causeSummBlk function

Block Version 2: Kernel causality summary of causal paths from three criteria

A block version of causeSummary() chooses new bandwidth for every ten (blksiz=10) observations chosen by the `np' package injecting flexibility. 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. The output table is a 5-column matrix identifying the names of variables, causal path directions, and path strengths re-scaled to be in the range [--100, 100], (table reports absolute values of the strength) plus Pearson correlation coefficient and its p-value.

causeSummBlk(
  mtx,
  nam = colnames(mtx),
  blksiz = 10,
  ctrl = 0,
  dig = 6,
  wt = c(1.2, 1.1, 1.05, 1),
  sumwt = 4
)

Arguments

• mtx: 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 the purpose of flipping.
• nam: vector of column names for mtx. Default: colnames(mtx)
• blksiz: block size, default=10, if chosen blksiz >n, where n=rows in the matrix then blksiz=n. That is, no blocking is done
• ctrl: data matrix for designated control variable(s) outside causal paths
• dig: The number of digits for reporting (default dig=6).
• wt: Allows user to choose a vector of four alternative weights for SD1 to SD4.
• sumwt: Sum of weights can be changed here =4(default).

Returns

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 a strength, or signed summary strength index forced to be in the range [-100,100] for easy interpretation. 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 the absolute value of a summary index in the range [0,100], providing a summary of causal results based on the preponderance of evidence from Cr1 to Cr3 from four orders of stochastic dominance, etc. The order of input columns matters. The fourth column of the output matrix entitled corr.' reports the Pearson correlation coefficient, while the fifth column of the output matrix has the p-value for testing the null hypothesis of a 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.

Details

The algorithm determines causal path directions from the sign of the strength index. The strength index magnitudes are computed by comparing three aspects of flipped kernel regressions: [x1 on (x2, x3, .. xp)] and its flipped version [x2 on (x1, x3, .. xp)]. The cause should be on the right-hand side of the regression equation. The properties of regression fit determine which flip is superior. We compare (Cr1) formal exogeneity test criterion, (residuals times RHS regressor, where smaller in absolute value is better) (Cr2) absolute values of residuals, where smaller in absolute value is better, and (Cr3) R-squares of the flipped regressions implying three criteria Cr1, to Cr3. The criteria are quantified by sophisticated methods using four orders of stochastic dominance, SD1 to SD4. We assume slightly declining weights on the sign observed by Cr1 to Cr3. The user can change default weights.

Note

The European Crime data has all three criteria correctly suggesting that a high crime rate kernel causes the deployment of a large number of police officers. Since Cr1 to Cr3 near-unanimously suggest crim' as the cause of off', a strength index of 100 suggests unanimity. attach(EuroCrime); causeSummBlk(cbind(crim,off))

Examples

## Not run:

mtx=as.matrix(mtcars[,1:3])
ctrl=as.matrix(mtcars[,4:5])
 causeSummBlk(mtx,ctrl,nam=colnames(mtx))
## 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[4]=NA;y2=y;y2[8]=NA;w2=w;w2[4]=NA
causeSummBlk(mtx=cbind(x2,y2), ctrl=cbind(z,w2))

References

Vinod, H. D. `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. '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

See Also

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

See someCPairs

siPairsBlk, causeSummary

Author(s)

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