Oil Threshold Value between Oil Price and Production

This study proposes a panel smooth transition regression (PSTR) model to investigate the nonlinear relationship between crude oil prices and crude oil production in 122 countries, both OPEC and non-OPEC, from March 1994 to October 2015. The statistical test for the existence of a threshold effect indicates that the relationship between oil prices and oil production is nonlinear, with different changes over time among the oil price and transition variables. Additionally, a threshold value exists. Furthermore, crude oil price volatility exhibits asymmetric responses to production volatility by fluctuating above or below the threshold value. Finally, when crude oil price volatility with a lag of two periods exceeds the threshold value, crude oil production changes have a positive impact on crude oil price volatility. In contrast, when crude oil price volatility with a lag of two periods is less than the threshold value, crude oil production changes have a negative impact on price volatility.

Understanding crude oil price movement is crucial to economic activities (Jungwook Park and Ronald A. Ratti 2008;Yanan He, Shouyang Wang, and Kin Keung Lai 2010;Stefan F. Schubert and Stephen J. Turnovsky 2011;Saidi Atanda Mustapha and Luqman Adedamola Sulaiman 2015). There are three oil surges: in 1973, from 1979to 1980, and from 2003to 2008. Fabian Kesicki (2010 found that the first two oil crises were rooted primarily in the market power of the Organization of Petroleum Exporting Countries (OPEC) and in political issues, whereas all three surges were spurred by high growth in demand. The price of crude oil is determined by market supply and demand (Jochen H. F. Güntner 2014). Recently, there has been increasing recognition that flow demand and supply shocks significantly contributed to most major oil price increases. Lutz Kilian (2009) showed that changes in crude oil prices were driven by demand shocks rather than supply shocks. This conclusion was later reconsidered by Marek Kolodzeij and Robert K. Kaufmann (2014), who found that it was not robust to alternative specifications. Their results differ from Kilian (2009) due to the aggregation of OPEC and non-OPEC production, inclusion of transportation costs, and use of a cointegrated vector autoregressive model (CVAR). The Arab Еmbargo (1973-1974), the Iranian Revolution (1978)(1979), and the Persian Gulf War (1990War ( -1991 caused considerable production losses by influencing the flow of

Literature Review
Although crude oil production significantly affects its price, the crude oil price-production relationship has not been explored in detail. Many previous studies strongly emphasize the impact of oil consumption on price and omit production from consideration. Recently, several papers reconsidered the role of crude oil production in its price. The results from Granger causality tests in Andres Gallo et al. (2010) generally indicated that the recent surges in oil prices are connected to oil production rather than consumption. Certain emerging countries, such as China, consume large quantities of PANOECONOMICUS, 2019, Vol. 66, Issue 4, pp. 487-505 oil, which could cause oil price fluctuations in the future. In addition, the level of demand for oil depends on particular countries. Hence, there is a scarcity of previous research based on changes in consumption, which have been responsible for previous fluctuations in oil prices. Additionally, Robert L. Linn (2006) concluded that the major effect of oil surges was to decrease planned production levels. Recently, Nicholas Apergis, Bradley T. Ewing, and James E. Payne (2016) indicated that the crude oil prices and rig counts positively influence oil production. Consequently, the investigative movement stops at the effect of crude oil price on its production, which is positive. However, the effect of crude oil production on crude oil prices and whether this effect is linear or nonlinear remain unknown.
Regarding the scope of empirical analyses relating to the threshold model, most studies focus primarily on the asymmetric effects of changes in crude oil prices on refined products, exchange rates, stock prices or other economic indexes rather than crude oil production. Bwo-Nung Huang, M. J. Hwang, and Hsiao-Ping Peng (2005) explored the asymmetric impact of oil price movement and volatility on economic variables including output, stock returns and interest rates in the United States (US) (a net oil importer), Canada (a net oil exporter), and Japan (a pure oil importer) from 1970 to 2002. Later, Jer-Yuh Wan and Chung-Wei Kao (2015) attempted to analyze the nonlinear correlation between oil and financial variables with a structural threshold vector autoregressive model (STVAR) model using monthly data on US interest rates, US dollar exchange rates, and financial stress indexes from 1975 to 2014. Consequently, there was an asymmetric impact of shocks in different financial stress regimes. Specifically, shocks are larger in stressed regimes than in normal regimes. Depreciation of the US dollar is prone to cause an increase in oil prices, whereas a positive oil shock can cause an increase in the US dollar. Empirical research from Yu Shan Wang and Yen Ling Chueh (2013) on the relationship between crude oil prices and other financial indicators (including the interest rate, the US dollar, and gold) from 1989 to 2007 shows the influence of these variables on each other. Several threshold models were adopted, including a momentum threshold autoregression (MTAR) model (to identify the optimal threshold level of each criterion) and a threshold error correction model (TECM) (to analyze the threshold effects). The authors suggested that above and below the threshold values, gold and crude oil prices influence not only each other but also the interest rate. In addition, the present value of the US dollar has no influence on the price of crude oil in the future. Ahmad and Hernandez (2013) detected the asymmetric adjustment between real oil prices and the real exchange rate of domestic countries with respect to the US dollar from 1970 to 2012. Their methodology included the threshold autoregressive (TAR) method and the MTAR method. Their results indicated the cointegration of five countries -Brazil, South Korea, Mexico, Nigeria, and the United Kingdom (UK) -and the European Union. In particular, Brazil, Nigeria and the UK exhibited greater adjustments in response to positive shocks than to negative shocks, which means that an increase in exchange rates following an increase in oil prices is eliminated faster than an increase in exchange rates following a decrease in oil prices. The topic of nonlinear cointegration between international crude oil prices and the exchange rate was also recently discussed by Sajal Ghosh and Kakali Kanjilal (2016). In the stock market field, Hui-Ming Zhu, Su-Fang Li, and Keming Yu (2011) PANOECONOMICUS, 2019, Vol. 66, Issue 4, pp. 487-505 adopted a panel threshold cointegration framework to study the linkages between crude oil prices and the stock markets of 14 countries, and their main finding indicated the presence of asymmetric threshold relations between crude oil prices and the stock markets. For example, crude oil prices rise 1% following a 0.43% increase in stock prices. In contrast, a 1% increase in stock prices leads to a 0.54% change in oil prices. Additionally, the adoption of a threshold generalized autoregressive conditional heteroskedasticity (TGARCH) model was used by Tzu-Yi Yang and Yu-Tai Yang (2015) to investigate the asymmetric effects of news on stock market behavior. Xiao Qin, Chunyang Zhou, and Chongfeng Wu (2016) investigated a rockets and feathers theory with a multiple threshold error-correction model (MTECM) and found a nonlinear relationship in the short-term between crude oil and gasoline prices in commodity and financial markets but not in refinery markets.
Regarding agriculture, Valeri Natanelov et al. (2011) first ran the vector error correction model (VECM) and the threshold vector error correction model (TVECM) based on Bruce E. Hansen and Byeongseon Seo (2002) identified linkages between crude oil prices (Brent) and the cocoa, wheat, and gold markets. There was no cointegration or threshold effect of the oil-corn relationship, which implies that biofuel policy buffers the co-movement of the oil and corn markets when crude oil futures prices exceed an estimated threshold level (US $75 per barrel in July 2006).
With respect to oil prices, Yudong Wang and Wu (2013) reconsidered the cointegration relationship between spot and future crude oil (West Texas Intermediate (WTI)) prices because many previous studies had shown linearity in a long-run equilibrium adjustment process. Instead of a conventional framework, they used a nonlinear TVECM and a threshold Lagrange Multiplier (LM) test proposed by Hansen and Seo (2002). In contrast to the linear results found in Søren Johansen (1988), they found a cointegration relationship that exhibited threshold effects. When the futures basis exceeds a threshold value, the crude oil spot and futures prices are cointegrated. Futures prices are expected to drive spot prices in the short-term, whereas both spot and futures prices can drive each other to long-run equilibrium levels. Hassan Belkacem Ghassan and Hassan Rafdan AlHajhoj (2016) calculated the asymmetric dynamics of OPEC and non-OPEC crude oil prices from 1973 to 2013 by running error correction model (ECM), TAR, and MTAR models with a threshold cointegration and component generalized autoregressive conditional heteroskedasticity (CGARCH) error framework. They detected differences in the speed of adjustment. In the case of positive deviation, for the long-run equilibrium, the OPEC crude oil price adjustment process is slower than the process for non-OPEC prices, which contrasts with the short-term equilibrium. This result implies that OPEC producers have less of an impact on crude oil prices in the long-term than non-OPEC producers have in the short-term. Moreover, both OPEC and non-OPEC prices have the same reaction to a negative regime when the oil price is too low.
Many threshold models have been adopted to analyze nonlinearity, including TAR, the Markov Switching (MS) model, the neural network (NN) model, smooth transition autoregressive (STAR), MTAR, TECM, and the PSTR model. As shown in Burcu Kiran (2012), the TAR model can derive endogenous threshold effects. However, the TAR model is not suitable for this study due to its time-series feature.
Additionally, the traditional threshold models for two regimes and a zero threshold level fail to expose asymmetric patterns (Qin, Zhou, and Wu 2016). The switching process of economic variables in an MS model is radical and discrete just for its actual movement. The NN model judges the regime process through the human brain and thus lacks objective meaning. Depending on the research purpose, these models are used to examine time series and panel data. The PSTR model is helpful in handling panel data with cross-sectional and time-series characteristics. The advantages of the PSTR model are clearly indicated in a number of studies, as mentioned below.
The recent empirical literature indicates that the adoption of the PSTR model to examine threshold effects has become a focal point. In the oil price field, Marc Joëts and Valérie Mignon (2012) used the PSTR model to study the cointegration relationship among the prices of oil, gas, coal, and electricity at 35 maturities because PSTR can model the nonlinear behavior of the forward energy price adjustment process to the equilibrium value given by the estimated long-term relationship between the prices of oil, gas, coal and electricity. The findings showed that the forward oil price adjustment process to its equilibrium value is nonlinear and asymmetric. The estimated threshold is 36%, which implies an asymmetric phenomenon wherein the adjustment process is at regime for high under-valuations, not over-valuations. Apergis and Payne (2014) detected the cointegrated relationship among renewable energy consumption per capita, real gross domestic product (GDP) per capita, carbon emission per capita, real coal prices, and real oil prices in seven Central American countries from 1980 to 2010. The estimated value of the threshold was -0.00175, reflecting the extreme regimes in the negative and positive values of renewable energy consumption per capita. Their results revealed that in the post-2002 period, the effect of renewable energy consumption per capita -specifically, on real coal and oil prices -is more sensitive to real GDP per capita than to carbon emissions per capita. In addition, Wang (2013) investigated the smooth transition effects of oil price changes on personal consumption expenditures in the G7 economies using quarterly data from 2005 to 2010. Using the PSTR model of González, Teräsvirta, and Van Dijk (2005), the author found a nonlinear, asymmetric relationship between crude oil price fluctuation and personal consumption expenditures. The estimated threshold level of oil prices after a lag of one period was 0.92, and the transition speed was 4.8, implying different effects of oil price changes on personal expenditures in cases above and below the threshold level. Below the threshold level, a 1% increase in oil prices will lead to a 0.6893% decrease in personal expenditures in G7 countries. In contrast, each 1% decrease in oil prices will increase the marginal effects of personal consumption expenditures by 0.0517%. Jean-Pierre Allegret et al. (2014) focused on the price of oil in their study of current account relationships across 27 oil-exporting countries from 1980 to 2010. As discussed in this paper, the PSTR model offers many advantages, including that it allows this relationship to vary over the time period associated with the level of financial development and that it estimates the threshold value of financial development. By following the PSTR model of González, Teräsvirta, and Van Dijk (2005), the dependent variable and independent variable are the current account to GDP ratio and the oil price, respectively. The transition variable was expressed by the degree of financial development. The results indicated a nonlinear impact of oil price fluctuation on the current account PANOECONOMICUS, 2019, Vol. 66, Issue 4, pp. 487-505 position according to the level of financial development of each country. The threshold value of financial depth is 25%. Oil price variations have a stronger effect on the current account position in less financially developed oil exporters than in exporters with a high degree of financial depth.
A review of the above studies reveals a gap in the research on nonlinearity and the asymmetric responses of the price of crude oil to its production and shows that the threshold model is typically adopted. This paper sheds new light on the nonlinear relationship between the price of crude oil and its production using a panel threshold model, thereby addressing the gap in the research and making both practical and empirical contributions to the field. More specifically, this study aims to detect nonlinear effects on the relationship between crude oil prices and crude oil production by adopting the PSRT model of González, Teräsvirta, and Van Dijk (2005). Details regarding the data, methodology, and model used will be provided in the following section.

Database
The dataset includes monthly oil price and production data from March 1994 to October 2015. Data for oil prices and oil production are obtained from databases of the International Monetary Fund (IMF 2016) 1 and the EIA (2016b) 2 , respectively. Oil price and production are measured in dollars per barrel and thousands of barrels per day, respectively.
As mentioned in the EIA (2014) 3 , the most significant benchmarks in crude oil pricing are Dubai, Brent, and WTI. Based on their specific characteristics, the EIA classifies these benchmarks based on the places where oil is priced. Brent and WTI are mostly used in Asia, Europe, and America. Hence, the data structure is divided into three regimes: Asia, Europe, and America. Therefore, the panel dataset of crude oil prices corresponds to the oil benchmarks used by the regimes.
This study leverages the EIA database by ascertaining monthly crude oil production in 12 OPEC countries and 110 non-OPEC countries, for 122 countries in total. These countries are listed in Table 1. The countries are classified as OPEC or non-OPEC countries in all years based on their status in the current year.
The data structure is cross-sectional among the crude oil production of these countries and crude oil prices. Thus, it requires the correct matching of data on crude oil production in each country to the appropriate oil benchmark (Dubai, Brent, and WTI). Specifically, Brent is used to price light, sweet crude oil that is produced and traded in Europe, the Mediterranean, Africa, Australia and certain countries in Asia, including Indonesia, Malaysia, and Vietnam. WTI is an oil benchmark for medium, sour crude oil produced in the Gulf of Mexico; light, sweet crude oil produced in the United States; and imported crude oil produced in Canada, Mexico and South America. Finally, Dubai is the benchmark for medium, sour crude oil that is produced in the Middle East and exported to Asian markets.

Description of Variables
This work applies the PSTR model developed by González, Teräsvirta, and Van Dijk (2005). This nonlinear model contains three main parts -the dependent variable, transfer variable and independent variable -which allows the sequence to move smoothly in two regimes with different values for the transition variable. The aim of this study is to analyze the threshold effect of crude oil prices on its production with the PSTR model, using changes in crude oil price and production as the dependent and independent variable, respectively. The following sections describe these data.
The dependent variable indicates monthly crude oil price volatility and can be written as ∆ , . This variable represents crude oil price volatility that is consistent with an oil benchmark at a specific time where = 1, 2, 3 denotes the oil benchmark -Dubai, Brent, and WTI -and = 1, 2, 3 … denotes time. ∆ , is the monthly crude oil price volatility of an oil benchmark (Dubai, Brent, or WTI) in period ( ). The value of the dependent variable at the current time is evaluated as the crude oil price at present minus the price in the previous month.
The independent variable is implied by changes in monthly world crude oil production, which is the total of OPEC and non-OPEC crude oil production. It is signified by ∆ , , where represents the cross-section of countries ( = 1,2,3 … ) and is the time period ( = 1,2,3 … ). ∆ stands for changes in crude oil production. ∆ , denotes changes in the crude oil production of a specific regime ( ) at time ( ). The value of changes in monthly global crude oil production can be calculated as the difference between the present data and previous data.
The transfer variable plays an important role in the PSTR model and is a previous crude oil transition function that is denoted by ( ; , ). Its value can be expressed by crude oil volatility with a lag of two periods, ∆ , . Specifically, ∆ , denotes the crude oil price volatility of a particular oil benchmark ( ) at a specific time ( − 2). To calculate the crude oil price-production relationship, the data flow from March 1994 to October 2015 is chosen because of a requirement in the previous data for ∆ , . The transition function describes the smooth switching process of the crude oil price. The optimal lagged transition variable is determined by the minimum Akaike information criterion (AIC) and Bayesian information criterion (BIC). The transition variable can be written as follows: where > 0 and ≤ ≤ ⋯ ≤ . When = 1 and → ∞, the PSTR model is reduced to a panel transition regression model. González, Teräsvirta, and Van Dijk (2005) considers only two cases, = 1 and = 2, to capture nonlinearities caused by regime switching. As noted by González, Teräsvirta, and Van Dijk (2005), the transition function is bounded between 0 and 1. Additionally, the extreme values are consistent with the regression coefficients and + . In addition, is the observable variable that determines the value of the transition function ( ; , ) and thus the effective regression coefficient + ( ; , ) for individual ( ) at time ( ). Table 2 presents the names, codes, measurements, and data sources of the variables. Crude oil price volatility ∆ , Crude oil price at present minus this value in the previous month of a specific oil benchmark ( ).

IMF (2016)
Crude oil price volatility with a lag of two periods ∆ , Crude oil price at present minus this value in the previous two months of a specific oil benchmark ( ).

IMF (2016)
Changes in crude oil production ∆ , Value of crude oil production of regime ( ) at present minus this value in the previous month.

EIA (2016b)
Notes: (1) ∆ , presents the monthly crude oil price volatility of a specific oil benchmark ( ) at time ( ). ∆ , 2 , which is a lag of two periods of ∆ , , means the monthly crude oil price volatility of oil benchmark ( ) at time ( − 2). ∆ , is the monthly crude oil production of regime ( ) at time ( ); (2) The sampling period is from March 1994 to October 2015.

The Panel Smooth Transition Regression Model
As discussed by , the PSTR model is more flexible than the panel threshold regression (PTR) model. Indeed, the PSTR model offers the advantage of allowing crude oil price volatility regression coefficients to vary across countries and time depending on the level of the transition variable. PSTR also allows for smooth changes in cross-sectional correlations, cross-sectional heterogeneity, and the time instability of the impact. PSTR is especially useful when measuring threshold effects because it shows different responses of the independent variable to the dependent variable to coincide with levels above, below, and equal to threshold value. Therefore, it is appropriate to adopt the method developed by González, Teräsvirta, and Van Dijk (2005) to simultaneously evaluate nonlinear effects and resolve heterogeneity problems. The model can be written as follows: where = 1,2, … , denotes the number of transition functions, ( + 1) is the number of regimes, and is the time period ( = 1,2,3 … ).
Denoting the dependent, independent, and transition variables above, the PSTR model is given by: where = 1,2, … denotes the number of transition functions and ( + 1) is the number of regimes.
; , is a transition function with as a transition variable and , as the transition parameter and transition threshold value. ∆ , is the monthly crude oil price volatility of a particular oil benchmark (Dubai, Brent, or WTI) in period ( ). It is a dependent variable. ∆ , represents changes in the crude oil production of specific regime ( ) at time ( ). It is an independent variable.

Estimation and Specification Test
There are three main phases in the testing process. First, the panel unit root test is employed to test a stationary set of variables. The explanation may be that the characteristics of variables across nations and time series result in a nonstationary series.
Then, if the test shows stationary characteristics of variables, the test of nonlinearity will be used to answer the major question presented at the beginning of this paperthat is, whether crude oil prices and crude oil production have a nonlinear relationship. If not, then the next stage will be implemented, which is the examination of the number of threshold points in the relationship between crude oil price and production. González, Teräsvirta, and Van Dijk (2005)  If the null hypothesis of linearity is not rejected, there are transition effects. Thus, the next step is to determine the number of transition functions. If the hypothesis for one threshold value is rejected, then the model has at least one threshold value. In this case, a test to confirm the number of threshold values is required. The testing procedure is continued until the hypothesis without an additional threshold is not rejected. Finally, to estimate the parameters of Equation (3) where is the number of explanatory variables. Under the null hypothesis, the statistic has an asymptotic ( ) distribution.

Descriptive Statistics
The observed variables for crude oil price and crude oil production during the given time period are displayed in Table 3. The minimum, maximum and average values and the standard deviations are provided in the columns corresponding to each variable. For the first variable, ∆ , , the Dubai oil benchmark has the largest range between the minimum (-27.35) and the maximum (15.48). For ∆ , , changes in Dubai oil prices are largest, with a maximum value of 24.12, whereas the WTI has a minimum value of -46.65. In the case of ∆ , , changes in the production of the Dubai oil regime are highest, with a maximum of 1263.627, whereas the WTI has the lowest minimum, -1701.742.

Correlation and Collinearity
It is necessary to test the correlation among the variables. If they are aggressively correlative, then there is collinearity. Thus, the results become less useful because the variables partly explain each other.
It is obvious from Table 4 that there is no collinearity problem among the explanatory variables because they are not aggressively correlated. Specifically, the correlation coefficients between ∆ , and ∆ , , between ∆ , and ∆ , and between ∆ , and ∆ , are 0.3699, -0.0190 and 0.0253, respectively. Therefore, the correlation between ∆ , and ∆ , and between ∆ , and ∆ , are positive, which means that when changes in the crude oil price volatility with a lag of two periods increase, the value of crude oil price volatility and changes in crude oil production also rise. However, the value of the correlation coefficient between ∆ , and ∆ , is 0.0253. The positive correlation implies that as the value of crude oil price volatility with a lag of two periods increases, the value of changes in crude oil production also increases. The correlation coefficient between ∆ , and ∆ , is higher, with a value of 0.3699. The correlation coefficient between ∆ , and ∆ , is -0.019, indicating a negative correlation. There is also a difference in the tendency of movement between them. When changes in crude oil production increase, crude oil price volatility decreases. Notes: Same as Table 2.
Source: Authors' estimation based on data from EIA (2016b).

Panel Unit Root Test
This step applies the Levin-Lin-Chu (LLC) panel unit root test method (Andrew Levin, Chien-Fu Lin, and Chia-Shang James Chu 2002) to examine the relevant variables and determine whether they are stationary or nonstationary. Specifically, the testing hypothesis for the panel unit root test is indicated below: H 0 : Has a unit root. H 1 : Does not have a unit root.
Source: Authors' estimation based on data from EIA (2016b).
It is apparent from Table 5 that the results are significant for all variables, indicating that H 0 is rejected and H 1 is supported. Here, the hypothesis "does not have a unit root" is accepted. This result reveals that the variables in the panel data that were contributed by cross-sectional and time-series sections are in a stationary series. Additionally, this result implies that it is possible to test for nonlinearity.

Linear Tests
As shown by the results of the panel unit root test, all variables are consistent with a stationary series. Therefore, it is logical to continue testing to determine whether the model reveals a nonlinear relationship between crude oil price and crude oil production.
Based on the work of Po-Chin Wu, Shiao-Yen Liu, and Sheng-Chieh Pan (2013), this paper examines the linearity testing of Equation (4) by its first-order Taylor expansion to displace the transition function ( ; , ). Hence, the auxiliary equation showing their relationship becomes the following: where = 0, 1, 2, 3, 4, 5 to allow for a lag of two periods of crude oil price volatility. ∆ , represents the monthly crude oil price volatility of specific oil benchmark ( ) at time ( ). ∆ , is a lag of two periods of ∆ , . It represents the monthly crude oil price volatility of oil benchmark ( ) at time ( − 2). ∆ , is the monthly crude oil production of regime ( ) at time ( ).
First, the hypothesis of linearity is tested to calculate the relationship between crude oil price and production and determine whether it is nonlinear or linear: H 0 : ′ = ′ = 0 (Linear model). H 1 : ′ ≠ ′ ≠ 0 (PSTR model with at least one threshold variable).
If the null hypothesis of linearity is rejected, the next step is to test the null hypothesis of a single threshold model against a double threshold model. Two cases are tested: one and two location parameters. The second case aims to reconfirm the results of the first test, which would imply that the results are more trustworthy. The results are in Table 6. Notes: *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively.
Source: Authors' estimation based on data from EIA (2016b). Table 6 presents the results of the Wald, Fisher, and LRT tests at a confidence level of 90%. The null hypothesis of linearity in the case of one location parameter is rejected. These estimates show clearly that the relationship between crude oil price and crude oil production is nonlinear. The principle of a minimum of the AIC or BIC reveals that the transition function fits the PSTR model.

The Optimal Number of Threshold Regime Tests
Due to the nonlinearity of the relationship between crude oil price and crude oil production, this paper further analyzes the optimal number of threshold variables. The hypothesis is as follows: H 0 : PSTR model with one threshold variable ( = 1). H 1 : PSTR model with at least two threshold variables ( ≥ 2). According to the estimation presented in Table 7, all tests do not reject the null hypothesis for one location parameter. Therefore, the optimal number of transition functions is one.

Empirical Results
Following the above tests (panel unit root test, linearity test, and the test for the optimal number of threshold regimes), the next step is to use the PSTR model to estimate the effects of crude oil prices on crude oil production during the studied period across 122 countries worldwide. This work also presents the results of the linear model to show the differences between the PSTR model and the traditional linear model. All empirical results of the two models are presented in Table 8 Table 6.
Source: Authors' estimation based on data from EIA (2016b). Table 8 shows the results of the PSTR model. The threshold value and transition parameter are -2.9332 and 1.7686, respectively. The explanation and implication are stated in detail as follows. In the PSTR model, the relationship between crude oil prices and crude oil production does not follow the same trend in different regimes, i.e., regimes below and regimes above the threshold value. The threshold value of crude oil volatility with a lag of two periods is -2.9332. In two extreme cases, ∆ , ; 1.7686, −2.9332 = 0 and ∆ , ; 1.7686, −2.9332 = 1, the effects are -0.0035 and 0.0006, respectively. Consequently, the tendency of this relationship is negative when the regime is below the threshold level but is positive when it exceeds the threshold level. The values of AIC and BIC are small enough to show that the relationship fits the PSTR model.

Linear Model
The purpose of this section is to present the linear model and compare its results with those of the PSTR model. In the linear model, the Durbin-Watson test statistic is 0.596032, which is not significant. Hence, the result supports the type of data that should be used in an empirical random-effects model. From Table 8, it is clear that the relationship between crude oil price and crude oil production is negative, with a coefficient of -0.000281.
Compared to the PSTR model, the linear model provides biased estimated results. Indeed, the effect of crude oil price on crude oil production is fixed at -0.000281. In contrast, as discussed above, when the PSTR model is used, the effects are based on whether the transition variable is below or above the threshold value (-2.9332). In addition, for ∆ , ; 1.7686, −2.9332 = 0 and ∆ , ; 1.7686, −2.9332 = 1, the effects are -0.0035 and 0.0006, respectively. Thus, unlike the PSTR model, a linear model cannot clearly reflect the relationship between crude oil price and crude oil production. With a given data set across time and countries, the PSTR model is appropriate to identify the effects of crude oil price on crude oil production using threshold points.

Estimation Results
As discussed in previous sections, the PSTR model surpasses the shortness of the linear model by providing more precise results. These results reveal that the relationship is nonlinear, with different effects in two extreme regimes. The threshold value and the transition parameter are -2.9332 and 1.7686, respectively. The coefficient variables are -0.0035 and 0.0041.
The equation that expresses the relationship between crude oil price and crude oil production can be written as follows: ∆ , = − 0.0035∆ , + 0.0041∆ , G ∆ , ; 1.7686, −2.9332 + , (6) where ∆ , represents the monthly crude oil price volatility of specific oil benchmark ( ) at time ( ). ∆ , is the lag of two periods of ∆ , and represents the monthly crude oil price volatility of oil benchmark ( ) at time ( − 2). ∆ , is the monthly crude oil production of regime ( ) at time ( ).
By estimating the threshold model equation for crude oil price volatility and oil production changes, the outcome shows that there is one threshold value: -2.9332. The effects of crude oil price on crude oil production reveal differences between two circumstances, namely, regimes below and above the threshold value. In two extreme cases, ∆ , ; 1.7686, −2.9332 = 0 and ∆ , ; 1.7686, −2.9332 = 1, the effects are -0.0035 and 0.0006, respectively. Regarding the first case, when a lag of crude oil price volatility of two periods is less than the threshold value of -2.9332, each 1-unit increase in crude oil production volatility will lead to a 285.7-unit decrease in crude oil price volatility, showing a negative effect. It is well-known in supply-demand economics that price will decrease if supply significantly increases and other conditions are unchanged. Here, a 1-unit increase in crude oil production volatility causes a 285.7-unit decrease in crude oil price volatility only when the value of the transition variable is under the threshold point (-2.9332). In contrast, this relationship shows the opposite tendency whenever the transition variable exceeds threshold value. Specifically, when crude oil volatility with a lag of two periods is higher than the estimated threshold level of -2.9332, each 1-unit increase in crude oil production changes will cause a 1666.6-unit increase in crude oil price volatility. In summary, the effect of crude oil production on price is nonlinear, with a reversal in tendency when the transition variable is below or above the estimated threshold value.

Concluding Remarks
The importance of crude oil prices in the global economy has been considered in a variety of studies. However, the majority of the research focuses on the relationships among physical products and financial variables, such as the exchange rate, gold, stock prices, rig counts, interest rates, and others. Moreover, many studies argue that the impact of oil prices is consistent with oil demand and fail to consider oil production. However, a growing number of studies are researching the actual role of oil production in oil prices. In addition, a recent oversupply situation led to a significant decrease in oil prices, which raised concerns for the global economy. To reduce the unfavorable consequences of extreme oil prices caused by oversupply, OPEC members have announced a production freeze solution. The EIA has also mentioned the importance of oil production in driving oil prices. Hence, it is important to thoroughly understand the oil price-production relationship. According to the empirical results, three implications should be noted. First, the existence of the threshold value proves the nonlinear relationship between oil price and production. Second, above the threshold value, oil production changes have a positive effect on oil price volatility. Specifically, a oneunit increase in oil production changes leads to a 1666.6-unit increase in oil price volatility. Third, under the threshold value, the effect of oil production changes on oil price volatility is negative. Specifically, a one-unit increase in oil production changes causes a 285.7-unit decrease in oil price volatility.
Thus, this study makes a contribution to both academic research and practical situations. To prevent extreme price situations, policy makers must create a strategy that predicts the trends of crude oil prices. For investors, this study is a useful reference for calculating oil price movements due to changes in oil production. For producersespecially OPEC members -this study can be used to predict oil price volatility caused by changes in oil production. Producers will thus be able to avoid oversupply situations by planning suitable levels of oil production.