Hosts: Vancouver, British Columbia, Canada June 16-18,

Hosts: Vancouver, British Columbia, Canada June 16-18, 2013 www.iarfic.org

Financial climate instruments as a guide to facilitate planting of winter wheat in Saskatchewan G Cornelis van Kooten Professor and Canada Research Chair and Fan Zhang PhD Candidate Department of Economics University of Victoria

Why plant winter wheat? Reduces machinery operations and spreads them over time Enhances access to moisture: crop can take advantage of spring runoff and early spring rains Higher yields that spring wheat Reduces soil erosion Provides habitat for migratory waterfowl that breed in early spring Ducks Unlimited: more farmers should plant winter wheat Disadvantage: Potential winterkill leads to added costs associated with spring replanting

Selection equation: Methods: Heckman Model z t = a 0 + a 1 E t + a 2 ΔE t + b 1 N t + b 2 ΔN t + ξ t, where z t is binary (1 if winter wheat planted, 0 otherwise) E t = 6-month (March to September) standardized average El Niño 3.4 index N t = 6-month standardized average value of North Atlantic Oscillation (NAO) ΔE t and ΔN t represent simple trends of the two climate series* a i and b j are parameters to be estimated. * If during the 6-month period prior to fall planting, a trend is positive, indicating that the index is rising, it is assigned a value of 1; if the value of the standardized climate index never deviates by more than one unit of the initial (March) value of the index, there is no significant change and the trend is considered to be stable and a value of 0 is assigned; and a value -1 is given if the trend is negative, indicating the index is declining

Methods: Heckman Model (cont) Outcome equation: y t,j = α + Σ β i P t,i,j + δ 1 G t,j + δ 2 (G t,j ) 2 + γ S t,j + Σ θ j D j + ε t. where y t,j = crop yield in year t in region/district j P t,i,j = precipitation in year t, month i of growing season and region j G t,j = growing degree days during April-July growing season, region j S t,j = snowfall from November through March in region j D j = dummy variable for region j (j are three soil zones) α, β i, δ 1, δ 2, γ, and θ i are parameters to be estimated. ε ~ N(0,σ) where σ is unknown and to be estimated.

Standardized climate indexes 3 2.5 El Niño 2 NAO 1.5 1 0.5 0-0.5-1 -1.5-2 1950 1957 1964 1971 1978 1985 1992 1999 2006

GIS Map of Saskatchewan Rural Municipalities, Crop Districts and Soil Zones

Average Annual Yields of Spring and Winter Wheat, 1938-2008, Saskatchewan 45 40 Winter wheat 35 bu/ac 30 25 20 Spring wheat 15 10 5 0 1938 1948 1958 1968 1978 1988 1998 2008

Weather Data

Summary Statistics Data from 1992-2006 Variable Mean Std. Dev. Min Max Winter wheat yield 33.34 9.86 5.00 70.00 El Niño (non-standardized) 27.37 0.53 26.33 28.47 NAO (non-standardized) -0.34 0.98-1.50 1.88 April precipitation 24.13 18.12 0.00 97.80 May precipitation 44.62 31.96 0.70 176.67 June precipitation 66.10 42.31 0.00 183.72 July precipitation 53.21 38.60 0.05 191.10 August precipitation 43.02 34.68 1.00 135.24 Growing degree days (April to August) 1,020.57 526.38 68.58 1,708.15 Snowfall (November to March) 87.43 81.05 0.05 259.55

Summary Statistics by Soil Zone Variable Black Dark Brown Brown Winter wheat yield 34.99 (9.56) 33.62 (10.1) 30.11 (9.34) April precipitation 27.75 (20.1) 26.22 (17.8) 21.04 (16.4) May precipitation 45.83 (31.1) 51.93 (35.7) 47.34 (27.7) June precipitation 75.74 (47.9) 75.96 (39.6) 74.17 (38.1) July precipitation 67.75 (41.4) 56.84 (36.9) 46.02 (34.8) August precipitation 60.23 (44.6) 51.89 (42.1) 41.83 (31.7) Growing degree days (April to August) 1406.98 (240.5) 1473.43 (337.9) 1511.31 (310.1) Snowfall (November to March) 98.12 (39.2) 88.24 (42.0) 70.73 (32.8) Observations 288 269 167 Observations by Crop District [# obs] 1B[72] 5A[78] 5B[49] 8A[26] 8B[28] 9A[11] 9B[24] 1A[78] 2A[17] 2B[24] 6A[64] 6B[35] 7B[11] 3AS[28] 3AN[12] 3BS[33] 3BN[29] 4A[33] 4B[19] 7A[13]

Selectivity Equation: Estimated logit Variable Estimated Standard error Coefficient a Standardized El Niño (E ) 0.77 0.052 Standardized NAO (N ) -0.25 0.041 El Niño trend (ΔE) 1.64 0.112 NAO trend (ΔN) -0.43 0.054 Constant -2.29 0.048 All estimated coefficients are significant at the 0.01 level of statistical significance. A test for sample selectivity bias indicated that this was not a problem so the selectivity and outcome equations could be estimated independently.

Panel Regression Results for Winter Wheat Yield Outcomes Variable Model #1 Model #2 Model #3 Model #4 Estimated Coefficient Standar d Error Estimated Coefficient Standar d Error Estimated Coefficient Standar d Error Estimated Coefficient Standard Error April precipitation 0.1013 *** 0.0196 0.0875 *** 0.0202 0.1167 *** 0.0220 0.1094 *** 0.0224 May precipitation 0.0633 *** 0.0115 0.0652 *** 0.0116 0.0596 *** 0.0116 0.0597 *** 0.0117 June precipitation 0.0224 ** 0.0089 0.0301 *** 0.0093 0.0201 ** 0.0090 0.0265 *** 0.0093 July precipitation -0.0232 ** 0.0096-0.0276 *** 0.0098-0.0242 ** 0.0096-0.0295 *** 0.0097 August precipitation -0.0040 0.0093-0.0061 0.0099-0.0006 0.0094 0.0017 0.0101 Snow (Nov through Mar) -0.0144 0.0095-0.0184 * 0.0096-0.0116 0.0096-0.0142 0.0096 GDD (April to August) 0.0069 0.0059 0.0030 0.0059 0.0108 * 0.0062 0.0087 0.0061 GDD squared -4.5E-06 * 2.4E-06-2.93E-06 2.4E-06-5.1E-06 ** 2.4E-06-3.7E-06 2.4E-06 Std. Dev. of GDD -0.0398 * 0.0195-0.0661 *** 0.0203 Black soil dummy 30.1908 *** 3.8012 33.9411 *** 3.8569 30.9328 *** 3.8092 35.6752 *** 3.8655 Dark brown soil dummy 28.6662 *** 3.6518 32.0331 *** 3.6929 29.4469 *** 3.6627 33.7908 *** 3.7053 Brown soil dummy 25.7662 *** 3.6347 29.2733 *** 3.6805 26.5162 *** 3.6442 31.0641 *** 3.6947 Standardized El Niño (E ) -1.2180 ** 0.4785-1.4783 *** 0.4818 Standardized NAO (N ) 0.8874 ** 0.3632 0.8125 ** 0.3613 El Niño trend (ΔE) -0.5688 0.8812-0.7227 0.8761 NAO trend (ΔN) 1.1284 * 0.5769 1.4097 ** 0.5792 Standard error of residuals 9.1705 9.0644 9.1489 8.9999 ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

Panel Regression Results for log of GDDs and Winter Snowfall GDD Winter Snow Variable Estimated Coefficient Standard Error Estimated Coefficient Standard Error Standardized El Niño (E ) -0.0142 0.0150 0.0559 ** 0.0262 Standardized NAO (N ) -0.0067 0.0112 0.0510 *** 0.0195 El Niño trend (ΔE) -0.0047 0.0295 0.1937 *** 0.0514 NAO trend (ΔN) 0.0164 0.0186 0.0480 0.0324 Black soil dummy 7.2368 *** 0.0195 4.8048 *** 0.0340 Dark brown soil dummy 7.2516 *** 0.0212 4.6447 *** 0.0369 Brown soil dummy 7.2982 *** 0.0250 4.4406 *** 0.0437 Standard error of the residuals 0.3069 0.5340 ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

Panel Regression Results for Standardized Monthly Precipitation April May June Variable Estimated Coefficient Standard Error Estimated Coefficient Standard Error Estimated Coefficient Standard Error Standardized El Niño (E ) -0.0456 0.0471-0.1427 *** 0.0483 0.0951 * 0.0487 Standardized NAO (N ) 0.2378 *** 0.0350-0.0130 0.0359 0.1671 *** 0.0361 El Niño trend (ΔE) 0.0066 0.0923 0.1023 0.0947 0.2908 *** 0.0954 NAO trend (ΔN) 0.0951 0.0581-0.2364 *** 0.0596 0.1754 *** 0.0601 Black soil dummy 0.2155 *** 0.0610-0.1156 0.0626 1.2581 *** 0.0631 Dark brown soil dummy 0.1250 ** 0.0662 0.0963 0.0679 0.9662 *** 0.0684 Brown soil dummy -0.1311 * 0.0784-0.0456 0.0804 0.4394 *** 0.0808 SE of the residuals 0.9609 0.9854 0.9908 ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

Financial Weather Derivatives Focus on outcomes equation; future research to examine hedging against winterkill Burn analysis (bootstrapping, 10,000 iterations) Growing degree days is not the appropriate weather index to employ in our study region (at least for winter wheat yields) Cumulative spring rainfall (April, May, June) is a potential index

NOTE: Slight upward trend indicates greater spring precipitation increases yields Black Soil Zone yield 0 20 40 60 80 50 100 150 200 250 300 rainfall

Simulated Spring Rainfall and Winter Wheat Yields by Soil Zone, and Observed Spring Rainfall Item Negative obs (out of Mean Stan dev Min Max 10,000) Yield black zone (bu/ac) 36.48 9.77-5.67 78.59 8 Yield dark brown zone (bu/ac) 34.98 9.69-12.36 78.79 10 Yield brown zone (bu/ac) 32.10 9.66-7.97 73.98 27 Spring rainfall (mm) 165.4 41.65 31.27 300.20 0 Observed rainfall (mm) Study region total 151.03 56.86 Black soil zone 149.32 60.54 Dark brown soil zone 142.55 49.88 Brown soil zone 154.11 56.21

Estimated Relations between Spring Rainfall and Winter Wheat Yields by Soil Zone Soil zone Black (Simulation) Black (Simple regression) Dark Brown Brown Intercept 29.1974 (0.3928) 25.7439 (6.0828) 28.0439 (0.3905) 24.9383 (0.3889) Estimated coefficient on spring rainfall 0.0441 (0.0023) 0.0801 (0.0399) 0.0419 (0.0023) 0.0433 (0.0023) Regression Information R 2 = 0.0353 SE residuals = 9.592 R 2 = 0.1545 SE residuals = 4.429 R 2 = 0.0325 SE residuals = 9.536 R 2 = 0.0348 SE residuals = 9.496

Can farmers benefit from hedging against adverse weather (too little spring rainfall)? Farmer s revenue with no financial hedge: R(CSR) = P y j (CSR), where y j (CSR) is yield in period j as a function of the cumulative spring rainfall CSR and P refers to price (=$7.20/bu) With a put option on cumulative spring rainfall: R(CSR, q, K) = P y j (CSR) + q[α(k CSR) O(K)] where α = tick size ($ / CSR set to $1), K = strike (trigger) level for the put option O(K) = option price (premium) as a function of strike level α(k CSR) O(K) = net payoff to the option q = number of options purchased.

Results Spring No weather With weather derivative Year rainfall (mm) Yield (bu/ac) derivative revenue ($/ac) Payoff ($/ac) Revenue ($/ac) 1992 114.3 34.9 251.2 5.6 256.8 1993 144.4 37.3 268.5-24.4 244.1 1994 170.0 39.3 283.3-50.1 233.2 1995 142.8 37.2 267.6-22.9 244.7 1996 128.6 36.0 259.4-8.7 250.7 1997 124.9 35.7 257.3-5.0 252.3 1998 193.6 41.2 296.9-73.7 223.2 1999 178.5 40.0 288.2-58.6 229.6 2000 165.1 38.9 280.4-45.1 235.3 2001 118.7 35.2 253.7 1.2 254.9 2002 131.0 36.2 260.8-11.0 249.8 2003 132.3 36.3 261.6-12.4 249.2 2004 168.1 39.2 282.2-48.1 234.0 2005 211.5 42.7 307.2-91.5 215.6 2006 122.2 35.5 255.8-2.3 253.5 Mean 149.74 37.72 271.61-29.81 241.80 Stan dev 29.67 2.37 17.09 29.67 12.58

Determining contract choice EV utility function is: U(CSR, q, K) = E[R(CSR, q, K)] λv[r(csr, q, K)] where λ=0.40 is the risk aversion coefficient. Given OTC contracts and cumulative rainfall, agricultural decision maker must choose a strike level (K) and the number of option contracts (q). Let U 0 be utility without purchase of financial weather derivative and U 1 with such purchase

Utility Benefits from Purchasing Protection against Adverse Spring Rainfall Outcomes U 1 /U 0 1.25 1.20 1.15 1.10 1.05 1.00 0.95 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Strike Level (standard deviations below mean rainfall)

Threshold Determining whether to Purchase a Hedge against Adverse Spring Rainfall Outcomes: Combinations below the Line are Optimal 1.16 Hedges purchased 1.12 1.08 1.04 1 0.96 U 1 =178.5; U 0 =154.8; q=1, K=1.8 0 0.5 1 1.5 2 Strike Level (standard deviations below mean rainfall)

Conclusions A weather derivative based on spring rainfall might increase farmers utility from planting winter wheat Future research needs to: compare the ability of farmers to use weather derivatives in diversifying between winter and spring wheat consider the use of financial derivatives based on climate indexes such as NAO and El Nino Policy implication: Ducks Unlimited might be able to use the results of this research to improve the current incentives it uses to elicit greater planting of winter wheat