Management of Climate Risks in Agriculture -Will Weather Derivatives Permeate?

Keywords: Weather derivatives, precipitation risk, hedging effectiveness, local basis risk, geographical basis risk

Introduction

Weather is an important production factor and at the same time one of the greatest sources of risk in agriculture. Perhaps, the most obvious impact of weather is on crop production (cf. e.g., [START_REF] Isik | An Analysis of the Impact of Climate Change on Crop Yields and Yield Variability[END_REF]. There is scarcely a year in which there are no drought periods or extreme precipitation in the most diverse regions of the world leading to crop failures. The impact of the weather risk is not limited to crop production. The performance of livestock farms, the turnover of processors, the use of pesticides and fertilizers as well as the demand for many food products also depends on weather. Hence, large parts of the agribusiness are affected by weather risks.

It is expected that fluctuations in temperature and rainfall will increase in the wake of global climate change and thereby the volumetric risk will rise further. At the same time, the susceptibility of farms to risk will rise as a result of the increasing capital intensity of agriculture and the associated increasing debt ratio. Therefore, it will become increasingly necessary for farmers to insure themselves against weather risks.

Farmers have always been confronted with risks. In the past, farmers tried to protect themselves against the negative economic consequences of bad weather events by using on-farm risk management instruments like choosing less weather-dependent production activities, choosing a widely diversified production program, procuring overcapacities or investing in technologies to control the environment (e.g. irrigation technologies). Additionally, farmers have tried to share risks through buying damage-based insurances (cf. e.g., [START_REF] Mishra | Revenue Insurance Purchase Decisions of Farmers[END_REF]. Agricultural policy support (e.g., direct government aids in response to natural calamities and disasters) can also yield an insurance effect (cf. e.g., [START_REF] Thompson | The Real Rate of Protection: The Income and Insurance Effects of Agricultural Policy[END_REF].

From the end of the 1990s onwards, there has been a discussion about the use of indexbased instruments, also called weather derivatives, as a new instrument to safeguard against volumetric risks (cf. [START_REF] Tigler | Weather Derivatives, A Quantitative Analysis[END_REF][START_REF] Cao | A New Class of Financial Instruments[END_REF][START_REF] Berg | Weather Derivatives as a Risk Management Tool in Agriculture[END_REF][START_REF] Jewson | Weather Derivative Valuation[END_REF]. Weather derivatives are financial market products, such as futures, options or swaps, which allow exchanging weather risks. They are related to objectively measurable weather variables (temperature, rainfall, wind etc.). Until now, weather derivatives have been used mainly by energy companies. Trading of weather derivatives also occurs predominantly in the over-thecounter (OTC) market. This means that the contracting parties have to establish their contract specification bilaterally. As a contractual partner for a farmer wishing to be insured against in-F o r P e e r R e v i e w 3 sufficient rainfall during the growth phase of crops, for instance, the tourist industry (e.g., theme parks) can be considered, which exhibits a contrary risk exposure with regard to rainfall. However, weather derivatives also offer attractive opportunities for institutional investors such as insurers or banks to diversify a portfolio, since the weather-related risks are only correlated relatively weakly with the systematic risk of a national economy.

Whereas traditional damage-based insurances predominantly protect against damages from catastrophic events (e.g. hail), weather derivatives can be designed to release payments even for less drastic events (e.g. insufficient rainfall). A holder of a traditional insurance must also prove the damage in order to obtain indemnity payments. Unlike conventional damage-based instruments, the hedge from weather derivatives results from payments which are tied to weather variables that are measured objectively at a specified location; that is, weather derivates are not impact-oriented, but cause-oriented. Weather derivatives thus offer administrative advantages over traditional insurances. Furthermore, weather derivatives, unlike insurances (cf. e.g., [START_REF] Jin | Binary Choice Models for Rare Events Data: A Crop Insurance Fraud Application[END_REF], are not affected by moral hazard problems and adverse selection. Therefore, weather derivatives have the advantage of relatively low transaction costs.

Although (i) agriculture is directly dependent on the weather, (ii) experts point out numerous potential applications of weather derivatives especially because of the advantages named above (cf. [START_REF] Turvey | Weather Derivatives for Specific Event Risks in Agriculture[END_REF][START_REF] Skees | The Potential Role of Weather Markets for U.S. Agriculture[END_REF], and (iii) there have already been some promising practical experiences in the USA and Canada, the market for weather derivatives in agriculture is currently still relatively small. This may partly be accounted for by the fact that farmers are not yet familiar with using weather derivatives. Another problem is that different valuation methods for weather derivatives can provide different prices. A possible consequence is that no unique price is found which market participants consider to be fair. The market then lacks liquidity and there is consequently a lack of orientation for other potential market participants. Another possible obstacle to their application can be seen in the basis risk which remains with the farmer when he uses weather derivatives, and which means that yield variations are not compensated exactly by corresponding payoffs from the weather derivative. One cause of the basis risk is that yield variations are generally not perfectly correlated with the relevant weather variable (local basis risk). For example, the weather derivative could refer to the rainfall sum at the place of production in May, although e.g. the rainfall at other time periods, the timing of the rainfall and the temperature also influence the yield in the crop production. On the other hand, there is a geo- 4 graphical basis risk. In this context, this means the non-insurable risk which results from the difference between the weather event at the reference point of the derivative and the site of agricultural production. Although this aspect is not so important for temperature-related instruments, it cannot be neglected in the analysis of the hedging effectiveness of rainfall derivatives, as there is a high spatial variability of rainfall.

An increasing number of publications investigate the usefulness of weather derivatives as a risk management instrument in agribusiness. Previous studies have focussed on the one hand on theoretical questions of pricing weather derivatives and on the other hand on analysing temperature-related instruments (cf. [START_REF] Van Asseldonk | Insurance Against Weather Risk, Use of Heating Degree-days from non-local Stations for Weather Derivatives[END_REF][START_REF] Richards | Pricing Weather Derivatives[END_REF][START_REF] Manfredo | Hedging Yield with Weather Derivatives, A Role for Options[END_REF][START_REF] Turvey | The Pricing of Degree-day Weather Options[END_REF]. For agricultural applications, rainfall-related instruments ought to play a greater role. Hitherto, however, there have been very few publications especially on the analysis of the hedging effectiveness of precipitation-based instruments (cf. [START_REF] Turvey | Weather Derivatives for Specific Event Risks in Agriculture[END_REF][START_REF] Stoppa | Design and Use of Weather Derivatives in Agricultural Policies: the Case of Rainfall Index Insurance in Morocco[END_REF]. As yet, therefore, it is unclear whether weather derivatives will permeate in agriculture [START_REF] Edwards | Preliminary Results for the Measurement of Willingness to Pay for Climate Derivatives[END_REF].

The aim of this study is to clarify the risk-reducing effect of using rainfall options, specifically by considering wheat production in northeast Germany by means of a with/without derivative comparison. Special attention will be given to quantifying the basis risk, which will be divided into the previously mentioned components (i) local basis risk and (ii) geographical basis risk. The separation of the basis risk, which to our knowledge has not been treated previously in literature, will provide important findings for the design of weather derivatives and their potential for usage in agriculture. Thus, the questions dealt with here will be relevant both for farmers and for potential sellers of weather derivatives.

The remainder of the paper is structured as follows: In Section II, the database and methodical procedure are described. In Section III, the analysis of the hedging effectiveness of rainfall options for a representative cash crop farm in northeast Germany is carried out. The paper ends with conclusions for the design of weather derivatives (Section IV).

II. Data and methodical procedure

Grain production in northeast Germany, Brandenburg in particular, is highly affected by rainfall risk. During the important grain-yield months of April to June, the rainfall sum in Brandenburg was between 64 and 258 mm over the last 20 years (at an average of 141 mm and a standard deviation of 46 mm) -measured at the Berlin-Brandenburg central weather station in Berlin- For a farm-specific analysis of the hedging effectiveness of weather derivatives, a representative cash crop farm with approximately 850 ha of acreage operating in the Federal State of Brandenburg, more precisely in Ketzin, is considered. The farmer wishes to be insured against weather-related yield losses in wheat production. Wheat is the major production activity with a crop proportion of more than one third. Without a weather station or a suitable contractual partner, it is difficult for the farmer to obtain a derivative which refers directly to the weather on site of production. Nonetheless, it is assumed that derivatives which refer to the rainfall measured at the weather station in Berlin-Tempelhof are available on the OTC market. Ketzin is situated about 39 km west of Berlin-Tempelhof. Both causes of basis risk which have previously been outlined are evident here: on the one hand, a number of weather variables influence the wheat yield while the payoff of the derivative and the indemnity payments is solely derived from rainfall. On the other hand, Ketzin is 39 km away from Berlin-Tempelhof, which means that the rainfall in each location can be completely different in principle. Thus, even if the agricultural production were only dependent on the rainfall, indemnity payments and yield failure could still be different on account of the spatial distance.

In order to evaluate the hedging effectiveness of weather derivatives, a weather variable must first be specified and the production function must be estimated in which the weather is not -as is usual -a part of the error term, but a non-controllable (though measurable) production factor. Derivatives, which refer to the weather variable in the production function, are then specified. Before the hedging effectiveness of weather derivatives can be quantified, the derivatives -which do not yet exist but which could be available in principle -must be priced. The elements of a farm-specific analysis of the hedging effectiveness of weather derivatives are summarized in Fig. 1.

On the specification of the weather variables

Previous publications on rainfall-related derivatives have tended to refer to an accumulation index (cf. [START_REF] Turvey | Weather Derivatives for Specific Event Risks in Agriculture[END_REF][START_REF] Skees | Developing Rainfall-Based Index Insurance in Morocco, Policy Research Working Paper 2577[END_REF][START_REF] Stoppa | Design and Use of Weather Derivatives in Agricultural Policies: the Case of Rainfall Index Insurance in Morocco[END_REF][START_REF] Vedenov | Efficiency of Weather Derivatives as Primary Crop Insurance Instruments[END_REF].

The cumulative rainfall index C T I corresponds to the rainfall sum within a specific time period:

∑ = = x t t C T y I 1 (1)
Here, t y indicates the rainfall on day t and x indicates the length of the accumulation period.

Alternatively, the rainfall deficit index D T I is suggested here, which expresses the timing of rainfall in addition to the quantity:1

∑ ∑ = ⋅ + ⋅ - =         - = z min s s t t D T y y I 1 1 ) 1 ( , 0 min τ τ τ (2)
This index measures the shortfall of the rainfall sum in an s -days period relative to a reference level min y . This shortfall is cumulated over z periods. Hence, the construction principle is similar to that of degree-day-indices, which are widely used for the specification of temperature derivatives (cf. e.g. [START_REF] Alaton | On Modelling and Pricing Weather Derivatives[END_REF]Zeng, 2000a).

On the estimation of the production function

For the considered cash crop farm yield data for winter wheat over a period from 1993 to 2006 are available. Fourteen observations seem to be a poor database for the estimation of the yield model. However, a longer time series is not available for the new federal states in Germany in general and Brandenburg in particular, since production took place under totally different conditions prior to German reunification. Furthermore, it should also be noted that the yield data survey was not performed in accordance with the wheat variety, even though certain wheat varieties are better suited to regions with low rainfall such as Brandenburg and are preferred there for cultivation. Using statistical tests, no significant trend can be found for the wheat yields. There is some back coupling between the estimation of the production function and the precise specification of the rainfall indices, since weather variables are sought which are correlated as highly as possible to production output. Variant calculations are used to examine which reference period delivers the "best" rainfall sum index and which reference period allows the "best" rainfall deficit index. In order to do so, systematic variations for x as well as for z and s are carried out. min y was selected so as to provide a maximum correlation between the wheat yield and the deficit index.

Table 1 shows the parameter estimates and the explanatory power for selected production functions. Measured at R 2 , the best rainfall sum index for the accumulation period June and the best rainfall deficit index for the accumulation period April to June are obtained. It should be noted that the explanatory power between the wheat yield and the best rainfall deficit index 2 Several further functional forms for the yield model have been tested; in particular a quadratic and a logarithmic production functions. Nonetheless, the linear-limitational production function showed the best fit in terms of R 2 for the empirical data and both rainfall indices. It should be noted that this result cannot be generalized. VEDENOV and [START_REF] Vedenov | Efficiency of Weather Derivatives as Primary Crop Insurance Instruments[END_REF] point out that a suitable yield-rainfall-model is dependent on type of variety and region. (R 2 = 0.48) is considerably higher than that between the wheat yield and the best rainfall sum index (R 2 = 0.15).

Table 1 about here

The specification of derivatives which refer to the best rainfall sum or rainfall deficit index is described in the following.

On the specification of the weather derivatives

The revenue function of wheat production can be derived from the production function. As only volumetric risks are to be considered, it is assumed that the wheat price P is fixed by a forward contract and amounts to 10 €/dt. A derivative is now constructed respectively for the best rainfall sum index and the best rainfall deficit index in such a way that it compensates for expected revenue fluctuations precisely by corresponding payoffs. For a linear-limitational production function this can be achieved using an option. The payoff for a (European) put option corresponds to: In order to design the options in such a way that their payoff is complete inversely to the expected revenues from the wheat production (per ha), strike level and tick size must be selected as follows:

( ) V I S F T T ⋅ - = 0 , max (
2 a S = and P a V ⋅ = 1 . 3 As illustrated in Fig. 2, the options deliver 3 It should be noted that an option cannot be designed in such a way that its payoff is correlated perfectly negatively to the expected revenue from the production, if production function did not display a linear-limitational function form. To insure the production risk for a linear production function, a future can be used. For more complex production functions, several weather derivatives can be combined. In this way, a combination of put and call options

Fig. 2 about here

The contract specifications for the rainfall options which are considered here are summarized in Table 2.

Table 2 about here

On the calculation of the option price

If farmers wish to insure their revenue in wheat production by using a rainfall option, they must first spend the option price. As the options are not market-traded, their price must also be determined. Unfortunately, the preference-independent valuation procedures developed in the financial option pricing theory cannot be used, since the rainfall index which forms the basis of a rainfall option is non-tradable (cf. Jewson et al., 2005: 28-34;[START_REF] Richards | Pricing Weather Derivatives[END_REF]. In order to avoid the difficulties which are therefore associated with pricing weather derivatives, the price of both options is calculated as a "fair premium" in an actuarial sense, i.e. the profit expected from the option trade is precisely zero for both parties. Since therefore neither a risk premium from the seller or buyer nor transaction costs are taken into account, the option price can simply be calculated as the expected payoff of the option discounted with risk-free interest rate r :

( ) ( ) t r F E F T ∆ ⋅ - ⋅ = exp 0 ( 5
)
where t ∆ is the maturity of the option.

The fair premium can basically be determined by means of analytical procedures, historical simulation (burn analysis), index value simulation or daily simulation. Analytical procedures like the Black-Scholes formula require restrictive assumptions e.g. regarding the distribution for the weather variable underlying the derivative (cf. [START_REF] Hull | Options, Futures and other Derivatives[END_REF]. Option prices determined by means of historical simulation as a non-parametric procedure can be very imprecise, because for could be suitable for a quadratic production function. In the "left area" ("right area") of the production function, the put option (the call option) insures against volumetric risks. instance the length of the data series is too short to obtain a good approximation of the theoretical distribution for the weather index (Zeng, 2000b). Using the daily simulation based on a model for the daily rainfall, the volatility of the rainfall and thus the option price are systematically underestimated (cf. [START_REF] Dubrovsky | High-Frequency and Low-Frequency Variability in Stochastic Daily Weather Generator and its Effect on Agricultural and Hydrologic Modelling[END_REF][START_REF] Odening | Analysis of Rainfall Derivatives Using Daily Precipitation Models: Opportunities and Pitfalls[END_REF]. Therefore, the index value simulation is used here.

Using daily rainfall data which were measured in Berlin-Tempelhof between 1948 and 2006, the respective value for the rainfall index is calculated for each year. In the result, 59 empirical observations are available for each index. The MS-EXCEL-Add-In BEST-FIT is used to test which assumption regarding the distribution of the index is adequate. According to the standard tests (Chi-Square, Kolmogorov-Smirnov and Anderson-Darling test), the lognormal distribution shows the best fit to empirical distribution for the rainfall sum index and the Weibull distribution delivers the best fit for the rainfall deficit index; whereas only distributions were considered which did not permit a change of sign of the uncertain variable. In the context of the index value simulation, a value is randomly drawn 10 000 times from the estimated distribution for the rainfall index. 4 In each simulation run the payoff of the option is determined in accordance with (4). The discounted average payoff of the derivative corresponds to the fair premium (cf. ( 5)). Using a risk-free interest rate r of 5%, the fair premium amounts to 108.1 € for the rainfall sum index and 56.8 € for the rainfall deficit index.

On the estimation of the hedging effectiveness

General procedure

The risk-reducing effect which can be attained by using weather derivatives is usually quantified by a comparison of the revenue distribution with and without having a derivative (cf. e.g. [START_REF] Vedenov | Efficiency of Weather Derivatives as Primary Crop Insurance Instruments[END_REF]. Without a derivative, the revenue from wheat production 0 R (in €/ha) related to the time of buying the derivative corresponds to the wheat yield (in dt/ha) multiplied by the wheat price (in €/dt) and the discounting factor: 5

4 Regarding the number of required simulation runs, Haug (1998: 40), e.g., stipulates that at least 10 000 runs should be carried out. For technical details describing how to use stochastic simulation to model a wide variety of distributions with established software packages see e.g. [START_REF] Winston | Financial Models Using Simulation and Optimization[END_REF]. 5 We are only focussing on the risk-reducing effect of weather derivatives in wheat production, i.e. we abstract from cross effects resulting from the fact that the payoff of a weather derivative is correlated with the yields of several crops.

t r P I Q R T T ∆ ⋅ - ⋅ ⋅ = exp 0 (6)
With a derivative, the revenue ' 0 R (in €/ha) is to be calculated as follows:

( ) ( ) 0 0 ' 0 exp F t r I F R R T T - ∆ ⋅ - ⋅ + = (7)
If farmers wishing to be insured against volumetric risks using a derivative, at first, they have to pay the purchase price 0 F . Afterwards, farmers receive in addition to the revenue from wheat production 0 R the payoff of the derivative T F , whose level -just like the success of the production (cf. ( 3)) -is dependent on the weather variable T I .

On the separation of the basis risk

To separate the basis risk and its causes, three scenarios are considered when estimating the hedging effectiveness of rainfall options; two of these scenarios are synthesized in order to work on the specific effects. As the option is always related to the rainfall at the reference weather station Berlin-Tempelhof, the three scenarios are not distinguished with regard to the option price 0 F and the payoff of the option T F , but only in determining the production success of wheat production in T :

• In the first hypothetical scenario it is assumed that there is no basis risk. It is supposed that the location of the agricultural production is not in Ketzin, but in the immediate vicinity of the reference weather station in Berlin-Tempelhof ( T Q instead of T Q ~) and that the relationship between yield and rainfall index is not influenced by random effects ( 0 = T ε ). Technically, the wheat yield in scenario 1 1 T Q is derived directly from the rainfall index in Berlin-Tempelhof:

     < ⋅ + = otherwise , if , 3 2 1 0 1 a a I I a a Q T T T (8)
• In the second hypothetical scenario, the fact that the wheat production takes place 39 km away from the reference weather station is taken into account (geographical basis risk). However, it is further assumed that the relationship between yield and rainfall index at the site of production is purely deterministic ( 0 = T ε ). Technically, the wheat yield in scenario 2 2 ~T Q is directly derived from the rainfall index at the site of production in Ketzin ( T I ~ instead of T I ): • In the third scenario, the spatial distance between the reference weather station and the site of production as well as the stochastic relationship between yield and rainfall are taken into consideration (geographical basis risk and local basis risk). Technically, the wheat yield in scenario 3 3 ~T Q is derived from the relevant value for the rainfall index at the reference weather station Berlin-Tempelhof and while taking into consideration the error term of the production function T ε , which expresses both basis risks:

     < ⋅ + = otherwise , ĩf , 3 2 1 0 2 a a I I a a Q T T T (9)
     + < + ⋅ + = otherwise , if , ~3 2 1 0 3 T T T T T a a I I a a Q ε ε (10)
To determine the distribution for the revenues without option (cf. ( 6)) and with option (cf. ( 7)) in the three scenarios, the stochastic simulation (10 000 simulation runs) is used.

Decorrelation analysis

Usually, one would quantify geographical basis risk (second scenario) by means of comparing the hedging effectiveness of weather derivatives based on weather data measured at the production site versus taken weather data some distance apart. Unfortunately, for the showcased farm in Brandenburg weather data measured on the production location are not available. For that reason we have to replace actual weather data by randomly generated values using an appropriate correlation coefficient. This correlation coefficient is derived from a statistically estimated decorrelation function.

In order to estimate the correlation between the rainfall index at the site of production and the rainfall index at the reference weather station, data is used from 23 weather stations in Ber-

( ) 3 , 2 1 , exp c j i j i d c c ⋅ - ⋅ = ρ (11)
For the best rainfall sum index we find 1 c = 0.94, 2 c = 0.0033, 3 c = 0.88 and for the best rainfall deficit index 1 c = 0.92, 2 c = 0.0012, 3 c = 1.11. The R 2 is 0.24 for the rainfall sum index and 0.48 for the rainfall deficit index. The scatter diagram shown in Fig. 3 makes it clear, however, that the relationship between distance and correlation becomes more diffuse as the distance increases, that is the scatter plot reveals heteroscedasticity. It is also apparent that -as expected -

the correlation between the rainfall index at two weather stations decreases with the distance. At a distance of 39 km between Berlin-Tempelhof and production location in Ketzin the rainfall sum index has an expected correlation of 0.87 and the rainfall deficit index has an expected correlation of 0.86.

Fig. 3 about here

Since the correlation coefficient is derived from the decorrelation analysis it implies an estimation error. This estimation error is not taken into account in the subsequent analysis of the hedging effectiveness. Actually, we calculate only the hedging effectiveness for an average correlation. The geographical basis risk and the hedging effectiveness of an individual farm can differ from the depicted values. However, there is no systematic over-or underestimation of the results as long as the estimated correlation is unbiased.

III. Results

In Table 3 the expected value, the standard deviation and selected percentiles of the revenue distribution are given for all three scenarios in order to assess the hedging effectiveness of the two rainfall options described above. The situation without and with insurance by a rainfall option is considered for each scenario. Fig. 4 illustrates the revenue distributions for selected scenarios.

Fig. 4 about here

It is apparent first of all that there is no difference between the expected values for the revenue without and with the option. This is because the option price was calculated as a fair premium, therefore the insurance in average "brings as much as it costs". With regard to the hedging effectiveness of an option, the following can be established:

• Scenario 1: When there is no basis risk (site of production in immediate vicinity of reference weather station and deterministic relationship between yield and weather index), farmers can completely eliminate the revenue risk of wheat production by buying a put option on the rainfall sum or rainfall deficit index. This is possible because the payoff of the option is correlated perfectly negatively to the revenue from the wheat production (cf. Fig. 2).

• Scenario 2: When it is taken into consideration that the site of the agricultural production is 39 km away from the reference weather station, the revenue distribution without the option is unchanged in comparison to scenario 1, because the same distribution underlies the rainfall index in Ketzin as that in Berlin-Tempelhof (cf. footnote 6). Nonetheless, the standard deviation of the revenue in wheat production can only be reduced by about 45% using the put option on the rainfall sum index or on the rainfall deficit index. Eventually, there may be cases in which farmers obtain a payoff from the option even though no yield loss could be registered (and vice versa), because the rainfall in Ketzin is different from that in Berlin-Tempelhof. In comparison to the results from scenario 1, it is evident that the risk-reducing effect of the option decreases with increasing distance from the reference weather station.

• Scenario 3: When both the geographical basis risk and a stochastic relationship between yield and rainfall index are realistically taken into consideration, the standard deviation of the revenue in wheat production can only be reduced by 10% by buying the put option on the rainfall sum index. That is to say, the hedging effectiveness of a put option on the best rainfall sum index is nearly completely eroded when the geographical basis risk and the lo- rainfall option on the rainfall deficit index is that the explanatory power of the production function for the wheat yield depending on the rainfall deficit index is much higher than that depending on the rainfall sum index. The reduction of the hedging effectiveness of both options, in comparison to scenario 2, is to be attributed to the additional consideration of the local basis risk.

IV. Conclusions and outlook

The model calculations have shown that by using rainfall options a very considerable riskreducing effect can be obtained when the reference weather station is located in the immediate vicinity of the site of production and when there is a very close relationship between yield and rainfall index. That is, while not being able to avoid climate change on a farm-level, such instruments could generate valuable support for those farming under risky conditions.

However, the model calculations also demonstrated that the basis risk has an extraordinarily high influence on the hedging effectiveness of rainfall options. When the site of agricultural production is only at a relatively small distance from the nearest reference weather station (e.g.

39 km in the application available here), the hedging effectiveness is considerably reduced. If, in addition, an index which only shows a small correlation to the yield underlies the option (as is established here between the wheat yield and the rainfall sum index, which is often suggested in literature), the hedging effectiveness decreases even further.

One could be tempted to conclude from a low hedging effectiveness that the farmers' potential demand would be low. However, such an interpretation would disregard the difference between effectiveness and efficiency. The potential demand for a weather derivative results from the ratio of its costs and its benefits. Derivatives which are based on simple indices and which display low effectiveness lead to a lower willingness-to-pay on the part of the farmers. However, as a result of their lower transaction costs they can also be provided at lower prices. We can, therefore, not a priori conclude that weather derivatives with a low hedging effectiveness are "inapplicable" or that they do not have a trading potential.

However, if potential sellers of rainfall options wish to increase the hedging effectiveness, they should permit a dense network of weather stations as reference points and a widely diversified spectrum of differently specified weather derivatives. Of course, it is inconceivable that derivatives will be offered for every weather station. The demand for products of this kind would certainly be too low. A compromise could be to select the average derived from the values of a There is a further need for research with regard to the specification of the payoff function of an option. Rainfall sum indices dominating the scientific discussion until now are not sufficiently target-orientated in the opinion of many producers. An alternative suggestion was made here in the form of a rainfall deficit index. From an agronomic viewpoint, however, it could also be advisable to incorporate not only the rainfall but also the temperature, the wind etc. in the index underlying the option. In this way, for instance, allowance could be made for a situation in which low rainfall at high temperatures would lead to higher yield losses than at lower temperatures. Another task of research concerns the question which was consciously avoided here, namely of valuing weather derivatives.

  grain yields have fluctuated similarly, due to the sandy soil possessing little water-storing capacity and a lack of artificial irrigation facilities. Currently there exists no opportunity of insuring against yield losses caused by rainfall. During the drought years 2000 and 2003, disaster relief was even granted by the government on account of the extreme harvest failures, in order to protect farms against insolvency. Of course, such government supports are not always be guaranteed. Therefore, there is a pronounced interest among affected farmers for a routine form of hedging weather-related risks.

  Fig. 1 about here

  data measured at the weather station in Berlin-Tempelhof, the rainfall indices described in (1) and (2) for the years 1993 between the rainfall sum or rainfall deficit index observed in Berlin-Tempelhof b I and the wheat yield observed for the farm in Ketzin b Q ~, a linear-limitational (Leontief) production function seems most suitable: 2 makes it clear that the yield at the farm location in Ketzin is meant, whereas the weather index is related to weather data measured in Berlin-Tempelhof ( b I instead of b I ~). 0 a , 1 a , 2 a and 3 a describe the parameters of the production function to be estimated. When 0 1 > a , then drought-related yield losses are to be expected for the rainfall index below 2 a mm. If values for the rainfall index are above 2 a mm the expected wheat yield corresponds to 3 a dt/ha. b ε indicates the normally distributed error term with a standard deviation of ε σ . It should be noted that this error term expresses both the local basis risk and the geographical basis risk: on the one hand, the yield-explaining weather index only refers to rainfall in a specific accumulation period. On the other hand, the production function is determined on the basis of yield data at the site of production and the weather event at the reference weather station.

  4) At expiry time T the put option generates a positive payoff T F when the rainfall index T I is below the strike level S . If the strike level is above the index, the payoff is zero. The tick size V monetizes the positive difference between S and T I . One put option relates to the cumulative index C T I which is measured in June 2007 at the weather station at Berlin-Tempelhof. The second put option refers to the rainfall deficit index D T I between the 7-day rainfall measured at the weather station in Berlin-Tempelhof and 7.4 mm cumulated during the period April to June 2007. Farmers can obtain each of the two options in July 2006.

  yield-reducing rainfall. However, there is no payoff if the weather is suitable for yield-formation.

  the rainfall index in Ketzin T I ~ is derived from the value for the rainfall index in Berlin-Tempelhof T I while taking a correlation yet to be determined into consideration (see below).

  lin and Brandenburg from 1983 to 2003, all located within a 100 km radius of Berlin-Tempelhof and relatively uniformly distributed over the area. The correlation coefficients j i, ρ between the values for the rainfall index at the weather stations i and j are determined. Then the distances j i d , between the individual weather stations are calculated. On the basis of the correlation coefficients and each respective distance a so-called decorrelation function can be estimated.

  suggests the following non-linear decorrelation function for modelling spatial correlation for rainfall in Europe: 6

  cal basis risk are considered; even though the option was explicitly tailored to the revenue function of the farm. Using the put option on the rainfall deficit index results in a 30% reduction of the standard deviation. The reason for the greater hedging effectiveness of the

  several weather stations as a weather variable underlying the option. The recommendation for offering differently specified weather derivatives affects the derivative type on the one hand (cf. footnote 3) and the design of the index, the tick size and the strike level on the other hand. Many reference weather stations and weather derivatives designed in very different ways result in a fragmentation of the demand.

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 1. Elements in a farm-specific analysis of the hedging effectiveness of weather derivatives

Table 3 about here

 3

Table 1 . Estimates for different production functions* Rainfall sum index Rainfall deficit index

 1 The t-values are given in parentheses. The critical t-value is 1.81 or 1.37 at a probability of error of 5 or 10%.

	Period	June Jan. -	June April -	June May -	June	June Jan. -	June April -	June April -	June April -	June
	x	181	91	61	30	-	-	-	-	-
	z	-	-	-	-	26	19	13	11	4
	s	-	-	-	-	7	5	7	9	7
	y min	-	-	-	-	7.5	2.9	7.4	22.1	7.5
	a 0	0	0	50.9	54.9	88.5	137.9	107.8	87.8	81.8
		(0.00)	(0.00)	(4.91)	(8.10)	(6.84)	(13.17)	(8.81)	(4.96)	(15.67)
	a 1	0.28	0.58	0.10	0.14	0.38	3.73	1.35	0.22	1.98
		(5.23)	(7.23)	(1.20)	(1.38)	(2.06)	(6.40)	(3.62)	(1.45)	(3.81)
	a 2	233.1	109.6 220.1 144.3	-39.8	-19.0	-29.4	-53.6	-7.1
	a 3	64.6	64.1	73.7	75.5	73.4	67.1	68.0	76.0	67.7
		(1.11)	(3.88)	(1.37)	(2.68)	(2.08)	(2.38)	(2.15)	(1.91)	(2.80)
	σ ε	10.2	11.0	11.1	10.9	9.9	8.7	8.7	10.8	9.0
	R 2	0.10	0.09	0.13	0.15	0.30	0.47	0.48	0.17	0.43
	*

Table 2 . Specification of rainfall options under consideration

 2

			Option 1	Option 2
		Designation	Cumulative rainfall index	Rainfall deficit index
	Weather index	Reference point Accumulation period June Rainfall data at the weather sta-tion in Berlin-Tempelhof Calculation	Rainfall data at the weather sta-tion in Berlin-Tempelhof April -June

Page 24 of 25 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

		Submitted Manuscript
	Option type	(European) put	(European) put
	Strike level S	144.3 mm	-29.4 mm
	Tick size V	1.4 €/index point	13.5 €/index point
	Maturity ∆t Expiry time T Payoff F T	1 year (01.07.2006 to 30.06.2007) 2007 ( ) 4 . 1 0 , 3 . 144 max ⋅ -C T I F o r	1 year (01.07.2006 to 30.06.2007) 2007 ( ) 5 . 13 0 , 4 . 29 max ⋅ --D T I
		P
		e
		e r
		R
		e
		v i e
			w

This definition may appear unusual since the rainfall deficit index will take negative values. However, the definition is convenient for the present application because then the relationship between yield and rainfall deficit index is similar to that between yield and rainfall sum index.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The de-correlation function is invariant regarding direction. Thus, topographical differences potentially influencing precipitation are neglected. In Brandenburg, topographical conditions play to the assumption of a correlation independent of location and direction.

< G3 -Corporate Finance and Governance < G -Financial Economics, Q12 -Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets < Q1 -Agriculture < Q -Agricultural and Natural Resource Economics


Jani Beko

Timotej Jagric
email: timotej.jagric@uni-mb.si.

DEMAND MODELS FOR DIRECT MAIL AND PERIODICALS DELIVERY SERVICES: RESULTS FOR A TRANSITION ECONOMY

Keywords: C22 -Time-Series Models < C2 -Econometric elasticity of demand, direct mail and periodicals market, demand factors, estimation

This paper examines the demand for services of the Slovenian national postal operator for the direct mail and periodicals market and separately for the direct mail market. The main factors of the demand are found to be various price indicators with respect to individual market, two income series and the variable of economic environment. The results of our empirical analysis suggest that the price elasticity of demand on both markets is below zero.

The autonomy in price increases is limited due to positive cross-price elasticity of demand for direct mail with regard to price fluctuations for TV commercials. Substitution effects on the direct mail market are even more evident with regard to price fluctuations for advertisements in magazines and daily papers. An additional finding is that the demand on both markets varies seasonally in all models estimated by us. Finally, coefficients of income elasticity of demand for direct mail services show that the total number of mail deliveries on the direct mail market increases faster than the retail revenue in real terms.

INTRODUCTION

Although national postal operators possess the attributes of a natural monopoly and are subject to state control, they are exposed to increasing competition pressure as a result of the current process of mail market deregulation and the liberalisation of network industries (see, for example, [START_REF] Wik | Main developments in the postal sector[END_REF][START_REF] Jung | Competition and investment in telecommunications[END_REF]. Competition between mail service providers is increasingly more pronounced as far as the price and the quality (timeliness, reliability and adaptability) of the existing services are concerned [START_REF] Albon | Some observations on the efficiency of British postal pricing[END_REF][START_REF] Filippini | Economies of scale and cost efficiency in the postal services: empirical evidence from Switzerland[END_REF][START_REF] Franses | Estimating the stock of postwar Dutch postal stamps[END_REF] and is even increased through the emergence of new modes of communication that are frequently very attractive alternatives to traditional mail services supplied by the national postal operators [START_REF] Goel | Demand elasticities for Internet services[END_REF].

Bearing in mind the dynamics of national (and international) mail markets, it is understandable that there is a need for as precise as possible knowledge of demand factors. Extensive efforts have been invested in estimations of demand functions for mail. Collected empirical evidence is thus considerable, but rather fragmented according to market segments and limited to mail markets of developed economies. Valid estimations of demand functions exist separately for first and second class inland letter traffic for Great Britain [START_REF] Cuthbertson | An econometric study of the demand for first and second class inland letter services[END_REF][START_REF] Nankervis | Disaggregated letter traffic demand in the UK, in Postal and Delivery Services: Pricing, Productivity, Regulation and Strategy[END_REF], Finland [START_REF] Nikali | Demand models for letter mail and its substitutes: results from Finland, in Managing Change in the Postal and Delivery Industries[END_REF] and France [START_REF] Rycke | Mail use by firms[END_REF], for inland letter traffic for Great Britain [START_REF] Nankervis | Aggregate letter traffic demand in the United Kingdom and the economy, in Commercialization of Postal and Delivery Services: National and International Perspectives[END_REF][START_REF] Nankervis | How important have price and quality of services been to mail volume growth[END_REF] and Portugal [START_REF] Pimenta | Demand for letters in Portugal, in Emerging Competition in Postal and Delivery Services[END_REF], for direct mail services for Portugal [START_REF] Santos | The demand for direct mail in Portugal, in Future Directions in Postal Reform[END_REF], for four groups of addressed mail, without separately considering direct mail, for France [START_REF] Cazals | Econometrics of mail demand, a comparison between crosssection and dynamic data[END_REF], for postal delivery services at the household level in the United States [START_REF] Wolak | Changes in the household-level demand for postal delivery services from 1986 to 1994[END_REF], and estimation of demand functions for parcel services in the United States [START_REF] Nissen | Price elasticity of the demand for parcel post mail[END_REF]. Results of empirical studies depend not only on differences in definitions of estimated market segments but also on whether the studies concern applications of dynamic models based on aggregate time series or microeconomic models applied to cross-section data (see [START_REF] Cazals | Econometrics of mail demand, a comparison between crosssection and dynamic data[END_REF]. Being aware of the risks of generalizing empirical findings, we can nevertheless series applied to the direct mail and periodicals market segment and the direct mail market segment. To the best of our knowledge there are no studies on elasticities of demand for mail services for (advanced) transition economies. Furthermore, as the overview of literature above testifies, even studies focusing on the demand factors of direct mail services in individual developed country are rather rare.

Post of Slovenia first offered the delivery of unaddressed direct mail in 1997, while the delivery of printed matter and other types of addressed mail had been offered already before that. In 2002, the direct mail and periodicals services were officially declassified as reserved postal services in Slovenia. Delivery of direct mail and other related matter have become the most dynamic component of postal services provided by the Slovenian postal operator in recent years. In 2005, revenues from direct mail, periodicals and inserts (which amount to a good fifth of revenues from postal services of Post of Slovenia) increased by 16% compared to the year before and were higher than revenues from letter and parcel services as well as express mail. In the same period, an above-average increase in the number of services related to the delivery of addressed and partially addressed direct mail (a 58% increase), unaddressed periodicals and inserts (a 28% increase), and unaddressed direct mail (a 10% increase) was recorded. As a In addition to the introduction, the paper consists of four further chapters. Chapter two presents a range of available data sets belonging to potentially relevant explanatory variables in models of demand in terms of content criteria and the selection procedure for series actually used in this estimation. Chapter three explains the specifications of functions of demand for direct mail and periodicals delivery services and for direct mail delivery services. Chapter four includes testing of selected demand models and an explanation of results obtained. The paper ends with a presentation of key findings.

FACTORS AFFECTING DEMAND FOR DIRECT MAIL AND PERIODICALS DELIVERY SERVICES IN SLOVENIA

As a rule, five groups of explanatory variables, which can be divided into two sets in terms of content, are included in the design of demand functions for postal services in various segments and at various levels of the aggregation. The selection and grouping of variables were guided by similar studies for developed economies [START_REF] Cuthbertson | An econometric study of the demand for first and second class inland letter services[END_REF] , 2001;[START_REF] Cazals | Econometrics of mail demand, a comparison between crosssection and dynamic data[END_REF][START_REF] Nankervis | Disaggregated letter traffic demand in the UK, in Postal and Delivery Services: Pricing, Productivity, Regulation and Strategy[END_REF].

In terms of content, the first set includes variables trying to encompass socio-economic demand Estimated demand equations are based on aggregate data sets, since the dependent variable captures the total number of mail deliveries received in two service segments. The first segment, hereinafter called the direct mail and periodicals market (DMP), consists of direct mail (addressed, partially addressed and unaddressed mail) together with periodicals and respective inserts (addressed, partially addressed and unaddressed periodicals and inserts in periodicals).

The other, narrower segment referred to as the direct mail market (DM) consists of addressed direct mail, unaddressed direct mail not including unaddressed periodicals, and inserts in periodicals. The definition of only two types of dependent variables is unavoidable because a more detailed disaggregation along the above mentioned mail segments, which should of course be methodologically comparable to reference calculations of price variables, is not available, in particular not for the generation of sufficiently long minimum required data sets. Namely, Post The introduction of qualitative variables requires a possibility to monitor (empirically noted) impact of non-price competition factors on the structure of the market as a unit, that is on the volume of deliveries by individual mail subgroups. Direct mail customers place much impact on the availability (accessibility) of mail recipients in addition to reliable mail services. Thus companies or postal operators with the largest distribution and data networks enjoy comparative advantage in attracting customers. For the direct mail and periodicals segment and the direct mail segment, the Slovenian postal operator normally performs delivery within the time required by customers or within two days after the day of mailing. In addition, direct mail delivery is an upgrade of the basic mail service. Thus all variables included in the second content-related set in Chapter 2 are excluded from the range of theoretically appropriate (direct) explanatory variables.

In conducting econometric assessment of variables we can rely on socio-economic variables, having a possibility to choose among various time series (Table 1).

<TABLE 1 ABOUT HERE>

In generating average nominal prices for direct mail and periodicals services, we used sampling data on mailed items (direct mail and periodicals and separately direct mail) to calculate the average weight, which was then multiplied by the rate from the price list for the particular weight valid in a particular period. For the calculation of discount prices, their amount was deducted from financial statements on revenues from services concerned. advertising media could be a competitor to direct mail, yet often their relationship can be complementary. Complementarity or substitutionality between various media depends to a large degree (at least at the level of customers) on content-related and technical characteristics of advertising messages sent to consumers. In addition to two pairs of price variables for direct mail and periodicals and for direct mail, three price variables for alternative media can be included. In all cases they have been converted to the number of advertising messages communicated, that is the average nominal price for TV commercials as listed in TV operators' price lists, the average nominal price for advertisements in magazines as listed in publishers' price lists, and the average nominal price for advertisements in daily papers as listed in publishers' price lists. Average prices of marketing messages in all three media were also calculated according to the number of seconds for commercial broadcasts on TV or square meters in printed media, respectively, but thus defined variables did not prove as statistically significant during testing.

It should be underlined that comparable price series for other advertising media, e.g. billboards, cinema, Internet, and radio, were not available. Series allowing for the exact amount of discounts to be contained in data on advertising prices were also unavailable.

Because all price series are expressed in nominal terms it is appropriate to convert them into a real category. We can choose from among three deflators: consumer price index (CPI), communications price index (PC), and services price index (PS). Content-wise, the latter is placed between CPI, which is the widest category, and PC, which is the most narrow price category (regarding the content of the paper). The communications price index covers price fluctuations in prices for mail and telephone services and related products. The importance of purchasing power for explaining the dynamics of direct mail (and periodicals) delivery services is expectedly different from its importance in the case of traditional letter mail services. Direct mail is a service targeted at the business sector; therefore it involves derived demand. The demand does not directly reflect consumers' preferences for this particular service, but is dependent on preferences of end users, that is buyers of products produced by the direct mail customer (direct user). We thus differentiate between the impact of service users' income (the demand of companies for direct mail services is dependent on the dynamics of sales, available advertising and marketing budgets, maturity of sales markets, etc.)

and the income impact resulting from the secondary demand chain. Between January 2000 and September 2006, 95.7% of all direct mail was delivered to households and the rest to companies according to the estimation of Post of Slovenia. The same is true for periodicals.

The set of income variables offers a choice between domestic consumption in real terms variables can be used due to the selected methodology for estimating functional relationships.

Taking into account content-related relevance and constraints resulting from the method for elasticity estimations used, a selection from among available time series was performed. The entire set of available data series can be narrowed to the set of usable series (Table 2). The series of this set meet content-related and methodological criteria, in addition to which the following technical characteristics of the usable series must be met: (1) number of observations;

( Taking into account the above mentioned criteria, we can perform the selection of time series on the basis of data from Table 2. Such time series meet content-related and methodological criteria as well as technical characteristics and are thus appropriate for the estimation of demand functions for direct mail and periodicals delivery services and direct mail delivery services. The string of time series appropriate for econometric estimation available at the monthly level without structural breaks and identified as I(0) (at the 5% significance level at least) is defined in the form of base coefficients (1999M8=1; in this way the influence of the unit of measure was at least partly removed) and marked in Table 2 with sign "*".

SPECIFICATION OF DEMAND FUNCTIONS FOR DIRECT MAIL AND PERIODICALS DELIVERY SERVICES

It is particularly important to assure sufficient model sensitivity in estimating functions. Thus a model will be sufficiently sensitive to demand analysis if the economic mechanism characteristics that influence demand for mail services of interest in the actual economic process will be explicitly present in the model structure specification. The sensitivity of the model is Many sophisticated econometric techniques like co-integration analysis have been applied to the analysis of demand functions in different areas (see, for example, the electricity demand forecasting in [START_REF] Engle | Merging short and long run forecasts: an application of seasonal cointegration to monthly electricity sales forecasting[END_REF]. The technique of co-integration (see [START_REF] Engle | Cointegration and error correction: representation, estimation and testing[END_REF] and error correction (see Hendry et al., 1984, among others) in the process of estimating demand functions avoids problems of spurious relationships that can bias the results and provides a convenient and rigorous way to discern between short-run and long-run effects of pricing policies. There are, however, some important limitations if one chooses such an approach. One important drawback of this methodology is the lack of power of the unit root tests needed to construct the co-integrating regressions. But more important in our case is that the time series should be tested for seasonal unit roots in order to correctly apply co-integration analysis. Since we use monthly time series, the seasonally component is probably present and significant. If we would ignore this fact the results of unit root test would be misleading.

A number of seasonal unit root tests have been proposed for the case of monthly data [START_REF] Franses | Seasonality, nonstationarity and forecasting of monthly time series[END_REF][START_REF] Beaulieu | Seasonal unit roots in aggregate U.S. data[END_REF] as an extension to the one suggested by [START_REF] Hylleberg | Seasonal integration and cointegration[END_REF]. A characteristic of seasonal unit root tests is that they exhibit poor power performance in small samples and that the power deteriorates as the number of unit roots under examination increases. For example, in a simple test regression with no deterministic variables, the HEGY test procedure [START_REF] Hylleberg | Seasonal integration and cointegration[END_REF] in the quarterly context requires the estimation of four parameters, whereas in a monthly context this number increases to twelve. In addition, the and the associated computational burden non-negligible. In special cases these problems can be partially avoided by applying method proposed by [START_REF] Rodrigues | A sequential approach to testing seasonal unit roots in high frequency data[END_REF]. In our case the sample is small even if we use monthly data (data is available for less then seven years, 1999M8-2006M4). If we would be forced to use quarterly data, the results of unit root test would definitely exhibit poor power performance.

Considering the limitations presented above, we decided to use standard ordinary least square regression (OLS) and to support the estimated functions by a battery of specification tests.

Following the empirical analyses [START_REF] Nikali | Demand models for letter mail and its substitutes: results from Finland, in Managing Change in the Postal and Delivery Industries[END_REF][START_REF] Pimenta | Demand for letters in Portugal, in Emerging Competition in Postal and Delivery Services[END_REF][START_REF] Nankervis | Disaggregated letter traffic demand in the UK, in Postal and Delivery Services: Pricing, Productivity, Regulation and Strategy[END_REF] we employed the exponential specification of the population function of demand for direct mail and periodicals delivery services and separately for the demand for direct mail delivery services. Due to the fact that we decided to use OLS for the estimation of the parameters, all exponential functions are formulated in double-log form. Theoretical specifications of population regression equations in four versions are given in the continuation.

Equation 1: Model of demand for the direct mail and periodicals market using dummy variables

ESTIMATION RESULTS

To estimate the parameters of population functions specified in Chapter 3 we used the OLS method. In order to meet the assumptions of this method, we run a series of test on each methods can negatively impact characteristics of time series [START_REF] Stock | New indexes of coincident and leading economic indicators[END_REF][START_REF] Jagric | A nonlinear approach to forecasting with leading economic indicators[END_REF] and can cause a change of a phase in the spectrum, which is known as phase delay [START_REF] Jagric | A nonlinear approach to forecasting with leading economic indicators[END_REF][START_REF] Castro | The consequences of seasonal adjustment for periodic autoregressive processes[END_REF][START_REF] Mir | Seasonal adjustment and the detection of business cycle phases[END_REF]. In the continuation of the analysis we therefore decided for a more conservative approach based on the identification of seasonal influences within the basic regression model using dummy varibles. Further, the verification of characteristics of dummy variables showed that the eleventh month was always statistically significant and robust (eliminating sixty-six versions). Eighteen versions of regression equations can be removed because the number of work days series could not be included as an additional explanatory variable into any of the specifications defined (atypical parameter), while further twelve versions of equations can be excluded because the real net wages paid variable is not statistically significant in specified models without delayed effect.

Hence eleven functions remain for each market segment. As we wish to estimate the influence of all time series by all types of deflators on both market segments separately but in a pair of comparable specifications on both segments, the following ten estimated specifications can be included in the final analysis, of which five specifications for the direct mail and periodicals market segment (E1-E5 represent notations of sample regression models -see The results of parameter estimations derived from models E1-E10 are shown under heading A of Table 3 andTable 4. The following findings can be reported. Point estimates of price elasticity of demand on the direct mail and periodicals market amount to -0.9 (equations E1-E5). If the direct mail market only is taken into account, estimates of price elasticity of demand are slightly lower (in the absolute sense) yet highly synchronized again at -0.7 (equations E6-E10). It can be inferred from calculations that a one-percent increase in real prices of direct mail and periodicals and of direct mail, discounts taken into account, will lead to a 0.90 percent decrease in the volume of demand on the direct mail and periodicals market and a 0.7 percent decrease in the volume of demand on the direct mail market on the average.

<TABLE 3 ABOUT HERE>

In equations E2 and E4 partial regression coefficients expressing the impact of the average real price of TV commercials on the volume of demand on the direct mail and periodicals segment are statistically insignificant. From analogue estimates of specifications on the direct mail market segment (equations E7 and E9) it can be inferred that a 1 percent increase in the average real price of TV commercials results in a 0.2 percent increase in demand for direct mail delivery services.

<TABLE 4 ABOUT HERE>

With regard to changes in prices of magazine advertisements, estimates of cross-price elasticity of demand on the direct mail and periodicals market as well as on the direct mail market are reached at the 5 percent significance level at least, using all three kinds of price deflators. It can be inferred from the results that a 1 percent increase in average real prices of magazine advertisements will lead to a 0.4-0.5 percent increase in the volume of demand for services on the direct mail and periodicals market and on the direct mail market. Regarding changes in prices of advertisements in daily papers, no significant deviations occur in connection with estimates of cross-price elasticity of demand when those estimates are compared according to various price deflators or both markets analyzed. The results can lead to a conclusion that the number of mail pieces on the direct mail and periodicals market and on the direct mail market will increase by 0.2-0.3 percent in case of a 1 percent increase in the average real price of advertisements in daily papers.

Estimates of dependence of service trends on the direct mail and periodicals market and on the direct mail market from changes in real net wages paid are given with at least 5 percent level of significance of the test. For this variable, partial regression coefficients in equations E1-E10 indicate that the total number of mail pieces on the direct mail and periodicals market and on the direct mail market will increase by 0.5 percent and 0.8 percent at the most, respectively, if real net wages paid increase by 1 percent, with other conditions unchanged.

In contrast to the estimates of the income parameter measured with retail revenue in real terms in equations E1-E5, it can be stated that the demand for services on the direct mail market is elastic with respect to income (equations E6-E10). Thus an increase in retail revenue in real terms by 1 percent will on the average lead to a 1.2 percent increase in the total number of mail pieces on the direct mail market. Estimates of partial regression coefficients are highly statistically significant in all ten functions.

In case of the parameter from the group of the economic environment variables it can be inferred that a 10 percent increase in industrial production will on the average increase activities on the direct mail and periodicals market segment and on the direct mail market segment by 9 percent (equations E1, E3, E5, E6, E8) or by 10 percent (equations E2, E4, E10), measured with the total number of mail pieces sent. 3 andTable 4).

It shows that all estimated equations have a satisfactory explanatory power. 95 and 91 percent, respectively, of variance in changes in the number of pieces mailed on the direct mail and periodicals market segment and on the direct mail market segment can be explained by a combination of variables included in ten model specifications. On the basis of the results of the Durbin-Watson d-statistics it has also been stated (at the 1 percent significance level) that none of the estimated equations shows a problem of autocorrelation of residuals, which is also supported by the values of Ljung-Box Q-statistics (detailed test results for equations E1-E10 can be obtained from the authors). The list of econometric tests in Table 3 andTable 4 also displays a test of residuals distribution for equations selected. The results of the Jarque-Bera test performed lead to a conclusion on a normal distribution of residuals of all regression models. For all estimated elasticity coefficients from equations E1-E10 it has been stated that they are structurally stable at the satisfactory level of the test significance ( =0.05).

The identified own-price inelasticity of demand for both service segments makes it possible for the Slovenian postal operator to maintain a positive marginal revenue in spite of increases in prices for the delivery of direct mail and periodicals and prices for direct mail delivery. Such price response of demand reflects current advantages of the national postal operator, as its mail network already put in place and a wide data base enable a more competitive response to market needs in terms of costs and time. It is therefore not surprising that business success of (potential) direct mail customers (real revenue in retail trade) greatly influences the dynamics of those services of the national postal operator. Thus Post of Slovenia has a definite comparative advantage over specialized companies engaging in the transfer of unaddressed mail, newspaper publishers and publishing companies delivering unaddressed commercial inserts in their own publications, and companies themselves delivering their unaddressed mail. In the light of a growing importance of marketing communications in business environments (influence of a wider economic environment) increased demand for all tools of marketing communication with final users, including direct mail delivery services, can be expected in the future. Technological factors (expansion of electronic communications), innovative marketing strategies of companies (sales promotion on the Internet and by electronic mail), and changes in relative prices will determine the share of individual communication channels on the market [START_REF] Goel | Demand elasticities for Internet services[END_REF].

CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH

The paper presents evidence on elasticities of demand for services of Post of Slovenia on the basis of a range of available variables separately for two market segments: the direct mail and periodicals market and the direct mail market. The outcomes of the analysis can be summarized in three conclusions. First, the value of price elasticity of demand is below zero for both markets. Taking into account estimates of demand functions, we can infer that in case of an increase in the average real price of direct mail and periodicals delivery as well as direct mail delivery the percentage of decrease in the number of mail pieces delivered on either of the market segments analyzed will be smaller than the percentage of the reference price increase on the markets. Reported inelasticity of demand suggests that the revenue of the Slovenian postal Third, coefficients of income elasticity of demand for direct mail services defined by retail revenue in real terms show that the total number of mail deliveries on the direct mail market increases faster than the real retail revenue. Of all explanatory variables, the latter most strongly influences changes in the quantity of direct mail.

Since the elasticity coefficients presented are a result of estimates of aggregate functions of demand, there are two potential avenues to expand the current analysis in the future. The range of time series presented in this article should be tested on the error correction model, whilst coefficients of own-price and cross-price elasticity obtained with time series should be compared with estimates of demand functions using cross-section data for a sample of companies that are customers of direct mail services of Post of Slovenia. Both empirical approaches would add additional insights in to the functioning of the Slovenian direct mail market, however more time is needed in order to have sufficient amount of data for the required estimation procedures. Note: N -number of observations (all time series are on monthly frequency), S.b. -structural brake. For easier understanding of the specification of demand equations for direct mail and periodicals delivery services and direct mail delivery services, designations were ascribed to series used as functional variables. The following signs were used: Q DMP -volume of demand on the direct mail and periodicals market, Q DM -volume of demand on the direct mail market, P DMP -price of direct mail and periodicals,

  of functions of mail demand indicate at least three facts. First, price elasticity of mail demand is normally inelastic (or limited), whereby demand sensitivity to changes in (relative) prices increases across time. Second, substitution effects are often identified on mail markets but vary in significance and duration. Third, the impact of income on change in demand for various types of mail services cannot be neglected. The present paper is part of research conducted during the proceedings of the Competition Protection Office of the Republic of Slovenia against the Slovenian national postal operator, Posta Slovenije d.o.o. (Post of Slovenia), for alleged abuse of its dominant position on the unaddressed direct mail market. The aim of this paper is to present estimations of demand functions for mail services of the Post of Slovenia in inland postal traffic by analyzing time

  2005 the share of unaddressed direct mail, unaddressed periodicals and inserts in the total number of all postal services of Post of Slovenia increased by three percentage points in comparison with the previous year and reached51% (Post of Slovenia, 2006). The above described boost in the volume of direct mail services benefited significantly from favorable economic trends (for example, in the 2000-2005 period the average annual real growth rate of Slovenia's GDP amounted to 3.6%) triggering advertising and marketing activities, and in particular from bustling trade activities. Thus, in the 2000-2005 period, the average annual real growth rate of value added in wholesale and retail trade, and in maintenance and repair of motor vehicles amounted to 3.1%. According to the estimations of Post of Slovenia, in the same period 95% of clients for direct mail and periodicals delivery services were in the trade sector. The rest of businesses demanding those services were in the financial intermediation, industry, and transport, warehousing and distribution sectors.

  factors. Five groups of variables can be identified: (1) price variables; (2) income variables; (3) economic environment variables; (4) seasonal factors; and (5) other socio-economic factors. The other set in terms of content includes two groups of variables expressing quality components of demand factors: (1) timeliness (speed) of mail transport or delivery, and (2) range of services complementing the base service (mail transport).The actual selection of explanatory variables used from among the range of those recommended in terms of content and theory depends on the selected methodological procedure for the estimation of parameters in the demand equation for postal services, determination of markets or postal services observed, level of aggregation of demand functions, and actually available statistics.

  only disaggregated annual data on direct mail and periodicals subsegments from 1997 onwards.

  representing the real gross domestic product excluding the net exports of goods and services, registered real household income, real net wages paid, domestic revenue in mining (C) and manufacturing (D) in real terms, domestic revenue in manufacturing (D) in real terms, and revenue in retail trade (excluding motor fuel sales) in real terms. The registered real household income variable includes real net wages, non-wage employment-related benefits in real terms and real transfer receipts. Data on net revenue, in real terms, from sales to 50 largest customers of direct mail services of Post of Slovenia are available at annual level only.Four indicators are given for economic environment variables: gross domestic product in real terms, economic activity in the mining sector (C), manufacturing (D) and electricity, gas and water supply (E), economic activity in manufacturing industries (D), and the number of existing and new housing units. Consumer price index was used for deflating all nominal income series and nominal economic environment series. An a priori choice between the stated income indices and economic environment indices is not possible, thus the final choice of variables will be made on the basis of objective criteria of the econometric analysis.

  of demand for mail services it is appropriate to assume the influence of seasonal factors. In estimating elasticity, the selected methodological procedure can be used to include seasonal influence in two ways: (1) by introducing dummy variables or (2) by seasonally adjusting the time series (multiplicative method X-12).Other socio-economic factors are included by the following data: number of households in houses and multiunit buildings, number of "No Unaddressed Direct Mail" stickers, number of P.O. Box holders and users, number of P.O. Boxes for distribution, and number of work days in a certain time period. Because full evidence for the first four data series is available at the annual level only, nothing but the last series from the above listed other socio-economic

  the extent to which the aggregation of economic variables is such that variations in demand for mail services concerned are sufficiently clearly pronounced in statistical data on individual economic variables. In addition, the length of the period during which the model is estimated also influences the accuracy of the model, because the characteristics of the economic and technical structure and norms of behavior contributing to the shaping of demand for direct mail and periodicals services and direct mail services, respectively, must be significantly present in the period concerned.

  seasonal unit root tests is more involved than in the quarterly case

  regression model. We tested the stationarity of time series (ADF test with intercept and trend, time lag selection based on the Schwarz information riterion -SIC), distribution of residuals (JB test of normality), autocorrelation (Q-statistics from first to twelfth order, DW-statistics), significance of coefficients (t-statistics), stability/specification of regression equations (inclusion of different deflators, Cusum and Cusum Q test, White test), and the explanatory power (adj. R 2 and F test). All calculations and tests of models were performed with the aid of Eviews 4.0 software package.When parallel estimations of the direct mail and periodicals market and separately of the direct mail market, number of time series versions in a particular group of variables, and two base approaches to including the seasonal component are considered, the total number of regression equation versions that can be estimated is one hundred sixty-four. Estimated regression equations with seasonally adjusted data show statistically insignificant parameters and low explanatory power (adjusted coefficients of determination, information criteria), (forty-six versions). Research in the field of time series analysis also indicates that seasonal adjustment

  explanatory power of estimated regression equations can be made on the basis of the value for adjusted coefficients of determination (heading B in Table

  hand estimations of cross-price elasticity on both market segments show a distinctive importance of indirect competition (including, in the broadest sense of the word, all non-postal channels of marketing communication) that Post of Slovenia faces. TV commercials and advertisements in printed media (magazines and daily papers) compete with direct mail services offered by the Slovenian postal operator. There is substitution among various forms of accessing customers. On the basis of their business objectives and according to the prices of marketing communication services offered, companies optimize their marketing budgets.

  both market segments as a result of increases in the average real prices of direct mail and periodicals delivery and the average real price increases in direct mail delivery.Second, autonomy in price increases is limited, since the analysis of demand functions for direct mail shows positive cross-price elasticity of demand with regard to price fluctuations for TV commercials. Substitution effects on the direct mail market are even more clearly expressed with regard to price fluctuations for advertisements in magazines and daily papers. Although this concerns exploratory results, they indicate competition pressures faced by the direct mail market segment. The efficiency of increases in prices for mail deliveries on the direct mail and periodicals market segment by the Slovenian postal operator is also limited, since the estimates of cross-price elasticity show that placements of advertisements in magazines and daily papers are competitive with direct mail and periodicals delivery services.

  set of available data series has been compiled using the data of Post of Slovenia, Mediana, Statistical Office of the Republic of Slovenia, and the Bank of Slovenia.

P

  DM -price of direct mail, P -price of advertisements and commercials, I -revenue, EE -economic environment and O -other socio-economic variables. Because several time series are available for certain variables, numerical designations were added. Sign "*" indicates variables, which are selected for final models. All time series marked with sign "*" include in final models 81 observations and cover the time period 1999M8-2006M4.

  First, with the exception of the interpolation of the total number of housing units generated from quarterly data, all data series have originally been obtained at monthly intervals. Second, it is recommendable to operate with the largest possible data sample, as there are five groups of explanatory variables: two types of price variables, income variables, economic environment variables, and other economic factors variables. If we used quarterly data, only three or four observations for each group of variables, respectively, would be available. This would cause the effect of memorizing the data in the model instead of model learning. And third, many tests used in this research are asymptotic in nature, which means that the reliability of statistic inference increases with the size of the sample. The requirement that time series must not contain structural breaks is coupled with the requirement that time series should be stationary, which prevents the possibility for spurious regression.

	10
	F o r
	P
	e
	e r
	R e v
	i e
	w
	<TABLE 2 ABOUT HERE>
	Because of structural breaks in average discount direct mail prices in real terms and the length
	of the registered real household income series and the real net wages paid series, a new data

2) frequency of the time series (monthly, quarterly); and (3) structural breaks in recording data for individual series. period has been defined to balance the data base. Consequently, 81 observations at the monthly level and 26 at the quarterly level are available for the 1999M8-2006M4 period. In the continuation we based the estimation of functions on monthly data series for several reasons.

P

  ,cth price variable for magazine advertisements in period t where c=4, 5, 6. ,dth price variable for advertisements in daily papers in period t where d=7, 8, 9.

				13 14
	t PSA , -cth price variable for magazine advertisements in period t where c=4, 5, 6; d t c
	t 3 -real net wages paid in period t, I , (seasonally adjusted),
	t 6 -retail revenue in real terms in period t, I , t d PSA , -dth price variable for advertisements in daily papers in period t where d=7, 8,
	t 2 -industrial production in period t, EE , 9; (seasonally adjusted),
	t 3 -real net wages paid in period t (seasonally adjusted), ISA ,
	t 1 -number of work days in period t, O ,
	t 6 -retail revenue in real terms in period t (seasonally adjusted), ISA ,
	t D , -dummy variable to cover jth seasonal component in period t where j
	F o r { }, 12 ,..., 2 t EESA , 2 -industrial production in period t (seasonally adjusted), = j ) ln( 1 -regression constant, 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , D j -partial regression coefficients where t OSA , 1 -number of work days in period t (seasonally adjusted), F o r ) ln( 1 -regression constant,
	j	P P 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 -partial regression coefficients, { }, 12 ,..., 2 =
	e e r r e u -random variable in period t. t e t u -random variable in period t.
	t c u P i t j t D + , , 4 ) ln( e D j t b P + 12 j , ) ln( + 3 ) R v e + Equation 2: Model of demand for the direct mail and periodicals market using seasonally t t t t t d DMP t a DMP t O EE I I P P Q + + + + + + = , 1 9 , 2 8 , 6 , 3 6 , 5 , 2 1 ln( ) ln( ) ) ln( ) ln( ) ln( ) ln( ) adjusted series t d t c t b DMP t a DMP t PSA PSA PSA PSA QSA + + + + + = ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( , 5 , 4 , 3 , 2 1 Equation 3: Model of demand for the direct mail market using dummy variables R e t t d t c t b DM t a DM t I P P P P Q + + + + + + = , 3 6 , 5 , 4 , 3 , 2 1 ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( v i e t j t j D j t t t u D O EE I + + + 12 + , , 1 9 , 2 8 , 6 ) ln( ) ln( ) ln( 7 = 2 ln( w t t t t t u OSA EESA ISA ISA + + + + ) ln( ) ln( ) ln( ) ln( , 1 9 , 2 8 , 6 7 , 3 6 w ln( 7 = 2 Symbols: DM t Q -number of pieces mailed on the direct mail market,
	Symbols:	DMP t QSA DM	-number of pieces mailed on the direct mail and periodicals market
		a	t
	Symbols: DMP t Q (seasonally adjusted), -number of pieces mailed on the direct mail and periodicals market,
	DMP t a P , -ath price variable for the direct mail and periodicals market in period t where DMP t a PSA , -ath price variable for the direct mail and periodicals market in period t where
	a=1, 2, 3. a=1, 2, 3; (seasonally adjusted),
	t PSA , -bth price variable for TV commercials in period t where b=2, 3; (seasonally b
	adjusted),

t b P ,bth price variable for TV commercials in period t where b=2, 3. t c P

P

  ,ath price variable for the direct mail market in period t where a=1, 2, 3.

																			15 16
	t 6 -retail revenue in real terms in period t, I , t ISA , 3 -real net wages paid in period t (seasonally adjusted),
	t 2 -industrial production in period t, EE , t ISA , 6 -retail revenue in real terms in period t (seasonally adjusted),
	t 1 -number of work days in period t, O , t EESA , 2 -industrial production in period t (seasonally adjusted),
	t D , -dummy variable to cover jth seasonal component in period t where j t OSA , 1 -number of work days in period t (seasonally adjusted),
	{ 2 ,..., 12 }, ) ln( 1 -regression constant, = j
	) ln( 1 -regression constant, 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 -partial regression coefficients,
	2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , D j -partial regression coefficients where u -random variable in period t. t
	F o r { }, 12 ,..., 2 u -random variable in period t. = j t F o r
						P P
	e Equation 4: Model of demand for the direct mail market using seasonally adjusted series e
							e r e r
	DM t ISA QSA ln( ln( 3 6	t ) ,	+ = ) ln(	7	ISA + ln( ) 6 2 1	t ln( + PSA a DM t ln( ) 8 , ,	R e v t t b OSA EESA PSA + + + ln( ) ) ln( ) 1 ln( t + PSA t c u ) , 9 , 2 4 , 3 R e v	,	t	)	+	5	ln(	d PSA	,	t	)	+
	Symbols:	i e QSA -number of pieces mailed on the direct mail market (seasonally adjusted), DM t i e
	w PSA , -ath price variable for the direct mail market in period t where a=1, 2, 3; DM t a w
	(seasonally adjusted),
	t PSA , -bth price variable for TV commercials in period t where b=2, 3; (seasonally b
	adjusted),
	t P , -bth price variable for TV commercials in period t where b=2, 3. b t c PSA , -cth price variable for magazine advertisements in period t where c=4, 5, 6;
	t P , -cth price variable for magazine advertisements in period t where c=4, 5, 6. c (seasonally adjusted),
	t PSA , -dth price variable for advertisements in daily papers in period t where d=7, 8, d
	, 9; (seasonally adjusted),

t d P ,dth price variable for advertisements in daily papers in period t where d=7, 8, 9. t I

Table 2

 2

	for the

TABLE 2 : DEFINITION OF USABLE TIME SERIES

 2

	Desig-	Series name	N	S.b.	Time period
	nation
	*Q DMP	Number of pieces of direct mail and periodicals	105	. . .	1998M1-2006M9
	*Q DM	Number of direct mail pieces	105	. . .	1998M1-2006M9
	*P1 DMP	Average discount price, in real terms, for direct mail and periodicals (CPI	105	. . .	1998M1-2006M9
		deflator)
	*P2 DMP	Average discount price, in real terms, for direct mail and periodicals (PS	105	. . .	1998M1-2006M9
		deflator)
	*P3 DMP	Average discount price, in real terms, for direct mail and periodicals (PC
		deflator)

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript