Introduction to Econometrics. Bacisc of Regression Analysis

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1.2 Econometrics Elements

Specification of the econometric model that we think (hope) about generated the sample data. It consists of:

- An economic model: specifies the dependent variable to be explained and the independent variables thought to be related to the dependent [14; 16]

- Suggested or derived from theory

- Sometimes obtained from informal intuition/ observation

- A statistical model: specifies the statistical elements of the relationship under investigation, in particular the statistical properties of the random variables in the relationship [4; 14].

Figure 1.3 (see Appendix A) shows basic steps in econometrics model building.

Collecting and coding the sample data

- Most economic data is observational, or non-experimental

- Sample data consist of observations on randomly selected members of populations (individual persons, households or families, firms, industries, provinces or states, countries)

Estimation consists of using the sample data on the observable variables to compute estimates of the numerical values of all the unknown parameters in the model [14].

Inference consists of using the parameter estimates computed from sample data to test hypotheses about the numerical values of the unknown population parameters that describe the behavior of the population from which the sample was selected.

1.3 Econometrics Methodology

Econometrics is a branch of science, the aim of which is to give a quantitative measure of economic relations. This method of measuring the economy emerged as a way of overcoming the problems that distort the results of the use of classical statistical methods [5]. These include:

- Asymmetrical relations;

- Multicollinearity of explanatory variables;

- Autocorrelation;

- Spurious correlation;

- The effect of heteroscedasticity - lack of normal distribution for residuals of the regression function;

- Closed communication mechanism between the variables in the regression isolated;

- The presence of lags.

The use of econometrics can solve the following problems [10; 11]:

- Qualitative analysis of the relations of economic variables;

- Selection of the necessary data;

- Specification forms the link between economic variables;

- Evaluation of model parameters;

- Testing of hypotheses about the properties of probability distributions for the random component (the variance covariance);

- Analysis of multicollinearity of explanatory variables, evaluation of its statistical significance, identifying the variables responsible for it;

- The introduction of dummy variables;

- Identification and autocorrelation lag;

- Identification of cyclical and random component, the trend;

- Check balances for heteroscedasticity;

- Analysis of the structure of relations and building a system of simultaneous equations;

- Check the conditions of identification;

- Parameter estimation system of simultaneous equations using various methods;

- Modeling based on a system of time series;

- Construction of recursive models;

- Problems of definition and estimation of parameters.

Econometrics models are based on the assumption that there are variables related to a specific nature of the relationship between them. Priority in the description of such connection is given to the qualitative analysis. Econometric study carried out in several stages:

- the problem to be solved with the help of econometric methods is determined;

- all the necessary data and the analysis of their quality is gathered;

- the specification of the model is determined;

- parameters assessment is carried out;

- there is an interpretation of the results.

These stages pass any study, regardless of its orientation on the spatial or temporal data [9; 16]. Broadly speaking, traditional econometric methodology proceeds along the following lines:

1. Statement of theory or hypothesis.

2. Specification of the mathematical model of the theory

3. Specification of the statistical, or econometric, model

4. Collecting the data

5. Estimation of the parameters of the econometric model

6. Hypothesis testing

7. Forecasting or prediction

8. Using the model for control or policy purposes.

In order to understand interconnection among econometric methodology lines, see Figure 1.2 (Appendix A).

To illustrate the preceding steps, let us consider the well-known Keynesian theory of consumption [1; 12].

- Statement of Theory or Hypothesis

Keynes states that on average, consumers increase their consumption as their income increases, but not as much as the increase in their income (MPC

2. Specification of the Mathematical Model of Consumption (single-equation model)

Y = β1 + β2X 0 2 (1.1)

Y = consumption expenditure and (dependent variable)

X = income, (independent, or explanatory