The full project on the unemployment rate in Ghana. This data was taken from the world bank website. Secondary data was used for the analysis.

1. C. K. TEDAM UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES
SCHOOL OF MATHEMATICAL SCIENCES
MARKOV CHAIN ANALYSIS OF UNEMPLOYMENT RATE IN GHANA
DENNIS ATAWOJE DIDERA
2023

2. C.K. TEDAM UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES
SCHOOL OF MATHEMATICAL SCIENCES
MARKOV CHAIN ANALYSIS OF UNEMPLOYMENT RATE IN GHANA
BY
DENNIS ATAWOJE DENNIS
(20200409043)
A PROJECT WORK SUBMITTED TO THE DEPARTMENT OF STATISTICS AND
ACTUARIAL SCIENCE, SCHOOL OF MATHEMATICAL SCIENCES, C. K. TEDAM
UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES IN PARTIAL
FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF BACHELOR OF
SCIENCE DEGREE IN ACTUARIAL SCIENCE/STATISTICS
SEPTEMBER, 2023.

3. i
DECLARATION
I hereby declare that; this thesis is the result of my own work and that it has previously not
been submitted for the award of any other degree in this University or elsewhere.
…….……………….… ………………………
Dennis Atawoje Didera Date
(20200409043)
…………………… ………………………
Prof. Suleman Nasiru Date
(Supervisor)
……………………… ………………………
Prof. Suleman Nasiru Date
(Head of Department and Actuarial Science)

4. ii
ABSTRACT
Unemployment is a global socioeconomic issue affecting countries like Ghana, a
developing West African nation. It is a key economic indicator indicating the percentage
of the labor force actively seeking work.
The unemployment rate in Ghana is a complex and variable, with an average rate of 5.622
and a variance of 2.117. The data is categorized into quartiles, median, and maximum
values, with a skewness and kurtosis indicating asymmetric distribution. The study predicts
a rapid decrease in Ghana's unemployment rate from 1991 to 2022, indicating improved
labor market conditions. The transition probability matrix (M) shows the likelihood of
moving from low to high unemployment rates. The Markov chain consists of three states:
Low, Moderate, and High, with the Low state taking 4.414 steps to return to the "Low"
state, the Moderate state taking 1.934 steps, and the High state falling between the Low
and Moderate states.
There is a decline of unemployment rate in Ghana over the years and the Markov Chain's
steady-state probabilities show long-term unemployment distribution among states at the
67th
iteration, with high unemployment having long-lasting years and low unemployment
having short-lasting years. Low unemployment takes longer to return to the state.

5. iii
ACKNOWLEDGEMENTS
I would like to thank my supervisor Prof. Suleman Nasiru for his guidance, mentoring and
patience throughout the compilation of this project work.
I am very grateful to my family and their support since my the one of entering into this
institution. May almighty God richly bless everyone who made it possible for me get to
this point.

6. iv
DEDICATION
This work is dedicated to my entire family.

7. v
TABLE OF CONTENTS
DECLARATION................................................................................................................ i
ABSTRACT....................................................................................................................... ii
ACKNOWLEDGEMENTS ............................................................................................ iii
DEDICATION.................................................................................................................. iv
LIST OF FIGURES....................................................................................................... viii
LIST OF TABLES........................................................................................................... ix
LIST OF ACRONYMS .....................................................................................................x
CHAPTER ONE ................................................................................................................1
INTRODUCTION..............................................................................................................1
1.1 Background........................................................................................................1
1.2 Statement of the problem...................................................................................5
1.3 General Objective..............................................................................................7
1.4 Specific Objectives............................................................................................7
1.5 Research Questions............................................................................................7
1.6 Significance of the study ...................................................................................7
1.7 Scope of the study..............................................................................................8
1.8 Organization of the study ..................................................................................8
CHAPTER TWO................................................................................................................9
LITERATURE REVIEW...................................................................................................9
2.0 Introduction...........................................................................................................9
2.1 Review of previous works on unemployment rate................................................9
CHAPTER THREE.........................................................................................................17
METHODOLOGY ..........................................................................................................17
3.1 Introduction .....................................................................................................17
3.2 Data source ......................................................................................................17

8. vi
3.3 Markov Chain Model.......................................................................................17
3.4 Markov Chain Modeling .................................................................................18
3.5 Trend analysis..................................................................................................20
3.6 Lake model for employment flow ...................................................................22
3.7 Steady state probability ...................................................................................23
CHAPTER FOUR............................................................................................................24
DATA ANALYSIS AND INTERPRETATION OF FINDINGS.................................24
4.1 Introduction..................................................................................................24
4.2 Presentation of descriptives statistics of the unemployment rate in Ghana.24
4.1 The measure of accuracy of the models.......................................................25
4.3 The trend analysis for unemployment rate in Ghana...................................26
4.4 10 years forecast of unemployment rate in Ghana.......................................27
4.5 The Markov Chain Transition Probability Matrix (M) of unemployment rate
in Ghana 28
4.6 The steady state probabilities for unemployment rate in Ghana..................29
4.7 Expected length of unemployment rate in Ghana........................................30
4.8 Expected recurrent time for each unemployment state................................30
CHAPTER FIVE .............................................................................................................31
SUMMARY, CONCLUSION AND RECOMMENDATIONS ...................................31
5.1 Summary ..................................................................................................31
5.2 Conclusions..............................................................................................32
5.3 Recommendations....................................................................................33
REFERENCE...................................................................................................................35

9. vii
APPENDIX.......................................................................................................................41

10. viii
LIST OF FIGURES
Figure 4.1: Trend analysis of unemployment in Ghana 1991 to 2022...............................26
Figure 4.2: 10 years forecast of unemployment rate in Ghana 1991 to 2022............ Error!
Bookmark not defined.
Figure 4.3: A graph of the recurrent times and length of each unemployment state.........29

11. ix
LIST OF TABLES
Table 4.1: Descriptive Statistics of Unemployment rate of Ghana ...................................25
Table 4.2: Measure of Accuracy........................................................................................26

12. x
LIST OF ACRONYMS
MAD Mean Absolute Deviation
MSD Mean Square Deviation
MAPE Mean Absolute Percentage Error
VAR Vector Autoregression
MCMC Markov Chain Monte Carlo
RMSE Root Mean Square Error
GDP Gross Domestic Product
MANOVA Multivariate Analysis of Variance
ARDL Autoregressive Distributed Lag
OLS Ordinary Least Square
RGDP Real Gross Domestic Product
VECM Vector Error Correction Model
SPSS Statistical Package for Social Science
EM Employment
UN Unemployment

13. 1
CHAPTER ONE
INTRODUCTION
1.1 Background
Unemployment is a major socioeconomic issue that affects countries all over the world.
Unemployment rate is a key economic indicator that denotes the proportion of the labor
force that is actively looking for work but is unable to find it (Мудрак et al., 2018). Ghana,
a developing West African country, is not immune to the issues posed by unemployment.
Understanding the patterns and features of unemployment in Ghana is critical for
policymakers and scholars who want to establish effective methods and policies to address
the problem.
A country's unemployment rate is an important economic statistic that reflects the
percentage of the labor force that is jobless and actively looking for work. It is impacted
by a variety of elements, including the following primary components: Labor Force,
Employed, Unemployed and Not in the Labor Force.
Unemployment is a complex phenomenon with many elements. It is an economic
phenomenon and one of the most serious economic challenges confronting the majority of
the world's countries, independent of their economic and political systems. Unemployment
concerns both industrialized and developing nations due to its societal effects, and it is
currently recognized as one of the world's most significant issues (Lewis, 2019).
Youth unemployment and joblessness negatively impact income generation and living
standards. Full employment is seen as an antidote to poverty and economic growth, while

14. 2
unemployment breeds poverty and wastes essential human resources (Makinde and
Adegbami, 2019).
Kwarteng and Mensah (2022) said obviously troubling unemployment situation in Ghana,
in particular (Baah-Boateng, 2015; Affum-Osei et al., 2019; Ampong, 2020), gives the
impression that either work opportunities are restricted or graduates are not developed
enough for the present job vacancies.
Unemployment Rate is the percentage of a country's labor force without jobs. It increases
during recessions with scarce jobs, while falling during growth and relatively sufficient
jobs. The rate is expressed as a percentage (Yarquah, et al, 2012; Baah-Boateng et al,
2013;Teye P et al., 2019).
Unemployment refers to the proportion of the labor force that is unemployed yet available
for and seeking work. Iraq is considered one of the countries rich in its economic resources
and diversified in their forms in large quantities, which is supposed to be at the forefront
of the industrialized countries and also operating levels at the highest level and yet Iraq's
unemployment rate in 2021 was 14.19%, up by 0.1% from 2020 and 2021 unemployment
rate was 14.09%, up by 1.23% from 2019(Iraq - The World Factbook, 2023.).
A study conducted by Affum-Osei et al. (2019) reveals that unemployment continues to
rise, making it tough to enter the labor market and that employment success in such a
limited labor market is likely to be influenced by "whom you know."

15. 3
Markov Chain is a random process of the happenings of an event within time sequence
which depends on the immediate past of the happenings of the event to predict the
immediate future happenings of that event.
Odah, (2021) indicate that Markov chain is a mechanism for analyzing current variables of
a certain phenomenon in order to predict future variables of the same phenomenon. It is a
subset of random processes.
The Markov chain is a mathematical approach for anticipating changes in certain variables
based on prior changes (Dyer et al., 2006;Sutopo et al., 2018). This approach just requires
data from one period in the past to forecast future market share. The calculation via the
Markov chain approach is straightforward and yields results for the following periods
(Sutopo et al., 2018).
According to Kovacs and Marta, (2018) Markov chains are commonly used for market
share forecasting in various economic sectors, particularly in marketing. Banks are ranked
annually based on net asset balances to assess their performance and potential prospects.
This ranking is crucial for economic agents, customers, and potential clients to monitor the
market share dynamics of banks.
Waller et al., (2019)suggested Markov Chains to anticipate future economic variables using
theories such as Stochastic Process, Discrete Time Markov Chain, Probability and
Statistics, and Transitional Matrix. Economic variables, such as population, poverty,
inflation, resources, and real GDP, as well as unemployment, inflation, interest, stock
market, and exchange rates, are used to measure economic functions. Markov Chains

16. 4
accurately anticipate future occurrences by recognizing beginning states and anticipating
the next state.
Unemployment is a major concern in many nations, including Ghana. It is one of the most
serious economic issues confronting not only Ghana, but the whole developing world.
Various attempts have been made by successive governments and other policymakers to
solve these issues, but the problems continue to worsen year after year as the population
grows and the number of graduates from various tertiary institutions grows. This is quite
concerning and demands immediate response; else, the harm done now will be felt by the
nation for decades. To assist alleviate these issues, it is critical to first explore the reasons,
which has resulted in several research projects.
A study conducted by Lewis, (2019) showed that inflation rate and GDP growth rate affects
unemployment and that high inflation rate results to high unemployment rate whereas
strong GDP growth the unemployment rate raises quickly and abruptly at the onset of
contractions and declines slowly and gradually during expansions.
A study conducted by Ferraro (2017) pattern produces positive skewness in the distribution
of unemployment rate changes, while the model produces a counterfactually negative
skewness. The key feature of the model responsible for this counterfactual prediction is the
convexity of hiring costs in aggregate employment, which leads to excessive
responsiveness of job vacancies to positive shocks in periods of high unemployment.
A persistently high level of unemployment is one of the most challenging and complex
problems in macroeconomics. The issue is particularly pressing today: the employment-to-

17. 5
population ratio fell from 63% in 2007 to 58% in 2009, where it stands as of the summer
of 2011. The problem has been difficult to handle in part due to a lack of agreement on the
causes of unemployment. Many ideas have been advanced to explain employment losses,
including a fall in aggregate demand, company uncertainty, and labor force structural
adjustment (Mian and Sufi, 2012).
Job search theory predicts an uncertain link between the business cycle and the duration of
unemployment. Increases in unemployment will decrease the reservation wage but also the
likelihood of obtaining a job offer (Kovacs and Marta, 2018).
1.2 Statement of the problem
Ghana faces significant challenges related to unemployment, affecting both educated and
illiterate individuals, worsening socioeconomic inequality and hindering progress.
Youth unemployment is high, and underemployment occurs when employees cannot find
suitable jobs. The informal sector faces low job security, benefits, and earnings. The
education system may not align with market demands, limiting employment opportunities.
Oyebade (2003);Makinde and Adegbami (2019b), identifies unemployment as one-time
job loss, layoffs, and unappointment youths. Unemployment arises from labor force's
inability to meet job requirements due to insufficient productivity (Baah-Boateng, 2015).
Rural areas have higher unemployment rates than metropolitan ones, causing migration to
cities. Ghana's job creation rate has lagged behind the growing labor force, partly due to
poor economic development, limited investment, and corporate access to capital and
resources. According to Oluwajodu et al., (2015), graduate unemployment is a problem

18. 6
because it wastes scarce human capital, which has a negative long-term impact on the
economy.
Nigerian youth face daily unemployment, causing poverty and low income, as the
government's inaction and increased budgets continue to worsen the issue (Makinde and
Adegbami, 2019).
Unemployed workers are unable to contribute to the growth of the GDP. Every nation faces
a serious unemployment issue, so efforts are being made to address it (Cristescu, 2017).
A study conducted by (Chan, 2015) evaluates Malaysia's labor market response to
economic globalisation, focusing on the long-run impact on unemployment between 1980
and 2014 in Malaysia. The integration with the world market may bring prosperity but may
also negatively affect developing and transitional economies. Ghana's low employment
content despite great growth over three decades is attributed to rapid expansion in low-
generating sectors and slow growth in high labor-absorptive sectors (Baah-Boateng, 2014).
In Ghana, education and age are important variables in influencing unemployment rates.
Unemployment rises with education, whereas it falls with age. Unemployment rates are
also influenced by demand variables such as full-time job searchers and those seeking
formal or pay work. Unemployment is also influenced by factors such as reservation salary,
marital status, gender, poverty, and rural-urban location (Baah-Boateng, 2015).

19. 7
1.3 General Objective
The main objective of the study is to perform Markov Chain analysis of unemployment
rate in Ghana.
1.4 Specific Objectives
1. Investigate the pattern of the unemployment rate in Ghana
2. Construct the states of unemployment rate and determine their corresponding
probabilities.
3. Estimate the expected length of each unemployment state.
4. Determine the expected recurrent times for each unemployment state.
1.5 Research Questions
1. What is the pattern of the unemployment rate in Ghana?
2. What are the states of employment rate and determine their corresponding
probabilities?
3. What is the expected length of each unemployment state?
4. What are the expected recurrent times for each unemployment state?
1.6 Significance of the study
This study has an influence on Ghana's employment-related policies and choices. By
examining unemployment rate trends, policymakers can pinpoint times of high and low
unemployment. Targeted policies are created by estimating state transitions and focusing
on certain labor market segments. It is possible to develop measures to reduce the length

20. 8
and frequency of unemployment by understanding unemployment dynamics and
foreseeing jobless spells and repeating periods.
(Baah-Boateng, 2015) identified in his research on unemployment in Ghana that, there is a
high level of unemployment among the youth than the older ones.
1.7 Scope of the study
This research will focus on analyzing the unemployment rate in Ghana, primarily using
Markov Chain analysis. The study will consider historical data over the last decade,
covering the employment status transitions of the working-age population. The analysis
will be based on available data from 1991 up to the year 2022, and any developments
beyond that period will not be accounted for in this study.
1.8 Organization of the study
The thesis is divided into five chapters. Chapter one describes the study's background,
research questions, problem statement, objectives, and justification. Chapter two presents
relevant literature on forecasting techniques that have been used over the years to model
and forecast on unemployment rate. The methodology for the study is presented in chapter
three. The study's findings and discussion are presented in chapter four. Finally, in chapter
five, the study's conclusions and recommendations are presented.

21. 9
CHAPTER TWO
LITERATURE REVIEW
2.0 Introduction
This chapter presents previous literature relevant to the unemployment rate in Ghana.
2.1 Review of previous works on unemployment rate
Nordmeier and Weber (2013) used a structural Vector Autoregression (VAR) approach,
reveals various patterns of unemployment dynamics that is the worker reallocation process
is not constant across the identified shocks. The significance of the transition rates varies
with the different types of shocks. The impulse responses indicate a larger role of the job
finding rate after a technology shock and a monetary policy shock, while the separation
rate appears as the dominant margin after a fiscal policy shock. In line with the
unconditional movements of the transition rates, the transmission mechanism through the
job finding margin is relatively persistent, while the effects along the separation margin are
sharp and short-lived. Several robustness checks reinforce this clear-cut pattern. The
forecast error variance decomposition demonstrates that the identified shocks account for
40% of the variations in the job finding rate and 30% of the variations in the separation
rate. Thereby, the technology shock plays a substantial role. In our benchmark sample, the
technology shock shows traditional features, that is an increase in productivity reduces
unemployment. Once we restrict our time period to reunified Germany, we also observe
Schumpeterian features that is an increase in productivity leads to higher separations. In
addition, the relative importance of technology shocks shrinks over time.

22. 10
Monetary policy shocks seem to have become less important for unemployment dynamics
in Germany. Especially after the reunification, changes in the interest rate account for just
1% of the variations in the transition rates. The loss of importance can be reconciled with
the implementation of the EMU. Nevertheless, it should be noted that those results do not
concern the functioning of rule-based monetary interventions. Accordingly, the results may
also indicate that the monetary authority does rarely deviate from its policy rule or that
discretionary policy interventions are anticipated due to a transparent strategy. Instead,
fiscal policy shocks may be a more promising instrument to account for unemployment
dynamics. The effects of the government spending shock are significant for different
specifications and the fiscal multipliers of the transition rates have increased over time.
However, our analysis points to several limitations as well. First, the effects of a
government spending shock turn out to be very short-lived. Second, there are indications
of a Ricardian equivalence behavior, though this observation is not stable. Third, the fiscal
multipliers are of a moderate magnitude which might fuel concerns about fiscal debt levels.
Forth, the transmission of a government spending shock works primarily through the
separation rate, and thus fiscal policy may be less suitable to control rises in long-term
unemployment triggered by other factors. Hence, further evidence on the sources and
mechanisms of labor market dynamics seems
to be crucial for determining an optimal policy instrument. A key result from our study is
that those analyses should not neglect the separation margin, especially when shocks tend
to be less persistent.

23. 11
Ali and H. Kadhim (2021) used frequentist and Bayesian approaches for the linear
regression model to predict future observations for unemployment rates in Iraq. Parameters
are estimated using the ordinary least squares method and for the Bayesian approach using
the Markov Chain Monte Carlo (MCMC) method. Calculations are done using the R
program. The analysis showed that the linear regression model using the Bayesian
approach is better and can be used as an alternative to the frequentist approach. Two
criteria, the root mean square error (RMSE) and the median absolute deviation (MAD)
were used to compare the performance of the estimates. The results obtained showed that
the unemployment rates will continue to increase in the next two decades.
Sutopo et al., (2018) used Markov chain method was to forecast the market share due to its
simplicity and accuracy as well as characteristic of the battery as yet-launched product.
Based on the result, there is a tendency of motorcycle battery consumer in Indonesia to
switch from wet and dry cell battery to lithium iron phosphate battery. This study could
not explore the challenges in the market shares of the motorcycle battery consumer faces
and how solve complex problems to construct a proper value chain of electric vehicle.
Chan, (2015) used autoregressive distributive lags method to examine the pattern of the
relationship unemployment and economic globalisation. The results showed that economic
globalisation have significant and positive impact on reducing unemployment in Malaysia
in the long run. These findings indicated that policy-makers in Malaysia should facilitate
the economy globalisation to maintain the current low level of unemployment rate.

24. 12
According to Lewis (2019) MSMEs in Ghana offer 82% employment to the working
population, with 81% permanent and 86% temporary, with micro enterprises employing a
larger percentage.
In 2023, South Africa had the highest unemployment rate in Africa, with 30% of its labor
force unemployed. Djibouti and Eswatini followed with unemployment rates of 28% and
25%, respectively. Niger and Benin had the lowest rates, with the continent's average of
8%. The young population is more likely to face unemployment, with Djibouti having the
highest rate at almost 80%. Female unemployment in Africa is also high, with Djibouti and
South Africa having the highest rates at 39% and 36%, respectively (Unemployment Rate
in Africa by Country 2023 | Statista, n.d.).
Nyarko Philomena, (2010)conducted a survey in 2010 PHC which shows that 48% of youth
were self-employed, with 21% involved in family work. Over 19% were employees, and
7.14% were apprentices. Females dominated self-employment, while males dominated
employees. Females dominated in apprenticeships, contributing family workers, and
domestic employees, while male youth dominated casual work.
According to Makinde and Adegbami (2019), Nigeria's youth unemployment has increased
due to the rise in graduates from higher education institutions. According to the Nigerian
National Bureau of Statistics, unemployed individuals are those aged 15-64 actively
seeking work but couldn't find it for less than 20 hours. The unemployment and
underemployment rates increased to 23.1% and 16.6% in 2018, respectively.

25. 13
Teye P et al. (2019) used linear regression and found that Exchange Rate and
Unemployment Rate contribute 0.15 to Ghana's Real Gross Domestic Product Growth
Rate. Exchange rate positively and insignificantly affects GDP, while unemployment rate
negatively and insignificantly affects GDP. A unit increase in Exchange rate leads to an
increase in GDP, while a unit increase in unemployment rate causes a decrease.
The Unemployment Rate coefficient is -0.390, with a P-value of 0.083. This indicates an
insignificant negative relationship between unemployment rate and GDP, indicating a
0.390 unit decrease in GDP for a unit increase in unemployment rate.
Baah-Boateng (2013) used a regression model in Ghana reveals a significant relationship
between demand factors and unemployment, with limited effects on economic growth and
employment creation. Youth and urban dwellers are more susceptible, with education and
gender being explanations. Reservation wages also contribute to increased unemployment.
Sulemana et al. (2019) used a regressions and instrumental variables analyzed the link
between unemployment and self-rated health in Ghana. Results showed a negative
relationship between unemployment and health.
Owusu Ansah et al. (2021) used partial least squares model to investigate the relationship
between unemployment and Ghana's single spine pay policy was investigated. An
exploratory sequential mixed design strategy was used to collect data from 413 business
owners and managers from manufacturing businesses, service sectors, wholesalers, and
small and medium-sized organizations. The single spine pay policy was discovered to have
a significant influence on unemployment.

26. 14
Adarkwa et al. (2017) used Pearson r, linear regression, and multivariate analysis of
variance (MANOVA) and found that the service sector significantly impacted Ghana's
unemployment rate from 1991 to 2014. (Amissah and Nyarko, 2017) also examined the
impact of youth unemployment on young people's mental health. The study analyzed data
from 1991 to 2014, finding that young people without jobs had worse psychological health
than those with jobs.
Misini and Badivuku-Pantina (2017) Examining the relationship between nominal GDP
and unemployment using linear regression, empirical results reveal detrimental effects on
both factors. The study analyzed simple linear regression and nominal GDP compared to
unemployment, finding a negative effect. A 1% increase in nominal GDP reduced
unemployment by -0.43%, indicating economic growth under nominal GDP influences
unemployment alleviation. Chand et al. (2018) used correlation and regression analysis
which revealed a strong negative correlation between economic growth and unemployment
rates, with GDP accounting for 48% of the change in unemployment rates. This aligns with
Okun's law and previous studies.
Khrais and Al-Wadi (2016) used simple linear regression to analyze the impact of GDP on
unemployment in all involved countries. The significance level was greater than 0.05,
indicating no significant impact on gross GDP (annual) from labor numbers. The impact
value was very small (0.009), suggesting that other factors may affect unemployment
beyond GDP.
Shah et al., (2022) used the Autoregressive Distributed Lag (ARDL) technique to
investigate the relationship between GDP growth rate, unemployment, population growth

27. 15
rate, inflation rate, foreign direct investment, and government expenditure. Results show a
negative relationship between these variables, while population growth rate has a positive
impact. Short-run cointegration exists between the variables, suggesting that government
measures should be taken to generate employment opportunities and accelerate economic
growth.
Ademola and Badiru (2016) used the Ordinary Least Square (OLS) technique and
diagnostic tests to analyze data from 1981 to 2014. Results showed a stationary data set
and two cointegrating equations, suggesting a long-run relationship between RGDP,
unemployment, and inflation. The results showed a positive relationship between
unemployment, inflation, and RGDP, suggesting that Nigeria's RGDP is driven by oil
revenue, limited skilled labor, and externally determined crude oil output prices, which
may not align with expected output growth. The originality of the study lies in the
interpretation of the regression analysis results.
Jajere, (2017) used Ordinary Least Square regression to show that unemployment doesn't
significantly impact economic growth. However, a good economy's performance in per
capita growth may be attributed to other factors affecting economic growth.
Idris (2021) examines the impact of unemployment and inflation on Nigeria's economic
growth from 1986 to 2020. The study used ordinary least square technique to examine the
model coefficient. Results show that unemployment has a significant negative effect on
Nigeria's economic growth, while inflation has a positive effect.

28. 16
Bhowmik, (2018) examines the relationship between growth and unemployment rates in
India from 1991-2016 using regression models, Granger Causality test, Johansen
Cointegration test, and Vector Error Correction model. The output gap is measured by
deducting Hodrick-Prescott Filtered trend value from the actual output, while the
unemployment gap is measured by deducting natural growth rate of unemployment from
the actual unemployment rate. Data from the World Bank is used to analyze the data. The
paper finds a significant negative growth-unemployment nexus at a 10% level, with a co-
integrated relationship. The VECM model is stable and non-stationary, with a high and
significant error correction process speed. The nexus between output and unemployment
is negative but not co-integrated. The VAR model is a good fit for variables related to
previous periods. The relationship between growth and unemployment is insignificantly
negative and co-integrated, with a stable but non-stationary VECM and a fast adjustment
speed.
Kaur (2014) examines the relationship between unemployment, GDP growth rate, inflation
rate, and exchange rate in India from 1990 to 2013. It uses the ordinary least square method
or simple linear regression model to analyze data. Results show that inflation and exchange
rates significantly affect unemployment in India. Chand et al. (2018) investigates the
impact of economic growth on India's unemployment rate using Gross Domestic Product
as an indicator. Data on GDP and unemployment rate were collected from secondary
sources like the World Bank database. Correlation and regression analysis were used to
study the relationship. Results showed a strong negative correlation between economic
growth and unemployment rate, with GDP accounting for 48% of the change in
unemployment rate. These findings align with Okun's law and previous studies.

29. 17
CHAPTER THREE
METHODOLOGY
3.1 Introduction
This chapter talks about data and statistical techniques that were used in order to achieve
the objectives of the study. This chapter is divided into four main sections namely; data
and source, Markov chain model, Markov chain modeling, trend analysis, lake model of
employment and limiting distribution.
3.2 Data source
To attain the objectives of this study, secondary data on unemployment rate of Ghana was
obtained from the world bank database. The data consist of infant mortality rate from 1991
to 2022. The data was analyzed using R software, SPSS and excel contain the dataset.
3.3 Markov Chain Model
A Markov chain or Markov process, named after Russian mathematician, Andrew Markov
(Shannon, 1948) is a mathematical system that undergoes transitions from one state to
another, that is from a finite or countable number of possible states in a chain like manner,
Markov chain is a random process governed by a Markov property.
The Markov property means that evolution of the Markov process in the future depends
only on the present state and does not depend on past history. This means that, Markov
process does not remember the past if the present state is given and this makes the Markov
property a memory less property of a stochastic process.
Since the system changes randomly, it is generally impossible to predict the exact state of
the system in the future.

30. 18
Mostly, a Markov chain would be defined for a discrete set of time (i.e a discrete time
Markov chain) although some authors use the same terminology where time can take
continuous values. The use of the term in Markov chain methodology covers cases where
the process is in discrete time with a continuous state space.
A discrete time random process means a system which is in a certain state at each step with
the state changing randomly between steps. The steps are often thought of a s time, but
they can equally refer to physical distance or any other discrete measurement. The steps
are just the integers or natural number, and the random process is a mapping of these two
states, that is, discrete time with a continuous space.
Since the system changes randomly, it is mostly or generally impossible to predict the exact
state of the system in future. However, the statistical properties of the system’s future can
be predicted. The changes of the state of the systems are called transitions and the
probabilities associated with the various state-changes are called transition probabilities.
The set of all states and probabilities completely characterizes a Markov chain. In many
applications, it is these statistical properties that are of use or important.
3.4 Markov Chain Modeling
The Markov chain model is explained as follows;
The probability of going from state I, to j in n times steps is given as
(n)
i,j n 0
p =p(x =j|x =i) (3.1)
And the single-step transition is
i,j k+n 0
p =p(x =j|x =j) (3.2)

31. 19
For a time-homogeneous Markov chain:
(n)
i,j k+n k
p =p(x =j|x =i) (3.3)
and
i,j k+1 k
p = p(x = j| x = i) (3.4)
The n-step transition probabilities satisfy the Chapman-Kolmogorov equation (Papoulis,
1984), that for any k such that 0<k<n
(n) (k) (n-k)
i,j i,r rj
res
p = p p
 (3.5)
Where, S is the state space of the Markov chain. The marginal distribution P 0
(x =x) is the
distribution over states at time n. The initial distribution is P 0
(x =x) The evolution of the
process through one time step is described by
n rj n-1
res
P = (x =j) = p p(x =r)
 (3.6)
( )
0
( )
n
res rj
p p x r
 
 .
The (i, j) th
element of the matrix product n-1 n
p . p = p , which confirms (n) n
p = p . The
residual (n) 0 n
p = p p is obtained by nothing that
P n n 0 0
res
(x = j)= p(x = j |x = i) p(x = i)
 (3.7)
From this theory, the n-step transitions probabilities can be easily obtained by simple
matrix multiplication, for larger state space efficient of n
p are needed.

32. 20
3.5 Trend analysis
Trend analysis is the process of looking at the current trends in order to predict future ones
and is considered a form of comparative analysis.
The methods and formulas of trend analysis are of different forms which consists of linear,
Quadratic, Exponential growth, S-curve, Forecasts, mean absolute percentage error
(MAPE), Mean absolute deviation (MAD), and mean squared deviation (MSD).
The linear trend model is given as,
t 0 1 t
Y = β + β t+ e (3.8)
Where 0
β is constant, 1
β is the average change from one period to the next, t is the value
of the time unit and t
e is the error term.
The quadratic model is accounts for simple curvature in the data and it’s given as,
2
0 1 t
t β +βt+ β t
= + e
Y (3.9)
Where 0
β is the constant, 1
β is the average change from one period to the next, t is the
value of the time unit, and t
e is the error term.
The exponential growth trend model is given as,
t
t
t
0 1
β β
= + e
Y (3.10)
where 0
β is a constant, 1
β is the coefficient, t is the value of the time unit, and t
e is the
error term.

33. 21
The mean absolute percentage error measures the accuracy of fitted time series values.
MAPE expresses accuracy as a percentage. The formula is given as,
t t
t
t
|(y -y )/y | 100
MAPE = × %,(y ¹0)
n
 (3.11)
Where t
y is the actual observation values at time t, t
y is the fitted value, and n is the
number of observations.
The mean absolute deviation measures the accuracy of the fitted time series values.
MAD expresses the accuracy in the same units as the data, which helps conceptualize the
amount of error. The formula is given as,
n
t t
t=1
|y -y |
MAD =
n
 (3.12)
Where t
y is the actual value at time t, yt is the fitted value, and n is the number of
observations.
The squared deviation is always computed using the same denominator n, regardless of the
model, MSD is a more sensitive measure of an unusually large forecast error than MAD.
The formula is given as,
n 2
t t
t=1
| y - y |
MSD =
n
 (3.13)
Where t
y is the actual at time t, t
y is the fitted value, and n is the number of observations.

34. 22
With Forecasts, R software is used to model the trend equation to calculate the forecast for
specific time values. Data before the forecast origin are used to fit the trend.
3.6 Lake model for employment flow
In a year unemployed (people looking for job) and employed (people working and not
looking for alternative)
1 – λ 1 − φ
EM denotes the employment and UN denotes unemployment with a unit of time of one
year with λ denoting the probability that a worker loses his or her job within a year and φ
denoting the probability of a person gets a job within a year.
Where λ, φ [0,1] being the transition probabilities with the assumption that λ and φ are
independent typically on the person nor on time.
For n = 0, 1, 2, . . ., let n
X denote the (random) state of employment of such person.
We have
n+1 n n-1 n-2 n-k n+1 n
P(X =EM|X =UN,X =...,X =...,X =...)=P(X =EM|X =UN)=φ
n+1 n n-1 n-2 n-k n+1 n
P(X =UN|X =EM,X =...,X =...,X =...)=P(X =UN|X =EM)=λ
n+1 n
P( X = EM | X = EM)= 1 - λ (3.14)
φ
λ
UN
EM

35. 23
n+1 n
P( X = UN| X = UN)=1 - φ (3.15)
At any time, regardless of the information about the past years, the next-year state of
employment depends uniquely on the present one.
3.7 Steady state probability
The steady-state (stable state ( )) probability vector in a Markov chain represents the long-
term probabilities of being in each state after many time steps, assuming the Markov chain
has reached a stable state.
Mathematically:
p
π
π (M-I) = 0 (3.16)
Where π is the stable state vector
M is the probabilities transition matrix
I is the identity matrix
p is the number of iterations for the matrix to reach a stable state
 is the stable state vector

36. 24
CHAPTER FOUR
DATA ANALYSIS AND INTERPRETATION OF FINDINGS
4.1 Introduction
This chapter analyzes data on the unemployment rate, focusing on patterns and trends of
unemployment rate in Ghana. It provides a thorough account of the data preparation
process and presents descriptive statistics. The chapter examines unemployment rate trends
over time, revealing trends of the rate.
4.2 Presentation of descriptives statistics of the unemployment rate in Ghana
Table 1 describes the unemployment rate variable in the dataset, it is measured using
various statistics, including mean, SE Mean, StDev, and variance.
The dataset contains data on the unemployment rate, with an average rate of 5.622. The
standard error of the mean is 0.374, indicating the standard deviation of the sample means.
The standard deviation is 2.117, indicating greater variability. The variance measures the
dispersion of unemployment rate values around the mean. The data is categorized into
quartiles, median, and maximum values. The minimum unemployment rate is 2.17, while
the first quartile (Q1) rate is 3.88. The median rate is 5.175, the middle value when data is
sorted. The third quartile (Q3) rate is 6.972. The maximum unemployment rate is 10.46.
Skewness and kurtosis indicate asymmetry in the distribution, with a skewness of 0.74
indicating a skewed distribution and a kurtosis of -0.14 indicating fewer extreme values.
These statistics provide a comprehensive overview of the unemployment rate variable's

37. 25
characteristics and distribution, helping to understand the central tendency, spread, shape,
and range of the data.
Table 4.1: Descriptive Statistics of Unemployment rate of Ghana
Variable Unemployment rate
Mean 5.622
SE Mean 0.374
StDev 2.117
Variance 4.483
Minimum 2.17
Q1 3.88
Median 5.175
Q3 6.972
Maximum 10.46
Skewness 0.74
Kurtosis -0.14
Table 4.1 Source: World bank data, 1991 to 2022
4.1 The measure of accuracy of the models
The results from table 2 evaluate the performance of various models using metrics like
Mean Absolute Percentage Error (MAPE), Mean Absolute Deviation (MAD), and Mean
Squared Deviation (MSD), which are crucial in forecasting and predictive modeling.
The MAPE (Mean Absolute Percentage Error) for the linear model is 25.6068%, indicating
an average deviation of 25.61% from actual values. The quadratic model's MAPE is
26.8517%, slightly worse than the linear model's, while the exponential model's MAPE is
24.5424%, slightly better than both.
The Exponential Model has the lowest MAPE (24.5424), suggesting slightly better
accuracy of measurement compared to Linear and Quadratic Models.

38. 26
Table 4.2: Measure of Accuracy
Model MAPE MAD MSD
Linear Model 25.6068 1.3176 3.1245
Quadratic Model 26.8517 1.3206 2.634
Exponential Model 24.5424 1.3303 3.3505
Table 4.2 Source: World bank data, 1991 to 2022
4.3 The trend analysis for unemployment rate in Ghana
Exponential Model (Growth Curve Model)
Fitted Trend Equation
Yt = 7.546 × (0.97831^t)
Figure 4.1: Trend analysis of unemployment in Ghana 1991 to 2022
Figure 4.1 Source: World bank data, 1991 to 2022

39. 27
Figure 4.1 is the exponential model plot with the lowest MAPE (24.5424) value suggesting
that it is slight better in the measure of accuracy as compared to the linear and the quadratic
trend methods.
The plot has a positive exponential coefficient (0.97831) indicating the rate of change in
unemployment rate in Ghana over the years. The figure above suggests a fast reduce of
unemployment rate in Ghana from 1991 to 2022. It suggests that the unemployment rate
has been decreasing over time. This is a positive change as it indicates improvement of
labor market conditions.
4.4 10 years forecast of unemployment rate in Ghana from 1991 to 2022
Figure 4.2 Source: World bank data, 1991 to 2022
Figure 4.2, show a general decreasing trend as we move from period 2023 to period 2031.
This suggests that unemployment rate in Ghana is expected to decrease over time.

40. 28
4.5 The Markov Chain Transition Probability Matrix (M) of unemployment rate
in Ghana
The matrix (M) represents the transition probability matrix of unemployment rate in Ghana
indicating the transition probabilities from one state to the other or a current state to the
next state. This suggests that the probability of Ghana moving from low unemployment
rate back to low unemployment rate is 0.571, moving from low unemployment rate to
moderate is 0.429 and from low unemployment rate to high unemployment rate is 0. The
probability of moving from moderate unemployment rate to low unemployment rate is
0.188, moderate to moderate unemployment rate is 0.75 and moderate unemployment rate
to high unemployment rate is 0.062. The probability of moving from high unemployment
rate to low unemployment rate is 0, the probability of moving from high unemployment
rate to moderate unemployment rate is 0.125 and the probability of moving from high
unemployment rate to high unemployment rate is 0.875.
M=
Low Moderate High
Low 0.571 0.429 0
Moderate 0.188 0.75 0.062
High 0 0.125 0.875
 
 
 
 
 
 

41. 29
Figure 4.3: A graph of the recurrent times and length of each unemployment state
Figure 4.3 Source: World bank data, 1991 to 2022
4.6 The steady state probabilities for unemployment rate in Ghana
The steady-state probabilities of a Markov Chain represent its long-term distribution
among its states, providing long-run behavior of the system modeled by the Markov Chain
at the 67th
iteration. The low unemployment has a steady-state probability of approximately
0.227, indicating that expected times low unemployment rate is 22.7% spent in a long term.
The moderate state has a steady-state probability of approximately 0.517, suggesting that
the expected times of moderate unemployment rate is 51.7% spent in a long term. The high
state has a steady-state probability of approximately 0.256, indicating that the expected
times high unemployment rate is 25.6% in a long term.
SteadyState ( low moderate high
(π ,π ,π ) )=
.
L
5
ow
7
Mod
0
erat
0
e High
0.226566 0 1 0 4 .256430
 
 
 
 
 
0.57
0.75
0.88
0.43
0.19
0.06
0.12
Low
Moderate
High

42. 30
4.7 Expected length of unemployment rate in Ghana
The results indicate the expected length of unemployment rate in Ghana. Unemployment
rate is estimated to be low for an average length of 2.33, unemployment is estimated to be
moderate on an average length of 4.00 and unemployment rate is estimated to be high on
an average length of 8.00.
   
low moderate high
π ,π ,π = 2.33 4.00 8.00
4.8 Expected recurrent time for each unemployment state
The Markov chain has three states: Low, Moderate, and High. The Low state takes an
average of 4.414 steps or transitions to return to the "Low" state after starting in the "Low"
state. The Moderate state takes an average of 1.934 steps to return to the "Moderate" state,
with a shorter expected recurrent time compared to the "Low" state. The High state takes
an average of 3.900 steps to return to the "High" state, falling between the "Low" and
"Moderate" states in terms of its expected recurrent time.
 
low moderate high
π ,π ,π =
Low Moderate High
4.413725 1.934221 3.899700
 
 
 

43. 31
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
This chapter summarizes the findings, making conclusions and recommendations
necessary to unemployment situations in Ghana.
5.1 Summary
Table 4.1 presents the unemployment rate, with an average rate of 5.622. The standard
error of the mean is 0.374, indicating the standard deviation of the sample means. The
standard deviation is 2.117, indicating greater variability. The variance measures the
dispersion of unemployment rate values around the mean. The data is categorized into
quartiles, median, and maximum values. The minimum unemployment rate is 2.17, while
the first quartile (Q1) rate is 3.88. The median rate is 5.175, the middle value when data is
sorted. The third quartile (Q3) rate is 6.972. The maximum unemployment rate is 10.46.
Skewness and kurtosis indicate asymmetry in the distribution, with a skewness of 0.74
indicating a skewed distribution and a kurtosis of -0.14 indicating fewer extreme values.
These statistics provide a comprehensive overview of the unemployment rate variable's
characteristics and distribution, helping to understand the central tendency, spread, shape,
and range of the data.
The linear model has a 25.6068% MAPE, while the quadratic model has a 26.8517%
MAPE, and the exponential model has a 24.5424% MAPE, which suggested slightly better
measurement accuracy.
The plot shows a rapid decrease in Ghana's unemployment rate from 1991 to 2022,
indicating an improvement in labor market conditions.

44. 32
The matrix (M) represents Ghana's unemployment rate transition probability matrix,
indicating the likelihood of moving from low to high unemployment rates. The probability
of moving from low to low is 0.571, from low to moderate is 0.429, and from low to high
is 0. The probability of moving from moderate to low is 0.188, from moderate to low is
0.75, and from moderate to high is 0.062. The probability of moving from high to low is
0.125, and from high to high is 0.875.
The steady-state probabilities of a Markov Chain represent its long-term distribution
among states, providing insight into the system's equilibrium or long-run behavior. Low
unemployment has a steady-state probability of 0.227, indicating 22.7% spent in a long
term. Moderate unemployment has a steady-state probability of 0.517, indicating 51.7%
spent in a long term, and high unemployment has a steady-state probability of 0.256.
The study predicts that Ghana's unemployment rate will be low for an average length of
2.33, moderate for an average length of 4.00, and high for an average length of 8.00.
The Markov chain consists of three states: Low, Moderate, and High. The Low state takes
4.414 steps to return to the "Low" state, while the Moderate state takes 1.934 steps and has
a shorter expected recurrent time. The High state takes 3.900 steps, falling between the
Low and Moderate states.
5.2 Conclusions
The distribution of unemployment rate data is slightly skewed, with fewer extreme values,
as indicated by the skewness and kurtosis values.

45. 33
The exponential model demonstrated slightly better measurement accuracy than the linear
and quadratic models, as compared to their Mean Absolute Percentage Error (MAPE)
values.
The unemployment rate data plot reveals a significant decrease, indicating an improvement
in Ghana's labor market conditions.
The transition probability matrix (M) in the Markov Chain of unemployment rate dynamics
helps understand the likelihood of moving between states, highlighting that direct transition
from Low to High unemployment is impossible.
The Markov Chain's steady-state probabilities show long-term unemployment distribution
among states, with low unemployment at 0.227, moderate at 0.517, and high at 0.256,
indicating varying levels of long-term spending.
The study predicts that high unemployment has the long-lasting years and low
unemployment has short lasting years.
Low unemployment takes longer time to return to the state, high unemployment and
moderate unemployment.
5.3 Recommendations
Though the study reveals that there is a decline of unemployment rate in Ghana over the
years, the policy makers and stakeholders have to put up measures to sustain and improve
the on the interventions implemented. Hence from the conclusions derived from the study,
the following are recommended:

46. 34
1. Policymakers and stakeholders should implement initiatives to sustain and monitor
low unemployment rate.
2. Policymakers should be prepared to adjust their policies and interventions based on
the observed transition patterns.
3. Policymakers should focus on early intervention and support for individuals in the
moderate unemployment state to prevent them from falling into high
unemployment.

47. 35
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53. 41
APPENDIX
library(markovchain)
emstates<-c("Low", "Moderate", "High")
emsMatrix<-matrix(data=c(0.571,0.429,0,0.188,0.75,0.063,0,0.125,0.875), byrow=T,
nrow=3,dimnames=list(emstates, emstates))
emsMatrix<- matrix(data =c(0.571,0.429,0,0.188,0.75,0.060,0,0.125,0.875), byrow = T,
nrow =3,dimnames = list(emstates, emstates))
emsMatrix<-matrix(data=c(0.571,0.429,0,0.188,0.75,0.062,0,0.125,0.875),byrow =T,
nrow=3,dimnames=list(emstates,emstates))
mcem<-new("markovchain",states=emstates,byrow=TRUE,transitionMatrix=
emsMatrix,name="em")
print(mcem)
plot(mcem)
stable_state=steadyStates(mcem)
# Initialize an initial state vector
initial_state <- c(1, 0, 0) # Assuming you start in the first state
# Initialize variables for tracking
tolerance <- 1e-6 # Tolerance for convergence
max_iterations <- 1000 # Maximum number of iterations

54. 42
# Iterate to find the stable state
for (i in 1:max_iterations) {
new_state <- initial_state %*% emsMatrix
if (sum(abs(new_state - initial_state)) < tolerance) {
stable_state <- new_state
break
}
initial_state <- new_state
}
# Number of steps to reach the stable state
steps_to_stable_state <- i
# Print the stable state and the number of steps
cat("Stable State:", stable_state, "n")
cat("Number of Steps to Reach Stable State:", steps_to_stable_state, "n")