{smcl} {* *! version 1.0.6 06feb2023}{...} {title:Title} {phang} {bf:ardlbounds} {hline 2} tabulate critical values for ARDL bounds test {* foldend}{* foldbeg}{* * * SYNTAX * * *}{marker syntax}{...} {title:Syntax} {phang} Standard behavior {p 8 17 2} {cmd:ardlbounds} {cmd:,} {opt c:ase(#)} [ {opt s:tat(stattype)} {opt n(#)} {opt k(#)} {opt sr(#)} {opt sig:levels(levellist)} {opt pv:alue(statval)} ] {phang} Tabular presentation over the number of weakly exogenous model variables {it:k} {p 8 17 2} {cmd:ardlbounds} {cmd:,} {opt tab:le} {opt c:ase(#)} [ {opt s:tat(stattype)} {opt n(#)} {opt kmax(#)} {opt la:gs(#)} ] {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab: } {synopt:{opt c:ase(#)}}show CVs for {help ardl##deterministiccomponents:model deterministics case} {it:case}{p_end} {synopt:{opt s:tat(stattype)}}show CVs for statistic {it:stattype}; {it:stattype} is either 't' or 'F'{p_end} {synopt:{opt n(#)}}show CVs for sample size {it:n}; default: display asymptotic CVs{p_end} {synopt:{opt k(#)}}show results for {it:k} weakly exogenous model variables; default: {it:k}=0{p_end} {synopt:{opt sr(#)}}specify number of short-run coefficients; default: {it:sr}=0{p_end} {synopt:{opth sig:levels(numlist)}}show CVs for levels in {it:levelslist}; default: '10 5 1'.{p_end} {synopt:{opt pv:alue(statval)}}show p-value for value {it:statval} of the {it:stattype}-statistic{p_end} {synopt:{opt tab:le}}build table over weakly exogenous model variables{p_end} {synopt:{opt kmax(#)}}tabulate up to {it:kmax} weakly exogenous model variables{p_end} {synopt:{opt la:gs(#)}}show results for {it:lags} lags for all levels regressors in the model{p_end} {synoptline} {p2colreset}{...} {p 4 6 2}See {help ardl} for more information about ARDL estimation.{p_end} {* foldend}{* foldbeg}{* * * DESCRIPTION * * *}{marker description}{...} {title:Description} {pstd} {cmd:ardlbounds} displays critical values and approximate p-values for the bounds test for a level relationship based on the response surface regressions of {help ardl##KS2020:Kripfganz and Schneider (2020)}. As with many other test statistics in the analysis of non-stationary times series, these magnitudes are somewhat difficult to obtain since they relate to non-standard distributions. {pstd} Regression-based predicted critical values and approximate p-values can be obtained for any combination of values of the sample size, the number of weakly exogenous model variables, and the model lag structure. {pstd} The response surface regression methodology as used by {cmd:ardlbounds} was mainly developed by {help ardl##M1991:MacKinnon (1991)} and {help ardl##M1996:MacKinnon (1996)}. {* foldend}{* foldbeg}{* * * ABBREVIATIONS * * *}{marker abbreviations}{...} {title:Abbreviations and definitions used in this help entry} {pstd} See the {help ardl##abbreviations:abbreviations section of ardl}. {* foldend}{* foldbeg}{* * * OPTIONS * * *}{marker options}{...} {title:Options} {phang} {opt c:ase(#)} determines a particular {help ardl##deterministiccomponents:specification of model deterministics}. CVs differ across model deterministics cases. {phang} {opt s:tat(stattype)} determines one of two possible statistics to be checked. {it:stattype} must be either 't' or 'F', with 'F' being the default. The option is not case-sensitive. {phang} {opt n(#)} show CVs for the effective sample size {it:n}, i.e. the total number of observations minus the number of observations used up for lags. This magnitude is reported by {help ardl} in {bf:e(N)}. If the option is omitted, asymptotic CVs are displayed. {phang} {opt k(#)} show results for {it:k} weakly exogenous model variables. CVs differ across {it:k}. {marker options_sr}{...} {phang} {opt sr(#)} specifies the number of short-run coefficients. For an ARDL(p,q_1,...,q_k) model, {phang3}{it:sr} = max(0,p-1) + q_1 + ... + q_k {pmore} The number of short-run coefficients matters only for finite samples. This option is therefore ignored if {it:n} is not specified. {phang} {opt sig:levels(numlist)} shows CVs for levels in the {it:siglevels} {help numlist}, which must have at least one element and must be supplied in descending order. The default numlist is '10 5 1'. Levels are specified as percentiles but do allow for two digits after the decimal point. There are 221 different levels among which you can choose, indicated by the Stata numlist{...} {pmore2}{...} 00.01 00.02 00.05 00.10(00.10)00.90 01.00(00.50)98.50 99.00(00.10)99.90 99.95 99.98 99.99 {phang} {opt pv:alue(statval)} shows the (approximate) I(0)/I(1) p-values for value {it:statval} of the statistic. {pmore} Since the calculation of approximate p-values may fail to give sensible results for values of {it:statval} that are outside the range of the critical values for percentile levels 00.01-99.99, we set p-values to 0 or 1 in these cases. Therefore, in the returned matrix {bf:r(cvmat)}, a p-value exactly equal to 0 (1) should be interpreted as <0.0001 (>0.9999), which is unlikely to ever matter in practice. The calculation of approximate p-values follows {help ardl##M1996:MacKinnon (1996)}; see {help ardl##KS2020:Kripfganz and Schneider (2020)} for details. {phang} {opt tab:le} displays an expanded CV table over increasing numbers of weakly exogenous model variables. This options exists mainly to facilitate comparisons to the CVs tabulated in {help ardl##PSS2001:Pesaran, Shin, and Smith (2001)} and {help ardl##N2005:Narayan (2005)}, who provide non-regression-based, simulation design-specific critical value tabulations. {phang} Options {opt kmax} and {opt lags()} can only be used in conjunction with option {opt table}. {phang2} {opt kmax(#)} specifies that the tabulation of CVs ranges from zero up to {it:kmax} weakly exogenous model variables. {phang2} {opt la:gs(#)} show results for {it:lags} lags for all levels regressors in the model. {cmd:ardlbounds} calculates CVs according to the number of implied short-run coefficients for each level of {it:k}. For example, ARDL(3,3) and ARDL(3,3,3) models have 5 and 8 short-run coefficients, respectively. See option {opt sr()} above. The number of lags (short-run coefficients) matters only for finite samples. {* foldend}{* foldbeg}{* * * EXAMPLES * * *}{marker examples}{...} {title:Examples} {phang} We check {cmd:ardlbounds} against a few, randomly chosen numbers from the empirical example of {help ardl##PSS2001:PSS}. They report the following (p.311/312):{p_end} {pmore}I0/I1 5% level bounds of (3.05, 3.97) for : case 4, k=4, lags=4, n=1000{p_end}{...} {pmore}I0/I1 5% level bounds of (3.47, 4.57) for : case 5, k=4, lags=4, n=1000{p_end}{...} {pmore}I0/I1 5% level bounds of (3.19, 4.16) for : case 4, k=4, lags=4, n= 104{p_end}{...} {pmore}I0/I1 5% level bounds of (3.61, 4.76) for : case 5, k=4, lags=4, n= 104{p_end} {pmore} We compare this to the magnitudes returned by {cmd:ardlbounds}. Moreover, we supply the value of the F-statistic in question, 2.99, to get an approximate p-value as an additional piece of information. Note that the assumption of 4 lags per variable implies 3 + 4*4 = 19 short-run coefficients (see option {help ardlbounds##options_sr:sr()} above). {phang2}{stata ardlbounds , c(4) k(4) sr(19) n(1000) pval(2.99):. ardlbounds , c(4) k(4) sr(19) n(1000) pval(2.99)}{p_end} {phang2}{stata ardlbounds , c(5) k(4) sr(19) n(1000) pval(2.99):. ardlbounds , c(5) k(4) sr(19) n(1000) pval(2.99)}{p_end} {phang2}{stata ardlbounds , c(4) k(4) sr(19) n(104) pval(2.99):. ardlbounds , c(4) k(4) sr(19) n(104) pval(2.99)}{p_end} {phang2}{stata ardlbounds , c(5) k(4) sr(19) n(104) pval(2.99):. ardlbounds , c(5) k(4) sr(19) n(104) pval(2.99)}{p_end} {* gives:}{...} {* (3.05, 3.96) }{...} {* (3.48, 4.57) }{...} {* (3.04, 4.19) }{...} {* (3.45, 4.80) }{...} {pmore} While the numbers for the large sample (n=1000) are very close, some small differences arise for the small sample numbers (n=104). This, however, should mostly be unrelated to simulation or methodological differences, but to the fact that {cmd:ardlbounds} takes into account the number of short run regressors, which the simulations of PSS do not. Asymptotically, this does not matter, which is why the results for n=1000 are close. To confirm this, we re-run {cmd:ardlbounds}, setting the number of short-run coefficients to zero (the default): {phang2}{stata ardlbounds , c(4) k(4) n(104) pval(2.99):. ardlbounds , c(4) k(4) n(104) pval(2.99)}{p_end} {phang2}{stata ardlbounds , c(5) k(4) n(104) pval(2.99):. ardlbounds , c(5) k(4) n(104) pval(2.99)}{p_end} {* gives:}{...} {* 3.19, 4.13) }{...} {* 3.62, 4.75) }{...} {pmore} The resulting numbers are again fairly close to what PSS report. {* foldend}{* foldbeg}{* * * STOREDRESULTS * * *}{marker storedresults}{...} {title:Saved results} {pstd} {cmd:ardlbounds} saves the following in {cmd:r()}: {synoptset 20 tabbed}{...} {syntab:Scalars} {synopt:{cmd:r(k)}}# of weakly exogenous model variables{p_end} {synopt:{cmd:r(case)}}model deterministics case used for tabulation{p_end} {synopt:}{p_end} {synopt:if option {opt n()} was used:}{p_end} {synopt:{cmd:r(N)}}sample size used for tabulation{p_end} {synopt:{cmd:r(sr)}}# of short-run coefficients in the model{p_end} {syntab:Macros} {synopt:{cmd:r(stat)}}'t' or 'F'{p_end} {synopt:{cmd:r(siglevels)}}levels of critical values tabulated{p_end} {syntab:Matrices} {synopt:{cmd:r(cvmat)}}matrix of critical values; also contains approximate p-values if option {opt pvalue()} was used{p_end} {p2colreset}{...} {* foldend}{* foldbeg}{* * * AUTHORS * * *}{marker authors}{...} {title:Authors} {pstd} Sebastian Kripfganz, University of Exeter Business School, S.Kripfganz@exeter.ac.uk {pstd} Daniel C. Schneider, Max Planck Institute for Demographic Research, schneider@demogr.mpg.de {* foldend}{* foldbeg}{* * * ALSOSEE * * *}{marker alsosee}{...} {title:Also see} {psee} Other commands of the {cmd:ardl} package: {help ardl} {* foldend}