ardl: Stata module to estimate autoregressive distributed ...

1 IntroductionARDL modelBounds testingStata syntaxExampleConclusionardl: Stata module to estimateautoregressive distributed lag modelsSebastian Kripfganz1 Daniel C. Schneider21 University of Exeter Business School, Department of Economics, Exeter, UK2 Max Planck Institute for Demographic Research, Rostock, GermanyStata ConferenceChicago, July 29, 2016net install ardl, from( )S. Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models1/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionARDL: autoregressive distributed lag modelThe autoregressive distributed lag (ARDL)1model is beingused for decades to model the relationship between(economic) variables in a single-equation time-series popularity also stems from the fact that cointegration ofnonstationary variables is equivalent to an error-correction(EC) process, and the ARDL model has a reparameterizationin EC form(Engle and Granger, 1987; Hassler and Wolters, 2006).

2 The existence of a long-run / cointegrating relationship canbe tested based on the EC representation. A bounds testingprocedure is available to draw conclusive inference withoutknowing whether the variables are integrated of order zero orone,I(0) orI(1), respectively(Pesaran, Shin, and Smith, 2001).1 Another commonly used abbreviation is Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models2/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionARDL: autoregressive distributed lag modelLong-run relationship: Some time series are bound togetherdue to equilibrium forces even though the individual timeseries might move Wage (log)Labor Productivity (log)Data source: Pesaran, Shin, and Smith (2001).

3 S. Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models3/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionARDL: autoregressive distributed lag modelThe first public version of theardlcommand for theestimation of ARDL / EC models and the bounds testingprocedure in Stata has been released on August 4, indications for the popularity of the ARDL model:Google Scholar returns about 13,200 results when searching for autoregressive distributed lag , and more than 5,200 citationsfor the bounds testing paper by Pesaran, Shin, and Smith(2001).A sequence of blog posts by David Giles on ARDL modelestimation attracted more than 500 discussion topic on theardlcommand is ranked secondon Statalist in terms of replies (>100) and views (>20,000).

4 2 There are already at least 2 independent video tutorialsavailable on the web dealing with theardlcommand for Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models4/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionEstimating long-run relationshipsEngle and Granger (1987) two-step approach for testing theexistence of a long-run relationship:Assumption: (yt,xt) is a vector ofI(1) an OLS regression for the model in levels:yt=b0+ xt+vt,and test whether the residuals vt=yt b0 xtarestationary ( with a Dickey-Fuller test).2 estimate an EC model with the lagged residuals from the firststep included as EC term (provided they are stationary): yt=c0+ vt 1+p 1 i=1 yi yt i+q 1 i=0 xi xt i+ut,and test whether 1 < moduleegrangerby Mark E.

5 Schaffer (2010) on Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models5/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionEstimating long-run relationshipsDisadvantages of the Engle and Granger (1987) approach:The order of integration of the variables needs to bedetermined estimation of the static levels model may create bias infinite samples due to the omitted short-run dynamics(Banerjee,Dolado, Hendry, and Smith, 1986).The bias from the first step transmits to poor asymptotic distribution of the OLS estimator for thelong-run parameters is non-normal, invalidating standardinference based on pretesting problems: misclassification of variables asI(0) orI(1); false positives and false negatives at the first and Hansen (1990) proposed the fully-modified OLSestimator to overcome some of these Kripfganz and D.

6 C. Schneiderardl: Stata module to estimate autoregressive distributed lag models6/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionEstimating long-run relationshipsPesaran and Shin (1998) suggest to obtain the long-runparameters from an ARDL model:OLS estimators of the short-run parameters are T-consistentand asymptotically corresponding estimators of the long-run parameters aresuper-consistent if the regressors areI(1), and asymptoticallynormally distributed irrespective of the order of procedure for testing the existence of a long-runrelationship based on the EC representation of the ARDL model:Pesaran, Shin, and Smith (2001) tabulate asymptotic criticalvalues that span a band from all regressors being purelyI(0) toall regressors being purelyI(1).

7 Narayan (2005) computes corresponding small-sample criticalvalues for various sample Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models7/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionARDL modelARDL(p,q,..,q) model:yt=c0+c1t+p i=1 iyt i+q i=0 ixt i+ut,t= max(p,q),..,T, for simplicity assuming that the lagorderqis the same for all variables in theK 1 variables in (yt,x t) are allowed to be purelyI(0), purelyI(1), or optimal lag orderspandq(possibly different acrossregressors) can be obtained my minimizing a model selectioncriterion, the Akaike information criterion (AIC) or theBayesian information criterion (BIC).

8 43 For a full set of assumptions see Pesaran, Shin, and Smith (2001).4 The BIC is also known as the Schwarz or Schwarz-Bayesian information Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models8/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionEC representationReparameterization in conditional EC form: yt=c0+c1t (yt 1 xt 1)+p 1 i=1 yi yt i+ xt+q 1 i=1 xi xt i+ut,with the speed-of-adjustment coefficient = 1 pj=1 iandthe long-run coefficients = qj=0 j .Alternative EC parameterization: yt=c0+c1t (yt 1 xt)+p 1 i=1 yi yt i+q 1 i=0 xi xt i+ Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models9/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionTesting the existence of a long-run relationshipPesaran, Shin, and Smith (2001) approach:1 Decide about the inclusion of deterministic model componentsand obtain the optimal lag orderspandqbased on a suitablemodel selection criterion, AIC or BIC.

9 (When in doubt,choose higher lag orders for testing purposes.)2 estimate the chosen ARDL(p,q,..,q) model by theF-statistic for the joint null hypothesisHF0: ( = 0) ( qj=0 j=0)and compare it to the rejected, compute thet-statistic for the single nullhypothesisHt0: = 0 and compare it to the critical re- estimate a parsimonious version of the ARDL /EC Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models10/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionTesting the existence of a long-run relationshipPesaran, Shin, and Smith (2001) provide lower and upperbounds for the asymptotic critical values depending on thenumber of regressors, their order of integration, and thedeterministic model components:1No intercept, no time intercept, no time intercept, no time intercept, restricted time intercept, unrestricted time decisions.

10 Do not rejectHF0orHt0, respectively, if the test statistic iscloser to zero than the lower bound of the critical theHF0orHt0, respectively, if the test statistic is moreextreme than the upper bound of the critical existence of a (conditional) long-run relationship isconfirmed if bothHF0andHt0are Kripfganz and D. C. Schneiderardl: Stata module to estimate autoregressive distributed lag models11/20 IntroductionARDL modelBounds testingStata syntaxExampleConclusionStata syntax of theardlcommandSyntax:ardldepvar [indepvars] [if] [in] [, options]Selected options:lags(numlist): set lag lengths,maxlags(numlist): set maximum lag lengths,ec: display output in error-correction form,ec1: like optionec, but level variables int 1 instead oft,aic: use AIC as information criterion instead of BIC,exog(varlist): exogenous variables in the regression,noconstant: suppress constant term,trendvar(varname): specify trend variable,restricted.