Mathematical Economics

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus

Foreign Portfolio Investment and Economic Growth in Nigeria Democratic Settings

The study examined the relationship between foreign portfolio investment, democracy and economic growth in Nigeria. This was with a view to explore the nexus between foreign portfolio investment, democracy and economic growth in Nigeria.Secondary data were used in this study. Annual time-series data for the period 1986 to 2013 on foreign portfolio investment and maximum lending rate were obtained from Central Bank of Nigeria (CBN) Statistical Bulletin, while data on variables such as GDP growth rate and gross domestic savings were obtained from World Development Indicators (WDI) database, published by the World Bank. Data collected were analyzed with both descriptive statistics and econometric techniques. Time series properties of the variables were examined using both Augmented Dickey Fuller and Phillip Peron tests. Cointegration properties of the variables were also examined. Vector Auto-Regressive technique supported by Variance Decomposition and Impulse Response analysis were employed to empirically determine the relationship between foreign portfolio investment                                                                                                                                                                                            and economic growth in Nigeria. The results showed that foreign portfolio investment inflow was more stable in democratic periods between 1999 and 2013 than the military periods between 1986 and 1998 and that the correlation between economic growth and foreign portfolio investment is positive and very significant. The result showed that in the longrun foreign portfolio investment had positive and significant effect on the economic growth in Nigeria (t = 3.7, p < 0.05).it also showed that democracy had a positive and significant effect on economic growth (t = 2.7, p < 0.05), while it has positive but not significant effect on the relationship between foreign portfolio investment and economic growth (t = 1.92, p >0.05). This study therefore concluded; the impact of foreign portfolio investment on economic growth was very large and significant in the longrun; that democracy in itself affected economic growth significantly and positively but democratic government had no significant effect on the relationship between foreign portfolio and economic growth;. Keywords: Democracy, Foreign Portfolio Investment, Economic Growth: JEL CODES; F02, F3 O10

Foreign Portfolio Investment, Investment Policy and Economic Growth in Nigeria

The study examined the effect of investment policy of 1995 on the relationship between foreign portfolio investment and economic growth in Nigeria. This was with a view to explore the nexus between the investment policy, foreign portfolio investment and economic growth in Nigeria.Secondary data were used in this study. Annual time-series data for the period 1986 to 2013 on foreign portfolio investment and maximum lending rate were obtained from Central Bank of Nigeria (CBN) Statistical Bulletin, while data on variables such as GDP growth rate and gross domestic savings were obtained from World Development Indicators (WDI) database, published by the World Bank. Data collected were analyzed with both descriptive statistics and econometric techniques. Time series properties of the variables were examined using both Augmented Dickey Fuller and Phillip Peron tests. Cointegration properties of the variables were also examined. Vector Auto-Regressive technique supported by Variance Decomposition and Impulse Response analysis were employed to empirically determine the relationship between foreign portfolio investment and economic growth in Nigeria. The study revealed that though the investment policies of 1995 in itself had not led to economic growth but it had succeeded in attracting more foreign portfolio investment into the economic and that it aided the growth of the economy through these foreign portfolio investments

Foreign Portfolio Investment and Economic Growth in Nigeria Democratic Settings

The study examined the relationship between foreign portfolio investment, democracy and economic growth in Nigeria. This was with a view to explore the nexus between foreign portfolio investment, democracy and economic growth in Nigeria.Secondary data were used in this study. Annual time-series data for the period 1986 to 2013 on foreign portfolio investment and maximum lending rate were obtained from Central Bank of Nigeria (CBN) Statistical Bulletin, while data on variables such as GDP growth rate and gross domestic savings were obtained from World Development Indicators (WDI) database, published by the World Bank. Data collected were analyzed with both descriptive statistics and econometric techniques. Time series properties of the variables were examined using both Augmented Dickey Fuller and Phillip Peron tests. Cointegration properties of the variables were also examined. Vector Auto-Regressive technique supported by Variance Decomposition and Impulse Response analysis were employed to empirically determine the relationship between foreign portfolio investment                                                                                                                                                                                            and economic growth in Nigeria. The results showed that foreign portfolio investment inflow was more stable in democratic periods between 1999 and 2013 than the military periods between 1986 and 1998 and that the correlation between economic growth and foreign portfolio investment is positive and very significant. The result showed that in the longrun foreign portfolio investment had positive and significant effect on the economic growth in Nigeria (t = 3.7, p < 0.05).it also showed that democracy had a positive and significant effect on economic growth (t = 2.7, p < 0.05), while it has positive but not significant effect on the relationship between foreign portfolio investment and economic growth (t = 1.92, p >0.05). This study therefore concluded; the impact of foreign portfolio investment on economic growth was very large and significant in the longrun; that democracy in itself affected economic growth significantly and positively but democratic government had no significant effect on the relationship between foreign portfolio and economic growth;. Keywords: Democracy, Foreign Portfolio Investment, Economic Growth: JEL CODES; F02, F3 O10

A Microscopic View of the Exotic Influence of Fiscal Policy on Some Selected Macroeconomic Variables in Nigeria

The paper examines the impact of fiscal policy on certain macroeconomic variables in Nigeria from 1980 to 2015 We used Government Expenditure Total tax revenue Unemployment rate and Gross Domestic Product GDP variables data from CBN statistical bulletins Our econometric analysis used was the Ordinary Least Square OLS and cointegration The OLS result revealed that there is a significant relationship between government expenditure and unemployment rate as well as economic growth in Nigeria but there was no substantial relationship between government tax revenue and unemployment in Nigeria as well as no serious relationship existed between the government tax revenue and economic growth in Nigeria The results of the co- integration text revealed a long-run relationship among the variables and the study suggests that government should implement appropriate fiscal policies to stimulate the economy and also find answers to reduce the unemployment rate use necessary financial policy tools to fine-tune the economy in terms of government spending and taxation to enhance the economic growth of Nigeri

EXTERNAL DEBT SERVICING AND CAPITAL FORMATION IN GHANA: AN AUTOREGRESSIVE DISTRIBUTED LAG ANALYSIS

This study empirically examines the effects of external debt servicing on capital formation in Ghana. Using data from 1980 to 2019, the study estimates the Autoregressive Distributed Lag (ARDL) model and finds that the effect of external debt servicing is negative both in the long and the short run due to the tax disincentive effect. This suggests that as a result of the potentially high debt servicing due to the high debt stock, any future investment may attract high marginal tax rates and would tend to reduce investment in the economy. The result further shows that external debt servicing affects private capital formation more than public capital formation. However, the effect of the external debt stock on private investment is negative in the long run but positive in the short run confirming the direct effect of the debt hypothesis’ existence in Ghana suggesting that external debt discourages a long-term investment which is critical for economic growth. Additionally, there exists complementarity between public and private investments indicating that some public investments attract private ones into the country. Therefore, external debt service payment crowds out private investment through excessive interest charges, so government should determine a threshold of borrowing in order to minimize the high debt servicing. JEL: E22, E31, E62, F31, G31, H63, P24  Article visualizations

Local economic development: a study of Nelson Mandela Bay and Buffalo City Metropolitan Municipalities

Albeit in its infancy, South Africa’s LED practice is a benchmark of a large number of African countries in general and Sub-Saharan African countries in particular. The LED practice stands out, for widespread decentralisation of powers, massive and growing LED budgets, robust legal frameworks that govern its implementation and development of LED structures, amongst others. This study seeks to answer three critical questions: What theoretical LED facets (particular aspects) are available in literature? Are these facets being implemented in Nelson Mandela Bay Municipality (NMBM) and Buffalo City Metropolitan Municipality (BCMM)? Besides the effort and monies invested in ingraining LED in South Africa, are the levels of LED practices of the two municipalities deeply embedded in literature? The study utilises a purpose-built tool to measure the level at which LED practice of respective municipalities is ingrained in LED literature. The thesis employed both qualitative and quantitative research methods in order to provide scientifically adequate answers to this research. The former method was employed in identifying available LED facets while, the latter was useful in measuring the level at which LED practice in the two metros is embedded in LED theory. The research findings reveal presence of 6 LED facets, namely, enterprise development, locality development, livelihoods development, workforce development, community development and LED Governance. However, this study discovered that the aforementioned facets fail to cover other general items like the availability or unavailability of LED strategy, functional location of LED within municipal directorates and availability of a budget to drive the LED functions. In light of this, the researcher decided to group all the other key LED functions that he felt were not finding expression under the 6 facets identified in LED literature. This, then, led to the introduction of “General LED” facets. This facet, besides presenting a pre-cursor to the 6 other facets, manages to capture some key factors that are equally behind the success or failure of LED e.g. the LED strategy factor, a factor which a number of sources name “The heart” or “guiding compass” of successful LED implementation. The “General LED” facet contained other factors like: other plans that aided LED, experience of LED practitioners, budget allocation of the LED function, amongst others. The research found that all the 7 facets are being implemented in both municipalities, albeit to varying degrees. The two metropolitan municipalities’ LED practice, with respect to all the identified LED facets, provided some measure of their respective levels of embeddedness in LED theory using a purpose built tool. The embedded (ness) outcome proved that Nelson Mandela Bay Municipality’s LED practice was embedded in the LED theory across all the 7 facets, namely: general LED, enterprise development, locality development, community development, livelihood development, workforce development, and LED governance. The same analysis proved that Buffalo City Metropolitan Municipality’s LED practice was embedded in LED theory in all the other facets bar community development. The survey results revealed that there are inadequate or limited initiatives in Buffalo

Elasticity of the South African economy towards portfolio investments in BRICS countries

The emerging economies of Brazil, Russia, India, and China (BRIC) have been experiencing high growth rates since the turn of the millennium, whereas economic growth has been elusive in South Africa. As the newest member of BRICS, South Africa is expected to economically benefit through, amongst others, increases in capital flows, foreign investments by local firms, and increases in trade. Such benefits are anticipated to propel the country’s economic growth, thereby helping it to tackle its chronic problems of high unemployment, poverty, and economic inequality. The inclusion of South Africa in BRICS has, however, been viewed by critics as erroneous, since the country has, inter alia, poor economic growth; a small economy and population; and political instability. While foreign portfolio investment (FPI) inflows to South Africa have surged in recent years, economic growth has remained lacklustre. These flows have also faced sudden reversals, especially during the financial crisis of 2007-2009. With the potential to leverage its growth from intra-BRICS FPI inflows, it becomes of paramount significance for policymakers to have knowledge of the South African economy’s responsiveness to such inflows. With a theoretical framework based on the endogenous growth model, an augmented Cobb-Douglas production function was extended in this thesis in order to study the relationship between BRICS growth and intra-BRICS FPI in a dynamic panel data generalised method of moments (GMM) context. Similarly, the South African economy’s elasticity towards intraBRICS FPI was estimated. Vector autoregressive (VAR) analysis was used to evaluate the responsiveness of South Africa’s economy to an innovative shock to intra-BRICS FPI. Annual and quarterly data for the period 2000-2016 were used in panel data and VAR analysis, respectively. It was found that intra-BRICS FPI flows have a positive and statistically significant relationship with BRICS growth, while the elasticity of the South African economy to these flows is estimated at 0.007. Additionally, the efficiency and accessibility dimensions of financial market development do not assist FPI in promoting growth in BRICS, while financial market depth does. South Africa’s BRICS membership has a positive effect on its own growth, while for other BRICS nations, this membership is negative and insignificant. Credit rating downgrades have a negative and insignificant impact on economic growth, while the negative impact for inflation, government expenditure, and total labour employment is significant. Conversely, gross capital formation and trade openness have a positive and significant relationship with BRICS growth. The study also determined that a unit shock on intra-BRICS FPI resulted in negative fluctuations of South Africa’s economy within the first eight quarters before being positive and mostly constant thereafter. By supplementing domestic savings and facilitating the international integration of domestic financial markets, FPI promotes growth in BRICS. The short-term, ease of reversibility, and speculative nature of FPI are amongst some of the reasons for its destabilising effect on South Africa’s economy. Furthermore, inflation is a key determinant of FPI inflows to South Africa. Additional BRIC cooperation in FPI and trade; increased investments in domestic capital; reductions of inflation and corruption; investments in education and skills development; and stock market reforms are some of the recommendations for BRIC, and South Africa in particular. South Africa can consider prudential use of a mix of capital account controls, as well as fiscal and monetary policies to cushion its economy from FPI shocks in the short- to medium-term

The impact of government expenditure on economic growth of the economic community of West African states (ECOWAS)

Available statistics on growth trends in the Economic Community of West African States (ECOWAS) are wanting, particularly net per capita growth rates. The analysis of available data from 1970 to 2012 by this study, for instance, shows that the net real GDP growth rate for the ECOWAS is 0.52%. Only four countries had net growth rates above 1% per annum mean growth rate of ECOWAS region. At the estimated growth rate, the prospect of accelerated growth in ECOWAS is very weak. The Barro endogenous growth model states that government provision of services can generate externalities to the private productive activities. Government’s provision of productive services in ECOWAS can ensure long-run per capita output growth without the per capita growth rate running into steady state growth. However, there are divergent views as to whether government provision of services induces long run economic growth. These views are based on different schools of thought. For instance, the economic freedom school argues for minimum government involvement (small governments) to ensure economic and political freedom to induce private investors invest and encourage economic growth. The optimal government school of thought (medium size governments) argues that government spending enhances private productivity growth through the provision of infrastructure, spending on research and development, public education, sewage, other public goods and protection through functional law and order systems. The optimal school of thought also acknowledges that government expenditure can also reduce economic growth through increases in taxation. An increase in taxation reduces the returns on investment of physical and human capital and in research and development (R&D) of private firms. This thesis investigates the impact of government expenditure on the provision of public services on economic growth in ECOWAS. To assess the impact of government expenditure on the provision of services on economic growth of ECOWAS, this thesis assesses whether the size of government, government expenditure and economic institutions promoted economic growth in ECOWAS. The thesis also determines whether per capita government capital expenditure, per capita government consumption expenditure, per capita private capital stock, per capita manufacturing output, per capita services output and per capita agricultural output have any impact on per capita real GDP growth in ECOWAS. To carry out this study, data were collected from United Nations Conference on Trade and Development (UNCTAD) database and Transparency International (TI) database. The data used covered the period of 1970 – 2013. The statistical research methods applied are the time-series methods of panel unit root test, panel co-integration test, and panel regression analysis, using both panel OLS regression models and estimation and inferences in co-integrated panel data regression methods. The panel OLS regression models applied are the panel OLS regression; panel fixed effect model (FEM) regression and the panel random effect model (REM) regression. The estimation and inferences in co-integrated panel data regression models applied are panel VEC regression model, panel DOLS regression and panel FMOLS regression. The panel DOLS regression and panel FMOLS regression models do not have an intercept, unlike their pure time-series models, which have intercepted. To ensure that the parameters estimated are reliable, this thesis conducted diagnostic tests to subject the regression result to scrutiny. The estimated panel data regression using panel OLS regression, panel FEM regression and panel REM regression indicate that the results of the estimated parameters were spurious having both autocorrelations and heteroscedasticity. High values of adjusted R-squares that were approaching one and high significant values of t statistics but very low values of Durbin-Watson Statistics demonstrated the existence of heteroscedasticity and autocorrelation in residuals. The results of the diagnostic tests also show that the DOLS estimated regression model out-performed both VEC and FMOLS regression models based on both aggregate data and per capita data estimated parameters. The results of the parameter estimated using panel VEC and panel FMOLS regression models showed that both panel VEC and panel FMOLS regression models had the problems of their residuals having not only autocorrelations but heteroscedasticity. The panel DOLS regression results were satisfactory, having no multicollinearity, autocorrelations and heteroscedasticity. The estimated panel DOLS regression results were applied to test hypotheses formulated to guide this thesis. Results from panel DOLS estimated parameters show that the existing government size in ECOWAS stimulated economic growth. The results also showed that the government expenditure exhibited an inverted U-shape with respect to economic growth. The thesis also showed that existing government size in ECOWAS significantly stimulated economic growth in the region. The results of regression indicate that economic institutions contribute negatively to the economic growth of the ECOWAS. The results also established that government capital expenditure per capita has significantly engendered economic growth. Government consumption expenditure per capita stimulated economic growth. However, private capital stock per capita has not stimulated economic growth in ECOWAS. Service sector output per capita, agricultural output per capita and manufacturing output per capita stimulated significantly economic growth in the ECOWAS sub-region