1. AAMP Training Materials
Module 3.2: Measuring Food Price Transmission
Nicholas Minot (IFPRI)
This is the second section of the AAMP Price Analysis module.
Exercises for this module are found in the following Excel file:
Module 3.2 – Measuring Food Price Transmission.xls

2. Objectives Understand what price transmission is and why it occurs
Compute elasticity of price transmission
Measure price transmission
Simple percentage changes
Correlation analysis
Regression analysis
Examine non-stationary data

3. Background Material What is price transmission?
Why is it important to study price transmission?
Why does price transmission occur?
Introduction to elasticity of price transmission

4. What is price transmission?
Price transmission is when a change in one price causes another price to change
Three types of price transmission:
Spatial: Price of maize in South Africa  price of maize in Mozambique
Vertical: Price of wheat  price of flour
Cross-commodity: Price of maize  price of rice
Spatial price transmission occurs when a commodity is heavily traded between two regions or countries. For example, maize prices in the country that exports it (South Africa) strongly affect the price of the maize in the importing country (Mozambique). This is simple enough to understand. If the price of maize rises in South Africa, it will also rise in Mozambique because it costs more money to import.
Similarly, vertical price transmission occurs when the price of a good rises due to the rising price of one of the inputs used to make it. For example, if the price of wheat rises, this means that millers will have to spend more money to import wheat. If they spend more money importing wheat, they will raise the price of their flour to compensate. And further on up the chain, bakers may raise the price of bread in order to compensate for the higher price of flour.
A more complicated example of price transmission is cross-commodity price transmission. In this case, the price of a good which may be substituted for another good, such as rice and maize for example, may affect the price of the other good. If maize prices rise, and some households may be willing to shift to purchasing rice in larger-than -usual quantities. This increased demand then drives the price of rice up. So, an increase in the maize price may raise the price of rice.

5. Why is it important to study price transmission?
Study of price transmission helps to understand causes of changes in prices, necessary to address root causes
Example: If little price transmission from world markets, then trade policy will not be effective in reducing volatility
Study of price transmission may help forecast prices based on trends in related prices
Example: If changes in soybean prices transmitted to sunflower markets, then soybean futures markets may predict sunflower prices
Study of price transmission helps diagnose poorly functioning markets
Example: If two markets are close together, but show little price transmission, this may indicate problems with transportation network or monopolistic practices

6. Why does price transmission occur?
Maize prices in Maputo & Chokwe
Spatial price transmission occurs because of flows of goods between markets
If price gap > marketing costs, trade flows will narrow gap
If price gap < marketing cost, no flows
Therefore, price gap <= marketing cost
Chokwe is a maize surplus area in Mozambique, and Maputo is the capital city, with a large maize deficit. Whenever price gap between them exceeds cost of transporting maize between them, traders will find it profitable to transport maize from Chokwe to Maputo. The flow decreases supply in Chokwe, raising its price, while increasing the supply in Maputo, reducing its price. This reduces the gap between the prices until it is equal to or less than cost of transportation. Thus, a shock in either price can affect the other, and they tend to move together.

7. Why does price transmission occur?
Maize grain and maize meal
prices in Kitwe, Zambia
Vertical price transmission occurs because of flows of goods along marketing channel
Maize meal
Maize meal is simply ground maize grain. The bulk of the cost of producing and marketing maize meal is the price of the grain. Therefore, the price of maize meal closely tracks the price of maize grain. The price of maize meal may fall below the price of maize grain (as it did in early 2009) due to government sales of subsidized maize meal, imports of maize meal, or over-production of maize meal. This temporary disequilibrium cannot last long because consumers will not buy maize at a price higher than maize meal.
Maize grain

8. Why does price transmission occur?
Price of maize and rice in Maputo
Cross-commodity price transmission occurs because of substitution in consumption and/or production
The urban consumers of Maputo, Mozambique are willing to substitute maize for rice in their consumption baskets. If the price of rice rises, they will happily consume maize and vice versa. The two commodities are substitutes for one another. This willingness to substitute affects the price of both commodities. If the price of rice rises, some households switch to consuming maize. As many households make the switch, the increased demand for maize raises its price. The spike in maize price in December 2005 seems not to have affected the rice price. Perhaps the rice price is determined mainly by international markets, since (unlike maize) most rice is imported.

9. 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)
The high price of a commodity in one market should attract inflows of the commodity from another market. The effect is a lower price in the importing market and a higher price in the exporting market, keeping the prices close to each other (spatial price transmission). In general, both sides gain from trade (see the AAMP Module 4.4 – Gains from Trade for more).
However, if transportation costs or high trade barriers make trade unprofitable, price transmission does not take place and prices remain too high in one market and too low in the other.
Imperfect substitutes may limit cross-price transmission as well. If imported rice is greatly favored over local rice, a rise in the price of the imported rice may do nothing to the price of local rice. On the other hand, lowering the price of local rice may do nothing to the price of imported rice.
In addition, a lack of information about prices in other markets can reduce the effect of food price transmission as well. Not knowing that prices have spiked in Kenya, traders in neighboring Tanzania may miss an opportunity to export their relatively low cost commodities. The result: prices remain low in Tanzania and high in Kenya.
Finally, lagged food price transmission can occur if the time to transport from one market to another is exceptionally long. Anticipating a price spike, a trader may begin importing a commodity from overseas, but the price does not begin to subside until later, when the commodities arrive in the country.

10. 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

11. 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
Perfect transmission would be if a $100 increase in world price caused a $100 increase in local price
But transmission elasticity in this case would be (100/400)/(100/200)= .25 / .50 = 0.50
For imports, perfect transmission elasticity are < 1.0
For exports, perfect transmission elasticity are > 1.0

12. Measuring price transmission
There are several methods – four are discussed here
Ratio of percentage changes between two time periods
Correlation coefficient
Regression analysis
Co-integration analysis

13. Ratio of percentages
Ratio of percentage changes between two time periods
Elasticity of transmission is 1.34 (= .99 / .74)
Note that both prices increased by about $120/ton
Price of maize in Dar es Salaam
Price of US #2 Yellow Maize
US$ / ton
June 2007
120
165
June 2008
239
287
% Change
99%
74%
Measuring the percentage change between two prices:
(new price – old price) / old price = % change from old price to new price
So…
In the example above, for maize price in Dar es Salaam between 2007 and 2008:
( ) / 120 = .99
And…
The percentage change of US #2 Yellow Maize between 2007 and 2008:
(287 – 165) / 165 = 0.74

14. Ratio of percentages
Very crude method: only uses two points in time and does not take trends into account
Using the ratio of percentages method does not give a complete picture of price transmission. The only information used in the previous slide is the prices at two points in time (indicated by red lines), which imply that the Dar maize price and the world maize price rose together. But the figure above suggests that the two prices are not closely correlated. Choosing two other points on this timeline would yield completely different results.

15. Correlation coefficient – What is it?
Indicates the degree of relatedness of two variables
Two related measures
Pearson correlation coefficient = r
Coefficient of determination = R2 = r * r
In both cases
Correlation ranges between 0 and 1
0 means no relationship, 1 means perfect correlation
Advantage:
Easy to calculate and understand
R2 indicates share of variation in one variable explained by other variable
Disadvantage:
Only considers relationship between prices at same time, does not take into account lags
R2 has a convenient interpretation – it is the proportion of the variation in one variable that can be explained by variation in the other variable. For example, R2=0.50 means that one half of the variation in one variable can be explained by variation in the other variable.

16. Correlation coefficient – How to calculate?
Two methods using Excel
Use function correl(range1, range2) where the range1 and range2 describe the cells containing the two variables
For example, type into a cell =correl(B4:B56, C4:C56)
This will give r, R2 can be calculated by squaring r
Create scatterplot graph of the two variables, then add a trendline with R2
Click on graph, click “Add trendline”, then click “Display R2”
This will give R2

17. Examples of correlation coefficients (hypothetical prices)
Weak correlation
Strong correlation
Medium correlation

18. Correlation coefficient – Exercises
In Worksheet 1 [Tanzania example], type =CORREL(B5:B51,C5:C51) into cell F21 to calculate r
Then in F22 cell, type =F21*F21 (or = F21^2) to calculate R2
In Worsheet 8 [Data], calculate the value of R2 for the following pairs of prices:
Maize in Nampula and rice in Nampula
Rice in Nampula and rice in Maputo
Maize in Nampula and rice in Maputo
Open Module 3.2 – measuring food price transmission.xls, [1. Tanzania example] sheet 1.
R = .490 2.
R2 = .2405 3.
R2 = .559
R2 = .866
R2 = .606

19. Regression analysis
Multiple regression analysis finds the equation that best fits the 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

20. Regression analysis Method 1: The Scatter Graph Using Excel 2003
Mark columns with 2 prices
Insert/Chart/XY (Scatter) / Finish
Chart/Add trendline/ Linear
Click “Options”, then “Display equation”
Using Excel 2007
Mark columns with 2 prices
Insert/Scatter graph
Chart tools/Layout/Trendline/More
Click box for “Display equation on chart”
The scatter graph method is limited by the inability to include more than one explanatory variable (“x variables”). So, while it is possible to measure a change in price in one place given a change in price in another market, it is not possible to hold other potentially influential factors constant.
Note: only one “x” allowed with this method

21. Method 1: The Scatter Graph
Regression analysis
Method 1: The Scatter Graph
The trendline shows the line that best describes the relationship between P1 and P2. Technically, it is the line that minimizes the sum of the squared residuals, where residuals are the vertical distances between the points and the line. The coefficient on x (.9336) indicates that for a 10% increase in P1, P2 will increase 9.3%. This graph shows a medium level of correlation.

22. Regression analysis Method 2: Linear Estimation
= linest (y range, x range,1,1)
Mark 5x2 block around formula
F2 shift-control-enter
=linest(..
=linest(.. b a
Coef
0.999
236.3 SE
0.354
81.26 R2
0.119
137.8
7.98
58.00
155
1,112
First, type =linest(yrange, xrange, 1,1) in a cell, where y range indicates the column where the y variable is located and x range indicates the column(s) where the x variable(s) are found.
Second, mark a block of 5 rows x 2 columns with the “linest” cell in the upper left corner.
Third, type F2, then Shift-Control-Enter
Finally, it is useful to add labels. The first column is for the “b” coefficient (the slope or coefficient on x), the second column is for the “a” coefficient (the constant) . The first row is the estimated coefficient. The second row is the standard error of the coefficient, a measure of the accuracy of the estimated coefficient. The third row gives R2.
Note: Can use multiple x’s with this method

23. Regression analysis – Elasticity of Transmission
Calculating the elasticity of transmission from P1 to P2
Regression analysis of P2 = a + bP1
Regression coefficient b is ΔP2 / ΔP1
Transmission elasticity is (ΔP2 / P2) / (ΔP1 / P1)
So transmission elasticity = b * (AVP1 / AVP2)
where b = regression coefficient
AVP2 = average of P2
AVP1 = average of P1

24. Regression analysis
Is the relationship between prices statistically significant?
The t statistic indicates whether a relationship between two variables is statistically significant or not
The t statistic is calculated as t = b/SE where b is the coefficient and SE is the standard error of the coefficient
In general, a t statistic above 2 or below -2 is statistically significant
To get the t statistics, it is
necessary to use Method 2
and calculate t
In this example t > 2, so
there is a statistically significant
relationship b a
Coef
0.999
236.3 SE
0.354
81.26 R2
0.119
137.8
7.98
58.00
155
1,112
t stat
2.979
2.914

25. Regression analysis – Exercise Notes
In Worksheets 2-7,
The yellow cells (B4 – B9) define the characteristics of the random data generated, the “true” value of the parameters.
Columns B and C contain the prices generated
Graphs show the patterns in the price data
The scatter graph includes a trendline – the line best describing the relationship between the two prices
The green box shows the result of regression analysis on the price data, the estimated values of the parameters.
Each time you press F9, it will regenerate new prices, graphs, and regression results

26. Regression analysis – Exercise 1
In Worksheet 2,
Change the coefficient in the yellow box (cell B8) from 1 to 3 and observe the effect on the graphs and the regression results, particularly the estimated coefficient in cell F32
Notice that the estimated coefficient (F32) is similar to but not exactly equal to the “true” coefficient (F8)
Change the standard deviation of e (cell B9) from 10 to 40 and observe the effect on the graphs and the regression results, particularly the R2
In Worksheet 3,
Repeat the exercises above
Notice that the estimated coefficient is less accurate (ie not as close to the true value) as in Worksheet 2
In Worksheet 2, changing the coefficient in B8 from 1 to 3 makes the trendline higher and steeper. It increased the estimated coefficient in F32 from around 1.0 to around 3. Each time you press F9, you will get slightly different prices and different results.
Changing the standard deviation of e from 10 to 40 will make the dots on the graph spread out away from the trendline. It will also lower the R2 and make the estimated coefficient less accurate.
In Worksheet 3, these exercises will have the same effect, except that the dots on the graph are more spread out, the estimated coefficient is not as close to the true coefficient, and the R2 is lower.

27. Regression analysis – Exercise 2
In Worksheet 8 [Data],
Use regression analysis to examine the relationship between rice prices in Nampula and rice prices in Maputo
What is the coefficient? This question can be answered using either Method 1 (graph) or Method 2 (linest function)
What is the value of R2? This question can be answered using the correl function.
Is the relationship statistically significant? In order to calculate the t statistic, you will need to use Method 2 (linest function)
Note: A box has been created in sheet 8 [Data] to help with this exercise.
1) To calculate the coefficient using Method 1, type “=linest(G4:g75,H4:H75,1,1)” in cell K4.
Select all of the yellow highlighted squares and press F2, then Shift-Control-Enter. The value in the upper left cell is the coefficient:
2) To calculate the value of r, type correl(G4:G75,H4:H75). To calculate R2, multiply r x r.
The value of R2 is
3) To calculate t statistic, divide coefficient (upper left cell of regression results) by SE of coefficient (the cell below)
Result should be 21.23, meaning that the relationship is statistically significant

28. 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”
Stationary variable
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

29. 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 may indicate that there is a statistically significant relationship even when there is NO relationship

30. 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 African staple food prices tested, most (60%) were non-stationary

31. Non-stationarity – Solution
How do you analyze non-stationary prices?
Simple approach (with Excel)
First differences (ΔP = Pt – Pt-1) are usually 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
Long-run transmission
Short-run transmission
Speed of adjustment to long-run equilibrium

32. Non-stationarity – Exercise 1
Use Worksheet 4, which generates stationary data with no relationship between P1 and P2
Notice that the t statistic is small, indicating (correctly) that there is no relationship between P1 and P2
Use Worksheet 5, which generates non-stationary data with no relationship between P1 and P2
Notice that, although the graph shows that there is no relationship between P1 and P2, the t statistic is large, indicating (incorrectly) that there is a relationship
The important message here is that if data are NON-STATIONARY, then regression output will be MISLEADING!

33. Non-stationarity – Exercise 2
Use Worksheet 6, which generates non-stationary data with no relationship between P1 and P2
Calculate ΔP1 and ΔP2 in columns D and E
In D15, type =B15-B14
Copy and paste this equation to D15:E513 (cells in yellow)
The worksheet will automatically generate two graphs, correlation coefficient, and regression results
Verify that graphs of ΔP1 and ΔP2 correctly show no relationship between them
Verify that t statistic is high in spite of the fact that the prices are not related, confirming that regression results are misleading when data is non-stationary.
When the sheet is opened for the first time, cells D15:E513 are blank and the green box and the graph return no results.
Follow the instructions above to obtain results.

34. Non-stationarity – Exercise 3
Use Worksheet 7, which generates non-stationary data with a relationship between P1 and P2
Calculate ΔP1 and ΔP2 in columns D and E
In D15, type =B15-B14
Copy this equation to D15:E513
Worksheet will fill in the two blank graphs, correlation coefficient, and regression results
Verify that graphs of ΔP1 and ΔP2 correctly show a relationship between them
Verify that the R2 is relatively high
Verify that t statistic is high, correctly indicating a relationship between ΔP2 and ΔP1
Note: Because the data are randomly generated each time the sheet is opened or when F9 is pressed, R2 may occasionally be contradictory.

35. Conclusions
Price transmission occurs between markets, between stages of a market channel, and between commodities… but not always
Correlation coefficient is easy to calculate and interpret 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

36. Conclusions Non-stationarity If prices are non-stationary, need to
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)

37. References (1)
Conforti, P Price Transmission in Selected Agricultural Markets. FAO Commodity and Trade Policy Research Working Paper No. 7. Rome.
Dawe, D. (2008) Have Recent Increases in International Cereal Prices Been Transmitted to Domestic Economies? The experience in seven large Asian countries. ESA Working paper. Rome: FAO.
Keats, S., S. Wiggins, J. Compton, and M. Vigneri Food price transmission: Rising international cereals prices and domestic markets. London: ODI.

38. References (2)
Minot, N “Transmission of world food price changes to markets in sub-Saharan Africa.” Discussion Paper No International Food Policy Research Institute, Washington, DC.
Rashid, S Spatial integration of maize markets in post-liberalized Uganda. Journal of African Economies, 13(1),
Vavra, P. and B. K. Goodwin (2005), “Analysis of Price Transmission Along the Food Chain”, OECD Food, Agriculture and Fisheries Working Papers, No. 3, OECD.