Appendix B: Further Unobserved Components Model Results | RDP 2004-09: Co-Movement of Australian State Business Cycles

RDP 2004-09: Co-Movement of Australian State Business Cycles Appendix B: Further Unobserved Components Model Results

David Norman and Thomas Walker

October 2004

Table B1: Estimated Parameters for Hours Worked
State	Trend parameter, δ^h		Common cycle response parameter, γ^h
	1985:Q4–1994:Q4	1995:Q1–2003:Q2	Common cycle response parameter, γ^h
NSW	1.86	1.35	0.51
Vic	1.22	1.12	0.59
Q1d	3.40	2.03	0.48
WA	2.69	1.66	0.54
SA	0.84	0.72	0.40
Tas	0.77	0.30	0.65
National average	1.92	1.38	0.52
Notes: Trend parameter estimates can be interpreted as average annualised percentage growth rates. The ‘national average’ figures are calculated as the average of the state figures, weighted by their share of total hours worked.

Table B2: Estimated ρ and θ Parameters
State	Idiosyncratic cycle response coefficient, θ_i (for hours worked)
National cycle coefficient, ρ	0.94
National cycle error variance,	6.4×10⁻⁵
NSW	0.61
Vic	0.43
Q1d	0.54
WA	0.18
SA	0.25
Tas	0.21
Notes: Sample is 1985:Q3–2003:Q2, yielding 71 observations. Idiosyncratic response coefficients for SFD are constrained to equal 1.

Table B3: Idiosyncratic Cycle Equation Coefficients, Φ
State	NSW	Vic	Q1d	WA	SA	Tas
NSW	0.83	−0.08	−0.10	−0.07	−0.07	−0.11
Vic	0.20	0.58	−0.11	−0.02	−0.35	0.05
Q1d	0.69	0.41	0.95	0.65	0.59	0.45
WA	−0.63	−0.53	−0.52	0.46	−0.61	−0.14
SA	−0.10	−0.08	−0.11	−0.25	0.56	0.00
Tas	−0.34	0.14	0.27	−0.28	0.32	0.37

Table B4: Cumulative Responses to Shocks
Hours worked
State	Cumulative effect after eight quarters of a shock to:
	NSW	Vic	Q1d	WA	SA	Tas	National
NSW	2.7	−0.6	−0.7	−0.4	−0.7	−0.8	3.0
Vic	0.5	0.8	−0.4	0.1	−1.2	−0.2	3.5
Q1d	0.9	0.1	1.3	0.9	0.7	0.6	2.8
WA	−1.6	−0.5	−0.3	0.4	−0.5	−0.2	3.2
SA	0.5	0.2	0.2	−0.3	0.9	0.1	2.4
Tas	0.5	0.5	0.5	−0.1	0.7	0.7	3.9
Notes: The cumulative response is effectively the integral between the shocked level of hours worked and the no-shock counterfactual level from the shock quarter to the eighth quarter following the shock. The shocks to state idiosyncratic cycles are scaled to increase SFD in the shock state by 1 per cent in the first quarter; the shock to the common cycle is similarly scaled and is 1.95 per cent (see notes to Table 5). All shocks last one quarter, but the model dynamics imply a sustained decay path in each case.