Consciousness-Based Education - Maharishi University of ...

U.S.-Soviet Relations and the Maharishi Effectfor each variable rejected the null hypothesis of a unit root in the caseof all three regressions, including those with the superfluous trend andintercept parameters, for which the power of the test was lower.Transfer Function Estimates.The iterative model identification and estimation procedure describedabove led to the following unrestricted reduced-form TF model:USSR t= c + (ωB)US t+ (ω 20+ ω 22B 2 + ω 24B 4 )I t+ N t,with noise modelN t= 1/(φ B + φ 5B 5 + φ 6B 6 + φ 11B 11 ) a t,where N tis an autoregressive process with coefficients a tlags 1, 5, 6, and11, and at is a white noise random error term.Table 1:Tests for Mean Stationarity:Phillips-Perron Unit Root TestsVariableTest Statistic WithTrend and InterceptTest StatisticWith InterceptTest StatisticWithout Trend orInterceptUSSR t–5.5694** –4.9335** –4.4072**US t–8.2625** –7.6614** –7.5267**** Null hypothesis of a unit root is rejected at the .01 significance levelNotes:The Phillips-Perron (PP) test is based on ordinary least squares regression estimates of thefollowing equation:∆y t= æ + γ y t-1+ δt + u t. In this equation, y tis the variable to be tested for a unit root, ∆y tis the firstdifference of y t, æ is the regression intercept, γ is a slope coefficient, δ is a slope coefficient for thetime-trend variable t, and u is a random disturbance term that need not be serially uncorrelatedand identically distributed. Under the null hypothesis of a unit root, γ should be equal to zero.Critical values for testing the null hypothesis γ = 0 were calculated by MacKinnon’s (1991)response surface method for alternative specifications of the PP regression equation. The 5% (1%)critical values for sample size n = 93 are as follows:Equation with trend and intercept: –3.4581 (–4.0591)Equation with intercept: –2.8925 (–3.5015)Equation without trend or intercept: –1.9436 (–2.5880).In all PP regressions, the lag truncation for the Newey-West serial correlation correction was 3lags (Bartlett kernel).Using Dickey and Fuller’s (1981) tabled critical values, the trend and intercept terms were notsignificant at the .05 level for the Phillips-Perron test regressions, indicating that tests based onregressions without trend or intercept (column four) will have greatest power.469