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

Another View of the Maximum Principle for Infinite-Horizon Optimal Control Problems in Economics

We present a recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The peculiarity of the result is that the adjoint variable is explicitly specified by a formula which resembles the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the “standard” transversality conditions at infinity. Moreover, it can serve as their alternative. We provide examples demonstrating the ad- vantage of the suggested version of the maximum principle. In particular, we consider its applications to Halkin’s example, to Ramsey’s optimal growth model and to a basic model of optimal extraction of a non-renewable resource. An economic interpretation of the developed characterization of the adjoint variable is also presented

Monetary and fiscal policy effects on unemployment and inflation in Uganda

Over the recent past, Uganda has experienced disproportionate volatility in inflation alongside rapid growth of unemployment. Whilst inflation has been curtailed to single digit figures since the economic crisis of the 1970s, nevertheless, in the recent past, inflation volatility and unemployment have constrained Uganda’s growth outlook. Like many various developing countries, Uganda has interacted monetary and fiscal policy frameworks as macroeconomic tools to spur productive growth. Most developing countries like Uganda continue to grapple with the challenges of jobless growth which is largely attributed to unstable inflationary pressures as well as low investment which further eggravated rapid expansion in unemployment levels. Government policy efforts have recently been greatly inhibited by rising youth unemployment rates in the country, this has greatly affected Uganda’s growth dynamics. Whilst developed countries have successfully used monetary and fiscal policy frameworks in their pursuit to macroeconomic stability, due to their complex structural economic dynamics, low income countries face challenges in implementing both monetary and fiscal policy to stabilize their economies. Central banks across all countries strive for low and predictable inflation as key in fostering economic growth. The debate over the applicability between monetary and fiscal policy frameworks in the pursuit of enhanced growth continues among policy analysts. The general observation especially in low income countries pertains to the use and effective coordination of monetary and fiscal policy in efforts to stabilize these economies. Despite numerous public expenditure reforms implemented and decline in poverty levels in Uganda, unemployment continued to rise over the past decade consequently inhibiting the country’s growth prospects which has ultimately undermined the econoimy’s capacity to external shocks. Keynes and the monetarists ignited the contentious debate over the superiority between monetary and fiscal policy frameworks which has transformed macroeconomic policy application. A conducive private sector environment as well as large expansions of infrastructure are key fundamental aspects of the development strategy in developing countries, they enhance growth in per capita income. Whilst the monetary authority emphasizes price stability when formulating policies, the fiscal authority pursues its objectives accommodative of the underlying circumstances in the economy. This study aimed to establish an econometric model to predict the impact of monetary and fiscal policy on unemployment and inflation in Uganda using annual time series data for the period 1980 to 2013. The study sought to investigate the influence of monetary and fiscal policy variables on the Ugandan economy in relation to unemployment and inflation. The analysis in the study is based on a twofold oriented objective. The first objective was to investigate monetary and fiscal policy dynamics in Uganda in relation to unemployment. The second objective examined the conduct of monetary and fiscal policy framework on inflation in Uganda. The study analysis begins with a review of literature on the various monetarists and Keynesian theories in relation to the underlying monetary and fiscal policy frameworks. Considering the analysis was a twofold objective, two empirical models linked to unemployment and inflation as well as their relative determinants are specified. The Empirical literature review examined in the study is based on various monetary and fiscal policy theories as well as empirical works by Keynesians, classical economists and the Friedman views. The time series data used were obtained from published sources of the World Bank and IMF, the Uganda Bureau of Statistics (UBOS), Ministry of Finance, Planning and Economic Development (MoFPED) statistical reports and annual statistical drafts from the Uganda Revenue Authority (URA) and Bank of Uganda (BOU). To empirically investigate the influence of monetary and fiscal policy variables on unemployment and inflation in Uganda, considering the use of two dependent variables i. e unemployment and inflation, hence, two estimation techniques were applied in the study namely; the Modified Ordinary Least Squares that comprise of FMOLS and DOLS and the Autoregressive Distributed Lag (ARDL) approach. The estimation analysis in the study contains two main parts which are spread over two chapters. The first part of the analysis deals with the effects of fiscal and monetary policy on unemployment. The estimation techniques applied in the study included the Fully Modified Ordinary Least Squares (FMOLS) and Dynamic Ordinary Least Squares (DOLS) applied to a Vector Autoregressive (VAR) model. The analysis regressed monetary and fiscal policy aggregates on unemployment in a twofold objective. The first sub section regressed fiscal policy aggregates on unemployment using; total government expenditure, total government revenue, tax revenue and trade openness on unemployment using both FMOLS and DOLS techniques. The second sub-section regressed monetary policy on unemployment using; interest rates, money supply, real effective exchange rates and inflation being regressed against unemployment. To test for presence of unit root among the variables of the sample period of 1980 to 2013, the study employed three approaches; i.e. the Augmented Dickey Fuller (ADF) test, Phillips-Perron (PP) test and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test. Included in this analysis is the test for structural breaks to further determine stationarity in the data series. The results revealed the presence of structural breaks. Structural breaks tend to inhibit stationarity among the variables at levels. However, when presence of structural breaks is taken into consideration, it simplifies empirical estimation analysis under review. The Johansen Cointegration approach was further applied to establish existence of a stable long-run relationship between monetary policy and fiscal policy as well as their respective variables included in the model in relation to unemployment, this further entailed estimation of FMOLS and DOLS in the model estimation analysis. The results from the above analysys show a negative and statistically significant relationship between total government expenditure (LGOVTEXP) and unemployment (LUNEMPLOYMENT). However, tax revenue, trade openness as well structural reforms which denotes the (SB) coefficient all show a positive and significant relationship with unemployment. Additionally, total government revenue (LGOVTREV) shows a negative relationship with unemployment although statistically insignificant. The DOLS results in this analysis all show statistically insignificant results between all the variables and unemployment. The second subsection using DOLS, analysed the impact of monetary policy on unemployment, revealed a negative and significant relation between interest rates, real exchange rates and structural reforms (SB) with unemployment. Money supply indicates a negative but statistically insignificant relationship with unemployment. However, inflation has a positive and statistically significant relationship with unemployment. The normality tests conducted indicate normal distribution of the residuals. Similiraly, the AR inverse roots show stability of the models estimated whilst the multi-collinearity and Wald tests all showed unbiased estimation results. Having analysed the effects of fiscal and monetary policy on unemployment the interest was to further test the impact of fiscal and monetary policy on inflation. This part constitutes two sub-sections. The ARDL approach ws used to analyse the influence of fiscal policy on inflation. The results reveal a negative and statistically significant relationship between inflation (DLINF) and total government expenditure (DLGOVTEXP) both lagged twice. Similiraly, total government revenue (DLGOVTREV) and tax revenue (DLTAXREV) both lagged once indicate a negative and statistically significant relationship with inflation. However, unemployment lagged three times indicates a negative and statistically insignificant relationship with inflation whilst trade openness lagged three times has a positive and satatistically significant relationship with inflation. The Granger causality test results revealed among all the fiscal policy aggregates used, only inflation Granger causes total government revenue. The second part on the effects of fiscal and monetary policy on inflation used monetary variables; interest rates (DLINT), money supply (DLMS) and real exchange rates (DLREER). The ARDL results revealed all coefficients to have positive signs. Inflation and real exchange rates lagged five and four times respectively have a positive and significant relationship with the dependent variable of inflation. However, interest rate and money supply lagged five and three times respectively show a positive and statistically insignificant relationship with inflation. The estimated model showed no evidence of presence of serial correlation through numerous diagnostic tests performed. These include; heteroscedasticity, residual normality and misspecification tests as well as the Cusum stability tests. Under the analysis of monetary policy dynamics on inflation, the Granger causality test revealed that inflation Granger causes interest rates. Similiraly, real exchange rate Granger causes inflation. The ARDL results in this sub-section suggest that inflation regressed against its own lagged values is statistically significant in explaining variations on inflation. Further, interest rates, money supply and real exchange rates significantly explain variations in inflation during the period under review. The results from the above analysis suggest that firstly, the fiscal authority in Uganda should formulate dynamic as well as robust fiscal reforms that can effeficiently be coordinated with sound monetary policy reforms. This ought to stimulate meaningful economic growth in the economy which would further enhance employment growth. Secondly, policy authorities should implement macroeconomic policies which harmonise public spending whilst at the same keep inflation subdued. In this regard, inflation targeting policies should be strengthened. Thirdly, the macroeconomic policy framework in Uganda should be coordinated with strong employment targeting policies in an effort to broaden labour market dynamics

Essays on Inflation Volatility

Inflation volatility is one of the key constituents of inflation dynamics and has not received much attention in the literature. The study of inflation volatility is important because it has adverse economic consequences. This thesis aims to study the determinants of inflation volatility for advanced and developing countries. At the outset, I explore the empirical regularities of inflation volatility based on monthly and quarterly CPI inflation data (1968 to 2011) using time and frequency domain analysis. I establish a stylised fact that inflation is significantly more volatile in developing countries than advanced countries. This raises a research question why it is so. Using a New Keynesian paradigm, an answer to this research question is sought from two angles. First, a policy rule for interest rate (known as Taylor rule) is estimated over a balanced panel of advanced and developing countries to examine the difference in policy activism between these two groups of countries. This follows from the New Keynesian argument that an active monetary policy is a necessary condition for stable dynamics of inflation. Using the Generalized Method of Moments and the Arellano and Bover (1995) method of dynamic panel estimation, I find that monetary policy is active in advanced countries but passive in developing economies. This striking difference in the policy regimes between these two groups can be one of the reasons for the difference in inflation volatility. Second, motivated by the asymmetry in consumption basket of CPI between advanced and developing economies, a two-sector New Keynesian model with food and non-food is developed. The model features: i) composite consumption and labour index, ii) differential Calvo-type price adjustment of firms across sectors, and iii) Taylor type monetary policy rule. Characterising the distinct structures of advanced and developing economies by two different parameterizations, the model calibration shows that demand disturbance generated by the preference shock is one of the fundamental forces for inflation volatility. In addition, my simulation analysis demonstrates that other structural parameters such as the frequency of price adjustment, distribution of labour and the elasticity of labour substitution, and the policy parameter of inflation in the Taylor rule are also critical factors explaining the greater volatility of inflation in developing economies

Proceedings of USM-AUT International Conference 2012 Sustainable Economic Development: Policies and Strategies

This proceedings includes papers presented at the USM-AUT International Conference (UAIC 2012) carrying the theme “Sustainable Economic Development: Policies and Strategies”, held on 17-18 November 2012 at Bayview Beach Resort Penang Malaysia. This conference is jointly organized by the School of Social Sciences, Universiti Sains Malaysia (USM), Malaysia, and Faculty of Business and Law, Auckland University of Technology (AUT), New Zealand. We received a total of 167 papers from various institutions and organizations around the world where 82 papers were accepted for inclusion in this proceedings. The proceedings is compiled according to the three sub themes of the conference. It covers both theoretical and empirical works from the scholars globally. It is hoped that the collection of these conference papers will become a valuable reference to the conference participants, researchers, scholars, students, businesses and policy makers. The proceedings will be submitted to Thomson ISI for indexing