The ‘2’ in the name of the function suggests a second implementation
where exact stochastic dominance, ‘decileVote’ and ‘momentVote’ functions are used,
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 which regression
flip, (y on xi) or (xi on y) is the best. The “cause” is
always on the right-hand side of a regression equation, and
the superior flip gives the correct sign. The summary of all signs determines the
causal direction and unanimity index among three criteria. This is
a block version of
While allowing the researcher to keep some variables as controls,
or outside the scope of causal path determination
(e.g., age or latitude) this function produces detailed causal path information
in a 5 column matrix identifying the names of variables,
causal path directions, path strengths re-scaled to be in the
range [–100, 100], (table reports absolute values of the strength)
plus Pearson correlation and its p-value.
The algorithm determines causal path directions from the sign of the strength index and strength index values by comparing three aspects of flipped kernel regressions: [x1 on (x2, x3, .. xp)] and its flipped version [x2 on (x1, x3, .. xp)] We compare (i) formal exogeneity test criterion, (ii) absolute residuals, and (iii) R-squares of the flipped regressions implying three criteria Cr1, to Cr3. The criteria are quantified by new methods using four orders of stochastic dominance, SD1 to SD4. See Vinod (2021) two SSRN papers.
The data matrix with many columns, y the first column is a fixed target, and then it is paired with all other columns, one by one, and still called x for flipping.
vector of column names for
block size, default=10, if chosen blksiz >n, where n=rows in the matrix then blksiz=n. That is, no blocking is done
data matrix for designated control variable(s) outside causal paths
The number of digits for reporting (default
If there are p columns in the input matrix, x1, x2, .., xp, say,
and if we keep x1 as a common member of all causal-direction-pairs
(x1, x(1+j)) for (j=1, 2, .., p-1) which can be flipped. That is, either x1 is
the cause or x(1+j) is the cause in a chosen pair.
variables are not flipped. The printed output of this function
reports the results for p-1 pairs indicating which variable
(by name) causes which other variable (also by name).
It also prints the strength or signed summary strength index in
the range [-100,100].
A positive sign of the strength index means x1 kernel causes x(1+j),
whereas negative strength index means x(1+j) kernel causes x1. The function
also prints Pearson correlation and its p-value. This function also returns
a matrix of p-1 rows and 5 columns entitled:
“cause", “response", “strength", “corr." and “p-value", respectively
with self-explanatory titles. The first two columns have names of variables
x1 or x(1+j), depending on which is the cause. The ‘strength’ column
has an absolute value of the summary index in the range [0,100],
providing a summary of causal results
based on the preponderance of evidence from Cr1 to Cr3 from deciles, moments,
from four orders of stochastic dominance.
The order of input columns in "mtx" matters.
The fourth column, ‘corr.’, reports the Pearson correlation coefficient, while
the fifth column has the p-value for testing the null of zero Pearson coefficient.
This function calls
siPairsBlk, allowing for control variables.
The output of this function can be sent to ‘xtable’ for a nice Latex table.
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.
If Cr1 to Cr3 near-unanimously suggest ‘crim’ as the cause of ‘off’,
strength index would be near 100 suggesting unanimity.
Prof. H. D. Vinod, Economics Dept., Fordham University, NY.
Vinod, H. D. 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, doi: gffn86
Vinod, H. D. 'New exogeneity tests and causal paths,' Chapter 2 in 'Handbook of Statistics: Conceptual Econometrics Using R', Vol.32, co-editors: H. D. Vinod and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2019, pp. 33-64.
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
Vinod, Hrishikesh D., R Package GeneralCorr Functions for Portfolio Choice (November 11, 2021). Available at SSRN: https://ssrn.com/abstract=3961683
Vinod, Hrishikesh D., Stochastic Dominance Without Tears (January 26, 2021). Available at SSRN: https://ssrn.com/abstract=3773309
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