**3. Results**

#### *3.1. Identifying Structural Shocks*

Figures 1–4 summarize the empirical results of the SVAR model based on Equations (1)–(4) from Section 2. After obtaining the model estimates, we can calculate the structural residuals.

3.1.1. Quantifying the Evolution of Crude Oil and Natural Gas Demand and Supply Shocks

Figure 1 plots the time path of the structural shocks estimated by the model.

Figure 1 reveals that, at any point in time, the real price of crude oil was reacting to multiple shocks, the combination of which evolved:


(**oil**) aggregate demand shock

**Figure 1.** *Cont.*

**Figure 1.** Historical evolution of structural shocks. From top to bottom, column (**oil**) illustrates crude oil supply, aggregate demand, and oil-specific demand shocks from 1976 to 2019. From top to bottom, column (**gas**) illustrates natural gas supply, aggregate demand, and gas-specific demand shocks from 1996 to 2019. **Note:** Structural residuals implied by Equations (1)–(4), averaged annually.

#### 3.1.2. Responses to One-Standard-Deviation Structural Shocks

Figure 2 plots the responses of global oil and gas production, real economic activity, and the real price of oil and gas to a one-standard-deviation structural innovation.

Figure 2 reveals how global oil and gas production, real economic activity, and the real price of oil and gas responded to demand and supply shocks, respectively, in the crude oil and natural gas markets.

First, the empirical results for crude oil are as follows: Concerning oil supply shocks, we can interpret from the graph that positive oil supply shocks, in which production rose, caused a sharp increase, followed by a reversal of the increase to its initial level within the first quarter. At the same

time, one-standard-deviation oil supply shocks on the real price of oil and real economic activity are statistically insignificant at all observed time horizons observed.

**Figure 2.** *Cont.*

**Figure 2.** Responses to one-standard-deviation structural shocks. From top to bottom, the first column in (**oil**) illustrates the responses of crude oil production, real economic activity, and the real price of oil, to oil supply shocks, aggregate demand shock, and oil-specific demand shock, respectively. From top to bottom, the second column in (**gas**) illustrates the responses of natural gas production, real economic activity, and real price of gas to gas supply shocks, aggregate demand shock, and gas-specific demand shock, respectively. **Note:** Estimates based on Equations (1)–(4).

**Figure 3.** Historical decomposition of the real prices of crude oil and natural gas. From top to bottom, (**oil**) illustrates the cumulative effect of oil supply, aggregate demand, and oil market-specific demand shocks on the real price of crude oil. From top to bottom, (**gas**) illustrates the cumulative effect of gas supply, aggregate demand, and gas market-specific demand shocks on the real price of natural gas. **Note:** Estimates derived from Equations (1)–(4).

Regarding the effect of an aggregate demand expansion on real global economic activity, we can interpret from the graph that a positive aggregate demand shock caused a transitory but substantial increase that reached its maximum in period 2, followed by a gradual decline until the 8th month, and an increase again after 9 months. At the same time, a one-standard-deviation aggregate demand shock caused a very stable and statistically significant increase in the real price of oil.

The series of graphs showing the "(oil) response to an oil-specific demand shock" reveal that oil-specific demand increases had an immediate, large, persistent, and positive effect on the real price of crude oil in the first 2 months, which thereafter gradually declined but remained positive and highly statistically significant. At the same time, these shocks also triggered a statistically significant increase in real economic activity in the first 3 months, followed by a decrease that remained statistically significant until the 9th month. This compares to the results from Kilian [6], in which the statistical significance lasted until the 12th month. Regarding this difference, we estimate that the influence of specific demand shocks on global economic activity is shorter than it was before 2009, which provides evidence for the phenomenon that, as the new economic environment changes rapidly, the economic cycle shortens.

To summarize the crude oil results, aggregate demand shocks had a positive effect on both real global economic activity and the real price of crude oil. Precautionary demand shocks caused a relatively longer and positive effect on the real price of oil, and led to small, transitory increases in real economic activity. These results are generally the same as those reported by Kilian [6], except that Kilian's work showed that oil supply shocks caused a partially statistically significant and small decline in the real price of oil, and caused an extremely small increase in real economic activity, while our results showed that the shocks on the real price and the real economic activity are statistically insignificant.

**Figure 4.** The responses of US real GDP growth and CPI inflation to each structural shock. **Note:** The plots show the cumulative responses, as estimated from the regression models.

gas specific demand shock

oil specific demand shock

Second, the empirical results of natural gas are as follows: Concerning natural gas supply shocks, positive supply shocks where production rose caused small but sharp increases, followed by a return to its initial level within the first quarter. At the same time, a one-standard-deviation natural gas supply shock caused a partially statistically significant decline in the real price of natural gas in the first 3 months, and caused a negligible increase in real economic activity.

Regarding the e ffect of an aggregate demand expansion on real global economic activity, we can interpret from the graph that a positive aggregate demand shock caused a transitory and highly significant increase that reached its maximum level in the 2nd month, followed by a gradual decline until the 8th month, and an increase again after 9 months. This result is similar to the result of the crude oil model. Aggregate demand shocks also caused a very stable and statistically significant increase in the real price of natural gas.

The last natural gas graph reveals that gas-specific demand increases have an immediate, noticeable, stable, and statistically significant positive e ffect on the real price of natural gas that gradually declines after the 3rd month but remains positive. At the same time, these shocks also triggered extremely small increases in real economic activity, followed by declines and then small increases that were statistically insignificant by the 10th month. This result suggests that precautionary demand shocks to natural gas hardly a ffected real economic activity.

To summarize the natural gas results, aggregate demand shocks had a positive e ffect on real global economic activity and the real price of natural gas. Precautionary demand shocks caused a relatively shorter, positive e ffect on the real price of natural gas.

Comparing the results between crude oil and natural gas reveals that they are similar, with minor di fferences. The major distinction relates to the di fferent e ffects on real economic activity that result from precautionary demand shocks to crude oil versus natural gas.

#### 3.1.3. The Cumulative E ffect of Oil and Gas Demand and Supply Shocks on the Real Prices of Oil and Gas

According to the results of a historical decomposition of the data sets, the respective cumulative contributions of demand and supply shocks to the real prices of crude oil and natural gas are plotted in Figure 3.

Figure 3 reveals the respective cumulative contributions of oil and gas demand and supply shocks to the real prices of oil and gas.

First, the empirical results for crude oil are as follows: The top graph implies that real oil supply shocks have historically made relatively small contributions to the real price of crude oil. The biggest contributions have been oil market-specific demand shocks. While aggregate demand shocks led to long swings in real global economic activity, oil market-specific demand shocks were the primary reasons for relatively sharp and defined increases or decreases in the real price of oil. This result is consistent with the results investigated above, and provides further evidence for the proposition that precautionary demand shocks cause relatively immediate increases in real prices. Furthermore, the shocks cause relatively small but stable increases in real economic activity.

To summarize these results for crude oil, precautionary demand shocks made the greatest contributions to the real price of oil. Our results for crude oil are approximately similar to Kilian [6], but one concern is that, during the period 1985–2000, Kilian's study showed a negative cumulative effect of an aggregate demand shock on the real price of crude oil, while the e ffect in our study was extremely close to zero.

Second, the empirical results for natural gas are as follows: The first graph shows that real gas supply shocks have historically made relatively small contributions to the real price of natural gas. The largest contributions were due to global aggregate demand shocks and specific demand shocks in the oil market. However, aggregate demand shocks displayed a long-term and relatively smooth movement in the real price of natural gas. In contrast, gas market-specific demand shocks accounted for the sharply defined increases and decreases. This result implies the same suggestion that we already stated above regarding crude oil.

To summarize the natural gas results, the cumulative contribution of precautionary and aggregate demand shocks accounted for a large proportion of the real price of natural gas. From these empirical results for natural gas, attention should be paid to the fact that, during the years of financial crises in 1998 and 2008, the degree of the cumulative e ffect of the precautionary demand shocks was di fferent; specifically, the cumulative contribution of the oil-specific demand shock to the real price of oil is larger than the cumulative contribution of the gas-specific demand shock to the real price of gas. This issue remains open for investigation in the future.

Comparing these two results, the major di fference between oil and gas was the cumulative e ffect of precautionary demand shocks on their real prices.

#### *3.2. E*ff*ects on the US Economy*

Based on estimations from Equations (5)–(8), Figure 4 plots the responses of US real GDP and CPI to each of the three shocks defined previously.

The results in Figure 4 reveal important di fferences in how oil and gas demand and supply shocks that underlie the real prices of oil and gas a ffect US macroeconomic aggregates such as US real GDP growth and CPI inflation.

First, the empirical results for crude oil are as follows: The graphs of the (oil)-cumulative response of US real GDP/CPI levels to an oil supply shock imply that oil supply shocks created a partially statistically significant decrease in US real GDP from its initial level and a rise in the 3rd year. The effect on US real GDP was negative for all 16 quarters; however, the two standard error bands were statistically significant for only half a year, compared to the two years reported in Kilian [6]. In contrast, the corresponding e ffects on the CPI level were mostly statistically insignificant, and displayed a declining tendency.

The graphs of the (oil)-cumulated response of the US real GDP/CPI levels to an aggregate demand shock indicate that unanticipated aggregate demand shocks increased US real GDP statistically significantly in the first year, and then caused the GDP level to decline below its initial level in the 2nd year, with the decrease becoming statistically significant again after the 3rd year. In contrast, the corresponding e ffects on the level of CPI indicated a persistent, gradual increase that was statistically significant at all time horizons observed, whereas in Kilian's results it became statistically significant only after the 3rd quarter [6].

Finally, unanticipated oil-specific demand shocks lowered US real GDP gradually, and the reduction was statistically insignificant at all observed time horizons. In contrast with this result, Kilian [6] showed that the decline reached its maximum in the 3rd year, and implied statistical significance in the 3rd year of under one standard error band. It should be noted that Kilian's results were also statistically insignificant under two standard error bands. Meanwhile, these shocks led to a sustained, gradual, and statistically significant increase in the US CPI level, which is consistent with Kilian's results [6].

To summarize the results for crude oil, our first result was that oil supply shocks led to transitory reductions in the US real GDP level, and barely a ffected the CPI level. Second, aggregate demand shocks had positive e ffects on US GDP growth during the first year and stimulated immediate increases in the CPI level, which is a di fferent result from Kilian [6]. Kilian found that aggregate demand shocks caused delays in the rise of the CPI level for 3 quarters. Third, oil-specific demand shocks led to increases in the CPI inflation level and barely a ffected the US real GDP level.

Second, the empirical results for natural gas are as follows: The graphs of the (gas)-cumulative response of US real GDP/CPI level to a gas supply shock imply that the responses of the US real GDP and CPI levels to gas supply shocks are relatively small and statistically insignificant.

The graphs of the (gas)-cumulative response of US real GDP/CPI levels to an aggregate demand shock reveal that unanticipated aggregate demand shocks caused extremely small, statistically insignificant increases in the US real GDP level within 2 quarters, and then caused the real GDP level to decline below its initial level after the 3rd quarter, with the decrease becoming partially statistically significant after the 3rd year. In contrast, the corresponding e ffect on the level of CPI showed a sustained, gradual increase, and was statistically significant for all 16 quarters.

The graphs of the (gas)-cumulative response of US real GDP/CPI levels to a gas-specific demand shock indicate that unanticipated gas-specific demand shocks reduced the US real GDP level gradually, slightly, and statistically insignificantly. In contrast, these shocks led to sustained, gradual, but statistically insignificant increases in the US CPI level.

To summarize the results for natural gas, our first result was that gas supply shocks barely a ffected the level of US real GDP or CPI. Second, aggregate demand shocks caused a gradual decline in US real GDP growth that was partially statistically significant, but stimulated an immediate and statistically significant increase in the CPI level. Third, gas-specific demand shocks hardly a ffected the US real GDP and CPI inflation levels.

To compare these two results, the major di fference was that precautionary demand shocks in crude oil and natural gas had di fferent e ffects on CPI inflation. Oil market-specific demand shocks tended to statistically significantly increase the CPI inflation level greatly; in contrast, gas market-specific demand shocks led to a small and statistically insignificant increase in the CPI inflation level. Another point is that aggregate demand shocks in the oil market increase and then lower the US real GDP level significantly for the most part, whereas aggregate demand shocks in the gas market led to insignificant decreases in the US real GDP level for the most part.

## **4. Conclusions**

This paper investigated the response of US macroeconomic aggregates to price shocks in crude oil and natural gas markets using a two-step approach: firstly decomposing the price shocks to identify the structural shocks using a structural VAR model, and secondly, showing the response patterns of macroeconomic aggregates corresponding to each structural shock using a regression model.

Our main findings in this study are threefold. First, we found that there was a di fference in the effects on real economic activity due to precautionary demand shocks from crude oil versus natural gas. Second, the cumulative contribution of oil-specific demand shocks to real oil prices is larger than the cumulative contribution of gas-specific demand shocks to real gas prices. Third, precautionary demand shocks had di fferent e ffects on CPI inflation, depending on whether they were due to crude oil or natural gas. Therefore, economists, policymakers, and investors must decompose real prices of these important energy sources that have such significance in the economy and our daily lives. Finally, the most noteworthy of our findings is that oil market-specific demand shocks lead to statistically significant increases in the US CPI level, however, gas market-specific demand shocks barely a ffect the US CPI level. This result implies policymakers should react di fferently to gas-specific demand shocks and oil-specific demand shocks.

The similarities and di fferences between our empirical results and those of Kilian [6] can be summarized as follows. Firstly, comparing the results which showed the responses of global oil/gas production, real economic activity, and the real price of oil/gas to structural innovation reveal that they are alike with minor di fferences. The major distinction is the di fferent e ffects on real economic activity that result from precautionary demand shocks to crude oil versus natural gas. Another point is that the statistically significant lasting period of influence from oil-specific demand shocks on global economic activity were shorter than they were prior to 2009, as the results from Kilian [6] showed. Secondly, comparing the results of the historical decomposition of real prices, our results for crude oil are approximately similar to Kilian, but one concern is that, during the period 1985–2000, Kilian's study showed a negative cumulative e ffect of an aggregate demand shock on the real price of crude oil, while the e ffect in our study was extremely close to zero [6]. Thirdly, comparing the result of effects of respective shocks on the US macroeconomy, the empirical results are very similar with minor di fferences. The results of oil supply shocks on GDP showed that the two standard error bands were statistically significant for only half a year, compared to the two years reported in Kilian [6], which was explained by the one standard error band. Because of the di fferent adoption of the standard error band, unanticipated oil-specific demand shocks led to a statistically insignificant reduction in US real GDP for all observed time horizons, whereas Kilian's results implied statistical significance in the 3rd year [6].

Compared to previous literature, namely Zhang et al. (2017) [13], the similarities and discrepancies should be noted. Because not all natural gas price shocks cause GDP to decrease and the CPI to increase, when natural gas price increases originate from increasing uncertainty of the energy market, GDP would decline, and the CPI would rise. However, when natural gas price shocks are due to exogenous supply shocks, GDP would not always decrease, while the CPI would decline, which is a di fferent outcome from that relating to aggregate shocks and specific demand shocks.

In this paper, the empirical evidence may have some implications for economists, policymakers, and investors albeit their self-evidence. Because our empirical results showed that the response patterns vary depending on the causes of the price fluctuations, not only for the crude oil market, but also the natural gas market, economists should take this into account when they construct their models for researching about oil/gas price shocks. Regarding the policy-making implications, especially for governmen<sup>t</sup> monetary authorities such as central banks, there is a need to identify the underlying determinants that drive the price increases to make appropriate policy. For example, when the oil or gas price increase stems from an exogenous supply shock, there is almost no need to undertake any countermeasures because these kinds of shocks have a minimal e ffect on the macroeconomic aggregates. In contrast, with supply shocks, in which the price increases because of surging uncertainty in the oil market, thereby stimulating an increase in precautionary demand, monetary authorities should consider whether countermeasures should be undertaken to retard ongoing inflation; there is almost no need to take such countermeasures into account in the case of the gas market. Another implication concerns aggregate demand shocks: policymakers should distinguish where the aggregate demand shocks originated i.e., the crude oil market or the natural gas market. If the source of the shock lies in the oil market rather than the gas market, the corresponding responses should take into consideration prevention of a reduction of the GDP level over the long-run. As for the long-term investment implications, firstly, the investors must distinguish the origins of the oil/gas price fluctuation because the response pattern of each shock is di fferent and requires distinct investment adjustments. Secondly, investors should pay attention to global aggregate demand shocks, and the specific demand shock rather than supply shocks, when they reconsider their investment structure, because precautionary demands shocks make a greater contribution to real price fluctuations than exogenous supply shocks. Because of developing environmental awareness, the demand for natural gas is gradually increasing and growing in importance in energy markets, thus implying that investors should take natural gas as an alternative investment choice for their portfolio adjustment when turbulence occurs in crude oil markets.

Despite our findings, this investigation has several limitations. First, the range of the dataset of natural gas prices is from 1994, which makes it impossible to compare the cumulative e ffect of demand and supply shocks between crude oil and natural gas during the period 1973–1993. Second, we adopted the Kilian Index (Kilian [6]); however, whether the Kilian Index is an adequate reflection of overall economic activity after 2009 is beyond the scope of this study. Because the driving forces and factors which influence global economic activity may have changed after 2009, there may now be a more appropriate index. Third, as mentioned above, during the period 1985–2000, Kilian's study showed a negative cumulative e ffect of an aggregate demand shock on the real price of crude oil, while the e ffect in our study was extremely close to zero. The proper explanation for this outcome remains unknown and requires further research.

Therefore, in our future research, first, we plan to identify a more appropriate index to reflect overall global economic activity, and compare the results with those based on the Kilian Index. Second, as noted in Section 3.1.3, the cumulative contribution of an oil-specific demand shock to real prices is larger than the cumulative contribution of a gas-specific demand shock. Thus, we intend to identify the underlying determinants or causes of this issue. Third, in order to e ffectively apply our results to the policy-making process and inform appropriate monetary policy, we propose to extend the results by a machine learning approach to forecast price fluctuations corresponding to various kinds of uncertainty conditions, namely financial crises, wars, emergencies, disasters, etc. Fourth, the approach of Kilian [6], followed herein, did not include analysis of cointegration; thus, we plan to expand the analysis within the framework of cointegration. Finally, assessing the e ffects of oil/gas price shocks on other major countries' macroeconomic aggregates is also worthy of extending the current investigation in future research.

**Author Contributions:** Investigation, J.S.; writing—original draft preparation, J.S.; writing—review and editing, S.H.; project administration, S.H.; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript

**Funding:** This work was supported by JSPS KAKENHI Grant Number (A) 17H00983.

**Acknowledgments:** We are grateful to four anonymous referees for their helpful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
