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
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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
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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 101–200 of 1,057
Bäckman, S., Islam, K. M. Z., & Sumelius, J. (2011) · The Journal of Developing Areas · doi:10.1353/jda.2011.0001 · Cited by 70
“This second stage was criticised by Battese and Coelli (1995) and Wang and Schmidt (2002).”
BackgroundModel selection in stochastic frontier analysis with an application to maize production in Kenya
Liu, Y., & Myers, R. J. (2008) · Journal of Productivity Analysis · doi:10.1007/s11123-008-0111-9 · Cited by 71
“d) � N(l, ru ) ? , which is used in Wang and Schmidt (2002) .”
BackgroundMwalupaso, G. E., Korotoumou, M., Eshetie, A. M., et al. (2019) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2019.05.366 · Cited by 67
A time-varying true individual effects model with endogenous regressors
Kutlu, L., Tran, K. C., & Tsionas, E. G. (2019) · Journal of Econometrics · doi:10.1016/j.jeconom.2019.01.014 · Cited by 72
STATE VERSUS PRIVATE SECTOR PROVISION OF WATER SERVICES IN AFRICA: AN EMPIRICAL ANALYSIS
Kirkpatrick, C. H., Parker, D., & Zhang, Y. (2004) · Cited by 66
Huang, W., Brümmer, B., & Huntsinger, L. (2015) · Ecological Economics · doi:10.1016/j.ecolecon.2015.11.025 · Cited by 66
Farm size and production efficiency in Chinese agriculture: output and profit
Yan, J., Chen, C., & Hu, B. (2018) · China Agricultural Economic Review · doi:10.1108/caer-05-2018-0082 · Cited by 65
Hong, Y., Heerink, N., Zhao, M., et al. (2019) · Agricultural Systems · doi:10.1016/j.agsy.2019.03.007 · Cited by 65
Institutions and Bank Performance: A Stochastic Frontier Analysis*
Lensink, R., & Meesters, A. (2012) · Oxford Bulletin of Economics and Statistics · doi:10.1111/obes.12002 · Cited by 71
Nonparametric estimation of the determinants of inefficiency
Parmeter, C. F., Wang, H., & Kumbhakar, S. C. (2016) · Journal of Productivity Analysis · doi:10.1007/s11123-016-0479-x · Cited by 65
Self-citationForgione, A. F., Laguir, I., & Staglianò, R. (2020) · Corporate Social Responsibility and Environmental Management · doi:10.1002/csr.1950 · Cited by 63
What Have We Learned From the Application of Stochastic Frontier Analysis to U.S. Hospitals?
Rosko, M. D., & Mutter, R. L. (2010) · Medical Care Research and Review · doi:10.1177/1077558710370686 · Cited by 63
“Also, Carey (2003) used a two-stage SFA approach, which tends to inflate the standard errors of the regression coefficients (Wang & Schmidt, 2002).”
MethodThe impact of land fragmentation on milk production
del Corral, J., Méndez, J. A. P., & Roibás, D. (2010) · Journal of Dairy Science · doi:10.3168/jds.2010-3377 · Cited by 71
“As a result the second-step regression understates the effect of z on efficiency levels” (Wang and Schmidt, 2002; p. 130).”
BackgroundInfluentialTechnical Efficiency in a Semi‐Formal Financial Sector: The Case of Mexico*
Paxton, J. (2007) · Oxford Bulletin of Economics and Statistics · doi:10.1111/j.1468-0084.2007.00466.x · Cited by 61
Moral hazard: the effect of insurance on risk and efficiency
Roll, K. H. (2019) · Agricultural Economics · doi:10.1111/agec.12490 · Cited by 62
Seok, J. H., Moon, H., Kim, G., & Reed, M. R. (2018) · Sustainability · doi:10.3390/su10072137 · Cited by 72
“This single-stage approach is strongly supported by Monte Carlo evidence [30].”
MethodKaragiannis, R. (2013) · Annals of Operations Research · doi:10.1007/s10479-013-1367-7 · Cited by 61
The relative efficiency of charter schools: A cost frontier approach
Gronberg, T. J., Jansen, D. W., & Taylor, L. L. (2011) · Economics of Education Review · doi:10.1016/j.econedurev.2011.07.001 · Cited by 61
Land tenure security and technical efficiency: new insights from a case study in Northwest China
Ma, X., Heerink, N., Feng, S., et al. (2017) · Environment and Development Economics · doi:10.1017/s1355770x1600036x · Cited by 61
“The solution to these problems is the application of a onestep maximum likelihood procedure in which, at given levels of input use, the assumed relationship between the farm-specific driving factor(s) and TE is imposed in estimating the technology and the efficiency levels, not just at the second stage of the analysis…”
BackgroundImpact of Erratic Rainfall from Climate Change on Pulse Production Efficiency in Lower Myanmar
Mar, S., Nomura, H., Takahashi, Y., et al. (2018) · Sustainability · doi:10.3390/su10020402 · Cited by 61
“Wang [33] provided some theoretical insights into the bias problem in estimating the stochastic frontier function and farm-specific technical efficiency separately using a two-step approach.”
MethodBigerna, S., D’Errico, M. C., & Polinori, P. (2021) · Technological Forecasting and Social Change · doi:10.1016/j.techfore.2021.120648 · Cited by 64
Competition and efficiency in the non-life insurance market in South Africa
Alhassan, A. L., & Biekpe, N. B. (2016) · Journal of Economic Studies · doi:10.1108/jes-07-2015-0128 · Cited by 60
Energy consumption associated with urbanization in China: Efficient- and inefficient-use
Sheng, P., & Guo, X. (2018) · Energy · doi:10.1016/j.energy.2018.09.161 · Cited by 61
On the effect of prospective payment on local hospital competition in Germany
Herwartz, H., & Strumann, C. (2011) · Health Care Management Science · doi:10.1007/s10729-011-9180-9 · Cited by 59
“Firstly, two-stage approaches of SFA efficiency scores are generally not recommended because of an inherent bias problem on both stages [27, 49].”
BackgroundResultSources of Total-Factor Productivity and Efficiency Changes in China’s Agriculture
Liu, J., Dong, C., Liu, S., et al. (2020) · Agriculture · doi:10.3390/agriculture10070279 · Cited by 59
“The second step is to use the system ‐ GMM method to analyze the influence factors of TE, TC, and TFP.”
MethodAn analysis of cost efficiency in Swiss multi-utilities
Farsi, M., & Filippini, M. (2008) · Energy Economics · doi:10.1016/j.eneco.2008.11.009 · Cited by 58
“, 1991; Battese and Coelli, 1995) or as a general functional form (Wang and Schmidt, 2002).”
BackgroundDo agricultural services contribute to cost saving? Evidence from Chinese rice farmers
Tang, L., Liu, Q., Yang, W., & Wang, J. (2018) · China Agricultural Economic Review · doi:10.1108/caer-06-2016-0082 · Cited by 60
Abdul‐Salam, Y., & Phimister, E. (2016) · Journal of Agricultural Economics · doi:10.1111/1477-9552.12194 · Cited by 62
“…and idiosyncratic error, which prevents the formal testing of information effects 3 Described as Model 6 in Kumbhakar et al (2014). within this framework.4 This approach also requires a multi-stage estimation procedure which, as Wang and Schmidt (2002) showed, can lead to severely biased results.”
BackgroundMethodImpact of quality on estimations of hotel efficiency
Arbelo-Pérez, M., Arbelo, A., & Pérez-Gómez, P. (2017) · Tourism Management · doi:10.1016/j.tourman.2017.02.011 · Cited by 58
Martinez‐Cillero, M., Thorne, F. S., Wallace, M., Breen, J., & Hennessy, T. (2017) · Journal of Agricultural Economics · doi:10.1111/1477-9552.12259 · Cited by 61
A new stochastic frontier model with cross-sectional effects in both noise and inefficiency terms
Orea, L., & Ayuso, I. Á. (2019) · Journal of Econometrics · doi:10.1016/j.jeconom.2019.07.004 · Cited by 59
Rohde, M., & Breuer, C. (2018) · Sport Management Review · doi:10.1016/j.smr.2018.01.001 · Cited by 71
Do Power Cuts Affect Productivity? A Case Study Of Nigerian Manufacturing Firms
Moyo, B. (2012) · International Business & Economics Research Journal (IBER) · doi:10.19030/iber.v11i10.7262 · Cited by 56
“Thus, Wang and Schmidt (2002) argue that this approach 3 Since survey data are very prone to measurement errors, these methods are therefore not suitable for our study.”
BackgroundInfluentialEfficiency and environmental factors in the US electricity transmission industry
Llorca, M., Orea, L., & Pollitt, M. G. (2016) · Energy Economics · doi:10.1016/j.eneco.2016.02.004 · Cited by 55
Agasisti, T., Barra, C., & Zotti, R. (2016) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2016.06.002 · Cited by 56
“In this analysis, we do not impose the “scaling property” (for more details see Wang and Schmidt (2002), in the context of crosssectional data, and Alvarez et al. (2006), in the panel data context); indeed, as underlined by Wang and Ho (2010), “whether the scaling property holds in the data is…”
MethodEfficiency in the National Basketball Association: a stochastic frontier approach with panel data
Hofler, R. A., & Payne, J. E. (2006) · Managerial and Decision Economics · doi:10.1002/mde.1252 · Cited by 56
“However, this two-stage procedure is inferior to a single-stage procedure (see, for example, Wang and Schmidt, 2002 for an exploration of this issue.) Battese and Coelli (1995) provide a panel model that permits concurrently estimating the stochastic production frontier and the determinants of a team’s win efficiency.”
MethodEconomic and Environmental Efficiency, Subsidies and Spatio-Temporal Effects in Agriculture
Bernini, C., & Galli, F. (2024) · Ecological Economics · doi:10.1016/j.ecolecon.2024.108120 · Cited by 55
Estimation of hedonic price functions with incomplete information
Kumbhakar, S. C., & Parmeter, C. F. (2009) · Empirical Economics · doi:10.1007/s00181-009-0292-8 · Cited by 55
“19 This formulation is similar to the scaling method of Wang and Schmidt (2002) in a single-tier frontier”
MethodGong, S. X. H., Cullinane, K., & Firth, M. A. (2012) · Transport Policy · doi:10.1016/j.tranpol.2012.06.020 · Cited by 55
The cost efficiency impact of the university operation fund on public universities in Taiwan
Kuo, J.-S., & Ho, Y.-C. (2007) · Economics of Education Review · doi:10.1016/j.econedurev.2007.06.003 · Cited by 59
Kuosmanen, T., & Kuosmanen, T. (2006) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.11864 · Cited by 55
Price Dispersion in Farmland Markets: What Is the Role of Asymmetric Information?
Seifert, S., Kahle, C., & Hüttel, S. (2020) · American Journal of Agricultural Economics · doi:10.1111/ajae.12153 · Cited by 54
Missiame, A., Nyikal, R. A., & Irungu, P. (2021) · Heliyon · doi:10.1016/j.heliyon.2021.e07102 · Cited by 54
“Following Wang and Schmidt (2002), the effects of covariates on technical efficiency can be estimated in a one-step procedure.”
BackgroundLaudicella, M., Olsen, K. R., & Street, A. D. (2010) · Social Science & Medicine · doi:10.1016/j.socscimed.2010.06.049 · Cited by 54
Regulation and efficiency in transition: the case of Romanian banks
Asaftei, G., & Kumbhakar, S. C. (2007) · Journal of Regulatory Economics · doi:10.1007/s11149-007-9041-0 · Cited by 54
“Wang and Schmidt (2002) explain why the two-step procedure is bad, and present Monte Carlo evidence showing that the bias from the two-step procedure can be severe.”
BackgroundFan, X., Yu, B., Chu, Z., et al. (2020) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2020.140707 · Cited by 54
Bank efficiency differences in the new EU member states
Košak, M., Zajc, P., & Zorić, J. (2009) · Baltic Journal of Economics · doi:10.1080/1406099x.2009.10840462 · Cited by 53
“Wang and Schmidt (2002) argue that if any interesting effects are to be observed in the second step, then it follows from considerations of omitted variables that the first-step estimators are biased and inconsistent.”
BackgroundFilippini, M., Geissmann, T., Karplus, V. J., et al. (2019) · China Economic Review · doi:10.1016/j.chieco.2019.101364 · Cited by 53
“13 Wooldridge (2009) shows that the moment conditions of the complicated two-step semi-parametric approach of Olley and Pakes (1996) to control for the simultaneity bias and the modification to it proposed by Levinsohn and Petrin (2003) can be implemented in a GMM framework yielding more efficient estimates amongst ot…”
BackgroundEfficiency in Education: Research and Implications
Grosskopf, S., Hayes, K. J., & Taylor, L. L. (2014) · Applied Economic Perspectives and Policy · doi:10.1093/aepp/ppu007 · Cited by 52
Suyanto, S., Bloch, H., & Salim, R. A. (2012) · The Journal of Development Studies · doi:10.1080/00220388.2011.646992 · Cited by 52
Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis
Parmeter, C. F., & Zelenyuk, V. (2019) · Operational Research · doi:10.1287/opre.2018.1831 · Cited by 51
Silva, . V., Pede, V. O., Radanielson, A. M., Kodama, W., Duarte, A. J., de Guia, A. H., Malabayabas, A. J. B., Pustika, A. B., Argosubekti, N., Vithoonjit, D., et al. (2022) · Agricultural Systems · doi:10.1016/j.agsy.2022.103383 · Cited by 56
Chen, K. (2012) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2012.02.012 · Cited by 51
Kuosmanen, T. (2006) · SSRN Electronic Journal · doi:10.2139/ssrn.905758 · Cited by 51
The impact of ownership on the cost of bus service provision: an example from Italy
Ottoz, E., Fornengo, G., & Giacomo, M. D. (2008) · Applied Economics · doi:10.1080/00036840601007260 · Cited by 49
“See Wang and Schmidt ( 2002 ) for Monte Carlo evidence on the severity of the biases in two-step models.”
BackgroundMutoko, M. C., Hein, L., & Shisanya, C. A. (2014) · Journal of Rural Studies · doi:10.1016/j.jrurstud.2014.07.006 · Cited by 50
Product market regulation and innovation efficiency
Franco, C., Pieri, F., & Venturini, F. (2015) · Journal of Productivity Analysis · doi:10.1007/s11123-015-0441-3 · Cited by 49
“…capturing deviations from the frontier caused by a sub-optimal input usage, namely R&D inefficiency (Wang, 2007; Fu and Yang, 2009).3 To assess how product market regulation (PMR) affects innovation efficiency, we adopt the one-step estimator devised by Wang and Schmidt (2002) and Schmidt (2011).”
MethodPang, M., Tafti, A., & Krishnan, M. S. (2014) · MIS Quarterly · doi:10.25300/misq/2014/38.4.07 · Cited by 47
Agricultural Technical Efficiency of Smallholder Farmers in Ethiopia: A Stochastic Frontier Approach
Zewdie, M. C., Moretti, M., Tenessa, D. B., Ayalew, Z., Nyssen, J., Adgo, E., Minale, A. S., & Passel, S. V. (2021) · Land · doi:10.3390/land10030246 · Cited by 49
Kumbhakar, S. C., Badunenko, O., & Willox, M. (2022) · Energy Economics · doi:10.1016/j.eneco.2022.106359 · Cited by 49
Herwartz, H., & Strumann, C. (2013) · The European Journal of Health Economics · doi:10.1007/s10198-013-0464-5 · Cited by 49
“However, the application of two-stage procedures based on estimated SFA efficiency scores may lead to invalid conclusions [48].”
BackgroundMethodEnergy Efficiency Transitions in China: How Persistent are the Movements to/from the Frontier?
Zhang, L., & Adom, P. K. (2018) · The Energy Journal · doi:10.5547/01956574.39.6.lzha · Cited by 48
Analysing the drivers of the efficiency of households in electricity consumption
Romero‐Jordán, D., & RÍO, P. D. (2022) · Energy Policy · doi:10.1016/j.enpol.2022.112828 · Cited by 50
Assessing the Performance of Local Government
Stevens, P. A. (2005) · National Institute Economic Review · doi:10.1177/0027950105058565 · Cited by 43
Kouser, S., & Mushtaq, K. (2016) · Cited by 48
Vidoli, F., Cardillo, C., Fusco, E., et al. (2016) · Regional Science and Urban Economics · doi:10.1016/j.regsciurbeco.2016.10.003 · Cited by 48
Herwartz, H., & Schley, K. (2018) · Health Policy · doi:10.1016/j.healthpol.2018.01.004 · Cited by 48
Technical efficiency and its determinants in China's hog production
Tian, X., Sun, F., & Ying-heng, Z. (2015) · Journal of Integrative Agriculture · doi:10.1016/s2095-3119(14)60989-8 · Cited by 48
Crop diversification improves technical efficiency and reduces income variability in Northern Ghana
Mzyece, A., & Ng’ombe, J. N. (2021) · Journal of Agriculture and Food Research · doi:10.1016/j.jafr.2021.100162 · Cited by 48
“To avoid the bias associated with a two-step approach of computing efficiency and regressing exogenous varibles on the efficiency index (Wang & Schmidt, 2002; Kumbhakar et al., 2015), we use a one step approach proposed by Kumbhakar et al., (2015).”
MethodTemperature and production efficiency growth: empirical evidence
Kumar, S., & Khanna, M. (2019) · Climatic Change · doi:10.1007/s10584-019-02515-5 · Cited by 48
“5 Our application captures climate-driven changes in the “fatness” of efficiency growth distribution tails; the importance of which was stressed in Weitzman (2011).”
BackgroundFarmers’ health and agricultural productivity in rural Ethiopia
Ulimwengu, J. M., & Ulimwengu, J. M. (2009) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.56902 · Cited by 46
“Since variables influencing agricultural efficiency ( ) may also directly affect agricultural production ( ), I adopt the approach proposed by Wang and Schmidt (2002) and Liu and Myers (2009), where equation (7) is rewritten as follows:”
MethodCainelli, G., Ganau, R., & Iacobucci, D. (2015) · Growth and Change · doi:10.1111/grow.12112 · Cited by 45
Castiglione, C., & Infante, D. (2014) · Economic Modelling · doi:10.1016/j.econmod.2014.04.021 · Cited by 45
“This approach has been recognised (Wang and Schmidt, 2002) to be better than the two-stage estimation which inconsistently assumes the independence of the inefficiency effects.”
BackgroundSemiparametric smooth-coefficient stochastic frontier model
Sun, K., & Kumbhakar, S. C. (2013) · Economics Letters · doi:10.1016/j.econlet.2013.05.001 · Cited by 43
Choi, K., Kang, H. J., & Kim, C. (2021) · Tourism Management · doi:10.1016/j.tourman.2021.104348 · Cited by 48
Stochastic Frontier Analysis: Foundations and Advances I
Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (2020) · Springer eBooks · doi:10.1007/978-981-10-3450-3_9-2 · Cited by 65
Hospital Inefficiency: What is the Impact of Membership in Different Types of Systems?
Rosko, M. D., Proenca, J., Zinn, J. S., et al. (2007) · INQUIRY The Journal of Health Care Organization Provision and Financing · doi:10.5034/inquiryjrnl_44.3.335 · Cited by 45
“Thus, our results concur with Wang and Schmidt (2002), who wrote, ‘‘we would recommend against using two-step procedures in any circumstances we can”
ResultAn estimation of technical efficiency for Florida public elementary schools
Conroy, S. J., & Arguea, N. M. (2007) · Economics of Education Review · doi:10.1016/j.econedurev.2007.08.002 · Cited by 44
“5The recognition that the level of inefficiency is a function of exogenous variables is evident in recent work by Wang and Schmidt (2003), and previous work by Simar, Lovell, and Vanden Please cite this article as: Conroy, S. J., & Arguea, N. M.”
Investigating the Human Capital Development–growth Nexus
Barra, C., & Zotti, R. (2016) · International Regional Science Review · doi:10.1177/0160017615626215 · Cited by 44
“In this analysis, we do not impose the “scaling property” (for more details see Wang and Schmidt (2002) and Alvarez et al.”
MethodSchool district consolidation policies: endogenous cost inefficiency and saving reversals
Karakaplan, M. U., & Kutlu, L. (2017) · Empirical Economics · doi:10.1007/s00181-017-1398-z · Cited by 44
Financial stability efficiency of Islamic and conventional banks
Safiullah, M. (2021) · Pacific-Basin Finance Journal · doi:10.1016/j.pacfin.2021.101587 · Cited by 44
The difference between wages and wage potentials: Earnings disadvantages of immigrants in Germany
Lang, G. (2005) · The Journal of Economic Inequality · doi:10.1007/s10888-004-7581-4 · Cited by 44
“See also Wang and Schmidt [ 28 ] for a discussion of the single-stage versus the two-step procedure.”
BackgroundSchool district consolidation: Market concentration and the scale‐efficiency tradeoff
Gronberg, T. J., Jansen, D. W., Karakaplan, M. U., et al. (2015) · Southern Economic Journal · doi:10.1002/soej.12029 · Cited by 43
Clustering, Agency Costs and Operating Efficiency: Evidence from Nursing Home Chains
Lu, S. F., & Wedig, G. J. (2012) · Management Science · doi:10.1287/mnsc.1120.1611 · Cited by 43
“Under these assumptions, observed quality may be modeled using a stochastic frontier model (Wang and Schmidt 2002, Kumbhaker and Tsionas 2006).”
Technology Invention and Diffusion in Residential Energy Consumption. A Stochastic Frontier Approach
Marin, G., & Palma, A. (2016) · Energy Economics · doi:10.1016/j.eneco.2017.06.005 · Cited by 44
Piao, Z., Miao, B., Zheng, Z., et al. (2022) · Energy Economics · doi:10.1016/j.eneco.2022.106140 · Cited by 43
Kumbhakar, S. C., & Wang, H. (2005) · Journal of Econometrics · doi:10.1016/j.jeconom.2005.06.025 · Cited by 43
Self-citationTowards Cleaner Production: Certified Seed Adoption and Its Effect on Technical Efficiency
Baglan, M., Mwalupaso, G. E., Zhou, X., & Geng, X. (2020) · Sustainability · doi:10.3390/su12041344 · Cited by 54
Are board characteristics relevant for banking efficiency? Evidence from the US
Titova, Y. (2016) · Corporate Governance · doi:10.1108/cg-09-2015-0124 · Cited by 42
Accounting for Skewed or One-Sided Measurement Error in the Dependent Variable
Millimet, D. L., & Parmeter, C. F. (2021) · Political Analysis · doi:10.1017/pan.2020.45 · Cited by 41
“See text for further details.”
BackgroundMethodInfluentialThe underlying drivers of economy-wide energy efficiency and asymmetric energy price responses
Tajudeen, I. (2021) · Energy Economics · doi:10.1016/j.eneco.2021.105222 · Cited by 42
Energy Efficiency in OECD and non-OECD Countries: Estimates and Convergence
Liddle, B., & Sadorsky, P. (2020) · Energy Efficiency · doi:10.1007/s12053-021-09992-7 · Cited by 46
Likelihood ratio tests for model selection of stochastic frontier models
Lai, H., & Huang, C. J. (2009) · Journal of Productivity Analysis · doi:10.1007/s11123-009-0160-8 · Cited by 41
“When d = c in the GEM setting, one obtains the SF model with the scaling property suggested by Wang and Schmidt (2002) .”
BackgroundMethodECONOMICS OF THE WORKPLACE: SPECIAL ISSUE EDITORIAL
HARRIS, R. I. D. (2005) · Scottish Journal of Political Economy · doi:10.1111/j.0036-9292.2005.00347.x · Cited by 40
Evaluating the Contribution of Exporting to UK Productivity Growth: Some Microeconomic Evidence
HARRIS, R. I. D., & Li, Q. C. (2008) · World Economy · doi:10.1111/j.1467-9701.2007.01087.x · Cited by 42
“6), the omitted variable problem (Wang and Schmidt, 2002) in a two-stage model, and the endogeneity of inputs and outputs in a production model.”
BackgroundDjuraeva, M., Bobojonov, I., Kuhn, L., & Glauben, T. (2022) · Economic Analysis and Policy · doi:10.1016/j.eap.2022.11.008 · Cited by 48
Adom, P. K., & Adams, S. (2020) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2020.122670 · Cited by 41
Explaining Differences in Milk Quota Values: The Role of Economic Efficiency
Alvarez, A. M., Arias, C., & Orea, L. (2006) · American Journal of Agricultural Economics · doi:10.1111/j.1467-8276.2006.00846.x · Cited by 41
“Wang and Schmidt (2002) show that the efficiency scores are also biased.”
BackgroundRodrı́guez-Álvarez, A., & Tovar, B. (2012) · Transport Policy · doi:10.1016/j.tranpol.2012.06.004 · Cited by 40
Nurboja, B., & Košak, M. (2016) · Economic Systems · doi:10.1016/j.ecosys.2016.05.006 · Cited by 40
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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