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Forecasting Human Development Index (HDI)

using Time Series Analysis

Sahir Shiek – A003

Aayush Khandelwal – A005

Ritvik Saraf – A006

Utkarsh Jain – A040

Muskan Kothari – A041

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Mentor:

Dr. Leena Kulkarni

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Introduction

What is Human Development?

• Human development is defined as the process of enlarging people's freedoms and opportunities and improving their well-being.
• Based on the notion of human development, the Human Development Index (HDI) is constructed.
• The HDI value of India has been steadily catching up to the world average since 1990 – indicating a faster than global rate of progress of human development.
• However, in line with global trends From 0.645 in 2020, India’s HDI which was estimated to grow in 2021 dropped to 0.633

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Problem Statement

• Finding the most efficient model applicable to a particular time series data
• To comprehend the impact of Covid-19 on HDI values
• To aid in public policy by estimating indicators that influence the Education, Life Expectancy and National Income of countries
• To compare the growth profile of different types of countries

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Objectives

• Estimating the most significant conventional and non-conventional factors for the countries which impact the three sectors of HDI – Life expectancy, Education and GNI
• Finding the best model among ARIMA, ARIMAX & Exponential Smoothing using MAPE.
• Predicting HDI for years 2020-25, backtracking the impact caused due to Covid-19 and estimating the time required for recovery.

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Data Description

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The data set includes life expectancy, gross national income per capita, mean years of schooling and expected years of schooling of all the countries from the year 1990 to 2021.

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Data Description

Indicators

• Life expectancy at birth: The average number of years that a newborn could expect to live if he or she were to pass through life subject to the age-specific mortality rates of a given period.

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Data Description

Data Description

15 Factors related to Life Expectancy:

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Data Description

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• Gross National Income per capita:

It is defined as gross domestic product, plus net receipts from abroad of compensation of employees, property income and net taxes less subsidies on production.

GNI = GDP + (Ex-Im)

Indicators

Data Description

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17 Factors affecting GNI_pc:

Data Description

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• Mean Years of Schooling (MYS) - The average number of completed years of education of a population.
• Expected Years of Schooling (EYS) - The number of years a child of school entrance age is expected to spend at school, or university, including years spent on repetition.

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Indicators

12 Factors related to

Education:

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Data Description

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Data Description

Methodology

HDI Indicators

Exponential

Smoothing

ARIMA

ARIMAX

We choose the best model out of these

(Test data – 80%)

(Train data – 20%)

Methodology

Exponential Smoothing Method:

• Used by Charles Holt in 1954.
• Weighted averages of past observations
• Weights decrease in geometric progression, recent values have greater influence
• Components – Trend, Seasonality, Cyclic and Irregularities
• 3 Methods – Single, Double and Triple

Methodology

Holt’s double exponential smoothing method –

• Includes level and trend component, no seasonality component

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ARIMA:

• The ARIMA model was developed in the 1970s by George Box and Gwilym Jenkins.
• Autoregressive Integrated Moving Average
• Parameters – (p, d, q)

Assumptions of ARIMA model -

• Data should be stationary – Augmented Dickey Fuller test
• Data should be univariate

Pure AR(p) model is given by –

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Pure MA(q) model is given by –

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Methodology

Methodology

ARIMAX:

• Autoregressive Integrated Moving Average with Explanatory variables.
• Multivariate data

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Model is given by –

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Variables for linear regression can be selected by best subset regression.

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Methodology

Methodology

Data Analysis

INDIA GNI_PC (Finding significant factors)

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1. Stepwise VIF function –

• Input of all variables of GNI_PC
• Step by step removal of variables with highest VIF (>10)
• Stop when all variables have VIF below 10

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Factors remaining –

Net trade, government debt, natural resource yield, aid received, investments, FDI inflow, coal consumption, consumer price index for labor

Data Analysis

We performed similar tests on Life Expectancy and Education and further on all countries >>

INDIA GNI_PC (Finding significant factors)

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2. Best subset regression –

• Input of remaining variables of GNI_PC
• Best subset out of each group of ‘i’ variables (i = 1,2,,…n)
• Choosing the best model on the basis of R^2, AIC and Mallow’s CP

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Final Model –

Net trade, natural resource yield, FDI inflow and unemployment

Adjusted R^2 = 0.9063

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VIF of each variable –

Net trade: 3.035932, NR yield: 1.688412, FDI inflow: 2.446939,

Unemp: 2.930927

Summary of significant factors:

Data Analysis

HDI of India

Continent: Asia | Classification: Developing

Data Analysis

GNI of India - ARIMA

Assumptions to fulfill:

1. Time series data is univariate.

2. Time series data is stationarity

Dickey-Fuller Test for stationarity (p-value = 0.05)

H0: Data is not stationary

H1: Data is stationary

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Hence, data is not stationary. Hence, differencing is done.

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Data Analysis

GNI of India - ARIMA

Procedure:

• Automatically identifies most optimal parameters
• Conducts differencing tests to determine d
• Finds p, q by optimizing using AIC (Model with minimum AIC)
• p & q ϵ [0, 5]
• Equation –

(p=2, d=2, q=0)

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Data Analysis

GNI of India - ARIMA

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Data Analysis

• MAPE – 5.706%

GNI of India - Holt

Data Analysis

GNI of India - Holt

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• MAPE – 7.292%

Data Analysis

GNI of India - ARIMAX

Procedure:

• Found the significant factors
• Factors - array of exogenous variables.
• Train data – Modelled Yt with exogenous features (1990-2013)
• Forecasted the exogenous features using ARIMA.
• Test data – Forecast Yt (2014-2019)

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Equation – (p=1, d=0, q=0)

Data Analysis

GNI of India - ARIMAX

Significant Factors:

X1 = Net Trade

X2 = NR Yield

X3 = FDI Inflow

X3 = Unemployment %

Data Analysis

income on unemployment rate %

GNI of India - ARIMAX

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• MAPE – 23.451%
• ARIMA had the least MAPE

Data Analysis

Life Expectancy of India

Significant Factors:

X1 = Immunization

X2 = % Access to Clean fuels and technologies

X3 = BMI Mean

Data Analysis

LE on immunization

Life Expectancy of India

Best Model - Holt

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Data Analysis

ARIMA

Holt’s

ARIMAX

Education of India�

Significant Factors:

X1 = % People Using Internet

X2 = Gender Ratio of Mean years in school

Data Analysis

Education on non internet user

Education of India

Best Model - Holt

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Data Analysis

ARIMA

Holt’s

ARIMAX

HDI of India – Best Model

• Best model for each sector using MAPE
• Final model is trained by combining both train and test data.
• Predicted sector value for 2020-2025.
• Sector value to index - Max & Min taken from actual 2019 values.
• HDI is computed as simple average of all 3 sectors.

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Data Analysis

HDI of India - Forecasting

Data Analysis

HDI of China

Continent: Asia | Classification: Developed

Data Analysis

HDI of China - Forecast

Data Analysis

HDI of Developed Countries

• France | Continent: Europe United States | Continent: North America

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Data Analysis

HDI of France – Best Model

Data Analysis

HDI of United States – Best Model

HDI of Developed Countries - Forecast

Data Analysis

France

United States

HDI of Underdeveloped Countries

• Bolivia | Continent: South America Zimbabwe | Continent: Africa

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Data Analysis

HDI of Bolivia – Best Model

Data Analysis

HDI of Zimbabwe – Best Model

HDI of Underdeveloped Countries - Forecast

Data Analysis

Bolivia

Zimbabwe

Significant Factors

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• Homicide Rate - LE of United States, Bolivia, Zimbabwe

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• Gini Inequality – significant in Bolivia

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• Mean Annual Alcohol Consumption, BMI Mean in LE of Zimbabwe & India respectively.

Inferences

Developed vs Developing vs Underdeveloped

• FDI - Developed countries
• Foreign Aid and Govt Debt – Other countries
• CO2 emissions per Capita only in developed countries

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• Across all 3 sectors and HDI,
• Underdeveloped surpass Developed countries
• Developing countries significantly outperform both

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• Developed Countries most stable in growth, followed by Developing Countries.

Inferences

Competition among Countries

• In 2023, gap in Education Index between India and United States will expand to 6 years. �
• In 2024, China is forecasted to surpass US in Life Expectancy�
• In 2025, China will achieve a median GNI 3 times of India.

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Inferences

Best Model

Inferences

• Life Expectancy:

- Developed : ARIMAX (Nested Model)

- Developing : Holt’s

- Underdeveloped: ARIMA

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• Education: Holt performed best.
• GNI: ARIMA performed best.

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Impact of Covid-19 - Methodology

To estimate the adverse impact, following 4 measures are computed:

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1. Fall in HDI attributed to Covid-19 – point

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2. Fall in HDI attributed to Covid-19 – percentage

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3. Year HDI declined to due to Covid-19

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4. Years taken to recover to pre-Covid-19 Level: 2019 (assuming normal progress)

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Objective 3

Impact of Covid-19 – India HDI

Objective 3

Went back to 2017 level

Will reach pre-COVID-19 value during start of 2021

Impact of Covid-19 – All Countries

Objective 3

Impact of Covid-19 – Inferences

• Zimbabwe & China barely affected by Covid-19.
• India & Bolivia worst affected (10%+ fall)

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• France, a developed country, fell back to 2011 level or by 9 years
• France & Bolivia forecasted to achieve 2019 HDI in 2023

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Objective 3

• Common Significant factors include -

GNI : Natural Resources Yield (4 countries), Unemployment % (3)

LE: Immunization % (4 countries)

Edu: Total Dependency Ratio (3 countries), Fertility Rate (3)

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• After Covid-19 -

Median year countries declined to = 2017

Median years taken for recovery = 3 years

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Conclusion

• Small Sample Size
• Non-linear effect of factors not taken into account
• Correlation does not imply causation
• Long term predictions unreliable
• Over time, the model may become obsolete.
• Bold assumption of having normal growth post Covid-19
• Economy slowdown in 2019 not taken into account.

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Limitations

• Other factors (e.g. non-linear) can be included.
• Different growth profiles can be taken post Covid-19
• Geographical classification can be done.

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• Plotting Government Policies: Significant factors should be prioritized
• Focus on sectors of HDI
• Foreign Aid and Investment Decisions
• Better preparation for future calamities

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Future Scope

• Xu,Chenhui (2021). “A Comparative Study: Time-Series Analysis Methods for Predicting COVID-19 Case Trend.” KTH Royal Institute of Technology, Sweden
• UNESCOIS(2013). “Time Series- UIS Methodology For Estimation Of Mean Years of Schooling.” UNESCO Institute of Statistics
• Kovacevic, Milorad (2010). “Human Development Research Paper - Review of HDI Critiques and Potential Improvements.” UNDP

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Sources:

• UNDP
• World Bank
• Ourworldinadata.org
• National Government Sites
• Gapminder.org

References

THANK YOU