silentPairs function

No-print kernel causality scores with control variables Hausman-Wu Criterion 1

Allowing input matrix of control variables and missing data, this function produces a 3 column matrix summarizing the results where the estimated signs of stochastic dominance order values (+1, 0, -1) are weighted by wt=c(1.2,1.1, 1.05, 1) to compute an overall result for all orders of stochastic dominance by a weighted sum for the criteria Cr1 and Cr2 and added to the Cr3 estimate as: (+1, 0, -1), always in the range [--3.175, 3.175].

silentPairs(mtx, ctrl = 0, dig = 6, wt = c(1.2, 1.1, 1.05, 1), sumwt = 4)

Arguments

• mtx: 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 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 ctrl=0 which means that there are no control variables used.
• dig: 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

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 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.

Details

The reason for slightly declining weights on the signs from SD1 to SD4 is simply that the local mean comparisons implicit in SD1 are known to be more reliable than local variance implicit in SD2, local skewness implicit in SD3 and local kurtosis implicit in SD4. The source of slightly declining sampling unreliability of higher moments is the higher power of the deviations from the mean needed in their computations. The summary results for all three criteria are reported in a vector of numbers internally called crall:

Note

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. The command attach(EuroCrime); silentPairs(cbind(crim,off))

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.

Examples

## Not run:

options(np.messages=FALSE)
colnames(mtcars[2:ncol(mtcars)])
silentPairs(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[4]=NA;y2=y;y2[8]=NA;w2=w;w2[4]=NA
silentPairs(mtx=cbind(x2,y2), ctrl=cbind(z,w2))

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 bootPairs, silentMtx

See someCPairs, some0Pairs

Author(s)

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