Jul 31

Specify & test an econometric model (Quant: Econometrics)

by David Harper, CFA, FRM, CIPM

FRM | Quant |

Learning objective: Explain the process of specifying, interpreting, and validity testing an econometric model

To specify the model, we should first examine the scattergram (or scatter diagram). As a first approximation, can we draw (visualize) a straight line? There can be a relationship that is non-linear.

If we visually observe a linear relationship, we specify a mathematical model (the line):

chap1_1

As a first approximation, the mathematical model specifies a relationship between the independent (or explanatory) variable and the dependent variable. The ordinary least squares (OLS) approach will "draw a line" through the data. This generates estimators (statistics) which are estimates of the population parameters.

But we do not expect a perfect mathematical relationship, and so we will add a random error term. The inclusion of the error term implies the econometric (or statistical) model:

chap1_2

Because the sample statistics exhibit sampling variation, we can conduct hypothesis tests to ascertain the significance of the estimators.

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