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
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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.
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Claims the paper makes
39 Own interpretation · 37 Own result · 37 No basis given · 6 No full text of the sources · 3 Own method · 1 Sources not found · 1 Not checked yet
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.”
boosteddirect- Asserted: passes — The authors put it forward as true.
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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.”
plainSingle case- Asserted: passes — The authors put it forward as true.
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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)”
plainSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“For the one-step estimator, the true value of δ is not terribly important.”
plain- Asserted: passes — The authors put it forward as true.
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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).”
hedgedSingle case- Asserted: passes — The authors put it forward as true.
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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).”
plainn = 200- Asserted: passes — The authors put it forward as true.
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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).”
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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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- It may state two separate claims as one. 43
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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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
plaincorrelationaln = 200- Asserted: passes — The authors put it forward as true.
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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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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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).”
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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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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
“For this set of parameters, average technical efficiency is E(e -u ) = 0.5165.”
plainn = 200- Asserted: passes — The authors put it forward as true.
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Probably 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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Finally, the second-step estimate of δ is seriously biased even when ρ = 0, though its bias does grow with ρ .”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The standard deviations of the estimators fall as N increases, but nothing else changes much.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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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 | |”
plainn = 500- Asserted: passes — The authors put it forward as true.
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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 |”
plain- Asserted: unclear — It is unclear whether the authors put it forward as true.
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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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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“The true value of δ is one, so these are large biases indeed.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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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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 | | - | - | - | |”
plainn = 500- Asserted: passes — The authors put it forward as true.
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“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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In the paper
“| 17 | N=500 | ˆ γ | 1.0208 | 0.2393 | 0.0577 | | 53.4005 | 4.3493 | 2764.7151 | |”
plainSingle case- Asserted: passes — The authors put it forward as true.
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“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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“For larger γ , we estimate β a little worse, but we estimate δ and the individual ri a little better.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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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).”
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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.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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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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
“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”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“Presumably this is so because when δ is large, z correlates with u and is useful to help estimate u.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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.”
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably 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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“One important implication of this viewpoint, which is sometimes missed, is that the variables z that determine inefficiency must not be functions of y.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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 .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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 .”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“As µ → ∞ , the distribution of u becomes normal and presumably becomes confounded with the normal distribution of v (statistical noise).”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“All in all, the two-step estimator performs well when the second step is not needed ( δ = 0) but is otherwise unreliable.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“These biases are substantial enough that we would recommend against using two-step procedures in any circumstances that we can envision.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
Cited by
Sorted by citations
Items 401–500 of 1,057
TFP change and its components for Swedish manufacturing firms during the 2008–2009 financial crisis
Mattsson, P., Månsson, J., & Greene, W. H. (2019) · Journal of Productivity Analysis · doi:10.1007/s11123-019-00561-w · Cited by 16
Rural Organizations, Agricultural Technologies and Production Efficiency of Teff in EthiopiaPreprint
Hailu, G., Weersink, A. J., Minten, B., et al. (2015) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.211702 · Cited by 16
Shi, Y., Li, C., & Zhao, M. (2022) · Environment Development and Sustainability · doi:10.1007/s10668-022-02639-2 · Cited by 15
“Third, we estimated a Translog production function with the technical inefficiency model (i.e., one-step estimation) to conduct a robustness check (Wang and Schmidt 2002).”
MethodQuantile Methods for Stochastic Frontier Analysis
Papadopoulos, A., & Parmeter, C. F. (2022) · Foundations and Trends® in Econometrics · doi:10.1561/0800000042 · Cited by 15
Two-tier stochastic frontier analysis using Stata
Lian, Y., Liu, C., & Parmeter, C. F. (2023) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x231162033 · Cited by 15
Bank Ownership and Efficiency in the Aftermath of Financial Crises: Evidence from I ndonesia
PARINDURI, R. A., & Riyanto, Y. E. (2014) · Review of Development Economics · doi:10.1111/rode.12071 · Cited by 15
Improving the efficiency targeting of Malawi's farm input subsidy programme: Big pain, small gain?
Asfaw, S., Cattaneo, A., Pallante, G., & Palma, A. (2017) · Food Policy · doi:10.1016/j.foodpol.2017.09.004 · Cited by 15
Health care service provision in Europe and regional diversity: a stochastic metafrontier approach
Schley, K. (2018) · Health Economics Review · doi:10.1186/s13561-018-0195-5 · Cited by 15
“We base the formalisation of a one-step SFA model on an approach proposed by Wang and Schmidt [37].”
MethodInfluentialJu, Y., & Wang, X. (2019) · IEEE Access · doi:10.1109/access.2019.2933948 · Cited by 15
Re-study on Chinese city size and policy formation
Deng, Z., Qin, M., & Song, S. (2019) · China Economic Review · doi:10.1016/j.chieco.2019.101390 · Cited by 15
Wang, J., Etienne, X. L., & Ma, Y. (2020) · China Agricultural Economic Review · doi:10.1108/caer-11-2019-0197 · Cited by 15
Larochelle, C., & Alwang, J. (2012) · Journal of Agricultural Economics · doi:10.1111/j.1477-9552.2012.00367.x · Cited by 19
Johnson, A. L., & Kuosmanen, T. (2015) · Springer eBooks · doi:10.1007/978-81-322-2253-8_3 · Cited by 15
Inefficiency in Japanese water utility firms: a stochastic frontier approach
Phillips, M. A. (2013) · Journal of Regulatory Economics · doi:10.1007/s11149-013-9225-8 · Cited by 15
“In these models, both the stochastic frontier and the way in which the one-sided error depends on environmental variables can be estimated in a single step (Schmidt and Wang 2002).”
BackgroundEstimation of stochastic frontier models based on multimodel inference
Huang, C. J., & Lai, H. (2011) · Journal of Productivity Analysis · doi:10.1007/s11123-011-0260-0 · Cited by 15
“ui Nþ l; r2u : M3: The scaled Stevenson model (Wang and Schmidt 2002)”
InfluentialBank efficiency in New Zealand: a stochastic frontier approach
Lu, Y., Gan, C. E. C., Hu, B., et al. (2018) · New Zealand Economic Papers · doi:10.1080/00779954.2018.1455728 · Cited by 15
“Wang and Schmidt (2002) criticise that the standard two-step approach suffers from the assumption that the inefficiency terms are independently identical half- or truncated-normally distributed in the first step, while the inefficiency terms are assumed to be normally distributed and dependent on…”
BackgroundThe role of human capital on the performance of manufacturing firms in Bangladesh
Shamsuzzoha, & Tanaka, M. (2020) · Managerial and Decision Economics · doi:10.1002/mde.3210 · Cited by 15
Roudaut, N. (2006) · Journal of Productivity Analysis · doi:10.1007/s11123-006-7133-y · Cited by 14
Understanding Countries’ Tax EffortPreprint
Fenochietto, R., & Pessino, C. (2013) · SSRN Electronic Journal · doi:10.2139/ssrn.2372060 · Cited by 18
Institutions and Bank Performance: A Stochastic Frontier AnalysisPreprint
Lensink, R., & Meesters, A. (2007) · SSRN Electronic Journal · doi:10.2139/ssrn.965825 · Cited by 15
The Influence of Risk-Taking on Bank Efficiency: Evidence from ColombiaPreprint
Sarmiento, M., & Galán, J. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2700096 · Cited by 15
Dong, H., Wang, X., Cui, Z., et al. (2025) · Energy Economics · doi:10.1016/j.eneco.2025.108226 · Cited by 14
Economic modelling of grazing management against gastrointestinal nematodes in dairy cattle
van der Voort, M., Meensel, J. V., Lauwers, L., de Haan, M. H. A., Evers, A. G., Huylenbroeck, G. V., & Charlier, J. (2017) · Veterinary Parasitology · doi:10.1016/j.vetpar.2017.02.004 · Cited by 14
Simfukwe, K., Limuwa, M. M., & Njaya, F. J. (2022) · Sustainability · doi:10.3390/su142316018 · Cited by 14
Nonparametric estimation of stochastic frontier models with weak separability
Centorrino, S., & Parmeter, C. F. (2023) · Journal of Econometrics · doi:10.1016/j.jeconom.2023.105641 · Cited by 14
Profit efficiency among kenyan maize farmers
Ngeno, V. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e24657 · Cited by 14
“[46,48]: (i) due to the strong correlation between the input variables and the variables used to explain inefficiency, parameter estimates will be biased in the SF model; (ii) the inefficiency term ’ s explanatory variables are underestimated; and (iii) the inefficiency explanatory variables are…”
BackgroundAccounting for heterogeneity in cross-country bank efficiency comparisons
Košak, M., & Zorić, J. (2011) · Economics of Transition · doi:10.1111/j.1468-0351.2011.00419.x · Cited by 14
Elasticity of substitution and technical efficiency: evidence from the US electricity generation
Mugabe, D., Elbakidze, L., & Zaynutdinova, G. R. (2019) · Applied Economics · doi:10.1080/00036846.2019.1678733 · Cited by 14
“We estimate TFE-MLE andMMSLE using a one-step procedure (where β and δare estimated simultaneously combining steps one and two) following Caudill and Ford (1993) and Wang and Schmidt (2002).”
MethodEffects of diversification on bank efficiency: Evidence from Shinkin banks in Japan
Harimaya, K., & Ozaki, Y. (2020) · International Review of Economics & Finance · doi:10.1016/j.iref.2020.10.008 · Cited by 14
Specification and estimation of nonstandard profit functions
Khumbhakar, S. C. (2006) · Empirical Economics · doi:10.1007/s00181-005-0043-4 · Cited by 14
The big trade-off between efficiency and equity—is it there?
Andersen, T., & Maibom, J. (2016) · Oxford Economic Papers · doi:10.1093/oep/gpz040 · Cited by 24
Mesure de l’efficacité technique des riziculteurs du bassin du fleuve Sénégal
Ngom, C. A. B., Sarr, F., & Fall, A. (2016) · Économie rurale · doi:10.4000/economierurale.5021 · Cited by 19
The Influence of the Regulatory Environment on Chinese Urban Water Utilities
Li, F., & Phillips, M. A. (2016) · Water Resources Management · doi:10.1007/s11269-016-1519-z · Cited by 14
“This is done through a one-step approach in which both the stochastic and 4 Most of these results are not statistically significant at conventional levels. efficiency components are estimated simultaneously (Schmidt and Wang 2002).”
MethodDeterminants of the European electricity companies efficiency: 2005–2014
Coto‐Millán, P., de la Fuente, M., & Fernández, X. L. (2018) · Energy Strategy Reviews · doi:10.1016/j.esr.2018.06.001 · Cited by 14
Specification and estimation of nonstandard profit functions
Kumbhakar, S. C. (2006) · Empirical Economics · doi:10.1007/s00181-006-0054-9 · Cited by 14
“13 We need to multiply both the mean and standard deviation of u (μ and σu) by the h(w, y) function in the log-likelihood function given in equation (3.2.48), page 85. Since the technical inefficiency component in Eq. 22 is h(w, y) u, Wang and Schmidt (2002) labeled this as a scaling property where h(w, y) is the scal…”
BackgroundInfluentialStock option schemes and firm technical inefficiency: Evidence from Finland
Mäkinen, M. (2010) · Advances in the economic analysis of participatory and labor-managed firms · doi:10.1108/s0885-3339(2010)0000011010 · Cited by 14
Badiane, O., & Ulimwengu, J. M. (2009) · RePEc: Research Papers in Economics · Cited by 14
Geffersa, A. G. (2022) · International Journal of Productivity and Performance Management · doi:10.1108/ijppm-02-2022-0087 · Cited by 13
Impact of African Swine Fever Epidemic on the Cost Intensity of Pork Production in China
Yan, Z., Wang, M.-L., Li, X., et al. (2023) · Agriculture · doi:10.3390/agriculture13020497 · Cited by 13
“In this study, we follow the recommendations in current literature [38,48,55,56,59] and adopt the trans-log production function, which is a very flexible functional form and is a second-order approximation of any unknown function.”
MethodDoes Managerial Ability Really Drive Cost Efficiency? Evidence from Broiler Businesses
Dziwornu, R. K. (2016) · Managerial and Decision Economics · doi:10.1002/mde.2810 · Cited by 13
Cavalieri, M., Di, P., Guccio, C., et al. (2020) · Social Science & Medicine · doi:10.1016/j.socscimed.2020.113506 · Cited by 13
Guarini, G., Laureti, T., & Garofalo, G. (2020) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2020.100835 · Cited by 13
The impact of health on wages: evidence for Europe
Rodrı́guez-Álvarez, A., & Gutiérrez, C. R. (2018) · The European Journal of Health Economics · doi:10.1007/s10198-018-0966-2 · Cited by 13
Estimating efficiency effects in a panel data stochastic frontier model
Paul, S., & Shankar, S. (2019) · Journal of Productivity Analysis · doi:10.1007/s11123-019-00568-3 · Cited by 14
“Parmeter and Kumbhakar (2014) discuss a distribution free inefficiency effects model which was first proposed in Simar et al. (1994) and later explained in Wang and Schmidt (2002) and Alvarez et al. (2006).”
BackgroundDirected technological change, energy and more: a modern story
Hou, Z., Roseta‐Palma, C., & Ramalho, J. J. S. (2020) · Environment and Development Economics · doi:10.1017/s1355770x2000008x · Cited by 13
“Over the years this method has been developed by a great number of subsequent studies, including Kumbhakar (1990), Kumbhakar et al. (2000), Wang (2002), Wang and Schmidt (2002), Greene (2005), Kumbhakar andWang (2005), Chen et al. (2014), Parmeter and Kumbhakar (2014), and others.”
Fernández-López, X. L., & Coto‐Millán, P. (2015) · Construction Economics and Building · doi:10.5130/ajceb.v15i1.4168 · Cited by 13
Hailu, G., Goddard, E. W., Jeffrey, S. R., et al. (2005) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.19507 · Cited by 13
Yao, S., & Jiang, C. (2007) · SSRN Electronic Journal · doi:10.2139/ssrn.980935 · Cited by 13
“With extensive Monte Carlo evidence, Wang and Schmidt (2002) strongly recommend the one-stage models.”
Quiédeville, S., Grovermann, C., Leiber, F., et al. (2022) · The Journal of Agricultural Science · doi:10.1017/s0021859622000375 · Cited by 12
Technical and scale efficiencies of meat goat farms in the USA
Qushim, B., Gillespie, J., Paudel, K. P., et al. (2015) · Applied Economics · doi:10.1080/00036846.2015.1083531 · Cited by 12
Competitive intensity and inefficiency in European container ports
Merkel, A. (2018) · Maritime Business Review · doi:10.1108/mabr-01-2018-0003 · Cited by 12
Zeebari, Z., Månsson, K., Sjölander, P., et al. (2022) · Journal of Productivity Analysis · doi:10.1007/s11123-022-00651-2 · Cited by 12
“■ Wang and Schmidt (2009) show that the conditional mean shrinks towards the mean of inefficiency rather than towards inefficiency itself.”
BackgroundMaia, A. G., da Silveira, R. L. F., Fonseca, C. V. C., et al. (2021) · Climate and Development · doi:10.1080/17565529.2021.1904812 · Cited by 12
Ganbold, N., Fahad, S., Li, H., & Gungaa, T. (2021) · Environment Development and Sustainability · doi:10.1007/s10668-021-01821-2 · Cited by 15
“1 3 et al., (1991), Huang and Liu (1994), and Battese and Coelli (1995) proposed parameterizing the mean of the pre-truncated distribution as a way to study the exogenous influence on inefficiency (Wang, 2002).”
BackgroundShamohammadi, M., Park, Y., Choi, J. H., & Kwon, O. K. (2022) · Sustainability · doi:10.3390/su14074222 · Cited by 12
“Finally, whilst the utilization of the two-stage analytical approach using DEA, SFA, and Tobit models is popular among researchers, few studies such as [90] demonstrated that two-stage methods used to predict inefficiency might have some drawbacks.”
MethodDeep preferential trade agreements and export efficiency in Ghana: Do institutions matter?
Obeng, C. K., Boadu, M. T., & Ewusie, E. (2023) · Research in Globalization · doi:10.1016/j.resglo.2023.100112 · Cited by 12
Is austerity good for efficiency, at least? A counterfactual assessment for the Italian NHS
Guccio, C., Pignataro, G., Romeo, D., & Vidoli, F. (2024) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2023.101798 · Cited by 11
Mohanty, S. K., Lin, W. T., & Lin, H. (2013) · Journal of International Financial Markets Institutions and Money · doi:10.1016/j.intfin.2013.05.001 · Cited by 12
Shaik, S. (2015) · European Journal of Operational Research · doi:10.1016/j.ejor.2015.03.018 · Cited by 12
How can sedentarised pastoralists be more technically efficient? A case from eastern Inner Mongolia
Tan, S.-H., Li, T.-Y., Liu, B., & Huntsinger, L. (2018) · The Rangeland Journal · doi:10.1071/rj17128 · Cited by 10
Is the tax administration just a money machine? Empirical evidence on redistributive politics
Moré, A. E. (2011) · Economics of Governance · doi:10.1007/s10101-011-0095-1 · Cited by 13
“In fact, according to Wang and Schmidt (2002, p.132) , one of the advantages of this property is that it permits obtaining the estimates of partial effects as in any linear model.”
BackgroundHETEROSCEDASTICITY OR PRODUCTION RISK? A SYNTHETIC VIEW
Saastamoinen, A. (2013) · Journal of Economic Surveys · doi:10.1111/joes.12054 · Cited by 12
Do Creditor Rights and Information Sharing Affect the Performance of Foreign Banks?Preprint
Mamatzakis, E. C. M., & Kalyvas, A. N. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4196578 · Cited by 12
Joint Variable Selection for Data Envelopment Analysis via Group SparsityPreprint
Qin, Z. T., & Song, I. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2406690 · Cited by 12
“For those experiments concerned with correlated input variables, we adopt the following equation from Wang and Schmidt (2002) to establish the desired covariance structure of inputs. xi = ρi,jxj +w √ 1− ρ2i,j, i= 2,3,4, j =1,2,3, i 6= j. (30) Here, ρi,j is the correlation between xi and xj, and w…”
MethodImpact of Climate Change on Productivity and Technical Efficiency in Canadian Crop Production
Galushko, V., & Gamtessa, S. (2022) · Sustainability · doi:10.3390/su14074241 · Cited by 11
Trade development and agricultural productivity change: Evidence from China
Ma, Y., Brümmer, B., & Yu, X. (2023) · World Economy · doi:10.1111/twec.13389 · Cited by 11
Ayouba, K., Duvivier, C., & Bussière, C. (2024) · Agricultural Economics · doi:10.1111/agec.12862 · Cited by 19
Júnior, S. K., Borges, R. D. L. A., & de Prince, D. (2017) · Science and Public Policy · doi:10.1093/scipol/scx090 · Cited by 11
Technical Efficiency of Wheat Producers in North Shewa Zone of Amhara Region, Central Ethiopia
Getachew, T., Ketema, M., Goshu, D., et al. (2020) · Sustainable Agriculture Research · doi:10.5539/sar.v9n3p77 · Cited by 11
“As indicated in Wang and Schmidt's (2002) two-step estimation procedures results in biased coefficients.”
BackgroundTFP determinants in the manufacturing sector: the case of Ecuadorian firms
Camino‐Mogro, S. (2021) · Applied Economic Analysis · doi:10.1108/aea-10-2020-0142 · Cited by 14
Environmental efficiency of wine grape production in Mendoza, Argentina
Riera, F. S., & Brümmer, B. (2021) · Agricultural Water Management · doi:10.1016/j.agwat.2021.107376 · Cited by 11
Lema, T. Z., Massresha, S. E., Neway, M. M., & Demeke, E. M. (2022) · Cogent Economics & Finance · doi:10.1080/23322039.2022.2043509 · Cited by 11
“It is evident that estimation results from the two-step procedures are biased, and there is strong evidence showing that the bias can be very severe (Wang & Schmidt, 2002).”
BackgroundFDI horizontal and vertical effects on local firm technical efficiency
Nguyen, C. D., Simpson, G., Saal, D. S., et al. (2008) · Aston Publications Explorer (Aston University) · Cited by 11
Sources of technical inefficiency of smallholder farmers in milk production in Ethiopia
Adane, Z., Shiferaw, K., & Berhanu, G. (2016) · African Journal of Agricultural Research · doi:10.5897/ajar2015.10533 · Cited by 11
“Following Wang and Schmidt (2002), Equations 8 and 9 are estimated simultaneously.”
Economic Efficiency and Productivity of Maize Farmers in Ghana
Wongnaa, C. A. (2016) · doi:10.13140/rg.2.2.19830.80962 · Cited by 11
Sources of productivity growth in Ethiopian agriculture
Tenaye, A. (2020) · African Journal of Agricultural Research · doi:10.5897/ajar2019.14601 · Cited by 11
“Moreover, as noted by Wang and Schmidt (2002), the parameters of the technology and inefficiency are estimated using MLE in one-step to avoid biases associated with the two-step approach.”
MethodAssessing Ghana's bilateral exports potential and gap
Boadu, M. T., Obeng, C. K., Dasmani, I., et al. (2021) · African Development Review · doi:10.1111/1467-8268.12610 · Cited by 11
Geffersa, A. G., Agbola, F. W., & Mahmood, A. (2021) · Applied Economics · doi:10.1080/00036846.2021.1963415 · Cited by 11
“The approach helps overcome the limitation of the traditional two-step procedure while also accounting for a potential heteroscedasticity problem (Hadri, Guermat, and Whittaker 2003; Wang and Schmidt 2002).”
Wu, Z., Hua, W., Luo, L., et al. (2022) · Agriculture · doi:10.3390/agriculture12050649 · Cited by 11
MEAT GOAT ENTERPRISE EFFICIENCY ANALYSIS IN THE SOUTHEASTERN UNITED STATES
Qushim, B., Gillespie, J., & McMillin, K. (2016) · Journal of Agricultural and Applied Economics · doi:10.1017/aae.2016.1 · Cited by 11
Christian, C., & Felix, L. E. (2014) · Journal of Development and Agricultural Economics · doi:10.5897/jdae12.146 · Cited by 11
“(1991) and Reifschneider and Stevenson (1991) argue that this procedure is inconsistent and some of the assumptions of the error term, such as independent distribution are violated in the second stage (Pascoe and Mardle, 2003), and hence it is biased (Wang and Schmidt, 2002) and not as efficient as the single-stage pr…”
MethodResultInfluentialJohnson, A. L., & Kuosmanen, T. (2009) · SSRN Electronic Journal · doi:10.2139/ssrn.1485733 · Cited by 11
Dakpo, K. H., Latruffe, L., Desjeux, Y., et al. (2024) · Empirical Economics · doi:10.1007/s00181-024-02604-0 · Cited by 10
Ali, H. M., Guellil, M. S., Mokhtari, F., & Abderrahmane, T. (2024) · Discover Sustainability · doi:10.1007/s43621-024-00281-8 · Cited by 15
“Battese et al. [37] employed a method known as the “one-step” model, which specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example using maximum likelihood [38].”
The Cost Effects of Government‐Subsidised Credit: Evidence from Farmers’ Credit Unions in Taiwan
Wang, H., Chang, C. E., & Chen, P. (2007) · Journal of Agricultural Economics · doi:10.1111/j.1477-9552.2007.00137.x · Cited by 12
Self-citationBank performance and the financial crisis: evidence from Kazakhstan
Glass, A. J., Kenjegalieva, K. A., & Weyman–Jones, T. (2014) · Applied Financial Economics · doi:10.1080/09603107.2013.868584 · Cited by 10
“It is therefore free from the bias associated with two-stage SFA techniques (Wang and Schmidt, 2002).”
MethodWASTE MANAGEMENT SERVICE IN INDONESIA BASED ON STOCHASTIC FRONTIER ANALYSIS
Luthfiani, N. L., & Atmanti, H. D. (2021) · TRIKONOMIKA · doi:10.23969/trikonomika.v20i2.3952 · Cited by 10
Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares
Nguyen, B. H., Sickles, R. C., & Zelenyuk, V. (2022) · Springer eBooks · doi:10.1007/978-981-19-2023-3_3 · Cited by 18
Chen, Z., Yang, Z., & Yang, L. (2023) · Journal of the Knowledge Economy · doi:10.1007/s13132-023-01253-5 · Cited by 10
“On this basis, combined with the above-mentioned translog knowledge transfer function, a one-step estimation method is used to estimate all parameters, which can effectively reduce the estimation bias (Wang & Schmidt, 2002).”
Market access and seaport efficiency: the case of container handling in Norway
Rødseth, K. L., Holmen, R. B., Kuosmanen, T., et al. (2023) · Journal of Shipping and Trade · doi:10.1186/s41072-023-00134-z · Cited by 10
“We make the inefficiency term u correlated with one of the Harris measures of market access by using the formula by Wang and Schmidt (2002), specifically: where ρ is the correlation coefficient and wit is a random number drawn from the uniform distribution over the interval [0.5,1].”
MethodInfluentialAutomation and efficiency: A latent class analysis of Irish dairy farms
García, L. F., Läpple, D., Dillon, E., & Thorne, F. S. (2023) · Q Open · doi:10.1093/qopen/qoad015 · Cited by 10
Becchetti, L., & Pisani, F. (2015) · Annals of Public and Cooperative Economics · doi:10.1111/apce.12069 · Cited by 11
“Two-step approaches to the estimation of translog – first step the inefficiency and second step the coefficients of explicatory variables of the inefficiency (as in Pitt and Lee (1981) and Kalirajan (1981)) – are subject to the well-known bias described by Wang and Schmidt (2002).”
MethodDimelis, S. P., & Papaioannou, S. (2014) · International Review of Applied Economics · doi:10.1080/02692171.2014.907246 · Cited by 10
“Kumbhakar and Lovell (2000) and Wang and Schmidt (2002) argue that if the vector of efficiency variables is correlated with the vector of production function parameters, then the coefficient estimates of the production function will be biased.”
BackgroundDo Mergers Improve the Efficiency of Banks in Taiwan?: Evidence From Stochastic Frontier Approach
Lee, T.-H., Liang, L., & Huang, B.-Y. (2013) · The Journal of Developing Areas · doi:10.1353/jda.2013.0017 · Cited by 11
“As a result, the two-step procedure may suffer from estimation biases; Monte Carlo experiments show such biases are substantial (Wang and Schmidt, 2002).”
A post-truncation parameterization of truncated normal technical inefficiency
Amsler, C. E., Schmidt, P., & Tsay, W. (2014) · Journal of Productivity Analysis · doi:10.1007/s11123-014-0409-8 · Cited by 10
Self-citationThe impact of credit constraints on the performance of Chinese agricultural wholesalers
Hu, L., López, R. A., & Zeng, Y. (2019) · Applied Economics · doi:10.1080/00036846.2019.1584385 · Cited by 10
“This reduces the possibility of biased estimates when the stochastic term includes determinants of the deviations (Wang and Schmidt 2002).4”
BackgroundSugathan, A., Malghan, D. V., Chandrashekar, S., et al. (2019) · Energy · doi:10.1016/j.energy.2019.04.107 · Cited by 10
Pacheco, F., Sánchez, R., & Villena, M. G. (2020) · Applied Economics · doi:10.1080/00036846.2020.1808171 · Cited by 10
“This approach has been criticized by more recent literature (Wang and Schmidt, 2002) and a one stage approach has been suggested which solves the drawbacks of the two stage approach.”
MethodResultMnisi, K. P., & Alhassan, A. L. (2020) · Annals of Public and Cooperative Economics · doi:10.1111/apce.12295 · Cited by 10
Tax Effort of the Indian States from 2001–2002 to 2016–2017: A Stochastic Frontier Approach
Kawadia, G., & Suryawanshi, A. K. (2021) · Millennial Asia · doi:10.1177/09763996211027053 · Cited by 10
“Comparing with other models, the Battese and Coelli (1995) model captures the time-varying inefficiency from observable heterogeneity using maximum likelihood estimation (Belotti et al., 2013; Mukherjee, 2017; Wang & Schmidt, 2002).”
Method
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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