Strathmore 
UNIVERSITY 
Determinants of Total Factor Productivity in Kenya 
Ray Reuben Kibet 
070241 
Submitted in partial fulfillment of the requirements for the Degree of 
Actuarial Science at Strathmore Univer·sity 
School of Finance and Applied Economics 
Strathmore University 
Nairobi, Kenya 
!December 14, 20151 
This Research Project is available tor Library use on the understanding that it is copyright 
material and that no quotation from the Research Project may be published without proper 
acknowledgement. 
Declaration 
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Project contains no material previously published or written by another person except where due 
reference is made in the Research Project itself. 
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Strathmore University 
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School of Finance and Applied Economics 
Strathmore University 
11 
Contents 
Abstract ........................................................................................................................................... 1 
INTRODUCTION ................................................................................................................... 2 
1. 1 Background ...................................................................................................................... 2 
1.2 Motivation of the study ................................................. .. Error! Bookmark not defined. 
1.3 Statement of the problem ................................................................................................. 4 
1.4 Research Objectives ......................................................................................................... 4 
1.5 Research questions ........................................................................................................... 5 
1.6 Significance of study ........................................................................................................ 5 
1.7 Scope of study .................................................................................................................. 5 
2 Literature revie\v ...................................................................................................................... 6 
2.1 Introduction ...................................................................................................................... 6 
2.2 Detenninants of Total Factor Productivity ....................................................................... 8 
2.3 Etnpirical evidence ......................................................................................................... 10 
3 METHODOLOGY ................................................................................................................ 13 
3.1 Research design .............................................................................................................. 13 
3.2 Data and measurement of variables ............................................................................... 13 
3.3 Definition ofthe production function ............................................................................. 13 
3.4 Growth attribution and the endorsement of TFP growth ............................................... 15 
3.5 Definition of the Total Factor Productivity Regression Function .................................. 15 
3.6 Data and Data Collection ............................................................................................... 16 
3 .6. 1 Data Collection ....................................................................................................... 16 
3.7 Data Analysis ................................................................................................................. 17 
3. 7. l Regression Analysis ................................................................................................ 17 
3.7.2 Generation of the Total factor productivity Variable ............................................. 17 
Ill 
3.7.3 Pre-Estimation analysis and Adjusting ................................................................... 18 
3.7.4 Regression of Total Factor Productivity against its Detenninants ......................... 19 
4 Research findings .................................................................................................................. 20 
4.1 Pre-Estimations Results .................................................................................................. 20 
4.2 Estimation and analysis of the Regression Function Results ......................................... 21 
5 Conclusion and recommendations ......................................................................................... 25 
References ..................................................................................................................................... 26 
Appendix ....................................................................................................................................... 29 
IV 
List of Tables 
• Table 1: ADF Test Statistics Results 
• Table 2: OLS Estimation Results 
v 
Abstract 
Neoclassical growth accounting literature has shown that total factor productivity has a positive 
relationship with output. Based on OLS estimation techniques on data for Kenya between the 
years 2002 and 2013, this study finds that agglomeration economies, macroeconomic stability 
and political stability are good contributors of total factor productivity growth, which in turn 
leads to aggregate output growth. The findings of this study point to a shift from the notion that 
growth in National Income has to be stimulated by expansionary monetary spending. Other 
factors such as Population Density and attempts to stabilize the Macro economy can indirectly 
foster growth of National Income. Accordingly, the findings provide a basis for Policy makers' 
focus on Monetary Policy that keeps Inflation stable and the preservation of political stability 
and the absence of violence because this will lead to an increase in Total Factor Productivity and 
eventually National Output. 
Key words: National Income, Total Factor Productivity, Growth Accounting, Labor, Capital, 
Macro economy 
JEL Classification: EOl 0 
1 INTRODUCTION 
1.1 Background 
Is it possible to spur economic growth without necessarily increasing capital or labor? lf so, can 
we control such growth? 
Solow and Swan (1956) through their famous So low-Swan model show that it is indeed possible 
to increase output without increasing capital or labor. The authors contend that an increase in 
total factor productivity increases the output contribution of both the existing quantities of capital 
and labor. This means that holding constant amounts of capital and labor can lead to varied 
increments in output depending on Total Factor Productivity (TFP). 
This study builds on the findings of Solow and Swan ( 1956) that output responds positively to 
increments in total factor productivity and focuses solely on the effects of Total Factor 
Determinants on Total Factor Productivity. This is in tandem with the writings of Prescott (1998) 
where he says that standard economic growth theory first needs to analyze the TFP determinants 
to become also a theory of international income differences. Researchers examine a myriad of 
variables such as agglomeration of economies, social capital, human capital, average education 
of workforce, Research and Development Expenditure, Female labor Pmticipation, Foreign 
Direct Investment, Macroeconomic Factors and many more variables. Economists such as 
Romer (1986, 1990), Grossman and Help man ( 1991 ), Aghion and Howitt (1992), have studied 
select Determinants, and were able to show that there existed a relationship between the 
population of employees in the Research and Development Sector and growth in Total Factor 
Productivity. The establishemnent of such relationships has been met by contradictory findings 
for instance, Jones (1995) who upon examining time series plots of Total Factor Productivity 
Growth against growth rates of number of Scientists and Engineers across four countries (France, 
Germany. Japan and United States of America) invalidated the Research and Development based 
models that suggest their positive impact on Total Factor Productivity. 
(Audretsch, 20 15) in his paper rep01ts that an analysis of European countries' level of R&D 
investment between 2000 and 2009 revealed a positive correlation with their total factor 
productivity. 
2 
The results were summarized in the graph shown below: 
Figure I 
Figure 2. European countries' level of R&D investment is positively correlated with their __- -.... 
total factor productivity. 2000-2009 
8 
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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 
Average R&D intensity (%) 
Source: European Commission. Innovation Union Competitiveness Report 2011. Luxembomg: Publications Office of 
the European Union. 
'------------------------------ '') ~.c;.FI.4bo"" 
This graph shows the scatter plot between Total Factor Productivity and Average R&D Intensity 
for different European countries effectively implying a positive relationship 
Another Economist Lucas (1998) was able to conclude that growth models are heavily based on 
accumulations of human capital. 
Glaeser (2007) on the other hand writes about Agglomeration economies and how it contributes 
to growth in total factor productivity 
Dinda (2007) shows that social capital generates human capital and in an indirect fonn fosters 
growth in total factor productivity 
Factors such as levels of competition, improved business environment, improved trade, and trade 
openness have theoretical impacts on Total Factor Productivity but pose significant measurement 
problems. 
The contributions of the aforementioned among other economists who have through their 
research established how select Determinants of Total Factor Productivity affect Total Factor 
Productivity have led to the creation of an inquisitive spark to ascertain the nature of such a 
relation in the Kenyan context if at all it exists. This study confines itself to analyzing the impact 
of Female Labor Participation, agglomeration of economies, Inflation, Government Size, 
3 
Research and Development Expenditure, Average education of workforce, Sectorial 
Composition of Output and Foreign Direct Investment on total factor productivity. This is 
because they are easy to measure and theoretical literature supports a significant relationship 
between them and total factor productivity. Basically, this study hopes to illustrate how we can 
optimally utilize existing resources to achieve optimal output growth results by scaling up the 
total factor productivity. 
1.2 Statement of the problem 
The Solow-Swan model proposes total factor productivity as a factor that leads to growth of 
output independent of labor and capital. The question however is to what extent output grows 
relative to a change in total factor productivity in Kenya. Even in the determination of this 
elasticity of output to total factor productivity changes, a further question ensues as to what 
causes changes in total factor productivity and to what extent does total factor productivity 
change given a change in these factors. 
Having launched Vision 2030 on 10 June 2008, the economy's average Gross Domestic Product 
needs to grow at 10% per annum if Kenya is to achieve this vision. It is possible to achieve this 
target without necessarily increasing county government revenue allocation, but by smart and 
efficient allocation of County Resources. Following thorough review of Literature on the topic, 
researchers in various geographical jurisdictions have established how the aforementioned 
factors affect Total Factor Productivity. However, there exists a research gap in Kenya vis-a-vis 
this particular topic. Literature on such studies in Kenya is scarce particularly due to difficulties 
in data collection. 
This study attempts to establish the sensitivity of total factor productivity to changes m its 
determinants. 
1.3 Research Objectives 
The main objective of this research is to determine the determinants of total factor productivity 
in Kenya 
4 
1.4 Research questions 
The research question under investigation in this study is what are the detenninants of total 
factor productivity in Kenya? 
1.5 Significance of study 
The establishment of the response of Total Factor Productivity to changes in its determinants 
provides a basis for the allocation of government resources in its bid to achieve a desired rate of 
output growth. Policy makers can as well find grounding for their policy makers through 
reference to this kind of a study. Lots of research has been done on the determinants of total 
factor productivity; however, this research aims to determine the extent of movement of Total 
Factor Productivity to changes in its determinants in Kenya specifically. 
1.6 Scope of study 
This a localized study of Kenya's Total Factor Productivity Detenninants. It analyzes data from 
the period 2002-2013.This is to observe the effects of the total factor productivity related efforts 
by government within the period to boost the economy. Data will be drawn from several sources 
such as the World Bank, Nation master, Economic Research Depa1iment of the Federal Reserve 
Bank of St. Louis, Nation Master, Kenya national Bureau of statistics and the Kenyan economic 
survey. In the use of data, the source will be aforementioned. 
5 
2 Literature review 
2.1 Introduction 
Many scholars have contributed to growth accounting theory. Since the development of 
economic growth measurements such as Gross Domestic Product, Gross National Product and so 
on, it has been economists' concem to explain what exactly brings about economic growth. 
Production theory is one way of explaining economic growth. It explains that the outputs of a 
firm, economy or a nation are a function of the inputs it possesses. In other words, a firm, 
economy or nation converts its existing inputs into finished products called the outputs of 
production. 
By analyzing the yearly values of output m the economy, formerly measured by the Gross 
Domestic Product, we are able to tell whether the economy has grown, stagnated or is shrinking. 
Since it is desirable that the economy continually grow to enhance social welfare, it is important 
to understand what causes economic growth, that is, the Determinants of economic Growth. 
Economists, over the decades have successfully put up theories that explain how Total Factor 
Productivity is a major Determinant of Economic Growth. However, it is worth noting that Total 
Factor Productivity cannot exist in the absence of the input of production. Inputs have to exist to 
increase their productivity. This makes it impottant to make a brief identification of such factors. 
Several models create linkage between inputs and outputs of the production process. 
The Classical Growth Model is one such model. Developed and contributed to by many 
economists such as Adam Smith, David Ricardo and Thomas Malthus, it describes the life of 
economic growth in relation to population growth. Classical economists are of the opinion that 
economic performance has an impact on population and population itself has an impact on 
economic growth. The Model theorizes that economic grmvth stimulates an increase in 
population, which places pressure on resources. The resources become limited thus causing a 
decline in the economy's GDP. Over time, criticisms of the model have invalidated it especially 
because it makes a deadly explanation for economic growth in total disregard of the impact of 
6 
technology. However, this model acknowledged the fact that growth in output is dependent on 
the availability of resources. In their separate works, they identified such resources as capital and 
labor and land among others. 
The Harrod-Domar Model developed by Sir Roy Harrod (1939) and Evsey Domar (1946) IS 
another such model. The model attempted to summarize economic growth as dependent on the 
savings ratio in the economy and the Capital Output ratio. The Model assumes that capital is 
formed through investments, which are facilitated by saved funds. High levels of saving provide 
funds that can be borrowed and invested by firms, which in turn increase the country's capital 
stock and thus bring about economic growth. That been said, the economy would grow if the 
citizens saved more and ifthe capital created is productively utilized. The capital Output ratio is 
a statement of the quality/productivity of capital. The model however, falls shm1 when it makes 
the rather unrealistic assumption that production takes place in fixed proportions and that there 
exists no possibility of substituting labor for capital. Since this is a crucial assumption, then its 
reduction to the absurd also has a similar impact on the model itself. Nonetheless, what IS 
impm1ant and still stands is that an increase in inputs is expected to increase aggregate output. 
Robert Solow, the 1987 Nobel Laureate and Trevor Swan, whose growth accounting model 
(Solow, February 1956), developed an Improvement of the Harrod Domar Model, The So low-
Swan Growth Model, which identified capital, labor and new ideas/technological advancements 
alias the Solow Residual as the causers of growth in output. Their Model, simplified the 
economy to being a producer of a single commodity, output. Instead of assuming that production 
in the economy takes place in fixed propm1ions, the Solow-Swan Growth Model attempts to 
identity the time paths of both the capital and the labor force. Once these have been determined, 
it becomes easy to determine the time path of the real output. The Solow model is a good model 
in explaining development patterns across developing and developed nations. It explains why 
there exist high levels of economic growth developing relative to those in developed nations. The 
model introduces the concept of Diminishing Marginal Returns to capital and explains why this 
is the cause of discrepancies in the rate of economic growth due to identical increments of capital 
across nations of different wealth. The model even goes further to imply that due to varied 
sensitivities of economic growth to capital increments, developing countries, whose economic 
7 
growth is much more sensitive to capital increments will at some point actualize similar living 
standards as those of developed countries due to their lower sensitivity. 
The Solow Growth model also hints that there indeed exists an optimal level of capital necessary 
to attain a desirable level of economic growth. His model implies that capital accumulation 
comes with a cost. An increase in capital stock will increase the amount of money required to 
maintain and service existing capital. This makes therefore the decision on how to allocate a 
nation's resources in order to actualize its economic goals rather interesting (This is where this 
study picks up from). Allocation of resources towards capital has to be on a cost-benefit basis. 
The model reveals that due to capital depreciation and growth in population, capital economies 
eventually reach a point of economic stagnation if no more technological progress is actualized. 
They reach what is referred to as a "Steady state". By and by, what ensues from the Solow-Swan 
model is that beyond the optimal level of capital, economic growth is achievable by enhancing 
total factor productivity. 
(Aquilars M. Kalio, 2012) However concludes that in the Kenyan scenario, the accumulation of 
classical inputs, capital and labor, are more important than total factor productivity growth with 
contributions of71.4%, 25% and 3.6% 
Prescott ( 1998) writes that standard economic growth theory first needs to analyze the Total 
Factor Productivity determinants to become also a theory of international income differences. 
Though his was in the context of studying international income differences, the principle also 
applies in the time series analysis of output values. 
2.2 Determinants of Total Factor Productivity 
Literature on the Determinants of Total Factor Productivity ts widespread with several 
contributions from various economists streaming in by the day. This study highlights a number 
of these determinants as pointed out by various scholars. It restricts itself to those that are going 
to form part of the investigation for which this study will be done. 
Endogeneous Growth Models developed by Romer ( 1986, 1990), Grossman and Helpman 
(1991) and Aghion and Howitt (1992), were able to show that there existed a relationship 
between the population of employees in the Research and Development Sector and growth in 
Total Factor Productivity. Their models tended to show that technological innovations were the 
8 
byproduct of investments in Research and Deveelopment. However, empirical tests by Jones 
( 1995) whereby time series plots of Total Factor Productivity Growth against growth rates of 
number of Scientists and Engineers across four countries (France, Germany. Japan and United 
States of America) invalidated the Research and Development based models. Later on though, 
vast Macroeconomic works confirmed an empirircal linkage between Research and Development 
expenditures and Total Factor Productivity Growth for instance Cameron (2003) and Griffith et 
al. (2000,2003). To capture the effects of Reseach and Development on Total Factor 
Productivity, a measure of private enterprise spending on Research abd Development, number of 
researchers on total workforce among those used by Jones(l995) 
Lucas (1998) makes a ve1y important point by asseiiing that growth models are heavily based on 
accumulations of human capital. In order to exploit new technology or higher levels of 
technology, knowledge as to how to utilise that technology is impOiiant. This however, poses a 
great challenge as human ccapital is linked/can be referred to as an input in the production 
process as argued by Guido Ascari and Valeria Di Cosmo (2005) in their paper, Determinants of 
Total Factor Productivity in the Italian Regions. They however, go about this problem by 
constructing two different measures of Total Factor productivity. In one, they consider human 
capital as a production input while in another they do not. They measure human capital by 
considering average education attained by the workforce. In this study average number of years 
of education received by people ages 25 and older, converted from education attainment levels 
using official durations of each level is used as proxy for the measurement of human capital. 
According to Glaeser (2007) Agglomeration economies, which are the benefits derived by 
virtue of firms and people locating near each other in cities and industrial clusters, promotes 
trade oppenness and cost reduction e.g transport costs, which contributes to growth in total 
factor productivity. This makes perfect sense because if you think about it, cost reduction of 
the production process cases demand of financial capital to generate output opening it up for 
further production of extra output. Theoretical and empirical literature on economic geography 
and regional economics proposes that there exists as well the benefit economies of scale as a 
spillover effect of agglomeration of firms. In their bid to explain differences in productivity 
levels across Italian regions, Aiello and Scoppa (2000), used population density as a proxy for 
agglomeration economies. 
9 
Dinda (2007) shows that social capital generates human capital and in an indirect form fosters 
grovvth in total factor productivity. Dinda is just but among several scholars whose works have 
heightened the consideration of social capital as a total factor productivity grower. Guido and 
Cosmo (2005) state that unity and trust in the social community creates the right environment for 
economic activity development. However, there exist several challenges in the determination of 
the variable 'Social Capital' as concluded by Temple(2001). Degli Antoni(2004) constructed a 
measure of social capital through the consideration of the number of voluntary homicides 
experienced in an area. 
Public capital has also been proven to be positively related to total factor productivity. Destefanis 
and Sena ( 2005) provide quite convincing evidence through reference to the Italian region that 
public capital has a significant impact on the evolution of total factor productivity. BaiTo ( 1990) 
found that public capital is a possible source of growth. 
Jean-Claude Nachega and Thomson Fontaine (2006) explain that political instability is 
counteractive to economic growth. It negatively impacts the growth in TFP by disrupting the 
nmmal functioning of the business and economic environment. It also decreases ce1tainty and 
subsequently incentive to invest. 
Boileau Loko and Mame Astou Diouf (2009) in their works introduced other determinants of 
Total Factor Productivity as Government size, the sectoral composition of output, and the share 
of women in the labor force. They referred to these variables as the non-traditional determinants 
of Total Factor Productivity. 
(Aquilars M. Kalio, 2012) succesfully show how total factor productivity is influenced by 
determinants such as oppennes of the economy, instituitions and terms of trede. In their paper, it 
was established that the aforementioned had elasticities of0.3136, -0.3822 and -0.3352. 
2.3 Empirical evidence 
The whole empirical investigation of the effect of total factor productivity growth on economic 
growth is not a new concept. Jean-Claude Nachega and Thomson Fontaine (2006) in their 
working paper, "Economic Growth and Total Factor Productivity in Niger," established that 
there was erosion in output per capita over the sample period of their investigation that was as a 
result of negative growth of both total factor productivity and physical capital per capita. 
10 
On the Determinants of Total Factor Productivity, the following are analyses of whether or not 
theory holds: 
Theory categorises, factors affecting total Factor Productivity into various ypes. One such broad 
Category is Macroeconomic factors. Macroecconomic factors comprise of indicators such as 
Inflation and Government size. 
Based on works from several writer, it has been a common argument that macroeconomic 
stability, inflation to be more precise has a negative effect on economic performance. For this 
reason, inflation is widely taken to be an indicator of Macroeconomic stability. 
Governemnt size, measured as the portion of a country's GDP spent on public expenditures, has 
also been shown to have a positive effect on total factor productivity owing to positive 
externalities associable e.g development of legal and administrative instituitions, development of 
economic infrastruture as well as interventions to save the market from failures according to 
Ghali(l998). However, (Barro, 1991 ;Atul A. Dar, Khalkhali, 2002) have held contrary opinions 
in this regard based on their findings. They hold that large government spending can in fact 
inhibit TFP growth especially because of govemment ineffeciencies, the tax burden and 
distortions provoked by interventions to free markets. Most empirical findings supp01i this 
contradiction. 
Female labor participation also has proven to be key to total factor productivity growth. Studies 
have shown that educated women allocate high p01tions of household income to education and 
healthcare which in tum boost total factor productivity. According to McGuckin and Van Ark 
(2005), high female patticipation in labor may lead to productivity losses when new entrants are 
older women integrating into the work force on a part-time basis and after a period of inactivity, 
a contradiction to other scholars findings. DeJong and Tsiachristas (2008) provide empirical 
evidence of growth in TFP as a result of high female patiicipation. 
The promotion of women's education and the integration of women into the labor force may 
increase productivity and growth. In development economics, it is now fully acknowledged that 
educated women allocate a higher share of households' resources to education and health care-
two factors that are expected to boost productivity and growth in the long-run. A few studies 
have attempted to examine the im 
II 
Theoretical literature proposes that Foreign Direct Investments improve technology and 
productivity and thus economic growth (Borensztein et al., 1998). Foreign Direct Investment has 
positive externality effects on the host country such as introduction of new processes and 
managerial skills, know-how diffusion to the domestic market and introduction of new 
technologies. By considering the ratio of agriv Direct Investments to GOP, this study seeks to 
establish the exact effect on Total Factor Productivity since there exists contention as to the exact 
effect on TFP as proposed by Alaro et al (2009) 
A good number of empirical studies have concluded that a change of focus of economic activity 
from agriculture to nonagricultural sectors lead to total factor productivity grO\vth because it 
shifts energies from low-yield activities to high yield activities (Poirson, 2000; Jaumotte and 
Spatafora, 2007). Fwiher studies propose that nations with a higher share of high productivity 
growth sectors have high total factor productivity growth. The effect of sectoral composition on 
output is measurable by considering the share of agricultural value added to overall GOP. 
(Aquilars M. Kalio, 2012) succesfully show how total factor productivity in Kenya is influenced 
by determinants such as oppennes of the economy, instituitions and terms of trade. In their paper, 
it was established that the aforementioned had elasticities of 0.3136, -0.3822 and -0.3352. 
(Miller, 2000) made a similar conclusion. That higher openness positively influences total factor 
productivity. He goes on to say that in poor countries, human capital interacts with openness to 
yield a positive effect. 
(Aquilars M. Kalio, 20 l2)'s work provided some information as to the interaction between Total 
factor productivity and its determinants in Kenya. In their work factors such as openness of the 
economy, institutions and tenns of trade are considered. It is the objective of this study to 
examine how other such factors that have an impact on Total Factor Productivity actually affect 
it. 
12 
3 METHODOLOGY 
3.1 Research design 
This study involved empirical analysis of total factor productivity detenninants' effects on total factor 
productivity in Kenya. Considering Time series data of the detenninants of total factor productivity a 
regression function was fashioned to serve as an explanation of total factor productivity movements. Once 
data on the independent variables happened, tests for stationarity using the Augmented Dickey Fuller Test 
followed and adjustments made to make it stationary. Thereafter, pre-estimation tests such as tests for 
Heteroskedasticity, Normality of the residuals and Johansen Test of Cointegration were done. The 
adjusted data variables were then incorporated in a linear regression model and the relationship 
established between total factor productivity and its determinants. 
3.2 Data and measurement of variables 
The study used data from 2002 to 2013. This is because, the government has put in place some 
conscious investments in total factor productivity for instance, free primary education, increased 
the size of government, investment in social capital by deploying police to fight against terror 
and militia and so on. In addition, as a nation, Kenya has faced political instability periods within 
the 11 years post 2002. The study is of the Kenyan output growth response to changes in the 
determinants of Total Factor Productivity. Data sources are the World Bank, Economic Research 
Department of the Federal Reserve Bank of St. Louis, the International Monetary Fund (IMF), 
Economic Research Depariment of the Federal Reserve Bank of St. Louis, Nation Master, Kenya 
national Bureau of statistics and the Kenyan economic survey. 
3.3 Definition of the production function 
It would be appropriate to construct a Cobb-Douglas Function that explains the economy's 
output in tenns of the factor inputs namely capital and labor as expressed in the Solow-Swan 
model. The aggregate production function would appear as follows: 
(1) 
Where 
13 
-t is a time index, 
-Y is real GOP, 
-K is real capital stock, 
-Lis total employment, 
-a is the sensitivity of output to capital, 
- ( 1-a) is the sensitivity of output to labor, 
-Ao eb1is an expression of Total Factor Productivity (TFP) 
Total Factor Productivity (TFP) measures the shift in the production function at given levels of 
capital and labor. The fixed component ofTFP (Ao) is assumed to grow at a rate b. 
For the purpose of an easier regression analysis, it would help to divide both sides of equation ( 1) 
by L and take the natural logarithms of both sides as well to eliminate the power values (indices) 
in the equation. 
What you end up with is: 
y t = a + bt + akt (2) 
This is much simpler to manipulate in an econometric context. The lower case variables, k and y 
represent the natural logs of physical capital and output per capita respectively. In the course of 
our analysis, since we cannot exactly observe the natural logarithm of Ao, we would have to 
estimate it as the residuals of the second equation. This makes sense as it implies a movement in 
per capita output that does not result from movements in per capita capital, the definition of total 
factor productivity and thus the name Solow residual. 
The production function (2) is a good approximation of production possibilities because it 
exhibits the following properties: Perfect competition, Constant Factor Income shares and 
Constant Returns to scale; Properties that complement the application of the Solow Growth 
Model. 
14 
3.4 Growth attribution and the endorsement of TFP growth 
Jean-Claude Nachega and Thomson Fontaine (2006) propose a means for deriving total factor 
productivity. After the estimation of parameter a in equation (2), it is easy to breakdown the 
growth in output based on the factor contributions, i.e. stimulus of labor, stimulus of capital and 
stimulus of TFP to the output growth. If we assume that the production function exhibits 
Constant Returns to Scale and that the markets for goods and factors are competitive, the output 
growth rate (.1Y jY) can be re-written as: 
.1Y jY = a.1K/K + (1- a) .1LjL + .1AjA (3) 
Since the growth rate of Total Factor Productivity (.1AjA) cannot be measured directly, we 
make it the subject of the equation to express it in tenns of other measurable variables. We get: 
.1AjA = .1YjY- (a.1KjK + (1- a) .1LjL) (4) 
This implies that the growth in TFP is the portion of economic growth not explained by growth 
in the labor force and physical capital stock. 
We know that the Solow Growth model defines a scenario whereby economic growth is possible 
beyond the steady state through growth in the Total Factor Productivity. Therefore, if we assume 
that in the model, the key parameter (a) remains stable across time labor productivity(Y/ L) 
would have to increase to sustain increases in real wages (W/P) and eventually better life 
standard. 
Since at the steady state, the growth rate of capital per unit of labor is zero, we can have the 
growth attribution formula (3) written in terms of the labor productivity growth rate as below: 
.1(YjL)j(YjL) = .1A/A (5) 
Equation (5) holds in the steady state. 
3.5 Definition of the Total Factor Productivity Regression Function 
Having described the determinants of total factor productivity, the following will be the 
regression function used to examine their relationship with total factor productivity 
15 
lnTFPit = {31R&Dit + {32 FD!it + {33 EDUit + {34 /NFLit + {35AGR!Cit + {36 DENSITYit 
+ {37 GVTit + {38 FEMLABit + {39 POL!Tit + Vit 
Where: 
lnTFP -the natural logarithm ofTotal Factor Productivity 
DENSITY -agglomeration of economies as measured by population density 
FEMLAB -Female labor Participation as measured by number of percentage of 
women in employment 
R&D -Expenditure Research and Development 
INFL -Inflation as measured by CPI 
AGRIC -share of agricultural value added to overall GDP 
GVT -ratio of Government Spending relative to GDP 
EDU -average number of years of education received by people ages 25 and 
older 
FDI -Foreign Direct Investment 
POLI T -World Bank Governance Indicator on Political Stability and the absence 
of Violence 
Vit - Regression error 
This regression function is instrumental m determining whether there exists a meaningful or 
significant relationship between the determinants of total factor productivity and total factor 
productivity. This is imp01tant, as it will aid in policy making when generating policies aimed at 
increasing output through investment in total factor productivity. 
3.6 Data and Data Collection 
3.6.1 Data Collection 
Having defined the aggregate demand function and manipulated it into equation (2), what we 
need to do is to collect historical data on real capital stock labor force. Data on real capital stock 
is derivable from the Economic Research Department of the Federal Reserve Bank of St. Louis 
that possesses data on Capital Stock at Constant National Prices for Kenya among many other 
nations. Data on the labor force in Kenya is derivable from the Central Data Source, Nation 
16 
Master. The analysis of data will be an analysis over an 11 year period from 2002-13 and data 
collected will be on a quarterly basis 
Data for the detenninants will as well have to be collected for the regression of total factor 
productivity against its determinants. Data on Female labor participation, average age of 
workforce, Political stability and Research and Development expenditure can be found on the 
World Bank statistics database. Data on Foreign Direct Investment, Inflation, Agricultural value 
added share of GOP and Public Expenditure to GOP ratio can be found from the Kenya national 
Bureau of statistics and the Kenyan economic survey. Data on population density can be derived 
from census reports. 
3. 7 Data Analysis 
3.7.1 Regression Analysis 
Once the collected, data regression of the total factor productivity against its determinants follows. This 
occurs in three steps: 
3. 7.1.1 Generation oftlze Total factor productivity Variable 
As is illustrated from equation (2): 
yt = a + bt + akt 
The sensitivity of output to changes in capital (o:) will be generated using the formula below: 
This is on the deductional basis that both y1 and k 1 are natural logarithms and that the formula for 
calculating elasticity of output to capital is: 
aI n X o/o.Cl.x 
a=aI --=--nk %llk 
Iff: 
X = f(k, l) = aka zl-a 
17 
It is known that, the total factor productivity growth rate b1, is calculated using equation (5) 
whereby: 
b.(Y /L)/ (Y /L) = l'>.A/ A 
With this in mind, it seems reasonable to start by finding the growth rate of Total Factor 
Productivity so as to enable its inset1ion in the equation that will give us data on Total Factor 
Productivity, which is a manipulation of equation (5), i.e. 
a = Yt - b t- akt 
3. 7.1.2 Pre-Estimation analysis and Adjusting 
Before the use of collected data, the series will be tested for stationarity using the Dickey-Fuller 
unit root test and adjustments made to the series if necessary. Thereafter, a regression will be 
done to detennine the elasticity of output to total factor productivity and another to determine the 
relationship between total factor productivity and its determinants. 
Tests of significance of the regression itself will follow as well as of the estimates to provide 
validation for the regression results. 
18 
3. 7.1.3 Regression of Total Factor Productivity against its Determinants 
Once this is done, data on total factor productivity will have been arrived at and it thereafter 
becomes easy to regress it against its determinants. 
19 
4 Research findings 
Before the Running of the Regression, it was impmiant to test for stationarity to guard against 
generation of spurious results. Augmented Dickey Fuller Tests were done on all the Variables. 
The table below summarizes the results. The intention was to guarantee that all data used was 
stationary at a 99% confidence level. The data that was nonstationary was going to have to be 
differenced until it was stationary at the prescribed confidence level. The ADF test statistic was 
going to be compared to the I% critical values. 
Table 1: ADF Test Statistics Results 
Variable Stationary at Level Stationary at I st Stationary at 2"d 
Difference Difference 
LN(TFP) X X -! 
PO LIT X X -! 
FEMLAB X -! X 
GVT X X -! 
AGRIC X X -! 
EDUC X X -! 
R&D X X -! 
DENSITY X -! X 
!NFL X X -! 
FDI X X -! 
This table summarizes the results achieved C!fter subjecting the regression variables to Augmented Dickey 
Fuller Tests. Ticks (V) imply that at a d{[ference n, the time series variable is stationmJ'. Crosses(x) 
imply that at the difference n, the time series variable is nonstationw:v. 
20 
4.1 Pre-Estimations Results 
Alongside the Unit root test, the following tests were done: 
Johansen test of cointegration: To establish Long run association between Total Factor 
Productivity and its Determinants, it was impmiant for this test to be done. Data was evaluated 
after differencing. Considering the Trace Statistics, it was observed that the p values were less 
than 5% for null hypotheses that there existed up to 9 numbers of cointegrated equations. 
Effectively, such hypotheses were to be rejected. However, for the hypothesis that there exist at 
most nine cointegrated equations, p values as high as 41.09% were actualized hence the only 
possible option is to fail to reject the null hypothesis. This means that all that variables have an 
association 
Breusch Pagan Godfrey Test: This test was done to test for Heteroskedasticity. This is done to 
gain some level of trust in the standard errors and t statistics; and that the OLS estimation be 
efficient. Having fonnulated the Null hypothesis that there is homoscedasticity, the Breusch-
Pagan-Godfrey test was applied and the following results obtained: 
As can be seen (table 2 in the appendix), both the Prob. Chi-square p values and the Prob (F-
statistic) are greater than 5%. This means we can reject the null that there is homoscedasticity 
without incurring a type II error. 
Residual Normality Test: To trust the regression results, we need the residuals to be normally 
distributed. To test this, a histogram was plotted of the residuals. This was to be able to gain 
insight as to whether there is normality of the residuals. With a p value of 55.5016% we have to 
fail to reject the null hypothesis that the residuals are normally distributed. Based even on the 
graph (graph 1 in the appendix), it can be effectively concluded that the residuals are nonnally 
distributed. 
4.2 Estimation and analysis of the Regression Function Results 
After all such preliminary tests had been done, the Regression line function was estimated and 
the following results arrived at 
21 
Table 2: OLS Estimation Results 
Differenced Variable Coefficient t-statistic P values 
Agricultural share of GDP -1.3032 -0.4976 0.6221 
(2.6191) 
Agglomeration of 30.5567 7.2470 0.0000 
economies (4.2165) 
Average education of -166.0590 -3.0311 0.0047 
workforce (54.7847) 
Female Labor 10.8474 1.2895 0.2062 
Participation (8.4122) 
Foreign Direct -4.3700 -l.l316 0.2660 
(3.86 I 8) 
Government Size 1.563 I 0.3655 0.7170 
(4.2760) 
Inflation -4.365 I -6.3284 0.0000 
(0.6898) 
Political stability and the -69.6809 -2.3526 0.0248 
absence of Violence (29.61 83) 
Research and Development 24.4012 1.0656 0.2943 
Expenditure (22.8987) 
c -1275.276 -2.0480 0.0486 
(622.6965) 
R-Squared 0.7774 
Adjusted R-Squared 0.7167 
F- Statistic 12.8054 0.0000 
This table shows the OLS estimation results. In the parentheses is the standard deviation values of the 
variables regressed against the regressand It swnmarizes the co-ej]icienls, !-statistics and p-values as 
well as the R-Squared and F-Statistic values. 
22 
4.3 Discussion of Results 
As is seen from the results: 
There is a high R-squared: This is clear indication of how significant the regression IS at 
explaining the relationship between the regressand and regressors. An R-Square value of 0. 7774 
is much closer to 1 than it is to zero. The Regression line has explained largely the variance of 
the actual line from the mean is explained by this regression. 
The results are however quite revealing: Based on the p values where the focus is only on those 
variables with p values less than 5% (that is, only those co-efficient that are statistically 
significant are considered). In that regard, it is data on: agglomeration of economies, average 
number of years of education received by people ages 25 and older, Inflation and World Bank 
Governance Indicator on Political Stability and the absence of Violence that can be credibly 
analyzed. The rest that is, Female labor Participation, Expenditure Research and Development, 
share of agricultural value added to overall GDP, ratio of Government Spending relative to GDP, 
Foreign Direct Investment suggest a linear relationship with the natural Logarithm of Total 
Factor Productivity (TFP) but this relationship is statistically insignificant. This means we cannot 
credibly conclude that there is a relationship between the aforementioned variables and Total 
Factor Productivity as much as we cannot also credibly conclude that there is no relationship. 
Since it is more difficult to prove the negative connotation, we do not use such results. 
The results show that a unit change in agglomeration of economies as measured by Density will 
increase natural Logarithm of Total Factor Productivity (TFP) by 30.56 all other factors held 
constant. This is a positive acclamation of Glaeser (2007) suggestion that Agglomeration 
economies contributes to growth in total factor productivity. It means that the more the 
population grows, the moe beneficial it is to total factor productivity and effectively national 
output. 
The average number of years of education received by people ages 25 and older, is suggested to 
have an inverse relationship with total factor productivity; so much so that Ceteris Paribus, a unit 
increase in the average educational competence of the workforce would reduce total factor 
productivity by 166.05. This goes against all the findings metioned above in the Literature 
Review. However, these resuts ought be taken with a huge level of skepticism, especially 
23 
because the access of such data was quite difficlt and that this data has just recently started being 
collected. 
Inflation, predictably has a negative relationship with total factor productivity. As a proxy for 
Macroeconomic stability, it can be seen that Macroeconomic Instability hinders growth of total 
factor productivity. Inflation as a Macroconomic stability counter-proxy reduces total factor 
productivity by 4.365 times per unit increase in inflation levels. 
Political stability and the absence of violence as well was in tandem with the findings of Jean-
Claude Nachega and Thomson Fontaine (2006) who explain that political instability is 
counteractive to economic growth. From the Regression, a unit increase in the Indicator on 
Political instability reduces Total Factor Productivity by 69.68 per every unit increase. 
24 
5 Conclusion and recommendations 
Bearing the findings in mind, the following are recommended way forwards: 
Shift fi·om the notion that growth in National Income has to be stimulated by expansionary 
monetary spending. It has been seen that when you invest in the determinants of total factor 
productivity such as agglomeration economies, macroeconomic stability and maintenance of 
political stability. This in itself can lead to economic growth. 
The fact that agglomeration economies have a positive relationship with total factor productivity 
provides steady footing for policies that promote growth of population. This is because the 
greater the surface are of persons who are able and willing to transact with businesses, the 
cheaper it is to deliver products(distributional costs) and services and also the more efficient it 
becomes to produce the output due to economies of scale. This gives production agents better 
efficiency in convetiing its inputs into outputs. This is total factor productivity growth at its best. 
Based on the discovery on how Macroeconomic stability as measured by inflation is a 
precondition for the growth of Total Factor Productivity, policy makers ought to focus on 
measures that would keep Macroeconomic variables Inflation included within stable ranges. This 
is because the results show that there is an inverse relationship between inflation and Total 
Factor Productivity. This implies that a steep movement upwards by inflation, a characteristic of 
instability in the Macroeconomy, is likely to inhibit economic growth through grov.rth of Total 
Factor Productivity. 
In order to nurture Total Factor Productivity growth, leader ought to do their best to foster a 
healthy socio-political climate. Political instability or any such unpredictability is an absolute 
turn off to potential capital spending persons. Political instability causes a diversion of Foreign 
Investment, flight of local capital held by both local and foreign holders due to lost confidence in 
the protection of their business interests and property rights. This was even evidenced in the 
Kenyan economy where slowed and diminished grov.rth rates were witnessed in various sectors 
ofthe economy and the Macro-economy following the 2007-2008 post election violence. 
25 
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28 
Appendices 
Appendix 1: Johansen test of Cointegration 
Date: 12102115 Time: 13:35 
Sample (adjusted}: 200304 201304 
Included observations: 41 after adjustments 
Trend assumption: Linear deterministic trend 
Series: AGRICDIFF2 DENSITYDIFF1 EOUCDIFF2. FEMLABDIFF1 FDI2 GVTDIFF2 INFLDIFF2 LN_TFP_ DIFF2 POLITDif 
Lags interval (in first differences): 1 to 1 
Unrestricted Cointegration Rank Test (Trace) 
Hypothesized Trace 0.05 
No. ofCE{s) Eigenvalue Statistic Critical Value Prob.** 
None • 0.792800 315.0901 239.2354 0.0000 
At most 1 * 0.709126 250.5533 197.3709 0.0000 
At most2* 0.685247 199.9238 159.5297 0.0000 
At most 3* 0.581611 152.5292 125.6154 0.0004 
At most4 • 0.533365 116.8041 95.75366 0.0008 
At most5* 0.459500 85.55352 69.81889 0.0017 
Atmost6* 0.444723 60.32781 47.85613 0.0022 
At most7* 0.374325 3620803 29.79707 0.0080 
At most8 • 0.328141 16.98212 15.49471 0.0297 
At most 9 0.016356 0.676123 3.841466 0.4109 
Trace test indicates 9 cointegrating eqn(s} at the 0.051evel 
• denotes rejection of the hypothesis at the 0.05 level 
**MacKinnon-Haug-Michelis (1999) p-values 
29 
Appendix 2: Breusch Godfrey Pagan Test 
Heteroskedasticity Test: Breusch-Pagan-Godfrey 
F-stati sti c 1.334585 Prob. F(9,33) 0.2574 
Obs*R.-s quare di 11.47456 Prob. Chi-Square(9) 0.2446 
Scaled explained ss 7.492387 Prob~ Chi-Square(9) 0.5860 
Test Equation: 
Dependent Variable: RESID"2 
Method: Least Squares 
Date: 12102115 Time: 11:58 
Sample: 200302 201304 
Included observations: 43 
Variable Coefficient Std. Error t-Statistic Pro b. 
c 2353.311 3652.812 0.644246 0.5239 
AGRICDIFF2. 13.19192 15.36399 0.858626 0.3967 
DENSITYDJFF1 13.89989 24.73429 0.561969 0.5779 
EDUCDIFF2 -397.6048 321.3734 -1.237205 0.2247 
FDI2 5.483305 22.65380 0.242048 0.8102 
FEMLABDIFF1 -38.43378 49.34712 -0.778845 0.4416 
GVTDIFF2 -20.55667 25.08329 -0.819537 0.4184 
lNFLDIFF2 -1.357036 4.046269 -0.3353.79 0.7395 
POLITDIFF2 -201.2247 173.7442 -1.158167 0.2551 
R_DDIFF2 72.66194 1343264 0.540935 0.5922 
R-squared 0.266850 Mean dependent var 21.16830 
Adjusted R-squared 0.066900 S.D. dependent var 31.89386 
S.E. of regression 30.80854 ,A,kaike info criterion 9.893885 
Sum squared resid 31322.48 Schwarz criterion 10.30347 
Log likelihood -202.7185 Hannan-Quinn criter. 10.04493 
F-statistic 1.334585 Durbin-VIiatson stat 2.046061 
.f"r()[}_(F'::~ta,ti~tic!. 0.257370 
"u '""" w '~'0' 
30 
Appendix 3: Residual Histogram Plot 
31