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The modelling procedure consists of three stages: Specification,Estimation and Evaluation. The package offers tools helping the users toconduct model specification tests, to do PSTR model estimation, and todo model evaluation.
The cluster-dependency and heteroskedasticity-consistent tests areimplemented in the package.
The wild bootstrap and cluster wild bootstrap tests are alsoimplemented.
Parallel computation (as an option) is implemented in some functions,especially the bootstrap tests. Therefore, the package suits tasksrunning many cores on super-computation servers.
How to install
You can either install the stable version from CRAN
install.packages("PSTR")
or install the development version from GitHub
devtools::install_github("yukai-yang/PSTR")
provided that the package “devtools” has been installed beforehand.
Example
After installing the package, you need to load (attach better say) it byrunning the code
library(PSTR)
You can first check the information and the current version number byrunning
version()#> PSTR version 1.3.0 (Yellow Panel)
Then you can take a look at all the available functions and data in thepackage
In the package, a data set called “Hansen99” is offered to give promptexample. For details of the data set, you can run
?Hansen99
Initialization
You can create a new object of the class PSTR by doing
pstr= NewPSTR(Hansen99,dep='inva',indep=4:20,indep_k=c('vala','debta','cfa','sales'),tvars=c('vala'),im=1,iT=14)print(pstr)#> #################################################################################> ## PSTR 1.3.0 (Yellow Panel)#> #################################################################################> ********************************************************************************#> Summary of the model:#> --------------------------------------------------------------------------------#> time horizon sample size = 14, number of individuals = 560#> --------------------------------------------------------------------------------#> Dependent variable: inva#> --------------------------------------------------------------------------------#> Explanatory variables in the linear part:#> dt_75 dt_76 dt_77 dt_78 dt_79 dt_80 dt_81 dt_82 dt_83 dt_84 dt_85 dt_86 dt_87 vala debta cfa sales#> --------------------------------------------------------------------------------#> Explanatory variables in the non-linear part:#> vala debta cfa sales#> --------------------------------------------------------------------------------#> Potential transition variable(s) to be tested:#> vala#> #################################################################################> ********************************************************************************#> Results of the linearity (homogeneity) tests:#> ********************************************************************************#> Sequence of homogeneity tests for selecting number of switches 'm':#> ********************************************************************************#> ################################################################################
It says that the data set “Hansen99” is used, the dependent variable is“inva”, the variables in the data from column 4 to 20 are theexplanatory variables in the linear part (though you can write down thenames of them), the explanatory variables in the nonlinear part are thefour ones in “indep_k”, and the potential transition variable is “vala”(Tobin’s Q).
Now you can see that the “NewPSTR” is basically defining the settings ofthe model.
Note that you can print the object of the class PSTR. By default, itgives you a summary of the PSTR model. They are mainly about which oneis the dependent variable, which ones are explanatory variables andetc..
Specification
The following code does linearity tests
pstr= LinTest(use=pstr) print(pstr,"tests")#> #################################################################################> ## PSTR 1.3.0 (Yellow Panel)#> #################################################################################> ********************************************************************************#> Results of the linearity (homogeneity) tests:#> --------------------------------------------------------------------------------#> LM tests based on transition variable 'vala'#> m LM_X PV LM_F PV HAC_X PV HAC_F PV#> 1 125.3 0 28.99 0 30.03 4.819e-06 6.952 1.396e-05#> ********************************************************************************#> Sequence of homogeneity tests for selecting number of switches 'm':#> --------------------------------------------------------------------------------#> LM tests based on transition variable 'vala'#> m LM_X PV LM_F PV HAC_X PV HAC_F PV#> 1 125.3 0 28.99 0 30.03 4.819e-06 6.952 1.396e-05#> ********************************************************************************#> ################################################################################
You can see that the function “LinTest” takes the PSTR object “pstr” andoverwrites it when return. This is the way I recommend as the functionshandling the PSTR object in the package update the object by adding newatrributes or members. However, the same function will change the valuesof the attributes it adds. You can of course create new PSTR objects totake the return values in order to save the results from differentsettings of the model.
You can do the wild bootstrap and wild cluster bootstrap by running thefollowing code. (Warning! Don’t run it except that you have at least 50cores!)
iB=5000# the number of repetitions in the bootstraplibrary(snowfall)pstr= WCB_LinTest(use=pstr,iB=iB,parallel=T,cpus=50)
It takes a long long time to run the bootstrap. This function isdeveloped for those who work on some super-computation server with manycores and a large memory. Note that you will have to attach the“snowfall” package manually.
But of course, you can try the function on your personal computer byreducing the number of repetitions and the cores.
By default, the “optim” method “L-BFGS-B” is used, but you can changethe method for estimation by doing
pstr= EstPSTR(use=pstr,im=1,iq=1,useDelta=T,par=c(-0.462,0),method="CG")print(pstr,"estimates")#> #################################################################################> ## PSTR 1.3.0 (Yellow Panel)#> #################################################################################> ********************************************************************************#> Results of the PSTR estimation:#> --------------------------------------------------------------------------------#> Transition variable 'vala' is used in the estimation.#> --------------------------------------------------------------------------------#> Parameter estimates in the linear part (first extreme regime) are#> dt_75_0 dt_76_0 dt_77_0 dt_78_0 dt_79_0 dt_80_0 dt_81_0#> Est -0.002827 -0.007512 -0.005812 0.0003951 0.002464 0.006085 0.0004164#> s.e. 0.002431 0.002577 0.002649 0.0027950 0.002708 0.002910 0.0029220#> dt_82_0 dt_83_0 dt_84_0 dt_85_0 dt_86_0 dt_87_0 vala_0#> Est -0.007802 -0.014410 -0.0009146 0.003467 -0.001591 -0.008606 0.11500#> s.e. 0.002609 0.002701 0.0030910 0.003232 0.003202 0.003133 0.04073#> debta_0 cfa_0 sales_0#> Est -0.03392 0.10980 0.002978#> s.e. 0.03319 0.04458 0.008221#> --------------------------------------------------------------------------------#> Parameter estimates in the non-linear part are#> vala_1 debta_1 cfa_1 sales_1#> Est -0.10370 0.02892 -0.08801 0.005945#> s.e. 0.03981 0.04891 0.05672 0.012140#> --------------------------------------------------------------------------------#> Parameter estimates in the second extreme regime are#> vala_{0+1} debta_{0+1} cfa_{0+1} sales_{0+1}#> Est 0.011300 -0.00500 0.02183 0.008923#> s.e. 0.001976 0.01739 0.01885 0.004957#> --------------------------------------------------------------------------------#> Non-linear parameter estimates are#> gamma c_1#> Est 0.6299 -0.0002008#> s.e. 0.1032 0.7252000#> --------------------------------------------------------------------------------#> Estimated standard deviation of the residuals is 0.04301#> ********************************************************************************#> ################################################################################
The argument “useDelta” determines the type of the initial value for thesmoothness parameter. By default “useDelta = F” means that the firstinitial value in “par” is the “gamma” instead of “delta”. Here we usethe settings “useDelta = T” and “par = c(1.6, .5)” means that the firstvalue of “par” is the “delta” and its value is 1.6. Note that “delta”and “gamma” has the relationship “gamma = exp(delta)”. Thus, thefollowing two sentences are equivalent
Note that in the “EvalTest”, only one transition variable is taken eachtime for the no remaining nonlinearity test. This is different from the“LinTest” function which can take several transition variables. This isthe reason why I save the results into new PSTR objects “pstr1” insteadof overwriting. By doing so, I can save more test results from differenttransition variables in new objects.
The user can also do the wild bootstrap and wild cluster bootstrap inthe following way, provided that he or she has the super-computationresources.
Note that the evaluation functions do not accept the returned object“pstr0” from a linear panel regression model, as the evaluation testsare designed for the estimated PSTR model but not a linear one.
Plotting
After estimating the PSTR model, you can plot the estimated transitionfunction by running
plot_transition(pstr)
or a better plot with more arguments
plot_transition(pstr,fill='blue',xlim=c(-2,20),color="dodgerblue4",size=2,alpha=.3)+ggplot2::geom_vline(ggplot2::aes(xintercept=pstr$c- log(1/0.95-1)/pstr$gamma),color='blue')+ggplot2::labs(x="customize the label for x axis",y="customize the label for y axis",title="The Title",subtitle="The subtitle",caption="Make a caption here.")
You can also plot the curves of the coefficients, the standard errorsand the p-values against the transition variable.
The plotting functionplot_response, which depicts the relationshipbetween which I called response, some explanatory variablexi**t and the transition variableqi**t inthe PSTR model.
The response[ϕ0+ϕ1gi**t(qi**t;γ,c)]xi**tis actually the contribution that the varabilexi**tmakes to the conditional expectation of the dependentyi**t through the smooth transition mechanism.
We can see that the response against the variable is a straight line ifthere is no nonlinearity. We can plot a surface if the variablexi**t and the transition variableqi**tare distinct, with z-axis the response, x- and y- axises the twovariables. And it becomes a curve if the variablexi**tand the transition variableqi**t are identical.
ret takes the return value of the function. We make the graphs for allthe four variables in nonlinear part by usingvars=1:4 (variable namescan also be used for specification). Note that we do not do it for thevariables in the linear part, as they produce straight lines or planes.log_scale is a 2-vector of booleans specifying, for each graph,whether the first (some variable in the nonlinear part) or the second(the transition variable) should be log scaled.length.out gives thenumber of points in the grid for producing the surface or curve. Alength.out of 100 points looks fine enough.
You may think of “what if I don’t wanna make all the variables logscaled?”. The solution is to make the graphs separately by runningsomething like
We see thatret is a list containing elements whose names are thevariables’ names that we specified when runningplot_response.
Yes, but they are now plottable objects in the sense that you can simplyplot them by running
ret$vala
The numbers on the x-axis look not so good as it is difficult to findwhere the turning-point is.
Theggplot2 package allows us to manually paint the numbers (the PSTRpackage collaborates very well with some prevailling packages), and eventhe label on x-axis (and many more).
Now we see very clearly that the turning-point approximately 0.5 cut thecurve into two regimes, and the two regimes behave so differently. Thisgraph is about the lagged Tobin’s Q’s contribution to the expectedinvestment. Low Q firms (whose potentials are evaluated to be low by thefinancial market) look rather reluctant to change their futureinvestment plan, or maybe get changed.
Then let us proceed to the surfaces. Check the response from the debtaby running
ret$debta
The graph is “living” and you can scracth on it by using your mouse.“vala_y” shows that the y-axis is the Q, and “debta_x” shows that thex-axis is the debt. The tool bar on up-right helps you to rotate, pan,zoom and save the graph.
Note that the transition variable Q is in log scale while debt is not.
It is very clear that low Q firms’ future investment will be affected bythe current debt situation. The more debt there is, the less investmentthere will be. However, it is not the case for high Q firms who has goodpotential and is not sensitive to the debt.
The following two living graphs are for the cash flow and the sales.
ret$cfa
ret$sales
About
an R package for testing, estimating and evaluating the Panel Smooth Transition Regression (PSTR) model.
