The Principles of EconometricsLuis Alberto PalaciosBlockedUnblockFollowFollowingMar 31, 2018Literally, econometrics means economic measurement and is the art of identifying and quantifying the causal relationships inherent among economic phenomena.
It is also the study of the application of statistical methods for the analysis of economic phenomena.
After all, econometrics is the unification of economic theory, mathematical tools, and statistical methodology.
In a broader sense, econometrics is concerned with estimating economic relations, confronting theory with facts, testing hypotheses about economic behavior and forecasting the behavior of economic variables.
For its application, econometrics is composed of:Specification.
– The construction of models.
Estimate.
– Adjust the model to the data.
Verification.
– Test the model.
Prediction.
– Use the model.
Illustration:Specification of a Simple Econometric Model for the Keynesian Theory of Consumption.
(1)Where,Y = consumption expenditure; X = income; α, β = parameters.
Equation (1) is an example of a mathematical model.
A model is simply a set of mathematical equations.
The model given in (1) assumes that there is an exact or deterministic relationship between consumption and income; however, this will not generally be the case.
The above is due to the fact that in addition to income there are other variables that also affect consumption spending.
For example, family size, ages of family members and level of education, among others.
For an inaccurate relationship between the variables income and expenditure in consumption to be permissible, equation (1) should be modified as follows:(2)Equation (2) is an example of an econometric model.
By including the random (stochastic) variable ε, known as the error or perturbation term, we can hypothesize, in addition to a linear relationship between Y and X, that the relationship between the variables is not exact.
ε, the error term is due to:1) Omission of the influence of innumerable random events.
2) Errors in the measurement.
3) Indeterminate human behavior.
The term error is a random, stochastic and unknown variable.
Stochastic: for every value of x there exists a probabilistic distribution of values of y, which may never be exact.
The estimation of the model consists in obtaining the numerical values for the parameters from the available data.
The main statistical estimation tool is regression analysis.
The β’s are the parameters and are fixed in time and through individuals.
In order to determine the numerical values of the parameters, the choice of data is very important.
These could be:1) Time series2) Cross-sectional data3) Data panelThe verification is carried out by statistical inference to determine if the obtained estimates fulfill the expectations of the theory on which the model is based.
The prediction or forecast of the future values of a dependent variable is made on the basis of known or expected values of the explanatory variables and constitutes the most frequent use of an estimated econometric model.
The statistical procedure to estimate the values of the parameters in the general model:(3)Where:Yi = dependent variable stochasticα, β = unknown but estimable parametersXi = exogenous variableε = random error or disturbance termIt must possess certain statistical properties of the estimators that are considered desirable, such as that the estimator is unbiased, efficient or of minimum and consistent variance.
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