causeSum2Panel: Kernel regressions based causal paths in Panel Data.

In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

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
)

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

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.

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.

Note

The function prints to the screen some summaries of the three output matrices. It reports how often a variable is a cause in various pairs as time series or as cross sections. It also reports the average strengths of causal paths for "outt" and "outs" matrices. We compute the difference between two R-square values to find which causal direction is more plausible. This involves kernel regressions of y on its own lags and lags of a regressor. Unlike the usual Granger causality we estimate better-fitting nonlinear kernel regressions. If the averages in "outdif" matrix are negative, the Granger causal paths go from y to xj. This may be unexpected when the model assumes that y depends on x1 to xp, that is, the causal paths go from xj to y. In studying the causal pairs, the function creates mixtures of names y and xj. Character vectors containing the mixed names are are column names or row names depending on the context. For example, the output matrix grangerAns column names help identify the relevant regressor name. The first row of the grangerAns matrix has column averages of outdiff matrix to help get an overall estimate of the Granger-causal paths. The second row of the grangerAns has the Studentized test statistic for formal testing of the significance of Granger causal paths. Collecting the results for the time dimension strengths with suitable sign (negative strength means cause reversal xj->y) is output named strentime. The corresponding Pearson correlations as an output is named pearsontime. Collecting the results for the space dimension strengths with suitable sign (negative strength means cause reversal xj->y) is output named strenspace. The corresponding Pearson correlations are named pearsonspace. A grand summary of average strengths and correlations is output matrix named grandsum. It is intended to provide an overall picture of causal paths in Panel data. These paths should not be confused with Granger causal paths which always involve time lags and causes are presumed to precede effects in time.

Author(s)

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

References

Vinod, H. D. 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, \Sexpr[results=rd]{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

## Not run: 
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)

## End(Not run)

generalCorr documentation built on Oct. 10, 2023, 1:06 a.m.