- The integrated estimation steps are as follows: 1. Run an unrestricted VAR and find . Implement Cholesky decomposition to extract .<sup>14</sup> 2. Draw a random orthogonal matrix uu and compute  and compute . ΣΣ<sup>�</sup> PP<sup>�</sup>

1. Run an unrestricted VAR and find 2. Draw a random orthogonal matrix uu and compute  and compute .<sup>�</sup>

3. Compute impulse responses using QQ BB<sup>�</sup> = PPQQ<sup>��</sup> 2. Draw a random orthogonal matrix and compute . 3. Compute impulse responses using calculated in the step 2. If all implied impulse response<sup>�</sup> functions satisfy the sign restrictions ( **Table 2** ), retain . Otherwise discard . BB<sup>�</sup> 4. Repeat the first two steps 50,000 times, recording each that satisfies the restrictions and BB<sup>�</sup> BB<sup>�</sup> record the corresponding impulse response functions. About one-fifth of the draws are discarded. BB<sup>�</sup> The commodity price data for aluminum, copper, lead, nickel, oil, tin, and zinc are drawn from the World Bank’s Commodities Price Data ( _Pink Sheet_ ). The price for oil is the unweighted average of the Brent, West Texas Intermediate, and Dubai oil prices. These commodity prices are deflated by the U.S. CPI from the Federal Reserve Economic Data (FRED) database. Quarterly GDP growth rates are from Haver Analytics, with forecasts based on the World Bank’s June 2022, _Global Economic Prospects_ report. Commodity production for aluminum, copper, zinc, lead, nickel, oil, tin, and zinc is drawn from the World Bureau of Metal Statistics. Quarterly averages of monthly data are available for 2000—2022Q1.

# **3.4 Oxford Economics Model (OEM)**

The OEM is a macroeconometric model that is routinely used for growth forecasting in many international institutions and central banks (Guenette and Yamazaki 2021). It includes price series for world food, world beverages, world agricultural raw materials, aluminum, copper, iron, lead, nickel, tin, zinc, coal, oil, and natural gas.<sup>15</sup> These are extracted from the latest OEM forecasts.

The OEM is a macroeconometric model with 46 countries, 6 regional blocs and the Eurozone (Oxford Economics 2019). Most components are specified as error correction models. In the short run, shocks to demand generate economic cycles that can be influenced by fiscal and monetary policy. Over the long-run, output is determined by supply side factors: investment, demographics, labor participation and productivity. The resulting dynamics of short-run fluctuations and long-run trend are integrated in terms of cointegration. We use biannual (Q1 and Q3) forecast data from – 2015Q1 2022Q1 due to data availability.<sup>16</sup>

## **3.5 Machine learning approach**

The EMD-based support vector regression and GARCH model of Zhang, Zhang and Zhang (2015) is selected as a machine learning approach, in line with its generally successful forecast

> 14 We adopt the Gibbs-sampler, an estimation approach that allows for structural identifications such as elasticity and sign restrictions and prior beliefs about future economic events, to estimate a restricted VAR. Although the identification procedure is not required for forecasting, we impose sign-restrictions to ensure compatibility between prediction and scenario analyses.

> 15 Natural gas is a composite of Henry Hub, Japan, and European natural gas prices.

> 16 Since the OEM uses biannual forecasts while other models use quarterly forecasts, its performance may be underestimated by Diebold-Mariano statistic in **Figure 3** because the number of forecasts for OEM is smaller than other models.

14