Long-Term Forecasting Models of Oil Demand Emerging from the Global Petrochemical Sector

Abstract

In the global energy mix by 2040, the growth in demand for oil and gas will be predominantly driven by the petrochemical sector across all regions of the world. The strong performance of this industry is anticipated to necessitate additional volumes of key feedstocks. Therefore, understanding the demand dynamics within the petrochemical sector is crucial for policy makers and industry stakeholders to make informed decisions regarding economic diversification, economic planning, and environmental sustainability. However, there is a notable lack of existing literature that explicitly addresses comprehensive regional and product-level demand modeling for petrochemical feedstocks. In this context, this study aims to estimate the demand for four main petrochemical feedstocks (Naphtha, Ethane, Liquefied Petroleum Gas (LPG), and other petrochemical feedstocks) across eight regions of the world. By estimating a total of 30 equations for price and income elasticities of demand in both the short and long term, the study provides detailed insights into the factors driving demand across different regions. The results demonstrate the robustness of the model, with good econometric properties and significant coefficients. In-sample regional simulations revealed small percentage errors across all regional equations, highlighting the model’s accuracy in tracking historical data. For each of the four feedstocks, an aggregate world equation—in other words, one single econometric world equation for each of the four petrochemical feedstocks’ categories mentioned earlier—was also estimated and compared against the aggregation of the regional simulations, with the latter found to track the history of global petrochemical feedstock demand better in-sample than a single econometric world equation. Overall, the study offers valuable contributions to the existing literature by filling a gap in comprehensive demand modeling for petrochemical feedstocks. It underscores the importance of regional and product-level analyses in understanding global demand patterns and informing strategic decisions in the industry.

1. Introduction

Some long-term forecast scenarios suggest that oil will continue to dominate the energy mix through 2050, primarily driven by demand in the transportation and petrochemical sectors [1,2,3]. Oil and gas combined are still expected to make up more than 50% of the global energy mix by 2040. Over the past decade, the petrochemical sector has seen significant growth in oil demand [4]. Demand growth from industry is driven mainly by the petrochemical sector, with its global demand forecast to increase by 3.7 million barrels per day (MMb/d) from 2021 to 2045 [3]. The strong performance of the petrochemical industry is expected to require additional volumes of natural gas as feedstock.

When examining patterns of petrochemical feedstock demand, we see different concentrations of petrochemical feedstock demand globally. According to Figure 1, and as reported by the IEA [5], naphtha is more in demand in Asia and Europe while ethane is more in demand in North America. Being a large exporter, the Middle East shows a balanced mix of ethane and naphtha demand.

However, it is anticipated by [4] that 2030 will see a slowdown of demand in emerging economies. They also surmise that this will eventually limit any intent to increase petrochemical plant capacities, inducing manufacturers to find solutions that will provide higher levels of productivity, especially in large-scale projects (e.g., [6]).

The importance of the petrochemical industry to overall industrial demand necessitates the construction of a long-term petrochemical demand model that forms part of a group of sectorial long-term oil demand models. These models should enable policy makers to understand the potential opportunities related to the demand for various oil products from different regions and sectors—the petrochemical sector being one of them. Indeed, such an understanding is crucial for oil-based economies, especially when experiencing adverse shocks from the oil market. Oil-based economies need to have a tool that enables them to foresee changes in oil demand to realize any opportunities and mitigate against potential challenges across all sectors (petrochemical, aviation, and maritime, among others). Non-oil-based economies and other entities can also benefit from such forecasting models. Furthermore, international agencies are likely to publish outlooks influenced by their member countries’ policies, making an independent long-term oil demand outlook useful.

However, forecasting sectoral oil demand presents several challenges due to the unique characteristics of each sector (e.g., [7]). Accurately predicting oil demand requires a deep understanding of these characteristics. To gain such insights, a set of seven models was planned, each focusing on one of the following sectors: aviation transport, maritime transport, land transport, the power sector, residential and commercial buildings, agriculture, and the petrochemical sector (e.g., [8]). This paper contributes to this objective by developing one of these models, specifically regional econometric demand models for oil demand in the global petrochemical sector.

In this paper, we present the methodology of the oil demand model for the petrochemical sector. The model is set at an annual frequency, with the estimation period running from 1970 to 2019.

The model is structured around four main products: naphtha, ethane, liquified petroleum gas (LPG), and other petrochemical feedstocks. It covers eight regions of the world: OECD Americas; OECD Europe; OECD Asia Oceania; Middle East and Africa; Latin America; Eurasia; Asia excluding China; and China. The first four represent industrialized regions, while the remaining regions represent a mix of emerging and developing economies, with the Middle East and Africa having a diverse range of development levels.

This paper is organized as follows. Section 2 presents the literature review of previous studies that have investigated the modeling of the petrochemical industry. Section 3 presents the detailed work of constructing the data bank of the petrochemical model and the estimation results. Section 4 shows the dynamic simulations in-sample. Section 5 presents the conclusion.

2. Related Literature

The literature on the modeling of the petrochemical industry is not vast. The majority of the work is on the estimation of the elasticity of oil demand, and a large number of studies focus on the demand for transportation fuels, like gasoline and diesel, analyzing household behavior. Some studies analyze business behavior for a variety of energy inputs, but, surprisingly, there is not much analysis of petrochemical feedstocks.

Ref. [9] constructed a model of the petrochemical industry that is considered a classic work. It is a detailed econometric paper that analyzes major basic, intermediate, and final petrochemical product demand at the regional level worldwide using old-fashioned techniques like static linear logarithmic equations.

Ref. [10] contributed to the book Energy Economy, Finance and Geostrategy with their article “Analyzing the Relationship Between Oil Prices and Basic Petrochemical Feedstocks”. The study focuses on understanding the interdependencies between oil prices and basic petrochemical feedstocks, and their impact on the petrochemical industry. The authors employ econometric analysis and time series models to examine the relationship between oil prices and petrochemical feedstock prices. They investigate the transmission mechanisms and dynamics of price movements between these two variables, considering both short-term and long-term effects. The study covers a wide range of basic petrochemical feedstocks, including ethylene, propylene, benzene, and toluene. It is an interesting piece of work because, with error correction modeling, the authors find that there is a cointegration between the prices of feedstock and oil. Furthermore, they notice that the price of naphtha has a long-run unit elasticity with respect to the oil price, while the prices of other feedstock, like propylene and ethylene, have less than unity elasticity in the short run. The long-run cointegration between petrochemical and oil prices is relevant for constructing a robust, long-run assumption for simulating demand. The study also highlights the asymmetry in price adjustments, indicating that feedstock prices respond more strongly to increases than to decreases in oil prices.

Ref. [11] provided a comprehensive survey of the demand elasticities of oil products in developing countries. It recognizes the importance of understanding price sensitivities and the responsiveness of oil product demand in these economies. The author gathers data from multiple developing countries and analyzes the relationship between oil product prices and demand. The research focuses on estimating price elasticities and identifying the factors that influence demand behavior, such as income levels, population growth, and energy policies. The findings of the study provide insights into the demand dynamics of oil products in developing countries. The research reveals variations in price elasticities across different countries and oil product categories. It also highlights the influence of income levels and population growth on demand patterns. The paper indicates through its results that the demand for other petrochemical feedstock products, including LPG, among others, appears to be price inelastic but income elastic. However, there is a large variation across studies, with some indicating no price response or income elasticities greater than 3. The research findings contribute to a better understanding of the factors shaping oil product demand and assist in the formulation of effective strategies for energy security and sustainability. The article offers valuable insights into the responsiveness of demand to price changes. The research findings have practical implications for policy makers and industry stakeholders, aiding in the development of targeted policies and strategies to meet energy needs and promote sustainable development in these economies.

Ref. [12] investigate, through a comparative analysis, the reactions of China’s petrochemical markets to oil price jumps. The research aims to understand how the petrochemical industry responds to oil price fluctuations, focusing on both equity and commodity markets, adopting a comparative analysis approach. The findings of the study provide valuable insights into the interplay between oil prices and China’s petrochemical industry. The research reveals that both equity and commodity markets react significantly to oil price jumps, indicating the strong influence of oil prices on the country’s petrochemical sector. Furthermore, the results of this study find that the returns of petrochemical stocks and petrochemical commodities are negatively affected by oil price jumps in the current period. This is possibly the result of market turbulence associated with a heightened perceived risk. However, both markets have been positively correlated with oil prices during past oil price spikes, which may be an indication of rational market expectations of future returns. These results highlight the importance of the dynamics in the econometric estimation of both price and income variables in capturing the short-term effect of prices, alongside the structural long-term effect of the level of economic activity. The comparative analysis approach employed in this study enhances the comprehension of market responses and provides a broader perspective on the impact of oil price fluctuations on the petrochemical industry.

Ref. [13] focus on forecasting naphtha demand and supply using time series data causal analysis. Naphtha is a crucial feedstock in the petrochemical industry, and forecasting its demand accurately is essential for effective production planning and resource allocation. The authors employ advanced analytical techniques to establish causal relationships between naphtha demand, supply, and other relevant factors. By utilizing time series data and causal analysis, the study identifies key variables that influence naphtha demand and supply patterns. The research incorporates several factors of petrochemical plants that affect the demand for naphtha. Those factors are the operational rate, which depends on the plant’s margin, its capacity, and its use of LPG. The operational rate variable is predicted by the plant’s operating margin using a time series regression. As the operating margin of a petrochemical plant increases, the operational rate of that petrochemical plant will also increase. Therefore, the demand for naphtha as a raw material used to produce final petrochemical products will increase too. The plant’s operating margin is the difference between the prices of the final products it produces and the price of naphtha, which plants use as a raw material for production. The prices of naphtha and the final petrochemical products therefore play a vital role in determining petrochemical plants’ demand for naphtha. The price of LPG also influences the demand for naphtha by petrochemical plants, since the use of LPG—a perfect alternative to naphtha as raw material to produce final petrochemical products—will depend heavily on its price. The findings of the study provide valuable insights into the dynamics of naphtha supply and demand. The research reveals the significant impact of economic factors and industry-specific variables on naphtha consumption and production. By accurately forecasting naphtha demand and supply, stakeholders in the petrochemical industry can optimize their operations, plan inventory levels, and respond effectively to market fluctuations. The study contributes to the existing body of knowledge on demand and supply forecasting for the petrochemical industry, particularly in the context of naphtha. In summary, the study’s emphasis on causal analysis enhances the understanding of the underlying drivers of naphtha demand and supply, enabling stakeholders to navigate market dynamics more effectively.

Ref. [14] focus on analyzing and predicting the demand for petroleum products in India. The study recognizes the importance of accurate demand forecasting for effective energy planning, policy formulation, and investment decisions in the petroleum sector. The authors employ a comprehensive analytical framework that incorporates both macroeconomic factors and sector-specific variables to model petroleum product demand. They analyze historical data and employ econometric techniques to establish relationships between demand and key drivers such as income, population, industrial activity, and transportation sector growth. The findings of the study provide insights into the factors influencing petroleum product demand in India. The research reveals the significant impact of economic growth, urbanization, and transportation sector expansion on petroleum consumption. The study also highlights the importance of considering the variations in sectoral demand patterns, as different products exhibit different sensitivities to several factors. One of the main findings is that demand for naphtha in India stagnated due to its decreasing importance in the petrochemical and fertilizer sectors, where gas is becoming an alternative fuel. By accurately forecasting petroleum product demand, the study assists policy makers, industry stakeholders, and investors in making informed decisions related to capacity expansion, infrastructure development, and energy security. The research findings can contribute to the formulation of effective energy policies, demand management strategies, and sustainable development initiatives in India’s petroleum sector.

Ref. [15] developed an econometric model for oil product demand in Spain, estimating a broad range of elasticities for oil products. The main conclusions were that real income was one of the main factors driving demand, and that the distinction between short- and long-term coefficients is important from a policy perspective. This is because all elasticities are larger in the long run, meaning that any policy should plan for the long term in order to obtain structural effects.

In summary, the main findings of the existing literature relevant to this paper are the importance of considering both price and income effects, both short-run and long-run effects, and conducting the analysis at the regional level. There are structural differences in the level of technological development, demand, and the interdependence of international trade flows, which can only be captured with a detailed, disaggregated analysis.

3. Data and Empirical Estimation

3.1. Data

The data bank for the petrochemical model was constructed using three main steps (see Appendix A for details). The first step in constructing the data bank of the petrochemical models is the construction of the quantity demanded for the four main dependent variables, namely naphtha, ethane, LPG, and other petrochemical feedstocks, all at the regional level.

The second step in constructing the data bank involves the construction of the macro variables at the regional level, which are used as a scale driver of the demand functions. The third step involves constructing the prices of the four products at the regional level. As referred to earlier, the general structure of the model comprises eight regions of the world: OECD Americas; OECD Europe; OECD Asia and Oceania; the Middle East and Africa; Latin America; Eurasia; Asia excluding China; and China. This gives a total of 32 elementary demand equations to be estimated and simulated. A further description of the above steps is presented in Appendix A.

3.2. Estimation

The theoretical foundation of the demand function is the optimization behavior theory, which specifies that the level of demand is a function of prices and income (e.g., [15]). We followed this approach, estimating a dynamic specification for each of the above regions and for each product. The demand variables are for ethane, naphtha, LPGs, and other petrochemical feedstocks. The price and income variables are assumed to be the main independent drivers. Given our aggregate approach to the demand function, we also considered some other exogenous variables to capture the specific regional and product characteristics of demand.

We model demand functions for eight regions and four feedstocks as a function of prices, gross domestic product (GDP), and other exogenous variables, with annual data for 1971–2019.

We cast a general ARDL model in log with lag = 1:

ln(X_ij,t) = a_0,ij + a_ij ln (p_ij,_t) + b_i Y_i,t + Σ_k c_i,k Z_i,t,k + d_ij ln(X_ij,t−1) + e_ij,t

(1)

where

j = naphtha, ethane, LPG, and other petrochemical feedstock products;

i = world, OECD Americas, OECD Asia Oceania, OECD Europe, Africa and Middle East, non-OECD Americas, non-OECD Europe and Eurasia, non-OECD Asia (excluding China), China (People’s Republic of China and Hong Kong, China);

X_ij = quantity demand, by product and region;

p_ij = prices, by product and region;

Y_i = GDP, by region;

Z_i,k = other exogenous variables, by region i, where k = {population, GDP per capita, percentage of urban population}.

Note that in Equation (1), the main drivers for each sector’s oil demand are taken to represent changes and developments in economic growth, economic structure, population, and price.

For each equation, we performed a preliminary test for integration for all the variables in log, noting that there are both I(1) and I(0) series based on the significance of the Dicky–Fuller (DF) test. Therefore, we conducted a bound test ([16]) analysis for the four equations for the world, i.e., i = WORLD in Equation (1) for the purpose of comparison. The results in

Table 1. Bound test.

Variable	LT	NT	ET	OT
F-test value	6.25	5.95	5.05	7.18

Source: Authors.

confirm the existence of a long-run relationship among the quantity demand, price, and GDP for all variables, as the critical value of the upper bound of the F test at 5% is 4.35, thus allowing us to reject the null hypothesis of no long-run relationship.

We estimated the demand equation for all products and regions. We performed robustness checks for each equation using four main tests: the Godfrey Breusch test for autocorrelation, given that there is a lag-dependent variable; the Jarque–Bera test for the normality of the residual; Ramsey’s RESET test for misspecification; and the Lagrange multiplier (LM) test for heteroskedasticity. For all equations, the robustness tests are non-significant, showing that there is no autocorrelation, the residuals are normal, there is no evidence of misspecification, and there is no evidence of heteroskedasticity.

The existence of a valid long-run relationship allows us to recover both the short-run and long-run price and income elasticities from the model of Equation (1). Since Equation (1) is expressed in a natural log format, the short-run elasticities are the estimated coefficients of the natural log of prices and income.

The long-run elasticity can be derived from the steady-state solution, i.e., when X_ij,t = X_ij,t−1.

The long-run equation is without time subscript:

ln(X_ij) (1 − d_ij) = a₀ + a_ij ln (p_ij) + b_i Y_i + Σ_k c_i,k Z_i,k

(2)

The long-run price and income elasticities are for every i, j, respectively:

E_xij,pij = a_ij/(1 − d_ij) and E_xij,Yi = b_i/(1 − d_ij)

(3)

3.2.1. Ethane

The estimation results for ethane are reported in

Table 2. Ethane demand estimation.

Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia
Dep. var.	ln(ET1)	ln(ET2)	ln(ET3)	ln(ET4)	ln(ET5)	ln(ET6)	ln(ET7)
Regressors
C	−26.7 **	−13.95 **	−11.41 **	−8.25 **	−25.5 **	−8.55 **	−12.1 **
ln(Yj)t−1	0.57 **	0.77 **	0.66 **	0.89 **	0.30 **	0.67 **	0.41 **
ln(Pj)	−0.17 **	−0.29 **	−0.11 **	−0.09 **	−0.15 **	−0.26 **
ln(GDPREj)		0.50 **	0.35 **
ln(GDPREj)t−1	0.90 **			1.09 **	0.82 **	0.29 **
ln(GDPPCj)
ln(Urbanj)							2.84 *
dln(popj)			62.55 **
ln(pop)t−1				−2.06 **
ln(pj/pw)							−0.52 *
R-square	0.84	0.90	0.85	0.99	0.85	0.86	0.92
S.E.	0.06	0.10	0.07	0.08	0.23	0.11	0.27
F-test	865 **	52.4 **	22.0 **	2983.9 **	38.6 **	26.5 **	69.5 **
G.-Breusch	0.55	0.06	0.22	0.07	0.05	0.39	3.1
Jarque-Bera	14.7 **	0.60	1.13	2.99	0.11	2.31	2.47
LM het.	1.4	0.02	3.1	1.35	0.59	0.25	5.69 *
RESET	2.43	2.8	0.001	0.5	4.5 *	1.01	0.02

Source: Authors. Note: ** significant at 1%; * significant at 5%. Dependent variable (dep. var.): Y_j is the demand for ethane in region j = (1,2, …, 8). ln(Y_j)_t−1 is the log of the lagged dependent variable for region j = (1,2, …, 8). p_j is the price for region j. p_w is the average world price. GDPRE_j is the real GDP for region j. GDPPC_j is the real GDP per capita for region j. Urban_j is the percentage of the population living in urban areas for region j. ln(pop_j) is the log of the population for region j. dln(pop_j) is the growth rate of the population for region j. S.E. = Standard Error. LM het. = Lagrange Multiplier Test Statistic for Heteroskedasticity. G.-Breusch = Breusch–Godfrey Test Statistic.

. The specification is adapted to the data for each region (dummy variables are not reported in the table).

The coefficients are all significant. The F-test for a joint coefficient is significant. The robustness tests show no autocorrelation, a normality of errors, an absence of heteroskedasticity, and an absence of misspecification (in the equation for the Middle East and Africa, the RESET test is mildly significant).

The short- and long-term elasticities of the demand for ethane are reported in

Table 3. Ethane demand elasticities.

Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia
Short term
Income	0.90	0.50	0.35	1.09	0.82	0.29	2.84
Price	−0.17	−0.29	−0.11	−0.09	−0.15	−0.26	−0.52
Long term
Income	2.09	2.17	1.0	9.9	1.17	0.88	4.8
Price	−0.39	−1.26	−0.32	−0.81	−0.21	−0.79	−0.67

Source: Authors.

. The price elasticities are generally inelastic, except for OECD Asia. The long-run elasticities are very high for the Middle East and Africa, and Asia. This shows the need for more investigation of the data and the estimation.

3.2.2. Naphtha

The estimation results for naphtha are reported in

Table 4. Naphtha demand estimation.

Estimation of the Demand for Naphtha
Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia	China
Dep. var.	ln(NT1)	ln(NT2)	ln(NT3)	ln(NT4)	ln(NT5)	ln(NT6)	ln(NT7)	ln(NT8)
Regressors
C	−3.41 *	−11.77 **	0.31	−11.98 *	−13.8 **	−92.1 **	3.15 *	−8.82 **
ln(Yj)t−1	0.82 **	0.80 **	0.68 **	0.68 **	0.68 **	0.50 **	0.96 **	0.88 **
ln(Pj)	−0.09 **	−0.09 **	−0.04 *	−0.04 **	−0.11 **	−0.18 **	−0.106 *	−0.10 *
ln(GDPREj)	0.12 *	0.42 **	0.57 **	0.69 **	0.57 **	4.70 **	0.10 *	0.31 **
ln(GDPPCj)				−0.90 **	−0.79 **	−4.73 **
dln(GDPPCj)	−1.90 *	−0.159 *	0.68
Urbanj
Ln(Urbanj)			−4.08 **
Ln(pop)t−1
R-square	0.61	0.98	0.88	0.95	0.98	0.89	0.99	0.994
S.E.	0.09	0.07	0.06	0.20	0.09	0.18	0.07	0.08
F-test	13.3 **	676.7 **	49.2 **	147.4 **	447.6 **	48.1 **	1937.6 **	1209.9 **
Breusch-G	3.33	1.17	0.09	0.52	0.67	2.30	1.88	0.44
Jarque-Bera	0.13	3.03	3.60	3.47	1.63	1.91	0.52	0.66
LM-het.	0.12	5.6 *	0.02	1.26	4.49 *	0.77	0.12	0.91
RESET	0.09	0.17	0.10	3.01	0.79	0.75	0.50	3.0

Source: Authors. Note: ** significant at 1%; * significant at 5%. Dependent variable (dep. var.): Y_j is the demand for ethane in region j = (1,2, …, 8). ln(Y_j)_t−1 is the log of the lagged dependent variable for region j = (1,2, …, 8). P_j is the price for region j. GDPRE_j is the real GDP for region j. GDPPC_j is the real GDP per capita for region j. Urban_j is the percentage of the population living in urban areas for region j. ln(pop_j) is the log of the population of region j. S.E. = Standard Error. LM-het. = Lagrange Multiplier Test Statistic for heteroskedasticity. Breusch-G = Breusch–Godfrey Test Statistic.

. The specification is adapted to the data for each region (dummy variables are not reported in the table). The coefficients are all significant. The price variable for OECD Americas is one period lagged. The price variable for Asia is the log difference ([ln(p)-ln(p-1)]. The F-test for the joint coefficient is significant. The robustness tests show an absence of autocorrelation, a normality of errors, an absence of heteroskedasticity, and an absence of misspecification (in the equations for Latin America, the LM test is mildly significant). The short- and long-term elasticities of the demand for naphtha are reported in

Table 5. Naphtha demand elasticities.

Estimation of the Short- and Long-Term Price and Income Elasticities for Naphtha
Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia	China
Elasticities
Short term
Income	0.12	0.42	0.57	0.69	0.57	4.70	0.01	0.31
Price	−0.09	−0.09	−0.04	−0.04	−0.11	−0.18	−0.06	−0.10
Long term
Income	0.66	2.1	1.78	4.05	1.78	9.4	2.5	0.61
Price	−0.18	−0.45	−0.13	−0.106	−0.34	−0.36	−1.5	−0.19

Source: Authors.

. The price is generally inelastic, except in Asia in the long run. The long-run elasticities are higher for the Middle East and Africa, and Eurasia.

3.2.3. LPG

The estimation results for LPG are reported in

Table 6. LPG demand estimation.

Estimation of the Demand for LPG
Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia	China
Dep. var.	ln(LT1)	ln(LT2)	ln(LT3)	ln(LT4)	ln(LT5)	ln(LT6)	ln(LT7)	ln(LT8)
Regressors
C	−10.77 **	−5.54 **	−15.74 **	−32.33 **	−23.8 *	−21.4 *	−11.4 **	−26.8 **
ln(Yj)t−1	0.62 **	0.82 **	0.79 **	0.21 **	0.65 **	0.59 **	0.91 **	0.54 **
ln(Pj)	−0.12 **	−0.38 **	−0.11 *	−0.26 **	−0.28 **	−0.48 **	−0.57 **	−0.56 **
ln(GDPREj)	0.36 **	0.18 **	0.51 **	1.05 **	0.82 **	0.733 **	0.50 *	0.98 **
R-square	0.986	0.95	0.97	0.99	0.89	0.94	0.99	0.98
S.E.	0.10	0.10	0.11	0.18	0.20	0.20	0.21	0.18
F-test	34.5 **	189.2 **	253.6 **	1992.4 **	55.2 **	44.1 **	811 **	228 **
G.-Breusch	0.76	0.03	2.07	0.43	6.20 *	0.80	1.45	0.09
Jarque-Bera	0.67	0.77	2.87	1.59	8.7 **	3.10	1.41	0.26
LM-het.	1.38	1.48	2.84	1.24	6.9	3.6	1.08	1.42
RESET	0.28	0.01	0..01	2.04	0.02	1.95	3.32	0.08

Source: Authors. Note: ** significant at 1%; * significant at 5%. Dependent variable (dep. var.): Y_j is the demand for ethane for region j = (1,2, …, 8). ln(Y_j)_t−1 is the log of the lagged dependent variable for region j = (1,2, …, 8). P_j is the price for region j. GDPRE_j is the real GDP for region j. S.E. = Standard Error. LM-het. = Lagrange Multiplier Test Statistic for Heteroskedasticity. G.-Breusch = Breusch–Godfrey Test Statistic.

. The specification is adapted to the data for each region (dummy variables are not reported in the table). The coefficients are all significant. The F-test for a joint coefficient is significant. The robustness tests show an absence of autocorrelation, a normality of errors, an absence of heteroskedasticity, and an absence of misspecification (in the equation for Latin America, normality and autocorrelation tests are significant). For OECD Asia, OCED Europe, and Latin America, the price term is the difference between the regional price and the world price.

The short and long-term elasticities of LPG demand are reported in

Table 7. LPG demand elasticities.

Estimation of the Short- and Long-Term Price and Income Elasticities for LPG
Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia	China
Elasticities
Short term
Income	0.36	0.18	0.51	1.05	0.82	0.73	0.50	0.98
Price	−0.12	−0.38	−0.11	−0.26	−0.28	−0.48	−0.57	−0.56
Long term
Income	0.95	1.00	1.64	1.18	2.42	1.78	5.55	2.13
Price	−0.32	−2.11	−0.052	−0.29	−0.80	−1.17	−5.18	−1.21

Source: Authors.

. The price elasticities are both elastic and inelastic. The long-run elasticities of price and income are very high for Asia.

3.2.4. Other Petrochemical Feedstocks

The estimation results for the demand for other petrochemical feedstocks are reported in

Table 8. Other petrochemical feedstock demands estimation.

Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia
Dep. var.	ln(OT1)	ln(OT2)	ln(OT3)	ln(OT4)	ln(OT5)	ln(OT6)	ln(OT7)
Regressors
C	11.7 **	−22.42 **	−27.19 **	−15.99 **	−9.50 *	−25.37 **	−1.57 **
Ln(Yj)t−1	0.77 **	0.75 **	0.21 *	0.66 **	0.87 **	0.46 **	0.78 **
Ln(Pj)	−0.20 **	−0.09 *	−0.10 *	−0.12 **	−0.10 *	−0.67 **	−0.11 **
Ln(GDPREj)		0.75 **	0.85 **	0.52 **	0.33 *	0.94 **
ln(GDPPCj)	−0.23 **
urbanj							0.04 **
R-square	0.97	0.97	0.87	0.81	0.96	0.83	0.99
S.E.	0.20	0.17	0.13	0.06	0.122	0.36	0.12
F-test	146.1 **	375.7 **	55.5 **	18.111	222.5 **	29.7 **	588.2 **
G.-Breusch	0.1	7.26 *	1.88	0.07	0.39	0.36	2.59
Jarque-Bera	1.02	0.44	1.55	1.40	0.49	3.2	1.71
LM-het.	0.32	0.67	1.26	0.02	2.67	1.76	4.2 *
RESET	2.19	1.35	2.29	0.33	0.86	0.26	0.62

Source: Authors. Note: ** significant at 1%; * significant at 5%. Dependent variable (dep. var.): Y_j is the demand for ethane from region j = (1,2, …, 8). ln(Y_j)_t−1 is the log of the lagged dependent variable for region j = (1,2, …, 8). P_j is the price for region j. GDPRE_j is the real GDP for region j. urban_j is the percentage of the population living in urban areas. S.E. = Standard Error. LM-het. = Lagrange Multiplier Test Statistic for Heteroskedasticity. G.-Breusch = Breusch–Godfrey Test Statistic.

. The specification is adapted to the data for each region (dummy variables are not reported in the table). The coefficients are all significant. The F-test for the joint coefficient is significant. The robustness tests show an absence of autocorrelation, a normality of errors, an absence of heteroskedasticity, and an absence of misspecification (in the equation for OECD Asia, the autocorrelation test is mildly significant).

The short- and long-term elasticities of demand for other petrochemical feedstocks are reported in

Table 9. Other petrochemical feedstock demand elasticities.

Region	OECD Americas	OECD Asia	OECD Europe	Middle East and Africa	Latin America	Eurasia	Asia
Elasticities
Short term
Income	−0.23	0.75	0.85	0.52	0.33	0.94	0.04
Price	−0.20	−0.09	−0.10	−0.12	−0.10	−0.67	−0.11
Long term
Income	−1.0	1.0	1.08	1.53	2.54	1.74	0.18
Price	−0.86	−0.36	−0.13	−0.35	−0.77	−1.24	−0.50

Source: Authors.

. The prices are generally inelastic, except in Eurasia and the Americas. The income elasticities are positive, except for OECD Americas, where the strong downward trend of the dependent variable results in negative income elasticity.

4. In-Sample Simulation

The equations have been dynamically simulated within the sample period. The common period of simulation is 1995–2019. We report, in Figure 2, the fitted values of the global equation for each product (the aggregated approach) and the sum of the fitted values of the regions’ equations for each product (the disaggregated approach). These results are reported to show the difference between the aggregated and disaggregated approach.

In each panel of Figure 2, the right-hand graph depicts the difference between the sum of the fitted values of the regions’ equations for a given product and the sum of the actual observations of the same regions from the year 1995 to 2019 for a given product. However, the left-hand graph depicts the difference between the fitted values of the global equation for a given product and the sum of the actual observations of the regions for a given product. We report the historical values of the demand for naphtha, ethane, LPG, and other petrochemical products with the following respective variable labels: NT0, ET0, LT0, and OT0. We report the fitted values of the previously mentioned variables with the same labeling but with an ‘F’ prefix. For instance, ET0 is the sum of the actual observations for ethane demand across all regions’ products at time t; FET0 is the sum of the fitted values of the aggregate global equation for ethane at time t; FETW is the sum of the fitted values of the regions’ equations for ethane at time t.

Note that the sum of the disaggregated results seems to track the historical data better: FLTW is closer to the historical data than FLT0, and FOTW is closer to the historical data than FOT0. This is confirmed by the correlation shown in

Table 10. Correlation coefficients—world historical vs. aggregate and disaggregated values.

	Correlation Coefficients
	Aggregate Equation	Disaggregated Equations
LPG	0.91	0.91
Other oil	0.94	0.98
Naphtha	0.94	0.96
Ethane	0.99	0.97

Source: Authors.

, where the first column shows the correlation between actual and fitted values for the aggregate equation, and the second column shows the correlation between actual and fitted values for the sum of the disaggregated regional equations. The correlation is similar for LPG and ethane, but it is higher for other petrochemical feedstocks and naphtha.

The detailed simulations for each product for all regions are reported in Figure 3, Figure 4, Figure 5 and Figure 6. In each figure, the regions are identified with a numerical suffix: 1 = OECD Americas, 2 = OECD Asia, 3 = OECD Europe, 4 = Middle East and Africa, 5 = Latin America, 6 = Eurasia, 7 = Asia (other), 8 = China. In the case of ethane, we note the erratic pattern of historical data for region 6 and the lack of recent historical data for region 7. In both cases, the fitted values are smoother.

The correlation coefficients and the root mean square errors of actual and historical data are reported in

Table 11. Correlation coefficients and RMSE—regions’ historical vs. fitted values.

Region	OECD AM	OECD AS	OECD EU	Middle East and Africa	Lat Am	Eurasia	Asia	China
Correlation coefficients
Other oil	0.96	0.49	0.59		0.55	0.75	0.96
Naphtha	0.65	0.78	0.78	0.34	0.27	0.68	1.00	0.99
Ethane	0.86	0.88	0.86	0.98	0.17		0.94
LPG	0.90	0.84	0.98	0.91	0.29	0.94	0.97	0.99
Root mean square error
Other oil	0.02	0.01	0.01		0.01	0.00	0.01
Naphtha	0.04	0.12	0.05	0.02	0.01	0.05	0.03	0.03
Ethane	0.04	0.12	0.05	0.02	0.01		0.03
LPG	0.06	0.01	0.01	0.01	0.01	0.02	0.01	0.01

Source: Authors. Note: AM = Americas; AS = Asia; EU = Europe; Lat Am = Latin America.

. Note that the correlation coefficients are generally high, with only a few exceptions. Note that the root mean square errors of the dynamic simulations are quite good, in the order of 1–3% for most equations, with only some values between 5% and 12% for naphtha and ethane in OECD Asia, OECD Europe, and Eurasia.

5. Conclusions

This paper has shown the methodology and results for a model that forecasts long-term regional demand for oil from the petrochemical sector. The general structure of the model comprises four main products: naphtha, ethane, LPG, and other petrochemical feedstocks for eight regions of the world: OECD Americas, OECD Europe, OECD Asia and Oceania, the Middle East and Africa, Latin America, Eurasia, Asia (excluding China), and China, for a total of 32 demand equations.

Due to the unavailability of demand data for certain feedstocks for two regions, we estimated 30 rather than 32 equations. We note that the results are quite satisfactory, with good econometric properties for all the equations estimated. We conducted significance tests, and all the coefficients are significant, so it is possible to estimate both price and income elasticities with the dynamic specification in the short and long term. We conducted the in-sample simulation of all the equations, finding that the percentage error of the simulation is satisfactorily small for all the equations. In particular, the dynamic simulations show a percentage error in the order of 1–3% for most equations, with only some values between 5% and 12% for naphtha and ethane in OECD Asia, OECD Europe, and Eurasia.

We also estimated an aggregate world equation and compared the results of that simulation with the results of the aggregation of the regional simulations. We find that the aggregation of the regional equations tracks the historical data in-sample better than a single econometric world equation. This indicates that disaggregating the analysis of demand into regional and product levels for petrochemical feedstocks facilitates valuable analysis.

The main contribution of this study is to provide a comprehensive model for estimating and potentially forecasting the demand for oil stemming from the petrochemical industry. In an era of significant changes driven by climate change mitigation efforts, decarbonization policies, and shifts in the global energy mix forecasted for the coming decades, it is crucial to focus on the main determinants of demand for petrochemical feedstocks. These feedstocks remain a crucial driver of oil and natural gas demand worldwide.

This study offers econometric estimations of price and income elasticities of petrochemical demand functions, which are valuable for both the oil and gas industry, as suppliers of feedstocks, and the petrochemical industry, as consumers of these feedstocks. Our methodology is beneficial for both industry stakeholders and policy makers worldwide, providing a better understanding of the non-energy use of hydrocarbons in the future. Additionally, this model serves as a valuable tool for future research, enabling the simulation of long-term forecasting scenarios.

Despite the robust results and significant findings presented in this study, we acknowledge that there may be some limitations that could stimulate future research. To address these limitations, extending the model to include other significant factors such as technological innovations, regulatory changes, and environmental considerations would provide a more comprehensive understanding of the sector. Furthermore, future studies could benefit from employing advanced econometric techniques or machine learning algorithms to enhance predictive accuracy and adapt to structural changes in the industry. Exploring the interactions between different sectors and their combined impact on petrochemical feedstock demand could also yield valuable insights.

Finally, as the global push for sustainability and carbon reduction intensifies, future research should incorporate scenarios that reflect potential shifts toward alternative energy sources and their impact on the petrochemical sector. Such future research would help policy makers and industry stakeholders better navigate the transition toward a more sustainable energy landscape.