AAMP Training Materials

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AAMP Training Materials

• Module 3.2 Measuring Food Price Transmission

Nicholas Minot (IFPRI) n.minot_at_cgiar.org
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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

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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

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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

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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

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Why does price transmission occur?
Maize prices in Maputo Chokwe

• Spatial price transmission occurs because of
  flows of goods between markets
• If price gap gt marketing costs, trade flows will
  narrow gap
• If price gap lt marketing cost, no flows
• Therefore, price gap lt marketing cost

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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 grain
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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

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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)

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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

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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
  lt 1.0
• For exports, perfect transmission elasticity are
  gt 1.0

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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

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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 US / ton
June 2007 120 165
June 2008 239 287
Change 99 74
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Ratio of percentages

• Very crude method only uses two points in time
  and does not take trends into account

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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

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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(B4B56,
  C4C56)
• 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

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Examples of correlation coefficients(hypothetical
prices)
Weak correlation
Strong correlation
Medium correlation
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Correlation coefficient Exercises

• In Worksheet 1 Tanzania example, type
  CORREL(B5B51,C5C51) into cell F21 to calculate
  r
• Then in F22 cell, type F21F21 (or F212) 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

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Regression analysis

• Multiple regression analysis finds the equation
  that best fits the data Y a bX1 cX2
• Advantages
• Gives information to calculate transmission
  elasticity
• Can test relationships statistically
• Can take into account lagged effects, inflation,
  and seasonality
• can analyze relationship of gt 2 prices
• Disadvantages
• Awkward to do in Excel (easier with Stata or
  SPSS)
• Misleading results if data are non-stationary

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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

Note only one x allowed with this method
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Regression analysis
Method 1 The Scatter Graph
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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

Note Can use multiple xs with this method
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Regression analysis Elasticity of Transmission

• Calculating the elasticity of transmission from
  P1 to P2
• Regression analysis of P2 a bP1
• Regression coefficient b is ?P2 / ?P1
• Transmission elasticity is (?P2 / P2) / (?P1 /
  P1)
• So transmission elasticity b (AVP1 / AVP2)
• where b regression coefficient
• AVP2 average of P2
• AVP1 average of P1

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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 gt 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
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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

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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

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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.

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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
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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

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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

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Non-stationarity Solution

• How do you analyze non-stationary prices?
• Simple approach (with Excel)
• First differences (?P Pt Pt-1) are usually
  stationary
• Regress ?P1 on ?P2, possibly with lags
• Co-integration analysis (with Stata)
• Test to see if prices are co-integrated, meaning
  that P2-bP1-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

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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

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Non-stationarity Exercise 2

• Use Worksheet 6, which generates non-stationary
  data with no relationship between P1 and P2
• Calculate ?P1 and ?P2 in columns D and E
• In D15, type B15-B14
• Copy and paste this equation to D15E513 (cells
  in yellow)
• The worksheet will automatically generate two
  graphs, correlation coefficient, and regression
  results
• Verify that graphs of ?P1 and ?P2 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.

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Non-stationarity Exercise 3

• Use Worksheet 7, which generates non-stationary
  data with a relationship between P1 and P2
• Calculate ?P1 and ?P2 in columns D and E
• In D15, type B15-B14
• Copy this equation to D15E513
• Worksheet will fill in the two blank graphs,
  correlation coefficient, and regression results
• Verify that graphs of ?P1 and ?P2 correctly
  show a relationship between them
• Verify that the R2 is relatively high
• Verify that t statistic is high, correctly
  indicating a relationship between ?P2 and ?P1

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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

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Conclusions

• 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)

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References (1)

• Conforti, P. 2004. Price Transmission in Selected
  Agricultural Markets. FAO Commodity and Trade
  Policy Research Working Paper No. 7. Rome.
  http//www.fao.org/docrep/007/j2730e/j2730e00.htm
  Contents
• 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. 2010. Food price transmission Rising
  international cereals prices and domestic
  markets. London ODI. http//www.odi.org.uk/resour
  ces/download/5079.pdf

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References (2)

• Minot, N. 2010. Transmission of world food price
  changes to markets in sub-Saharan Africa.
  Discussion Paper No. 1059. International Food
  Policy Research Institute, Washington, DC.
  http//www.ifpri.org/publication/transmission-worl
  d-food-price-changes-markets-sub-saharan-africa
• Rashid, S. 2004. Spatial integration of maize
  markets in post-liberalized Uganda. Journal of
  African Economies, 13(1), 103-133.
• 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. http//www.oecd-ilibrary.org/docserve
  r/download/fulltext/5lgjlnpcnrvh.pdf?expires13001
  81573id0000accnameguestchecksumE74FDB4F6B649
  23819186AA5E7EF54E5