Table 2: Sign Restrictions on Impulse Response Functions

||**Non-US**<br>**Oil Supply**|**Economic**<br>**Activity**|**Precautionary**<br>**Oil Demand**|**US**<br>**Oil Supply**|**US**<br>**Energy Efciency**|
|---|---|---|---|---|---|
|_Non-US Oil Production_|+|+|+|-|-|
|_Global GDP Factor_|+|+|-|+|+|
|_Real Price of Oil_|-|+|+|-|-|
|_US Oil Production_|-|+|+|+|-|
|_US Oil Consumption_|+|+|-|+|-|
|_Oil Importer/Exporter GDP_|+/-|+|-/+|+/-|+/-|

of structural impulse responses—the estimated impulse response functions (IRFs) are only setidentified because sign restrictions represent inequality constraints. In other words, instead of a unique structural impact multiplier matrix, **B0** , a set of models (i.e., a set of matrices _B_ = _{_ **B0** _|_ **B0B0**<sup>_′_</sup> = **Σu** _}_ ) satisfy the maintained sign restrictions, where some of the admissible models may be empirically implausible. In particular, in the context of oil markets, the empirical evidence indicates that the short-run price elasticity of oil supply is close to zero (see Kilian, 2020, for a survey). Thus, retaining all admissible models may imply magnitudes for the impact price elasticity of oil supply that contradict the existing evidence in the literature.<sup>15</sup>

To mitigate this problem, I follow Kilian & Murphy (2012) to narrow down the set of admissible impulse responses by constructing an upper bound on the one-quarter price elasticity of oil supply. Kilian & Murphy (2012) define the impact price elasticity of oil supply as the ratio of the impact responses of oil production and the real price of oil to an oil demand shock. They compute a value of 0.0258 as an upper bound for this ratio. The rationale behind this computation is as follows: the Iraqi invasion of Kuwait in August 1990 was an exogenous event that partially disrupted oil supply from these two countries and increased demand for oil produced outside Iraq and Kuwait. Moreover, a positive precautionary oil demand shock based on the expectation that Iraq would attack Saudi Arabia next, further raised oil demand. Consequently, the real price of oil increased by 45.3 percent. However, even with the large increase in the oil price, oil production outside Iraq and Kuwait only increased by 1.17 percent. Thus, the ratio of the percent change in oil production outside Iraq and Kuwait to the percent change in the oil price in August 1990 (i.e., 1 _._ 17 _/_ 45 _._ 3 = 0 _._ 0258) can be considered as an estimate of the one-month price elasticity of oil supply (Kilian & Murphy, 2012; Kilian, 2020).<sup>16</sup> The above approach, therefore, motivates the imposition of an upper bound on the ratios of elements of the structural impact multiplier matrix, **B0** . In particular, I restrict the ratios of the impact response of oil production (U.S and non-U.S.) and of the real price of oil to an unexpected increase in aggregate economic activity, precautionary oil demand, and U.S. energy efficiency. This restriction corresponds to selecting admissible models where the ratios _a_ 12 _/a_ 32, _a_ 42 _/a_ 32, _a_ 13 _/a_ 33, _a_ 43 _/a_ 33,

> 15Kilian & Lütkepohl (2017) argue that for sign-identified SVAR models, the burden of proof is on the researcher to use all available information to pin down the magnitudes of interest.

> 16This is regarded as an upper bound on oil supply elasticity during normal times by Kilian & Murphy (2012) because of excess capacity in 1990 and because “there was rare unanimity among oil producers in 1990 that it was essential to offset market fears about a wider war in the Middle East.”

15