reg GDP BOARD USER HIGH MOBILE SERVER

Source ss af MS Number of obs = 110

Adj R-squared = 0.9139 Total 6.4406e+12 109 5.9088e+10 Root MSE = 71320

GDP Coef Std Err t P>ltl [95% Conf Interval]

BOARD -.0146694 0043049 -3.41 0.001 -.0232063 -.0061326 USER -288.639 371.4158 -0.78 0.439 -1025.17 447.8925 HIGH 2.55e-06 2.50e-07 10.20 0.000 2.05e-06 3.04e-06 MOBILE 0028511 0001136 25.09 0.000 0026257 0030764 SERVER -.2170239 155576 -1.39 0.166 -.525537 0914893 _cons 9286.917 12746.06 0.73 0.468 -15988.99 34562.83

Summarize GDP BOARD USER HIGH MOBILE SERVER

Variable Obs Mean Std Dev Min Max

GDP BOARD USER HIGH MOBILE SERVER

4 Joint effect testing between Internet users and Secure Internet Servers

5 Regression result for restricted model

- reg GDP BOARD HIGH MOBILE

Source ss af MS Number of obs 110

GDP Coef Std Err t P>|tl (953 Conf Tnterval]

Consistency of the regression results with the theories

The regression analysis confirms that the estimators are consistent with our economic theory outlined in Section 1, demonstrating reliable results Specifically, the positive coefficients for high-tech exports and mobile cellular subscriptions indicate a strong positive relationship with GDP, supporting the neoclassical growth theory These findings highlight the significant role of technological advancement and telecommunications in driving economic growth, aligning with established economic principles.

The model’s coefficient of determinations cece eee eeeeee senna 22 3.8 The regression coeffici@nnẽS eee nh nh HH kh rệt 23 3.8.1 Meaning of the estimated coefficierS nhe ke 23 3.8.2 RecommendatiOnS .-c chén Tnhh 23

The R-squared coefficient is 0.9179, indicating that 91.79% of the variation in GDP is explained by the five independent variables in the model However, relying solely on R-squared can be misleading, as it tends to increase with each added variable, which may lead to overfitting To address this, the adjusted R-squared has been used, providing a more accurate measure of the model's explanatory power by penalizing unnecessary variables and preventing overfitting.