Econometrics for Finance_Ch_1

1. Chapter One :Introduction By: Adisie T. ASU, Dep’t of Economics November 26, 2022 By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 1/24

2. Chapter Outline 1 What is Econometrics? 2 Models: Economic vs. Econometric models 3 Methodology of Econometrics Research 4 Desirable Properties of an Econometric Model 5 Goals of Econometrics 6 The Types, Sources and Nature of Data By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 2/24

3. 1.1.What is Econometrics? The literal meaning of econometrics is ’economic measure- ment”. The first four letters of the word suggest correctly that the origins of econometrics are rooted in economics. However, the main techniques employed for studying economic problems are of equal importance in financial applications. Econometrics may be defined as the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena. Econometrics is concerned with the empirical determination of economic laws By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 3/24

4. Econometrics is based upon the development of statistical meth- ods for estimating economic relationships, testing economic the- ories, and evaluating and implementing government and busi- ness policy. Financial econometrics will be defined as the application of statistical techniques to problems in finance. Financial econometrics can be useful I for testing theories in finance; testing hypotheses concerning the relationships between variables, I for forecasting future values of financial variables and I for financial decision-making By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 4/24

5. Is financial econometrics different from ‘economic econometrics’ Although the tools frequently used in financial applications are basically the same as those used in economic applications, the emphasis and sets of difficulties that are likely to be faced when analyzing the two types of data are somewhat different. Lack of data, measurement error, and data revision are all seri- ous issues in economic econometrics’. These economic data- related difficulties are rarely of issue in finance. Financial data comes in a variety of shapes, sizes, and frequencies. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 5/24

6. 1.2. Economic vs. Econometric models An economic model is a simplified version of reality that allows us to observe, understand and make prediction about economic behavior. I It does not claim to be able to predict the specific behavior of any individual or firm, but rather describes the average or systematic behavior of many individuals or firms. I It consists of mathematical equations that describe various re- lationships. Y = f (X) (1) Mathematical models or equations are deterministic or exact or systematic in nature. I A relationship between two variables X and Y is deterministic or exact if for each value of variable X, there is one and only one corresponding values of variable Y. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 6/24

7. An econometric model consists of a set of equations describ- ing the behavior.These equations are derived from the economic theory and have two parts 1 The deterministic part,Y = f (X), which is the part of Y determined by X, and 2 The random and unpredictable part, usually denoted by ? or u, which represents the part of Y that is not determined by X. Y = f (X) + ? We can incorporate some of these variables, the variables other than X, in the model,but we can never eliminate ? entirely. Therefore, in every econometric model, there is a systematic or deterministic portion, f(X), and an unobservable random component, ?. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 7/24

8. However, in any particular problem, one challenge is to deter- mine a functional form that is compatible with economic theory and the data. It needs paying due effort. The functional form represents a hypothesis about the relationship between the variables. In order to investigate the relationship between economic vari- ables, we must first build an economic model with the ap- propriate functional form and then a corresponding econo- metric model. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 8/24

9. For instance, according to Keynes theory of consumption, con- sumption is a linear function of income. Thus, the mathe- matical expression of the economic model will be as follows Y = f (X) = β0+ β1X (2) The corresponding econometric model is Y = f (X) + ? = β0+ β1X + ? (3) The coefficients β0 and β1 are unknown parameters of the model that we estimate using economic data and an econo- metric technique. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 9/24

10. Hence, an econometric model I is a simplified version of the real world process, explaining complex phenomena. I includes information regarding observed variables and disturbances. I consists of a set of equations, derived form economic theory, mathematical models and statistical tools that is regression. Regression is a method to determine the statistical relation- ship between a dependent variable (usually denoted by Y) and one or more independent variables (usually denoted by X). By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 10/24

11. A variable is any characteristic or attribute which is subject to change and can have more than one value An independent variable is variable that is presumed to influ- ence other variable. A dependent variable is a variable that is affected by the independent variable. I For example, suppose you are interested in ”How income affect consumption expenditure?” I In this situation, income is an independent variable influencing consumption, while consumption is a dependent variable influ- enced by income.. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 11/24

12. 1.3. Methodology of Econometrics Research To conduct an empirical economic study, we must follow the fol- lowing steps or methodology By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 12/24

13. 1 Statement of the economic theory or hypothesis I The process starts with a review of the theory, hypothesis, or circumstance under question.This phase entails identifying the theory or hypothesis to be tested as well as specifying the vari- ables to be explored for the cause-and-effect relationship. At this time, the hypothesis simply provides qualitative links and does not present any numerical relationships. 2 Specification of the economic or mathematical model I Once we have set the hypothesis, we need to express economic theory or hypothesis in mathematical form using the appro- priate functional form. That means a mathematical model, for instance, for Keynes consumption theory as follows Y = f (X) = β0+ β1X ; 0 < β1< 1 (4) By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 13/24

14. 3 Specification of the Econometric Model: in order to test the hypothesis, it’s essential to modify the mathematical expression of economic model into an econometric model( statistical form) as follow: Y = f (X) + ? = β0+ β1X + ? (5) Based on the variables and data types, we may have different econometric models. Some of these are 1 Linear regression:Includes simple, Multiple, and multivariate linear regressions 2 Binary choice models: Binary logit and probit. 3 Multiple choice models: Multinomial and ordered probit and logit, 4 Limited dependent variable models: Tobit, Truncated , and Heckman regression models. 5 Count data models: Possion, Negative binomial, and zero inflated models. 6 Time series models: Uni-variate and Multivariate Time series models. 7 Panel Models: Fixed and random effects model By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 14/24

15. 4 Obtaining data I To estimate the econometric model that means to obtain numeri- cal values for β0and β1, we need data. The data can be obtained from primary or secondary sources. It can also be cross-section, time series or panel data. 5 Estimation of the econometric model I Here we obtain numerical values(estimates) for β0and β1. Re- gression analysis is the main tool used to obtain the estimates as follows Y = 184.08 + 0.7064X + ? (6) 6 Hypothesis Testing:it refers to a formal process of investigating a supposition or statement to accept or reject it. I If it is consistent with the hypothesis, it is accepted, otherwise it is rejected. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 15/24

16. 7 Forecasting or prediction: I If the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value of the dependent or forecast variable Y on the basis of the known or expected future value of the explanatory or predictor, variable X. 8 Use of models for control or policy purpose I Lastly, if the theory seems to make sense and the econometric model was not refuted on the basis of the hypothesis test, we can go on to use the theory for policy recommendation or decision making . By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 16/24

17. 1.4 Desirable Properties of an Econometric Model The followings are the desirable properties of an econometric model 1 Theoretical plausibility: the model should be compatible with the postulates of economic theory. 2 Explanatory ability: the explanatory power of the model should be adequate. 3 Accuracy of the estimates of the parameters: the estimates of the parameters should be accurate in the sense that they should approximate as best as possible. In other words, the estimates should posses the desirable properties of unbiasedness, con- sistency, and efficiency. 4 Forecasting ability: the model should produce satisfactory pre- dictions of future values of the dependent variable. 5 Simplicity: the model should represent the economic relation- ships with maximum simplicity. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 17/24

18. 1.5. Goals of Econometrics The three main goals of Econometrics are 1 Analysis: testing economic theory 2 Policy making: obtaining.numerical estimates of the coefficients of economic relationshipss for policy simulations. 3 Forecasting:using the numerical estimates of the coefficients in order to forecast the future values of economic magnitudes By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 18/24

19. 1.6. The Types, Sources and Nature of Data In order to carry out an econometric research and conduct a sta- tistical inference, we must have data. Data are the different values associated with a variable. Based on the type of the variable, data can be: I Quantitative data such as prices or income that may be ex- pressed as numbers or some transformation of them, such as real prices or per capita income. or I Qualitative data- outcomes that are of an “either-or” situation. For example, a consumer either did or did not make a purchase of a particular good, or a person either is or is not married. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 19/24

20. Data may be collected at various levels of aggregation: I Micro data collected on individual economic decision-making units such as individuals, households, and firms. I Macro data resulting from a pooling or aggregating over individuals, households, or firms at the local, state, or national levels. Data can be obtained either from I Primary sources: primary data are the data which the researcher collects, for the very first time, from the original source through experiment, questionnaire, interview, mail, etc. • These data are also called first hand data. I Secondary sources: secondary data are data collected by any person,organization,or agency in the past through experimental or survey method, for some other purpose, but used by a researcher to to deal with some problem at hand. • These data type are called second hand data. Example; Data obtained from CSA, MoFED, WB, IMF, WDI, etc are secondary data. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 20/24

21. Data, in general, economic data, in particular, may have either cross-sectional, time series, pooled, or panel nature. 1 Cross-sectional data I Consists of a sample of individuals, households, firms, countries, etc. taken at a given point in time I Each observation is a new individual, firm, etc. with information at a point in time. I We often assume that the data are obtained by random sam- pling from the underlying population. I Re-ordering of data doesn’t matter because it doesn’t take ‘pe- riod of time’ into account. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 21/24

22. 2 A time series data I consists of observations on a variable or several variables over time. I Examples: stock prices, money supply, CPI, GDP, sales, inflation rate, unemployment rate etc. I Data frequency (usually daily, weekly, monthly, quarterly and annually) and ordering is important. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 22/24

23. 3 Pooled cross-sections I Pooling cross sections from different years is often an effec- tive way of analyzing the effects of a new government policies, programs etc.(i.e.the before and after change). I As an example, consider the following data set on housing prices taken in 1993 and 1995, before and after a reduction in prop- erty taxes in 1994. I 250 randomly selected houses for 1993 and again 270 randomly selected houses for 1995. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 23/24

24. 4 Panel or longitudinal data I consists of a time series for each cross-sectional member in the data set. I Same cross-sectional units (individuals, firms, or countries) are followed over a given time period I Example, suppose we have number murders and unemployment rate of 150 cites of a-year period. I While in pooled data the observations in each cross-section do not necessarily refer to the same unit, in panel data the same cross-sectional units observed at multiple points in time. By: Adisie T. (ASU, Dep’t of Economics) Applied Econometrics for Finance November 26, 2022 24/24