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Asymmetric Impact of Oil Price Changes on Stock Prices: Evidence from Country and Sectoral Level Data

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Abstract

This paper examines the symmetric and asymmetric effects of oil price changes on stock prices using the linear and non-linear Autoregressive Distributed Lag (ARDL) approach to cointegration and error-correction modeling. For the country-level analysis, monthly data from Brazil, Canada, Chile, Japan, S. Korea, Malaysia, Mexico, the U.K., and the U.S. have been considered. The results show that oil price changes have asymmetric effects on stock prices mostly in the short run. To dig deeper into the asymmetric relationship between oil and stock prices, I disaggregate data at the sectoral level by focusing on eleven U.S. sectoral stock indices to investigate the performance of different sectors. This helps solve the problem of aggregation bias that is associated with country-level data. The findings show that changes in oil price have significant asymmetric effects in nine out of the eleven sectors in the short run. In most of these sectors, the short run asymmetric relationship translates into the long run.

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Notes

  1. A detailed description on the data period and data source is provided in Appendix 1.

  2. Pesaran et al. (2001, p. 291) write “our approach is quiet general in the sense that we can use a flexible choice for the dynamic lag structure in... as well as allowing for short-run feedbacks.”.

  3. See Bahmani-Oskooee and Tanku (2008) for more on this method.

  4. For more on the application of this concept see Apergis and Miller (2006), Delatte and Lopez-Villavicencio (2012), Verheyen (2013), Bahmani-Oskooee and Bahmani (2015), Bahmani-Oskooee and Saha (2016a) and Shin et al. (2014).

  5. A similar model is explained by Bahmani-Oskooee and Saha (2016b) for the relationship between stock prices and exchange rates.

  6. The critical value comes from Pesaran et al. (2001, Table CI, Case III, p. 300).

  7. The critical value comes from Pesaran et al. (2001, Table CII, Case III, p. 303).

  8. At least one of the coefficients associated with the lags is positive.

  9. Among the short-run coefficient estimates, only the ones associated with oil price are reported for brevity. The short run estimates of the remaining variables are available upon request. But the normalized long-run estimates for all the variables and the diagnostic statistics for all the sectors have been reported.

  10. At least one of the coefficients associated with the lags is significant at the 10% level.

  11. The coefficient for POS is positive except for one lag.

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Acknowledgements

I express my deepest gratitude and thankfulness to my summer research interns: Patrick Carper ’21, Wabash College, who helped me with the initial literature review, and the initial regression results for the country-level analysis, and to Nieshaal Thambipillay ’22, Wabash College, who helped me with data cleaning and the initial regression results for the sectoral-level analysis. I also sincerely thank the anonymous reviewers for their valuable comments and suggestions. Any remaining errors, however, are mine. 

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Authors and Affiliations

  1. Department of Economics, Wabash College, Crawfordsville, IN, USA

    Sujata Saha

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  1. Sujata Saha
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Correspondence to Sujata Saha.

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Appendix 1

Appendix 1

1.1 Data definitions and sources

1.1.1 The data come from the following sources

  1. a.

    Yahoo Finance.

  2. b.

    Bank for International Settlements (BIS).

  3. c.

    International Financial Statistics (IFS) database of International Monetary Fund (IMF).

  4. d.

    Federal Reserve Bank of St. Louis (FRED) Database.

1.1.2 Variables

SPi = Country-level or the U.S. Sectoral Stock Price Indices. Data come from source a.

OPi = Spot Crude Oil Price, West Texas Intermediate (WTI), Dollars per Barrel. Data come from source d.

EX = Nominal Effective Exchange Rate of the U.S. Data come from source b.

IPI = Industrial Production Index, base year = 2010. Data come from source c.

CPI = Consumer Price Index of the U.S., base year = 2010. Data come from source c.

MS = Nominal Money Supply (M2 for Malaysia and M3 for the rest of the countries), source d.

1.1.3 Data period and stock price indices for the country-level analysis

Country

Data Period

Stock Price Index Name

Brazil

1994 – 2019

IBOVESPA

Canada

1986 – 2019

S&P/TSX Composite Index

Chile

1997 – 2019

IPSA Santiago de Chile

Japan

1994 – 2019

Nikkei 225

S. Korea

1997 – 2019

KOSPI Composite Index

Malaysia

2000 – 2019

FTSE Bursa Malaysia KLCI

Mexico

1994 – 2019

IPC

U.K

1986– 2019

FTSE 100

U.S

1986 – 2019

S&P 500

1.1.4 Data period and stock price indices for the sectoral-level analysis

Index

Description

Data period

Dow Jones Industrial Average

Comprises of 30 large publicly owned companies

1986: M1–2020:M5

Dow Jones Transportation Average

Tracks stock prices of twenty transportation corporations

1992: M1–2020:M5

Dow Jones Utility Average

Tracks the performance of 15 prominent utility companies

1986: M1–2020:M5

NASDAQ Bank

Includes banks providing financial services such as retail banking, loans, and money transmissions

1990: M11–2020:M5

NASDAQ Biotechnology

Includes biotechnology and pharmaceutical equities

1993: M11–2020:M5

NASDAQ Computer

Includes companies from the computer industry

1995: M8–2020:M5

NASDAQ Industrial

Includes around 950 companies

1990: M11–2020:M5

NASDAQ Insurance

Includes around 46 insurance companies

1990: M11–2020:M5

NASDAQ Telecommunications

Includes around 118 telecom companies

1996: M6–2020:M5

NASDAQ Transportation

Tracks around 50 transportation companies

1990: M11–2020:M5

PHLX Semiconductors

Tracks 30 companies involved in manufacturing and sale of semiconductors

1994: M8–2020:M5

Table 1

Table 1 ADF unit root test results
Full size table

1.1.5 Tables for the country-level (aggregate-level) analysis:

Notes:

  1. i.

    Numbers inside the parentheses are the absolute values of the t-ratios. *, ** indicate coefficient estimates are significant at the 10% and 5% level respectively.

  2. ii.

    The upper bound critical value of the F-test for cointegration when k = 5 is 3.35 (3.79) at the 10% (5%) level of significance. These values come from Pesaran et al. (2001, Table CI, Case III, p. 300). “k” denotes the no. of exogenous variables. Shin et al. (2014) recommend considering POS and NEG (the two partial sum variables) as one variable. Thus, the critical values of the F test are same for both the linear and non-linear models.

  3. iii.

    The critical value of the t-test for significance of ECMt-1 is -3.86 (-4.19) at the 10% (5%) level when k = 5, and, is − 4.04 ( − 4.38) at the 10% (5%) level when k = 6. These values come from Pesaran et al. (2001, Table CII, Case III, p. 303).

  4. iv.

    LM is the Lagrange Multiplier statistic to test for autocorrelation and RESET is Ramsey’s test for misspecification. They are distributed as χ2 with one degree of freedom individually. The critical value is 2.70 (3.84) at the 10% (5%) level. The WALD statistic is also distributed as χ2 with one degree of freedom.

Tables 2, 3, 4, 5, 6, 7, 8, 9, 10

Table 2 Full-information estimates of models (2) and (4) for Brazil. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

 

 − 0.10 (1.61)

0.00 (0.08)

0.07 (1.19)

0.14 (2.45)**

 − 0.07 (1.20)

 − 0.10 (1.82)*

 

Δ POSt

0.14 (3.61)**

       

Δ NEGt

0.20 (2.11)**

 − 0.13 (1.30)

 − 0.16 (1.60)

 − 0.16 (1.70)*

    

Δ lnEXt

0.72 (5.26)**

       

Δ lnIPIt

0.14 (0.88)

       

Δ lnCPIt

0.07 (0.05)

1.39 (0.77)

 − 3.7(2.02)**

 − 3.22 (1.77)*

 − 1.35 (0.75)

0.51 (0.29)

 − 0.15 (0.09)

 − 5.01(3.38)**

Δ lnMSt

1.47 (2.45)**

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

0.52 (5.61)**

 − 0.27 (2.28)**

1.03 (2.86)**

0.68 (1.41)

 − 0.26 (0.16)

 − 2.16 (3.40)**

68.07 (4.00)**

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

5.76**

 − 0.16(6.41)**

0.10

4.92

0.25

S (S)

2.39

9.75**

Table 3 Full-information estimates of models (2) and (4) for Canada. I. Full-information estimates of the linear model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

       

0

1

2

3

4

5

6

7

Δ lnSPt

        

Δ POSt

0.01 (0.57)

       

Δ NEGt

0.00 (0.04)

       

Δ lnEXt

0.69 (4.69)**

0.25 (1.69)*

      

Δ lnIPIt

0.28 (1.23)

0.50 (2.22)**

      

Δ lnCPIt

0.63 (1.00)

 − 0.02 (0.03)

 − 0.75(1.24)

 − 0.71 (1.17)

 − 1.55(2.57)**

 − 1.16 (1.92)*

  

Δ lnMSt

0.38 (0.79)

0.86 (1.81)*

      

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

0.12 (0.59)

 − 0.01 (0.04)

0.30 (0.36)

1.10 (1.37)

0.97 (0.58)

 − 0.53 (0.47)

12.10 (0.45)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

1.87

 − 0.06 (3.64)

0.68

13.25

0.12

S (S)

0.02

0.55

Table 4 Full-information estimates of models (2) and (4) for Chile. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

0

1

2

3

4

5

6

7

Δ lnSPt

 

0.05 (0.77)

0.02 (0.29)

 − 0.07 (1.04)

0.16 (2.54)**

   

Δ POSt

0.07 (4.52)**

       

Δ NEGt

0.08 (1.53)

       

Δ lnEXt

 − 0.00 (0.03)

0.05 (0.37)

 − 0.22 (1.50)

 − 0.15 (1.01)

 − 0.35(2.44)**

 − 0.04 (0.25)

 − 0.20 (1.42)

 − 0.39(2.79)**

Δ lnIPIt

0.09 (1.34)

       

Δ lnCPIt

 − 0.04 (0.16)

       

Δ lnMSt

 − 0.29(3.91)**

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

0.52 (5.61)**

 − 0.27 (2.28)**

1.03 (2.86)**

0.68 (1.41)

 − 0.26 (0.16)

 − 2.16 (3.40)**

68.07 (4.00)**

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

5.72 **

 − 0.14 (6.37)**

0.61

0.43

0.18

S (S)

0.01

25.38**

Table 5 Full-information estimates of models (2) and (4) for Japan. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

        

Δ POSt

0.15 (2.09)**

       

Δ NEGt

 − 0.02 (1.40)

       

Δ lnEXt

 − 0.79(6.10)**

       

Δ lnIPIt

0.57 (3.40)**

       

Δ lnCPIt

0.32 (0.80)

       

Δ lnMSt

 − 0.12 (0.85)

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

 − 0.36 (1.09)

 − 0.61 (1.31)

 − 0.16 (0.15)

0.98 (0.51)

8.37 (0.96)

 − 3.17 (0.91)

75.85 (0.64)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

1.40

 − 0.04 (3.10)

0.00

1.79

0.17

S (S)

0.29

1.71

Table 6 Full-information estimates of models (2) and (4) for S. Korea. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

 

0.08 (1.22)

0.02 (0.39)

0.16 (2.76)**

 − 0.02 (0.44)

0.10(1.96)**

  

Δ POSt

0.17 (1.66)*

0.03 (0.36)

 − 0.07 (0.77)

0.19 (2.17)**

0.12 (1.36)

 − 0.20(2.27)**

  

Δ NEGt

0.23 (2.71)**

 − 0.18(2.00)**

      

Δ lnEXt

0.83 (4.07)**

 − 0.96(4.37)**

 − 0.43(1.86)*

     

Δ lnIPIt

0.44 (2.16)**

0.38 (1.85)*

0.25 (1.34)

     

Δ lnCPIt

0.36 (0.29)

 − 5.37(4.53)**

 − 0.73 (0.59)

 − 1.54 (1.27)

 − 2.96(2.62)**

 − 0.09 (0.08)

 − 2.87(2.62)**

 

Δ lnMSt

 − 0.29 (1.39)

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

0.30 (1.24)

0.07 (0.39)

0.82 (1.85)*

 − 0.06 (0.10)

5.35 (1.54)

 − 2.05 (1.32)

50.37 (1.17)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

4.13**

 − 0.14 (5.42)**

0.45

0.06

0.38

S (S)

0.35

0.31

Table 7 Full-information estimates of models (2) and (4) for Malaysia. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

        

Δ POSt

 − 0.06(2.23)**

       

Δ NEGt

0.15 (2.89)**

0.06 (1.05)

0.06 (1.00)

0.17 (3.28)**

0.06(1.18)

0.10 (2.03)**

  

Δ lnEXt

0.39 (1.74)*

 − 0.35 (1.67)*

 − 0.18 (0.84)

 − 0.39 (1.76)*

    

Δ lnIPIt

0.10 (1.54)

       

Δ lnCPIt

 − 1.75(2.70)**

0.02 (0.03)

 − 1.16 (1.55)

 − 0.39 (0.45)

 − 2.34(3.12)**

   

Δ lnMSt

0.21 (0.78)

0.58 (2.29)**

      

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

 − 0.43 (2.10)**

 − 0.27 (2.32)**

0.89 (1.37)

 − 0.10 (0.18)

 − 1.64 (0.72)

1.81 (3.27)**

 − 12.80 (1.14)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

2.71

 − 0.14 (4.39)**

0.09

2.62

0.30

S (S)

15.85**

0.55

Table 8 Full-information estimates of models (2) and (4) for Mexico. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

 

 − 0.12 (1.89)*

      

Δ POSt

0.15 (1.71)*

       

Δ NEGt

0.04 (1.97)**

       

Δ lnEXt

0.39 (2.99)**

0.33 (2.50)**

 − 0.19 (1.53)

     

Δ lnIPIt

0.65 (1.85)*

0.70 (2.10)**

0.04 (0.12)

 − 0.65(2.00)**

    

Δ lnCPIt

1.38 (1.40)

 − 2.81(2.55)**

2.09(2.34)**

     

Δ lnMSt

0.05 (0.17)

0.51 (1.74)*

 − 0.67(2.26)**

 − 0.47 (1.56)

    

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

0.58 (2.55)**

0.80 (1.63)

 − 2.65 (1.11)

0.55 (0.19)

 − 1.53 (0.57)

1.06 (0.55)

 − 3.32 (0.10)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

1.00

 − 0.03 (2.32)

0.08

2.17

0.15

S (U)

0.67

2.57

Table 9 Full-information estimates of models (2) and (4) for U.K. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Variables

Lags

       
 

0

1

2

3

4

5

6

7

Δ lnSPt

        

Δ POSt

 − 0.01 (1.38)

       

Δ NEGt

 − 0.01 (1.19)

       

Δ lnEXt

 − 0.33(2.34)**

0.20 (1.42)

 − 0.12 (0.89)

0.37 (2.65)**

    

Δ lnIPIt

0.58 (2.36)**

0.47 (1.82)*

0.48 (1.86)*

     

Δ lnCPIt

 − 0.34 (0.51)

 − 0.87 (1.37)

0.69 (1.07)

 − 1.25 (1.94)*

 − 0.72 (1.12)

 − 1.43(2.21)**

  

Δ lnMSt

 − 0.28 (1.25)

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

-0.29 (1.34)

 − 0.19 (1.13)

 − 0.25 (0.33)

 − 0.11 (0.08)

 − 0.54 (0.26)

1.15 (1.56)

 − 19.37 (1.28)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

2.82

 − 0.05 (4.46)**

0.20

0.75

0.08

S (S)

0.38

1.18

Table 10 Full-information estimates of models (2) and (4) for U.S. I. Full-Information Estimates of the Linear Model (2)
Full size table

II. Full-Information Estimates of the Non-Linear Model (4)

Panel A: Short Run

Variables

Lags

 

0

1

2

3

4

5

6

7

Δ lnSPt

        

Δ POSt

 − 0.03 (1.85)*

       

Δ NEGt

 − 0.01 (0.13)

0.08 (1.64)*

0.08 (1.78)*

     

Δ lnEXt

 − 0.37(2.28)**

0.28 (1.76)*

      

Δ lnIPIt

 − 0.85(2.20)**

0.52 (1.35)

0.72 (1.87)*

     

Δ lnCPIt

 − 0.17 (1.33)

       

Δ lnMSt

-0.05 (0.62)

       

Panel B: Long Run

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

 − 0.58 (1.62)

 − 1.08 (2.47)**

 − 2.35 (1.52)

3.48 (2.80)**

 − 3.82 (1.13)

 − 1.02 (0.60)

46.62 (0.81)

Panel C: Diagnostics

F

ECM t-1

LM

RESET

R bar Squared

CUSUM (CUSUM2)

Wald-Short

Wald-Long

2.56

 − (0.04) 4.25 *

0.81

10.19

0.09

S (S)

3.38*

1.52

1.1.6 Tables for the sectoral-level analysis

Notes:

  1. i.

    Numbers inside the parentheses are the absolute values of the t-ratios. *, ** indicate coefficient estimates are significant at the 10% and 5% level respectively.

  2. ii.

    The upper bound critical value of the F-test for cointegration when k = 5 is 3.35 (3.79) at the 10% (5%) level of significance. These values come from Pesaran et al. (2001, Table CI, Case III, p. 300). “k” denotes the no. of exogenous variables. Shin et al. (2014) recommend considering POS and NEG (the two partial sum variables) as one variable. Thus, the critical values of the F test are same for both the linear and non-linear models.

  3. iii.

    The critical value of the t-test for significance of ECMt-1 is − 3.86 ( − 4.19) at the 10% (5%) level when k = 5, and, is − 4.04 ( − 4.38) at the 10% (5%) level when k = 6. These values come from Pesaran et al. (2001, Table CII, Case III, p. 303).

  4. iv.

    LM is the Lagrange Multiplier statistic to test for autocorrelation and RESET is Ramsey’s test for misspecification. They are distributed as χ2 with one degree of freedom individually. The critical value is 2.70 (3.84) at the 10% (5%) level. The WALD statistic is also distributed as χ2 with one degree of freedom.

Tables 11, 12

Table 11 Full-information estimates of the linear model (2) for the sectoral-level analysis. I. Short-Run Coefficient Estimates of the Linear ARDL Model (2)
Full size table

II. Long-Run Coefficient Estimates of the Linear ARDL Model (2)

U.S. sectoral indices

Long-run coefficient estimates

ln OP

ln EX

ln IPI

ln CPI

ln MS

Constant

Dow Jones Industrial Average

 − 0.53(2.51)**

 − 0.96 (1.02)

2.21 (2.81)**

0.88 (0.69)

0.61 (1.45)

 − 16.22(2.29)**

Dow Jones Transportation Average

 − 0.30 (1.24)

 − 1.78 (1.75)*

2.13 (1.82)*

 − 3.08 (0.69)

2.03 (1.51)

 − 38.12 (1.74)*

Dow Jones Utility Average

 − 0.32 (1.27)

 − 2.02 (1.54)

2.69 (2.00)**

 − 3.69 (1.84)*

1.84(2.95)**

 − 33.49(3.18)**

NASDAQ Bank

0.08 (0.15)

2.22 (0.86)

0.30 (0.08)

0.41 (0.05)

0.28 (0.12)

 − 14.32 (0.36)

NASDAQ Biotechnology

0.66 (0.78)

 − 4.87 (0.88)

6.50 (1.39)

 − 42.71 (1.51)

14.73(1.69)*

 − 245.24(1.93)*

NASDAQ Computer

 − 2.20 (1.62)

 − 10.54(1.68)*

3.13 (0.84)

 − 22.97 (1.05)

10.13 (1.39)

 − 144.84 (1.40)

NASDAQ Industrial

 − 0.83(2.98)**

 − 3.77(2.77)**

4.05 (2.99)**

 − 8.95(2.19)**

4.31 (3.39)**

 − 77.09(3.74)**

NASDAQ Insurance

 − 0.28(3.53)**

 − 0.57 (1.66)*

1.85 (4.66)**

1.50 (1.25)

0.68 (1.87)*

 − 23.66(3.82)**

NASDAQ Telecommunications

 − 5.45 (1.40)

 − 37.59 (1.35)

13.67 (1.32)

 − 86.34 (1.12)

29.75 (1.14)

 − 348.81 (1.06)

NASDAQ Transportation

 − 0.13 (0.65)

 − 1.51 (1.74)*

2.93 (2.88)**

 − 6.24 (1.92)*

2.97 (3.00)**

 − 58.02(3.48)**

PHLX Semiconductors

 − 0.04 (0.06)

 − 3.34 (1.17)

4.77 (1.72)*

 − 35.42(2.13)**

12.52(2.30)**

 − 210.3(2.51)**

III. Diagnostics of the Linear ARDL Model (2)

U.S. sectoral indices

Statistical diagnostics

F

ECM t-1

LM

RESET

R bar squared

CUSUM (CUSUM2)

Dow Jones Industrial Average

2.70

 − 0.06 (4.05)*

0.14

10.30

0.08

S(S)

Dow Jones Transportation Average

2.17

 − 0.06 (4.05)*

0.11

0.14

0.08

S(S)

Dow Jones Utility Average

2.28

 − 0.04 (3.70)

0.02

4.22

0.08

S(S)

NASDAQ Bank

2.80

 − 0.03 (4.11)*

0.01

40.93

0.09

S(S)

NASDAQ Biotechnology

2.35

 − 0.03 (3.76)

0.20

3.74

0.12

S(S)

NASDAQ Computer

3.36

 − 0.03(4.47)**

0.31

7.61

0.10

S(S)

NASDAQ Industrial

2.61

 − 0.06 (3.98)**

0.99

6.94

0.12

S(S)

NASDAQ Insurance

3.74*

 − 0.13 (4.77)**

0.38

10.65

0.11

S(S)

NASDAQ Telecommunications

7.60**

 − 0.02 (6.80)**

0.02

3.13

0.19

S(S)

NASDAQ Transportation

3.00

 − 0.07 (4.26)**

0.49

6.15

0.08

S(S)

PHLX Semiconductors

3.46*

 − 0.05 (4.55)**

0.001

3.11

0.07

S(S)

Table 12 Full-information estimates of the non-linear model (5) for the sectoral-level analysis. I. Short-Run Coefficient Estimates of POS for the Non-Linear ARDL Model (5)
Full size table

II. Short-Run Coefficient Estimates of NEG for the Non-Linear ARDL Model (5)

U.S. sectoral indices

Short-run coefficient estimates

∆ NEGt

∆ NEGt-1

∆ NEGt-2

∆ NEGt-3

∆ NEGt-4

Dow Jones Industrial Average

0.13 (2.83)**

    

Dow Jones Transportation Average

 − 0.04 (1.92)*

    

Dow Jones Utility Average

 − 0.02(1.99)**

    

NASDAQ Bank

0.23 (4.00)**

0.11 (1.90)*

   

NASDAQ Biotechnology

0.02 (0.67)

    

NASDAQ Computer

0.15 (2.00)**

    

NASDAQ Industrial

0.12 (1.96)**

0.01 (0.22)

0.05 (0.68)

0.17 (2.46)**

 − 0.12 (1.80)*

NASDAQ Insurance

0.08 (1.70)*

0.08 (1.67)*

   

NASDAQ Telecommunications

0.10 (1.27)

    

NASDAQ Transportation

 − 0.01 (0.48)

    

PHLX Semiconductors

0.14 (1.47)

    
  1. * The maximum number of lags imposed was 8. But the optimum lag for Δ NEGt based on the Akaike Information Criterion (AIC) was not more than 4 lags for each non-linear model

III. Long-Run Coefficient Estimates of the Non-Linear ARDL Model (5)

U.S. sectoral indices

Long-run coefficient estimates

POS

NEG

ln EX

ln IPI

ln CPI

ln MS

Constant

Dow Jones Industrial Average

 − 0.25 (1.02)

 − 0.75(2.77)**

 − 1.34 (1.31)

3.24(3.62)**

 − 2.97 (1.24)

 − 1.63 (1.24)

58.68 (1.33)

Dow Jones Transportation Average

 − 0.16 (0.48)

 − 0.42(2.01)**

 − 2.01(2.28)**

3.19(2.45)**

 − 5.60 (1.04)

0.98 (0.67)

 − 1.67 (0.04)

Dow Jones Utility Average

0.11 (0.36)

 − 0.45 (1.57)

 − 1.98 (1.55)

3.30(2.2)**

 − 7.27(2.08)**

 − 0.86 (0.49)

53.97 (0.93)

NASDAQ Bank

 − 0.35 ( − 0.43)

 − 0.22 ( − 0.41)

1.05 (0.47)

1.40 (0.43)

 − 0.12 (0.01)

1.41 (0.36)

 − 43.41 (0.36)

NASDAQ Biotechnology

2.62 (1.23)

0.73 (0.68)

 − 9.71 (1.04)

14.24 (1.39)

 − 89.76 (1.38)

16.29(1.37)

 − 100.3(0.53)

NASDAQ Computer

 − 0.80 (0.66)

 − 2.07 (1.87)*

 − 10.1(1.86)*

6.81 (1.95)*

 − 39.31 (1.83)*

6.10 (0.86)

16.54 (0.11)

NASDAQ Industrial

 − 0.28 (0.80)

 − 1.07(3.94)**

 − 3.98(3.35)**

5.7(4.07)**

 − 16.14(3.1)**

1.17 (0.74)

34.02 (0.67)

NASDAQ Insurance

 − 0.31(2.3)**

 − 0.27(3.19)**

 − 0.61 (1.75)*

1.89(4.1)**

1.78 (1.05)

0.86 (1.38)

 − 30.87 (1.58)

NASDAQ Telecommunications

 − 2.68 (1.11)

 − 4.33 (1.84)*

 − 26.29(1.69)*

13.9(1.86)*

 − 73.09 (1.50)

13.48(0.86)

 − 7.50 (0.03)

NASDAQ Transportation

0.19 (0.51)

 − 0.11 (0.49)

 − 1.54 (1.60)

3.62(2.7)**

 − 9.96 (1.86)*

2.00 (1.23)

 − 17.85 (0.35)

PHLX Semiconductors

1.05 (1.73)*

 − 0.44 (0.90)

 − 2.21 (1.36)

7.65(3.8)**

 − 38.3(3.47)**

2.91 (0.87)

60.79 (0.75)

IV. Diagnostics of the Non-Linear ARDL Model (5)

U.S. sectoral indices

Statistical diagnostics

F

ECM t-1

LM

RESET

R bar squared

CUSUM (CUSUM2)

Wald-short

Wald-long

Dow Jones Industrial Average

2.82

 − 0.06(4.47)**

0.56

10.43

0.09

S(S)

2.63

2.96*

Dow Jones Transportation Average

2.98

 − 0.08(4.59)**

0.04

0.11

0.95

S(S)

9.71**

0.64

Dow Jones Utility Average

2.39

 − 0.04 (4.12)*

0.04

5.03

0.08

S(S)

0.79

2.24

NASDAQ Bank

2.43

 − 0.03 (4.15)*

0.08

30.18

0.09

S(S)

4.75**

0.06

NASDAQ Biotechnology

3.27

 − 0.02(4.57)**

0.02

10.88

0.10

S(S)

0.10

0.72

NASDAQ Computer

3.32

 − 0.03(4.80)**

0.29

8.74

0.10

S(S)

0.03

1.36

NASDAQ Industrial

4.00**

 − 0.07(5.32)**

1.63

4.40

0.12

S(S)

1.75

3.72*

NASDAQ Insurance

2.97

 − 0.13(4.59)**

1.07

7.90

0.12

S(S)

1.61

0.08

NASDAQ Telecommunications

6.54**

 − 0.02(6.82)**

0.00

3.38

0.19

S(S)

0.01

0.93

NASDAQ Transportation

2.19

 − 0.07 (3.92)

0.11

4.74

0.09

S(S)

0.25

0.86

PHLX Semiconductors

4.04**

 − 0.08(5.35)**

0.001

0.89

0.09

S(S)

0.01

7.97**

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Saha, S. Asymmetric Impact of Oil Price Changes on Stock Prices: Evidence from Country and Sectoral Level Data. J Econ Finan 46, 237–282 (2022). https://doi.org/10.1007/s12197-021-09559-3

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