Measuring food price transmission
Nicholas Minot (IFPRI)
Presented at the Comesa training course on
“Food price variability: Causes, consequences, and policy options"
on 28-29 January 2010 in Maputo, Mozambique
under the Comesa-MSU-IFPRI African Agricultural Markets Programme (AAMP)
Outline
 What is price transmission?
 Why does price transmission occur?
 What is an elasticity of price transmission?
 How do we measure price transmission?
 Simple percentage changes
 Correlation analysis
 Regression analysis
 Non-stationarity and co-integration analysis
 Summary
What is price transmission?

Price transmission is when changes in one price
cause another price to change

Types of price transmission:
 Spatial: Price of maize in South Africa  price of maize
in Maputo
 Vertical: Price of wheat  price of flour
 Cross-commodity: Price of maize  price of rice
Why does price transmission occur?
 Spatial price
transmission occurs
because of flows of
good between markets
 If price gap > marketing
costs, trade flows will
narrow gap
 If price gap < marketing
cost, no flows
 Therefore, price gap <=
marketing cost
Maize prices in Maputo and Chokwe
Why does price transmission occur?

Vertical price
transmission
occurs because
of flows of
goods along
marketing
channel
Maize grain and maize meal prices in Kitwe, Zambia
2500
2000
1500
1000
500
2 2009
8 2008
11 2008
5 2008
2 2008
8 2007
11 2007
5 2007
2 2007
8 2006
11 2006
5 2006
2 2006
8 2005
11 2005
5 2005
2 2005
8 2004
11 2004
5 2004
2 2004
8 2003
11 2003
5 2003
0
Why does price transmission occur?

Crosscommodity
price
transmission
occurs because
of substitution in
consumption
and/or
production
Price of maize and rice in Maputo
Rice
Maize
Why might price transmission not occur?





High transportation cost makes trade
unprofitable
Trade barriers make trade unprofitable
Goods are imperfect substitutes (e.g. imported
rice and local rice)
Lack of information about prices in other
markets
Long time to transport from one market to
another (lagged transmission)
What is an elasticity of price transmission?

Price transmission elasticity: % change in one
price for each 1% increase in the other price

Example: if a 10% increase in the world price of
maize causes a 3% increase in the local price of
maize, then price transmission elasticity is
0.03/0.10 = 0.3
What is an elasticity of price transmission?

Elasticity of 1.0 is not always “perfect transmission”
Example:
 World price = $200/ton
 Local price = $400/ton
 $100 increase in world price causes $100 increase in local price
 But transmission elasticity is (100/400)/(100/200)= 25%/50% =
0.50
For imports, perfect transmission elasticity can be less
than 1.0
 For exports, perfect transmission elasticity can be more
than 1.0

How do we measure price transmission?
 Ratio of percentage changes between two time




periods
Correlation coefficient
Regression analysis
Co-integration analysis
Other methods
Ratio of percentages
 Ratio of percentage changes between two time
periods

Price of US Price of No 2 maize in yellow Dar in maize in US$/ton US$/ton
June 2007
120
165
June 2008
Percent change
239
287
99%
75%
Elasticity of transmission is 1.32 (=.99/.75)
Ratio of percentages
Very crude method: only uses two points in time, does
not take trends into account
450
Maize, Dar es Salaam wholesale
400
Maize, US No 2 yellow maize, FOB Gulf
350
300
250
200
150
100
50
Nov‐09
Jul‐09
Sep‐09
May‐09
Jan‐09
Mar‐09
Nov‐08
Jul‐08
Sep‐08
May‐08
Jan‐08
Mar‐08
Nov‐07
Jul‐07
Sep‐07
May‐07
Jan‐07
Mar‐07
Nov‐06
Jul‐06
Sep‐06
May‐06
Jan‐06
0
Mar‐06
Price (US$/metric ton) 
Correlation coefficient
 Correlation coefficient measures the degree of




relatedness of two variables
In Excel: =correl(range1, range2)
Advantage: easy to calculate and understand
Disadvantage: only considers relationship between
prices at same time, does not take into account lags
Exercise
In “correlation” worksheet, change b9 and look at
effect on correlation in graph
2) In “Data” worksheet, calculate correlation coefficient
of two prices
1)
Correlation coefficient
700
700
600
500
400
P2 P2 R² = 0.4812
600
R² = 0.9027
500
300
400
300
200
200
100
100
0
0
0
100
200
300
400
0
100
200
P1 300
400
P1 450
1000
900
800
700
600
500
400
300
200
100
0
Maize, Dar es Salaam wholesale
400
Maize, US No 2 yellow maize, FOB Gulf
350
300
250
200
150
100
R2= 0.075
50
Jul‐09
Sep‐09
Nov‐09
Jan‐09
Mar‐09
May‐09
Jul‐08
Sep‐08
Nov‐08
Jan‐08
Mar‐08
Jul‐07
Sep‐07
Nov‐07
Jan‐07
Mar‐07
May‐07
Jul‐06
0
Sep‐06
400
Nov‐06
P1 300
Jan‐06
200
Mar‐06
100
May‐06
0
May‐08
P2 Price (US$/metric ton) R² = 0.1191
Regression analysis
 Multiple regression analysis finds equation that best
fits data: Y = a + b*X1 + c*X2 …
 Advantages
Gives information to calculate transmission elasticity
 Can test relationships statistically
 Can take into account lagged effects, inflation, and
seasonality; can analyze relationship of >2 prices

 Disadvantages
Awkward to do in Excel
(easier with Stata or SPSS)
 Misleading results if data are non-stationary

Regression analysis
 Using Excel 2003 for
 Using Excel 2007 for
regression analysis
(method 1)
regression analysis
(method 1)
Mark columns with two
prices
2) Insert/Chart/XY(Scatter
) /Finish
3) Chart/Add trendline/
Linear
4) Click “Options”, then
“Display equation”
1)
1)
Mark columns with two
prices
2) Insert/Scatter graph
3) Chart tools/Layout/
Trendline/More
trendline options
4) Click box for “Display
equation on chart”
Note: only one “x” allowed with this method
Regression analysis
600
500
P2 400
300
200
y = 0.9366x + 212.96
100
0
0
100
200
300
400
P1 Regression analysis
 Using Excel for regression analysis (method 2)
=linest(y range, x range,1,1)
2) Mark 5x2 block around formula
3) F2 shift-control-enter
Note: Can use multiple x’s with this method
1)
b
=linest(..
=linest(..
a
Coef
0.999
236.3
SE
0.354
81.26
R2
0.119
137.8
7.98
58.00
155
1,112
Regression analysis
 Calculating transmission elasticity from regression
coefficient
Regression coefficient b = ΔP2/ΔP1
Transmission elasticity is (ΔP2/P2) / (ΔP1/P1)
So transmission elasticity = b*(P1/P2)



where b = regression coefficient
P2 = price on left side (Y variable)
P1 = price on right side (X variable)
 Exercise
In “Regression” worksheet, change green cells and examine
effect on results and graph
In “Data” worksheet, use regression analysis to analyze
relationship between two prices


Non-stationarity - definition
 What is a non-stationary variable?

A variable that does not tend to go back to a mean
value over time, also called “random walk”
Non-stationary variable
Tends to go back toward mean
Does not tend to go back to mean
Finite variance
Infinite variance
Regression analysis is valid
Regression analysis is misleading
400
700
350
600
300
500
P1 and P2
P1 and P2
Stationary variable
250
200
150
100
400
300
200
100
50
0
0
1 5 9 13172125293337414549535761
Month
1 6 11 16 21 26 31 36 41 46 51 56 61
Month
Non-stationarity - problem
 Why are non-stationary variables a problem?
If prices are non-stationary, regression analysis will
give misleading results
 With non-stationary variables, regression analysis
will say there is a statistically significant
relationship even when there is NO relationship

 Exercise

Use worksheet “Non-stationarity 1” to see that
regression gives a high t statistics when there is no
relationship
Non-stationarity - diagnosis
 How do you identify non-stationarity?
Several tests, most common one is the Augmented
Dickey-Fuller test
 Cannot easily be done in Excel, but Stata and SPSS
can do it easily
 Price data are usually non-stationary
 Of 62 staple food prices tested, most (60%) were
non-stationary

Non-stationarity - solution
 How do you analyze non-stationary prices?

Simple approach (with Excel)
 First differences (ΔP = Pt – Pt-1) are generally stationary
 Regress ΔP1 on ΔP2,, possibly with lags

Co-integration analysis (with Stata)
 Test to see if prices are co-integrated, meaning that P2-b*P1-a
is stationary
 If prices are co-integrated, run error correction model (ECM)
 ECM gives estimates of
1) Long-run transmission
2) Short-run transmission
3) Speed of adjustment to long-run equilibrium
Non-stationarity - solution
 Exercise
Use “Stationarity 2” worksheet to see that regressing
ΔP1 and ΔP2 correctly shows no relationship
 Examine “Stationarity 3” to see how regressing ΔP1
and ΔP2 correctly shows a relationship that exists
 Use “Data” to calculate first differences in two price
and regress ΔP2 on ΔP1

Summary
 Price transmission occurs between markets, between stages of a
market channel, and between commodities… but not always
 Correlation coefficient is easy but gives limited info
 Regression analysis
 Can be done in Excel but easier in Stata
 Gives estimate of price transmission
 Can take into account lagged effects
 But is misleading if prices are non-stationary
 Non-stationarity
 Means prices follow a “random walk”
 Can be tested with Stata
 If prices are non-stationary, need to
 At minimum, regress first-differences (can be done in Excel)
 Preferably, carry out co-integration analysis (requires Stata)