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.

Distributions

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

For multiple variables, pieces of linear algebra notation are introduced. For example, the joint statement of exogeneity and homoskedasticity is:

Statistics

The average outcome is:

The variance is:

The standard deviation is:

The covariance between the treatment and outcome is:

The correlation between the treatment and outcome is:

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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