Econometrics

Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference." An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships." Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today.

A basic tool for econometrics is the multiple linear regression model. Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.

Some of the forerunners include Gregory King, Francis Ysidro Edgeworth, Vilfredo Pareto, and Sir William Petty's Political Arithmetick. Early pioneering works in econometrics include Henry Ludwell Moore's Synthetic Economics.

A basic tool for econometrics is the multiple linear regression model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis. Estimating a linear regression on two variables can be visualized as fitting a line through data points representing paired values of the independent and dependent variables.

For example, consider Okun's law, which relates GDP growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate (${\displaystyle \Delta \ {\text{Unemployment}}}$) is a function of an intercept (${\displaystyle \beta _{0}}$), a given value of GDP growth multiplied by a slope coefficient ${\displaystyle \beta _{1}}$ and an error term, ${\displaystyle \varepsilon }$:

The unknown parameters ${\displaystyle \beta _{0}}$ and ${\displaystyle \beta _{1}}$ can be estimated. Here ${\displaystyle \beta _{0}}$ is estimated to be 0.83 and ${\displaystyle \beta _{1}}$ is estimated to be -1.77. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77 * 1 points, other things held constant. The model could then be tested for statistical significance as to whether an increase in GDP growth is associated with a decrease in the unemployment, as hypothesized. If the estimate of ${\displaystyle \beta _{1}}$ were not significantly different from 0, the test would fail to find evidence that changes in the growth rate and unemployment rate were related. The variance in a prediction of the dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares.

Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. An estimator is unbiased if its expected value is the true value of the parameter; it is consistent if it converges to the true value as the sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size. Ordinary least squares (OLS) is often used for estimation since it provides the BLUE or "best linear unbiased estimator" (where "best" means most efficient, unbiased estimator) given the Gauss-Markov assumptions. When these assumptions are violated or other statistical properties are desired, other estimation techniques such as maximum likelihood estimation, generalized method of moments, or generalized least squares are used. Estimators that incorporate prior beliefs are advocated by those who favour Bayesian statistics over traditional, classical or "frequentist" approaches.

Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.