RDP 2011-06: Does Equity Mispricing Influence Household and Firm Decisions? Appendix B: Specification Tests

James Hansen

December 2011

Table B1 highlights that the null of a unit root cannot be rejected for each of the endogenous regressors using either Augmented Dicky-Fuller or Phillips-Perron tests.

Table B1: Unit Root Tests
March 1953–June 2010 sample period
Variable ADF test statistic(a) PP test statistic(b)
Consumption −1.71 −2.48
Dividends −1.53 −1.37
Non-US-equity net worth −0.79 −0.70
Labour income −1.32 −1.83
Equity quantities −1.04 −0.93
Equity prices −1.91 −1.93
Notes: All tests include four lags in their construction; ***,**,* denote test statistics that reject the null of a unit root at the 1, 5 and 10 per cent significance levels
(a) Augmented Dicky-Fuller test statistic
(b) Phillips-Perron test statistic

Table B2 reports results from lag-order selection criteria tests, and Table B3 reports results from Johansen Trace Tests concerning the rank of the cointegration matrix.

Table B2: Lag-order Selection Criteria
March 1953–June 2010 sample period
Lags LR(a) FPE(b) AIC(c) HQIC(d) SBIC(e)
0   3.4 × e−15 −33.42 −33.42 −33.42
1 3651.9 5.9 × e−22 −48.99 −48.77 −48.45
2 197.67 3.4 × e−22* −49.53* −49.10* −48.46*
3 67.15 3.5 × e−22 −49.51 −48.86 −47.90
4 56.61* 3.8 × e−22 −49.45 −48.58 −47.29
Notes: * denotes lag length selected
(a) Likelihood ratio test statistic
(b) Final prediction error
(c) Akaike information criterion
(d) Hannan Quinn information criterion
(e) Schwarz Bayesian information criterion
Table B3: Johansen Trace Tests
Maximum rank Trace test statistic Trace test statistic Critical value(a)
Mar 1953–Jun 2010 Jun 1986–Jun 2010
0 111.95 110.68 94.15
1 73.74 71.33 68.52
2 41.84* 38.75* 47.21
3 22.92 19.71 29.68
4 10.27 9.76 15.41
5 2.69 3.29 3.76
Notes: * Denotes the implied rank of the cointegration matrix
(a) 5 per cent level of signficance

Table B4 reports results from Lagrange Multiplier tests for up to third-order serial correlation in the VECM residuals (estimated subject to the restrictions that the cointegration rank r = 2 and that Inline Equation. A check on the stability properties of the eigenvalues for this restricted VECM are consistent with estimated model being stable.

Table B4: Lagrange Multiplier Tests for Residual Serial Correlation
June 1986–June 2010 sample period
Lags Test statistic P-value(a)
1 50.40 0.06
2 40.00 0.30
3 43.45 0.18
Note: (a) Obtained from a Chi-squared distribution with 36 degrees of freedom