Intrinsic bubbles and Granger causality in the Hong Kong residential property market

Frontiers of Business Research in China

Table 4 Granger causality tests under asymmetric VECM

Period	Bubble	Null hypothesis	Chi ²	Sig
1993–2019	Yes	H₀ : γ_p = 0and \( {\alpha}_{21}={\alpha}_{22}=\dots ={\alpha}_{2{k}_2} \) =0.	10.34355	0.4109
1993–2019	Yes	H₀ : γ_d = 0 and \( {\beta}_{11}={\beta}_{12}=\dots ={\beta}_{1{k}_4}=0 \).	127.1764	0.0000^a

Notes. \( {H}_0:{\gamma}_p={\alpha}_{21}={\alpha}_{22}=\dots {\alpha}_{2{k}_2}=0 \) tests the joint null hypothesis of no causality from long-run deviation effect and lagged changes in the rental price index to changes in the property price index returns. Chi² test is for joint test
\( {H}_0:{\gamma}_d={\beta}_{11}={\beta}_{12}=\dots {\beta}_{1{k}_4}=0 \) tests the joint null hypothesis of no causality from long-run deviation effect and lagged changes in the property price index returns to changes in the rental price index returns. Chi² test is for joint test. ^a indicates statistical significance at the 0.01 level