{smcl} {* *! version 1 24mar2017}{...} {cmd:help adfmaxur}{right: ({browse "http://www.stata-journal.com/article.html?article=st0511":SJ18-1: st0511})} {hline} {title:Title} {p2colset 5 17 19 2}{...} {p2col :{hi:adfmaxur} {hline 2}}Calculate Leybourne (1995) ADFmax unit-root test statistic along with finite-sample critical values and associated p-values{p_end} {p2colreset}{...} {title:Syntax} {p 8 16 2} {cmd:adfmaxur} {varname} {ifin} [{cmd:,} {cmd:noprint} {cmdab:maxl:ag(}{it:integer}{cmd:)} {cmdab:trend}] {p 4 6 2} The {cmd:by} prefix is not allowed. The routine can be applied to a single unit of a panel.{p_end} {p 4 6 2} Before using {opt adfmaxur}, you must {opt tsset} your data; see {manhelp tsset TS}.{p_end} {p 4 6 2} {it:varname} may contain time-series operators; see {help tsvarlist}.{p_end} {p 4 6 2} Sample may not contain gaps.{p_end} {title:Description} {pstd} {cmd:adfmaxur} computes Leybourne (1995) ADFmax unit-root tests against the alternative of stationarity. The command accommodates {varname} with nonzero mean and nonzero trend. It also allows for the lag length to be either fixed ({cmd:FIXED}) or determined endogenously using information criteria such as Akaike and Schwarz, denoted {cmd:AIC} and {cmd:SIC}, respectively. A data-dependent procedure often known as the general-to-specific (GTS) algorithm is also permitted, using significance levels of 5 and 10%, denoted {cmd:GTS05} and {cmd:GTS10}, respectively; see, for example, Hall (1994). Approximate p-values are also calculated. {pstd} Both the finite-sample critical values and the p-value are estimated based on an extensive set of Monte Carlo simulations, summarized by means of response surface regressions; for more details, see Otero and Smith (2012). {title:Options} {phang} {opt noprint} specifies that the results be returned but not printed. {phang} {opt maxlag(integer)} sets the number of lags to be included in the test regression to account for residual serial correlation. By default, {hi:adfmaxur} sets the number of lags following Schwert (1989) with the formula {cmd:maxlag()}=int{12*(T/100)^0.25}, where T is the total number of observations. In either case, the number of lags appears in the row labeled {cmd:FIXED} of the output table. {phang} {opt trend} specifies the modeling of intercepts and trends. By default, {cmd:adfmaxur} assumes {varname} is a nonzero mean stochastic process, so a constant is included in the test regression. If, on the other hand, the {cmd:trend} option is specified, {it:varname} is assumed to be a nonzero trend stochastic process, in which case a constant and a trend are included in the test regression. {title:Examples} {pstd} We begin by using the data and verifying that they have a time-series format. If needed, install bcuse from the SSC Archive.{p_end} {phang2}{bf:. {stata "bcuse usurates":bcuse usurates}}{p_end} {phang2}{bf:. {stata "tsset date":tsset date}}{p_end} {pstd} We would like to test whether the unemployment rate in each state contains a unit root against the alternative that it is a stationary process. For practical purposes, visual inspection of the time plot of the variable of interest often provides useful guidelines as to whether a linear trend term should be included in the test regressions. For our purposes, given that each unemployment series has a nonzero mean, but not trending behavior, the relevant test regression includes constant but not trend, which is the default option for {cmd:adfmaxur} {pstd} Setting a {opt maxlag} of p=12, the application of {cmd:adfmaxur} to the unemployment rate in the state of, say, Alabama, denoted ALUR, is implemented as follows: {phang2}{bf:. {stata "adfmaxur ALUR, maxlag(12)":adfmaxur ALUR, maxlag(12)}}{p_end} {pstd} This second illustration is the same as above but uses a subsample of the data that starts in the first month of 2000:{p_end} {phang2}{bf:. {stata "adfmaxur ALUR if tin(2000m1,), maxlag(12)":adfmaxur ALUR if tin(2000m1,), maxlag(12)}}{p_end} {pstd} We can perform the ADFmax test using all the available observations but with the number of lags determined based on Schwert's formula:{p_end} {phang2}{bf:. {stata adfmaxur ALUR:adfmaxur ALUR}}{p_end} {pstd}Finally, we can also work with a long form of the data, in which a single variable UR contains all states' unemployment rates, and the sample is restricted to one state: {pstd}First, rename the variables so that they are in a suitable format to apply the command {cmd:reshape}; see {manhelp reshape D}: {phang2}{bf:. {stata "rename *UR UR*":rename *UR UR*}}{p_end} {phang2}{bf:. {stata "reshape long UR, i(date) j(state) string":reshape long UR, i(date) j(state) string}}{p_end} {pstd}Next, {opt encode} the state variable, and declare the dataset as a panel using {opt xtset}; see {manhelp encode D} and {manhelp xtset XT}, respectively: {phang2}{bf:. {stata "encode state, gen(stcode)":encode state, gen(stcode)}}{p_end} {phang2}{bf:. {stata "xtset stcode date":xtset stcode date}}{p_end} {pstd}Lastly, apply the command{p_end} {phang2}{bf:. {stata "adfmaxur UR if stcode==1, maxlag(12)":adfmaxur UR if stcode==1, maxlag(12)}}{p_end} {title:Stored results} {pstd} {cmd:adfmaxur} stores the following in {cmd:r()}: {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Scalars}{p_end} {synopt:{cmd:r(N)}}number of observations in the test regression{p_end} {synopt:{cmd:r(minp)}}first period used in the test regression{p_end} {synopt:{cmd:r(maxp)}}last period used in the test regression{p_end} {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Macros}{p_end} {synopt:{cmd:r(varname)}}variable name{p_end} {synopt:{cmd:r(treat)}}either {cmd:constant} or {cmd:constant and trend}{p_end} {synopt:{cmd:r(tsfmt)}}time-series format of the time variable{p_end} {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Matrices}{p_end} {synopt:{cmd:r(results)}}results matrix, 5x6{p_end} {pstd} The rows of the results matrix indicate which method of lag length was used: {cmd:FIXED} (lag selected by user, or using Schwert's formula); {cmd:AIC}; {cmd:SIC}; {cmd:GTS05}; or {cmd:GTS10}.{p_end} {pstd} The columns of the results matrix contain, for each method, the number of lags used; the ADFmax statistic; its p-value; and the critical values at 1%, 5%, and 10%, respectively.{p_end} {title:References} {phang} Hall, A. 1994. Testing for a unit root in time series with pretest data-based model selection. {it:Journal of Business and Economic Statistics} 12: 461-470. {phang} Leybourne, S. J. 1995. Testing for unit roots using forward and reverse Dickey-Fuller regressions. {it:Oxford Bulletin of Economics and Statistics} 57: 559-571. {phang} Otero, J., and J. Smith. 2012. Response surface models for the Leybourne unit root tests and lag order dependence. {it:Computational Statistics} 27: 473-486. {phang} Schwert, G. W. 1989. Tests for unit roots: A Monte Carlo investigation. {it:Journal of Business and Economic Statistics} 7: 147-159. {title:Authors} {pstd} Jes{c u'}s Otero {break} Universidad del Rosario{break} Bogot{c a'}, Colombia{break} jesus.otero@urosario.edu.co {pstd} Christopher F. Baum {break} Boston College{break} Chestnut Hill, MA{break} baum@bc.edu {title:Also see} {p 4 14 2} Article: {it:Stata Journal}, volume 18, number 1: {browse "http://www.stata-journal.com/article.html?article=st0511":st0511}{p_end}