generalCorr (version 1.2.6)

silentPair2: kernel causality (version 2) scores with control variables

Description

This function uses flipped kernel regressions to decide causal directions. This version 2 avoids Anderson's trapezoidal approximation used in `silenPairs.' It calls functions: decileVote, momentVote, exactSdMtx, and summaryRank after stochastic dominance is computed. It computes an average of ranks used. The column with the ``choice'' rank value helps in choosing the flip having the lowest Hausman-Wu (residual times RHS regressor) and secondly the lowest absolute residual. The chosen flipped regression defines the ``cause" based on the variable on its right-hand side. In portfolio selection, choice rank 1 has the highest return. Here we want low residuals and low Hausman-Wu value, hence we choose choice=2 as the desirable flip.

The function develops a unanimity index regarding the particular flip (y on xi) or (xi on y) is best. A summary of all relevant signs determines the causal direction and unanimity index among three criteria. The `2' in the name of the function suggests a second implementation where exact stochastic dominance, decileVote, and momentVote algorithms are used.

Usage

silentPair2(mtx, ctrl = 0, dig = 6)

Value

A matrix with p columns in mtx argument to this function, x1 can be paired with a total of p-1 columns (x2, x3, .., xp). Note we never flip any of the control variables with x1. This function produces i=1,2,..,p-1 numbers representing the summary sign, or `sum' from the signs sg1 to sg3 associated with the three criteria: Cr1, Cr2, and Cr3. Note that sg1 and sg2 themselves are weighted signs using a weighted sum of signs from four orders of stochastic dominance. In general, a positive sign in the i-th location of the `sum' output of this function means that x1 is the kernel cause while the variable in (i+1)-th column of mtx is the `effect' or `response' or `endogenous.' The magnitude represents the strength (unanimity) of the evidence for a particular sign. Conversely, a negative sign in the i-th location of the `sum' output of this function means that the first variable listed as the input to this function is the `effect,' while the variable in (i+1)-th column of mtx is the exogenous kernel cause.

Arguments

mtx

The data matrix with p columns. Denote x1 as the first column, which is fixed in all rows of the output and then it is paired with all other columns, say: x2, x3, .., xp, one by one for the purpose of flipping with x1. p must be 2 or more

ctrl

data matrix for designated control variable(s) outside causal paths, default is ctrl=0, which means that there are no control variables used.

dig

Number of digits for reporting (default dig=6).

Author

Prof. H. D. Vinod, Economics Dept., Fordham University, NY.

References

H. D. Vinod 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, tools:::Rd_expr_doi("10.1080/03610918.2015.1122048")

Vinod, H. D. Causal Paths and Exogeneity Tests in Generalcorr Package for Air Pollution and Monetary Policy (June 6, 2017). Available at SSRN: https://www.ssrn.com/abstract=2982128

See Also

See summaryRank, decileVote

See momentVote, exactSdMtx

Examples

if (FALSE) {
options(np.messages=FALSE)
colnames(mtcars[2:ncol(mtcars)])
silentPair2(mtcars[,1:3],ctrl=mtcars[,4:5]) # mpg paired with others
}

options(np.messages=FALSE)
set.seed(234)
z=runif(10,2,11)# z is independently created
x=sample(1:10)+z/10 #x is somewhat indep and affected by z
y=1+2*x+3*z+rnorm(10)
w=runif(10)
x2=x;x2[4]=NA;y2=y;y2[8]=NA;w2=w;w2[4]=NA
silentPair2(mtx=cbind(x2,y2), ctrl=cbind(z,w2))