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Monetary Policy in Estimated Models of Small Open and Closed Economies

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Abstract

This paper compares monetary policy effects in New-Keynesian models of small open and closed economies fit to Canada. A monetary policy rule allows the central bank to systematically manage the nominal interest rate in response to inflation, output, and money growth variations. The structural parameters of a small open-economy (SOE) and a closed-economy (CE) models are estimated using a maximum-likelihood procedure with a Kalman filter. Estimation results show that the SOE and CE models lead to qualitatively similar estimates for the Canadian economy. Also, the effects of monetary policy shocks, and of other domestic shocks, generated in the SOE model resemble to those generated in the CE model. In addition, the forecast-error decomposition shows that foreign shocks account for small fractions of the variability observed in Canadian macroeconomic variables.

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Notes

  1. Lane (2001) gives detailed surveys of this literature.

  2. Smets and Wouters (2002) estimate only the degree of domestic and import price stickiness using data from the euro area and the United States. Their method consists of minimizing the difference between the empirical and theoretical impulse responses to monetary policy and exchange rate shocks.

  3. Ghironi (2000) uses a non-linear least-squares method at the single-equation level to estimate the structural parameters of a SOE model using data from Canada and the United States.

  4. Examples of studies that treat Canada as a closed economy are: Dib (2003, 2006), Dib et al. (2008), and Covas and Zhang (2008), while those treat Canada as a small open economy are: Lubik and Schorfheide (2007), Dib (2008), Bouakez and Rebei (2008), and Justiniano and Preston (2009).

  5. This assumption implies a stationary steady state for consumption and net foreign bonds, and allows equations that describe equilibrium in a stochastic model to be derived.

  6. For example, Ireland (2003), Bergin (2003), Dib (2003, 2006), Christensen and Dib (2008), and others.

  7. This is consistent with main findings in Justiniano and Preston (2009).

  8. When the share of imports and exports in GDP are close to 0, the bloc of foreign variables becomes disconnected from that of domestic ones and the small open-economy version of the model converges to that of the closed economy version. Therefore, CE model is nested in the SOE model.

  9. McCallum and Nelson (1999) and Kollmann (2002) use an exogenous risk-premium term that follows an AR(1) process.

  10. The price of domestic bonds is 1/R t units of domestic output; however, the price of foreign bonds on the international financial market is \(1/R^*_t\) units of foreign output. It is assumed that foreigners purchase only the bonds denominated in their own output.

  11. An economy is a net debtor if \(B^*_t<0\), and it must pay a risk premium, κ t , in addition to \(R^*_t\).

  12. In models with incomplete asset markets, if φ = 0, when domestic and world real interest rates are equal to 1/β, there is hysteresis and temporary shocks have permanent effects on the level of macroeconomic variables.

  13. Inputs in Eq. 9 are \(y_{dt}= \big(\int_{0}^{1}y_{dt}(j)^{\frac{\theta -1}{\theta}}dj\big)^{ \frac{\theta}{\theta -1}}\) and \(y_{ft}(j) = \big(\int_{0}^{1}y_{ft}(j)^{\frac{\theta -1}{\theta}}dj\big) ^{ \frac{\theta}{\theta -1}} \) where θ > 1 is the constant elasticity of substitution. The demand functions derived from the aggregate demand in the monopolistically competitive market are \(y_{dt}(j) = \big(\frac{p_{dt}(j)}{p_{dt}}\big)^{-\theta}y_{dt}\) and \(y_{ft}(j) = \big(\frac{p_{ft}(j)}{p_{ft}}\big)^{-\theta}y_{ft}\).

  14. Note that \(p_{dt}= \big(\int_{0}^{1}p_{dt}(j)^{1-\theta}dj\big)^{\frac{1}{1-\theta}}\) and \(p_{ft}=\big(\int_{0}^{1}p_{ft}(j)^{1-\theta}dj\big)^{\frac{1}{1-\theta}}\).

  15. For example, Ireland (2003), Dib (2006), and Christensen and Dib (2008).

  16. Originally, it was assumed that the Bank of Canada also responds to real exchange rate deviations, but estimates of its coefficient are too small and statistically insignificant, so it is omitted from the final rule.

  17. For example, Ireland (2003), Bergin (2003), Dib (2003, 2008), and Justiniano and Preston (2009).

  18. The value of ψ is also set at 10 and 20, but the estimated parameters are only marginally affected.

  19. The value of φ is set at 0.004 and 0.006, but the estimated parameters are only marginally affected.

  20. When ω f  = ϖ = 0, exports and imports are equal zeros. Thus, the final good is simply the domestic output, the CPI is equal to the PPI, the relative output price is equal to 1, and foreign real bonds evolve exogenously.

  21. Ireland (2003) introduces price rigidity by assuming quadratic adjustment costs.

  22. The RSOE and USOE models generate very similar impulse responses to different shocks, so only those of the RSOE model are reported.

  23. We firstly estimated the SOE model with different price rigidity parameters. The estimated values were very similar, so we re-estimated under the assumption of the same Calvo parameter in the two sectors.

  24. Using a CE framework for the Canadian economy, Dib (2006) estimates that, on average, domestic prices remain unadjusted for about 2.10 quarters in a standard sticky-price model.

  25. Imports depends on the final-good demand and on the relative import price, which in turn depends on the real exchange rate. Following a tightening monetary policy shock, the final-good demand falls and the real exchange rate appreciates. The drop in the final-good demand offsets the increase in imports induced by the real exchange rate appreciations.

  26. In theory, the intertemporal substitution and expenditure-switching effects affect aggregate demand in opposite directions following a change in the real interest rate.

  27. In the SOE model, the autoregressive coefficient of technology shocks, ρ A , is set at 0.88, as estimated in the CE model.

  28. In this economy, the home country is a net debtor, so it reduces its foreign debt stock after a positive home technology shock.

  29. This result is obtained by simulating the SOE model with the parameter ϕ set equal to 0.93 in the import sector.

  30. This is consistent with the results reported in Ireland (2003) and Dib (2006) that estimate closed-economy models for the U.S. and Canada, respectively. The large contribution of preference shocks are explained by the absence of habit formation in the model.

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Authors and Affiliations

  1. International Economic Analysis Department, Bank of Canada, 234 Wellington St., Ottawa, ON, K1A 0G9, Canada

    Ali Dib

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  1. Ali Dib
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Correspondence to Ali Dib.

Additional information

I am grateful to an anonymous referee, Steve Ambler, Hafedh Bouakez, Brain Doyle, Kevin Moran, and Nooman Rebei for their useful comments and discussions. The views expressed in this paper are those of the author. No responsibility of them should be attributed to the Bank of Canada.

Appendix: First-order conditions

Appendix: First-order conditions

1.1 A1 Households

$$ \frac{a_{t}c_{t}^{-\frac{1}{\gamma }}}{c_{t}^{\frac{\gamma -1}{\gamma } }+b^{\frac{1}{\gamma}}_{t} \left(M_{t}/p_{t}\right)^{\frac{\gamma -1}{\gamma }}}=\lambda _{t}; $$
(A1)
$$ \frac{a_{t}b^{\frac{1}{\gamma}}_{t}\left( M_{t}/p_{t}\right)^{-\frac{1}{\gamma } }}{c_{t}^{\frac{\gamma -1}{\gamma }}+b^{\frac{1}{\gamma}}_{t}\left( M_{t}/p_{t}\right) {}^{ \frac{\gamma -1}{\gamma }}}=\lambda _{t}-\beta E_{t}\left( \frac{ p_{t}\lambda _{t+1}}{p_{t+1}}\right); $$
(A2)
$$ \frac{\eta }{1-h_{t}}=\lambda _{t}w_{t}; $$
(A3)
$$\begin{array}{lll} &&\beta E_{t}\left[ \frac{\lambda _{t+1}}{\lambda_{t}}\left( \frac{R_{kt+1}}{p_{t+1}}+1-\delta + \psi\left(\frac{k_{t+2}}{k_{t+1}}-1\right)\frac{k_{t+2}}{k_{t+1}}\right)\right]\nonumber \\ &&\quad=\psi\left(\frac{k_{t+1}}{k_{t}}-1\right)+1; \end{array}$$
(A4)
$$ \frac{1}{R_t}=\beta E_t \left[\frac{p_t\lambda_{t+1}}{p_{t+1}\lambda_{t}}\right]; $$
(A5)
$$ \frac{1}{\kappa_t R^*_t}=\beta E_t \left[\frac{e_{t+1} p_t\lambda_{t+1}}{e_t p_{t+1}\lambda_{t}}\right]; $$
(A6)

where λ t is the marginal utility of consumption.

1.2 A2 Domestic-intermediate-goods producer

The first-order conditions are:

$$ \frac{R_{kt}}{p_t} = \alpha \frac{y_{t}(j)}{k_{t}(j)}q_{t};$$
(A7)
$$ \frac{W_{t}}{p_t} = (1-\alpha )\frac{y_{t}(j)}{h_{t}(j)}q_{t}; $$
(A8)
$$ \bar{p}_{dt}(j) = \frac{\theta}{\theta-1} \frac{E_t \sum_{l=0}^{\infty} (\beta \phi)^l\lambda_{t+l} y_{dt+l}(j) q_{t+l}/p_{t+l} } {E_t \sum_{l=0}^{\infty} (\beta \phi)^l\lambda_{t+l} y_{dt+l}(j)/p_{t+l} }, $$
(A9)

where q t is the real marginal cost.

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Dib, A. Monetary Policy in Estimated Models of Small Open and Closed Economies. Open Econ Rev 22, 769–796 (2011). https://doi.org/10.1007/s11079-010-9173-1

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