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

Transcription

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

2 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

3 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

4 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

5 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.

6 Standardized climate indexes El Niño 2 NAO

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

8 Average Annual Yields of Spring and Winter Wheat, , Saskatchewan Winter wheat 35 bu/ac Spring wheat

9 Weather Data

10 Summary Statistics Data from Variable Mean Std. Dev. Min Max Winter wheat yield El Niño (non-standardized) NAO (non-standardized) April precipitation May precipitation June precipitation July precipitation August precipitation Growing degree days (April to August) 1, , Snowfall (November to March)

11 Summary Statistics by Soil Zone Variable Black Dark Brown Brown Winter wheat yield (9.56) (10.1) (9.34) April precipitation (20.1) (17.8) (16.4) May precipitation (31.1) (35.7) (27.7) June precipitation (47.9) (39.6) (38.1) July precipitation (41.4) (36.9) (34.8) August precipitation (44.6) (42.1) (31.7) Growing degree days (April to August) (240.5) (337.9) (310.1) Snowfall (November to March) (39.2) (42.0) (32.8) Observations 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]

12 Selectivity Equation: Estimated logit Variable Estimated Standard error Coefficient a Standardized El Niño (E ) Standardized NAO (N ) El Niño trend (ΔE) NAO trend (ΔN) Constant 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.

13 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 *** *** *** *** May precipitation *** *** *** *** June precipitation ** *** ** *** July precipitation ** *** ** *** August precipitation Snow (Nov through Mar) * GDD (April to August) * GDD squared -4.5E-06 * 2.4E E E E-06 ** 2.4E E E-06 Std. Dev. of GDD * *** Black soil dummy *** *** *** *** Dark brown soil dummy *** *** *** *** Brown soil dummy *** *** *** *** Standardized El Niño (E ) ** *** Standardized NAO (N ) ** ** El Niño trend (ΔE) NAO trend (ΔN) * ** Standard error of residuals ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

14 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 ) ** Standardized NAO (N ) *** El Niño trend (ΔE) *** NAO trend (ΔN) Black soil dummy *** *** Dark brown soil dummy *** *** Brown soil dummy *** *** Standard error of the residuals ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

15 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 ) *** * Standardized NAO (N ) *** *** El Niño trend (ΔE) *** NAO trend (ΔN) *** *** Black soil dummy *** *** Dark brown soil dummy ** *** Brown soil dummy * *** SE of the residuals ***, ** and * indicate statistical significance at the 0.01, 0.05 and 0.1 levels of significance

16 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

17 NOTE: Slight upward trend indicates greater spring precipitation increases yields Black Soil Zone yield rainfall

18 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) Yield dark brown zone (bu/ac) Yield brown zone (bu/ac) Spring rainfall (mm) Observed rainfall (mm) Study region total Black soil zone Dark brown soil zone Brown soil zone

19 Estimated Relations between Spring Rainfall and Winter Wheat Yields by Soil Zone Soil zone Black (Simulation) Black (Simple regression) Dark Brown Brown Intercept (0.3928) (6.0828) (0.3905) (0.3889) Estimated coefficient on spring rainfall (0.0023) (0.0399) (0.0023) (0.0023) Regression Information R 2 = SE residuals = R 2 = SE residuals = R 2 = SE residuals = R 2 = SE residuals = 9.496

20 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.

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22 Results Spring No weather With weather derivative Year rainfall (mm) Yield (bu/ac) derivative revenue ($/ac) Payoff ($/ac) Revenue ($/ac) Mean Stan dev

23 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

24 Utility Benefits from Purchasing Protection against Adverse Spring Rainfall Outcomes U 1 /U Strike Level (standard deviations below mean rainfall)

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

26 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