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BACHELOR OF COMMERCE (HONS) DEGREE IN FINANCE INTRODUCTION TO FINANCIAL ECONOMETRICS AND DATA ANALYSIS [CFI 4208] (2022) LECTURER – Z. CHIKAZA Introduction ▪ The application of mathematical statistics to economic data to lend empirical support to models constructed by mathematical economics and to obtain numerical estimates (Samuelson et al., Econometrica,1954). ▪ Financial econometrics is the application of statistical techniques to problems in finance. ▪ It is the quantitative measurement and analysis of actual economic and business phenomena. ▪ Econometrics is used for: – Estimating Economic Relationships – Testing Economic Theories – Evaluating & Implementing Policy – Forecasting What Econometrics Addresses ▪ There are three basic types of econometric questions namely: ⮚ Descriptive Questions - Descriptive statistics is analysis of data that helps describe, show or summarize data in a meaningful way such that patterns might emerge from the data. Eg ⮚How much do men and women earn annually on average in the Zimbabwe? ▪ Forecasting Questions - is the process of making predictions for the future. ⮚Which Political Party will wins elections in Zimbabwe in the next 10 years? ⮚What is the expected growth of GDP for SSA countries in the next 2 years? ▪ Highly visible applications of forecasts are macroeconomic indicators (interest rates, inflation, GDP etc.) ▪ Causal Questions - Causation or causality is the capacity of one variable to influence another. ⮚If the federal reserve lowers interest rates today, what will happen to inflation tomorrow? ⮚How much more money will you earn as a result of taking this course? ▪ The presence of a causal link is suggested by economic theory (or common sense), the goal of econometric analysis is either to empirically verify or quantify this causal link. Types of Economic Data ▪ All empirical analysis requires data. There are different structures of data that you come across if you do empirical analysis in economics: ▪ The special features of the data sets must be accounted for or should be exploited to make correct predictions. ⮚Cross-sectional data ⮚Time series data ⮚Pooled cross sections ⮚Panel (or longitudinal) data Cross-Sectional Data ▪ A cross-sectional dataset consists of a sample of individuals, households, firms, … taken at a given point in time ▪ Cross-sectional datasets are often obtained from random sampling from the underlying population. ▪ Cross-sectional data are usually collected from respondents making up the sample within a relatively short time frame (field period). ▪ In a cross-sectional study, time is assumed to have random effect that produces only variance, not bias. Example 1 Example 2 Time Series Data ▪ A time series data set consists of observations on one or several variables over time. ▪ Unlike the arrangement of cross-sectional data, the chronological ordering of observations in a time series is important. ▪ A key feature of time series data that makes them more difficult to analyze than cross-sectional data is that observations are unlikely to be independent over time. ▪ One can quote numerous examples: monthly unemployment, weekly measures of money supply, daily closing prices of stock indices, and so on. ▪ The interval between observations can be any time interval (hours within days, days, weeks, months, years, etc). Example Some examples of time series are: ▪ ▪ ▪ ▪ Monthly closings of the stock exchange index Malaria incidence or deaths over calendar years Daily maximum temperatures Hourly records of babies born at a maternity hospital Pooled Cross-Sections ▪ Some datasets have both cross-sectional and time series features. ▪ Example: household surveys from 1985 and 1990 which are combined to yield one dataset containing observations from both years. ▪ May be a useful basis for analysis of change of policy, for example, we often include time (year) as an additional explanatory variable in regressions based on pooled cross-sections Panel Data / Longitudinal Data ▪ Panel Data is data in which we observe repeated cross-sections of the same individuals. ▪ Fortunately all of the standard techniques and analysis in econometrics are equally valid for time series and cross sectional data ▪ Have dimensions of both time series and cross sections ▪ Examples: ⮚ Annual unemployment rates of each state over several years ⮚ Quarterly sales of individual stores over several quarters ⮚ Wages for the same worker, working at several different jobs Example ▪ The key feature of panel data is that we observe the same individual in more than one condition. ▪ In pure panel data, we are following the same units i.e. the same households or individuals over time. Steps in Empirical Model Building ▪ There is need to come up with an appropriate economic analysis to have reliable results. 1. Formulate the Question of Interest. ▪ The first important step in conducting any regression analysis is to specify the problem and the objectives to be addressed by the regression analysis. ▪ The wrong formulation or the wrong understanding of the problem will give the wrong statistical inferences. ▪ The choice of variables depends upon the objectives of study and understanding of the problem. 2. Choice of Relevant Variables ▪ It has to be kept in mind that the correct choice of variables will determine the statistical inferences correctly. ▪ For example, in any agricultural experiment, the yield depends on explanatory variables like quantity of fertilizer, rainfall, irrigation, temperature etc. ▪ These variables are denoted by 1 2 , ,..., XX Xk as a set of k explanatory variables. Step 3: Collection of data on relevant variables ▪ One important aspect is to collect data on such relevant variables. ▪ The data is essentially the measurement on these variables. ▪ It is also important to decide that whether the data has to be collected on variables as quantitative variables or qualitative variables. Step 4: Find a suitable economic model. ▪ The experimenter or the person working in the subject usually help in determining the form of the model. ▪ If a model contains only one explanatory variable, then it is called as simple linear regression model. ▪ When there are more than one independent variables, then it is called as multiple regression model. ▪ When there are more than one study variables, the regression is termed as multivariate regression. ▪ The simple and multiple regression are determined by the number of explanatory variables whereas univariate and multivariate regressions are determined by the number of study variables. Step 5: Choice of method for fitting the data ▪ After the model has been defined and the data have been collected, the next task is to estimate the parameters of the model based on the collected data. ▪ This is also referred to as parameter estimation or model fitting. ▪ The most commonly used method of estimation is the ordinary least squares method (OLS) ▪ Under certain assumptions, the least squares method produces estimators with desirable properties. ▪ The other estimation methods are the maximum likelihood method, ridge method, principal components method Step 6: Fitting of model ▪ The estimation of unknown parameters using appropriate method provides the values of the parameter. ▪ Substituting these values in the equation gives us a usable model and this is termed as model fitting . ▪ The fitted equation is used for prediction. Step 7: Model criticism and selection ▪ The validity of statistical method to be used for regression analysis depends on various assumptions. ▪ These assumptions become essentially the assumptions for the model and the data. ▪ The quality of statistical inferences heavily depends on whether these assumptions are satisfied or not ▪ The validation of the assumptions must be made before drawing any statistical conclusions. EMPIRICAL ECONOMIC ANALYSIS ▪ They come into play either when we have an economic theory to test or when we have a relationship in mind that has some importance for business decisions or policy analysis. ▪ Econometrics should always be linked to economic reasoning ▪ An empirical analysis uses data to test a theory or to estimate a relationship ▪ A common goal for applied economists is to estimate the causal effect of one variable on some outcome of interest. ▪ Ceteris paribus: other relevant factors being equal, what is the effect of… ⮚ Price increase on consumer demand ⮚ Training on worker productivity ▪ In economic thinking, causal relations are strongly connected with the notion of ceteris paribus (other things being equal) ▪ example: consumer demand analysis – increasing a price makes consumers buy less ceteris paribus (however, if other factors change, anything can happen) ▪ Therefore, if one could run an experiment with ceteris paribus conditions enforced, it would be easy to verify and evaluate the causal link. Economic Model of Crime - Example ▪ Econometric model to specify the crime rate 1. crime is the frequency of criminal activity, 2. wagem is the wage that can be earned in legal employment, 3. othinc is the income from other sources (assets, inheritance) 4. freqarr is the frequency of arrests for prior infractions (to approximate the probability of arrest) 5. freqconv is the frequency of conviction 6. avgsen is the average sentence length after conviction. ▪ The term u contains unobserved factors, such as the wage for criminal activity, moral character, family background and errors in measuring things like criminal activity and the probability of arrest. Points to consider when using models ▪ Does the work involve testing or developing theory or it is merely a technique to motivate certain issues. ▪ Are data of good quality and is it from a reliable source and is the size of the sample large enough for the model estimation task at hand. ▪ Have the techniques been validly applied. Have tests been conducted for possible violations of any assumptions made in the estimation of the model. ▪ Have the results been interpreted sensibly. Is the strength of the results exaggerated . Do the results actually obtained relate to the questions posed by the author. ▪ Can the results be replicated by other researchers. ▪ Are the conclusions drawn appropriate given results have been overstated. Is Econometrics Necessary? ▪ Despite inherent inaccuracies in trying to use the regression analysis, econometrics drives policy setting and planning ▪ Econometrics is necessary to move forward in today’s ever-changing and highly interactive business environment. ▪ It enables policy makers to formulate a skilful mix of quantitative methods which enable sound judgement for the benefit of our economies. ▪ In most organizations, we find financial experts who through ignorance and fear of quantitative techniques and computers relies solely on qualitative and fail to formulate good policies. ▪ Econometrician may acquire skills in sophisticated data manipulation skills but unwilling to relate that to the needs of the organization. ▪ Analysis, judgement, common sense and business experience should be combined to generate good decisions for the firms. Macroeconomic Considerations ▪ There is also a growing interest for predicting or forecasting important variables for the entire economy. ▪ Economic policy is based on projections of important economic indicators. ▪ It is very necessary to improve forecasting techniques to improve economic performance especially for African Economies. TYPES OF FINANCIAL ECONOMETRICS ▪ Econometrics may be divided into two broad categories: theoretical econometrics and applied econometrics. ▪ Theoretical econometrics is concerned with the development of appropriate methods for measuring economic relationships specified by econometric models. In this aspect, econometrics leans heavily on mathematical statistics. ▪ In applied econometrics we use the tools of theoretical econometrics to study some special field(s) of economics and finance, such as the production function, investment function, demand and supply functions, portfolio theory etc. ▪ Applied econometric methods will be used for estimation of important quantities, analysis of economic outcomes, markets or individual behaviour, testing theories and for forecasting. Classical ▪ The philosophical approach to model-building used here throughout is based on classical statistics. ▪ This involves postulating a theory and then setting up a model and collecting data to test that theory ▪ Based on the results from the model, the theory is supported or refuted Bayesian ▪ Here, the theory and model are developed together ▪ The researcher starts with an assessment of existing knowledge or beliefs formulated as probabilities known as priors ▪ The priors are combined with the data into a model ▪ The beliefs are then updated after estimating the model to form a set of posterior probabilities (the statistical probability that a hypothesis is true calculated in the light of relevant observations).