generalCorr (version 1.2.6)

causeSum2Panel: Kernel regressions based causal paths in Panel Data.

Description

The algorithm of this function uses an internal function fminmax=function(x)min(x)==max(x). The subsets mtx2 of the original data da for a specific time or space can become degenerate if the columns of mtx2 have no variability. The apply function of R is applied to the columns of mtx2 as follows. "ap1=apply(mtx2,2,fminmax)." Now, "sumap1=sum(ap1)" counts how many columns of the data matrix are degenerate. We have a degeneracy problem only if sumap1 is >1 or =1. For example, the panel consists of data on 50 United States and 20 years. Now, consumer price index (cpi) data may be common for all states. That is, the min(cpi) equals max(cpi) for all states. Then, the variance of cpi is zero, and we have degeneracy. When this happens, the regressor cpi should not be involved in determining causal paths. We identify degeneracy using "fminmax=function(x)min(x)==max(x)"

Usage

causeSum2Panel(
  da,
  fn = causeSummary2NoP,
  rowfnout,
  colfnout,
  fnoutNames,
  namXs,
  namXt,
  namXy,
  namXc = 0,
  namXjmtx,
  chosenTimes = NULL,
  chosenSpaces = NULL,
  ylag = 0,
  verbo = FALSE
)

Value

The causeSum2Panel(.) produces many output matrices and vectors. The first "outt" gives a 3-dimensional array of panel causal path output focused on time series for each space value using fixed space value. It reports causal path directions, and strengths for (y, xj) pairs. The second output array, called "outs", gives similar 3D panel causal path output focused on space cross sections using fixed time value. The third output matrix called "outdif" gives causal paths using Granger causality for each pair (y, xj). They are not causal strengths but differences between Rsquare values of two flipped kernel regressions. The summary of Granger causality answer is an output matrix called grangerAns (first row average of differences in R-squares and second row has its test statistic with degrees of freedom n-1), and grangerStat for related t-statistic for formal inference. based on column means and variances of "outdif". This function also produces a matrix summarizing "outt" and "outs" into two-dimensional matrices reporting averages of signed strengths as "strentime" and "strenspace", Also, "pearsontime" reports the Pearson correlation coefficients for various time values and their average in the last column. It determines the overall direction of the causal relation between y and xj. For example, a negative average correlation means y and xj are negatively correlated (xj goes up, y goes down). Similarly, "pearsonspace" summarizes "outs" correlations.

Arguments

da

panel dat having a named column for space and time

fn

an R function causeSummary2NoP(mtx)

rowfnout

the number of rows output by fn

colfnout

the number of columns output by fn

fnoutNames

the column names of output by fn, for example, fnoutNames=c("cause","effect","strength","r","p-val")

namXs

title of the column in da having the space variable

namXt

title of the column in da having the time variable

namXy

title of the column in da having the dependent y variable

namXc

title(s) of the column(s) in da having control variable(s), default=0 means none specified

namXjmtx

title(s) of the column(s) in da having regressor(s)

chosenTimes

subset of values of time variable chosen for quick results, There are NchosenTimes values chosen in the subset. default=NULL means all time identifiers in the data are included.

chosenSpaces

subset of values of space variable chosen for quick results, There are NchosenSpaces values chosen in the subset. default=NULL means all space identifiers are included. The degrees of freedom for Studentized statistic for Granger causality tests are df=(NchosenSpaces -1).

ylag

time lag in Granger causality study of time dimension the default ylag=0 is not really zero. It means ylag= min(4, round(NchosenTimes/5,0)), where NchosenTimes is the length of chosenTimes vector

verbo

print detail results along the way, default=FALSE

Author

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

Details

We assume that panel data have space (space=individual region) and time (e.g., year) dimensions. We use upper case X to denote a common prefix in the panel data. Xs =name of the space variable, e.g., state or individual. The range of values for s is 1 to nspace. Xt =name of the time variable, e.g., year. The range of values for t is 1 to ntime. Xy =the dependent variable(s) value at time t in state s. Since panel data causal analysis can take a long computer time, we allow the user to choose subsets of time and space values called chosenTimes and chosenSpaces, respectively. Various input parameters starting with "nam" specify the names of variables in the panel study.

The algorithm calls some function fn(mtx) where mtx is the data matrix, and fn is causeSummary2NoP(mtx). The causal paths between (y, xj) pairs of variables in mtx are computed following 3 sophisticated criteria involving exact stochastic dominance. Type "?causeSummary2" on the R console to get details (omitted here for brevity). Panel data consist of a time series of cross-sections and are also called longitudinal data. We provide estimates of causal path directions and strengths for both the time-series and cross-sectional views of panel data. Since our regressions are kernel type with no functional forms, fixed effects for time and space are being suppressed when computing the causality.

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

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

See Also

See causeSummary2

See causeSummary is subject to trapezoidal approximation.

Examples

if (FALSE) {
library(plm);data(Grunfeld)
options(np.messages=FALSE)
namXs="firm"
print("initial values identifying the space variable")
head(da[,namXs],3)
print(str(da[,namXs]))
chosenSpaces=(3:10)                        
if(is.numeric(da[,namXs])){
  chosenSpaces=as.numeric(chosenSpaces)}
if(!is.numeric(da[,namXs])){
  chosenSpaces=as.character(chosenSpaces)}

namXt="year"
print("initial values identifying the time variable")
head(da[,namXt],3)
print(str(da[,namXt]))
chosenTimes=1940:1949
if(is.numeric(da[,namXt])){
  chosenTimes=as.numeric(chosenTimes)}
if(!is.numeric(da[,namXt])){
  chosenTimes=as.character(chosenTimes)}

namXy="inv"
namXc=0
namXjmtx=c("value","capital")
p=length(namXjmtx)
fn=causeSummary2NoP
fnout=matrix(NA,nrow=p,ncol=5)
fnoutNames=c("cause","effect","strength","r","p-val")
causeSum2Panel(da, fn=causeSummary2NoP,
               rowfnout=p, colfnout=5, 
               fnoutNames=c("cause","effect","strength","r","p-val"),
               namXs=namXs,
               namXt=namXt,
               namXy=namXy,
               namXc=namXc,
               namXjmtx=namXjmtx,
               chosenTimes=chosenTimes,
               chosenSpaces=chosenSpaces,
               verbo=FALSE)
}