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One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels
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## TL;DR
This paper compares one-step and two-step estimation for stochastic frontier models when exogenous variables affect technical inefficiency. In Monte Carlo simulations, the one-step estimator performs well, while the two-step procedure shows serious bias in both the first and second stages.
## Key findings
- In the base case simulation (200 replications, sample size \(N=200\)), the one-step estimator is close to unbiased: \(\hat\beta=-0.0010\), \(\hat\delta=1.0010\), and average estimated efficiency \(E(\hat e^{-u})=0.5141\) versus the true \(0.5165\).
- Under the same base case, the two-step estimator is badly biased: \(\hat\beta=-0.3064\), estimated efficiency \(E(\hat e^{-u})=0.4482\) versus true \(0.52\) (table reports \(0.5165\) in the design and about \(0.52\) in results discussion), and the second-step estimate of \(\delta\) is \(0.3539\) versus the true value \(1\).
- The paper reports that the two-step bias persists even when \(x\) and \(z\) are independent: for \(\rho=0\), the second-step estimate of \(\delta\) is still \(0.4069\), and the estimated efficiencies remain underdispersed and downward biased.
- Increasing sample size from \(N=200\) to \(N=500\) and \(N=1000\) lowers standard deviations but does not remove the two-step biases; for example, the two-step \(\hat\delta\) stays around \(0.35\)–\(0.36\) while the true value is \(1\).
## Methods
- The paper studies a stochastic frontier model in which inefficiency depends on exogenous variables \(z\), emphasizing a “scaling property” specification where the one-sided inefficiency term is a function of \(z\) times a basic one-sided error.
- It uses Monte Carlo simulations with 2,000 replications per design point. The base case sets \(\beta=0\), \(\delta=1\), \(\rho=0.5\), \(\gamma=1\), \(\sigma_v=1\), \(\mu=0\), and \(N=200\).
- One-step estimation is maximum likelihood under the correctly specified model; two-step estimation first sets \(\delta=0\) in the frontier MLE, then regresses \(\ln(\hat u)\) on \(z\) to estimate \(\delta\).
## Limitations
- The paper’s own simulation evidence is limited to one simple model with the scaling property and a specific truncated-normal basic distribution; results may not generalize beyond that setup.
- The text makes evident, though it does not frame it as a formal limitation, that some parameters (\(\mu\) and \(\gamma\)) are “hard” to estimate and produced outliers severe enough that the authors truncated the most extreme 0.3% of replications for those parameters.
- Not stated in the paper.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Our simulations strongly confirm the relevance of this observation, since the two-step estimates of the effect of z on efficiency levels are seriously biased downward in all cases.”
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In the paper
“We first note that the one-step estimates look pretty good. In particular, there is no evidence of significant bias.”
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In the paper
“The parameters of the truncated normal base distribution ( µ and γ ) have rather large variances (their standard deviations are definitely not small relative to the parameter values themselves)”
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In the paper
“For the one-step estimator, the true value of δ is not terribly important.”
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In the paper
“But this does not seem to cause any problems for the parameters of main interest ( β , δ and the individual ri).”
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In the paper
“Second, the estimates of the ri (the technical efficiencies) are biased downward (mean = 0.45, compared to the mean of the actual ri of 0.52).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Changing β has no substantive effects on our results.”
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In the paper
“First, the estimate of β is biased downward (mean = -0.31, compared to the true value = 0).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Third, the second-step estimator of δ is very significantly biased downward (mean = 0.35, compared to the true value = 1).”
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In the paper
“Changing δ makes very little difference to the properties of the estimates of β , δ or σ v.”
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In the paper
“The bias of the estimate of β and of the two-step estimate of δ increases, and the estimates of the ri are also more biased, and less correlated with the true ri, compared to Case 1.”
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In the paper
“As expected, the bias of the first-step estimate of β is effectively zero when δ = 0, and it grows with δ .”
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In the paper
“All of these biases are in the expected direction, and the size of the biases is definitely not small.”
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In the paper
“They are less strongly correlated with the true ri and they are underdispersed, compared to the estimates from the one-step model.”
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In the paper
“The individual ri are seriously biased for δ = 1 but not for the smaller values of δ .”
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In the paper
“The two-step estimator of δ is biased for both δ = 1 and δ = 0.5, but the bias disappears as δ → 0.”
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“An interesting curiosity is the bias in the two-step estimator of δ based on the estimates of ui from the one-step model (mean estimate = 0.92, compared to the true value of δ = 1). This is not just finite-sample bias (it persists with larger sample sizes).”
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In the paper
“The mean of the estimate (both one-step and two-step) of β changes by the same amount that β is changed, so that the bias, standard deviation and MSE of the estimates of β are unchanged.”
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In the paper
“For this set of parameters, average technical efficiency is E(e -u ) = 0.5165.”
Strength:plain· not yet calibratedn = 200Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“As δ → 0, our ability to estimate µ (and γ , to a lesser extent) deteriorates seriously.”
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In the paper
“The estimates of the individual ri become slightly more biased, and noticeably less strongly correlated with the true ri, when δ is small.”
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In the paper
“We find serious bias at all stages of this procedure. The size of the bias is very substantial and should argue strongly against two-step procedures.”
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“For the two-step estimates, surprisingly, imposing µ = 0 makes things worse (even though µ = 0 is a correct restriction).”
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In the paper
“As γ increases, the bias of the estimate of β increases, but the bias of the second-step estimate of δ decreases quite noticeably.”
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“Finally, the second-step estimate of δ is seriously biased even when ρ = 0, though its bias does grow with ρ .”
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In the paper
“The standard deviations of the estimators fall as N increases, but nothing else changes much.”
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In the paper
“For example, the mean of the two-step estimator of δ is 0.35 for σ v = 1, 0.12 for σ v = 3, and 0.05 for σ v = 5.”
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In the paper
“| 9 | µ = 1 | ˆ β | -0.0013 | 0.0963 | 0.0093 | | -0.3914 | 0.1191 | 0.1674 | |”
- Also stated in: § 4. CONCLUDING REMARKS · plain
“| 17 | N=500 | ˆ β | -0.0005 | 0.0572 | 0.0033 | | -0.3062 | 0.0661 | 0.0981 | |”
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- Also stated in: § 4. CONCLUDING REMARKS · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“| 9 | | E ( ˆ e - u ) | 0.3850 | 0.0294 | 0.0285 | 0.8387 | 0.3499 | 0.0197 | 0.0513 | 0.6891 |”
- Also stated in: § 4. CONCLUDING REMARKS · plain
“| 17 | N=500 | E ( ˆ e - u ) | 0.5160 | 0.0220 | 0.0338 | 0.8145 | 0.4470 | 0.0146 | 0.0615 | 0.6591 |”
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- Also stated in: § 4. CONCLUDING REMARKS · plain
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In the paper
“For the two-step estimators, we see more differences as µ changes, but they are still not really important or striking.”
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In the paper
“The true value of δ is one, so these are large biases indeed.”
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In the paper
“| 9 | E ( e - u ) | ˆ µ | 1.0591 | 0.3951 | 0.1595 | | -37.2499 | 1.1759 | 1464.4405 | |”
- Also stated in: § 4. CONCLUDING REMARKS · plain
“| 13 | E ( e - u ) | ˆ µ | 0.0429 | 0.4471 | 0.2016 | -37.2787 | 0.1688 | 1389.7299 | |”
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- Also stated in: § 4. CONCLUDING REMARKS · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“| 9 | | ˆ δ | 1.0002 | 0.0850 | 0.0072 | | - | - | - | |”
- Also stated in: § 4. CONCLUDING REMARKS · plain
“| 17 | N=500 | ˆ δ | 0.9995 | 0.0724 | 0.0052 | | - | - | - | |”
Strength:plain· not yet calibratedn = 500Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Also stated in: § 4. CONCLUDING REMARKS · plain
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In the paper
“The results are quite consistent with these expectations.”
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In the paper
“| 9 | | ˆ δ -2S | 0.9317 | 0.0888 | 0.0125 | 0.8025 | 0.4986 | 0.0566 | 0.2546 | 0.3469 |”
- Also stated in: § 4. CONCLUDING REMARKS · plain
“| 17 | N=500 | ˆ δ -2S | 0.9134 | 0.0736 | 0.0129 | 0.7911 | 0.3520 | 0.0336 | 0.4210 | 0.2375 |”
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- Also stated in: § 4. CONCLUDING REMARKS · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| 17 | N=500 | ˆ γ | 1.0208 | 0.2393 | 0.0577 | | 53.4005 | 4.3493 | 2764.7151 | |”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
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In the paper
“For the one-step estimators, the value of ρ is not important. The results are essentially identical across all these cases.”
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In the paper
“For larger γ , we estimate β a little worse, but we estimate δ and the individual ri a little better.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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“As µ moves from plus one to negative one, the estimates of β improve a little, and the estimates of the individual ri perhaps improve a little.”
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“As is often the case in simulations that involve numerical maximization, there were some problems with outliers, especially in estimation of γ and µ (the parameters of the truncated normal distribution).”
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In the paper
“This bias in the second-step regression, due to underdispersion in the estimates of u that do not take into account the effect of z on u, does not seem to be systematically discussed in the literature.”
What the sources say
- Not checked — no full text of the sourcecites Kumbhakar and Lovell (2000, p. 119) source
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In the paper
“That is, if the estimates of u are constructed ignoring the effect of z on σ u 2 , they will show less dependence on z than they should, and we should expect the second-step regressions to give downward biased estimates of the effect of z on u.”
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“Some but not all of the models in the literature have this property.”
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In the paper
“The one-step MLE will be based on the correctly specified model, and will therefore be consistent and asymptotically efficient.”
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In the paper
“For example, Caudill and Ford (1993) provide evidence on the bias of the estimated technological parameters, but not on the efficiency levels themselves or their relationship to the explanatory variables z.”
What the sources say
- Not checked — no full text of the sourcecites Caudill and Ford (1993) source
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In the paper
“For example, if h(z, δ ) = exp(z' δ ) and δ > 0, then large z will on average be associated with large u and also with large σ u 2”
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In the paper
“Presumably this is so because when δ is large, z correlates with u and is useful to help estimate u.”
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In the paper
“Saying the same thing, if we ignore the dependence of σ u 2 on z, we will shrink the observations with large u too much, and the observations with small u too little, and our estimates of u will be underdispersed.”
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“It is widely appreciated that the severity of the bias in estimation of the technological parameters (coefficients of x) depends on the magnitude of the correlation between x and z.”
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In the paper
“A second and less widely recognized problem is that the first-step technical efficiency measures are likely to be seriously underdispersed, so that the results of the second-step regression are likely to be biased downward. This is true regardless of whether x and z are correlated.”
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In the paper
“The first of these is that it captures the idea, which we find intuitively reasonable and appealing, that the shape of the distribution of u is the same for all firms.”
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In the paper
“That is, the second-step estimator of δ may be able to tell us whether or not z affects u (whether or not δ = 0) 3 but it cannot accurately estimate the effect of z on u when this effect exists.”
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“Models based on some other simple distributions, such as exponential, would also have the scaling property.”
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In the paper
“Our summary statistics are averages and are very sensitive to extreme outliers.”
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In the paper
“Importantly, this is true whether or not x and z are correlated.”
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In the paper
“One important implication of this viewpoint, which is sometimes missed, is that the variables z that determine inefficiency must not be functions of y.”
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In the paper
“This truncation of the results made very little difference for the parameters other than µ and γ .”
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In the paper
“Increasing σ v increases the amount of statistical noise in the model, and should increase the bias and/ or variance for each of the estimated parameters.”
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In the paper
“However, as long as δ is non-zero, this argument may be less than compelling, because the distribution of u depends on z whereas the distribution of v does not, and this is another way to distinguish u from v.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: The distribution of u depends on z whereas the distribution of v does not.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Increasing γ while holding σ v constant has the effect of increasing the size of inefficiency relative to noise, and should tend to make it easier to estimate technical inefficiency precisely.”
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, when µ is large and positive, the degree of truncation is very small, and the shape of the distribution (if it can be separated from that of v) contains a lot of information about the parameters µ and σ 2 .”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this case the first-step estimator of β is unbiased, and we then estimate the ri under the correct assumption that they do not depend on the zi, so we ought to do well in this case.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As µ → ∞ , the distribution of u becomes normal and presumably becomes confounded with the normal distribution of v (statistical noise).”
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When µ is large (in absolute value) but negative, on the other hand, we observe only the extreme right tail of the distribution, whose shape may not be very informative about µ and σ 2 , and the estimation problem may be harder just on that basis.”
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“All in all, the two-step estimator performs well when the second step is not needed ( δ = 0) but is otherwise unreliable.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These biases are substantial enough that we would recommend against using two-step procedures in any circumstances that we can envision.”
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence.
The authors state this as an assumption.
In the theoretical exploration of underdispersion, x and z are independent.
“To explore this point more precisely, suppose that x and z are independent, so that the first-step regression is unbiased.”
The paper relies on this without support.
The distribution of u depends on z whereas the distribution of v does not.
“because the distribution of u depends on z whereas the distribution of v does not”
The paper relies on this without support.
The biases identified above are expected to persist asymptotically.
“the biases we have identified above are expected to persist asymptotically”
The paper relies on this without support.
The one-step estimators are based on a correctly specified model and are asymptotically optimal.
“The one-step estimators are based on a correctly specified model and are asymptotically optimal.”
Citations
Cites
Battese, G. E., & Coelli, T. J. (1995) · Empirical Economics · doi:10.1007/bf01205442 · Cited by 5,978
Kumbhakar, S. C., & Lovell, C. A. K. (2000) · doi:10.1017/cbo9781139174411 · Cited by 4,358
Battese, G. E., & Coelli, T. (1988) · Journal of Econometrics · doi:10.1016/0304-4076(88)90053-x · Cited by 1,919
Kumbhakar, S. C., Ghosh, S., & McGuckin, J. T. (1991) · Journal of Business & Economic Statistics · doi:10.1080/07350015.1991.10509853 · Cited by 1,162
Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency
Reifschneider, D. L., & Stevenson, R. (1991) · International Economic Review · doi:10.2307/2527115 · Cited by 686
Estimation of a non-neutral stochastic frontier production function
Huang, C. J., & Liu, J.-T. (1994) · Journal of Productivity Analysis · doi:10.1007/bf01073853 · Cited by 593
Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity
Caudill, S. B., Ford, J. M., & Gropper, D. M. (1995) · Journal of Business and Economic Statistics · doi:10.1080/07350015.1995.10524583 · Cited by 390
Biases in frontier estimation due to heteroscedasticity
Caudill, S. B., & Ford, J. M. (1993) · Economics Letters · doi:10.1016/0165-1765(93)90104-k · Cited by 256
Pitfalls of Normal-Gamma Stochastic Frontier Models
Ritter, C., & Simar, L. (1997) · Journal of Productivity Analysis · doi:10.1023/a:1007751524050 · Cited by 174
Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity
Caudill, S. B., Ford, J. M., & Gropper, D. M. (1995) · Journal of Business and Economic Statistics · doi:10.2307/1392525 · Cited by 116
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Cost efficiency and technological gap in Western European banks: A stochastic metafrontier analysis
Lee, C., & Huang, T. (2016) · International Review of Economics & Finance · doi:10.1016/j.iref.2016.12.003 · Cited by 41
Mutz, R., Bornmann, L., & Daniel, H. (2017) · Journal of Informetrics · doi:10.1016/j.joi.2017.04.009 · Cited by 41
Inference‐in‐residuals as an Estimation Method for Earnings Management
Christodoulou, D., Ma, L., & Vasnev, A. L. (2018) · Abacus · doi:10.1111/abac.12121 · Cited by 40
Zhou, Y., Shi, X., Heerink, N., et al. (2018) · Applied Economics · doi:10.1080/00036846.2018.1543941 · Cited by 40
“However, this two-step approach was criticized for the inconsistency between the independency assumption of ui in the first step and the dependency assumption in the second step (Wang and Schmidt 2002).”
BackgroundBaležentis, T., & Sun, K. (2020) · European Journal of Operational Research · doi:10.1016/j.ejor.2020.02.032 · Cited by 40
Cost efficiency in Swedish public transport
Vigren, A. (2016) · Research in Transportation Economics · doi:10.1016/j.retrec.2016.05.009 · Cited by 39
Estimation of the two-tiered stochastic frontier model with the scaling property
Parmeter, C. F. (2017) · Journal of Productivity Analysis · doi:10.1007/s11123-017-0520-8 · Cited by 39
Identifying the Demand and Supply Effects of Financial Crises on Bank Credit—Evidence from Taiwan
Chen, N., & Wang, H. (2008) · Southern Economic Journal · doi:10.1002/j.2325-8012.2008.tb00890.x · Cited by 38
Self-citationAnalysis of production efficiency of beef cow/calf farms in Alberta
Samarajeewa, S., Hailu, G., Jeffrey, S. R., et al. (2011) · Applied Economics · doi:10.1080/00036846.2010.507173 · Cited by 38
“effects models are estimated simultaneously in a single stage (Coelli, 1995; Wang and Schmidt, 2002).”
BackgroundEfficiency externalities of trade and alternative forms of foreign investment in OECD countries
Iyer, K. G., Rambaldi, A. N., & Tang, K. K. (2008) · Journal of Applied Econometrics · doi:10.1002/jae.1024 · Cited by 38
Mugera, A. W., & Nyambane, G. G. (2014) · Australian Journal of Agricultural and Resource Economics · doi:10.1111/1467-8489.12075 · Cited by 38
Bucci, V., Ferrara, G., & Resce, G. (2023) · Applied Economics · doi:10.1080/00036846.2023.2169241 · Cited by 49
“Therefore, we assume that the inefficiency term depends on a set of exogenous covariates via the so-called ‘scale’ transformation (Wang and Schmidt 2002) of some underlying process η i : where z it is a vector of contextual variables, γ is a vector of unknown coefficients and η it is an i.i.d.…”
BackgroundLee, K., Ha, S. M., Gurudatt, N. G., Heo, W., Hyun, K.-A., Kim, J., & Jung, H. (2023) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2023.132775 · Cited by 37
Do farmers choose to be inefficient? Evidence from Bicol
Larson, D. F., & Plessmann, F. (2009) · Journal of Development Economics · doi:10.1016/j.jdeveco.2007.04.003 · Cited by 37
Llorca, M., Orea, L., & Pollitt, M. G. (2014) · Operations Research Perspectives · doi:10.1016/j.orp.2014.03.002 · Cited by 37
“However, theway in which our DGP is defined here is not uncommon in efficiency analysis papers and can be found both in the SFA literature (see for instance [28]; or [29]) and in the DEA literature (see for instance [30]; or [31]).”
BackgroundWhich firms benefit from foreign direct investment? Empirical evidence from Indonesian manufacturing
Suyanto, S., Salim, R. A., & Bloch, H. (2014) · Journal of Asian Economics · doi:10.1016/j.asieco.2014.05.003 · Cited by 37
An analysis of the productivity and technical efficiency of smallholder irrigation in Ethiopia
Makombe, G., Namara, R. E., Awulachew, S. B., et al. (2017) · Water SA · doi:10.4314/wsa.v43i1.08 · Cited by 37
Heterogeneous spillovers among Spanish provinces: a generalized spatial stochastic frontier model
Gude, A., Ayuso, I. Á., & Orea, L. (2018) · Journal of Productivity Analysis · doi:10.1007/s11123-018-0540-z · Cited by 37
Zhang, F. (2021) · Journal of Environmental Management · doi:10.1016/j.jenvman.2021.113388 · Cited by 37
Stochastic Frontier Analysis: Foundations and Advances II
Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (2020) · Springer eBooks · doi:10.1007/978-981-10-3450-3_11-1 · Cited by 45
Consistent Estimation of the 'True' Fixed-Effects Stochastic Frontier ModelPreprint
Belotti, F., & Ilardi, G. (2012) · SSRN Electronic Journal · doi:10.2139/ssrn.2045474 · Cited by 37
D’Errico, M. C. (2024) · Energy Economics · doi:10.1016/j.eneco.2024.107447 · Cited by 39
Tran, K. C., & Tsionas, E. G. (2009) · Economic Modelling · doi:10.1016/j.econmod.2009.02.011 · Cited by 36
Banking efficiency in Gulf Cooperation Council (GCC) countries: A comparative study
Mohanty, S. K., Lin, H., Al-Juhani, E. A., & Bardesi, H. J. (2016) · Review of Financial Economics · doi:10.1016/j.rfe.2016.06.004 · Cited by 36
Barra, C., Lagravinese, R., & Zotti, R. (2017) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2017.09.002 · Cited by 36
Nguyen, H., Ngo, T., Le, T., Ho, H., & Nguyen, H. T. (2019) · Sustainability · doi:10.3390/su11092472 · Cited by 44
“Again, it supports the argument of References [7,8], saying that farms can improve their efficiency by minimizing the use of pesticides to achieve sustainable goals.”
MethodEstimation and determinants of efficiency among rice farmers in Benin
Houngue, V., & Nonvide, G. M. A. (2020) · Cogent Food & Agriculture · doi:10.1080/23311932.2020.1819004 · Cited by 36
Birhanu, M. Y., Alemayehu, T., Bruno, J. E., et al. (2021) · Sustainability · doi:10.3390/su13158539 · Cited by 36
Bank efficiency and local market conditions. Evidence from Italy
Aiello, F., & Bonanno, G. (2015) · Journal of Economics and Business · doi:10.1016/j.jeconbus.2015.09.002 · Cited by 36
Karagiannis, G. (2005) · European Review of Agricultural Economics · doi:10.1093/erae/jbi004 · Cited by 37
“15 Claudill, Ford and Gropper (1995) have considered a different specification of the variance function, which however is equivalent to (7b) if a constant is included in the z vector (Wang and Schmidt, 2002).”
Financial liberalization, financial regulation and bank efficiency: a multi-country analysis
Hermes, N., & Meesters, A. (2015) · Applied Economics · doi:10.1080/00036846.2015.1005815 · Cited by 35
Effects of redistributing policy support on farmers’ technical efficiency
Bonfiglio, A., Henke, R., Pierangeli, F., et al. (2019) · Agricultural Economics · doi:10.1111/agec.12556 · Cited by 35
Zheng, B., Wang, Y., Kamal, M. A., & Ullah, A. (2020) · International Journal of Emerging Markets · doi:10.1108/ijoem-10-2019-0789 · Cited by 38
Excessive focus on risk? Non‐performing loans and efficiency of microfinance institutions
Zamore, S., Beisland, L. A., & Mersland, R. (2021) · International Journal of Finance & Economics · doi:10.1002/ijfe.2477 · Cited by 35
“Moreover, Wang and Schmidt (2002) show that the two-step approach produces biased coefficients since it suffers from the assumption that the efficiency term is independent and identically truncated and normally distributed in the first step, while in the second step the efficiency terms are assumed…”
BackgroundJonghe, O. D., Disli, M., & Schoors, K. J. L. (2011) · Journal of Financial Services Research · doi:10.1007/s10693-011-0115-x · Cited by 35
“Wang and Schmidt (2002) provide persuasive Monte Carlo evidence explaining why both stages of the two-stage procedure are seriously biased. efficiency levels.”
Tax revenue potential and effort - an empirical investigation
Langford, B. (2016) · Cited by 35
Shaik, S., Allen, A. J., Edwards, S., & Harris, J. (2012) · Journal of the Transportation Research Forum · doi:10.5399/osu/jtrf.48.3.2311 · Cited by 35
Structural reforms and banking efficiency in the new EU States
Koutsomanoli‐Filippaki, A., Mamatzakis, E. C. M., & Staikouras, C. (2008) · Journal of Policy Modeling · doi:10.1016/j.jpolmod.2008.03.005 · Cited by 34
“Wang and Schmidt (2002) provide compelling Monte Carlo evidence explaining why both stages of the two-stage procedure are seriously biased.”
BackgroundSources of productivity growth on Finnish dairy farms—application of an input distance function
Sipiläinen, T. (2007) · Food Economics - Acta Agriculturae Scandinavica Section C · doi:10.1080/16507540701379694 · Cited by 34
“@The aim of this paper is to investigate the sources of productivity change by decomposing the Malmquist productivity index. This paper provides a detailed analysis of productivity changes for a sample of specialized Finnish dairy farms in the 1990s. A decomposition is presented that can recognize essential productivi…”
BackgroundInfluentialHou, X., Li, S., Pin, G., et al. (2018) · International Review of Economics & Finance · doi:10.1016/j.iref.2018.01.019 · Cited by 34
Bayesian estimation of inefficiency heterogeneity in stochastic frontier models
Galán, J., Veiga, H., & Wiper, M. P. (2013) · Journal of Productivity Analysis · doi:10.1007/s11123-013-0377-4 · Cited by 33
“…or in a particular case of truncated normal inefficiency where both parameters are an exponential function of firm characteristics as follows (see Wang and Schmidt 2002; Alvarez et al. 2006): uit Nþðlit; r2uitÞ lit ¼ l expðzitdÞ ruit ¼ ru expðzitdÞ: ð4Þ Specification (4) for the inefficiency is…”
Land reform in NE Brazil: a stochastic frontier production efficiency evaluation
de Magalhães, M. M., Filho, H. M. D. S., de Sousa, M. R., et al. (2011) · Revista de Economia e Sociologia Rural · doi:10.1590/s0103-20032011000100001 · Cited by 33
Women Participation: A Productivity Strategy in Rice Production
Rasheed, A. A., Mwalupaso, G. E., Abbas, Q., et al. (2020) · Sustainability · doi:10.3390/su12072870 · Cited by 33
“It also provides additional labor in essential farming activities and contributes essential skills [42] that could be pivotal for increasing rice productivity.”
BackgroundClassifying Ports for Efficiency Benchmarking: A Review and a Frontier-based Clustering Approach
Tovar, B., & Rodríguez-Déniz, H. (2015) · Transport Reviews · doi:10.1080/01441647.2015.1016473 · Cited by 33
“This model did not need to recur to second-stage analysis, thus avoiding inconsistency problems; see Wang and Schmidt (2002). However, they proposed the re-estimation of the model within a Fixed Effect Model (FEM) framework, by introducing port authorities dummy variables”
MethodAllocative efficiency of rural water supply – a globally flexible SGM cost frontier
Sauer, J., & Frohberg, K. (2006) · Journal of Productivity Analysis · doi:10.1007/s11123-006-0024-4 · Cited by 33
“Wang and Schmidt 2002 ) and modern software consequently includes a one-stage estimation procedure with respect to the error components model.”
MethodEconomic performance and efficiency determinants of crop-producing farms in Norway
Alem, H., Lien, G., & Hardaker, J. B. (2018) · International Journal of Productivity and Performance Management · doi:10.1108/ijppm-01-2018-0026 · Cited by 32
Land Use Transitions and Farm Performance in China: A Perspective of Land Fragmentation
Wang, S., Li, D., Li, T., et al. (2021) · Land · doi:10.3390/land10080792 · Cited by 32
“[46], the SFA approach was adopted for the current study.”
MethodInfluentialBasel regulations and banks’ efficiency: The case of the Philippines
Manlagñit, M. C. V. (2015) · Journal of Asian Economics · doi:10.1016/j.asieco.2015.06.001 · Cited by 32
Vertical integration and efficiency: an application to the Italian machine tool industry
Pieri, F., & Zaninotto, E. (2011) · Small Business Economics · doi:10.1007/s11187-011-9367-y · Cited by 32
Stochastic Frontier Estimation of Market Power in the Food Industries
López, R. A., He, X., & AZZAM, A. M. (2017) · Journal of Agricultural Economics · doi:10.1111/1477-9552.12219 · Cited by 32
On estimating efficiency effects in a stochastic frontier model
Paul, S., & Shankar, S. (2018) · European Journal of Operational Research · doi:10.1016/j.ejor.2018.05.052 · Cited by 31
Measuring overeducation with earnings frontiers and multiply imputed censored income data
Jensen, U., Gartner, H., & Rässler, S. (2006) · Social Science Open Access Repository (GESIS – Leibniz Institute for the Social Sciences) · Cited by 32
Duras, T., Javed, F., Månsson, K., et al. (2023) · Energy Economics · doi:10.1016/j.eneco.2023.106621 · Cited by 31
Deng, Z., Zhao, Q., & Bao, H. X. H. (2020) · Land · doi:10.3390/land9090311 · Cited by 31
“Wang and Schmidt [49] explained theoretically why two-step SFA procedures are biased, while Simar and Wilson [50,51], Cazals et al. [52], and Simar et al. [53] explained theoretically why two-step DEA procedures are biased.”
MethodFood Security Through Increasing Technical Efficiency
Bakhsh, K., Ahmad, B., & Hassan, S. (2006) · Asian Journal of Plant Sciences · doi:10.3923/ajps.2006.970.976 · Cited by 31
Liao, H., Liu, X., & Wang, C. (2011) · International Review of Applied Economics · doi:10.1080/02692171.2011.619970 · Cited by 31
“Wang and Schmidit ( 2002 ) have cautioned against this, arguing that the omission of the covariates at the ‘first step’, is tantamount to the omitted variable problem in the ordinary regression.”
BackgroundPublic sector enterprise disinvestment in India: Efficiency gains in a political context
Jain, R. (2017) · Journal of Asian Economics · doi:10.1016/j.asieco.2017.10.002 · Cited by 30
Njuki, E., & Bravo‐Ureta, B. E. (2018) · Water Resources and Economics · doi:10.1016/j.wre.2018.02.004 · Cited by 31
Sedebo, D. A., Li, G., Abebe, K. A., Etea, B. G., Ahiakpa, J. K., Ouattara, N., Olounlade, A., & Frimpong, S. (2021) · Agronomy Journal · doi:10.1002/agj2.20900 · Cited by 30
Economic, environmental, and energy equity convergence: Evidence of a multi-speed Europe?
Llorca, M., & Rodrı́guez-Álvarez, A. (2024) · Ecological Economics · doi:10.1016/j.ecolecon.2024.108133 · Cited by 30
Stochastic Frontier Analysis and Efficiency Estimation
Cornwell, C. M., & Schmidt, P. (2008) · Springer eBooks · doi:10.1007/978-3-540-75892-1_21 · Cited by 34
“Kumbhakar (1990) and Battese and Coelli (1992) proposed time-varying efficiency specifications of the form uit = γ(t, θ )δi , (21.40)”
BackgroundInfluentialSelf-citationIntegrating ESG Factors Into Cost‐Efficiency Frontier: Evidence From the European Listed Banks
Algeri, C., Brighi, P., & Venturelli, V. (2025) · Business Strategy and the Environment · doi:10.1002/bse.4140 · Cited by 29
Impact of Logistics on Technical Efficiency of World Production (2007–2012)
Coto‐Millán, P., Fernández, X. L., Pesquera, M. Á., & Agüeros, M. (2015) · Networks and Spatial Economics · doi:10.1007/s11067-015-9306-6 · Cited by 29
Bank ownership and cost efficiency: New empirical evidence from Russia
Mamonov, M. E., & Vernikov, A. V. (2017) · Economic Systems · doi:10.1016/j.ecosys.2016.08.001 · Cited by 33
Nonparametric estimation of the determinants of inefficiency in the presence of firm heterogeneity
Zhou, J., Parmeter, C. F., & Kumbhakar, S. C. (2020) · European Journal of Operational Research · doi:10.1016/j.ejor.2020.04.005 · Cited by 30
Saastamoinen, A., & Kuosmanen, T. (2014) · Energy Economics · doi:10.1016/j.eneco.2014.04.016 · Cited by 29
Green Inventions: Is Wait-and-see a Reasonable Option?
Stucki, T., & Wörter, M. (2016) · The Energy Journal · doi:10.5547/01956574.38.4.tstu · Cited by 30
“…consensus on a strict theoretical framework, which would be important to separate heterogeneity from efficiency in the estimated model (Green 2005a and Wang and Schmidt 2002 for the “left-out variable problem”) and to ensure that the estimation of the technological inefficiency is unbiased; this…”
BackgroundGalli, F. (2022) · Spatial Economic Analysis · doi:10.1080/17421772.2022.2097729 · Cited by 28
“In particular, we specify f (Zit , f) = exp (Zitf) and we apply the logarithm to ũit , as suggested by Wang and Schmidt (2002), to generate a very simple expression for the effect of the generic determinant Z on firms’ inefficiency level.”
BackgroundMethodInfluentialvan der Voort, M., Meensel, J. V., Lauwers, L., et al. (2014) · Journal of Dairy Science · doi:10.3168/jds.2013-7444 · Cited by 28
“The 1-step approach applied with SF analysis, the “inefficiency effect” model (Kumbhakar et al., 1991; Battese and Coelli, 1995; Wang and Schmidt, 2002), overcomes these problems.”
MethodChen, Z., Yang, Z., & Yang, L. (2019) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2019.04.004 · Cited by 28
The relationship between agritourism and social capital in Italian regions
Galluzzo, N. (2022) · Journal of Rural Studies · doi:10.1016/j.jrurstud.2022.06.010 · Cited by 36
Race, Technical Efficiency, and Retention: The Case of NBA Coaches
Fort, R., Lee, Y. H., & Berri, D. J. (2008) · International Journal of Sport Finance · doi:10.1177/155862350800300201 · Cited by 28
Do Institutions Matter for University Cost Efficiency? Evidence from Germany
Kempkes, G., & Pohl, C. (2008) · CESifo Economic Studies · doi:10.1093/cesifo/ifn009 · Cited by 32
“For these reasons, Wang and Schmidt (2002) strongly advocate single-stage procedures, in which efficiency estimates and the influence of environmental variables on the efficiency scores are estimated simultaneously.”
BackgroundInfluentialGlobalisation and technological convergence in the EU
Mastromarco, C., Serlenga, L., & Shin, Y. (2012) · Journal of Productivity Analysis · doi:10.1007/s11123-012-0308-9 · Cited by 28
“…expected to overcome two main shortcomings associated with some studies in modelling efficiency dynamics: the complexity of the likelihood function observed in the onestage approach by Battese and Coelli (1995) and the downward bias of the two-stage estimation documented in Wang and Schmidt (2002).”
Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data
Yao, F., Zhang, F., & Kumbhakar, S. C. (2017) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2017.1390467 · Cited by 27
Geffersa, A. G., Agbola, F. W., & Mahmood, A. (2019) · Outlook on Agriculture · doi:10.1177/0030727019830416 · Cited by 25
“Despite the popularity of the two-stage estimation procedure, several scholars (see McDonald, 2009; Wang and Schmidt, 2002) criticize this procedure for two main reasons.”
BackgroundMethodEfficiency evaluation of hotel chains: a Spanish case study
Deng, Y., Veiga, H., & Wiper, M. P. (2019) · SERIEs · doi:10.1007/s13209-019-0188-6 · Cited by 27
Oumer, A. M., Mugera, A. W., Burton, M. P., & Hailu, A. (2022) · Journal of Productivity Analysis · doi:10.1007/s11123-022-00627-2 · Cited by 35
Jaenicke, E. C., Frechette, D. L., & Larson, J. A. (2003) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.31059 · Cited by 27
The internal market and hospital efficiency: a stochastic distance function approach
Ferrari, A. (2006) · Applied Economics · doi:10.1080/00036840500427437 · Cited by 27
“One approach to do so is the estimation of a ‘one-step model’ (Wang and Schmidt, 2002), which, however, failed to converge to a maximum.”
BackgroundManagement systems and productive efficiency along the certification life-cycle
Hernández-Vivanco, A., & Bernardo, M. (2023) · International Journal of Production Economics · doi:10.1016/j.ijpe.2023.109028 · Cited by 38
Sheng, P., Zhai, M., Zhang, Y., et al. (2020) · Environmental Pollution · doi:10.1016/j.envpol.2020.115350 · Cited by 26
Impact of regional trade agreements on export efficiency – A case study of India
Kaushal, L. A. (2021) · Cogent Economics & Finance · doi:10.1080/23322039.2021.2008090 · Cited by 32
“Wang and Schmidt (2002) highlights that the neglected resistance variables in the first stage affecting the final inefficiency estimates is the main drawback of this approach.”
BackgroundRakshit, B. (2022) · International journal of organizational analysis · doi:10.1108/ijoa-06-2021-2802 · Cited by 26
The Role of Financial Innovations in the Current Global Financial Crisis
Park, Y. S. (2009) · Seoul National University Open Repository (Seoul National University) · Cited by 26
Profit and cost efficiency in the Italian banking industry (2006-2011)
Aiello, F., & Bonanno, G. (2013) · Economics and Business Letters · doi:10.17811/ebl.2.4.2013.190-205 · Cited by 26
“4 As shown by Lensink and Meesters (2012) and Wang and Schmidt (2002), the two-step approach suffers from the fact that the inefficiency is assumed to be identically and independently distributed in the main frontier equation, while it depends on other variables in the inefficiency equation.”
BackgroundDoes tenure security matter? : rural household responses to land tenure reforms in northwest China
lei, X. M. X. (2013) · doi:10.18174/281615 · Cited by 26
Pross, C. M., Strumann, C., Geißler, A., et al. (2018) · PLoS ONE · doi:10.1371/journal.pone.0203017 · Cited by 25
Goods and Services Tax efficiency across Indian States: panel stochastic frontier analysis
Mukherjee, S. (2020) · Indian Economic Review · doi:10.1007/s41775-020-00097-z · Cited by 25
Barbero, J., Diukanova, O., Gianelle, C., et al. (2021) · Regional Studies · doi:10.1080/00343404.2021.1926959 · Cited by 25
Stochastic Frontier Analysis: Foundations and Advances I
Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (2020) · Springer eBooks · doi:10.1007/978-981-10-3450-3_9-1 · Cited by 27
Are multi‐resort ski conglomerates more efficient?
Falk, M. (2009) · Managerial and Decision Economics · doi:10.1002/mde.1470 · Cited by 25
“…the inefficiencies are assumed to be independently and identically half-normally distributed (iid), while in the second stage the estimated inefficiencies are assumed to be a normally distributed and a function of a number of firm-specific factors (Coelli et al., 1998; Wang and Schmidt, 2002).”
BackgroundStationary Points for Parametric Stochastic Frontier Models
Horrace, W. C., & Wright, I. (2018) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2018.1526088 · Cited by 24
Haider, S., & Bhat, J. A. (2018) · International Journal of Energy Sector Management · doi:10.1108/ijesm-05-2017-0008 · Cited by 24
Huang, T. (2005) · Journal of Productivity Analysis · doi:10.1007/s11123-005-4933-4 · Cited by 26
“Wang and Schmidt (2002) instead suggested the use of one-step models, whenever the inefficiency term has the “scaling property.” In fact, they recommended against using two-step procedures in any cases.”
MethodResultInfluentialModelling environmental technical efficiency and phosphorus pollution abatement cost in dairy farms
Adenuga, A. H., Davis, J., Hutchinson, G., et al. (2020) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2020.136690 · Cited by 24
Determining the efficiency of residential electricity consumption
Andor, M., Bernstein, D. H., & Sommer, S. (2020) · Empirical Economics · doi:10.1007/s00181-020-01967-4 · Cited by 24
Stochastic frontier models using the Generalized Exponential distribution
Papadopoulos, A. (2021) · Journal of Productivity Analysis · doi:10.1007/s11123-020-00591-9 · Cited by 24
Managing Agricultural Water Use in a Changing Climate in China
An, Y., Li, Q., & Zhang, L. (2022) · Sustainable Production and Consumption · doi:10.1016/j.spc.2022.08.023 · Cited by 24
Looking at the determinants of efficiency in banking: evidence from Italian mutual-cooperatives
Aiello, F., & Bonanno, G. (2016) · International Review of Applied Economics · doi:10.1080/02692171.2015.1122747 · Cited by 24
“As shown by Lensink and Meesters (2014) and Wang and Schmidt (2002), the standard two-step approach suffers from the fact that the inefficiency is assumed to be identically and independently distributed in the main frontier equation, while it is determined by other variables in the inefficiency…”
BackgroundMethod
Metadata
- Authors
- Wang, H.-J., & Schmidt, P.
- Affiliations
- Institute of Economics, Academia Sinica (TW)
- Michigan State University (US)
- Venue
- Journal of Productivity Analysis
- Published
- 2002-09
- Volume
- 18
- Issue
- 2
- Pages
- 129-144
- ISSN
- 0895-562X (ISSN-L)
- 1573-0441
- OpenAlex
- W1524136776
- Semantic Scholar
- 0ba29f8abcbf8683e8286f2af42fa42ac20b1c6f
- Cited by
- 1,045
- References
- 10
- Citations by year
- 2026: 42 · 2025: 56 · 2024: 63 · 2023: 65 · 2022: 61 · 2021: 74 · 2020: 63 · 2019: 64 · 2018: 70 · 2017: 51 · 2016: 48 · 2015: 55 · 2014: 49 · 2013: 39 · 2012: 34
- FWCI
- 17.56
- Type
- journal article
- Language
- en
- Open access
- Licence
- Locations
- Journal of Productivity Analysis (publishedVersion)
- Munich Personal RePEc Archive (Ludwig Maximilian University of Munich) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Efficiency Analysis Using DEA
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Economic Growth and Productivity
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- stochastic frontier analysis, technical efficiency, firm characteristics, one-step estimation, maximum likelihood estimation, Monte Carlo simulation
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