RDP 2014-09: Predicting Dwelling Prices with Consideration of the Sales Mechanism Appendix A: Specification Checks

David Genesove and James Hansen

September 2014 – ISSN 1320-7229 (Print), ISSN 1448-5109 (Online)

To choose the appropriate number of lags in both the in- and out-of-sample analysis we use likelihood ratio tests, information criteria and tests for low-order serial correlation in the VAR residuals (see Table A1). Taking these results into consideration, and the relative sample size, we use four lags for Sydney and three lags for Melbourne in our analysis (when working with data in its first-difference or VECM representation).

Table A1: Lags Suggested According to Selection Criteria and Model
VAR in auction and all-sale prices VAR in private-treaty and all-sale prices VAR in auction and private-treaty prices
Sydney
Sequential LR tests(a) 7 5 1
Akaike information criteria 7 2 1
Sequential serial correlation tests(b) 7 7 7
Melbourne
Sequential LR tests(a) 4 6 4
Akaike information criteria 4 4 4
Sequential serial correlation tests(b) 4 4 4
Notes: (a) Denotes the number of lags suggested by applying sequential likelihood ratio (LR) tests (with a maximum lag length of 8)
(b) Denotes the number of lags by parring back the number of lags using sequential Lagrange-multiplier tests; starting with a maximum lag length of 8, lags are sequentially dropped until the null hypotheses of no low order (first or second) serial correlation is rejected at the 5 per cent level of significance

To test the order of integration of prices, Dickey-Fuller (DF) GLS regressions (Elliott, Rothenberg and Stock 1996; Ng and Perron 2001) are estimated (Table A2). Other tests for a unit root are also consistent with the prices data being I(1).

Table A2: Dickey-Fuller GLS Regressions
Lags
 		 DF GLS τ
test statistic		 5 per cent
critical value
Sydney auction prices
Ng-Perron sequential t(a) 2 −0.97 −3.06
Minimum Scharwz criteria(b) 1 −0.60 −3.08
Minimum modified AIC(c) 2 −0.97 −3.06
Sydney private-treaty prices
Ng-Perron sequential t(a) 10 −1.54 −2.78
Minimum Scharwz criteria(b) 1 −0.90 −3.08
Minimum modified AIC(c) 1 −0.90 −3.08
Melbourne auction prices
Ng-Perron sequential t(a) 1 −2.04 −3.09
Minimum Scharwz criteria(b) 1 −2.04 −3.09
Minimum modified AIC(c) 1 −2.04 −3.09
Melbourne private-treaty prices
Ng-Perron sequential t(a) 6 −2.05 −2.93
Minimum Scharwz criteria(b) 3 −1.82 −3.04
Minimum modified AIC(c) 3 −1.82 −3.04
Notes: (a) Lag length selected using Ng-Perron sequential t method as suggested by Ng and Perron (1995)
(b) Lag length selected using Scharwz criteria
(c) Lag length selected using modified Akaike information criteria (AIC)

Table A3 suggests that auction and private treaty sales prices are cointegrated when using Johansen's trace test. Evidence of cointegration is also found at conventional significance levels assuming a known cointegrating vector, [1 −1], and using univariate unit root tests such as augmented Dickey-Fuller and Phillips-Perron tests (results are available on request).

Table A3: Cointegration Test Results
City H0: No cointegration H0: Single cointegrating vector Lags
Test statistic(a) Critical value(b) Test statistic(a) Critical value(b)
Sydney 19.71 15.41   3.04 3.76 5
Melbourne 16.21 15.41   1.42 3.76 4
Notes: (a) Johansen's trace test statistic
(b) The critical values reported are measured at the 5 per cent level of significance