Estimating the Small Open Economy Model | RDP 2010-07: Monetary Policy and the Exchange Rate: Evaluation of VAR Models

RDP 2010-07: Monetary Policy and the Exchange Rate: Evaluation of VAR Models 3. Estimating the Small Open Economy Model

Jarkko Jääskelä and David Jennings

September 2010

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3.1 Parameter Estimates

In order to derive parameter estimates for our controlled experiment, we estimate the DSGE model's parameters with Bayesian techniques (for a survey, see An and Schorfheide 2007) using quarterly Australian and US data. For the large US economy, we use quarterly linearly-detrended log real GDP (), demeaned CPI inflation excluding food and energy () and the demeaned US federal funds rate (), for the sample period 1984:Q1–2009:Q4. For the small open economy, Australia, we use quarterly linearly-detrended log real GDP (x_t), demeaned trimmed mean inflation excluding interest and taxes (π_t), the demeaned RBA cash rate (r_t) and linearly-detrended log of the bilateral real exchange rate (q_t) for the same sample period, which covers the post-float period for the Australian dollar. Table 1 summarises the results of the estimation of this DSGE model. The posterior statistics are based on 1 million draws using the Markov Chains Monte Carlo (MCMC) methods with a 20 per cent burn-in period. We calibrate the discount factor β to be 0.99 (for both the large and small economies); the degree of openness, α, is set at 0.25, consistent with the value of the share of foreign goods in the Australian consumption basket. Finally, for both economies we calibrate σ, τ, ι and ϕ to be 1.5, 1.0, 1.0 and 3.0, respectively, in line with other studies. The persistence parameters ρ_a and ρ_x are calibrated to be 0.85 and 0.80, respectively. We choose to calibrate these two parameters as their estimates have a lot of probability mass around 1. This highlights the fact that the model has no endogenously generated persistence, thus the only way to match the level of persistence in the data is to opt for highly persistent shocks.

Table 1: Parameter Estimates of the DSGE Model
Parameters	Prior mean	Posterior mean	90 per cent probability intervals		Prior distribution	Prior std dev
Calibrated parameters
β	0.99	0.99
σ	1.50	1.50
τ	1.00	1.00
ι	1.00	1.00
ϕ	3.00	3.00
Calvo parameter
θ	0.60	0.60	[0.44	0.77]	Beta	0.10
Domestic monetary policy
ρ_r	0.80	0.86	[0.84	0.89]	Beta	0.02
α_x	0.05	0.28	[0.22	0.34]	Normal	0.10
α_π	0.40	0.60	[0.45	0.74]	Normal	0.10
Foreign monetary policy
	0.80	0.81	[0.76	0.84]	Beta	0.10
	0.05	0.15	[0.03	0.27]	Normal	0.10
	0.40	0.46	[0.32	0.59]	Normal	0.10
Persistence of shocks
ρ_π	0.80	0.84	[0.81	0.87]	Beta	0.02
	0.70	0.90	[0.88	0.93]	Beta	0.05
	0.70	0.89	[0.86	0.92]	Beta	0.10
Standard deviations of shocks (×10⁻²)
σ_a	1.00	3.45	[2.96	3.91]	Inv gamma	2
σ_x	1.00	9.80	[8.68	10.92]	Inv gamma	2
σ_π	1.00	0.69	[0.52	0.86]	Inv gamma	2
σ_r	1.00	2.35	[1.90	2.80]	Inv gamma	2
	1.00	0.84	[0.74	0.94]	Inv gamma	2
	1.00	1.97	[1.59	2.34]	Inv gamma	2
	1.00	0.22	[0.19	0.25]	Inv gamma	2

3.2 True Impulse Responses

The ‘true’ impulse response functions (IRFs) generated by the DSGE model (based on the posterior mean of the estimated parameters) are presented in Figure 1. A contractionary monetary policy shock has a negative effect on the output gap and lowers inflation while the real exchange rate appreciates instantaneously (and depreciates thereafter consistent with the UIP condition). Most of the variables return to baseline relatively quickly. More generally, and consistent with other general equilibrium models, all variables respond to the monetary policy shock contemporaneously. This is inconsistent with the standard assumption used to estimate recursive VARs, suggesting that these models will encounter problems identifying monetary policy shocks using simulated data from this model.