Hedging against weather risks for a wheat producer in Tasmani

Hedging against weather risks for a wheat

producer in Tasmani

a:

The use of weather derivatives

Jannes Gerrit Lenting S2389312 Thesis MSc Finance Supervisor: dr. P.P.M. Smid 26th of June 2014 Word count: 11,163 Abstract

The focus in this paper is on managing the weather risks faced in agricultural production, in this case the production of wheat in Tasmania. Weather derivatives could be of use in managing weather risks, but before it is possible to use these it must be established how crop yields, and in the end proceeds, are affected by the weather. The regression analyses performed shows that the identified variables do not have a clear and consistent significant effect on the dependent variables. Based on these results it is concluded that hedging with weather derivatives for wheat producers is not an efficient option.

Keywords

General financial markets, Agricultural finance, Weather derivatives, Portfolio choice; investment decisions

JEL codes

2

1. Introduction

In any sector of business there are a number of risks that are faced by entrepreneurs. There are regular business risks that threaten profits, for example related to sales volume or competition and there is price risk. The focus in this paper will be on weather risk faced in agricultural production that threatens net cash flow. Weather is an origin of risk particularly important in agriculture, it has an important influence on crop yields and each crop reacts to weather conditions in its own way. Of course crop producers will choose a crop that requires the conditions that are found on the particular stretch of land they use for production. However, even if the crop matches the conditions as closely as possible, it will never be a perfect match. Weather, or even climate, is not invariable and variations will occur from season to season and even from day to day. The producer now is at risk of variations in the weather. There are conventional risk management techniques that can be employed by crop producers. Techniques like irrigation and crop rotation are ways for producers to diversify and become less dependent on the weather in one particular period. Crop rotation in particular has been researched by Makus, Wang and Chen (2007), where they defined crop rotation as the growing of one crop during summer and another during winter. They came to the (intuitive) conclusion that diversification through crop rotation has the potential of changing the variance of profit on an individual farm in a major way. Besides these techniques traditional crop insurance policies might be in place. The problem with these is however that individual inspection is required to estimate the amount of losses that producers have had due to adverse weather. Another problem is that these policies might cause moral hazard concerns. Producers might not take advantage of available conventional risk management if they believe their losses will be covered by the traditional insurance anyway. This moral hazard of producers not trying to maximize their profits by using conventional risk management techniques is avoided when using weather derivatives1_.

This paper will investigate the possibility of decreasing the variability of net cash flows caused by the weather with the use of weather derivatives. In this paper I will focus on a (generic) wheat producer from Tasmania, Australia. Proceeds will be used as a proxy for net cash flow, making the assumption that costs are relatively fixed for a wheat producer and so variation in proceeds will be the cause of variation in net cash flow. The aim of this paper is to answer the following question: Can weather derivatives be used effectively by wheat producers in Tasmania to hedge against weather risks? To be able to answer

3 this question, some sub questions need to be answered first. What weather variables pose a risk to the producer and how can these risks be hedged? How big is the influence of the weather variables on proceeds? What would be a suitable design for a hedge to deal with these risks? To answer these questions, first chapter two provides an overview of relevant literature. Chapter three describes the data that was used. This data consists of production numbers from the Australian ministry of agriculture, weather data from the Australian bureau of meteorology and wheat prices collected from the Food and Agriculture Organisation of the United Nations. Chapter four deals with the methodology employed, regressions are used to determine the extent to which weather variables have an influence on crop yields and proceeds. This is followed by the results in chapter five and finally some concluding remarks are made in chapter six.

Even though Tasmania is not one of the main wheat producing states of Australia2_{, I picked it}

because it presents a secluded area for which data is available. The climate in certain parts of Australia is very suitable for the production of wheat, which makes wheat production an important industry for the country. In value, it is the second biggest commodity produced in Australia. With this production Australia is the fifth largest producer of wheat in het world3_{. Because of its size, Tasmania is only}

responsible for between 0.12% and 0.20%4 _{of this production. However, over the years Tasmania has}

succeeded in obtaining crop yields that are far above the Australian average. These crop yields were also consistently in excess of the crop yields found in any of the other states.5 _{The importance of agriculture}

to the Tasmanian economy is also evident from the fact that 16% of its GDP is accounted for by agriculture (higher than in any other state). Also, nearly a third of the surface area is committed to agriculture.6 _{It is unclear whether the high crop yields can be attributed to extra effort (e.g.}

technologically more advanced production methods) or that conditions are simply more favourable (fertility of the soil as well as climate). The first could make crop yields less dependent on weather variables (e.g. replacing rain with irrigation), which would mean a reduction of weather risk.

The influence that the weather continues to have on crop yields will also affect proceeds. Weather derivatives were developed initially in the 1990s and have opened up possibilities for companies whose cash flows are strongly linked to the weather to hedge against weather risks. Initially, the derivatives were mostly used by electricity companies to be able to protect themselves from

2 _{www.daff.gov.au/agriculture-food/crops/wheat (retrieved 29th March 2014)} 3 _{2012 data from FAOSTAT, retrieved from faostat.fao.org (29th March 2014)} 4 _{Calculated from yearly data (2006-2011) from the Australian Bureau of Statistics}

5 _{Grain yearbook 2012 as found on www.ausgrain.com.au/Back%20Issues/217ybgrn12/217ybgrn12.pdf (retrieved 29th March} 2014)

4 weather risk. When a summer was mild and customers used their air-conditioning less or when a winter was mild and less heating was required they could be protected from falling revenues. This led to the development of the concepts of heating and cooling degree days (HDDs and CDDs respectively). Degree days make clear how much degrees of heating (respectively cooling) was needed over a given period. The use of weather derivatives did not remain limited to electricity companies however. People soon came to realise that a lot of companies from different sectors are also dependent on the weather. This ranges from companies from the leisure and entertainment industry to the agricultural businesses considered in this paper. And just like with temperature, derivatives could easily be developed for hedging against risks associated with rainfall. But the use of weather derivatives in agriculture is not as straightforward as it might seem. Weather conditions can be very place specific and different crops require very different growing conditions and respond differently when these conditions are not met. As a result of this the effectiveness of hedging with weather derivatives can also differ significantly between crops (Heimfarth and Musshof, 2011). Also a producer that is (or is thinking about) using weather derivatives should beware of partial hedging. The hedge should in the end stabilize net cash flow and when partial hedges are not taken into consideration the use of weather derivatives might even lead to more variability. Weather derivatives can also be employed on levels beyond individual producers (Skees, Varangis, Larson and Siegel, 2002). Some even conclude that providers of reinsurance will be the most likely end-users (Woodard and Garcia, 2008).

2. Literature review

5 Skees et al. (2002) discuss the benefits of weather options in developing countries. They discuss four main purposes for weather derivatives: To provide direct insurance (against e.g. droughts and floods) for any producer or company at risk; To facilitate the creation of mutual insurance or other forms of collective risk sharing; To provide reinsurance possibilities to any private or public body that offers insurance against weather effects; To accommodate the (instant) distribution of disaster aid. Skees et al. (2002) stress however that these weather derivatives should be properly designed. Another key point is that there needs to be a reliable (public) source of historical weather data to create affordable and efficient risk sharing instruments for the four mentioned purposes. Data availability is also mentioned by Richards et al. (2004), they see it as one of the factors holding back the weather derivative market. According to Ray (2004) there is a need for at least 30 months of weather data in order to be able to design a derivative contract.

Richards et al. (2004) talk about a lack of liquidity of the trade in weather derivatives in general (not just in developing countries). They mention four factors that contribute to this: the absence of a forward market, basis risk, weather data and lack of a common pricing model. Elaborating on this last point, a couple of different methods have been proposed since preference-free Black-Scholes pricing models cannot be used. Because weather is not a tradable asset, the market price of risk has to be reflected in the pricing of the derivatives. The risk premium can even represent a significant share of the estimated price (Cao and Wei, 2004). Multiple papers have used the model developed by Lucas (1978) for pricing (Richards et al. 2004, Cao and Wei, 2004). In this way the observed seasonalities, time varying volatility (also described by Benth and Benth, 2007) and mean reversion can be incorporated.

6 commodity trades. These findings effectively create a market for the offer of, and trading in, tailor made weather derivatives by professional parties. This will in turn create more opportunities for agricultural producers seeking protection from weather irregularities.

7 location and the location of interest. This is also identified as the reason for the lower effectivity of precipitation derivatives (since precipitation varies more than temperature). The reference location that is important with respect to the amount of spatial basis risk is one of five essential elements to every weather contract. The other four elements are the underlying weather index, a predetermined period of time, the value attached to each node of the underlying index and a strike value (Richards et al. 2004).

8 temperature, resulting in higher basis risk. The use of multiple weather stations seems to be effective in dealing with this.

Whether or not the use of aggregated data causes a bias is investigated by Heimfarth, Finger and Musshof (2012). They find that the estimated effectiveness of the hedge when aggregated data is used will be higher than what is actually realizable on an individual farm. However, hedging on an individual basis with a hedge designed on aggregated data is still able to lead to a notable risk reduction. In conclusion, the use of weather derivatives by individual producers is possible and can, even when based on aggregated data, be used successfully to reduce risk (Heimfarth et al. 2012).

On the basis of the literature discussed above I have chosen to use the types of basis risk identified by Manfredo and Richards (2009) and their terminology for the remainder of this paper. Because of the findings of Martin et al. (2001) I will also examine whether or not the use of multiple weather stations is beneficial when dealing with precipitation variables.

3. Data

For this research data was used covering the period from 1970 until 2010. A few different types of data were required, first of all daily weather data, but also data on wheat production and prices. Weather data is available through the Australian governments bureau of meteorology for a large number of weather stations across the country7_{. For all stations information is accessible about the exact location}

and the site surrounding the station, this can be used to make sure the data is representable. However, not all stations have gathered data continuously and not all measuring frequency is the same. So there can be years where no data was collected or there can be shorter hiatuses in the data. Also data availability can be different for rainfall data compared to temperature data. One station that offered continuous data in the period considered for both rainfall and temperature was Hobart (Ellerslie Road). This was selected as the main source of weather data. There were some very small hiatuses in the temperature data. Where the minimum or maximum temperature was not available for a day (it was never missing for more than one day) the average was taken of the temperatures from the days immediately preceding and following this day.

9

𝑇𝑖= (𝑇𝑖−1+ 𝑇₂ 𝑖+1) (1)

Where 𝑇𝑖 is the temperature on day i that was missing, 𝑇𝑖−1 the temperature on the preceding day and 𝑇𝑖+1 the temperature on the following day (all temperatures in degrees celsius). The total number of days for which data was collected is 14,975, on six days the minimum temperature was unavailable and the maximum temperature was unavailable on only one day. When the average temperature was used to calculate the number of degree days, there were thus seven days for which the data was manipulated. Given this small scale (less than 0.05%) I consider these hiatuses negligible for the final outcomes and the manipulation justified.

As discussed in the literature review and will be explained in more detail in the methodology section, data from multiple weather stations will be used to avoid spatial basis risk. Hobart (Ellerslie Road) was used for this as well as four additional stations, Cape Grim (Woolnorth), Epping Forest (Forton), Western Creek (Somer Hill) and Ouse (Millbrook). The locations of these stations are depicted in map 1. Their selection was based on completeness of data and geographical location in order to get a good representation of rainfall in the whole of Tasmania.

Map 1: Weather station locations

Source: mapsof.net

10 of the number of days over which the rainfall was aggregated next to the amount of rainfall. I have chosen to ignore this for the a couple of reasons. First, just as with the temperature data it only affected a small amount of the observations. Second, it would only influence the regression variables when rainfall would be attributed to a different month (for instance when the rainfall on the 31st of January was added to that on the first of February). And finally, as will be shown in equation (11), an average was then taken of the recorded rainfall from the five stations. The effect of this small inadequacy is therefore very limited and considered negligible here. An impression of the weather data collected is given in graphs 1 and 2, where the rainfall (both for the single weather station as well as for the five station average) and average monthly temperatures are shown.

0 100 200 300 400 500 600 700 800 900 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 Rainfall (mm) Year

Graph 1: Cumulative rainfall during the growing season (May to December)

Hobart (Ellerslie road) Five weatherstation average 9.5 10 10.5 11 11.5 12 12.5 13 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 Average monthly temperature (°C) Year

11 Other than weather data also data on wheat production was required. The Australian bureau of statistics offers an overview of statistics for the production of a number of agricultural products from 1861 onwards through their website8_{. Here data is gathered, not only on the produced quantities, but}

also on how much land was used for the production on a state level. The average crop yield per year in Tasmania was then easy to construct by dividing the produced quantity in kilograms by the hectares used for production.

The final piece of information that had to be obtained to be able to determine the proceeds for a wheat producer was the price they receive for the crop. It would be possible to use the market price of wheat for this, however this creates a number of problems. First of all, what market price would be appropriate? There is a market price for winter wheat (the type of wheat produced in Tasmania) available, but it is unclear how relevant this is to a producer. More important is the fact that producers mainly care about the price at the moment they sell the harvest. So the average price during a year would probably be irrelevant to them. The average price during the month of December, when harvest takes place, might then be better, but uncertainty remains. Fortunately the FAO, the Food and Agriculture Organization of the United Nations, is able to calculate annual producer prices per country9_.

This is done by way of annual questionnaires to be able to determine the actual price received by the producers at the first point of sale (or at the farm-gate). The actual prices received by the producers are recorded in the questionnaires and then an annual average is calculated per country. The producer price is available from 1966 onwards valued in the local currency (here the Australian dollar), starting in 1991 it is also available in (US) dollars. I will use the prices in Australian dollar for determining the proceeds per hectare, not only since this is the only price available for the entire research period, but also since this probably concerns Australian producers the most.

4. Methodology

This chapter will focus on the methodology employed in this paper. To determine the relationship between the weather and proceeds for a wheat producer two sets of regressions are used. The first set of regressions investigates the actual relationship between weather variables and crop yield. The second set is used to see whether this relationship is still in place when looking at proceeds, so when wheat prices are also accounted for. This second step is important to make sure that there is no partial

8 _{www.abs.gov.au (last accessed 25th of June 2014)}

12 hedging. As explained in the introduction the wheat price could be (partly) dependent on the crop yield, resulting in a natural hedge compensating producers for lower crop yields. Each set of regressions consists of ten regressions. In each regression degree days are used, so the first step here is to explain the computation of degree days. As mentioned succinctly in the introduction a degree day makes clear how much degrees of heating (respectively cooling) was needed on a given day. The calculation of degree days is determined for a large part by the selected base temperature. Traditionally this base temperature was the base temperature of a building, an outside air temperature below which the building needs heating and above which it needs cooling. This base temperature can be selected to match the individual needs of any individual. For reasons of convenience and uniformity standard base temperatures are often used. While the common US base temperature is 65 degrees Fahrenheit (or 18.33°C) the common UK base temperature is 15.5°C (or approximately 60 degrees Fahrenheit). In this paper I will first use degree days based on the common UK base temperature. Then I will examine whether or not the use of a base temperature that reflects the growth requirements of wheat will be better.

Next to the base temperature another aspect is important for the calculation of degree days. To come to the most accurate determination of the amount of degree days on a given day an infinite amount of data would be required. Then each second the difference between the actual and the base temperature could be recorded and aggregated to come to degree days. Even though the use of degree seconds, -minutes or -hours would give a more reliable estimate of the actual amount of degree days, this is not achievable. Since temperature data is not collected (or available) every second of every day. Instead I will use the methodology that was also employed by Cao and Wei (2004). The average temperature on a given day is determined as the mean of the daily minimum and maximum temperatures. Degree days are thus calculated according to equations (2) and (3).

𝐻𝐷𝐷

= max �0, 𝑏𝑎𝑠𝑒 − �

��

𝐶𝐷𝐷

= max �0, �

� − 𝑏𝑎𝑠𝑒�

13 respectively and base is the selected base temperature. Both types of degree days must always be positive or zero.

But for degree days to be used in a regression it is necessary to know over what period they need to be aggregated. The cumulative degree days over a certain period of time is a variable that can be used in a regression. What periods to use is determined here by the growth characteristics of wheat. Research has found that wheat growth can be divided into a lot of different stages. Zadoks, Chang and Konzak (1974) determined ten main stages of growth that could be divided into even smaller sub-stages. This division remains relevant today as it was mentioned also by White and Edwards (2008). However, based on Slafer and Rawson (1994), Acevedo, Silva and Silva (2002) propose the use of three growth stages. Combining the findings of Acevedo et al. (2002), Herbek and Lee (2009) and White and Edwards (2008) I will divide the total growth period of wheat (from May to December) into three periods. In the first period (May to July) seeds germinate, plants are formed and leaves begin to develop. During the second period (August and September) the wheat plant grows bigger, its stem grows longer and leaves develop. The final period (October to December) covers the emergence of flowers and the development of the actual grains until they are harvested. Each stage of growth has certain requirements, moderate temperature and rainfall during the first, warmer temperatures and high rainfall in the second, and not too hot in the third. Based on this information a regression will be run of the following form:

𝑌𝑡 = 𝛼 + 𝑎𝑌𝐸𝐴𝑅𝑡+ 𝑏𝐻𝐷𝐷𝑃1𝑡+ 𝑐𝐻𝐷𝐷𝑃2𝑡+ 𝑑𝐻𝐷𝐷𝑃3𝑡+ 𝑒𝐶𝐷𝐷𝑃1𝑡 (4) +𝑓𝐶𝐷𝐷𝑃2𝑡+ 𝑔𝐶𝐷𝐷𝑃3𝑡+ ℎ𝑅𝑃1𝑡+ 𝑖𝑅𝑃2𝑡 + 𝑗𝑅𝑃3𝑡+ 𝜀

14 A Different way to look at the growth of wheat is to consider only the stages where weather influences are most important. The base temperature for the calculation of degree days can then be adapted to the specific requirements during these stages. In the first month of growth when seeds germinate temperatures should ideally be between 12°C and 25°C (Acevedo et al., 2002). The temperature data, showed that temperatures never exceeded the upper boundary so that only the lower boundary needed to be taken into account. The cumulative HDDs over the month of May should than have a negative effect. Another important stage for wheat growth is vernalization, a colder period that is necessary to induce flowering in the plant. This stage can last up to eight weeks10 _{and typically}

occurs during the months July and August. Research is divided as to below what temperature vernalization actually occurs, estimates range from 7°C (Acevedo et al., 2002) to 11°C1_{. I will use the}

cumulative HDDs over July and August with a base temperature of 10°C, which is the suggested temperature boundary by Herbek and Lee (2009). This variable is expected to have a positive effect. A final risk associated with temperature is that of heat stress. This can occur if temperatures are above 25°C (Acevedo et al., 2002), this risk exists mainly at the end of the growing cycle when plants are already fully grown. This would be during early summer in Tasmania (November and December). CDDs over this period with a base temperature of 25°C are thus expected to have a negative effect. Next to temperature variables, rainfall variables need to be accounted for as well for some key influences. Water stress can have an effect on the growth of wheat (Acevedo et al., 2002; White and Edwards, 2008; Herbek and Lee, 2009). That there is a risk of too little rainfall is easily imaginable, however White and Edwards (2008) note that there can also be a risk of too much rain. When soil is saturated and water remains at the surface (waterlogging) growth is seriously hampered. This risk is highest in winter (May) when temperatures and thus evaporation is lowest, but waterlogging could occur in other months as well. These rainfall related risks are captured by the following three variables for which a negative effect is expected. The amount of rainfall above 50 millimeters in May. And for the rest of the growing cycle, the cumulative monthly amount of rainfall below 30 or above 100 millimeters from June till December. These three variables are calculated as follows:

𝑅50𝑀

= max (0, 𝑅

− 50)

𝑅30𝐽𝐷

= ∑ max (0, 30 − 𝑅

)

15

𝑅100𝐽𝐷

= ∑ max (0, 𝑅

− 100)

Cumulative excess rainfall in May of year t above 50 millimeters is measured in 𝑅50𝑀𝑡. The other variables measure the cumulative rainfall deficit below 30 millimeters per month (𝑅30𝐽𝐷𝑡) and cumulative excess above 100 millimeters per month (𝑅100𝐽𝐷𝑡) from June to December of year t.

𝑅

One additional variable is included related to rainfall, the total amount of rainfall during August and September. This was shown to have a high correlation with crop yield for wheat (CelsiusPro, 2010). To control for the technological progress, the year is included here as well as a control variable, resulting in the following regression:

𝑌𝑡 = 𝛼 + 𝑎𝑌𝐸𝐴𝑅𝑡+ 𝑏𝐻𝐷𝐷12𝑀𝑡+ 𝑐𝐶𝐷𝐷10𝐽𝐴𝑡+ 𝑑𝐶𝐷𝐷25𝑁𝐷𝑡+ 𝑒𝑅50𝑀𝑡 (8) +𝑓𝑅𝐴𝑆𝑡+ 𝑔𝑅30𝐽𝐷𝑡+ ℎ𝑅100𝐽𝐷𝑡+ 𝜀

Here again, 𝑌𝑡 is the crop yield in kilograms per hectare for the first set of regressions and the proceeds in Australian dollars per hectare for the second set of regressions. 𝑌𝐸𝐴𝑅𝑡 is a variable to control for technological progress. 𝐻𝐷𝐷12𝑀𝑡 is the cumulative amount of HDDs (base 12°C) in May. 𝐶𝐷𝐷10𝐽𝐴𝑡 and 𝐶𝐷𝐷25𝑁𝐷𝑡 are the cumulative amounts of CDDs in July/August (base 10°C) and November/December (base 25°C) respectively. 𝑅𝐴𝑆𝑡 is the total amount of rainfall in August and September. Letters a through h represent the coefficients that show the effect each independent variable has on the dependent variable, 𝛼 is the constant and 𝜀 the error term.

16

𝐻𝐷𝐷

= max (0, 𝑏𝑎𝑠𝑒 − 𝑚𝑖𝑛𝑡

)

𝐶𝐷𝐷

= max (0, 𝑚𝑎𝑥𝑡

− 𝑏𝑎𝑠𝑒)

The explanation stays the same for all variables compared to equations (2) and (3).

The second robustness check has to do with the problem of spatial basis risk as identified by Manfredo and Richards (2009), Rao (2011) and Woodard and Garcia (2008). They find that spatial basis risk is particularly relevant when it comes to rainfall. Martin et al. (2001) propose a way of dealing with this by using multiple weather stations. Therefor all regressions will be performed with rainfall data from one, as well as the average from five weather stations.

𝑅

𝑅

= (∑ 𝑅

)/5

Where 𝑅𝑖𝑡𝑠 is the rainfall in month i of year t as recorded at weather station s.

17

Table 1: Descriptive statistics

Mean Median Maximum Minimum SD Skewness Kurtosis Observations

Dependent variables CROPYIELD (KG/HECTARE) 2783.542 2750.000 4375.000 1062.500 1040.483 0.017 1.551 41 Proceeds (AUD/HECTARE) 535.649 528.000 1472.113 79.167 342.139 0.524 2.713 41 Independent variables Periods HDDP1 546.707 551.250 622.650 429.000 50.646 -0.387 2.479 41 HDDP2 320.240 316.700 424.800 239.850 41.636 0.513 3.105 41 HDDP3 181.523 173.950 264.350 113.850 30.392 0.750 3.789 41 CDDP1 1.554 0.500 7.950 0.000 2.198 1.571 4.439 41 CDDP2 2.649 1.300 17.150 0.000 3.826 1.926 6.737 41 CDDP3 70.902 67.500 121.050 26.850 22.117 0.239 2.795 41 RP1 129.207 127.000 265.400 32.200 47.508 0.630 3.700 41 RP2 117.515 117.200 231.200 33.000 49.902 0.531 2.680 41 RP3 165.456 145.200 325.600 48.000 73.443 0.635 2.525 41 Alternative HDD12M 41.859 43.800 72.250 10.200 15.251 -0.037 2.424 41 CDD10JA 29.166 28.550 73.800 3.250 14.651 0.744 3.731 41 CDD25ND 0.575 0.000 6.950 0.000 1.487 3.009 11.599 41 R50M 5.890 0.000 48.700 0.000 12.663 2.098 6.236 41 RAS 117.515 117.200 231.200 33.000 49.902 0.531 2.680 41 R30JD 18.293 13.000 63.000 0.000 17.926 1.001 2.927 41 R100JD 19.541 2.600 106.400 0.000 29.468 1.491 4.198 41 5 rain RP1 218.495 216.520 390.260 141.880 49.007 1.084 4.904 41 RP2 166.131 161.440 272.840 78.300 50.283 0.210 2.228 41 RP3 183.356 173.980 290.440 78.960 59.193 0.200 2.053 41 R50M 20.356 5.480 78.080 0.000 25.883 0.935 2.342 41 RAS 166.131 161.440 272.840 78.300 50.283 0.210 2.228 41 R30JD 4.142 0.000 23.300 0.000 6.808 1.547 4.117 41 R100JD 27.673 16.600 126.020 0.000 30.158 1.140 3.975 41 MinMax HDD12M 139.795 146.200 189.200 66.800 28.589 -0.671 3.015 41 CDD10JA 186.988 184.900 271.200 130.800 33.988 0.440 2.720 41 CDD25ND 4.844 3.600 26.400 0.000 5.589 1.863 7.022 41

18 The use of minimum and maximum temperatures instead of averages also has a clear effect, this leads to both higher values and higher SD for the variables.

There is a problem however, because the heating degree days and cooling degree days are calculated using the same base temperature they can be expected to correlate. They are not each other’s opposites (since degree days are either positive or zero), but when the number of heating degree days on a particular day is positive, the number of cooling degree days must be zero. This creates a problem of multicollinearity between some of the variables (heating and cooling degree days in the same period). Following the method of Brooks (2008) to check for this the correlations between the degree day variables are depicted in table 2.

Table 2: Correlation HDDs and CDDs

HDDP1 HDDP2 HDDP3 CDDP1 CDDP2 CDDP3 HDDP1 1.000 - - - - - HDDP2 0.397 1.000 - - - - HDDP3 0.304 0.324 1.000 - - - CDDP1 -0.374 -0.297 -0.289 1.000 - - CDDP2 -0.206 -0.519 -0.102 0.241 1.000 - CDDP3 -0.339 -0.277 -0.568 0.259 0.105 1.000

Some correlation is to be expected (e.g. in a year with above average temperatures HDDs will be high in all periods), but from table 2 it can be seen that the correlations between HDDs and CDDs in periods two and three are strongly negative. Brooks (2008) suggests a number of ways to deal with multicollinearity. It can be ignored in some cases while in others it is more appropriate to drop one of the collinear variables. What way to proceed depends on the outcome of the regression and the theoretical reasons for including the variables. The differences between HDDs and CDDs is a theoretical reason for including them both in the regression. However, to see whether exclusion of one of them leads to lower standard errors and thus (more) significant results two additional regressions will be performed:

𝑌𝑡 = 𝛼 + 𝑎𝑌𝐸𝐴𝑅𝑡+ 𝑏𝐻𝐷𝐷𝑃1𝑡+ 𝑐𝐻𝐷𝐷𝑃2𝑡+ 𝑑𝐻𝐷𝐷𝑃3𝑡 (12)

19

𝑌𝑡 = 𝛼 + 𝑎𝑌𝐸𝐴𝑅𝑡+ 𝑏𝐶𝐷𝐷𝑃1𝑡+ 𝑐𝐶𝐷𝐷𝑃2𝑡+ 𝑑𝐶𝐷𝐷𝑃3𝑡 (13)

+ ℎ𝑅𝑃1𝑡+ 𝑖𝑅𝑃2𝑡+ 𝑗𝑅𝑃3𝑡+ 𝜀

First the CDD variables are dropped from the equation, then all HDD variables are dropped, the meaning of all symbols stays the same as in equation (4). In total this means that ten different regressions are performed for each of the two dependent variables.

5. Results

The results from the regressions where the crop yield was used as the dependent variable are presented in tables 3 and 4. Tables 5 and 6 contain the results for the set of regressions where the proceeds were the dependent variable. Tables 3 and 5 show the results from the regressions using the original specification of equation (4) or the adaptations of equations (12) and (13). Where the alternative specification of equation (8) is used for the regressions the results are shown in tables 4 and 6.

It is clear that the explanatory power of all regressions is quite high, the R2 _{and even the adjusted}

R2 _{are all around 70% or higher. For the second set of regressions (whit proceeds as dependent variable)}

20

Variables (1) (2) (3) (4) (5) (6)

original no cdd no hdd 5 rain 5 rain, no cdd 5 rain, no hdd YEAR Coëfficient 75.854*** 73.164*** 76.194*** 71.845*** 66.642*** 74.647*** SD 8.677 8.110 8.247 9.570 8.773 8.655 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) HDDP1 Coëfficient -4.84** -4.950** - -3.707 -4.042* -SD 2.253 2.086 - 2.550 2.380 -(0.040) (0.024) - (0.156) (0.099) -HDDP2 Coëfficient 3.543 2.386 - 2.475 0.398 -SD 2.966 2.601 - 2.971 2.658 -(0.242) (0.366) - (0.411) (0.882) -HDDP3 Coëfficient 0.186 1.727 - -1.194 0.518 -SD 3.806 3.293 - 3.823 3.283 -(0.961) (0.603) - (0.757) (0.876) -CDDP1 Coëfficient -8.969 - 7.520 -24.824 - -7.286 SD 46.064 - 45.096 47.627 - 44.574 (0.847) - (0.869) (0.606) - (0.871) CDDP2 Coëfficient 34.565 - 32.974 51.177 - 51.882* SD 30.745 - 28.114 30.682 - 25.663 (0.270) - (0.249) (0.106) - (0.051) CDDP3 Coëfficient -3.552 - -1.729 -2.821 - -1.032 SD 5.738 - 5.117 5.857 - 5.017 (0.541) - (0.738) (0.634) - (0.838) RP1 Coëfficient -0.615 -1.199 -0.752 -2.146 -2.783 -1.460 SD 2.040 1.872 2.087 2.304 2.083 2.223 (0.765) (0.526) (0.721) (0.359) (0.191) (0.516) RP2 Coëfficient -3.393 -4.451** -1.773 0.431 -0.606 1.856 SD 2.222 2.000 2.111 2.180 2.088 1.903 (0.137) (0.033) (0.407) (0.845) (0.774) (0.337) RP3 Coëfficient -0.154 0.186 0.440 0.638 0.921 1.266 SD 1.454 1.298 1.442 1.799 1.661 1.727 (0.916) (0.887) (0.762) (0.726) (0.583) (0.469) R2 _{0.783 0.772 0.745 0.773 0.749 0.754} Adjusted R2 _{0.711 0.724 0.691 0.697 0.696 0.702} Probability of F-statistic (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Residual tests Jarque-Bera 2.140 4.268 1.597 1.300 2.469 0.702 (0.343) (0.118) (0.450) (0.522) (0.291) (0.704) White 0.927 0.742 1.062 0.743 0.726 0.717 (0.523) (0.638) (0.409) (0.680) (0.651) (0.658) Breusch-Godfrey 1.217 1.015 0.480 0.911 1.022 0.876 (0.338) (0.461) (0.886) (0.542) (0.456) (0.568)

between parentheses and significance is indicated as follows: Significant at 1% ***

Significant at 5% ** Significant at 10% *

White and Breusch-Godfrey tests the F-statistics are given. There are ten lags included in the Breusch-Godfrey test. All p-values are given Table 3: Regression analysis cropyields (kg/hectare)

21

Variables (7) (8) (9) (10)

5 rain MinMax MinMax, 5 rain

YEAR Coëfficient 75.764*** 74.949*** 68.743*** 69.727*** SD 8.648 8.922 8.754 8.763 (0.000) (0.000) (0.000) (0.000) HDD12M Coëfficient 9.944 6.963 8.410** 6.140* SD 6.684 6.622 3.331 0.371 (0.147) (0.301) (0.017) (0.078) CDD10JA Coëfficient 3.774 1.519 6.374** 5.363* SD 7.241 6.845 3.103 2.867 (0.606) (0.826) (0.048) (0.071) CDD25ND Coëfficient 71.757 82.786 21.980 21.221 SD 65.925 68.601 17.889 18.588 (0.285) (0.236) (0.228) (0.262) R50M Coëfficient 4.046 -1.304 0.137 -1.614 SD 7.874 4.151 7.551 3.953 (0.611) (0.756) (0.986) (0.686) RAS Coëfficient -3.402* -0.170 -3.070 0.235 SD 1.972 2.449 1.850 2.282 (0.094) (0.945) (0.107) (0.917) R30JD Coëfficient -3.746 -18.945 -8.348 -18.638 SD 6.262 16.165 6.084 15.462 (0.554) (0.250) (0.180) (0.237) R100JD Coëfficient -1.775 1.250 -4.616 1.188 SD 3.728 3.855 3.528 3.619 (0.637) (0.748) (0.200) (0.745) R2 _{0.754 0.741 0.791 0.773} Adjusted R2 _{0.693 0.677 0.739 0.716} Probability of F-statistic 0.000 0.000 0.000 0.000 Residual tests Jarque-Bera 0.146 0.446 0.992 0.395 (0.929) (0.800) (0.609) (0.851) White 1.034 1.085 0.999 0.746 (0.432) (0.399) (0.456) (0.651) Breusch-Godfrey 1.178 1.105 0.936 1.123 (0.356) (0.401) (0.521) (0.390)

significance is indicated as follows: Significant at 1% ***

Significant at 5% ** Significant at 10% *

There are ten lags included in the Breusch-Godfrey test. All p-values are given between parentheses and Table 4: Regression analysis cropyields (kg/hectare) II

22

Variables (11) (12) (13) (14) (15) (16)

no cdd no hdd 5 rain 5 rain, no cdd 5 rain, no hdd YEAR Coëfficient 26.634*** 26.028*** 27.215*** 26.114*** 24.659*** 27.020*** SD 2.214 2.149 2.096 2.388 2.238 2.153 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) HDDP1 Coëfficient -1.274** -1.122* - -0.900 -0.810 -SD 0.575 0.553 - 0.636 0.607 -(0.034) (0.051) - (0.168) (0.191) -HDDP2 Coëfficient 0.474 0.508 - 0.383 0.141 -SD 0.757 0.689 - 0.741 0.678 -(0.536) (0.466) - (0.609) (0.836) -HDDP3 Coëfficient 0.231 1.067 - -0.370 0.646 -SD 0.971 0.872 - 0.954 0.8.8 -(0.814) (0.230) - (0.701) (0.446) -CDDP1 Coëfficient 1.921 - 7.232 0.475 - 5.456 SD 11.752 - 11.461 11.885 - 11.085 (0.871) - (0.532) (0.968) - (0.626) CDDP2 Coëfficient 2.366 - 4.129 5.738 - 7.075 SD 7.843 - 7.145 7.656 - 6.382 (0.765) - (0.567) (0.459) - (0.276) CDDP3 Coëfficient -2.923* - -2.432 -3.000** - -2.464* SD 1.464 - 1.300 1.462 - 1.248 (0.055) - (0.070) (0.049) - (0.057) RP1 Coëfficient 0.426 0.116 0.428 0.170 -0.277 0.343 SD 0.520 0.496 0.530 0.575 0.531 0.553 (0.420) (0.816) (0.426) (0.769) (0.606) (0.539) RP2 Coëfficient -0.049 -0.717 -0.113 0.500 0.341 0.834* SD 0.567 0.530 0.537 0.544 0.533 0.473 (0.398) (0.185) (0.834) (0.366) (0.526) (0.087) RP3 Coëfficient -0.530 -0.235 -0.341 -0.729 -0.376 -0.575 SD 0.371 0.344 0.367 0.449 0.424 0.430 (0.164) (0.499) (0.532) (0.115) (0.381) (0.190) R2 _{0.869 0.852 0.848 0.869 0.849 0.859} Adjusted R2 _{0.826 0.851 0.816 0.826 0.817 0.830} Probability of F-statistic (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Residual tests Jarque-Bera 1.097 6.016** 3.192 2.039 15.179*** 8.437** (0.578) (0.049) (0.203) (0.361) (0.001) (0.015) White 1.804 2.481** 2.087* 1.393 1.742 1.668 (0.103) (0.036) (0.073) (0.231) (0.133) (0.151) Breusch-Godfrey 2.204* 3.144** 1.301 0.881 1.054 0.810 (0.064) (0.011) (0.287) (0.565) (0.433) (0.622) Significant at 1% *** Significant at 5% ** Significant at 10% *

heteroscedasticity (White) and auto-correlation (Breusch-Godfrey). For both the White and Breusch-Godfrey tests the F-statistics are given. There are ten lags included in the Breusch-Godfrey test. All p-values are given between parentheses and significance is indicated as follows:

Table 5: Regression analysis proceeds (AUD/hectare)

23

Variables (17) (18) (19) (20)

5 rain MinMax MinMax, 5 rain

YEAR Coëfficient 26.775*** 25.382*** 26.249*** 24.706*** SD 2.284 2.180 2.545 2.339 (0.000) (0.000) (0.000) (0.000) HDD12M Coëfficient -0.283 -0.875 0.894 0.311 SD 1.766 1.618 0.968 0.900 (0.874) (0.592) (0.363) (0.732) CDD10JA Coëfficient -2.441 -2.377 0.235 0.386 SD 1.913 1.672 0.902 0.765 (0.211) (0.165) (0.797) (0.617) CDD25ND Coëfficient 9.103 1.641 0.924 -1.807 SD 17.415 16.757 5.201 4.962 (0.605) (0.923) (0.860) (0.718) R50M Coëfficient -0.476 -1.367 -0.255 -1.144 SD 2.080 1.014 2.195 1.055 (0.820) (0.187) (0.908) (0.286) RAS Coëfficient -0.398 0.306 -0.447 0.420 SD 0.521 0.598 0.538 0.609 (0.451) (0.612) (0.412) (0.496) R30JD Coëfficient -0.118 3.986 -1.013 4.163 SD 1.654 3.949 1.736 4.128 (0.944) (0.320) (0.571) (0.321) R100JD Coëfficient 0.539 0.513 -0.084 0.425 SD 0.985 0.942 1.026 0.966 (0.588) (0.590) (0.935) (0.663) R2 _{0.842 0.857 0.837 0.850} Adjusted R2 _{0.802 0.822 0.796 0.813} Probability of F-statistic (0.000) (0.000) (0.000) (0.000) Residual tests Jarque-Bera 6.556** 2.734 10.438*** 10.302*** (0.038) (0.255) (0.005) (0.006) White 2.915** 3.665*** 2.610** 2.958** (0.015) (0.004) (0.026) (0.014) Breusch-Godfrey 3.796*** 2.047* 2.236* 1.834 (0.004) (0.078) (0.056) (0.113)

All p-values are given between parentheses and significance is indicated as follows: Significant at 1% ***

Significant at 5% ** Significant at 10% *

Table 6: Regression analysis proceeds (AUD/hectare) II

24 The third and last variable where a significant effect is found (when using degree days with a standard base temperature) is for the total rainfall in period 2, but only when multiple weather stations are used and CDD’s are dropped from the equation. This is also a negative effect and it is of about the same magnitude as the one for HDDP1, but both are relatively small. The results of Celsiuspro (2010) are not corroborated here, since the coefficient on the total rainfall in August and September is only significant in one of the regressions presented in table 4. It is only significant at the 10% level and beyond that the coefficient is negative contrary to expectations. The number of HDDs in May (with a base of 12°C) and CDDs in July and August (base 10°C) only have a significant effect when the minimum and maximum temperatures are used instead of the average daily temperature. Their effect becomes less significant when multiple weather stations are used and also here the signs of the coefficients are not in line with the theory that would suggest a negative effect.

When reviewing the results from the second set of regressions in tables 5 and 6 it is apparent that they are similar to the ones from tables 3 and 4. As already mentioned, the R2 _{and the adjusted R}2

are higher than for the first set at around 80%. However the amount of coefficients that indicate a significant effect of the independent variables on the dependent variable is even lower. It seems that YEAR here has even more power in explaining the differences in proceeds. When looking at the coefficients that are significant, it is visible that HDDP1 has a significant effect (small and negative) which becomes less significant when corrected for multicollineairity (without CDD variables) and loses significance altogether when multiple weather stations are used. CDDP3 has a significant (small and negative) effect to, however this effect becomes more significant in the ‘5 rain’-regression. This effect is less pronounced when HDD variables are dropped from the equation. None of the coefficients for any of the variable from equation (8) is significant and other than that, coefficients are small and sometimes not in line with theory. It is clear that standard deviations are high in relation to the coefficients (resulting in insignificance), it does seem however that for most of the variables p-values decrease when multiple weather stations are used.

25 and 6 however, there is evidence that not all assumptions hold for each regression, the results are quite inconsistent though. Non-normality as indicated by the Jarque-Bera test could mean OLS is not an appropriate method to use, but it also could be a result of some outliers in the data. Both heteroscedasticity and autocorrelation will not affect the coefficients, but they do influence standard deviations. This makes it hard to draw strong conclusions based on the results affected by these problems. The use of White’s modified standard error estimates could solve heteroscedasticity, however this leads to very marginal changes in the results (not affecting the reported significance) and are thus not included here. The incorporation of producer prices by using proceeds as the dependent variable thus leads to problems with the model employed here. The results from both sets of regressions are however in line with each other, these doubts about the adequacy of the model do not have a big impact on the conclusions reached.

26 amount of rainfall of abnormal temperatures. It might be that only extreme events or these abnormalities have an impact (and regular variations do not), however this is not investigated here (related to product basis risk as identified by Rao, 2011). Protection from these kinds of events might also already be provided through the government or insurance policies.

6. Conclusion

27 impact of extreme weather events. A possible research questions here could be: is insurance the only way for an agricultural producer to get protection from extreme weather events?

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