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tHw~XX$X)Jset)))x)))$o{{222Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe
Laure LATRUFFE
INRA Rennes, France
Sophia DAVIDOVA
Imperial College, UK
Kelvin BALCOMBE (
Reading University, UK
For correspondence
Laure Latruffe
INRA Unit ESR
4 Alle Bobierre CS 61103
35011 Rennes Cedex
France
tel + 33 2 23 48 56 08
Email: HYPERLINK "mailto:Laure.Latruffe@rennes.inra.fr" Laure.Latruffe@rennes.inra.fr
Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe
Abstract
The paper provides one of the first applications of the double bootstrap procedure (Simar and Wilson, 2006) in a twostage estimation of the effect of environmental variables on nonparametric estimates of technical efficiency. This procedure enables consistent inference within models explaining efficiency scores, while simultaneously producing standard errors and confidence intervals for these efficiency scores.
The application is to 88 livestock and 256 crop farms in the Czech Republic, split into individual and corporate.
Keywords: double bootstrap, DEA, truncated maximum likelihood, individual farms, corporate farms, Czech Republic
JEL classification: D24, Q12
Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe
This paper provides one of the first applications of the double bootstrap (Simar and Wilson, 2006) that enables consistent inference within models explaining efficiency scores, while simultaneously producing standard errors and confidence intervals for these efficiency scores. The study investigates a range of variables that impact on the technical efficiency of Czech farms emerging from the transition from collectivised and stateowned farming to market oriented private agriculture.
The double bootstrap is applied to a truncated regression of nonparametric Data Envelopment Analysis (DEA) efficiency estimates on explanatory variables in a twostage procedure explaining the sources of efficiency variations within samples of individual and corporate farms in the Czech Republic. In this study, the two management types of farms are treated separately as it is assumed that individual and corporate farms do not have the same production possibility frontier. For example, many individual farmers lack the managerial experience acquired by the corporate farms managers in the period before transition. Farms are furthermore separated into production types, crop and livestock, as their technology is different. The latter is often used in farm level efficiency studies (Mathijs and Vranken, 2001; Latruffe et al., 2005). Therefore, the underlying assumption of our analysis is that different production and management types operate under different technology and with different factor endowments.
In the literature concerning farm efficiency within countries in transition, there are numerous studies that employ DEA (e.g. Mathijs and Swinnen, 2001; Mathijs and Vranken, 2001). However, only a few recent analyses have applied the smoothed homogenous bootstrap, in conjunction with the procedure proposed by Simar and Wilson (1998 and 2000), in order to determine the variability of DEA efficiency estimates (Brmmer, 2001; Latruffe et al. 2005). Therefore, the problem of serial correlation among estimated efficiencies highlighted in Simar and Wilson (2006) has not been tackled in any of these studies. This issue is accordingly addressed in this paper.
This paper is structured as follows. The next section explains the methodology employed and the second section describes the database. The third section summarises the empirical results and the fourth section concludes.
Methodology
Efficiency measurement
DEA is used in the first stage for estimating technical efficiency. The motivation and details of DEA have appeared elsewhere and will not be reiterated here (for more details see Charnes et al., 1978; Fre et al., 1994; Thiele and Brodersen, 1999). In this study, an outputorientated farm level model is used because it is assumed that, in the absence of output quotas, farm managers have more control over output quantities than over inputs. In the outputoriented model, the efficiency score is unbounded from above, but bounded from below at 1. In order to ease the interpretation of results presented in this paper, it is useful to recall that in the outputorientated DEA model an efficiency score EMBED Equation.3 is calculated for the ith farm by solving the following program:
(1) EMBED Equation.3 EMBED Equation.3
subject to EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
The above specification is under constant returns to scale (CRS); for a specification under variable returns to scale (VRS) the additional constraint EMBED Equation.3 is added, where EMBED Equation.3 is a vector of ones.
As the efficiency score is bounded on the left at 1 (1( EMBED Equation.3 ), EMBED Equation.3 1 is the proportional increase in outputs that could be achieved by the ith farm with input quantities held constant (Coelli et al., 1998). What is reported as an efficiency estimate in this study is EMBED Equation.3 with EMBED Equation.3 1 representing the potential output expansion. Thus, inefficiency is used as a dependent variable in the secondstage truncated regression.
The model used in this study includes one output variable and four inputs. Total output value is used as the measure of output. This aggregate variable has been constructed by the Czech Institute of Agricultural Economics (VUZE) which is responsible for the Farm Accountancy Data Network (FADN), based on information available in farms accountancy books. Farms value their quantities at the specific market prices that they face. Therefore, an aggregated output variable measured by value implies that technical efficiency scores include some adjustments for output quality and market environment. The four inputs included are: utilised agricultural area (UAA) in hectares (ha) as a land factor; annual work units (AWU) as a labour factor; depreciation plus interest as a capital factor; and the value of intermediate consumption as a variable input factor. Value units are expressed in Czech Koruna (CZK). Four frontiers are estimated, one for each specialisation, livestock and crop, and each management form, individual and corporate farms.
Secondstage regression
In a second stage, truncated maximum likelihood estimation is used to regress efficiency scores ( EMBED Equation.3 1) on a set of explanatory variables. Since the main interest of the study is in investigating management rather than scale inefficiencies, the pure technical inefficiency score is chosen as the dependent variable. Truncated maximum likelihood is estimated for each of the four subsamples (livestock/crop, individual/corporate).
Based on previous research on farm efficiency in developing and transition countries, a number of explanatory variables are considered. UAA for crop farms and livestock units for livestock farms are used as a size variable. The impact of size on technical efficiency is a recurrent issue in the efficiency literature. It has been widely discussed in relation to transition countries due to its important policy implications regarding the postreform land redistribution in Central Europe (Gorton and Davidova, 2004). For example, Curtiss (2002) found that for crop production in the Czech Republic, farms with a larger land area were more technically efficient.
The ratios of capital to labour and land to labour are technology proxies. These relative intensities in factor use reflect important aspects of farm performance in transition countries, where farms are often overmanned which acts as a constraint to their efficiency. Evidence for this has been found for Poland by Latruffe et al. (2004). The degree of integration in factor markets is represented by the shares of hired labour in total labour input, and of rented land in UAA. Some individual farms that emerged after the beginning of transition are not integrated into factor markets and rely almost entirely on their family endowments. In the case of labour, for example, this might mean that they do not use labour with special technical skills. These shares are not included in the corporate farms regressions as they are nearly 100 per cent for all observations.
A ratio of interest plus rentals to total output is included as an indicator of the financial stress on the farm caused by repayments of loans and rents, and which may affect its performance. The effect of debt repayments on technical efficiency can be twofold. While the free cash flow approach (Jensen, 1986) expects a positive effect due to the pressure on farmers to repay their debts and thus to limit their resource waste, the agency theory (Jensen and Meckling, 1976) hypotheses the opposite. Lenders transfer their costs for screening and monitoring the loans to borrowers. Consequently, highly indebted farmers bear high costs from receiving credit. The scope of management decisions is restricted and, efficiency is reduced. The agency theory approach is likely to be valid for the Czech Republic during the period of transition as both commercial banking and business borrowing do not have a long history. There is a lack of well established relationships and information flows between bankers and farmers are poor. Our prior knowledge of the Czech farms indicates that corporate farms have more liabilities than individual farms. However, a high proportion of these debts stem from the reform process itself. So far, corporate farms pay very little or zero interest on these debts, so they exhibit low financial stress (Davidova et al., 2003). This may not be the case of the de novo individual farms, as they are required to pay off debts to commercial lenders according to tight schedules. Therefore, the agency theory approach might mainly hold for individual farms.
Four regional and two legal form dummies are also used as explanatory variables. The Czech Republic is divided into five large agrienvironmental regions. Hughes (2000) labels these as maize, sugar beet, cereal, potato, and mountainousforage regions. The maize region is the most favourable for farming and the mountainousforage region the least. Regional dummies are employed as proxies for environment characteristics (DREG1, DREG2, DREG3 and DREG4) with region 5, mountainousforage, used as a reference. For the corporate farms regression, the two dummies are DLTD for limited companies and DJSTOCK for joint stock companies, with cooperatives used as a reference group.
Bootstrap
Simar and Wilson (2006) noted that the DEA efficiency estimates are biased and serially correlated, which invalidates conventional inference in twostage approaches. These authors proposed a procedure, based on a double bootstrap, that enables consistent inference within models explaining efficiency scores while simultaneously producing standard errors and confidence intervals for these efficiency scores.
The rationale behind bootstrapping is to simulate a true sampling distribution by mimicking the data generating process. The procedure applied in this study follows Simar and Wilsons (2006) Algorithm 2. It consists of the following steps. Firstly, standard DEA efficiency point estimates are calculated (step (i) in Appendix 1). Secondly, truncated maximum likelihood estimation is used to regress the efficiency scores against a set of explanatory variables (ii). These estimates are then integrated into a bootstrap procedure that is similar to the smoothed bootstrap procedure of Simar and Wilson (2000) (iii). This bootstrap procedure allows to correct for bias (iv). Finally, the bias corrected scores produced by the preceding bootstrap are used in a parametric bootstrap on the truncated maximum likelihood (vvi), thus producing standard errors for the regression parameters. Confidence intervals are then constructed, for the regression parameters as well as for the efficiency scores (vii). This procedure is described in more detail in Appendix 1 (drawn from Simar and Wilson, 2006, Algorithm 2).
The results throughout this paper were obtained from 2,500 bootstrap iterations, in both parts of the double bootstrap, and in total required slightly less than 24 hours of computer time, running on Gauss for Windows on a modern desktop PC.
Description of data
This study draws data from the 1999 Czech FADN dataset. The initial set included 1,087 farms. After checking for missing or inconsistent data the useable sample was reduced to 753 farms. From these 753 farms, two subsamples were constructed depending on whether farms specialise in crop or livestock, defined here as farms for which at least 65 per cent of the value of total agricultural output comes from crop or livestock. The extracted livestock subsample contains 88 farms and the crop subsample, 256 farms. The farms were also split according to their management form into individual and corporate subsamples. The individual farms are the most numerous group, 274 in all. They account for 86 per cent of the crop farms and 60 per cent of the livestock farms. The summary statistics of the variables of interest for the sample farms are presented in Table 1.
The sample farms are located in different agrienvironmental regions. Within the subsamples, no individual livestock farm is located in the maize region and no corporate crop farm in the mountainousforage region. For this reason, region 4, potato, is used as a reference for the corporate crop farms instead of region 5, mountainousforage when conducting the truncated maximum likelihood regression.
<< Table 1 about here >>
Empirical results
Technical efficiency: comparison of point and interval estimates
Estimates of total technical, pure technical and scale efficiency are presented in Table 2. The percentage of efficient farms represents the share of farms with an efficiency score of unity. DEA estimates, presented in Table 2, reveal that corporate farms appear to be more totally technically efficient than individual farms in the sense that the observations lie, on average, closer to the efficiency frontier within the corporate subsample. The main total technical efficiency differences between individual and corporate farms appear in livestock production. The differences in average total efficiency estimates between the two management types in crop production are small. However, in terms of pure technical efficiency, corporate farms are closer to the efficiency frontier for both crop and livestock specialisations. A larger variation of management practices within individual farms is consistent with the expectations based on a lack of prereform managerial experience.
By specialisation, among individual farms crop farms are clustered closer to their own frontier than livestock farms. Among corporate farms, the opposite is true. In terms of pure technical and scale efficiency, the relationships between specialisations are the same as in the case of the total technical efficiency.
<< Table 2 about here >>
The confidence intervals of the efficiency scores, constructed with bootstrapping, are wide (Table 3). This is particularly true for individual livestock farms, in terms of both total and pure technical efficiency. This finding proves a high statistical variability of DEA efficiency estimates. Similarly wide intervals were found for a sample of farms in Poland (Latruffe et al., 2005). Both Brmmer (2001) and Latruffe et al., found that the interval width varies considerably over the samples.
<< Table 3 about here >>
Table 4 reports the mean bias, and lower and upper confidence bounds for total technical efficiency scores by subsample. The biases are substantial for all subsamples except corporate livestock farms. The interval results confirm only some of the rankings produced by point estimates. Within corporate farms, on average, the livestock subsample is more totally technically efficient as the mean upper bound for livestock farms is strictly less than the mean lower bound for crop farms. However, within the group of individual farms, the results are inconclusive as intervals overlap. The comparison between the corporate and individual farms shows that corporate farms are relatively more totally technically efficient than individual farms in livestock production. It is more difficult to draw this conclusion for crop farms due to overlapping intervals. However, when the interval bounds for pure technical efficiency are compared, there is clearcut evidence that the corporate farms in both specialisation lie nearer to their frontiers than the individual farms.
<< Table 4 about here >>
Factors accounting for technical efficiency variations
The secondstage results from the double bootstrap estimation are presented in Table 5 and the results from a standard estimation using non bias corrected efficiency scores in Table 6. As already mentioned, the dependent variable represents inefficiency. Therefore, the parameters with negative signs indicate sources of efficiency and vice versa.
As shown by Table 5, within the livestock farms, size, measured in livestock units, is an important source of efficiency for individual farms. The dispersion around the mean size is much greater for individual than for corporate livestock farms. This corroborates the conclusions made by Hughes (2000) and may suggest that some individual farms, which are de novo postreform farm structures, have not yet had the time to develop management skills and sufficient capital in order to reach the minimum efficient size.
<< Table 5 about here >>
The ratio of capital to labour negatively affects the efficiency of individual livestock farms but has no impact on corporate farms. Again, as above, the coefficient of variation is greater for individual than for corporate farms, which indicates a greater dispersion. It appears that some individual farms are overcapitalised. Recalling that capital is measured by depreciation plus interest, this result may indicate weaknesses in management decisions regarding the purchase of machinery and equipment, the construction of new buildings irrespective of the farm size, as well as the potential efficiency with which capital could be used. On the other hand, some individual farmers have old and obsolete capital stock. The maintenance costs for such stock are usually high and often require loans and payment of interest. A similar situation has been described for Poland (Latruffe et al., 2005).
For individual farms, the share of hired labour has a positive impact on technical efficiency. The share of rented land has a negative effect. The direction of the effects is consistent with our a priori expectations. Hired labour might be more qualified and more able to perform specialised tasks than family labour. Concerning rented land, as shortterm tenancy contracts prevailed in the Czech Republic during the first decade of transition, tenant farmers might have not had incentives to maintain the soil quality. In this case, the share of rented land could be considered as a proxy for land quality. However, the relationships are only significant for crop farms.
Financial stress lowers the efficiency of individual farms of both specialisations, and of corporate livestock farms, supporting the agency theory approach. As expected, the relationship is stronger for the individual farms, confirming that the corporate farms are subject to less rigorous budget constraints.
The secondstage regression in Table 5 indicates that most of the variables impact significantly on individual farm technical efficiency. The land to labour ratio has a positive significant influence. Some individual farms appear overmanned for the land area cultivated, which is the case in many of the Central European countries as agriculture has been used as a shelter from industrial unemployment during the process of transition. Individual farms that rely mainly on family labour will achieve efficiency gains through the higher use of hired labour. The latter normally bring specialised skills. The share of rented land (the largest proportion of land in the Czech Republic is rented) has a negative impact on individual crop farms efficiency. The same relationship has been identified for financial stress, which takes into account the burden of the repayment of rentals and interest.
The results pertaining to regional dummies suggest that the performance of individual farms is more dependent on the agrienvironmental characteristics. This may indicate a lower input (more extensive) technology than corporate farms.
From a methodological point of view, the comparison of the double bootstrap estimation (Table 5) with standard estimation using non bias corrected scores (Table 6) shows only slight differences. Nevertheless, stronger relationships result from the application of Simar and Wilsons (2006) algorithm.
<< Table 6 about here >>
Conclusions
The paper provides one of the first applications of the double bootstrap procedure (Simar and Wilson, 2006) in a twostage estimation of the effect of a range of variables on nonparametric estimates of technical efficiency. Two main conclusions could be drawn from this application. Computationally, the procedure is straightforward, and reasonably efficient when using moderate sample sizes such as those employed here. Therefore, it is recommended for routine use in twostage estimation of the effect of environmental variables on nonparametric estimates of technical efficiency. However, the results using a simple twostage truncated regression on standard DEA scores did not differ substantively from those which employed the double bootstrap. Therefore, it is the contention here that the findings of previous studies, employing a simple twostep approach, largely remain valid.
Concerning the key issue addressed in this paper, the explanation of sources of variation in efficiency within the analysed farm subsamples, important insights were given by the confidence intervals and the consistent estimates of the secondstage regression. The efficiency results unambiguously revealed a larger average pure technical efficiency score for the corporate than for the individual farms. Both point and interval estimates indicated that the observations for the corporate farms lie closer to their respective efficient frontier, that is to say, that they have more homogenous management practices than de novo individual farmers. This finding is not surprising knowing that often the managers of the postreform corporate farms were members of the management team of the former collective and stateowned farms. At the same time, the majority of the individual farmers were either farm workers before the transition or were not involved in farming at all. The results of the secondstage regression indicated that individual farms pure technical efficiency was negatively influenced by a high capital intensity, small use of hired labour and by a high financial stress. This suggests that individual farmers still lack the managerial experience necessary for rational investment and labour decisions.
Appendix 1: Bootstrap procedure
The seven steps of the double bootstrap algorithm are as follows.
A DEA outputorientated efficiency score EMBED Equation.3 is calculated for each farm, i.e. the following program is solved for i=1,,n (CRS case):
(2) EMBED Equation.3 EMBED Equation.3
subject to EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
where yi and xi are respectively the original output and input matrices of the ith farm; Y and X are respectively the original output and input matrices of the sample; l is a nx1 vector of constants; the DEA score EMBED Equation.3 is bounded by one on the left: EMBED Equation.3 ( 1 for i=1, & n. For a specification under VRS the additional constraint EMBED Equation.3 is added, where EMBED Equation.3 is a vector of ones.
Maximum likelihood is used in the truncated regression of EMBED Equation.3 on zi, to provide an estimate EMBED Equation.3 of EMBED Equation.3 and an estimate EMBED Equation.3 of EMBED Equation.3 .
For each farm i=1,n, the next four steps (ad) are repeated B1 times to yield a set of B1 bootstrap estimates EMBED Equation.3 .
a) EMBED Equation.3 is drawn from the N(0, EMBED Equation.3 ) distribution with lefttruncation at EMBED Equation.3 .
b) EMBED Equation.3 is computed.
c) A pseudo data set ( EMBED Equation.3 ) is constructed, where EMBED Equation.3 and EMBED Equation.3 .
d) A new DEA estimate EMBED Equation.3 is computed on the set of pseudo data ( EMBED Equation.3 ), i.e. Y and X are respectively replaced by EMBED Equation.3 and EMBED Equation.3 in program (2).
For each farm i=1,,n, the biascorrected estimator EMBED Equation.3 is computed as follows:
(3) EMBED Equation.3
where EMBED Equation.3 is the bootstrap estimator of bias obtained as (Simar and Wilson, 1998):
(4) EMBED Equation.3 .
Maximum likelihood is used in the truncated regression of EMBED Equation.3 on zi, to provide an estimate EMBED Equation.3 of EMBED Equation.3 and an estimate EMBED Equation.3 of EMBED Equation.3 .
The next three steps (ac) are repeated B2 times to yield a set of B2 bootstrap estimates EMBED Equation.3 .
a) For each farm i=1,n, EMBED Equation.3 is drawn from the N(0, EMBED Equation.3 ) distribution with left truncation at EMBED Equation.3 .
b) For each farm i=1,n, EMBED Equation.3 is computed.
c) Maximum likelihood is used in the truncated regression of EMBED Equation.3 on zi, to provide an estimate EMBED Equation.3 of EMBED Equation.3 and an estimate EMBED Equation.3 of EMBED Equation.3 .
Confidence intervals are constructed. The estimated EMBED Equation.3 per cent confidence interval of the jth element EMBED Equation.3 of the vector EMBED Equation.3 , is as follows:
(5) EMBED Equation.3
where EMBED Equation.3 and EMBED Equation.3 are calculated using the empirical intervals:
(6) EMBED Equation.3
where EMBED Equation.3 EMBED Equation.3 + EMBED Equation.3
EMBED Equation.3 EMBED Equation.3 + EMBED Equation.3 .
The same method is applied to construct confidence intervals for the efficiency scores (Simar and Wilson, 2000).
References
Brmmer, B. (2001). Estimating Confidence Intervals for Technical Efficiency: The Case of Private Farms in Slovenia. European Review of Agricultural Economics 28(3), 285306.
Charnes, A., Cooper, W. and Rhodes, E. (1978). Measuring the Efficiency of Decision Making Units. European Journal of Operational Research 2, 429444.
Charnes, A., Cooper, W. and Rhodes, E. (1981). Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. Management Science 27(6), 668697.
Coelli, T., Rao, P. and Battese, G. (1998). An Introduction to Efficiency and Productivity Analysis. Norwell: Kluwer Academic Publishers.
Curtiss, J. (2002). Efficiency and Structural Changes in Transition: A Stochastic Frontier Analysis of Czech Crop Production. Institutional Change in Agriculture and Natural Resources, vol. 12. Aachen: Shaker Verlag.
Davidova, S., Gorton, M., Iraizoz, B. and Ratinger, T. (2003). Variations in Farm Performance in Transitional Economies: Evidence From The Czech Republic. Journal of Agricultural Economics 54(2), 227245.
Fre, R., Grosskopf, S. and Lovell, C. (1994). Production Frontiers. Cambridge: Cambridge University Press.
Gorton, M. and Davidova, S. (2004). Farm Productivity and Efficiency in the CEE Applicant Countries: A Synthesis of Results. Agricultural Economics 30(1), 116.
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Jensen, M. (1986). Agency Costs of Free Cash Flow, Corporate Finance and Takeovers. American Economic Review 76, 323329.
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Latruffe, L., Balcombe, K., Davidova, S. and Zawalinska, K. (2004). Determinants of Technical Efficiency of Crop and Livestock Farms in Poland. Applied Economics 36(12), 12551263.
Latruffe, L., Balcombe, K., Davidova S. and Zawalinska, K. (2005). Technical and Scale Efficiency of Crop and Livestock Farms in Poland: Does Specialisation Matter? Agricultural Economics 32(3), 281296.
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Table 1: Summary statistics for the sample farms according to specialisation and organisational form
VariablesMeanStandard deviationMinimum valueMaximum valueMeanStandard deviationMinimum valueMaximum valueIndividual farmsLivestock farms (53 farms)Crop farms (221 farms)DEA modelTotal output (000 CZK)3,7505,50622625,7842,8074,43811433,076Land (ha)142257101,400144195151,562Labour (AWU)4.687.030.9240.953.204.470.0735.00Capitala (000 CZK)570818204,79846285536,190Intermediate consumption (000 CZK)2,9374,82920130,4271,9722,85514122,789Secondstage regressionLivestock Units86.3135.36.2727.2Capitala / Labour (000 CZK /AWU)128101945614920621563Land / Labour (ha /AWU)281789360544486Share of hired labour (%)243401002131097Share of rented land (%)6533010068300100Financial stress ratio0.0320.03900.2010.0540.07100.490VariablesMeanStandard
DeviationMinimum
valueMaximum
valueMeanStandard
DeviationMinimum
valueMaximum
valueCorporate farmsLivestock farms (35 farms)Crop farms (35 farms)DEA modelTotal output (000 CZK)43,72730,2626,948127,95143,31334,1323,652131,928Land (ha)1,4807212203,0841,4988364243,952Labour (AWU)78.8754.6312.00253.0060.5938.1713.00140.23Capitala (000 CZK)6,0634,1591,33619,1865,6233,74282114,953Intermediate consumption (000 CZK)31,99819,2964,07373,89226,08817,5624,92873,454Secondstage regressionLivestock Units65.033.85.6195.2Capitala / Labour (000 CZK /AWU)853841197964042199Land / Labour (ha /AWU)231346729161270Share of hired labour (%)10001001001000100100Share of rented land (%)9928910098670100Financial stress ratio0.0400.04300.1970.0340.02800.117a Interest plus depreciationTable 2: Descriptive statistics of technical efficiency
Farm specialisation
and formMeanStandard deviationMinimumShare of farms with efficiency score of 1 (%)Total technical efficiencyIndividualLivestock
Crop1.99
1.640.58
0.613.47
4.943.8
6.3CorporateLivestock
Crop1.24
1.620.25
0.581.82
2.9825.7
8.6Pure technical efficiencyIndividualLivestock
Crop1.65
1.470.56
0.553.07
4.4718.9
18.1CorporateLivestock
Crop1.16
1.290.21
0.381.76
2.2937.1
31.4Scale efficiencyIndividualLivestock
Crop1.25
1.130.37
0.202.88
3.003.8
6.3CorporateLivestock
Crop1.07
1.280.10
0.441.44
2.8625.7
8.6Table 3: Width of efficiency estimates confidence intervals
Farm specialisation
and formWidth for total
technical efficiencyWidth for pure technical efficiencyIndividualLivestock
Crop1.87
1.232.18
1.41CorporateLivestock
Crop0.51
1.000.59
1.67
Table 4: Total technical efficiency DEA estimate, bias and confidence intervals bounds: means a
Farm specialisation and formDEA estimateBias Lower bound Upper bound IndividualLivestock
Crop1.99
1.643.54
2.844.61
3.896.79
5.30CorporateLivestock
Crop1.24
1.620.68
2.311.68
3.232.26
4.90a The lower bound indicates the highest efficiency and the upper, the lowest.
Table 5: Determinants of pure technical inefficiency: double bootstrap estimation
Individual farmsCorporate farmsLivestockCropLivestockCropConstant
Size variable a
Ratio capital/labour
Ratio land/labour
Share of hired labour
Share of rented land
Financial stress ratio
DLTD
DJSTOCK
DREG1
DREG2
DREG3
DREG4
3.35 **
(2.26, 4.45)
4.26 E2 **
(7.29, 3.31) E2
5.38 E2 **
(2.48, 8.89) E2
23.84 E2 **
(47.22, 5.55) E2
4.06 E2
(5.03, 15.29) E2
2.61 E2
(7.02, 13.54) E2
84.06 **
(7.49, 171.7)



16.55 **
(27.96, 8.89)
4.92
(14.80, 3.90 )
6.73
(17.07, 2.82)7.16 **
(5.39, 8.88)
0.11 E2
(1.09, 0.85 ) E2
0.03 E2
(0.07, 0.08) E2
6.96 E2 **
(11.6, 5.84) E2
10.78 E2 **
(19.1, 6.74) E2
5.58 E2 **
(1.39, 11.98) E2
43.04 **
(24.43, 72.87)


53.75 **
(73.49, 37.68)
50.00 **
(67.94, 33.92)
45.66 **
(62.95, 28.76)
41.03 **
(58.99, 23.13) 0.76 **
(0.44, 1.07)
2.27 E2
(5.37, 0.05) E2
2.04 E2
(4.62, 0.02) E2
1.55 E2
(7.32, 10.43) E2


4.91 **
(2.73, 7.77)
2.66 **
( 5.46, 0.28 )
1.33
(3.81, 0.39)
1.46
(4.93, 1.97)
27.35 **
(5.99, 48.44)
1.79
(3.94, 0.07)
1.60
(3.57, 4.40)0.51
(5.55, 1.10)
0.17 E2
(0.07, 0.51) E2
1.78 E2
(3.85, 8.27) E2
10.48 E2
(32.48, 6.48) E2


2.44
(3.01, 9.90)
3.83
(0.62, 9.50)
3.30
(2.41, 10.01)
2.42
(16.74, 9.62)
55.54
(19.73, 144.4)
2.08
(8.68, 3.15)

**: 5% significance. E2: 10 power 2. Lower and upper bounds for 5 percent confidence interval between brackets.
a UAA for crop farms, livestock units for livestock farms.
Table 6: Determinants of pure technical inefficiency: standard estimation
Individual farmsCorporate farmsLivestockCropLivestockCropConstant
Size variable a
Ratio capital/labour
Ratio land/labour
Share of hired labour
Share of rented land
Financial stress ratio
DLTD
DJSTOCK
DREG1
DREG2
DREG3
DREG4
0.86 **
(0.25)
1.17 E2**
(0.56 E2)
2.33 E2 **
(0.69 E2)
8.20 E2
(4.63 E2)
1.86 E2
(2.24 E2)
0.57 E2
(2.34 E2)
40.63 **
(17.63)



6.41 **
(2.09)
2.49
(2.04)
3.02
(2.20)2.32 **
(0.35)
0.03 E2
(0.22 E2)
0.14 E2
(0.19 E2)
2.07 E2 **
(0.73 E2)
3.38 E2 **
(1.37 E2)
0.70 E2
(1.14 E2)
18.35 **
(4.93)


20.00 **
(3.74)
18.59 **
(3.41)
16.86 **
(3.44)
14.75 **
(3.62)0.19
(0.11)
1.11 E2
(1.00 E2)
1.35 E2
(0.85 E2)
3.18 E2
(2.99 E2)


2.82 **
(0.87)
1.57
(0.91)
0.92
(0.66)
0.48
(1.24)
19.92 **
(7.07)
0.97
(0.69)
0.78
(0.75)0.02
(0.26)
0.07 E2
(0.08 E2)
0.77 E2
(1.79 E2)
3.41 E2
(5.91 E2)


0.56
(1.97)
2.12
(1.53)
1.44
(1.90)
2.23
(3.88)
33.21
(24.01)
1.33
(1.84)

**: 5% significance. E2: 10 power 2. Standard errors into brackets.
a UAA for crop farms, livestock units for livestock farms.
PAGE
PAGE
PAGE 27
PAGE
PAGE
( The authors are very grateful to Tomas Ratinger for making the data set available.
Although the effect of ownership structure on farm technical efficiency could be assessed with program efficiency based on the construction of an interenvelope for the whole sample (see Charnes et al., 1981), this paper is solely concerned with the efficiency variations within separate subsamples and their consistent explanation with the double bootstrap.
The technical efficiency calculated under CRS is called the total technical efficiency, and can be broken down into two components: the pure technical efficiency, that represents the management practices and that is given by the specification under VRS, and the residual, called the scale efficiency.
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