Observations on the Australian Business Cycle

Abstract

What accounts for the Australian business cycle, what caused the economic slumps and what factors contributed to the decades’ buoyancy? To understand these questions, the current paper decomposes the Australian business cycle into its sources for the period 1980–2014. Our main finding is that the efficiency wedge and the investment wedge are the major forces behind Australian output variations. The efficiency wedge is behind the growth slowdown that emerged in the mid 2000s.

Appendices

Appendix 1: Model

1.1 Additional Information on Accounting

Efficiency, labor and government consumption wedges can be measured directly from the data. The investment wedge involves computation of the model’s rational expectation solution. To do this, the equilibrium conditions are log-linearized around the steady-steady while assuming that the wedges follow first-order autoregressive processes. Observable variables are $y_{t}$, $x_{t}$, $h_{t}$ and $g_{t}$ while the state variables are $\log k_{t},$ $\log A_{t},$ $\tau _{ht},$ and $\tau _{xt}$. Furthermore, $\log k_{t+1}$ is a (policy) function of $\log k_{t},$ $\log A_{t},$ $\tau _{ht},$ $\tau _{xt},$ and $\log g_{t}$. Then, the state space representation of the model is given by

$$\begin{aligned} X_{t+1}=\mathbf {B}X_{t}+\mathbf {C}\zeta _{t+1} \end{aligned}$$

and

$$\begin{aligned} Y_{t}=\mathbf {D}X_{t}+\omega _{t} \end{aligned}$$

where $X_{t}=\left[ \log \widetilde{k}_{t},\log A_{t},\tau _{ht},\tau _{xt},\log \widetilde{g}_{t}\right] ^{\prime }$ and $Y_{t}=\left[ \log \widetilde{y}_{t},\log \widetilde{x}_{t},\log h_{t},\log \widetilde{g}_{t}\right] ^{\prime }$. The vector $\zeta _{t+1}$ contains shocks from the wedges and $\omega _{t}$ stands for residuals. Variables with tilde represent detrended per working age series. Let $s_{t}=[\log A_{t},\tau _{ht},\tau _{xt},\log g_{t}]^{\prime }$, thus,

$$\begin{aligned} s_{t+1}=\mathbf {P}_{0}+\mathbf {P}s_{t}+\epsilon _{t+1}. \end{aligned}$$

We assume that $\epsilon _{t}$ is independent and identically distributed and has a normal distribution with zero mean and covariance matrix $\mathbf {V}$. $\mathbf {V}$ is $\mathbf {QQ}^{\prime }$ where $\mathbf {Q}$ is the lower triangle matrix. Maximum likelihood is employed to estimate the stacked matrices $\mathbf {P}_{0}$, $\mathbf {P}$, and $\mathbf {Q}$. Finally, the maximum likelihood estimates are used to obtain the investment wedge. This generates the following results. The means of the wedges are

$$\begin{aligned} \left[ 0.3609 \quad 0.4293 \quad 0.2248 \quad {-}1.1735\right] \end{aligned}$$

the coefficient matrix $\mathbf {P}$ on lagged state variables is

$$\begin{aligned} \left[ \begin{array}{cccc} 0.9142 &{} {-}0.0594 &{} 0.0565 &{} 0.0185 \\ {-}0.0509 &{} 0.9365 &{} 0.0545 &{} {-}0.0008 \\ {-}0.0136 &{} 0.0129 &{} 0.9774 &{} 0.0208 \\ {-}0.0845 &{} 0.0929 &{} 0.0719 &{} 0.9728\end{array}\right] \end{aligned}$$

and the coefficient matrix $\mathbf {Q}$ is

$$\begin{aligned} \left[ \begin{array}{cccc} 0.0128 &{} 0 &{} 0 &{} 0 \\ 0.0049 &{} 0.0068 &{} 0 &{} 0 \\ -0.0090 &{} 0.0036 &{} 0.0151 &{} 0 \\ 0.0040 &{} 0.0161 &{} 0.0095 &{} 0.0201\end{array}\right] . \end{aligned}$$

1.2 Small Open Economy Extension

The small open economy is described by

$$\begin{aligned}&\max _{c_{t},h_{t},k_{t+1},b_{t+1}}E_{0}\left[ \sum _{t=0}^{\infty }\beta ^{t}\left( 1+\eta \right) ^{t}\left[ \left( 1-\phi \right) \ln c_{t}+\phi \ln (1-h_{t})\right] \right] \\&(1+\eta )(1+\lambda )b_{t+1}+c_{t}+(1+\tau _{xt})x_{t}\\&\quad =(1-\tau _{ht})w_{t}h_{t}+r_{t}k_{t}+(1+\tau _{bt})(1+r_{t}^{*})b_{t}+\tau _{t} \\&(1+\eta )(1+\lambda )k_{t+1}=(1-\delta )k_{t}+x_{t} \\&1+r_{t}^{*}=(1+r^{*})\left( \frac{b_{t}}{b^{*}}\right) ^{\vartheta } \\&y_{t}=A_{t}k_{t}^{\alpha }[(1+\lambda )^{t}h_{t}]^{1-\alpha }. \end{aligned}$$

Following Schmitt-Grohé and Uribe (2003) we assume the existence of an upwardly sloping supply of funds. This is done to allow applying local solution methods to the model economy. The calibration involves $\vartheta =0.0001$ and $b/y=0.39$ which corresponds to the 1979–2004 average of Australia’s net foreign assets to (annual) GDP ratio (taken from Lane and Milesi-Ferretti 2007).

Appendix 2: Data

The seasonally adjusted quarterly data used in our quantitative analysis are obtained from the Australian Bureau of Statistics (ABS) unless otherwise noted. The data are defined as follows.

Output: GDP minus sales tax plus services from consumer durable goods and depreciation of consumer durable goods.

Sales tax: Sales tax plus goods and services tax.

Consumer durable goods: Household final consumption expenditure on furnishings and household equipment and purchase of vehicles. As the ABS does not provide the data of services of consumer durable goods and depreciation of consumer durable goods, we use the details of these data in the literature. The services from consumer durable goods are equal to 17 % per annum as in Chari et al. (2007). The depreciation rate of consumer durable goods is 16 % per annum as suggested by the average ratio of durable goods depreciation to the stock of durable goods in the U.S. during 1960–2006. This is similar to the depreciation rate of durable goods in Baxter (1996) of which is 15.6 % per annum.

Consumer non-durable goods: Household final consumption expenditure excluding final consumption expenditure on furnishings and household equipment and purchase of vehicles.

Consumption: Consumer non-durable goods minus sales tax on consumer non-durable goods plus services from consumer durable goods and depreciation of consumer durable goods.

Investment: Private and public gross fixed capital formation plus changes in inventories and consumer durable goods minus sales tax on consumer durable goods.

Government consumption: Government final consumption expenditure.

Net exports: Exports minus imports.

Price deflator: Implicit price deflator.

Real value: Series are deflated by price deflator.

Total hours worked: the average weekly hours worked for wages and salary earners multiplied by employed persons and multiplied by 12 weeks.

Population: Civilian non-institutional population aged 15-64.

Per capita: Series are divided by population.

Terms of trade: Terms of trade provided by RBA Economic and Financial Statistics.

Table 1 Correlations of actual output to measured wedge

Table 2 Correlations of actual output to model output

Table 3 Correlations of observed data to model prediction