causeSum2Blk: Block Version 2: Kernel causality summary of causal paths...

Description Usage Arguments Value Note Author(s) References See Also Examples

View source: R/causeSum2Blk.R


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 causeSummary2(). 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.


causeSum2Blk(mtx, nam = colnames(mtx), blksiz = 10, ctrl = 0, dig = 6)



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 mtx. Default: colnames(mtx)


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 dig=6).


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. The control 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. attach(EuroCrime); causeSum2Blk(cbind(crim,off))


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:

Vinod, Hrishikesh D., R Package GeneralCorr Functions for Portfolio Choice (November 11, 2021). Available at SSRN:

Vinod, Hrishikesh D., Stochastic Dominance Without Tears (January 26, 2021). Available at SSRN:

See Also

See bootPairs, causeSummary has an older version of this function.

See someCPairs

siPair2Blk, causeSummary2


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generalCorr documentation built on Jan. 4, 2022, 1:08 a.m.