Stats Regression panelregression firstdifference

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PanelRegression.FirstDifference

Fits least squares on the differences between adjacent periods of each entity, FirstDifferenceOLS(y, x).fit().

public static PanelSummary FirstDifference(PanelDesign design, PanelOptions options)

public static PanelSummary FirstDifference(PanelDesign design, ReadOnlySpan<int> clusters, PanelOptions options)

options is required, since the default adds the constant a difference removes: pass WithIntercept = false. The second overload clusters by the caller's labels, which must not change between two rows that are differenced.

Parameters — design is the panel, with no constant column. clusters is one label per row. options chooses the covariance.

Returns — a PanelSummary over the differenced rows: ObservationCount counts the differences, one fewer per entity, and one fewer again per gap.

Exceptions — ArgumentOutOfRangeException when ExogenousCount is below one or the confidence level is outside (0, 1). ArgumentException when a block's length is not its width times the rows, when two rows share an entity and a period, when no residual degree of freedom is left, when a Bartlett or Parzen bandwidth reaches past the periods, or when the options set a value this estimator does not read. ArgumentNullException when the clustered overload gets no options. ArgumentException too when the regressors hold a constant or WithIntercept is set, when there are fewer than two periods, when a cluster label changes between differenced rows, or when the options cluster by period. ArgumentException naming design also when the rows times the parameters, or times the parameters plus one where no column is constant and the constant search appends one, are more cells than one array holds (#1614).

Example — the same panel, differenced.

using Lodestar.Stats.Regression;
using Lodestar.Stats.Regression.Panel;

int[] entities = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4];
int[] periods = [2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023, 2020, 2021, 2022, 2023];
double[] x = [0.5, 1.1, 1.9, 2.4, 1.2, 1.8, 2.9, 3.1, -0.3, 0.4, 0.8, 1.6, 2.0, 2.2, 3.1, 3.9];
double[] y = [2.1, 3.0, 4.2, 4.9, 4.4, 5.1, 6.8, 7.0, 0.2, 1.3, 1.7, 3.1, 6.1, 6.3, 7.9, 9.2];

var design = new PanelDesign(y, x, 1, entities, periods);

PanelSummary summary = PanelRegression.FirstDifference(design, new PanelOptions { WithIntercept = false });

double slope = summary.Coefficients[0];      // => 1.551418439…
double error = summary.StandardErrors[0];    // => 0.0574956411…
int differences = summary.ObservationCount;  // => 12

Remarks — a difference is taken only between adjacent periods of the sorted period labels; a missing year leaves its two neighbours undifferenced. The reference reads its period axis in the order periods are first seen, so an unbalanced panel whose first entity misses a period differences the wrong pairs there; the sorted axis is used here, and the two agree whenever the first entity is complete.

Applies to — net10.0, netstandard2.0.

See also — PanelRegression.FixedEffects.