Block version allows a new bandwidth (chosen by the np package)
while fitting kernel regressions for each block of data. This may
not be appropriate in all situations. Block size is flexible.
The function develops a unanimity index regarding the particular
flip (y on xi) or (xi on y) is best. Relevant signs determine 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 are used.
It avoids Anderson's trapezoidal approximation.
The summary results for all
three criteria are reported in a vector of numbers
The data matrix with p columns. Denote x1 as the first column, which is fixed and then paired with all other columns, say: x2, x3, .., xp, one by one flipping with x1.The number of columns, p, must be 2 or more
data matrix for designated control variable(s) outside causal paths. The default ctrl=0 means that there are no control variables used.
Number of digits for reporting (default
block size, default=10, if chosen blksiz >n, where n=rows in the matrix, then blksiz=n. That is, no blocking is done
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
the 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
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.
The European Crime data has all three criteria correctly suggesting that
high crime rate kernel causes the deployment of a large number of police officers.
returns only one number: 3.175, implying the highest unanimity strength index,
with the positive sign suggesting ‘crim’ in the first column kernel causes
‘off’ in the second column of the argument
mtx to this function.
Prof. H. D. Vinod, Economics Dept., Fordham University, NY.
H. D. Vinod 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, 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
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## Not run: options(np.messages=FALSE) colnames(mtcars[2:ncol(mtcars)]) siPair2Blk(mtcars[,1:3],ctrl=mtcars[,4:5]) # mpg paired with others ## End(Not run) 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=NA;y2=y;y2=NA;w2=w;w2=NA siPair2Blk(mtx=cbind(x2,y2), ctrl=cbind(z,w2))
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