- Email: [email protected]
Commodity price changes and the predictability of economic policy uncertainty
Economics Letters 127 (2015) 39–42
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Commodity price changes and the predictability of economic policy uncertainty Yudong Wang a,∗ , Bing Zhang b , Xundi Diao c , Chongfeng Wu d a
School of Economics and Management, Nanjing University of Science and Technology, China
b
School of Business, Nanjing University, China
c
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China
d
Antai College of Economics and Management, Shanghai Jiao Tong University, China
highlights • This is the first paper to reveal the predictability of economic policy uncertainty. • We use commodity price changes to detect the predictability. • The forecast combinations with time-varying parameter models are employed.
article
info
Article history: Received 21 October 2014 Received in revised form 17 December 2014 Accepted 22 December 2014 Available online 31 December 2014
abstract In this study, we forecast economic policy uncertainty (EPU) using input on 23 commodity price changes. We reveal the significant predictability of EPU using three forecast combinations. This indicates that commodity price changes can be taken as a leading indicator of EPU. © 2014 Elsevier B.V. All rights reserved.
JEL classification: C53 E44 E52 E60 E62 Keywords: Commodity prices Economic policy uncertainty Forecast combination
1. Introduction
Economic policy uncertainty (EPU) is an important factor leading to a larger drop in economic activity at the beginning of the recession and a slower subsequent recovery (Baker et al., 2013). It is documented that EPU can also affect stock prices (Pastor and Veronesi, 2012). Therefore, the predictability of EPU has important
∗ Correspondence to: XiaoLinwei Street 200, Xuanwu District, Nanjing, China. Tel.: +86 13681663442. E-mail addresses: [email protected] (Y. Wang), [email protected] (B. Zhang), [email protected] (X. Diao), [email protected] (C. Wu). http://dx.doi.org/10.1016/j.econlet.2014.12.030 0165-1765/© 2014 Elsevier B.V. All rights reserved.
implications for analyzing business cycles and making financial investment decision. In this study, we reveal the predictability of EPU using commodity price changes. The economic rationale is that commodity prices are always determined in auction markets. These prices are informationally efficient and respond quickly to general economic conditions. Therefore, commodity prices can provide instantaneous information about the state of the economy (Codey and Mills, 1991; Gospodinov and Ng, 2013; Marquis and Cunningham, 1990). Moreover, because many primary commodities (such as crude oil) are important inputs into the production of manufactured goods, changes in commodity prices directly affect production costs (Garner, 1989). Thus, the commodity market activity is likely to be taken into account in formulating economic policies and may provide useful information for future policy uncertainty.
40
Y. Wang et al. / Economics Letters 127 (2015) 39–42 Table 1 Out-of-sample performance of forecast combinations. Forecasting horizons
Time-varying parameter model Mean combination ∗∗∗
Trimmed mean ∗∗∗
Constant coefficient model Inverse MSPE ∗∗∗
Mean combination ∗∗∗
Trimmed mean
Inverse MSPE
∗∗∗
0.710∗∗∗ (0)
h=1
0.792 (0)
0.789 (0)
h=3
0.852∗∗∗ (0)
0.863∗∗∗ (0)
0.824∗∗∗ (0)
0.802∗∗∗ (0)
0.811∗∗∗ (0)
0.768∗∗∗ (0)
h = 12
0.923∗∗ (0.038)
0.923∗∗ (0.039)
0.901∗∗∗ (0.004)
0.897∗∗ (0.016)
0.889∗∗ (0.012)
0.870∗∗∗ (0.001)
0.774 (0)
0.715 (0)
0.706 (0)
Notes: this table reports the MSPE ratios of three forecast combinations relative to the benchmark of AR(1) in predicting changes of EPU. The numbers in parentheses are p-values of the Diebold and Mariano (1995) test. We obtain the p-values using the bootstrap of White (2000) reality check. We perform 5000 bootstraps. The asterisks *, ** and *** denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.
We predict EPU using a basket of 23 commodity price changes. To the best of our knowledge, this study is the first one to test the predictability of EPU. We use a panel of regressions to forecast US EPU, where the predictor in each regression is price changes of an individual commodity. Three econometric methods are applied to average the forecasts generated from individual models. Our results suggest that the combinations of forecasts can significantly beat the AR(1) benchmark, regardless of whether time-varying parameter or constant-coefficient specifications are used. The revealed predictability is further demonstrated to be robust in the evolution of the evaluation period. The predictability can be further explained by the effects of commodity price changes on the disagreement among forecasters. The remainder of this study is organized as follows. Section 2 briefly describes the predictive models and the three methods of forecast combinations. Section 3 shows the data and reports the main empirical results. Section 4 presents our conclusions. 2. Econometric methodology In this section, we will first briefly describe the methodology of predictive regressions. Then, we will discuss how to combine the forecasts of individual predictive models based on three methods of forecast combinations. 2.1. Time-varying parameter (TVP) model
We use the Kalman filtering approach to estimate and forecast parameters recursively (Hamilton, 1994). Starting the Kalman (k) filter, we use a diffusion prior θ0 ∼ N (0, 100Imk ), where mk is the number of explanatory variables in model k for k = 1, . . . , K . The recursive forecasting procedure is started by choosing π0|0,k for k = 1, . . . , K , and we choose π0|0,k = K1 as a noninformative prior. 2.2. Forecast combinations As the predictive ability of a single model is very unstable over time (Stock and Watson, 2003), we use the method of forecast combinations. This is also more consistent with practical operations because policy makers are more concerned about a basket of commodity price changes rather than only an individual commodity weakening the possibility that relative price changes lead to inappropriate policy (Codey and Mills, 1991). We consider three popular forecast combinations. The first is the mean combination, which uses the equal weighted average of forecasts of each model. The second method is the trimmed mean combination. At time t, it drops the forecast with the greatest squared predictive error1 at time t − 1 and then averages over the remaining forecasts. The third method is the inverse MSPE combination. This combination takes the weighted average of forecasts, where the weights of individual models are recursively determined by their past performances (Stock and Watson, 2004). The forecasts based on this combination can be written as follows: n
wi,t yˆ i,t ,
wi,t = gi−,t1−1 /
n
gk−,t1−1 ,
For the time t = 1, 2, . . . , T , the standard TVP model can be written as,
yˆ i,v =
yt = xt −1 θt + εt ,
where n is the number of models and gi,t is the mean squared t ˆ i,j )2 . predictive error (MSPE), i.e., gi,t = j=1 (yi,j − y
θt = θt −1 + ηt ,
(1)
where yt is the change of EPU; xt −1 is a 1 × 3 vector for the series of explanatory variables that are used to predict yt , including the intercept, the lagged EUP and lagged price changes of an individual commodity; and θt is a 1 × 3 vector of time-varying regression coefficients, εt ∼ N (0, Ht ) and ηt ∼ N (0, Qt ). The errors εt and ηt are assumed to be mutually independent at all leads and lags. As a special case, Qt = 0 is related to the constant coefficient model. We use a truncated rolling revision of plug-in approach (Koop and Korobilis, 2012) to model the conditional volatility, Ht . To be precise, let
ˆt = H
˜ t if H˜ t > 0 H ˆ t −1 otherwise H
(2)
i=1
(4)
k=1
3. Data and empirical results We downloaded Baker et al.’s (2013) index of EPU from the website of Economic Policy Uncertainty (http://www. policyuncertainty.com/index.html). This index has been widely applied in recent studies (see, e.g., Antonakakis et al., 2013, Colombo, 2013, Karnizova and Li, 2014, Klößner and Sekkel, 2014). The commodity price data are available at the World Bank Web site (www.worldbank.org).2 Our whole sample period is from January 1985 to December 2013 and the forecast evaluation period starts from January 1990. Table 1 shows the performances of three forecast combinations in predicting the changes of EPU relative to the benchmark of
where
˜ t = 1 Σjt=t −t ∗ +1 [(yt − xt θˆt −1 )2 − xt Σt |t −1 x′t ]. H t∗
(3)
We set t ∗ = 24 and thus use a rolling estimator based on two years of monthly data.
1 It is defined as l = (y − yˆ )2 , where yˆ is the forecast of Model i at month i,t i,t i,t i,t t and yi,t is the true change of EPU. 2 We choose the prices of 23 popular commodities. They are crude oil, natural gas, cocoa, coffee, tea, palm oil, soybean, soybean oil, barley, maize, wheat, beef, sheep meat, cotton, aluminum, copper, lead, tin, nickel, zinc, gold, silver and platinum.
Y. Wang et al. / Economics Letters 127 (2015) 39–42
41
Fig. 1. Recursive MSPE ratios of forecast combinations for TVP models.
Fig. 2. Recursive MSPE ratios of forecast combinations for constant coefficient models.
AR(1). We report the MSPE ratios of three forecast combinations relative to the AR(1). An MSPE ratio smaller than one implies that the corresponding strategy generates more accurate forecasts of EPU than AR(1). The accuracy of forecasts is evaluated over three horizons of one month, three months and twelve months. We use the Diebold and Mariano (1995) test to examine whether the loss differences between the combination methods and the benchmark are significant. The critical value of this test is generated from the bootstrap of White (2000) ‘‘Reality Check’’.3
3 The p-values are obtained according to 5000 bootstraps.
For the three horizons, the MSPE ratios of all combinations are smaller than one, implying better forecasting performances than the benchmark of AR(1). The bootstrapped p-values of DM test indicate that the AR(1) can be significantly outperformed. The superiority of forecast combinations over AR(1) does not depend on whether TVP or constant coefficient regressions are used. As the forecasting horizons increases, the MSPE ratios become greater. For the horizon of one month, forecast combinations can reduce more than 20% of the forecasting losses relative to the AR(1). When the horizon increases to 12 months, the MSPE reduction decreases to approximately 10%. This finding indicates that the predictive ability of commodity price changes for EPU is weaker when the forecasting horizon becomes longer.
42
Y. Wang et al. / Economics Letters 127 (2015) 39–42 Table 2 Performances of forecasts for the index of economic forecaster disagreement. Time-varying parameter model Mean combination 0.538 (0)
∗∗∗
Trimmed mean ∗∗∗
0.543 (0)
Constant coefficient model Inverse MSPE 0.345 (0)
∗∗∗
Mean combination ∗∗∗
0.559 (0)
Trimmed mean 0.566 (0)
∗∗∗
Inverse MSPE 0.372∗∗∗ (0)
Notes: this table reports the MSPE ratios of three forecast combinations relative to the benchmark of AR(1). The numbers in parentheses are p-values of Diebold and Mariano (1995) test. We obtain the p-values using the bootstrap of White (2000) reality check. We perform 5000 bootstraps. The asterisks *, ** and *** denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.
Figs. 1 and 2 plot the recursive MSPE ratios from the year 2000 onwards for combinations of TVP and constant coefficient regressions, respectively. We can find that MSPE ratios are smaller than one at each point of time. This suggests that the superiority of forecast combinations is robust to the change of time horizon. We further detect why commodity price changes can predict EPU. The EPU index of Baker et al. (2013) is constructed from three types of underlying components. One of these components is the disagreement among economic forecasters. Diebold et al. (1997) show that during the period of some oil shocks in 1990s, the forecasters are more uncertain than they should have been. The density forecasts reported in the Survey of Professional Forecasters are affected by these shocks. This motivates us to find whether the predictability comes from the predictive content of commodity price changes to the dispersion measures of the Survey of Professional Forecasters.4 For this purpose, we use commodity price changes to predict the dispersion in the forecasts for economic variables as uncertainty about monetary policy and about government purchases of goods and services at the federal level. The results in Table 2 show that three forecast combinations can significantly outperform the benchmark model for all cases.5 This finding confirms that the predictability can be explained by the influences of commodity price changes on dispersion in forecasters. 4. Concluding remarks We have examined the predictability of economic policy uncertainty (EPU) using input from a basket of 23 commodity price changes. The forecast combinations based on TVP and constant coefficient regressions can significantly beat the AR(1) benchmark. This finding indicates that commodity price changes can provide useful information for future policy changes. In other words, commodity price changes can be taken as a leading indicator of EPU.
4 We also thank a referee for this helpful suggestion. 5 As the Baker et al. (2013)’s data for dispersion amongst forecasters are quarterly, we use the commodity prices in the last month of each quarter to match the data frequency. We just report the one-quarter-ahead forecasting results because they are enough to explain the source of revealed predictability. This is also to save space in this letter.
Acknowledgment This study is supported by the National Science Foundation of China (No. 71401077 and 71320107002). References Antonakakis, N., Chatziantoniou, I., Filis, G., 2013. Dynamic co-movements of stock market returns, implied volatility and policy uncertainty. Econom. Lett. 120, 87–92. Baker, S.R., Bloom, N., Davis, S.J., 2013. Measuring economic policy uncertainty. Working Paper, Stanford University. Codey, B.J., Mills, L.D., 1991. The role of commodity prices in formulating monetary policy. Rev. Econ. Stat. 73, 358–365. Colombo, V., 2013. Economic policy uncertainty in the US: does it matter for the Euro area? Econom. Lett. 121, 39–42. Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. J. Bus. Econom. Statist. 13, 253–263. Diebold, F.X., Tay, A.S., Wallis, K.F., 1997. Evaluating density forecasts of inflation: the survey of professional forecasters. NBER Working Paper, No. 6228. Garner, C.A., 1989. Commodity prices: policy target or information variable? J. Money Credit Bank. 21, 508–514. Gospodinov, N., Ng, S., 2013. Commodity prices, convenience yields, and inflation. Rev. Econ. Stat. 95, 206–219. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Karnizova, L., Li, J., 2014. Economic policy uncertainty, financial markets and probability of US recessions. Econom. Lett. 125, 261–265. Klößner, S., Sekkel, R., 2014. International spillover of policy uncertainty. Econom. Lett. 124, 508–512. Koop, G., Korobilis, D., 2012. Forecasting inflation using dynamic model averaging. Internat. Econom. Rev. 53, 867–886. Marquis, M.H., Cunningham, S.R., 1990. Is there a role for commodity prices in the design of monetary policy? Some empirical evidence. South. Econ. J. 57, 394–412. Pastor, L., Veronesi, P., 2012. Uncertainty about government policy and stock prices. J. Finance 67, 1219–1264. Stock, J.H., Watson, M.W., 2003. Forecasting output and inflation: the role of asset prices. J. Econom. Lit. 41, 788–829. Stock, J.H., Watson, M.W., 2004. Combination forecasts of output growth in a seven country data set. J. Forecast. 23, 405–430. White, H., 2000. A reality check for data snooping. Econometrica 68, 1097–1127.
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Commodity price changes and the predictability of economic policy uncertainty Yudong Wang a,∗ , Bing Zhang b , Xundi Diao c , Chongfeng Wu d a
School of Economics and Management, Nanjing University of Science and Technology, China
b
School of Business, Nanjing University, China
c
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China
d
Antai College of Economics and Management, Shanghai Jiao Tong University, China
highlights • This is the first paper to reveal the predictability of economic policy uncertainty. • We use commodity price changes to detect the predictability. • The forecast combinations with time-varying parameter models are employed.
article
info
Article history: Received 21 October 2014 Received in revised form 17 December 2014 Accepted 22 December 2014 Available online 31 December 2014
abstract In this study, we forecast economic policy uncertainty (EPU) using input on 23 commodity price changes. We reveal the significant predictability of EPU using three forecast combinations. This indicates that commodity price changes can be taken as a leading indicator of EPU. © 2014 Elsevier B.V. All rights reserved.
JEL classification: C53 E44 E52 E60 E62 Keywords: Commodity prices Economic policy uncertainty Forecast combination
1. Introduction
Economic policy uncertainty (EPU) is an important factor leading to a larger drop in economic activity at the beginning of the recession and a slower subsequent recovery (Baker et al., 2013). It is documented that EPU can also affect stock prices (Pastor and Veronesi, 2012). Therefore, the predictability of EPU has important
∗ Correspondence to: XiaoLinwei Street 200, Xuanwu District, Nanjing, China. Tel.: +86 13681663442. E-mail addresses: [email protected] (Y. Wang), [email protected] (B. Zhang), [email protected] (X. Diao), [email protected] (C. Wu). http://dx.doi.org/10.1016/j.econlet.2014.12.030 0165-1765/© 2014 Elsevier B.V. All rights reserved.
implications for analyzing business cycles and making financial investment decision. In this study, we reveal the predictability of EPU using commodity price changes. The economic rationale is that commodity prices are always determined in auction markets. These prices are informationally efficient and respond quickly to general economic conditions. Therefore, commodity prices can provide instantaneous information about the state of the economy (Codey and Mills, 1991; Gospodinov and Ng, 2013; Marquis and Cunningham, 1990). Moreover, because many primary commodities (such as crude oil) are important inputs into the production of manufactured goods, changes in commodity prices directly affect production costs (Garner, 1989). Thus, the commodity market activity is likely to be taken into account in formulating economic policies and may provide useful information for future policy uncertainty.
40
Y. Wang et al. / Economics Letters 127 (2015) 39–42 Table 1 Out-of-sample performance of forecast combinations. Forecasting horizons
Time-varying parameter model Mean combination ∗∗∗
Trimmed mean ∗∗∗
Constant coefficient model Inverse MSPE ∗∗∗
Mean combination ∗∗∗
Trimmed mean
Inverse MSPE
∗∗∗
0.710∗∗∗ (0)
h=1
0.792 (0)
0.789 (0)
h=3
0.852∗∗∗ (0)
0.863∗∗∗ (0)
0.824∗∗∗ (0)
0.802∗∗∗ (0)
0.811∗∗∗ (0)
0.768∗∗∗ (0)
h = 12
0.923∗∗ (0.038)
0.923∗∗ (0.039)
0.901∗∗∗ (0.004)
0.897∗∗ (0.016)
0.889∗∗ (0.012)
0.870∗∗∗ (0.001)
0.774 (0)
0.715 (0)
0.706 (0)
Notes: this table reports the MSPE ratios of three forecast combinations relative to the benchmark of AR(1) in predicting changes of EPU. The numbers in parentheses are p-values of the Diebold and Mariano (1995) test. We obtain the p-values using the bootstrap of White (2000) reality check. We perform 5000 bootstraps. The asterisks *, ** and *** denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.
We predict EPU using a basket of 23 commodity price changes. To the best of our knowledge, this study is the first one to test the predictability of EPU. We use a panel of regressions to forecast US EPU, where the predictor in each regression is price changes of an individual commodity. Three econometric methods are applied to average the forecasts generated from individual models. Our results suggest that the combinations of forecasts can significantly beat the AR(1) benchmark, regardless of whether time-varying parameter or constant-coefficient specifications are used. The revealed predictability is further demonstrated to be robust in the evolution of the evaluation period. The predictability can be further explained by the effects of commodity price changes on the disagreement among forecasters. The remainder of this study is organized as follows. Section 2 briefly describes the predictive models and the three methods of forecast combinations. Section 3 shows the data and reports the main empirical results. Section 4 presents our conclusions. 2. Econometric methodology In this section, we will first briefly describe the methodology of predictive regressions. Then, we will discuss how to combine the forecasts of individual predictive models based on three methods of forecast combinations. 2.1. Time-varying parameter (TVP) model
We use the Kalman filtering approach to estimate and forecast parameters recursively (Hamilton, 1994). Starting the Kalman (k) filter, we use a diffusion prior θ0 ∼ N (0, 100Imk ), where mk is the number of explanatory variables in model k for k = 1, . . . , K . The recursive forecasting procedure is started by choosing π0|0,k for k = 1, . . . , K , and we choose π0|0,k = K1 as a noninformative prior. 2.2. Forecast combinations As the predictive ability of a single model is very unstable over time (Stock and Watson, 2003), we use the method of forecast combinations. This is also more consistent with practical operations because policy makers are more concerned about a basket of commodity price changes rather than only an individual commodity weakening the possibility that relative price changes lead to inappropriate policy (Codey and Mills, 1991). We consider three popular forecast combinations. The first is the mean combination, which uses the equal weighted average of forecasts of each model. The second method is the trimmed mean combination. At time t, it drops the forecast with the greatest squared predictive error1 at time t − 1 and then averages over the remaining forecasts. The third method is the inverse MSPE combination. This combination takes the weighted average of forecasts, where the weights of individual models are recursively determined by their past performances (Stock and Watson, 2004). The forecasts based on this combination can be written as follows: n
wi,t yˆ i,t ,
wi,t = gi−,t1−1 /
n
gk−,t1−1 ,
For the time t = 1, 2, . . . , T , the standard TVP model can be written as,
yˆ i,v =
yt = xt −1 θt + εt ,
where n is the number of models and gi,t is the mean squared t ˆ i,j )2 . predictive error (MSPE), i.e., gi,t = j=1 (yi,j − y
θt = θt −1 + ηt ,
(1)
where yt is the change of EPU; xt −1 is a 1 × 3 vector for the series of explanatory variables that are used to predict yt , including the intercept, the lagged EUP and lagged price changes of an individual commodity; and θt is a 1 × 3 vector of time-varying regression coefficients, εt ∼ N (0, Ht ) and ηt ∼ N (0, Qt ). The errors εt and ηt are assumed to be mutually independent at all leads and lags. As a special case, Qt = 0 is related to the constant coefficient model. We use a truncated rolling revision of plug-in approach (Koop and Korobilis, 2012) to model the conditional volatility, Ht . To be precise, let
ˆt = H
˜ t if H˜ t > 0 H ˆ t −1 otherwise H
(2)
i=1
(4)
k=1
3. Data and empirical results We downloaded Baker et al.’s (2013) index of EPU from the website of Economic Policy Uncertainty (http://www. policyuncertainty.com/index.html). This index has been widely applied in recent studies (see, e.g., Antonakakis et al., 2013, Colombo, 2013, Karnizova and Li, 2014, Klößner and Sekkel, 2014). The commodity price data are available at the World Bank Web site (www.worldbank.org).2 Our whole sample period is from January 1985 to December 2013 and the forecast evaluation period starts from January 1990. Table 1 shows the performances of three forecast combinations in predicting the changes of EPU relative to the benchmark of
where
˜ t = 1 Σjt=t −t ∗ +1 [(yt − xt θˆt −1 )2 − xt Σt |t −1 x′t ]. H t∗
(3)
We set t ∗ = 24 and thus use a rolling estimator based on two years of monthly data.
1 It is defined as l = (y − yˆ )2 , where yˆ is the forecast of Model i at month i,t i,t i,t i,t t and yi,t is the true change of EPU. 2 We choose the prices of 23 popular commodities. They are crude oil, natural gas, cocoa, coffee, tea, palm oil, soybean, soybean oil, barley, maize, wheat, beef, sheep meat, cotton, aluminum, copper, lead, tin, nickel, zinc, gold, silver and platinum.
Y. Wang et al. / Economics Letters 127 (2015) 39–42
41
Fig. 1. Recursive MSPE ratios of forecast combinations for TVP models.
Fig. 2. Recursive MSPE ratios of forecast combinations for constant coefficient models.
AR(1). We report the MSPE ratios of three forecast combinations relative to the AR(1). An MSPE ratio smaller than one implies that the corresponding strategy generates more accurate forecasts of EPU than AR(1). The accuracy of forecasts is evaluated over three horizons of one month, three months and twelve months. We use the Diebold and Mariano (1995) test to examine whether the loss differences between the combination methods and the benchmark are significant. The critical value of this test is generated from the bootstrap of White (2000) ‘‘Reality Check’’.3
3 The p-values are obtained according to 5000 bootstraps.
For the three horizons, the MSPE ratios of all combinations are smaller than one, implying better forecasting performances than the benchmark of AR(1). The bootstrapped p-values of DM test indicate that the AR(1) can be significantly outperformed. The superiority of forecast combinations over AR(1) does not depend on whether TVP or constant coefficient regressions are used. As the forecasting horizons increases, the MSPE ratios become greater. For the horizon of one month, forecast combinations can reduce more than 20% of the forecasting losses relative to the AR(1). When the horizon increases to 12 months, the MSPE reduction decreases to approximately 10%. This finding indicates that the predictive ability of commodity price changes for EPU is weaker when the forecasting horizon becomes longer.
42
Y. Wang et al. / Economics Letters 127 (2015) 39–42 Table 2 Performances of forecasts for the index of economic forecaster disagreement. Time-varying parameter model Mean combination 0.538 (0)
∗∗∗
Trimmed mean ∗∗∗
0.543 (0)
Constant coefficient model Inverse MSPE 0.345 (0)
∗∗∗
Mean combination ∗∗∗
0.559 (0)
Trimmed mean 0.566 (0)
∗∗∗
Inverse MSPE 0.372∗∗∗ (0)
Notes: this table reports the MSPE ratios of three forecast combinations relative to the benchmark of AR(1). The numbers in parentheses are p-values of Diebold and Mariano (1995) test. We obtain the p-values using the bootstrap of White (2000) reality check. We perform 5000 bootstraps. The asterisks *, ** and *** denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.
Figs. 1 and 2 plot the recursive MSPE ratios from the year 2000 onwards for combinations of TVP and constant coefficient regressions, respectively. We can find that MSPE ratios are smaller than one at each point of time. This suggests that the superiority of forecast combinations is robust to the change of time horizon. We further detect why commodity price changes can predict EPU. The EPU index of Baker et al. (2013) is constructed from three types of underlying components. One of these components is the disagreement among economic forecasters. Diebold et al. (1997) show that during the period of some oil shocks in 1990s, the forecasters are more uncertain than they should have been. The density forecasts reported in the Survey of Professional Forecasters are affected by these shocks. This motivates us to find whether the predictability comes from the predictive content of commodity price changes to the dispersion measures of the Survey of Professional Forecasters.4 For this purpose, we use commodity price changes to predict the dispersion in the forecasts for economic variables as uncertainty about monetary policy and about government purchases of goods and services at the federal level. The results in Table 2 show that three forecast combinations can significantly outperform the benchmark model for all cases.5 This finding confirms that the predictability can be explained by the influences of commodity price changes on dispersion in forecasters. 4. Concluding remarks We have examined the predictability of economic policy uncertainty (EPU) using input from a basket of 23 commodity price changes. The forecast combinations based on TVP and constant coefficient regressions can significantly beat the AR(1) benchmark. This finding indicates that commodity price changes can provide useful information for future policy changes. In other words, commodity price changes can be taken as a leading indicator of EPU.
4 We also thank a referee for this helpful suggestion. 5 As the Baker et al. (2013)’s data for dispersion amongst forecasters are quarterly, we use the commodity prices in the last month of each quarter to match the data frequency. We just report the one-quarter-ahead forecasting results because they are enough to explain the source of revealed predictability. This is also to save space in this letter.
Acknowledgment This study is supported by the National Science Foundation of China (No. 71401077 and 71320107002). References Antonakakis, N., Chatziantoniou, I., Filis, G., 2013. Dynamic co-movements of stock market returns, implied volatility and policy uncertainty. Econom. Lett. 120, 87–92. Baker, S.R., Bloom, N., Davis, S.J., 2013. Measuring economic policy uncertainty. Working Paper, Stanford University. Codey, B.J., Mills, L.D., 1991. The role of commodity prices in formulating monetary policy. Rev. Econ. Stat. 73, 358–365. Colombo, V., 2013. Economic policy uncertainty in the US: does it matter for the Euro area? Econom. Lett. 121, 39–42. Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. J. Bus. Econom. Statist. 13, 253–263. Diebold, F.X., Tay, A.S., Wallis, K.F., 1997. Evaluating density forecasts of inflation: the survey of professional forecasters. NBER Working Paper, No. 6228. Garner, C.A., 1989. Commodity prices: policy target or information variable? J. Money Credit Bank. 21, 508–514. Gospodinov, N., Ng, S., 2013. Commodity prices, convenience yields, and inflation. Rev. Econ. Stat. 95, 206–219. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Karnizova, L., Li, J., 2014. Economic policy uncertainty, financial markets and probability of US recessions. Econom. Lett. 125, 261–265. Klößner, S., Sekkel, R., 2014. International spillover of policy uncertainty. Econom. Lett. 124, 508–512. Koop, G., Korobilis, D., 2012. Forecasting inflation using dynamic model averaging. Internat. Econom. Rev. 53, 867–886. Marquis, M.H., Cunningham, S.R., 1990. Is there a role for commodity prices in the design of monetary policy? Some empirical evidence. South. Econ. J. 57, 394–412. Pastor, L., Veronesi, P., 2012. Uncertainty about government policy and stock prices. J. Finance 67, 1219–1264. Stock, J.H., Watson, M.W., 2003. Forecasting output and inflation: the role of asset prices. J. Econom. Lit. 41, 788–829. Stock, J.H., Watson, M.W., 2004. Combination forecasts of output growth in a seven country data set. J. Forecast. 23, 405–430. White, H., 2000. A reality check for data snooping. Econometrica 68, 1097–1127.