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The role of temporal dependence in factor selection and forecasting oil prices

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Abstract

Extracting information from high-dimensional time series in the form of underlying factors is an increasingly popular methodology in forecasting applications. In this paper, principal component analysis (PCA) and three other methods for factor extraction are compared based on their deterministic and probabilistic forecasting performances using factor-augmented vector autoregressive (FAVAR) models. The existing PCA-based methods use only the contemporaneous covariance matrix of the data, while the other methods rely on weighted lagged cross-covariance matrices. Our empirical study considers four crude oil future price instruments and a 241 variable dataset of global energy prices and quantity, macroeconomic indicators, and financial series which are thought to influence oil price movements. Overall empirical findings are: (1) the PCA-based method performs better at shorter forecast horizons whereas the new methods involving lagged cross-covariance matrices tend to perform better at longer horizons (2 months or greater); (2) the performance ranking of the four methods under both deterministic and probabilistic forecasting is greatly affected by the number of factors included in the FAVAR models; (3) the forecast performances of the four methods are close to each other and no method performs uniformly better than the others. More research on the role of temporal dependence in determining the number of factors is warranted.

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Notes

  1. The authors thank the referee for suggesting this extension and the use of Alessi et al. (2010) criterion for determining the number of lags.

Abbreviations

AIC:

Akaike information criteria

PCA:

Asymptotic principal components analysis

BIC:

Bayesian information criteria

CCM:

Cross-covariance matrices

CDF:

Cumulative distribution function

FAVAR:

Factor-augmented vector autoregressive

GLY:

Generalized Lam and Yao

LY:

Lam and Yao

MLY:

Modified Lam and Yao

PFS:

Prequential forecasting system

PSM:

Multiple probability score

RMSE:

Root-mean-squared error

VAR:

Vector autoregressive

MinVar(f):

The dispersion of probability forecasts, which cannot be explained by the conditional dispersion

Scat(f):

The weighted average of the conditional variances

Var(d):

Variance of the outcome index

Bias2 :

The mis-calibration of the forecast

Cov(f, d):

Covariance between the forecasts and the outcome index

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Author information

Authors and Affiliations

  1. Federal Reserve Bank of Chicago, 230 S. LaSalle St., Chicago, IL, 60604, USA

    Kyle E. Binder

  2. Department of Statistics, Texas A&M University, College Station, TX, USA

    Mohsen Pourahmadi

  3. Department of Agricultural Economics, Texas A&M University, College Station, TX, USA

    James W. Mjelde

Authors
  1. Kyle E. Binder
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  2. Mohsen Pourahmadi
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  3. James W. Mjelde
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Corresponding author

Correspondence to James W. Mjelde.

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Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of Chicago, the Federal Reserve System, or Texas A&M University.

Appendices

Appendix A: Data series used in the empirical analyses

Series description

Units

Source

Transformationa

Category

Cushing, OK WTI spot price

USD/barrel

DS

3

 

WTI 1-month-ahead futures

USD/barrel

DS

3

 

WTI 6-month-ahead futures

USD/barrel

DS

3

 

WTI 12-month-ahead futures

USD/barrel

DS

3

 

F.O.B. Cost of Crude Oil Imports From Mexico

USD/barrel

EIA

3

Import costs

F.O.B. Cost of Crude Oil Imports From All OPEC Countries

USD/barrel

EIA

3

 

F.O.B. Cost of Crude Oil Imports From All Non-OPEC Countries

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Angola

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Canada

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Mexico

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Nigeria

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Saudi Arabia

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Venezuela

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From Persian Gulf Nations

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From All OPEC Countries

USD/barrel

EIA

3

 

Landed Cost of Crude Oil Imports From All Non-OPEC Countries

USD/barrel

EIA

3

 

Unleaded Regular Gasoline, US City Average Retail Price

USD/gal

EIA

3

Refined

Unleaded Premium Gasoline, US City Average Retail Price

USD/gal

EIA

3

 

All Grades of Gasoline, US City Average Retail Price

USD/gal

EIA

3

 

Refiner Price of Finished Motor Gasoline to End Users

USD/gal

EIA

3

 

Refiner Price of Kerosene-Type Jet Fuel to End Users

USD/gal

EIA

3

 

Refiner Price of No. 2 Diesel Fuel to End Users

USD/gal

EIA

3

 

Refiner Price of Finished Motor Gasoline for Resale

USD/gal

EIA

3

 

Refiner Price of Kerosene-Type Jet Fuel for Resale

USD/gal

EIA

3

 

Refiner Price of No. 2 Fuel Oil for Resale

USD/gal

EIA

3

 

Refiner Price of No. 2 Diesel Fuel for Resale

USD/gal

EIA

3

 

Refiner Price of Residual Fuel Oil, Sulfur Content Less Than or Equal to 1 Percent, Sales for Resale

USD/gal

EIA

3

 

Refiner Price of Residual Fuel Oil, Sulfur Content Less Than or Equal to 1 Percent, Sales to End Users

USD/gal

EIA

3

 

Refiner Price of Residual Fuel Oil, Sulfur Content Greater Than 1 Percent, Sales to End Users

USD/gal

EIA

3

 

Refiner Price of Residual Fuel Oil, Average, Sales for Resale

USD/gal

EIA

3

 

Refiner Price of Residual Fuel Oil, Average, Sales to End Users

USD/gal

EIA

3

 

Coal Consumed by the Commercial Sector

Trillion Btu

EIA

3

Consumption

Natural Gas Consumed by the Commercial Sector (Excluding Supplemental Gaseous Fuels)

Trillion Btu

EIA

4

 

Petroleum Consumed by the Commercial Sector (Excluding Biofuels)

Trillion Btu

EIA

3

 

Total Fossil Fuels Consumed by the Commercial Sector

Trillion Btu

EIA

4

 

Conventional Hydroelectric Power Consumed by the Commercial Sector

Trillion Btu

EIA

2

 

Geothermal Energy Consumed by the Commercial Sector

Trillion Btu

EIA

3

 

Biomass Energy Consumed by the Commercial Sector

Trillion Btu

EIA

3

 

Total Renewable Energy Consumed by the Commercial Sector

Trillion Btu

EIA

3

 

Total Primary Energy Consumed by the Commercial Sector

Trillion Btu

EIA

4

 

Electricity Retail Sales to the Commercial Sector

Trillion Btu

EIA

4

 

Commercial Sector Electrical System Energy Losses

Trillion Btu

EIA

4

 

Total Energy Consumed by the Commercial Sector

Trillion Btu

EIA

4

 

Coal Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Natural Gas Consumed by the Electric Power Sector (Excluding Supplemental Gaseous Fuels)

Trillion Btu

EIA

4

 

Petroleum Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Total Fossil Fuels Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Nuclear Electric Power Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Conventional Hydroelectric Power Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Geothermal Energy Consumed by the Electric Power Sector

Trillion Btu

EIA

3

 

Solar/PV Energy Consumed by the Electric Power Sector

Trillion Btu

EIA

3

 

Biomass Energy Consumed by the Electric Power Sector

Trillion Btu

EIA

3

 

Total Renewable Energy Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Total Primary Energy Consumed by the Electric Power Sector

Trillion Btu

EIA

4

 

Natural Gas Consumed by the Residential Sector (Excluding Supplemental Gaseous Fuels)

Trillion Btu

EIA

4

 

Petroleum Consumed by the Residential Sector

Trillion Btu

EIA

4

 

Total Fossil Fuels Consumed by the Residential Sector

Trillion Btu

EIA

4

 

Geothermal Energy Consumed by the Residential Sector

Trillion Btu

EIA

3

 

Solar/PV Energy Consumed by the Residential Sector

Trillion Btu

EIA

3

 

Biomass Energy Consumed by the Residential Sector

Trillion Btu

EIA

3

 

Total Renewable Energy Consumed by the Residential Sector

Trillion Btu

EIA

3

 

Total Primary Energy Consumed by the Residential Sector

Trillion Btu

EIA

4

 

Electricity Retail Sales to the Residential Sector

Trillion Btu

EIA

4

 

Residential Sector Electrical System Energy Losses

Trillion Btu

EIA

4

 

Total Energy Consumed by the Residential Sector

Trillion Btu

EIA

4

 

Natural Gas Consumed by the Transportation Sector (Excluding Supplemental Gaseous Fuels)

Trillion Btu

EIA

3

 

Petroleum Consumed by the Transportation Sector (Excluding Biofuels)

Trillion Btu

EIA

4

 

Total Fossil Fuels Consumed by the Transportation Sector

Trillion Btu

EIA

4

 

Biomass Energy Consumed by the Transportation Sector

Trillion Btu

EIA

3

 

Total Primary Energy Consumed by the Transportation Sector

Trillion Btu

EIA

4

 

Electricity Retail Sales to the Transportation Sector

Trillion Btu

EIA

3

 

Transportation Sector Electrical System Energy Losses

Trillion Btu

EIA

3

 

Total Energy Consumed by the Transportation Sector

Trillion Btu

EIA

4

 

Crude Oil and Natural Gas Rotary Rigs in Operation, Onshore

Number of Rigs

EIA

4

Production

Crude Oil and Natural Gas Rotary Rigs in Operation, Offshore

Number of Rigs

EIA

4

 

Crude Oil Rotary Rigs in Operation

Number of Rigs

EIA

4

 

Natural Gas Rotary Rigs in Operation

Number of Rigs

EIA

4

 

Crude Oil and Natural Gas Rotary Rigs in Operation, Total

Number of Rigs

EIA

4

 

Active Well Service Rig Count

Number of Rigs

EIA

4

 

Wells Drilled, Exploratory, Crude Oil

Number of Wells

EIA

3

 

Wells Drilled, Exploratory, Natural Gas

Number of Wells

EIA

3

 

Wells Drilled, Exploratory, Dry

Number of Wells

EIA

4

 

Wells Drilled, Exploratory, Total

Number of Wells

EIA

4

 

Wells Drilled, Development, Crude Oil

Number of Wells

EIA

4

 

Wells Drilled, Development, Natural Gas

Number of Wells

EIA

4

 

Wells Drilled, Development, Dry

Number of Wells

EIA

4

 

Wells Drilled, Development, Total

Number of Wells

EIA

4

 

Wells Drilled, Total, Crude Oil

Number of Wells

EIA

4

 

Wells Drilled, Total, Natural Gas

Number of Wells

EIA

4

 

Wells Drilled, Total, Dry

Number of Wells

EIA

4

 

Crude Oil, Natural Gas, and Dry Wells Drilled, Total

Number of Wells

EIA

4

 

Total Footage Drilled

Thousand Feet

EIA

4

 

Fuel Ethanol, Excluding Denaturant, Feedstock

Trillion Btu

EIA

3

Renewable

Fuel Ethanol, Excluding Denaturant, Losses and Co-products

Trillion Btu

EIA

3

 

Fuel Ethanol Production

Trillion Btu

EIA

4

 

Fuel Ethanol Consumption

Trillion Btu

EIA

4

 

Conventional Hydroelectric Power Consumed by the Industrial Sector

Trillion Btu

EIA

3

 

Biomass Energy Consumed by the Industrial Sector

Trillion Btu

EIA

4

 

Total Renewable Energy Consumed by the Industrial Sector

Trillion Btu

EIA

4

 

Biofuels Production

Trillion Btu

EIA

3

 

Total Biomass Energy Production

Trillion Btu

EIA

4

 

Total Renewable Energy Production

Trillion Btu

EIA

4

 

Hydroelectric Power Consumption

Trillion Btu

EIA

4

 

Geothermal Energy Consumption

Trillion Btu

EIA

3

 

Solar/PV Energy Consumption

Trillion Btu

EIA

3

 

Wood Energy Consumption

Trillion Btu

EIA

4

 

Waste Energy Consumption

Trillion Btu

EIA

3

 

Biofuels Consumption

Trillion Btu

EIA

3

 

Total Biomass Energy Consumption

Trillion Btu

EIA

4

 

Total Renewable Energy Consumption

Trillion Btu

EIA

4

 

Asphalt and Road Oil Product Supplied

1000 Barrels/Day

EIA

4

Supplied

Aviation Gasoline Product Supplied

1000 Barrels/Day

EIA

3

 

Distillate Fuel Oil Product Supplied

1000 Barrels/Day

EIA

4

 

Jet Fuel Product Supplied

1000 Barrels/Day

EIA

4

 

Propane/Propylene Product Supplied

1000 Barrels/Day

EIA

4

 

Liquefied Petroleum Gases Product Supplied

1000 Barrels/Day

EIA

4

 

Motor Gasoline Product Supplied

1000 Barrels/Day

EIA

4

 

Residual Fuel Oil Product Supplied

1000 Barrels/Day

EIA

4

 

Other Petroleum Products Supplied

1000 Barrels/Day

EIA

4

 

Total Petroleum Products Supplied

1000 Barrels/Day

EIA

4

 

Crude Oil Imports, Total

1000 Barrels/Day

EIA

4

Imports

Distillate Fuel Oil Imports

1000 Barrels/Day

EIA

4

 

Jet Fuel Imports

1000 Barrels/Day

EIA

4

 

Propane/Propylene Imports

1000 Barrels/Day

EIA

4

 

Liquefied Petroleum Gases Imports

1000 Barrels/Day

EIA

4

 

Finished Motor Gasoline Imports

1000 Barrels/Day

EIA

4

 

Residual Fuel Oil Imports

1000 Barrels/Day

EIA

4

 

Other Petroleum Products Imports

1000 Barrels/Day

EIA

4

 

Total Petroleum Imports

1000 Barrels/Day

EIA

4

 

Crude Oil Exports

1000 Barrels/Day

EIA

4

Exports

Petroleum Products Exports

1000 Barrels/Day

EIA

4

 

Total Petroleum Exports

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Persian Gulf Nations

1000 Barrels/Day

EIA

4

World Production

Crude Oil Production, Canada

1000 Barrels/Day

EIA

4

 

Crude Oil Production, China

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Egypt

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Mexico

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Norway

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Russia

1000 Barrels/Day

EIA

4

 

Crude Oil Production, UK

1000 Barrels/Day

EIA

4

 

Crude Oil Production, USA

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Total Non-OPEC

1000 Barrels/Day

EIA

4

 

Crude Oil Production, World

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Algeria

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Angola

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Ecuador

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Iran

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Iraq

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Kuwait

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Libya

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Nigeria

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Qatar

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Saudi Arabia

1000 Barrels/Day

EIA

4

 

Crude Oil Production, United Arab Emirates

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Venezuela

1000 Barrels/Day

EIA

4

 

Crude Oil Production, Total OPEC

1000 Barrels/Day

EIA

4

 

Crude Oil Stocks, SPR

Million Barrels

EIA

4

Stocks

Crude Oil Stocks, Non-SPR

Million Barrels

EIA

4

 

Crude Oil Stocks, Total

Million Barrels

EIA

4

 

Distillate Fuel Oil Stocks

Million Barrels

EIA

4

 

Jet Fuel Stocks

Million Barrels

EIA

3

 

Propane/Propylene Stocks

Million Barrels

EIA

3

 

Liquefied Petroleum Gases Stocks

Million Barrels

EIA

4

 

Motor Gasoline Stocks (Including Blending Components and Gasohol)

Million Barrels

EIA

4

 

Residual Fuel Oil Stocks

Million Barrels

EIA

3

 

Other Petroleum Products Stocks

Million Barrels

EIA

4

 

Total Petroleum Stocks

Million Barrels

EIA

4

 

Crude Oil Refinery and Blender Net Input

1000 Barrels/Day

EIA

4

Refinery

Natural Gas Plant Liquids Refinery and Blender Net Inputs

1000 Barrels/Day

EIA

4

 

Other Liquids Refinery and Blender Net Inputs

1000 Barrels/Day

EIA

4

 

Total Petroleum Refinery and Blender Net Inputs

1000 Barrels/Day

EIA

4

 

Distillate Fuel Oil Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Jet Fuel Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Propane/Propylene Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Liquefied Petroleum Gases Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Finished Motor Gasoline Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Residual Fuel Oil Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Other Petroleum Products Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Total Petroleum Refinery and Blender Net Production

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, France

1000 Barrels/Day

EIA

4

World Consumption

Petroleum Consumption, Germany

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, Italy

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, UK

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, OECD Europe

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, Canada

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, Japan

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, South Korea

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, USA

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, Other OECD

1000 Barrels/Day

EIA

4

 

Petroleum Consumption, Total OECD

1000 Barrels/Day

EIA

4

 

Petroleum Stocks, France

Million Barrels

EIA

4

 

Petroleum Stocks, Germany

Million Barrels

EIA

4

 

Petroleum Stocks, Italy

Million Barrels

EIA

4

 

Petroleum Stocks, UK

Million Barrels

EIA

4

 

Petroleum Stocks, OECD Europe

Million Barrels

EIA

4

 

Petroleum Stocks, Canada

Million Barrels

EIA

4

 

Petroleum Stocks, Japan

Million Barrels

EIA

4

 

Petroleum Stocks, South Korea

Million Barrels

EIA

4

 

Petroleum Stocks, USA

Million Barrels

EIA

4

 

Petroleum Stocks, Other OECD

Million Barrels

EIA

4

 

Petroleum Stocks, Total OECD

Million Barrels

EIA

4

 

Yield on 10-year US treasury

Percent

DS

3

Financial

US Money Supply M1

Billion Dollars

DS

3

 

US Money Supply M2

Billion Dollars

DS

3

 

US Prime Rate Charged by Banks (month average)

Percent

DS

3

 

US Capacity Utilization Rate—All Industry

Percent

DS

3

 

US Consumer Confidence Index

Index

DS

3

 

US PPI—Finished Goods

Index

DS

3

 

US PPI—Finished Goods Less Foods & Energy (core)

Index

DS

3

 

US Federal Funds Target Rate—Middle Rate

Percent

DS

3

 

US Chain-Type Price Index for Personal Consumption Expenditures

Index

DS

3

 

US CPI—All Urban All Items

Index

DS

3

 

US Industrial Production—Total Index

Index

DS

3

 

US New Private Housing units Started (AR)

Index

DS

3

 

US Treasury Yield Adjusted to Constant Maturity—20 Years

Percent

DS

3

 

US Dow Jones Industrials Share Price Index

Index

DS

3

 

S&P 500 Composite Price Index

Index

DS

3

 

US Treasury Yield Adjusted to Constant Maturity—3 Year

Percent

DS

3

 

Volume 1 MO

Index

DS

3

 

Open Interest 1 MO

Index

DS

3

 

Volume 6 MO

Index

DS

3

 

Open Interest 6 MO

Index

DS

3

 

Open Interest 12 MO

Index

DS

3

 

Volume 3MO

Index

DS

3

 

Open Interest 3 MO

Index

DS

3

 

Exxon Mobil

Dollars

DS

3

 

BP SPN.ADR 1:6

Dollars

DS

3

 

Conoco Phillips

Dollars

DS

3

 

Royal Dutch Shell B

Dollars

DS

3

 

Chevron

Dollars

DS

3

 

Crude Oil-Dtd Brent UK Close U$/BBL

Dollars

DS

3

 

Crude Oil-Brent 1Mth Fwd FOB U$/BBL

Dollars

DS

3

 

US Treasury Bill Rate 3 Months

Percent

DS

3

 

US-DS Oil & Gas—Price Index

Index

DS

3

 

DAX 30 Performance Index

Index

DS

3

 

UK FTSE 100 Index

Index

DS

3

 

EK Industrial Production Excluding Construction

Index

DS

3

 

US $ TO UK £ (WMR)—Exchange Rate

Exchange Rate

DS

3

 

UK Index of Production Industries—All Production

Index

DS

3

 

DJGL World Industrials—Price Index

Index

DS

3

 

CBOE SPX Volatility Vix (new)—Price Index

Index

DS

3

 

NYM—Natural Gas Strip 1-month settled price

Dollars

DS

3

 

NYM-Natural Gas Strip M03—Settlement Price

Dollars

DS

3

 

NYM- Natural Gas Strip M06—Settlement Price

Dollars

DS

3

 

NYM-NY Heating Oil Strip M03—Settlement Price

Dollars

DS

3

 
  1. EIA, U.S. Energy Information Administration (2015); DS, Datastream (2015); 0, Levels; 1, Natural; Logarithm; 2, First Difference of Levels; 3, First Difference of Natural Logarithm; 4, First Difference of Natural Logarithm of Percentage
  2. aCorresponds to the following transformation

Appendix B: Graphs of the R2 of the individual explanatory variables and each of the five factors

See

figure a

,

figure b

,

figure c

,

figure d

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Binder, K.E., Pourahmadi, M. & Mjelde, J.W. The role of temporal dependence in factor selection and forecasting oil prices. Empir Econ 58, 1185–1223 (2020). https://doi.org/10.1007/s00181-018-1574-9

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