كاربرد روش¬هاي ناپارامتريك اصلاح شده در ارزيابي كارايي فني توليد چغندرقند ايران

Application of Modified Non-Parametric Models in Technical Efficiency of Iran’s Sugar Beet Production

علی¬رغم كاربرد فراوان روش¬های ناپارامتریك نظیر تحلیل پوششی داده¬ها (DEA) و تحلیل رویه آزاد (FDH)در محاسبه كارایی، اما این روش¬ها به دلیل ماهیت قطعی بودن این دو روش بوده زیرا نتایج نسبت به مشاهدات پرت و خطای اندازه¬گیری ناكارآمد تلقی می¬شود.در این راستا پیشرفت-های اخیر در ایجاد مرزهای جزئی تولید، نظیر رتبه-m و رتبه- ضعف¬های مربوط به الگوهای ناپارامتریك را رفع كرده است. بدین منظور در مطالعه حاضر جهت مقایسهتجربی چهار الگوی ناپارامتریك مذكور، كارایی فنی تولید چغندرقند در كشور با استفاده از داده¬های پانل مربوط به یازده استان¬ عمده تولیدكننده این محصول طیدوره زمانی91-1379 و بر اساس تحلیل پنجره¬ای مورد مطالعه قرار گرفت.به استناد یافته¬های حاصل و بر اساس الگوهای رتبه-m و رتبه- استان¬ كرمان به عنوان استان¬ فوق¬ كاراطبقه¬بندی شده و استان¬ اصفهان ناكاراترین استان¬ در تولید چغندرقند كشور می¬باشد. مطابق الگوهای تحلیل پوششی داده¬های پنجره¬ای و رویه دسترس آزاد پنجره¬ای نیز، استان¬های آذربایجان¬غربی، خراسان و لرستان جزء كاراترین استان¬ها در تولید چغندرقند كشور می¬باشند و استان فارس ناكاراترین استان در تولید این محصول محسوب می¬شود. با توجه به این¬كه الگوهای مرزی كامل نسبت به الگوهای مرزی جزئی دارای فروضی می¬باشند كه به واقعیت نزدیك¬تر است بنابراین نتایج حاصل از این الگوها مطلوب¬تر می¬باشند. از این رو پیشنهاد می¬گردد كه در مطالعات آتی جهت اندازه¬گیری كارایی فنی و رتبه¬بندی واحدهای تصمیم¬گیرنده از این الگوها بهره گرفته شود.

Introduction Despite their advantages, the DEA and FDH approaches have been criticized by econometricians for being deterministic, lacking a well-defined data generating process and for being highly sensitive to outliers and measurement errors. This objection was recently addressed by so-called partial frontier approaches, namely order-m and order-αefficiency measurement methods. To examine technical efficiency over time we used four non-parametric models using Window analysis which include Window-DEA, Window-FDH, Window order-α and Window order-m models. Window analysis uses moving average patterns in a way that every provincial observation in each period treated as if it is a different observation. Window analysis leads to a higher number of observations. The aim is to shed light on temporal patterns and heterogeneity in efficiency, time dependency and sensitivity of the results attributed to different efficiency measurement methodologies that are applied using the same dataset. In this study, we analyze the performance of cotton producing provinces in Iran over 2000-12. Materials and Methods Efficiency can be measured using parametric, semi-parametric and non-parametric approaches. In this study non-parametric approach was selected.The main contributions of this study are related to useing of four different Windows-based models to estimate technical efficiency using the same data and investigating the consistency of efficiency rankings. The DEA method is a non-parametric mathematical programming approach used to evaluate a set of comparable decision-making units (DMUs). Another method which has received a considerable amount of research attention is the FDH model which first formulated by Deprins et al., (1984).FDH estimator is both a deterministic and non-parametric tool for measuring productive efficiency. It is deterministic due to its inability to accommodate stochastic properties, it’s non- parametric nature arise from its lack of functional form specification. Like the DEA estimator, the FDH is also very sensitive to outliers/ extreme observations, susceptible to dimensionality problems and highly sensitive to noise. The basic motivation in FDH is to ensure that efficiency evaluations are affected only from actually observed performances. All the nonparametric envelopment estimators of frontiers are particularly sensitive to extreme observations, or outliers. These extreme points may disproportionately, and perhaps misleadingly, influence the evaluation of the performance of other firms. This drawback also plagues parametric frontier estimators when deterministic frontier models are considered. Then we use two partial frontier models: order-m and Order-α. According to Daraio and Simar (2007), order-m generalizes FDH by adding a layer of randomness to the computation of efficiency scores. Order-α is also a generalization of the FDH estimator which employs the (100-α)th percentile approach to minimize input consumption among available peers for benchmarking. At the end of the paper, we calculated the Spearman rank-order correlation coefficients (r) to determine how close the implied rankings of provinces were in each of the models. Results and Discussion This study analyzes the technical efficiency of Iran 's 13 major sugar beet producing provinces over the period 2000-2012. According to the results, mean technical efficiency of models Window-DEA, Window-FDH, Window order-m and Window order- were 0.67, 0.94, 0.80 and 0.77 respectively. According to Window order-α and Window order-m, Kerman is supper efficient province and Isfahan is the most inefficient province. Also with respect to Window-DEA and Window-FDH, West-Azerbayjan, Khorasan and Lorestan provinces are the most efficient provinces in Iran’s sugar beet production. When we drop the convexity assumption (that is, move from Window-DEA to Window-FDH), the estimated efficiency scores become higher (as expected since the best practice frontier then wraps itself closer around the data). According to Spearman rank-order correlation coefficient results there is a strong correlation between full frontier models. Technical efficiency correlation between model one and models three and four is positive but insignificant. A very strong correlation also is between model three and four, therefore these models could be substituted in technical efficiency studies. Conclusions According to the results and almost all of the models, Khorasan province is one of the most efficient provinces in Iran’s sugar beet production. Therefore it is recommended that policy makers have a special attention to this province as a potential to increase sugar beet production. It is also recommended that it would be better if experience could be transferred from efficient to non-efficient provinces. On the other hand, due to the fact that full frontier models have more realistic assumption than partial frontier models, it is recommended that the former ones be utilized in future studies to get more reliable efficiency scores.