CRUDE OIL IMPORT ELASTICITY OF DEMAND IN INDIA: AN EMPIRICAL ANALYSIS 1987-2016

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CRUDE OIL IMPORT ELASTICITY OF DEMAND IN INDIA: AN EMPIRICAL ANALYSIS 1987-2016 Rashmi Ranjan PAITAL *,

Subhendu DUTTA**, Aruna Kumar DASH ***

Abstract. This study analyses the crude oil import elasticity of demand during 1987-88 to 2016-17 by using Auto Regressive Distributed Lag (ARDL) cointegration technique.

By using macroeconomic variables such as real crude oil price and real GDP an attempt is made to determine the long-run and short-run elasticities of crude oil demand in Indian context. In our empirical analysis, we found that the long-run income elasticity coefficient was found to be statistically significant with expected sign. It was found that the crude oil import demand is highly elastic to income in the long-run suggesting that a one percentage increase in GDP of India leads to a 2.89 percentage increase in crude oil import demand. It was also revealed that the responsiveness of international crude oil price changes in import demand are insignificant. We can say crude oil demand in India is very sensitive to income rather than price changes.One of the reasons might be full control of the retail price of the petroleum products by the Government of India during our study period. Indian government fully regulated the petroleum prices for which any changes in international crude oil price have not reflected the Indian retail price. Another reason is that as a growing economy, the government needs to import large quantities of crude oil irrespective of price changes to meet the rising domestic demand. The paper suggests that there is a need for a policy framework for reducing the domestic crude consumption and exploring alternative energy sources.

Keywords: Crude oil elasticity of demand, Income and price elasticity, ARDL, India.

JEL Classifications: Q41,Q43,C32.

1. Introduction

Understanding the sensitivity of crude oil demand to changes in prices and income has important implications as it not only impacts macroeconomic variables but also offers meaningful interpretations to policy makers. Demand for crude oil has bearings on its growth and it is the economic growth that fuels more demand for crude oil (Mallick, 2009). However, for a developing country like India high demand for crude oil, albeit inevitable, is one of the reasons for high current account deficit. The oil price surge not only increases the government’s subsidy burden, but also widens the current account deficit and hence pressure on the rupee to depreciate. The rupee has depreciated 67% against the USD during the last 10 years. Looking at the current account deficit figure, it was evident that it widened to 1.2 % of gross domestic product, or $ 7.2 billion during July-Sept., 2017 from 0.6 % ($3.4 billion) in the same period a year ago.

India is the fourth largest importer of crude oil in the world. India’s domestic consumption of oil mainly depends imports. In 2017, its crude oil imports were worth

$60.2 billion, which was around 7% of the total imports of the world.

Rashmi Ranjan Paital *, Subhendu Dutta**, Aruna Kumar Dash ***,IBS Hyderabad, A constituent of ICFAI Foundation for Higher Education-Hyderabad, India. Email:

paital.rashmi@ibsindia.org, subhendu@ibsindia.org, akdash@ibsindia.org

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Agrawal (2012) projected India's petroleum demand for the period up to 2025, and found that demand for crude oil is expected to increase by about 90%. In order to have a sustainable growth in the future, India needs to explore its energy sources.

Agrawal (2012), Altinay (2007), Jobling and Jamasb (2015), Ashraf et al (2018), Ghosh (2009), Kubra et al (2018), Kohli and Morey (1990), Moore, (2011), Phoumin and Kimura (2014), Sultan (2010), De Vita et al (2006) and Ziramba (2010), applied ARDL bounds testing approach to cointegration to determine the elasticities of crude oil demand in different countries. Most of these studies reported that income and price elasticities of import demand for crude oil are inelastic both in the short and the

long run. Studies also reported that income and

price elasticities of import demand for crude oil are negative in the long run and positive in the short run, respectively. However, Kubra et al (2018), Jobling and Jamasb (2015), Ziramba (2010), Ghosh (2009), Sultan (2010) have found that long run income elasticity is positive and studies by Gorus and Ozgur (2017), Sultan (2010) shows that price elasticity is negative in the short run.

Literature on estimation of elasticities of crude oil demand reveals that a very few studies [Agrawal (2012, 2015) and Dash et al (2018)] were conducted in the Indian context. Moreover, there are a few studies which dealt with economic growth and energy consumption only [Mallick (2009), Ghosh (2009). Over and above, the energy demand in India has been rising at a rapid rate attributable to higher growth rate of the economy.

Per capita crude oil import demand in India has increased by 7.2 times over a period of 30 years from 1987-88 to 2016-17. Hence, there is a need to understand and estimate the short-run and long-run price and income elasticities of crude oil import demand of India, which the present paper attempted for a period covering 1987-88 to 2016-17, using econometric techniques of ARDL model.

1.1 An overview of India’s demand for crude oil

From figure 1, it is seen that India is one of the largest consumers of crude oil in the world whose share is (9%) followed by China (16.70%) and USA (16.50%).

Figure 1: World Top oil importers during 2015

Source: http://www.worldsrichestcountries.com/top_crude_oil_importers.html.

China;

16,70%

USA; 16,50%

India; 9%

South Korea;

6,90%

Japan;

5,60%

Others;

46,30%

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One of the reasons for this is a higher rate of growth, the country is treading on for a quite number of years. In addition to that , part of this crude oil demand growth has come from the effects of a low oil price. During the last decade, India’s growth rate has been almost 7%, which has put pressure on the demand for crude oil. Being an

emerging economy in the world, there is increasing demand for crude oil. As a largest consumer of crude oil, India used to meet its demand largely by crude oil imports, which is used to produce other goods and foster economic growth. Crude oil is the second largest source of primary energy in the country after coal, whose import share is 23% in 2016-17 (Figure 2).

Figure 2: India's share of oil imports during 2016-17

Source: Authors’ calculation based on the data obtained from RBI’s Handbook of Statistics on Indian Economy.

It is evident from the Figure 3 that, out of all the petroleum products, the consumption demand for diesel constitute a largest share, which was 41% during 2015-16 and the largest user of diesel is the transport sector, which alone consumes 70% of diesel at all India level.

Figure 3: Percentage share of petroleum products consumption in India during 2015-16

Source: Indian Petroleum & Natural Gas Statistics 2015-16.

Oil; 23%

Non-Oil;

77%

Diesel;

41%

Fuel Oil; 4%

Lubes; 2%

Bitumen; 3%

Petroleum Coke; 10%

Others; 3%

LPG; 11%

Motor Spirit; 12%

Naphtha;

7%

SKO; 4% ATF; 3%

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Figure 4: Per capita import demand for crude oil and per capita real GDP in India

10,000 20,000 30,000 40,000 50,000 60,000

0 50 100 150 200 250

88 90 92 94 96 98 00 02 04 06 08 10 12 14 16

per capita real GDP per capita Oil Import (kg)

Source: Authors’ calculation based on the data obtained from RBI’s Handbook of Statistics on Indian Economy. Real GDP per capita in INR at 2004-2005 Prices.

Figure 4 shows the graphical representation of per capita import demand for crude oil and per caita real GDP of India during 1987-88 to 2016-17. It is seen from the figure 4 that the demand for crude oil has increased significantly after 1990. The increase in per capita import demand for crude oil might be because of Liberalization, Privatization and Globalization (LPG) policy implemented by the government of India since 1990s. Since then GDP of the economy increases. The increase in GDP may fuel the per capita import demand for crude oil since 1990s. Figures A1 and A2 in the Annex relates the evolution of Energy consumption with economic development and with Oil imports.

2. Data and Methodology 2.1. Data

In this study, we have used annual data in our analysis. The data used in this study have been collected from various sources for the financial year starting from 1987- 88 to 2016-17. The quantity of crude oil imported (in million tonnes) and the Real GDP (GDP at factor cost in 2004-05 constant prices (in billion INR)) have been obtained from the ‘Handbook of Statistics on Indian Economy’ which is published by the Reserve Bank of India. The monthly Europe Brent spot crude oil price per barrel (in USD) has been collected from U.S. Energy Information Administration (EIA) and then converted to annual series for each financial year by taking a monthly average price from April to March.

The real price of crude oil in INR calculated by multiplying the nominal price in USD with the exchange rate and divided with GDP deflator. The data series and their summary statistics are reported in Table 1 and Table 2 respectively. The variable oil demand is represented by (OD) (Imported Crude quantity in million tonnes) the variable oil price is represented by (OP) (real crude oil price in INR) and finally the variable income is represented through (Y) respectively.

All the variables are expressed in the natural logarithmic form for which the variable can be interpreted as elasticity coefficient. LnOD, lnOP & LnY are natural log values of OD, OP & Y respectively. Before going for empirical estimation, we have

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plotted the raw data series to see their trends. The trends of the raw data series are presented in figures 5, 6 & 7 respectively.

Figure-5: Crude Oil Import Demand of India (in Million tonnes)

Source: Handbook of Statistics on Indian Economy.

Figure-6: Real Price of Crude (per Barrel in INR)

Source: Authors’ calculation based on the data from the U.S. Energy Information Administration (EIA) & Handbook of Statistics on Indian Economy.

Figure-7: Real GDP in Billion INR

Source: Handbook of Statistics on Indian Economy.

0,0 50,0 100,0 150,0 200,0 250,0

0,05,0 10,015,0 20,025,0 30,035,0 40,0

0,0 10000,0 20000,0 30000,0 40000,0 50000,0 60000,0 70000,0 80000,0

1987-88 1989-90 1991-92 1993-94 1995-96 1997-98 1999-00 2001-02 2003-04 2005-06 2007-08 2009-10 2011-12 2013-14 2015-16

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Table 1: Data Series of Oil demand, Oil price and Income Year LnOD LnOP LnY Crude Oil Import

Demand (OD) in Million Tonnes

Real Price of Crude (OP) per Barrel in

INR*

Real GDP(Y) in Billion INR

1987-88 2.89 2.03 9.30 18.0 7.6 10949.9

1988-89 2.94 1.92 9.40 19.0 6.8 12062.4

1989-90 3.04 2.17 9.46 21.0 8.8 12802.3

1990-91 3.09 2.39 9.51 22.0 10.9 13478.9

1991-92 3.40 2.35 9.52 30.0 10.5 13671.7

1992-93 3.40 2.50 9.58 30.0 12.2 14405.0

1993-94 3.43 2.23 9.63 31.0 9.3 15223.4

1994-95 3.30 2.18 9.69 27.0 8.8 16196.9

1995-96 3.30 2.21 9.76 27.0 9.1 17377.4

1996-97 3.53 2.39 9.84 34.0 10.9 18763.2

1997-98 3.53 2.17 9.88 34.0 8.7 19570.3

1998-99 3.69 1.85 9.95 40.0 6.4 20878.3

1999-00 4.06 2.44 10.02 58.0 11.4 22549.4

2000-01 4.30 2.72 10.06 74.0 15.2 23484.8

2001-02 4.37 2.54 10.12 79.0 12.6 24749.6

2002-03 4.41 2.68 10.15 82.0 14.6 25709.4

2003-04 4.50 2.64 10.23 90.0 14.1 27757.5

2004-05 4.56 2.94 10.30 96.0 18.9 29714.6

2005-06 4.60 3.20 10.39 99.0 24.6 32530.7

2006-07 4.72 3.26 10.48 112.0 26.2 35643.6

2007-08 4.80 3.34 10.57 122.0 28.2 38966.4

2008-09 4.89 3.41 10.64 133.0 30.2 41586.8

2009-10 5.07 3.19 10.72 159.0 24.4 45160.7

2010-11 5.10 3.29 10.80 164.0 26.8 49185.3

2011-12 5.15 3.54 10.87 172.0 34.4 52475.3

2012-13 5.22 3.58 10.92 185.0 36.0 55319.0

2013-14 5.24 3.61 10.98 189.0 36.8 58667.9

2014-15 5.24 3.35 11.05 189.0 28.6 62910.1

2015-16 5.31 2.83 11.13 203.0 16.9 67903.9

2016-17 5.37 2.85 11.19 214.0 17.2 72402.0

Source: Handbook of Statistics on Indian Economy (RBI) & U.S. Energy Information Administration (EIA)

*Author’s calculation.

Table 2: Summary Statistics of Variables of Oil demand, Oil price and Income Statistics Imported Crude Oil

Demand (OD) in Million Tonnes

Real Crude Oil Price (OP) per Barrel in INR

Real GDP(Y) in Billion INR

Mean 91.76 17.56 31736.56

Median 80.50 14.35 25229.49

Maximum 214.00 36.83 72402.03

Minimum 18.00 6.35 10949.92

Std. Dev. 65.80 9.49 18424.86

Sleekness 0.47 0.67 0.765519

Kurtosis 1.78 2.10 2.344998

Source: Authors’ calculation.

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Based on the consumer theory, the crude demand function is defined as follows:

𝐿𝑛𝑂𝐷_𝑡 = 𝛼 + 𝛽𝐿𝑛𝑂𝑃_𝑡+ 𝛾𝐿𝑛𝑌_𝑡

+ 𝑒_𝑡 (𝟏) Where, 𝐿𝑛𝑂𝐷_𝑡, 𝐿𝑛𝑂𝑃𝑡 𝑎𝑛𝑑 𝐿𝑛𝑌𝑡 are the natural log value of oil demand, oil price and income respectively. 𝛼 𝑎𝑛𝑑 𝑒_𝑡 are intercept and error term respectively. The estimated parameter 𝛽 𝑎𝑛𝑑 𝛾 are the price and income elasticities respectively. Economic theory tells that oil demand is inversely related to the price of oil and directly related to income.

Hence, we expect that the coefficient of price, i.e., (𝛽) to be less than zero(negative) and the coefficient of income i.e., (𝛾) to be greater than zero(positive).

An ARDL bounds testing approach to cointegration and error correction mechanism (ECM) have been applied to test the long-run and short-run behaviour of the demand function. The first step is to check the long-run behaviour through cointegration test and if a cointegration relationship is established among the variables, then the long- run elasticities can be computed from cointegration equation and the short-run elasticities can be computed from ECM in the next step.

3. Empirical Results

3.1. Cointegration test results

An ARDL (1, 2, 4) model has been selected on the basis of AIC lag length selection criterion. The bounds test shows a cointegrated long-run equilibrium relationship exists among the variables as the computed F-statistic value (6.90) exceeds the upper bound I (1) critical value (5.15) at the 1% level of significance which is shown in the Table 3.

Table 3: Bounds Test Results F-statistic Lower-bound critical values

I(0)

Upper-bound critical values

I(1) Cointegration

6.90 1% = 5.15, 5% = 3.79 &

10% = 3.17

1% = 6.36, 5% = 4.85 &

10% = 4.14 Yes

Table 4: Estimated Long Run Coefficients Using ARDL (1, 2, 4) Dependent Variable: LnOD

Variable Coefficient Std. Error t-Statistic Prob.

LnOP -2.17898 2.244327 -0.97088 0.3461

LnY 2.888443* 1.53688 1.87942 0.0785

C -20.907 11.23689 -1.86057 0.0813

* indicates 10% level of significance.

Based on the selected ARDL (1, 2, 4) model, the long-run estimated coefficients and their significance statistics are reported in the Table 4. The long-run price and income elasticities are -2.17 and 2.88, respectively. Both the price and income elasticities are expected sign and is based on the consumer theory of demand, i.e., as income (GDP) of the country increases, the demand for oil import increases and as the crude oil price

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decreases, the demand for oil import increases. Though both price and income elasticities are showing expected sign, the income elasticity is statistically significant at 10% level whereas the price elasticity is statistically insignificant. Hence, our oil import demand is highly sensitive to income than price change. A 1% increase in income of the country leads to a 2.89% increase in oil import demand in a year.

3.2. Error Correction Mechanism (ECM) Test Results

In the next step, we examined the short run behaviour of crude oil import demand by estimating error correction model. The results of the ECM test for the crude oil import demand based on the ARDL (1, 2, 4) are reported in the Table 5.

Table 5. Estimated Results of ECM Dependent Variable: D(LnOD)

Variable Coefficient Std. Error t-Statistic Prob.

Δ(LnOP) 0.024705 0.085785 0.287986 0.7771

Δ (LnOP(-1)) 0.336066 0.09776 3.437657 0.0034

Δ (LnY) 1.820242 1.053503 1.7278 0.1033

Δ (LnY(-1)) 0.365981 1.586171 0.230733 0.8204

Δ (LnY(-2)) -4.87952 1.618372 -3.01508 0.0082

Δ (LnY(-3)) 4.11265 0.996594 4.126707 0.0008

𝐸𝐶_𝑡−1 -0.13648 0.116532 -1.1712 0.2587

Source: Authors’ calculation.

The short-run price and income elasticities, i.e., 0.0247 and 1.820, respectively, are found to be statistically insignificant. Our results are similar with the results reported by Ghosh (2001) for India covering the data period during 1970–1971 to 2005–2006.

4. Economic development of India and energy consumption per capita

As seen in Figure 8, energy consumption per capita is very low in India, in comparison with more developed countries.The perspectives of increase are important even if there is a policy of austerity in this regard, and thus India should afford to pay for energy imports increasing its exports of goods ans services, in order to get sustainable development and avoid uneven and unsustainable trade balance.

Figure 8. Energy use per capita: international comparisons

Source. The World Bank : Kilograms of oil equivalent (2011)

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In Guisan(2004) there is a comparison of economic development ad trade of India with China, Japan and other areas. The low values of exports of goods and services per capita in India are mainly due to the low level of industrial development. Fostering the increase of industry per head and tourism may contribute to sustainable development in spite of the increase of oil imports per head. In Guisan and Exposito (2004) is presented an econometric study of Asia showing the important positive effect of industry on exports and the capacity to import.

4. Conclusions and Policy Implications

This study analyses the crude oil import demand as a function of real crude price and real GDP using annual data covering the period 1987-88 to 2016-17. An ARDL bounds testing approach to cointegration and an error correction mechanism (ECM) have conducted to determine the long-run and short-run elasticities, respectively. The bounds test shows that a cointegrated long-run equilibrium relationship exists between crude oil import demand, crude price and GDP. In our study, we found some interesting results.

We found that in long-run, the price elasticity is statistically insignificant, whereas the income elasticity is statistically significant. Hence, we can say that in long run, crude oil demand is very sensitive to income changes than price changes. The long-run income elasticity is 2.89. A 1% increase in income of the country, leads to a 2.89% increase in oil import demand in the long-run. Thus, India’s crude oil import demand is found to be highly elastic to the income in the long-run. So far as short-run is concerned, we found different results.

In the short-run, both price and income elasticities are found to be statistically insignificant. The insignificant responsiveness of international crude price changes in import demand can be explained as follows: During our study period, in most of the times, the retail price of the petroleum products in India is administrated by the governments. Since the retail price of crude oil was free from the market mechanism, the changes in the international crude price would not have impacted much on domestic price and demand as well. Another reason may be that as the economy grows, the government needs to import large quantities of crude oil irrespective of price changes to meet the domestic demand. Hence, there is a need for policy implications.

India needs to frame policies relating to the reduction of the domestic crude oil consumption and explore various alternative energy sources. Moreover, measures towards improving energy efficiency are required to be taken. There is a need for proper planning and care in the use of petroleum in order to have sustainable economic growth.

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Kubra, K.T. Mahmood, M.T., Sher, F. and Awan, R. U. (2018), Income and Price Elasticities of Demand for Imported Crude Oil in Pakistan. Pakistan Economic Review, 1(1) (Summer 2018), 12-29.

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Pesaran, M.H. & Shin, Y. (1999), An autoregressive distributed lag modelling approach to cointegration analysis. In: Storm, S. (Ed.), Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposium. Cambridge University Press, Cambridge, pp. 1–31 (Chapter 11).

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Annex to section 1: Dual graphs relating development, energy use and oil imports

Figure A1. Real GDP per capita Energy use

20,000 40,000 60,000 80,000 100,000

300 400 500 600 700

88 90 92 94 96 98 00 02 04 06 08 10 12 14

Real GDP per capita (INR at 2011 prices) Energy use (kg of oil equivalent per capita)

Figure A2. Energy Use and Oil Imports (kg per capita)

0 100 200 300 400 500

88 90 92 94 96 98 00 02 04 06 08 10 12 14

per capita Oil Import (Kg)

Energy use (kg of oil equivalente per capita)

Note: Data of real GDP per capita at 2011 prices and Energy use from WB(2019).

Annex to section 2.

2.2.1. Cointegration Test

An ARDL-Bounds testing approach has been conducted to examine the long- run relationship between Oil Demand, Oil Price and Income. An ARDL model uses the lagged values of the dependent variable along with the contemporaneous and lagged values of independent variables as explanatory variable in the model. This approach has several advantages over the conventional cointegration technique like Engle and Granger two step approach (1987) and the Johansen maximum likelihood approach (1990). The first advantage is that there is no pre-condition to satisfy the stationary properties of the variables before conducting the test. It is applicable if the variables are stationary, i.e, I(0), or non-stationary, i.e, I(1) or a combination of both. Moreover, this approach

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produces robust results in case of small and finite sample size like the present one (Pesaran and Shin, 1999 and Pesaran et al 2001 ). Furthermore, it reduces the autocorrelation problem by introducing lagged dependent variable as one of the explanatory variables. The ARDL representation of oil demand function is represented by (Equation 1) which is as follows:

∆𝐿𝑛𝑂𝐷_𝑡 = 𝑎₁+ ∑ 𝑏_1𝑖∆𝐿𝑛𝑂𝐷_𝑡−𝑖

𝑛

𝑖=1 + ∑ 𝑐_1𝑖∆𝐿𝑛𝑂𝑃_𝑡−𝑖

𝑛

𝑖=0 + ∑ 𝑑_1𝑖∆𝐿𝑛𝑌_1𝑡−𝑖

𝑛 𝑖=0

+ 𝛿1𝐿𝑛𝑂𝐷𝑡−1+ 𝛿2𝐿𝑛𝑂𝑃𝑡−1+ 𝛿3𝐿𝑛𝑌𝑡−1

+ 𝑒_1𝑡 (𝟐)

Where ∆ & 𝑒_𝑡 stand for first difference and error terms respectively. 𝑏_2𝑖, 𝑐_2𝑖, 𝑑_2𝑖𝑎𝑛𝑑 𝛿′^𝑠 are the parameters to be estimated. 𝑒_1𝑡 is the serially uncorrelated error term. In the ARDL-bounds testing approach, the first step is to estimate the Equation 2 by the ordinary least square (OLS) technique. Here F-test is used to check the joint significance of the lagged coefficient of the level variables in the equation. The null hypothesis is that there is no cointegrating long-run relationship among the variables in the equation. In our case, the null hypothesis is 𝐻₀: = 𝛿₁= 𝛿₂= 𝛿₃= 0 against an alternative hypothesis 𝐻₁: ≠ 𝛿₁≠ 𝛿₂ ≠ 𝛿₃≠ 0. The null hypothesis of no cointegration can be rejected if the computed F-statistic value exceeds the upper bound I (1) critical values and accepted when computed F-statistic value lower than the lower bound I (0) critical values. Once the cointegration relationship is established among the variables, then the next step is to measure the long-run elasticities using the below cointegrating Equation 3.

𝐶𝑜𝑖𝑛𝑡𝑒𝑞 = 𝐿𝑛𝑂𝐷_𝑡− (𝛽𝐿𝑛𝑂𝑃_𝑡+ 𝛾𝐿𝑛𝑌_𝑡+ 𝛼) (𝟑) Here, the coefficients 𝛽 𝑎𝑛𝑑 𝛾 are long-run price and income elasticities respectively.

2.2.2. Error Correction Mechanism (ECM)

Cointegration implies long-run equilibrium relationship among the variables in the demand equation, but in the short-run, there might be disequilibrium problem which can be corrected through error correction mechanism (ECM). The following error correction model has been estimated to check the short-run behaviour of the oil demand function.

∆𝐿𝑛𝑂𝐷𝑡 = 𝑎2+ ∑ 𝑏2𝑖∆𝐿𝑛𝑂𝐷𝑡−𝑖 𝑛

𝑖=1 + ∑ 𝑐2𝑖∆𝐿𝑛𝑂𝑃𝑡−𝑖

𝑛

𝑖=0 + ∑ 𝑑2𝑖∆𝐿𝑛𝑌1𝑡−𝑖

𝑛 𝑖=0

+ 𝜋₁𝐸𝐶_𝑡−1

+ 𝜇_𝑡 (𝟒) Where, 𝑏_2𝑖, 𝑐_2𝑖 𝑎𝑛𝑑 𝑑_2𝑖 are parameters to be estimated. 𝜇_𝑡 is the serially uncorrelated error term. 𝐸𝐶_𝑡−1 is the previous period error correction term derived from the cointegrating Equation 3. Parameter 𝜋₁ is the speed of adjustment towards long-run equilibrium. The coefficients 𝑐₂₀ 𝑎𝑛𝑑 𝑑₂₀are short-run price and income elasticities respectively.

Journal published by the EAAEDS: http://www.usc.es/economet/eaat.htm