The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index; none of the 12 sources its claims cite is checked for support yet.
One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels
Open accessOverview
AI snapshot
Written from the paper’s full text.
## 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.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 12 cited sources checked · 0 supported · 0 flagged
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.”
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
“We first note that the one-step estimates look pretty good. In particular, there is no evidence of significant bias.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
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)”
Strength:plain· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ 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
“For the one-step estimator, the true value of δ is not terribly important.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ 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
“But this does not seem to cause any problems for the parameters of main interest ( β , δ and the individual ri).”
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
“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.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ 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
“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).”
Load-bearingStrength:boosted· not yet calibratedTests✓ 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
“Changing δ makes very little difference to the properties of the estimates of β , δ or σ v.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
- It may state two separate claims as one. 43
- Probably not a substantial claim. 16
- The quote only partly states this claim. 5
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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“As expected, the bias of the first-step estimate of β is effectively zero when δ = 0, and it grows with δ .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“All of these biases are in the expected direction, and the size of the biases is definitely not small.”
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“They are less strongly correlated with the true ri and they are underdispersed, compared to the estimates from the one-step model.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“The individual ri are seriously biased for δ = 1 but not for the smaller values of δ .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“The two-step estimator of δ is biased for both δ = 1 and δ = 0.5, but the bias disappears as δ → 0.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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).”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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.”
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.
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
“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.
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
“As δ → 0, our ability to estimate µ (and γ , to a lesser extent) deteriorates seriously.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“The estimates of the individual ri become slightly more biased, and noticeably less strongly correlated with the true ri, when δ is small.”
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 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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“For the two-step estimates, surprisingly, imposing µ = 0 makes things worse (even though µ = 0 is a correct restriction).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“As γ increases, the bias of the estimate of β increases, but the bias of the second-step estimate of δ decreases quite noticeably.”
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.
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
“Finally, the second-step estimate of δ is seriously biased even when ρ = 0, though its bias does grow with ρ .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“The standard deviations of the estimators fall as N increases, but nothing else changes much.”
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 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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“| 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 | |”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- 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 |”
Load-bearingStrength:plain· not yet calibratedTests? Asserted: unclear✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
- 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
“For the two-step estimators, we see more differences as µ changes, but they are still not really important or striking.”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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
“The true value of δ is one, so these are large biases indeed.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“| 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 | |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- 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
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
“The results are quite consistent with these expectations.”
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.
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 -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 |”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✗ Asserted: fails✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The authors may not put it forward as true. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- 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.
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
“For the one-step estimators, the value of ρ is not important. The results are essentially identical across all these cases.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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
“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.
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
“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.”
Strength:hedged· not yet calibratedCausal:conditional· 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.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“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).”
Strength:plain· 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.
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
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“Some but not all of the models in the literature have this property.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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
“The one-step MLE will be based on the correctly specified model, and will therefore be consistent and asymptotically efficient.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
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
“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”
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
“Presumably this is so because when δ is large, z correlates with u and is useful to help estimate u.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one. The quote only partly states this claim.
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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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.”
Strength:boosted· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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
“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.”
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
“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.”
Strength:plain· 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.
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
“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.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“Models based on some other simple distributions, such as exponential, would also have the scaling property.”
Strength:hedged· 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.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Our summary statistics are averages and are very sensitive to extreme outliers.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. 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
“Importantly, this is true whether or not x and z are correlated.”
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
“One important implication of this viewpoint, which is sometimes missed, is that the variables z that determine inefficiency must not be functions of y.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“This truncation of the results made very little difference for the parameters other than µ and γ .”
Strength:plain· 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.
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 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.”
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
“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
Flagged first, then by citations
Cited by
Sorted by citations
Items 701–800 of 1,057
Climate change and productivity of northeastern dairy farms
López, R. A., Laughton, C., Kim, D., & Suh, H. S. (2022) · Agricultural and Resource Economics Review · doi:10.1017/age.2022.2 · Cited by 3
“This reduces the possibility of biased estimates when the stochastic term includes determinants of the deviations (Wang and Schmidt 2002).”
Performance of Microfinance Institutions: A Review*
Parmeter, C. F., & Hartarska, V. (2022) · Springer eBooks · doi:10.1007/978-981-10-3455-8_33 · Cited by 3
Inkoom, E. W., Acquah, H. D.-G., & Dadzie, S. K. N. (2022) · Ghana Journal of Development Studies · doi:10.4314/gjds.v19i2.1 · Cited by 3
Hospital cost efficiency: an examination of US acute care inpatient hospitals
Linde, S. (2023) · International Journal of Health Economics and Management · doi:10.1007/s10754-023-09356-x · Cited by 3
Airports’ public infrastructure and sources of inefficiency
Ripoll-Zarraga, A. E. (2023) · Journal of Economics, Finance and Administrative Science · doi:10.1108/jefas-12-2021-0269 · Cited by 3
Jeon, Y., & Nam, J. (2023) · Sustainability · doi:10.3390/su152015026 · Cited by 3
Lundgren, T., & Vesterberg, M. (2024) · Journal of Productivity Analysis · doi:10.1007/s11123-024-00724-4 · Cited by 3
Nguyen, D. T., & Le, T. (2025) · Total Quality Management & Business Excellence · doi:10.1080/14783363.2025.2472962 · Cited by 3
“We estimate the translog stability function and the model of stability inefficiency using one-step procedure proposed by Battese and Coelli (1995), which is more efficient than a two–step procedure (Wang & Schmidt, 2002).”
Productivity change in the privatized water sector in China (1999–2006)
Zhao, J. (2020) · Journal of Productivity Analysis · doi:10.1007/s11123-019-00572-7 · Cited by 3
Helping or hampering banks competition? The Asian experience after the Asian financial crisis
Ferrari, A., & Tran, V. H. T. (2021) · Journal of International Financial Markets Institutions and Money · doi:10.1016/j.intfin.2021.101486 · Cited by 3
Caloric consumption efficiency and import dependency: Evidence from Sri Lanka
Wijesinghe, A., & Kaushalya, T. (2022) · Economic Analysis and Policy · doi:10.1016/j.eap.2022.08.017 · Cited by 4
Eekhout, T., Berrou, J., & Combarnous, F. (2023) · Journal of International Development · doi:10.1002/jid.3734 · Cited by 7
Being Efficient to Stay Strong in a Weak Economy. The Case of Calabrian Manufacturing Firms
Aiello, F., & Castiglione, C. (2014) · Technology and Investment · doi:10.4236/ti.2014.52010 · Cited by 3
ROLE OF CREDIT TO ENHANCE COTTON PRODUCTION IN PUNJAB, PAKISAN
Kouser, S., Mushtaq, K., & Mazhar, I. (2006) · Cited by 3
Efficiency of Australian technical and further education providers
Fieger, P., Villano, R. A., & Cooksey, R. (2016) · International Journal of Training Research · doi:10.1080/14480220.2016.1152030 · Cited by 3
“Wang and Schmidt (2002) have demonstrated that this two step procedure is biased and that instead stochastic frontier models and the way in which efficiency u1 depends on predictors can and should be estimated in one single step using maximum likelihood estimation.”
BackgroundLand Reform and Technical Efficiency: theory and panel data evidence from Brazil
de Magalhães, M. M., & Lambais, G. (2013) · Cited by 3
Performance of smallholder minisett seed yam farm enterprises in Cameroon
Nchinda, V. P., Villano, R. A., Hadley, D., & Morales, E. L. (2016) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.252458 · Cited by 3
Danquah, M., & Ouattara, B. (2018) · Journal of Economic Development · doi:10.35866/caujed.2018.43.3.005 · Cited by 3
SALARIO EFICIENTE Y CRECIMIENTO ECONÓMICO PARA EL CASO DE AMÉRICA LATINA
Rodríguez, T. G., Bolívar, H. R., & Aali-Bujari, A. (2018) · Ensayos Revista de Economía · doi:10.29105/ensayos37.2-4 · Cited by 3
Banking Efficiency and Stock Performance in the EU Markets: The Impact of the World Financial CrisisPreprint
Janoudi, S. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2513272 · Cited by 3
Rahman, S. (2003) · RePEc: Research Papers in Economics · Cited by 3
Abdul‐Salam, Y., Phimister, E., Abdul-Salam, Y., et al. (2015) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.204302 · Cited by 3
Estimation of a panel stochastic frontier model with unobserved common shocks
Hsu, C., Lin, C., & Yin, S.-Y. (2012) · Munich Personal RePEc Archive (Ludwig Maximilian University of Munich) · Cited by 3
Evaluating the Impact of Policies on Production Efficiency of Nigeria's Rice Economy
Rapu, S. C. (2016) · ScholarWorks (Walden University) · Cited by 3
Market Competition and Bank Efficiency: A Post GFC Assessment of Australia and New ZealandPreprint
Din, S. U., Tripe, D., & Kabir, M. N. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3021357 · Cited by 3
Energy Efficiency Transitions in China: How Persistent are the Movements To/From the Frontier?Preprint
Zhang, L., & Adom, P. K. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3201238 · Cited by 3
Jangili, R. (2019) · RePEc: Research Papers in Economics · Cited by 3
Jonghe, O. D., Disli, M., & Schoors, K. J. L. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1898879 · Cited by 3
School Breakfast and Student BehaviorPreprint
Cuadros‐Meñaca, A., Thomsen, M. R., & Nayga, R. M. (2021) · SSRN Electronic Journal · doi:10.2139/ssrn.3806620 · Cited by 3
Abate, G. T., Borzaga, C., & Getnet, K. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2402607 · Cited by 3
Estimating the Materials Balance Condition: A Stochastic Frontier Approach
Hampf, B. (2015) · TUbilio (Technical University of Darmstadt) · doi:10.26083/tuprints-00004699 · Cited by 3
Tavana, M., Toloo, M., Santos‐Arteaga, F. J., et al. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.127791 · Cited by 2
“As in Wang and Schmidt (2002) and Banker and Natarajan (2008), we run simulations to explore how the biased productivity estimators obtained in the second stage impact the estimates of the contextual variable ’ s weight in the third stage when considering one input and one contextual variable.”
Hussen, S. M., & Tenaye, A. (2025) · Discover Agriculture · doi:10.1007/s44279-025-00236-1 · Cited by 2
“However, according to [18], simultaneous production technology estimation and covariates of technical inefficiency are preferred over the traditional two-step procedure.”
Energy inefficiency in energy-poor households in Mumbai, India
Gupta, V., Sarkar, A., Deb, C., et al. (2025) · Energy and Buildings · doi:10.1016/j.enbuild.2025.116519 · Cited by 2
Mozahid, M. N., Gardebroek, C., Thorne, F. S., et al. (2025) · European Review of Agricultural Economics · doi:10.1093/erae/jbaf024 · Cited by 2
Assessing technical efficiency in ginger production using the Stochastic Frontier Approach
Bhandari, A., Airee, S., Mukherjee, A., et al. (2025) · Discover Food · doi:10.1007/s44187-025-00731-w · Cited by 2
“The two-stage approach has been shown to produce inconsistent and biased estimates, as the inefficiency effects estimated in the first stage are statistically dependent on the inputs included in the second stage [83].”
InfluentialNguyen, P., Trần, X. U., & Faye, B. (2026) · Economies · doi:10.3390/economies14010033 · Cited by 2
“Moreover, a reliance on two-stage estimation procedures in previous work risks biased results if the determinants of trade flows are correlated with the inefficiency term (Wang & Schmidt, 2002).”
Almanidis, P., Karagiannis, G., & Sickles, R. C. (2014) · Empirical Economics · doi:10.1007/s00181-014-0890-y · Cited by 2
Normal Exponential Exogenous Model and its Application
Khan, S. H., & Mary Louis., L. (2018) · Annals of Pure and Applied Mathematics · doi:10.22457/apam.v16n1a25 · Cited by 2
Generating well-being and efficiency: Evidence from Italy
Bonanno, G., D’Orio, G., & Lombardo, R. (2020) · Economic Analysis and Policy · doi:10.1016/j.eap.2020.02.006 · Cited by 2
Performance of Microfinance Institutions: A Review∗
Parmeter, C. F., & Hartarska, V. (2021) · Springer eBooks · doi:10.1007/978-981-10-3450-3_33-1 · Cited by 2
Frick, F., Jantke, C., & Sauer, J. (2021) · Applied Economics · doi:10.1080/00036846.2021.1912699 · Cited by 2
“…stochastic frontier estimation, which allows the simultaneous estimation of the influences of production inputs and efficiency determinants and avoids potentially inefficient or biased estimators associated with a two-step estimation procedure (Wang and Schmidt 2002; Battese and Coelli 1995).”
Nandan, A., & Mallick, H. (2021) · Competition and Regulation in Network Industries · doi:10.1177/17835917211029498 · Cited by 3
“This is another way to examine the effects of exogenous variables on inefficiency (Belotti et al., 2013; Kumbhakar et al., 2014; Wang, 2002; Wang & Schmidt, 2002).”
BackgroundGangopadhyay, P., Jain, S., & Bakry, W. (2022) · International Review of Financial Analysis · doi:10.1016/j.irfa.2022.102148 · Cited by 2
Application of Production Economics in the Electricity Distribution Sector
Mydland, Ø., & Lien, G. (2022) · Springer eBooks · doi:10.1007/978-981-10-3455-8_37 · Cited by 2
Harianto, H., & Keraru, E. N. (2022) · Journal of the Indonesian Tropical Animal Agriculture · doi:10.14710/jitaa.47.3.192-203 · Cited by 3
Adhi, A. K., Putri, T. A., Pambudy, R., et al. (2022) · IOP Conference Series Earth and Environmental Science · doi:10.1088/1755-1315/1107/1/012073 · Cited by 2
Jebuni-Dotsey, S., & Senadza, B. (2023) · Sustainable Agriculture Research · doi:10.5539/sar.v12n2p16 · Cited by 2
“Several writers have put up arguments against a two-stage estimation of parameters of the frontier and inefficiency function (Hung et al., 2014; Wang & Schmidt, 2002) Considering this, the frontier model specified by equation 3 is extended such that the one-sided error is a factor of some exogenous…”
BackgroundDegefa, H., Tenaye, A., Hagos, F. G., et al. (2024) · Irrigation and Drainage · doi:10.1002/ird.2927 · Cited by 2
“However, this procedure is criticized by Wang and Schmidt (2002) on the grounds that it will give biased results because the model estimated at the first step is misspecified.”
MethodThe impact of industry integration on industrial energy efficiency in China
Wei, H., & Ding, S. (2024) · Energy & Environment · doi:10.1177/0958305x241246191 · Cited by 2
Bilal, M. T., Tadjiev, A., & Djanibekov, N. (2024) · Journal of Agribusiness in Developing and Emerging Economies · doi:10.1108/jadee-06-2024-0207 · Cited by 2
The effect of private investment on landlord port authorities’ cost efficiency: The Spanish case
Hidalgo‐Gallego, S., & Núñez‐Sánchez, R. (2025) · Case Studies on Transport Policy · doi:10.1016/j.cstp.2025.101474 · Cited by 2
Energy use and efficiency in Ethiopia’s manufacturing sector: a stochastic frontier analysis
Yigezu, H., Söderbom, M., & Ferede, T. (2025) · Applied Economics · doi:10.1080/00036846.2025.2505801 · Cited by 2
“Recall that the inefficiency components η i and u it are assumed to follow half-normal distributions, � � We assume that σ η and σ u depend on z i and z it , respectively, in the following way: where γ and ω are parameter vectors (see Wang and Schmidt 2002).”
Threshold Effects of Technological Regimes for the Stochastic Frontier Model
Chen, K., & Ghosh, S. N. (2014) · The Journal of Developing Areas · doi:10.1353/jda.2014.0040 · Cited by 2
“For instance, Wang and Schmidt (2002) asserted that a one-step estimation of the effect of exogenous variables on technical efficiency outperforms the alternative two-step estimation.”
BackgroundMoyo, B. (2018) · Studies in Economics and Econometrics · doi:10.1080/10800379.2018.12097340 · Cited by 2
“As stated by Kneller and Stevens (2003) and Kumbhakar and Wang (2005), the translog form does not impose constant elasticity of substitution, as is the case with the Cobb Douglas model.”
Measuring the Cost Efficiency of Lebanese Commercial Banks using the Stochastic Frontier Approach
Berro, N. A. (2023) · doi:10.47260/jafb/1355 · Cited by 2
Impact of Trade Openness on Technical Efficiency: Agricultural Sector of the European Union
Hart, J., & Hart, J. (2013) · AgEcon Search (University of Minnesota, USA) · doi:10.22004/ag.econ.182500 · Cited by 2
Lower bounds of concentration in Taiwan's manufacturing industries: do exports matter?
Yang, C., & Kuo, C. (2007) · Applied Economics · doi:10.1080/00036840600606237 · Cited by 2
“Wang and Schmidt (2002) present Monte Carlo evidence showing that the bias of the two-step procedure can be very severe and argue strongly for a one-step model whenever one is interested in the effects of exogenous variables on efficiency levels.”
BackgroundA Stochastic Production Frontier Model of the Newfoundland Snow Crab Fishery
Roy, N. (2002) · Cited by 2
What Drives the Technical Inefficiency in the Tunisian Insurance Industry
Manel, R., Nejib, O. M., & Hachicha, N. (2016) · The Journal of Economics Studies and Research · doi:10.5171/2016.126946 · Cited by 2
“The first method is known as the one-stage method, which enables to estimate the relevant frontier and provide pertinent explanation on efficiency component by means of variable sets (see Battese and Coelli (1993), Wang and Schmidt (2002), Johnson and Kuosmanen ( 2011) ).”
MethodAccess to Dental Care and the Capacity of the California Dental Care System
Brown, T. T., Pourat, N., Glassman, P., et al. (2012) · Journal of the California Dental Association · doi:10.1080/19424396.2012.12220894 · Cited by 2
Mizutani, F., & Nakamura, E. (2016) · Journal of Industrial and Business Economics · doi:10.1007/s40812-016-0066-1 · Cited by 2
Shrestha, R. B., Huang, W. C., Pradhan, U., et al. (2017) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.266482 · Cited by 2
Yang, C., & Tsou, M. (2023) · Applied Economics · doi:10.1080/00036846.2023.2166670 · Cited by 2
“…the inefficiency effects of covariates obtained using the one-step approach are larger than those obtained using the two-step approach, echoing the argument in Schmidt (2011) and Schmidt and Wang (2002) that the two-step approach may underestimate the effect of firm characteristics on inefficiency.”
MethodTD 2693 - Cooperativismo e associativismo na produção agropecuária de menor porte no Brasil
Ramos, É. B. T., & Filho, J. E. R. V. (2021) · doi:10.38116/td2693 · Cited by 2
Yong-Han, J. E. O. N., & Sim, S.-H. (2023) · Journal of Fisheries and Marine Sciences Education · doi:10.13000/jfmse.2023.4.35.2.233 · Cited by 2
Wang, Z., & Zelenyuk, V. (2024) · Advances in econometrics · doi:10.1108/s0731-905320240000046013 · Cited by 2
Rauf, R. I., Olusegun, A. O., Hamidu, B. A., et al. (2024) · Asian Journal of Probability and Statistics · doi:10.9734/ajpas/2024/v26i9643 · Cited by 2
Is inefficiency under control in the justice administration
Queralt, M. E., & Moré, A. E. (2011) · RECERCAT (Consorci de Serveis Universitaris de Catalunya) · Cited by 2
Panel Data in Energy Economics
Atkinson, S. E. (2019) · Elsevier eBooks · doi:10.1016/b978-0-12-815859-3.00015-9 · Cited by 2
Efficiency in China’s Banking Sector: A Comparative Analysis of Pre- and Post-Basel II Eras
Mohanty, S. K., & Lin, H. (2021) · Review of Pacific Basin Financial Markets and Policies · doi:10.1142/s0219091521500107 · Cited by 2
NHS reforms and efficiency of hospital services: a stochastic distance function approachPreprint
Ferrari, A. (2004) · RePEc: Research Papers in Economics · Cited by 2
Low farm incomes and the rental market for cropland in Vietnam
Huy, H. T. (2013) · Lincoln University Research Archive (Lincoln University) · Cited by 2
Rässler, S., & Jensen, U. (2007) · Social Science Open Access Repository (GESIS – Leibniz Institute for the Social Sciences) · Cited by 2
Zhang, Y., Wang, X., Zhang, Y., et al. (2009) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.51954 · Cited by 2
Do Farm Programs Explain Mean and Variance of Technical Efficiency? Stochastic Frontier AnalysisPreprint
Ranjan, R., Shaik, S., Mishra, A. K., et al. (2010) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.56365 · Cited by 2
Erkoç, T. E. (2014) · Keele Research Repository (Keele University) · Cited by 2
Curtiss, J., Brümmer, B., Medonos, T., et al. (2005) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.24557 · Cited by 2
Does the Entry Mode of Foreign Banks Matter for Bank Efficiency? Evidence from Transition CountriesPreprint
Vencappa, D., & Thi, N. A. V. (2008) · SSRN Electronic Journal · Cited by 2
Evaluating Cost Effectiveness of the USDA's Expanded Food and Nutrition Education Program
Baral, R. (2013) · VTechWorks (Virginia Tech) · Cited by 2
Czekaj, T., & Czekaj, T. G. (2015) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.211555 · Cited by 3
“This specification is referred to as a scaling property of inefficiency (e.g. Alvarez et al., 2006; Simar et al., 1994; Wang and Schmidt, 2002).”
BackgroundFactores determinantes de la eficiencia económica : evidencias de la industria hotelera en España
Pérez, M. A. (2016) · doi:10.5821/dissertation-2117-96392 · Cited by 2
Qushim, B. (2014) · doi:10.31390/gradschool_dissertations.1099 · Cited by 2
“43 to be seriously under-dispersed, resulting in the second-step regression estimates being biased downward (Wang and Schmidt, 2002).”
BackgroundMethodInfluentialModelling Efficiency Effects in a True Fixed Effects Stochastic FrontierPreprint
Paul, S., & Shankar, S. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3193286 · Cited by 2
“Parmeter and Kumbhakar (2014) discuss a distribution free inefficiency effects model which was first proposed in Simar et al. (1994) and later explained in detail in Wang and Schmidt (2002) and Alvarez et al. (2006).”
BackgroundProduction Efficiency Analysis of Pineapple Farmers in the Akwapim-South District of Ghana
Ofori-Appiah, Y. (2018) · Cited by 2
Clustering, Agency Costs and Operating Efficiency: Evidence from Nursing Home ChainsPreprint
Lu, S. F., & Wedig, G. J. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1783054 · Cited by 2
Takele, A., Tesfaye, E., & Abelieneh, A. (2020) · doi:10.21203/rs.3.rs-88692/v1 · Cited by 2
“Some authors argued that the socioeconomic variables should be incorporated directly in the production frontier model because such variables have a direct impact on efficiency and it has a persistence bias that will affect the estimates of efficiency (Wang and Schmidt, 2002).”
BackgroundBank Ownership and Cost Efficiency in Russia, RevisitedPreprint
Mamonov, M. E., & Vernikov, A. V. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2646536 · Cited by 2
Irias, E. E. A. (2023) · eDiss (Georg-August-Universität Göttingen) · doi:10.53846/goediss-9719 · Cited by 2
Aye, G. C. (2011) · UpSpace Institutional Repository (University of Pretoria) · Cited by 2
Efficiency and productivity analysis in ten Asian banking industries
Zhi, S. (2010) · Loughborough University Research Repository (Loughborough University) · Cited by 2
Ntinyari, K. G., Kingori, G. G., & Kirimi, K. J. (2023) · Journal of Economics Management and Trade · doi:10.9734/jemt/2023/v29i101151 · Cited by 1
Arocena, P., Kumbhakar, S. C., & Lien, G. (2024) · Journal of Economic Surveys · doi:10.1111/joes.12656 · Cited by 1
Cao, Q., Xu, A., Wang, J., et al. (2024) · Economic Analysis and Policy · doi:10.1016/j.eap.2024.10.020 · Cited by 1
Xiaohui, Y. (2025) · Journal of Multinational Financial Management · doi:10.1016/j.mulfin.2025.100897 · Cited by 1
The effects of construction servitization on carbon emission: evidence from China
Deng, S., & Wang, S. (2025) · Proceedings of the Institution of Civil Engineers - Engineering Sustainability · doi:10.1680/jensu.23.00066 · Cited by 1
Are operationally efficient firms greener?
Wang, Z., Suo, Y., Wang, T., & Kumbhakar, S. C. (2025) · Empirical Economics · doi:10.1007/s00181-025-02760-x · Cited by 1
Productivity dynamics, innovation and endogeneity: A semiparametric stochastic frontiers approach
Alemayehu, F. K., Sun, K., & Kumbhakar, S. C. (2025) · European Journal of Operational Research · doi:10.1016/j.ejor.2025.08.028 · Cited by 1
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
