QMT 3033 ECONOMETRICS QMT 3033 ECONOMETRIC

Chapter 1 INTRODUCTION QMT 3033 ECONOMETRIC

Introduction to Econometrics Econometrics literally means “measurement in economics”. 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. QMT 3033 ECONOMETRIC

Econometrics is not mathematical economics Econometrics is not mathematical economics. It is about developing quantitative estimates of economics relations or models. QMT 3033 ECONOMETRIC

Economic Models A model is a simple representation of a real-world process. Models have to be simple to make them traceable. They also have to be general enough to be useful. Models explain the relationships between variables of interest. QMT 3033 ECONOMETRIC

Example The national income identity represents a simple economic model. For a closed economy, the following identity holds, Y = C + I + G where all variables are flows in real terms. QMT 3033 ECONOMETRIC

Hypotheses about the individual parts of this identity formed: Consumption C = f [(1-t) Y, r] 0 < f1 < 1, f2 < 0 Investment I = f [(1-t) Y, r] f1 > 0, f2 < 0 QMT 3033 ECONOMETRIC

The explanation is conditional upon the values of G, r and t. The model constitutes a theory about the joint determination of C, I and Y. C, I and Y are endogenous. The explanation is conditional upon the values of G, r and t. G, r and t are exogenous. QMT 3033 ECONOMETRIC

Limits of Economic Models Economic models leave many questions unanswered. Functional form. Data definition and measurement. Dynamic (lag) structure. Qualitative versus quantitative implications. Choice between competing theories. QMT 3033 ECONOMETRIC

The Econometrics Model The specification of a model with a deterministic component (the explanatory variables) and the stochastic error component is called the econometric model. It provides a link between the data and economic theory. QMT 3033 ECONOMETRIC

Economic vs Statistical Models Economic model explains the behaviour of one variable in terms of other variables. Eg. Q = f(P) Linear: Qt = β1 + β2Pt Log-linear: ln Qt = β1 + β2 ln Pt Statistical model: Qt = β1 + β2 Pt + ut QMT 3033 ECONOMETRIC

Writing Research Paper Research can be defined as an organized, systematic, data-based, critical, objective, specific inquiry or investigation into a specific problem, undertaken with the purpose of finding answers or solutions to it. Research provides the needed information that guide managers to make informed decisions to successfully deal with problems. QMT 3033 ECONOMETRIC

Theoretical framework Research Process The broad problem area Preliminary data gathering Problem definition Research design Hypothesis development Theoretical framework Data collection Data analysis and interpretation Research report QMT 3033 ECONOMETRIC

Review of Probability Concepts Basic Probability Concepts Probability is the likelihood or chance that a particular event will occur (always between 0 and 1). Event is each possible outcome of a variable. Simple Event is an event that can be described by a single characteristic. Sample Space is the collection of all possible events. QMT 3033 ECONOMETRIC

Assessing Probability A priori classical probability - Probability of occurrence: = where X = number of ways in which the event occurs T = total number of elementary outcomes QMT 3033 ECONOMETRIC

Subjective Probability Empirical Classical Probability - Probability of occurrence. Number of favorable outcomes observed Total number of elementary observed Subjective Probability - An individual judgment or opinion about the probability of occurrence. = QMT 3033 ECONOMETRIC

Conditional Probabilities A conditional probability is the probability of one event, given that another event has occurred: The conditional probability of A given that B has occurred QMT 3033 ECONOMETRIC

The conditional probability of B given that A has occurred Where P(A and B) = joint probability of A and B P(A) = marginal probability of A P(B) = marginal probability of B QMT 3033 ECONOMETRIC

Bayes’ Theorem Conditional probability takes into account information about the occurrence of one event to find the probability of another event. This concept can be extended to revise probabilities based on new information and to determine the probability that a particular effect was due to a specific cause. The procedure for revising these probabilities is called Bayes’ Theorem. QMT 3033 ECONOMETRIC

Bayes’ Theorem Formula Where Bi = ith event of k mutually exclusive and collectively exhaustive events A = new event that might impact P(Bi) QMT 3033 ECONOMETRIC

Discrete Probability Binomial Distribution Binomial distribution is used when discrete random variable of interest is the number of successes obtained in a sample of n observation. QMT 3033 ECONOMETRIC

Binomial distribution: QMT 3033 ECONOMETRIC

Poisson Distribution Poisson distribution is used when you wish to count the number of times an event occurs in a given area of opportunity. QMT 3033 ECONOMETRIC

Poisson Distribution Formula Where X = number of events in an area of opportunity  = expected number of events e = base of the natural logarithm system (2.71828...) QMT 3033 ECONOMETRIC