. tsset year Time variable: year, 1909 to 1970 Delta: 1 year . gen l_rgnp = ln(rgnp) . twoway (tsline l_rgnp) * osa 4 . pperron l_rgnp, trend regress Phillips–Perron test for unit root Number of obs = 61 Variable: l_rgnp Newey–West lags = 3 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(rho) -11.083 -26.074 -19.998 -16.954 Z(t) -2.420 -4.126 -3.489 -3.173 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.3691. Regression table ------------------------------------------------------------------------------ l_rgnp | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- l_rgnp | L1. | .8761941 .061104 14.34 0.000 .7538812 .998507 | _trend | .0041831 .0019412 2.15 0.035 .0002973 .0080688 _cons | .5863726 .2807 2.09 0.041 .0244904 1.148255 ------------------------------------------------------------------------------ . pperron l_rgnp if year <= y(1929), trend regress Phillips–Perron test for unit root Number of obs = 20 Variable: l_rgnp Newey–West lags = 2 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(rho) -9.067 -22.500 -17.900 -15.600 Z(t) -2.155 -4.380 -3.600 -3.240 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.5152. Regression table ------------------------------------------------------------------------------ l_rgnp | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- l_rgnp | L1. | .5637918 .206217 2.73 0.014 .128712 .9988717 | _trend | .0125485 .005692 2.20 0.042 .0005394 .0245576 _cons | 2.066752 .9714534 2.13 0.048 .0171649 4.11634 ------------------------------------------------------------------------------ . pperron l_rgnp if year >y(1929), trend regress Phillips–Perron test for unit root Number of obs = 41 Variable: l_rgnp Newey–West lags = 3 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(rho) -16.111 -24.548 -19.116 -16.368 Z(t) -3.240 -4.233 -3.536 -3.202 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0767. Regression table ------------------------------------------------------------------------------ l_rgnp | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- l_rgnp | L1. | .7514403 .0867805 8.66 0.000 .5757624 .9271183 | _trend | .0103873 .0034422 3.02 0.005 .003419 .0173556 _cons | 1.26946 .4385091 2.89 0.006 .3817447 2.157175 ------------------------------------------------------------------------------ * osa 5 . gen t = _n . by year: generate byte DU = (year > y(1929)) . by year: generate byte DTB = (year == y(1930)) * osa 6 . regress l_rgnp t DU DTB L. l_rgnp L(1/8).D.l_rgnp Source | SS df MS Number of obs = 53 -------------+---------------------------------- F(12, 40) = 469.97 Model | 14.5914744 12 1.2159562 Prob > F = 0.0000 Residual | .10349256 40 .002587314 R-squared = 0.9930 -------------+---------------------------------- Adj R-squared = 0.9908 Total | 14.694967 52 .282595519 Root MSE = .05087 ------------------------------------------------------------------------------ l_rgnp | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- t | .0267176 .00529 5.05 0.000 .0160261 .037409 DU | -.1893632 .0442148 -4.28 0.000 -.2787246 -.1000017 DTB | -.0184206 .062385 -0.30 0.769 -.1445053 .1076641 | l_rgnp | L1. | .2823268 .1427877 1.98 0.055 -.0062578 .5709115 LD. | .5788568 .126168 4.59 0.000 .3238619 .8338518 L2D. | .4104828 .1466317 2.80 0.008 .1141291 .7068365 L3D. | .2394295 .1478983 1.62 0.113 -.0594841 .5383432 L4D. | .1984949 .1345279 1.48 0.148 -.0733961 .4703859 L5D. | .1717006 .132337 1.30 0.202 -.0957624 .4391637 L6D. | .2057396 .125523 1.64 0.109 -.0479518 .4594311 L7D. | .2565991 .1262267 2.03 0.049 .0014853 .5117128 L8D. | .2577882 .1397217 1.85 0.072 -.0246 .5401763 | _cons | 3.200044 .6314557 5.07 0.000 1.923825 4.476264 ------------------------------------------------------------------------------ . display (.2823268-1)/.1427877 -5.0261556 * osa 7 . regress l_rgnp t DU Source | SS df MS Number of obs = 62 -------------+---------------------------------- F(2, 59) = 921.78 Model | 19.5174992 2 9.7587496 Prob > F = 0.0000 Residual | .62462379 59 .010586844 R-squared = 0.9690 -------------+---------------------------------- Adj R-squared = 0.9679 Total | 20.142123 61 .330198738 Root MSE = .10289 ------------------------------------------------------------------------------ l_rgnp | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- t | .0378143 .0012752 29.65 0.000 .0352625 .040366 DU | -.3148484 .04822 -6.53 0.000 -.4113364 -.2183603 _cons | 4.576579 .0264747 172.87 0.000 4.523603 4.629555 ------------------------------------------------------------------------------ . predict trend, xb . twoway (tsline l_rgnp) (tsline trend) . predict res, residuals . pperron res, noconstant regress Phillips–Perron test for unit root Number of obs = 61 Variable: res Newey–West lags = 3 H0: Random walk without drift, a = 0, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(rho) -15.853 -12.988 -7.744 -5.522 Z(t) -3.057 -2.616 -1.950 -1.610 -------------------------------------------------------------- Regression table ------------------------------------------------------------------------------ res | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- res | L1. | .7716177 .0786949 9.81 0.000 .6142045 .9290309 ------------------------------------------------------------------------------ * osa 8 . ssc install zandrews . help zandrews . zandrews l_rgnp, graph Zivot-Andrews unit root test for l_rgnp Allowing for break in intercept Lag selection via TTest: lags of D.l_rgnp included = 1 Minimum t-statistic -4.617 at 1930 (obs 22) Critical values: 1%: -5.34 5%: -4.80 10%: -4.58