Econometrics

Econometrics is a major field in contemporary mainstream/empirical economic research. It involves the use of statistical tools to analyze numerical data, estimate relationships between economic variables, and predict unobserved values of the given data based on the parameters estimated in the regression analysis.

Overview

The most basic, fundamental starting point of econometrics is linear regression by Ordinary Least Squares (OLS), in which econometricians estimate the slope(s) of a given linear mathematical function (called “regression analysis”) comprised of economic variables (both dependent and independent), represented by observed data points. OLS is a tool for finding the “line of best fit” through a plotted data set, in which each entry in the given X data is paired with an entry in the Y data, i.e., the two are “observed” together.

The linear regressions require at least one dependent variable (or “outcome variable” or “left-hand-side (LHS) variable”), at least one explanatory variable (or “independent variable” or “right-hand-side (RHS) variable”), an intercept term, and an error term. These components are combined to make one equation showing y (dependent variable) as a function of x (explanatory variable):

Y = α + βX + ε

where α is the intercept, β is the slope, and ε is the error term (disturbance).

The model can be expanded to include multiple explanatory variables, interaction terms (i.e., covarying explanatory variables explain the outcome variable), multiple dependent variables (panel models), time-series regression (observations over time, autoregressive (AR), moving average (MA), both (ARMA), vector autoregression (VAR), etc.), dummy variables (for variables with only two values, like yes/no, male/female, etc.), and many other considerations. There are numerous estimation processes designed to deal with specific problems in the data (assumption violations) or to more correctly identify relationships between variables under different circumstances than those fitting for OLS.

Least Squares

Ordinary Least Squares, as implied by the name, seeks to minimize the sum of the squared residuals (squared distance between actual data points and the prediction (estimation) based on the linear relationship between the variables. This process, given certain assumptions, yields statistically unbiased (best approximation of true relationship), consistent (estimates get closer to true relationship with an increasing number observations), and efficient (distance between actual and predicted values are smallest) estimates for the regression parameters.

Assumptions

For OLS to achieve unbiasedness, consistency, and efficiency (among other characteristics), a few assumptions about the regression model must hold. These are listed below with brief descriptions.

• Linearity
  • The regression model correctly describes the functional relationship between the given variables. If the relationship is non-linear, some transformation (e.g., log, semilog, translog) of the data is necessary. Other implications of this assumption are that the data represent the variables in the model (i.e., the econometrician knows what he or she is observing), and that the variables are indeed related to each other ("X causes Y").
• No multicollinearity
  • The explanatory variables aren't perfectly (or closely) correlated with each other.
• Homoskedasticity
  • The variance of the errors are constant across all observations and the covariance between errors is zero (nonautocorrelation).
• Exogeneity
  • The explanatory variables are not correlated with the error term. There is no "feedback loop" of causation between the Y and X variables.
• Disturbances have zero mean
  • The mean distance between the predicted and actual values is zero.
• Normality
  • The errors are normally distributed with mean zero and variance σ².