Econometrics Notation

Observations and Measurements

The number of observations is n.

The outcome variable is y. The outcome measurement for observation i is y_i.

If there is a single predictor, it may be specified as x; the measurement is x_i. More commonly, there is a set of predictors specified like x₁, x₂, and so on. The measurements are then x_1i, x_2i, and so on.

When expressing data with linear algebra, the outcome measurements are composed into vector y with size n, and the predictor measurements are composed into matrix X of shape n by p.

A very common exception: income is usually represented by Y or y. In relevant literature, expect to see different letters.

Error Terms

Error terms are variably represented by ε, e, u, or v. The error term for observation i would be represented like ε_i.

Statistics

Distributions

The normal distribution is frequently expressed in econometrics. The typical notation is x_i ~ N(μ, σ).

For multiple variables, at minimum the distribution is specified as NI to emphasize independence of the distributions. Some pieces of linear algebra notation are also introduced. For example, the joint statement of exogeneity and homoskedasticity is:

Note how the covariance matrix is fully expressed as the diagonal matrix of each term's variance.

Statistics

There is a mixture of notations for scalar statistics. The conventional estimators for population mean μ, variance σ², standard deviation σ, covariance σ_xy, and correlation ρ_xy are:

Based on OLS regression, the estimated outcome for observation i is:

No matter the regression method, the residual is:

And the coefficient of determination, a.k.a. the R², is:

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