AAMP Training Materials

1. AAMP Training Materials Nicholas Minot (IFPRI) n.minot@cgiar.org Module 3.2: Measuring Food Price Transmission

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

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? • 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 Maize prices in Maputo & Chokwe

7. 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 Maize meal Maize grain

8. Why does price transmission occur? • Cross-commodity price transmission occurs because of substitution in consumption and/or production Price of maize and rice in Maputo

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)

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

14. Ratio of percentages • Very crude method: only uses two points in time and does not take trends into account

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

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

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” Note: only one “x” allowed with this method

21. Regression analysis Method 1: The Scatter Graph

22. Regression analysis Method 2: Linear Estimation • = linest (y range, x range,1,1) • Mark 5x2 block around formula • F2 shift-control-enter 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

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

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.

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”

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

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.

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

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 • 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. 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/resources/download/5079.pdf

38. 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-world-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/docserver/download/fulltext/5lgjlnpcnrvh.pdf?expires=1300181573&id=0000&accname=guest&checksum=E74FDB4F6B64923819186AA5E7EF54E5