Formula Interface

ParsedSpatialFormula

The result of parsing a spatial @formula against a table: the response, the design blocks and their names, separated by role.

Carries y and lhs_name; X_exog/exog_names for the exogenous covariates; X_slag_source/slag_names for the terms marked with slag; X_endog/endog_names and Z_iv/iv_names for terms marked with endo; fe_symbols for those marked with fe; and the flags has_slag and is_full_sdm, the latter set when every covariate was lagged so the specification is a Spatial Durbin model.

Mostly an internal hand-off between the formula parser and the estimators; inspect it when a formula does not produce the design you expected.

endo(x...)

Mark endogenous regressors and their instruments inside a @formula.

Written endo(x_endog, z1 + z2): the first argument is the endogenous regressor, the rest are the excluded instruments for it. Identification needs at least as many instruments as endogenous regressors.

Only meaningful inside @formula, and only fit_gs2sls_panel consumes it — the likelihood-based estimators have no way to use instruments.

Examples

fit_gs2sls_panel(
    @formula(y ~ x1 + endo(x2, z1 + z2) + fe(region) + fe(year)),
    table, W; panel = :region, time = :year)

See also slag, fe.

extract_panel_permutation(table, panel_col, time_col) -> (perm, N, T_per)

Work out the reordering that puts a table into the stacking order the panel estimators require, along with the panel dimensions.

Sorts by period and then by unit, so units vary fastest within each period. Every panel entry point assumes that layout and none of them can detect a violation, so this is the safe way to get there from a table in arbitrary order.

Arguments

• table: any Tables.jl-compatible table.
• panel_col, time_col: the unit and period identifier columns.

Returns

(perm, N, T_per): the permutation, the number of units and the number of periods.

Throws an ArgumentError if N * T_per does not equal the number of rows, i.e. if the panel is unbalanced — none of the estimators here support that.

Examples

perm, N, T_per = extract_panel_permutation(df, :region, :year)
y = df.y[perm]
X = Matrix(df[perm, [:x1, :x2]])
m = fit_spatial_panel(SAR(), TwoWayFE(), W, X, y, N, T_per)

The formula methods call this for you, so passing panel and time to fit_spatial_panel avoids the step entirely.

See also fit_spatial_panel.

fe(x)

Mark a column as a fixed effect to absorb, inside a @formula.

The named variable is swept out rather than estimated, so no dummy coefficients appear in the output.

Only meaningful inside @formula.

Examples

fit_spatial(@formula(y ~ x1 + fe(region)), table, W)

See also slag, endo.

slag(x...)

Mark terms to be spatially lagged inside a @formula.

slag(x) adds W*x to the design. slag(x1, x2) lags several terms, and slag(x1 + x2) is equivalent. Lagging every covariate makes the specification a Spatial Durbin model, which the parser detects.

Only meaningful inside @formula; calling it directly raises an error.

Examples

fit_spatial(@formula(y ~ x1 + slag(x2)), table, W)
fit_spatial(@formula(y ~ slag(x1 + x2)), table, W)     # SDM

See also fe, endo.