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The analysis of the weather impact on the shape and shift of the production frontier
Hřebíková, Barbora ; Čechura, Lukáš (advisor) ; Peterová, Jarmila (referee)
Although weather is a significant determinant of agriculture production, it is not a common practice in production analysis to investigate on its direct impact on the level of final production. We assume that the problem is methodological, since it is difficult to find a proper proxy variable for weather in these models. Thus, in the common production models, the weather is often included into a set of unmeasured determinants that affects the level of final production and farmers productivity (statistical noise, random error). The aim of this dissertation is to solve this methodological issues and find the way to define weather and its impacts in a form of proxy variable, to include this variable into proper econometric model and to apply the model. The purpose of this dissertation is to get beyond the empirical knowledge and define econometric model that would quantify weather impacts as a part of mutually (un)conditioned factors of final production, to specify the model and apply it. The dissertation is based on the assumption that the method of stochastic frontier analysis (SFA) represents a potential opportunity to treat the weather as a specific (though not firm-controllable) factor of production and technical efficiency. SFA is parametric method based on econometric approach. Its starting point is the stochastic frontier production function. The method was presented in the work of Aigner, Lovell and Schmidt (1977) and Meusen and van den Broeck (1977). Unlike commonly used econometric models, SFA is based on analysis of production frontier that is formed by deterministic production frontier function and the compound error term. The compound error term consists of two parts -- random error (statistical noise, error term) and technical inefficiency. Technical inefficiency represents the difference in the actual level of production of the producer, and the maximum attainable (possible) level that would be achieved if the producer used a particular combination of production factors in a maximum technically efficient way. Over time, it has been developed on a number of aspects - see time variant and invariant inefficiency, heteroscedasticity, measurement and unmeasured heterogeneity. Along with the DEA, SFA has become the preferred methodology in the area of production frontier and productivity and efficiency analysis in agriculture. Lately, it has been applied for example by Bakusc, Fertő and Fogarasi (2008) Mathijs and Swinnen (2001), Hockmann and Pieniadz (2007), Bokusheva and Kumbhakar (2008) Hockmann et al. (2007), Čechura a Hockmann (2011, 2012), and Čechura et al. (2014 a, b). We assume that the weather impacts should be analysed with regard to technical efficiency, rather than as a part of statistical noise. Implementation of weather in part of deterministic production function rather than in the statistical noise is a significant change in the methodical approach within the stochastic frontier analysis. Analysis of the weather impacts on the changes in the level of TE has not been greatly recorded in the associated literature and is, therefore, considered as the main contribution of this work for the current theory of production frontier estimation, or the technological effectiveness, in the field of agriculture. Taking into account other variables that are important for the relationship and whose inclusion would enhance the explanatory power of the model was part of the objective of this work.Thus, the possible effect of heterogeneity was taken into account when models were formulated and final results discussed. The paper first defined and discussed possible ways how to incorporate the effects of the weather into production frontier model. Assessing the possibility of inclusion of weather in these models was based on the theoretical framework for the development of stochastic frontier analysis, which defines the concept of technical efficiency, distance functions theory, stochastic production function theory and the methodology and techniques that are applied within the framework of SFA, which were relevant for the purpose of this work. Then, the weather impacts on the shape and shift of production frontier and technical efficiency of czech cereal production in the years 2004-2011 was analyzed. The analysis was based on the assumption that there are two ways how to define variables representing weather in these models. One way is to use specific climatic data, which directly describe the state of the weather. For the purpose of this thesis, the variables mean air temperature (AVTit) and sum of precipitation (SUMPit) in the period between planting and harvest of cereals in the individual regions of Czech republic (NUTS 3) were selected. Variables were calculated from the data on monthly mean air temperatures and monthly sums of precipitation on the regional levels provided by Czech hydro-meteorological institute CHMI. Another way to define weather variable is to use a proxy variable. In this dissertation, the calculation of climatic index (KITit) was applied. Climatic index was calculated as a sum of ratios between the actual yield levels and approximated yield levels of wheat, barley and rye, weighted by the importance of each plant in a cereal production protfolio in each region of the Czech republic. Yield levels were approximated by the linear trend functions, yield and weights were calculated with the use of data on regional production and sown area under individual grains by year at the level of regional production (NUTS 3) provided by Czech Statistical Office. Both ways of weather definition are associated with some advantages and disadvantages. Particular climatic data are very precise specificatopn of the actual weather conditions, however, to capture their impacts on the level of final production, they must be implemented into model correctly along with the number of other factors, which have an impact on the level of final production. Climatic index, on the other hand, relates the weather impacts directly to the yield levels (it has been based on the assumption that the violation from yield trends are caused by the weather impacts), though, it does not accomodate the concrete weather characteristics. The analysis was applied on unbalanced panel data consisting of the information on the individual production of 803 producers specialized on cereal production, which have each the observations from at least two years out of total 8-years time serie. Specialization on crop production was defined as minimum 50% share of cereal production on the total plant production. Final panel consists of 2332 observations in total. The values of AVTit, SUMPit a KITit has been associated with each individual producer according to his local jurisdiction for a particular region. Weather impacts in the three specified forms were implemented into models that were defined as stochastic production frontier models that capture the possible heterogeneity effects. The aim is to identify the impact of weather on shift and shape of production frontier. Through the defined models, the production technology and technical efficiency were estimated. We assume that the proposed inclusion in weather impacts will lead to a better explanatory power of defined models, as a result of weather extraction from a random components of the model, or from a set of unmeasured factors causing heterogeneity of the sample, respectivelly. Two types of models were applied to estimate TE - Fixed management model (FMM) and Random parameter model (RPM). Models were defined as translogarithmic multiple-output distance function. The analyzed endogene variable is cereal production (expressed in thousands of EUR). Other two outputs, other plant production and animal production (both expressed in thousands of EUR) are expressed as the share on cereal production and they appear on the right side of the equation together with the exogene variables representing production factors labour (in AWU), total utilized land (in acres), capital (sum of contract work, especially machinery work, and depreciation, expressed in thousands of EUR), specific material (represented by the costs of seeds, plants, fertilisers and crop protection, expressed in thousands of EUR), and other material (in thousands of EUR). The values of all three outputs, capital, and material inputs were deflated by the the country price indexes taken from the EUROSTAT database (2005=100). In Random parameter model, heterogeneity is captured in random parameters and in the determinants of distribution of the technical inefficiency, uit. All production factors were defined as a random parameters and weather in form of KITit enters the mean of uit and so it represents the possible source of unmeasured heterogeneity of a sample. In fixed management model, heterogeneity is defined as a special factor representing firm specific effects, mi. This factor represents unmeasured sources of heterogeneity of sample and enters the model in interaction with other production factors and the with the trend variable, tit.Trend variable represents the impact of technological change at a time t for each producer i. The weather impacts in form of variables AVTit a SUMPit is, together with production factors, excluded from the set of firm specific effects and it is also numerically expressed. That way weather becomes a measured source of heterogeneity of a sample. Both types of models were estimated also without the weather impacts specification in order to obtain the benchmark against which the effects of weather impacts specification on production frontier and technical efficiency is evaluated. Easier interpretation of results was achieved by naming all five estimated models as follows: FMM is a name of fixed management model that does not include specified weather variables, AVT is a name for fixed management model including weather impacts in form of average temperatures AVTit, SUMP is name of model which includes weather impacts in form of sum of precipitations SUMPit, RPM is random parameter model that does not account for weather impacts, KIT is random parameter model that includes climatic index KITit into the mean of inefficiency. All estimated models fullfilled the conditions of monotonicity and kvasikonvexity for each production factor with the exception of capital in FMM, AVT, SUMP and RPM model. Violating the kvasikonvexity condition is against the theoretical assumptions the models are based on, however, since capital is also insignificant, it is not necesary to regard model as incorrect specification. Violation of kvasikonvexity condition can be caused by the presence of other factor, which might have contraproductive influence on final production in relation to capital. For example, Cechura and Hockann (2014) mention imperfections of capital market as possible cause of inadequate use of this production factor with respect to technological change. Insufficient significancy of capital can be the result of incorrect specification of variable itself, as capital is defined as investment depreciation and sum of contract work in the whole production process and not only capital related to crop production. The importance of capital in relation to crop production is, thus, not strong enough to be significant. Except of capital are all other production factors significant on the significancy level of 0,01. All estimated models exhibit a common pattern as far as production elasticity is concerned. The highest elasticity is attributed to production factors specific and othe material. Production elasticity of specific material reaches values of 0,29-0,38, the highest in model KIT and lowest of the values in model AVT. Production elasticity of other material reahed even higher values in the range 0,40-0,47. Highest elasticity of othe material was estimated by model AVT and lowest by model KIT. Lowest production elasticity are attributed to production factors labour and land. Labour reached elasticity between 0,006 and 0,129 and land reached production elasticity in the range of 0,114 a 0,129. All estimated models displayed simmilar results regarding production elasticities of production factors, which also correspond with theoretical presumptions about production elasticities -- highest values of elasticity of material inputs correspond with naturally high flexibility of these production factors, while lowest values of elasticity of land corresponds with theoretical aspect of land as relativelly inelastic production factor. Low production elasticity of labour was explained as a result of lower labor intensity of cereals sector compared to other sectors. Production elasticity of weather is significant both in form of average temperatures between planting and harvest in a given region, AVTit, and form of total precipitation between planting and harvest in a given region, SUMPit. Production elasticity of AVTit, reach rather high value of 0,3691, which is in the same level as production elasticities of material inputs. Production elasticity of SUMPit is also significant and reach rather high lower value of 0,1489. Both parameters shows significant impact of weather on the level of final crop production. Sum of production elasticities in all models reach the values around 1, indicating constant returns of scale, RS (RSRPM=1,0064, RSKIT=0,9738, RSSUMP =1,00002, RSFMM= 0,9992, RSAVT=1,0018.). The results correspond with the conclusion of Cechura (2009) and Cechura and Hockmann (2014) about the constant returns of scale in cereals sector in Czech republic. Since the value of RS is calculated only with the use of production elasticities of production factors, almost identical result provided by all three specifications of fixed management model is a proof of correct model specification. Further, the significance of technological change and its impact on final production and production elasticities were reviewed. Technological change, TCH, represents changes in production technology over time through reported period. It is commonly assumed that there is improvement on production technology over time. All estimated models prooved significant impact of TCH on the level of final production. All specified fixed management models indicate positive impaact of TCH, which accelerates over time. Estimated random parameter models gave contradicting results -- model KIT implies that TCH is negative and decelerating in time, while model RPM indicates positive impact of TCH on the level of final production, which is also decelerating in time. It was concluded, that in case that weather is not included into model, it can have a direct impact on the positive direction of TCH effect, which can be captured by implementing weather into model and so the TCH becomes negative. However, as to be discussed later, random parameter model appeared not as a suitable specification for analyzed relationship and so the estimate of the TCH impact might have been distorted. The impact of technological progress on the production elasticities (so-called biased technological change) is in fixed management models displayed by parameters representing the interaction of production factors with trend variable. The hypothesis of time invariant parameters (Hicks neutral technological change) associated with the production factors is rejected for all models except the model AVT. Significant baised technological change is confirmed for models FMM and SUMP. Biased technological change is other material-saving and specific material-intensive. In the AVT model, where weather is represented by average temperatures, AVTit, technological change is not significant in relation to any production factors. In both random parameter models, rejection of hypothesis of time invariant parameters only confirms significance of technological change in relation to final crop production. Nonsignificant effect of technological change on production elasticity of labor, land and capital indicates a generally low ability of farmers to respond to technological developments, which can be explained by two reasons. The first reason can the possible complications in adaptation to the conditions of the EU common agricultural market (eg. there are not created adequate conditions in the domestic market, which would make it easier for farmers to integrate into the EU). This assumption is based on conclusion made by Cechura and Hockmann (2014), where they explain the fact that in number of European countries there is capital-saving technological change instead of expected capital-using technical change as the effect of serious adjustment problems, including problems in the capital market.. Second possible reason for nonsignificant effect of technological change on production elasticity of labor, land and capital is that the financial support of agricultural sector, which was supposed to create sufficient conditions for accomodation of technological progress, has not shown yet. Then, the biased TCH is not pronounced in relation to most production factors. Weather impacts (SUMPit, AVTit) are not in significant relation to technological change. Both types of models, FMM and RPM were discussed in relation to the presence of the heterogeneity effects All estimated random parameters in both RPM models are statistically significant with the exception of the production factor capital in a model that does not involve the influence of weather (model RPM). Estimated parameter for variable KITit (0,0221) shows significant positive impact of the weather on the distribution of TE. That way, heterogeneity in relation to TE is confirmed, too, as well as significant impact of weather on the level of TE. Management (production environment) is significant in all three estimated fixed management models. In models that include weather impacts (AVT, SUMP), the parameter estimates indicates positive, slightly decreasing effect of management (or heterogeneity, respectivelly) on the level of final crop production. In model FMM, on the contrary, first and second order parameters of mangement indicate also significant, but negative and decelerating effect of management (heterogeneity) on final crop production. If weather impact is included into models in form of AVTit, or. SUMPit, the direction of the influence of management on the level of final crop production changes. Based on the significance of first order parameter of management, significant presence of heterogeneity of analyzed sample is confirmed in all three estimated fixed management models. As far as the effect of heterogeneity on single production factors (so called management bias) is concerned, the results indicate that in case of model that does not include weather impacts (model FMM) the heterogeneity has positive impact on production elasticities of land and capital and negative effect on the production elasticities of material inputs. In models that account for weather impacts, heterogeneity has negative effect on production elasticities of land and capital and positive effect on the elasticity of material inputs. Heterogeneity effect on the production elasticity of labor is insignificant in all models FMM. In all three estimated models, the effect of heterogeneity is strongest in case of production factors specific and othe material, and, also, on production factor land. In case of FMM model, heterogeneity leads to increase of production elasticity of land, while in AVT and SUMP heterogeneity leads to decrease of production elasticity of land. At the same time, the production elasticity of land, as discussed earlier, is rather low in all three models. This fact leads to a conclusion that in models that accomodate weather impacts (AVT and SUMP), as the effect of extraction of weather from the sources of unmeasured heterogeneity, the heterogeneity has a negative impact on production elasticity of land. It can be stated that the inclusion of weather effects into the sources of unmeasured heterogeneity overestimated the positive effect of unmeasured heterogeneity on the production factor land in the model FMM. Management does not have a significant effect on the weather in form of SUMPit, while it has significant and negative effect on the weather in form of average temperature, AVTit, with the value of -0.0622**. In other words, heterogeneity is in negative interaction with weather represented by average temperatures, while weather in form of the sum of precipitation (SUMPit) does not exhibit significant relation to unmeasured heteregeneity. In comparison with the model that does not include weather impacts, the effect of heterogeneity on the production elasticities has the opposite direction the models that include weather. Compare to the model where weather is represented by average temperature (model AVT), the effect of management (heterogeneity) on the production elasticity of capital is bigger in model with weather represented by sum of precipitations (model SUMP) while the effect of management (heterogeneity) on the production elasticity of land and material imputs is smaller in model with weather represented by sum of precipitations (model SUMP). Technical efficiency is significant in all estimated models. The variability of inefficiency effects is bigger than the variabilty of random error in both models that include weather and models where weather impacts are not specified. The average of TE in random parametr models reaches rather low value (setting the average TE = 54%), which indicates, that specified RPM models underestimate TE as a possible result of incorrect variable specification, or, incorrect assumptions on the distribution of the error term representing inefficiency. All estimated FMM models results in simmilar value of average TE (86-87%) with the simmilar variability of TE (cca 0,5%). Technological change has significant and positive effect on the level of TE in the model that does not specify the weather impacts (model FMM), with a value of 0,0140***, while in the models that include weather in form of average temperatures, or sum of precipitations, respectivelly, technological change has a negative effect on the level of TE (in model AVT = -0.0135***; in SUMP = -0.0114***). It can be stated, that in the model where the weather impacts were not specified, the effect of TCH on the level of TE may be distorted, because the parameter estimate implies also a systematic influence weather in the analyzed period. The effect of unmeasured heterogeneity on the level of TE is significant in all three estimated fixed management models. In models AVT and SUMP, heterogeneity has a positive effect on the level of TE (in AVT = 0.1413 and in SUMP =0,1389), while in the model that does not include weather variable the effect of heterogeneity on the level of TE is negative (in FMM =-0,1378). In models AVT and SUMP, the weather impacts were extracted from the sources of unmeasured heterogeneity, and so from its influence on the level of TE (together with other production factors weather becomes a source of measured heterogeneity). The extraction of the weather from the sources of unmeasured heterogeneity leads to change in the direction of heterogeneity effects on the level of TE from negative (in model where weather was part of unmeasured heterogeneity) to positive. The direct impact of weather on TE is only significant in case of variable AVTit, indicating that average temperatures reduce the level of TE (-0.0622**). Weather in form of sum of precipitations does not have a significant impact on the level of TE. It is evident that incorporating the effects of weather significantly changes the direction of the influence of management on the production of cereals and the direction of influence on the management of production elasticity of each factor in the final model. Analogically with the case of the influence of heterogeneity on the production elasticity of land, it is stated that the weather (included in sources of unmeasured heterogeneity) played a role in the underestimation of the impact of heterogeneity on the overall cereal production. Also, in case that weather was not extracted form the sources of unmeasured heterogeneity would play significant role in underestimation of the effect of heterogeneity on the level of TE. Based on the results of parameters estimates, and on the estimate of average values of TE and its variability, it is concluded, that the effect of inclusion of weather into defined models does not have significant direct impact on the average value of TE, however, its impact on the level of TE and the level of final crop production is pronounced via effects of unmeasured heterogeneity, from which the weather was extracted by its specification in form of AVTit a SUMPit. The analysis results confirms that it is possible to specify the impacts of weather on the shape and shift of production frontier, and, this to define this impact in a model. Results Aaso indicate that the weather reduces the level of TE and is an important source of inefficiency Czech producers of cereals (crop). The model of stochastic frontier produkction function that capture the weather impact was designed, thereby the goal of the dissertation was met. Results also show that unmeasured heterogeneity is an important feature of czech agriculture and that the identification of its sources is critical for achieving higher productivity and higher level of final output. The assumption about significant presence of heterogeneity in production technology among producers was confirmed, and heterogeneity among producers is a significant feature of cereal sector. By extracting weather from sources of unmeasured heterogeneity, the impact of real unmeasured heterogeneity (all that was not extracted from its sources) and the real impact of weather on the level of TE is revealed. If weather was not specified in a model, the TE would be overestimated. Model in form of translogarithmic multiple-output distance function well approximates the relationship between weather, technical efficiency, and final cereal production. Analysis also revealed, that the Random parameter model, which was applied in case that weather impacts were expressed as an index number, is not the suitable model specification due to underestimating of the average level of TE. The problem of underestimation of TE might be caused by wrong variable definition or incorrect assumptions about the distribution of inefficiency term. Fixed management model, on the other hand, appears as a very good tool for identification of weather impacts (in form of average temperatures and sum of precipitations in the period between planting and harvesting) on the level of TE and on the shape and shift of production frontier of czech cereals producers. The results confirm the assumption that it is important to specify weather impacts in models analyzing the level of TE of the plant production. By specification of weather impactzs in form of proper variables (AVTit, SUMPit), the weather was extracted from the sources of unmeasured heterogeneity. This methodical step will help to refine the estimate of production technology and sources of inefficiencies (or, the real inefficiency, respectivelly). That way, the explanatory power of model increase, which leads to generally more accurate estimate of TE. Dissertation has fulfilled its purpose and has brought important insights into the impact of weather on the TE, about the relationship between weather and intercompany unmeasured heterogeneity, about the effect of weather on the impact of technological change, and so the overall impact of weather specification on the shape and shift of production frontier. A model that is suitable application to define these relationships was designed. Placing the weather into deterministic part of production frontier function instead of statistical noise (or, random error, respectivelly) means a remarkable change in the methodical approach within the stochastic frontier analysis, and, due to the fact that the analysis of weather impacts on the level of TE to this extent has not yet been observed in relevant literature, the dissertation can be considered a substantial contribution to current theory of the estimate of technical efficiency of agriculture. The dissertation arose within the framework of solution of the 7th FP EU project COMPETE no 312029.
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