findOptimalFLCI: 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)

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.

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.

Author

Ashesh Rambachan

References

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