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Food and Agriculture Prices Across Countries and the Law of One Price

Ken Clements, Jiawei Si and Long Vo

Business School

The University of Western Australia

April 2017

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ENGEL’S LAW

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155 Countries in 2011

y = -11.15 log M + constant

(0.49)

Income p.c. ($)

Food share

(×100)

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CHEAPER FOOD IN �RICH COUNTRIES

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y = -6.18 log M + constant

(1.10)

Income p.c. ($)

Relative price of food

(×100)

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WHY IS FOOD CHEAPER �IN RICH COUNTRIES?

  • Data artefact?
  • Issues of quality of products?
  • Engel’s law
  • Productivity bias

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UNIFORM GROWTH

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Non-food

Food

Both sectors expand at the same rate

Without Engel’s law, both income elasticities are unity and relative prices unchanged

A

B

ICC

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GROWTH AND �ENGEL’S LAW

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Non-food

Food

When ηF < 1, at C excess supply of food and its relative price must fall

A

B

ICC0

ICC1

C

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PRODUCTIVITY IN FOOD �AND NONFOOD

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Solar powered tomato farm, Port Augusta, SA

University lecture

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BIASED GROWTH

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Non-food

Food

Rapid growth in food production causes it relative price to fall

A

B

ICC

Steeper

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TAKEAWAY

  • Food prices fall as country becomes richer because of:
    • Engel’s law
    • Productivity bias
    • Both effects operating simultaneously

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PRICE DISPERSION �ALSO FALLS

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Log variance

of 31 food items

Income p.c. ($)

y = -0.40 log M + constant

(0.03)

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WHY LOWER �DISPERSION?

  • Deeper, more elaborate distribution channels
  • Consumers better able to search for lower prices
  • Better transport systems
  • More price transparency
  • More competition?

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MODELLING �CONSUMER PRICES

  • For i = 1,…,n food items:

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  • Income elasticity of price of i is:

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TWO TYPES OF �INCOME ELASTICITIES

  • Income elasticity of price of i:

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  • Income elasticity of quantity demanded of i:

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  • Two elasticities are related:

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DISPERSION OF �INCOME ELASTICITIES

  • Weighted variance of the income elasticities of the prices is
  • As

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  • Variance of inc elasts of demand = variety of basket

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Weighted variance of inc �elasts of prices

constant

Weighted variance of inc

elasts of qty demanded

=

×

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APPLICATION

  • 2011 data from the International Comparison Program for n = 31 food items in 154 countries
  • For item i:

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  • 31 equations to estimate
  • Income elasticties for rich and poor:

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RESULTS FOR �SELECTED ITEMS

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Weighted variance × 100

4.45

2.78

Cheese

-0.13

0.16

Food item

Income elasticity of price

Rich

Poor

Eggs

-0.30

0.11

Other edible oils and fats

-0.49

-0.14

Jams, marmalades and honey

-0.16

0.20

⁞

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Spirits

0.03

0.07

Wine

-0.36

-0.05

Beer

-0.01

-0.06

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DISPERSION OF �ELASTICITIES

  • Variance of income elasticities of prices for rich 60% bigger than poor’s
  • Implies higher dispersion of income elasticities of quantities demand
  • More variety in rich’s consumption basket
  • Higher quality
  • Plausible

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LAW OF ONE PRICE

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PROBLEMS FOR LOP

  • For arbitrage mechanism to work need:
    1. Identical commodities – only difference is location &/or currency
    2. No barriers to trade
    3. No transport costs
    4. No non-traded component (wholesale/retail margins, for example)
  • Big ask!

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EXCHANGE RATES �AND PRICES

  • Dollar price of commodity equalised across countries:

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  • For a number of countries, regress local price on the ER:

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  • Test LOP via relationship between ERs and prices:

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THREE EXAMPLES

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Log Sc

Log Sc

Log Sc

Log pc

Log pc

Log GDPc

Gold

Big Macs

GPD per capita

 

 

 

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APPLICATION TO ICP

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All 198 Food Items

Cheese, processed

Spinach

Log Sc

Log pic

Log Sc

Log pc

Log Sc

Log pc

 

 

 

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198 CROSS-COUNTRY SLOPE COEFFICIENTS

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Cumulative Absolute t-value H0: β = 1

Cumulative Distribution

0.39

0.97

1.05

0.95

0.35

Frequency Distribution

Mean = 0.96

Median = 0.97

SD = 0.05

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PANEL DATA FROM FAO

  • Producer prices from Food and Agriculture Organisation:
    • 158 countries, 23 years, 1991–2013
    • 133 commodities, such as

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  • Missing observations = unbalanced panels

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Apples

Meat, chicken

Milk, whole fresh cow

Maize, green

Eggs, hen, in shell

Watermelons

Quinces

Honey, natural

Chick peas

Oats

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LOP DEVIATIONS

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  • Measure of world price:

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  • Deviation from LOP:

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LOP DEVIATIONS,�FAO DATA

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Mean = -0.27

Median = -0.23

SD = 0.86

0.49

0.3

-0.3

0.75

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SUMMARY

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ITEM

PRICE DISPERSION

Standard error of estimate/SD

Gold

0

Big Macs

0.34

GDP

1.22

ICP -- Cheese

0.32

Spinach

0.77

FAO -- 133 agricultural items

0.86

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MEAN REVERSION

  • Do LOP deviations tend to die out?
  • Is stationary?
  • Panel approach from Choi (2001) and Hartung (1999) to test for unit roots

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A PANEL APPROACH

  • Panel for item i:

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  • Allows for
    • Country-specific intercepts and slopes
    • Unbalanced panel
    • Cross-sectional dependence

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RESULTS

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  • Reject unit root for 80% of cases

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Mean = -3.24

Median = 3.28

SD = 1.90

-1.64

0.80

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WHAT HAS BEEN LEARNT?

  • Food prices are lower and less dispersed in rich countries
  • Prices are not equalised across countries
  • Use LOP as a benchmark
  • Considerable price dispersion
  • so currency changes flow more or less fully into prices, as predicted by the LOP
  • Deviations from LOP tend to be eliminated over time

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THE FUTURE

  • Relationship of LOP deviations to trade costs
  • Which groups of commodities and countries have the largest/smallest deviations?
  • Proportion of ER-changes passed through to consumer prices
  • Transmission of world prices to domestic prices

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THANK YOU

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REFERENCES

Choi, I. (2001). “Unit Root Tests for Panel Data.” Journal of International Money and Finance 20: 249-72.

Hartung, J. (1999). “A Note on Combining Dependent Tests of Significance.” Biometrical Journal 41: 849-55.

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