findOptimalFLCI {HonestDiD}

Constructs optimal fixed length confidence interval for \Delta = \Delta^{SD}(M).

Description

Computes the optimal FLCI for the scalar parameter of interest under \Delta = \Delta^{SD}(M).

Usage

findOptimalFLCI(betahat, sigma, M = 0,
                numPrePeriods, numPostPeriods,
                l_vec = .basisVector(index = 1, size = numPostPeriods),
                numPoints = 100, alpha = 0.05, seed = 0)

Arguments

betahat

Vector of estimated event study coefficients.

sigma

Covariance matrix of event study coefficients.

numPrePeriods

Number of pre-periods.

numPostPeriods

Number of post-periods.

l_vec

Vector of length numPostPeriods that describes the scalar parameter of interest, theta = l_vec'tau. Default equals to first basis vector, (1, 0, ..., 0)

M

Tuning parameter for \Delta^{SD}(M) that governs the degree of non-linearity allowed in the violation of parallel trends. Default equals 0

numPoints

Number of possible values when optimizing the FLCI. Default equals 100.

alpha

Desired size of the FLCI. Default equals 0.05 (corresponding to 95% confidence interval)

seed

Random seed for internal computations; included for reproducibility.

Value

Returns a list containing items

FLCI

Vector containing lower and upper bounds of optimal FLCI.

optimalVec

Vector of length numPrePeriods + numPostPeriods that contains the vector of coefficients associated with the optimal FLCI.

optimalPrePeriodVec

Vector of length numPrePeriods that contains the vector of coefficients for the optimal FLCI that are associated with the pre-period event study coefficients.

optimalHalfLength

A scalar that equals the half-length of the optimal FLCI.

M

Value of M at which the FLCI was computed.

status

Status of optimization.

Author(s)

Ashesh Rambachan

References

Rambachan, Ashesh and Jonathan Roth. "An Honest Approach to Parallel Trends." 2021.