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Phillips curve forecasting in a small open economy
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Economics Letters 98 (2008) 161 – 166 www.elsevier.com/locate/econbase
Phillips curve forecasting in a small open economy Troy D. Matheson ⁎ Economics Department, Reserve Bank of New Zealand PO Box 2498, Wellington, New Zealand Received 17 January 2006; received in revised form 23 April 2007; accepted 25 April 2007 Available online 3 May 2007
Abstract Using data for Australia and New Zealand, this paper finds that the open economy Phillips curve forecasts poorly relative to an autoregressive benchmark. However, its performance improves markedly when a sectoral Phillips curve is used, which weights together a closed economy Phillips curve for the non-tradable sector with an open economy Phillips curve for the tradable sector. © 2007 Elsevier B.V. All rights reserved. Keywords: Phillips curve; Small open economy; Forecasting JEL classification: C53; E31
1. Introduction While there is much empirical work exploring the forecasting performance of the Phillips curve in the US, research examining its performance in small open economies is more scarce, and does not explicitly account for the sectoral differences that result from trade. Yet, theory on the aggregation of economic series dating back to Theil (1954) shows that there can be efficiency gains from formally articulating sectoral differences in estimation. This paper adds to previous empirical work by considering a sectoral approach to forecasting with the Phillips curve in a small open economy. The paper proceeds as follows. Section 2 outlines the closed economy Phillips curve and its open economy analogue. We then describe our sectoral approach to forecasting with the open economy Phillips ⁎ Tel.: +64 4 471 3859; fax: +64 4 473 1209. E-mail address: [email protected]. 0165-1765/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2007.04.025
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T.D. Matheson / Economics Letters 98 (2008) 161–166
curve, which involves weighting a closed economy Phillips curve forecast for non-tradable inflation with an open economy Phillips curve forecast for tradable inflation. Our data and our forecasting experiment are outlined in Section 3. In Section 4, we evaluate the aggregate Phillips curve forecast against an autoregressive benchmark, and then compare forecasts from the sectoral and aggregate Phillips curves. We conclude in Section 5. 2. The Phillips curve The general closed economy Phillips curve specification used by Orphanides and van Norden (2005) for the US is: ptþh ¼ / þ bðLÞxt þ gðLÞpt þ etþh
ð1Þ
where πt +h = ln (Pt+h / Pt) is h-period inflation in the price level Pt and πt = ln(Pt / Pt − 1); xt is a measure of real demand (or costs) in the economy; and β(L) and γ(L) are polynomials of the lag operator L. In an open economy, it is typical to augment the Phillips curve with variables that capture the impact of swings in international competitiveness: ptþh ¼ / þ bðLÞxt þ dðLÞst þ gðLÞpt þ etþh
ð2Þ
where st is a measure of the tradable sector's international competitiveness, usually import price inflation (Batini et al., 2005). While this aggregate specification can be estimated directly, separate Phillips curves for each of the tradable and non-tradable sectors can also be specified. When an economy is closed, no goods and services are traded internationally—they are all non-tradable. The obvious choice for a non-tradable inflation π N specification is thus the closed economy Phillips curve: N N pN tþh ¼ / þ bðLÞxt þ gðLÞpt þ etþh
ð3Þ
where non-tradable inflation is driven by xN, real economic activity in the non-tradable sector, and by lags of non-tradable inflation. The more competitive the economy is with the rest of the world, the faster changes in world prices and the exchange rate will impact on prices in the tradable sector. Notwithstanding swings in international competitiveness, demand conditions will also influence inflation in the tradable sector, as in the economy more generally. Thus, inflation in the tradable sector will be guided by both fluctuations in international competitiveness and demand conditions. This makes the open economy Phillips curve (2) a natural choice for an empirical model of inflation in the tradable sector π T: pTtþh ¼ / þ bðLÞxTt þ dðLÞst þ gðLÞpTt þ etþh
ð4Þ
where tradable inflation is driven by xT, real economic activity in the tradable sector, a measure of the tradable sector's international competitiveness st, and lags of tradable inflation. Note that weighting together forecasts from Eqs. (3) and (4) yields a combined forecast for aggregate inflation: ptþh ¼ apTtþh þ ð1 aÞpN tþh
ð5Þ
where α is the size of the tradable sector in the open economy (a measure of the economy's openness).
T.D. Matheson / Economics Letters 98 (2008) 161–166
163
Our backward-looking specifications of the Phillips curve are analogous to those used in many papers examining the forecasting performance of the Phillips curve in the US.1 These backward-looking Phillips curves may seem at odds with recent literature that builds the microfoundations of the so-called hybrid New Keynesian Phillips curve, which features an important theory-based forward-looking component as well as a backward-looking component. However, it is straightforward to show that the (one-step-ahead) backward-looking Phillips curves described above nest reduced-form hybrid New Keynesian Phillips curves.2 Nevertheless, because our objective here is to forecast with the Phillips curve, we choose not to impose the restrictions implied by the New Keynesian model, in keeping with the Phillips curve forecasting literature for the closed economy. 3. Data and real-time experiment To estimate our Phillips curves, we use quarterly data for Australia and New Zealand from 1992Q1 to 2005Q2. The price level Pt is defined to be the Consumers Price Index (CPI) excluding interest charges. Tradable and non-tradable prices are defined to be the tradable and non-tradable sub-indices of the CPI in both countries. We use real aggregate demand xt as a proxy for xtN and xtT in Eqs. (3) and (4). For robustness, we estimate the models using several definitions of real demand xt: real GDP; total employment; the unemployment rate; capacity utilisation; and a diffusion index. The diffusion index is calculated as the first principal component from a large set of indicators of real economic activity (?). 3 We detrend real GDP, total employment, and the unemployment rate using two methods: (log) first differences and the Hodrick and Prescott (HP) filter. Note that the unemployment rate is not logged before differences are taken. We use log first differences in import prices as our measure of the international competitiveness of the tradable sector st. To simulate the forecasting performance of our empirical models, we extract all trends and estimate all equations recursively for each quarter from 1999Q4 to 2005Q1. The real-time forecasting performance of the models is then evaluated at horizons h of 2, 4 and 8 quarters ahead using expost inflation data from 2000Q1 to 2005Q2. The orders of the lag polynomials are chosen recursively for all Phillips curves using the Schwartz-Bayesian Information Criterion, where the order of the lag polynomial L can range from 1 to 4. 4. Results 4.1. Testing against and autoregressive benchmark Our benchmark is the iterated forecast from a one step ahead AR(1) model. Following Diebold and Mariano (1995), we test the null hypothesis that models i (the aggregate Phillips curve forecast) and j (the
1
See, for example, Stock and Watson (1999), Stock and Watson (2002) and Orphanides and van Norden (2005). An appendix showing how the reduced–form small open economy hybrid New Keynesian Phillips curves in Matheson (2006) are nested by Eqs. (2), (3), and (4) is available from the author on request. Similarly, Lindé (2005) shows that the closed economy hybrid New Keynesian Phillips curve is a restricted version of the backward-looking Phillips curve (Eq. (1)). 3 The data included in the diffusion index are detailed at http://www.rbnz.govt.nz/research/discusspapers/index.html. 2
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T.D. Matheson / Economics Letters 98 (2008) 161–166
Table 1 MSFEs: aggregate Phillips curve relative to AR Australia
New Zealand
h
2
4
8
2
4
8
Δln(gdp) hp(gdp) Δln(emp) hp(emp) Δ(unemp) hp(unemp) capu Factor
1.00 1.04 1.33 1.20 1.28 2.65 0.97 1.37
1.07 1.14 1.66 2.73 4.17 8.44 2.53 1.42
0.97 1.11 2.37 3.10 1.74 6.05 3.89 2.49
1.18 1.03⁎ 1.65 1.27 1.15 1.36 1.18⁎ 1.24
1.86 1.97 2.86 2.05 2.17 1.81 2.36 1.76
1.52 2.16 3.95 2.05 3.38 1.67 2.06 1.68
First differences (Δ), (log) first difference (Δln), HP filter (hp). GDP (gdp), total employment (emp), the unemployment rate (unemp), capacity utilisation (capu), diffusion index (factor). ⁎ denotes significance at the 10% level. The test is one-sided and bias-adjusted.
autoregressive benchmark forecast) have equal forecast accuracy. Specifically, squared forecast errors are constructed for each model: ei;tþh ¼ ðptþh pˆ i;tþh Þ2
ð6Þ
where πt+h is inflation at horizon h and πˆ t+h is a prediction from model i at time t. The squared forecast T , errors are then differenced dt = εj,t+h − εi,t+h, producing a series of squared error differentials {dt}t=1 where T = ((T2 − h) − T1) and T1 and T2 − h are the first and last dates over which the out-of-sample forecasts are made, respectively. When β(L) and δ(L) = 0 and γ (1), however, our null and alternative models are the same – they are nested – so that the distribution of dt is non-standard. Clark and West (2005) propose a bias adjustment to the mean square error differences. We use this adjusted statistic to test for equal forecast accuracy between our AR(1) benchmarks and the Phillips curves.4 The forecasting results for the aggregate Phillips curve relative to the autoregressive benchmark are displayed in Table 1. To ease interpretation, we display unadjusted MSFE ratios rather than adjusted MSFE differences in the results tables, where a number greater than 1 indicates a lower MSFE (better forecasting performance) from model j, the autoregressive benchmark. The autoregressive benchmark produced lower MSFEs in the vast majority of cases. In fact, for New Zealand, not a single aggregate Phillips curve forecast outperformed the benchmark on an unadjusted basis. The results are slightly more positive for Australia, where forecasts that use GDP and capacity utilisation produced better forecasts than the benchmark at some horizons. 4.2. Testing the sectoral approach Because of the recursive lag length selection in our models, at some dates the aggregate (Eq. (2)) and sectoral (Eq. (5)) models are nested and at some dates they are not, making Clark and West (2005) We estimate the variance of the mean difference in MSFEs using an HAC estimator, with a truncation lag of (h − 1), and compare the test statistic to a Student's t distribution with (T − 1) degrees of freedom. 4
T.D. Matheson / Economics Letters 98 (2008) 161–166
165
Table 2 MSFEs: sectoral relative to aggregate Phillips curves Australia
New Zealand
h
2
4
8
2
4
8
Δln(gdp) hp2(gdp) Δln(emp) hp2(emp) Δ(unemp) hp2(unemp) capu Factor
0.91 0.95† 1.03 0.94†† 0.69†† 0.51†† 0.87† 0.82
1.20† 1.12†† 1.05† 0.82†† 0.54†† 0.66†† 0.47 1.14
0.88†† 0.92†† 0.62†† 0.76†† 0.88†† 0.95† 0.64 0.71
0.76†† 1.00†† 0.60†† 0.74†† 0.71†† 0.73†† 0.60† 0.58††
0.55†† 1.09†† 0.48†† 0.46†† 0.37†† 0.64†† 0.70†† 0.69††
0.63†† 0.92†† 0.32†† 0.47†† 0.25†† 0.39†† 0.40†† 0.53††
See notes to Table 1. †† denotes significance at the 5% level. † denotes significance at the 10% level. The test is a one-sided Chong and Hendry (1986) encompassing test.
bias adjustment inappropriate. Thus, when testing the relative accuracy of the aggregate and sectoral Phillips curves, we report relative MSFEs only and not the statistical significance of the MSFE differentials. Instead, we report the significance of a Chong and Hendry (1986) encompassing test, which tests whether there is information in the sectoral forecast that improves the forecast from the aggregate Phillips curve. Table 2 contains the out-of-sample forecasting performance of the sectoral Phillips curve relative to the aggregate Phillips curve. The results are striking. In all but a handful of cases, the sectoral forecast outperformed the aggregate forecast according to MSFE comparisons. The value of the sectoral forecast is further confirmed by the encompassing test, which indicates that all but a few of the sectoral forecasts had predictive power over and above the corresponding aggregate forecasts at the 10% level. Moreover, most of the forecasts that failed the encompassing test have lower MSFEs than the corresponding aggregate forecasts. 5. Conclusion Across a range of different definitions of real demand, the aggregate open economy Phillips curve generally produces poor forecasting performance relative to an autoregressive benchmark in Australia and New Zealand. However, its performance improves markedly when a sectoral Phillips curve is used, which weights together a closed economy Phillips curve for the non-tradable sector with an open economy Phillips curve for the tradable sector. This suggests that, in addition to facilitating understanding about the inflation process, a sectoral approach to forecasting inflation with the Phillips curve is preferable to the aggregate approach in a small open economy. Acknowledgements I thank Dean Ford, Tim Hampton, Markus Hyvonen, and Giancarlo La Cava for their help with the Australian data. The views expressed in this paper do not necessarily reflect those of the Reserve Bank of New Zealand.
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T.D. Matheson / Economics Letters 98 (2008) 161–166
References Batini, N., Jackson, B., Nickell, S., 2005. An open-economy New Keynesian Phillips curve for the U.K. Journal of Monetary Economics 52, 1061–1071. Chong, Y.Y., Hendry, D.F., 1986. Econometric evaluation of linear macro-economic models. Review of Economic Studies 53 (4), 671–690. Clark, T.E., West, K.D., 2005. Approximately Normal Tests for Equal Predictive Accuracy in Nested Models. Manuscript. Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13 (3), 253–263 July. Lindé, J., 2005. Estimating New-Keynesian Phillips curves: a full information maximum likelihood approach. Journal of Monetary Economics 52 (6), 1135–1149. Matheson, T.D., 2006. Assessing the Fit of Small Open Economy DSGEs. Reserve Bank of New Zealand. Discussion paper 11. Orphanides, A., van Norden, S., 2005. The reliability of inflation forecasts based on output gap estimates in real time. Journal of Money, Credit and Banking 37 (3), 583-560. Stock, J.H., Watson, M.W., 1999. Forecasting inflation. Journal of Monetary Economics 44 (2), 293–335. Stock, J.H., Watson, M.W., 2002. Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20 (2), 147–162. Theil, H., 1954. Linear Aggregation of Economic Relations. North Holland, Amsterdam.
Economics Letters 98 (2008) 161 – 166 www.elsevier.com/locate/econbase
Phillips curve forecasting in a small open economy Troy D. Matheson ⁎ Economics Department, Reserve Bank of New Zealand PO Box 2498, Wellington, New Zealand Received 17 January 2006; received in revised form 23 April 2007; accepted 25 April 2007 Available online 3 May 2007
Abstract Using data for Australia and New Zealand, this paper finds that the open economy Phillips curve forecasts poorly relative to an autoregressive benchmark. However, its performance improves markedly when a sectoral Phillips curve is used, which weights together a closed economy Phillips curve for the non-tradable sector with an open economy Phillips curve for the tradable sector. © 2007 Elsevier B.V. All rights reserved. Keywords: Phillips curve; Small open economy; Forecasting JEL classification: C53; E31
1. Introduction While there is much empirical work exploring the forecasting performance of the Phillips curve in the US, research examining its performance in small open economies is more scarce, and does not explicitly account for the sectoral differences that result from trade. Yet, theory on the aggregation of economic series dating back to Theil (1954) shows that there can be efficiency gains from formally articulating sectoral differences in estimation. This paper adds to previous empirical work by considering a sectoral approach to forecasting with the Phillips curve in a small open economy. The paper proceeds as follows. Section 2 outlines the closed economy Phillips curve and its open economy analogue. We then describe our sectoral approach to forecasting with the open economy Phillips ⁎ Tel.: +64 4 471 3859; fax: +64 4 473 1209. E-mail address: [email protected]. 0165-1765/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2007.04.025
162
T.D. Matheson / Economics Letters 98 (2008) 161–166
curve, which involves weighting a closed economy Phillips curve forecast for non-tradable inflation with an open economy Phillips curve forecast for tradable inflation. Our data and our forecasting experiment are outlined in Section 3. In Section 4, we evaluate the aggregate Phillips curve forecast against an autoregressive benchmark, and then compare forecasts from the sectoral and aggregate Phillips curves. We conclude in Section 5. 2. The Phillips curve The general closed economy Phillips curve specification used by Orphanides and van Norden (2005) for the US is: ptþh ¼ / þ bðLÞxt þ gðLÞpt þ etþh
ð1Þ
where πt +h = ln (Pt+h / Pt) is h-period inflation in the price level Pt and πt = ln(Pt / Pt − 1); xt is a measure of real demand (or costs) in the economy; and β(L) and γ(L) are polynomials of the lag operator L. In an open economy, it is typical to augment the Phillips curve with variables that capture the impact of swings in international competitiveness: ptþh ¼ / þ bðLÞxt þ dðLÞst þ gðLÞpt þ etþh
ð2Þ
where st is a measure of the tradable sector's international competitiveness, usually import price inflation (Batini et al., 2005). While this aggregate specification can be estimated directly, separate Phillips curves for each of the tradable and non-tradable sectors can also be specified. When an economy is closed, no goods and services are traded internationally—they are all non-tradable. The obvious choice for a non-tradable inflation π N specification is thus the closed economy Phillips curve: N N pN tþh ¼ / þ bðLÞxt þ gðLÞpt þ etþh
ð3Þ
where non-tradable inflation is driven by xN, real economic activity in the non-tradable sector, and by lags of non-tradable inflation. The more competitive the economy is with the rest of the world, the faster changes in world prices and the exchange rate will impact on prices in the tradable sector. Notwithstanding swings in international competitiveness, demand conditions will also influence inflation in the tradable sector, as in the economy more generally. Thus, inflation in the tradable sector will be guided by both fluctuations in international competitiveness and demand conditions. This makes the open economy Phillips curve (2) a natural choice for an empirical model of inflation in the tradable sector π T: pTtþh ¼ / þ bðLÞxTt þ dðLÞst þ gðLÞpTt þ etþh
ð4Þ
where tradable inflation is driven by xT, real economic activity in the tradable sector, a measure of the tradable sector's international competitiveness st, and lags of tradable inflation. Note that weighting together forecasts from Eqs. (3) and (4) yields a combined forecast for aggregate inflation: ptþh ¼ apTtþh þ ð1 aÞpN tþh
ð5Þ
where α is the size of the tradable sector in the open economy (a measure of the economy's openness).
T.D. Matheson / Economics Letters 98 (2008) 161–166
163
Our backward-looking specifications of the Phillips curve are analogous to those used in many papers examining the forecasting performance of the Phillips curve in the US.1 These backward-looking Phillips curves may seem at odds with recent literature that builds the microfoundations of the so-called hybrid New Keynesian Phillips curve, which features an important theory-based forward-looking component as well as a backward-looking component. However, it is straightforward to show that the (one-step-ahead) backward-looking Phillips curves described above nest reduced-form hybrid New Keynesian Phillips curves.2 Nevertheless, because our objective here is to forecast with the Phillips curve, we choose not to impose the restrictions implied by the New Keynesian model, in keeping with the Phillips curve forecasting literature for the closed economy. 3. Data and real-time experiment To estimate our Phillips curves, we use quarterly data for Australia and New Zealand from 1992Q1 to 2005Q2. The price level Pt is defined to be the Consumers Price Index (CPI) excluding interest charges. Tradable and non-tradable prices are defined to be the tradable and non-tradable sub-indices of the CPI in both countries. We use real aggregate demand xt as a proxy for xtN and xtT in Eqs. (3) and (4). For robustness, we estimate the models using several definitions of real demand xt: real GDP; total employment; the unemployment rate; capacity utilisation; and a diffusion index. The diffusion index is calculated as the first principal component from a large set of indicators of real economic activity (?). 3 We detrend real GDP, total employment, and the unemployment rate using two methods: (log) first differences and the Hodrick and Prescott (HP) filter. Note that the unemployment rate is not logged before differences are taken. We use log first differences in import prices as our measure of the international competitiveness of the tradable sector st. To simulate the forecasting performance of our empirical models, we extract all trends and estimate all equations recursively for each quarter from 1999Q4 to 2005Q1. The real-time forecasting performance of the models is then evaluated at horizons h of 2, 4 and 8 quarters ahead using expost inflation data from 2000Q1 to 2005Q2. The orders of the lag polynomials are chosen recursively for all Phillips curves using the Schwartz-Bayesian Information Criterion, where the order of the lag polynomial L can range from 1 to 4. 4. Results 4.1. Testing against and autoregressive benchmark Our benchmark is the iterated forecast from a one step ahead AR(1) model. Following Diebold and Mariano (1995), we test the null hypothesis that models i (the aggregate Phillips curve forecast) and j (the
1
See, for example, Stock and Watson (1999), Stock and Watson (2002) and Orphanides and van Norden (2005). An appendix showing how the reduced–form small open economy hybrid New Keynesian Phillips curves in Matheson (2006) are nested by Eqs. (2), (3), and (4) is available from the author on request. Similarly, Lindé (2005) shows that the closed economy hybrid New Keynesian Phillips curve is a restricted version of the backward-looking Phillips curve (Eq. (1)). 3 The data included in the diffusion index are detailed at http://www.rbnz.govt.nz/research/discusspapers/index.html. 2
164
T.D. Matheson / Economics Letters 98 (2008) 161–166
Table 1 MSFEs: aggregate Phillips curve relative to AR Australia
New Zealand
h
2
4
8
2
4
8
Δln(gdp) hp(gdp) Δln(emp) hp(emp) Δ(unemp) hp(unemp) capu Factor
1.00 1.04 1.33 1.20 1.28 2.65 0.97 1.37
1.07 1.14 1.66 2.73 4.17 8.44 2.53 1.42
0.97 1.11 2.37 3.10 1.74 6.05 3.89 2.49
1.18 1.03⁎ 1.65 1.27 1.15 1.36 1.18⁎ 1.24
1.86 1.97 2.86 2.05 2.17 1.81 2.36 1.76
1.52 2.16 3.95 2.05 3.38 1.67 2.06 1.68
First differences (Δ), (log) first difference (Δln), HP filter (hp). GDP (gdp), total employment (emp), the unemployment rate (unemp), capacity utilisation (capu), diffusion index (factor). ⁎ denotes significance at the 10% level. The test is one-sided and bias-adjusted.
autoregressive benchmark forecast) have equal forecast accuracy. Specifically, squared forecast errors are constructed for each model: ei;tþh ¼ ðptþh pˆ i;tþh Þ2
ð6Þ
where πt+h is inflation at horizon h and πˆ t+h is a prediction from model i at time t. The squared forecast T , errors are then differenced dt = εj,t+h − εi,t+h, producing a series of squared error differentials {dt}t=1 where T = ((T2 − h) − T1) and T1 and T2 − h are the first and last dates over which the out-of-sample forecasts are made, respectively. When β(L) and δ(L) = 0 and γ (1), however, our null and alternative models are the same – they are nested – so that the distribution of dt is non-standard. Clark and West (2005) propose a bias adjustment to the mean square error differences. We use this adjusted statistic to test for equal forecast accuracy between our AR(1) benchmarks and the Phillips curves.4 The forecasting results for the aggregate Phillips curve relative to the autoregressive benchmark are displayed in Table 1. To ease interpretation, we display unadjusted MSFE ratios rather than adjusted MSFE differences in the results tables, where a number greater than 1 indicates a lower MSFE (better forecasting performance) from model j, the autoregressive benchmark. The autoregressive benchmark produced lower MSFEs in the vast majority of cases. In fact, for New Zealand, not a single aggregate Phillips curve forecast outperformed the benchmark on an unadjusted basis. The results are slightly more positive for Australia, where forecasts that use GDP and capacity utilisation produced better forecasts than the benchmark at some horizons. 4.2. Testing the sectoral approach Because of the recursive lag length selection in our models, at some dates the aggregate (Eq. (2)) and sectoral (Eq. (5)) models are nested and at some dates they are not, making Clark and West (2005) We estimate the variance of the mean difference in MSFEs using an HAC estimator, with a truncation lag of (h − 1), and compare the test statistic to a Student's t distribution with (T − 1) degrees of freedom. 4
T.D. Matheson / Economics Letters 98 (2008) 161–166
165
Table 2 MSFEs: sectoral relative to aggregate Phillips curves Australia
New Zealand
h
2
4
8
2
4
8
Δln(gdp) hp2(gdp) Δln(emp) hp2(emp) Δ(unemp) hp2(unemp) capu Factor
0.91 0.95† 1.03 0.94†† 0.69†† 0.51†† 0.87† 0.82
1.20† 1.12†† 1.05† 0.82†† 0.54†† 0.66†† 0.47 1.14
0.88†† 0.92†† 0.62†† 0.76†† 0.88†† 0.95† 0.64 0.71
0.76†† 1.00†† 0.60†† 0.74†† 0.71†† 0.73†† 0.60† 0.58††
0.55†† 1.09†† 0.48†† 0.46†† 0.37†† 0.64†† 0.70†† 0.69††
0.63†† 0.92†† 0.32†† 0.47†† 0.25†† 0.39†† 0.40†† 0.53††
See notes to Table 1. †† denotes significance at the 5% level. † denotes significance at the 10% level. The test is a one-sided Chong and Hendry (1986) encompassing test.
bias adjustment inappropriate. Thus, when testing the relative accuracy of the aggregate and sectoral Phillips curves, we report relative MSFEs only and not the statistical significance of the MSFE differentials. Instead, we report the significance of a Chong and Hendry (1986) encompassing test, which tests whether there is information in the sectoral forecast that improves the forecast from the aggregate Phillips curve. Table 2 contains the out-of-sample forecasting performance of the sectoral Phillips curve relative to the aggregate Phillips curve. The results are striking. In all but a handful of cases, the sectoral forecast outperformed the aggregate forecast according to MSFE comparisons. The value of the sectoral forecast is further confirmed by the encompassing test, which indicates that all but a few of the sectoral forecasts had predictive power over and above the corresponding aggregate forecasts at the 10% level. Moreover, most of the forecasts that failed the encompassing test have lower MSFEs than the corresponding aggregate forecasts. 5. Conclusion Across a range of different definitions of real demand, the aggregate open economy Phillips curve generally produces poor forecasting performance relative to an autoregressive benchmark in Australia and New Zealand. However, its performance improves markedly when a sectoral Phillips curve is used, which weights together a closed economy Phillips curve for the non-tradable sector with an open economy Phillips curve for the tradable sector. This suggests that, in addition to facilitating understanding about the inflation process, a sectoral approach to forecasting inflation with the Phillips curve is preferable to the aggregate approach in a small open economy. Acknowledgements I thank Dean Ford, Tim Hampton, Markus Hyvonen, and Giancarlo La Cava for their help with the Australian data. The views expressed in this paper do not necessarily reflect those of the Reserve Bank of New Zealand.
166
T.D. Matheson / Economics Letters 98 (2008) 161–166
References Batini, N., Jackson, B., Nickell, S., 2005. An open-economy New Keynesian Phillips curve for the U.K. Journal of Monetary Economics 52, 1061–1071. Chong, Y.Y., Hendry, D.F., 1986. Econometric evaluation of linear macro-economic models. Review of Economic Studies 53 (4), 671–690. Clark, T.E., West, K.D., 2005. Approximately Normal Tests for Equal Predictive Accuracy in Nested Models. Manuscript. Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13 (3), 253–263 July. Lindé, J., 2005. Estimating New-Keynesian Phillips curves: a full information maximum likelihood approach. Journal of Monetary Economics 52 (6), 1135–1149. Matheson, T.D., 2006. Assessing the Fit of Small Open Economy DSGEs. Reserve Bank of New Zealand. Discussion paper 11. Orphanides, A., van Norden, S., 2005. The reliability of inflation forecasts based on output gap estimates in real time. Journal of Money, Credit and Banking 37 (3), 583-560. Stock, J.H., Watson, M.W., 1999. Forecasting inflation. Journal of Monetary Economics 44 (2), 293–335. Stock, J.H., Watson, M.W., 2002. Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20 (2), 147–162. Theil, H., 1954. Linear Aggregation of Economic Relations. North Holland, Amsterdam.