Table 1: Sign Restrictions on Impulse Response Functions

||**Non-US**|**Economic**|**Precautionary**|**US**|**US**|
|---|---|---|---|---|---|
||**Oil Supply**|**Activity**|**Oil Demand**|**Oil Supply**|**Energy Efciency**|
|_Non-US Oil Production_|+|+|+|-|-|
|_Global GDP Factor_|+|+|-|+|+|
|_Real Price of Oil_|-|+|+|-|-|
|_US Oil Production_|-|+|+|+|-|
|_US Oil Consumption_|+|+|-|+|-|

The reduced-form representation of (5) is given by where **Ai** = **B**<sup>_−_</sup> **0**<sup>**1Bi**and</sup><sup>**ut**=</sup><sup>**B**</sup><sup>_−_</sup> **0**<sup>**1wt**arethemutuallycorrelatedreduced-forminnovationswith</sup> _K × K_ variance-covariance matrix _E_ ( _utu_<sup>_′_</sup> _t_<sup>) = Σ</sup><sup>_u_.</sup>

# **Identification of Structural Shocks**

The structural FAVAR model is set-identified based on a combination of sign and elasticity restrictions. In particular, sign restrictions are imposed on the impact response of endogenous variables to identify five structural shocks: (i) a non-U.S. oil supply shock, (ii) an aggregate economic activity shock, (iii) a precautionary oil demand shock, (iv) a U.S. oil supply shock, and (v) a U.S. energy efficiency shock. The baseline sign restrictions provide a set of candidate impulse responses that are further narrowed down using elasticity restrictions as discussed below.

**_Impact Sign Restrictions._** Table 1 provides the baseline sign restrictions, where signs are imposed on elements of the structural impact multiplier matrix, **B0** , and all shocks are positive by construction.<sup>13</sup> The sign restrictions are in line with the existing empirical literature.<sup>14</sup> For example, a positive oil supply shock, both U.S. and non-U.S., increases respective oil production, decreases the real price of oil, increases the global GDP factor, and increases U.S. oil consumption. Moreover, in response to a positive non-U.S. oil supply shock, U.S. oil production decreases (and vice versa) as real price of oil falls. Examples of positive oil supply shocks include discovery of a new offshore oil field or an unexpected improvement in U.S. shale extraction technology. However, disruptions in OPEC oil supply arising from a conflict in the Middle East or damage to oil platforms and pipelines following a hurricane in the United States are associated with negative non-U.S. and U.S. oil supply shocks, respectively.

> 13Note that since the sign restrictions are only imposed on the structural impact multiplier matrix, all responses following the impact period are unrestricted.

> 14The sign-restricted VAR model builds on the three-variable oil market model of Kilian & Murphy (2012). The signs imposed on oil production, global output, and the real price of oil are, therefore, consistent with Kilian & Murphy (2012), Peersman & Van Robays (2012), and the vast literature that has employed these identifying assumptions (see, amongst others, Kilian & Murphy, 2014; Kilian & Zhou, 2020). The sign-based identifying strategy to disentangle U.S. oil supply and U.S. energy efficiency shocks is a contribution to the literature. The reasoning behind the imposed signs is in line with the empirical evidence, as discussed in this section.

13