Business cycle accounting for New Zealand

ABSTRACT

Business cycle accounting is performed to identify the kinds of macroeconomic models that best explain economic fluctuations in New Zealand. We estimate four wedges and then create counterfactuals to distinguish the wedges that are important in accounting for fluctuations. The labour wedge plays the main role in explaining output and hours worked, while the net export wedge remains largely irrelevant. An existing equivalence result relates different kinds of macroeconomic dynamic stochastic general equilibrium models to the different wedges. Models that incorporate foreign shocks in the standard manner are equivalent to the wedge relating to net exports. The implication is that while foreign shocks may be important in explaining New Zealand's economic fluctuations, macroeconomists need to move away from modelling them in ways that work via the net export wedge.

KEYWORDS:

• Business cycle accounting
• DSGE models
• New Zealand

JEL Codes:

• E00
• E32
• E1

Notes

1. Some technical adjustments, described in full later, are made to the data so that the data and model variables are based on the same concepts, e.g. treatment of consumer durables.

2. A case of single-wedge-alone economy, where we simulate each variable with just one wedge, is also available from A.4.

3. The utility function here was taken from Cooley and Prescott (1995, p. 16). Chari et al. (2007) use a log–log utility function, which is nested as a limiting subcase of the utility function used here; log(c) + χlog(1 − l) is nested as χ = ψ/(1 − ψ) and limit as σ approaches 1.

4. Data used for the calibration were taken from http://research.stlouisfed.org/fred2/and http://www.stats.govt.nz/. A.2 contains full details on the data series as well as further details on how the parameters were calibrated.

5. The start date was chosen as the earliest date for which all the needed time-series data were available.

6. We provide the results for single-wedge-alone economies, in which three wedges are set to their steady-state values and only one wedge remains active in A.4. We focus here on the all-wedges-but-one economies because our use of second-order perturbation to solve for the optimal decision rules means that leaving only one wedge active is severely restricting as it also affects all of the cross-product terms of the wedges on which decisions are allowed to depend.

7. For precise details of how the counterfactuals given by the all-wedges-but-one economies are constructed, see A.3.

8. The importance of the labour wedge in explaining fluctuations in labour supply is not simply an assumption of business cycle accounting, unlike the case of government consumption.

9. The exact definition of the ψ-statistic is given by Equation (C3(C3) ) in A.3.

10. http://research.stlouisfed.org/fred2/

11. http://www.stats.govt.nz/

12. Dynare version 4.4.3 and Matlab version R2015a.

13. The ψ-statistic would be undefined if none of the wedges were of any importance in explaining {z_t}; however, this would require that all the data for {z_t} was a constant and so would never occur in practice.

14. Note that the y-axis is allowed to vary between figures. The fluctuations in investment are substantially larger than those in output and labour.