Efficiency Measurement - PowerPoint PPT Presentation

1 / 43
About This Presentation
Title:

Efficiency Measurement

Description:

(Samuelson Shephard duality results) ... Duality Production vs. Cost. Where to Next? Heterogeneity: 'Where do we put the z's? ... – PowerPoint PPT presentation

Number of Views:25
Avg rating:3.0/5.0
Slides: 44
Provided by: valued79
Category:

less

Transcript and Presenter's Notes

Title: Efficiency Measurement


1
Efficiency Measurement
  • William Greene
  • Stern School of Business
  • New York University

2
Session 5
  • Modeling Heterogeneity

3
Production Function Model with Inefficiency
4
The Stochastic Frontier Model
ui gt 0, but vi may take any value. A symmetric
distribution, such as the normal distribution, is
usually assumed for vi. Thus, the stochastic
frontier is ??xivi
and, as before, ui represents the inefficiency.
5
The Normal-Half Normal Model
6
Log Likelihood Function
Waldman (1982) result on skewness of OLS
residuals If the OLS residuals are positively
skewed, rather than negative, then OLS maximizes
the log likelihood, and there is no evidence of
inefficiency in the data.
7
Normal-Truncated Normal
8
Truncated Normal Model
9
Fundamental Tool - JLMS
We can insert our maximum likelihood estimates of
all parameters. Note This estimates Euvi
ui, not ui.
10
Estimated Translog Production Frontiers
11
Inefficiency Estimates
12
Estimated Inefficiency Distribution
13
Cost Inefficiency
  • y f(x) ?? C g(y,w)
  • (Samuelson Shephard duality results)
  • Cost inefficiency If y lt f(x), then C mustbe
    greater than g(y,w). Implies the idea of a cost
    frontier.
  • lnC lng(y,w) u, u gt 0.

14
Stochastic Cost Frontier
15
Estimates of Economic Efficiency
16
Duality Production vs. Cost
17
Where to Next?
  • Heterogeneity Where do we put the zs?
  • Other variables that affect production and
    inefficiency
  • Enter production frontier, inefficiency
    distribution, elsewhere?
  • Heteroscedasticity
  • Another form of heterogeneity
  • Production risk
  • Bayesian and simulation estimators
  • The stochastic frontier model with gamma
    inefficiency
  • Bayesian treatments of the stochastic frontier
    model
  • Panel Data
  • Heterogeneity vs. Inefficiency can we
    distinguish
  • Model forms Is inefficiency persistent through
    time?
  • Applications

18
(No Transcript)
19
Observable Heterogeneity
  • As opposed to unobservable heterogeneity
  • Observe Y or C (outcome) and X or w (inputs or
    input prices)
  • Firm characteristics z. Not production or cost,
    characterize the production process.
  • Enter the production or cost function?
  • Enter the inefficiency distribution? How?

20
Shifting the Outcome Function
Firm specific heterogeneity can also be
incorporated into the inefficiency model as
follows This modifies the mean of the truncated
normal distribution yi ??xi vi -
ui vi N0,?v2 ui Ui where Ui
N?i, ?u2, ?i ?0 ?1?zi,
21
Heterogeneous Mean
22
Estimated Economic Efficiency
23
One Step or Two Step
  • 2 Step Fit Half or truncated normal model,
    compute JLMS ui, regress ui on zi
  • Airline EXAMPLE Fit model without POINTS,
    LOADFACTOR, STAGE
  • 1 Step Include zi in the model, compute ui
    including zi
  • Airline example Include 3 variables
  • Methodological issue Left out variables in two
    step approach.

24
One vs. Two Step
0.8 0.9 1.0
Efficiency computed without load factor, stage
length and points served.
Efficiency computed with load factor, stage
length and points served.
25
Application WHO Data
26
Unobservable Heterogeneity
  • Parameters vary across firms
  • Random variation (heterogeneity, not Bayesian)
  • Variation partially explained by observable
    indicators
  • Continuous variation random parameter models
    Considered with panel data models
  • Latent class discrete parameter variation

27
A Latent Class Model
28
Latent Class Efficiency Studies
  • Battese and Coelli growing in weather regimes
    for Indonesian rice farmers
  • Kumbhakar and Orea cost structures for U.S.
    Banks
  • Greene (Health Economics, 2005) revisits WHO
    Year 2000 World Health Report
  • Kumbhakar, Parmeter, Tsionas (JE, 2013) U.S.
    Banks.

29
Latent Class Application
30
Inefficiency?
  • Not all agree with the presence (or
    identifiability) of inefficiency in market
    outcomes data.
  • Variation around the common production structure
    may all be nonsystematic and not controlled by
    management
  • Implication, no inefficiency u 0.

31
(No Transcript)
32
Nursing Home Costs
  • 44 Swiss nursing homes, 13 years
  • Cost, Pk, Pl, output, two environmental variables
  • Estimate cost function
  • Estimate inefficiency

33
Estimated Cost Efficiency
34
A Two Class Model
  • Class 1 With Inefficiency
  • logC f(output, input prices, environment) ?vv
    ?uu
  • Class 2 Without Inefficiency
  • logC f(output, input prices, environment) ?vv
  • ?u 0
  • Implement with a single zero restriction in a
    constrained (same cost function) two class model
  • Parameterization ? ?u /?v 0 in class 2.

35
LogL 464 with a common frontier model, 527 with
two classes
36
(No Transcript)
37
(No Transcript)
38
Heteroscedasticity in v and/or u
  • Varvi hi ?v2gv(hi,?) ?vi2
  • gv(hi,0) 1,
  • gv(hi,?) exp(?hi)2
  • VarUi hi ?u2gu(hi,?) ?ui2
  • gu(hi,0) 1,
  • gu(hi,?) exp(?hi)2

39
Application WHO Data
40
A Scaling Model
41
Unobserved Endogenous Heterogeneity
  • Cost C(p,y,Q), Q quality
  • Quality is unobserved
  • Quality is endogenous correlated with
    unobservables that influence cost
  • Econometric Response There exists a proxy that
    is also endogenous
  • Omit the variable?
  • Include the proxy?
  • Question Bias in estimated inefficiency (not
    interested in coefficients)

42
Simulation Experiment
  • Mutter, et al. (AHRQ), 2011
  • Analysis of California nursing home data
  • Estimate model with a simulated data set
  • Compare biases in sample average inefficiency
    compared to the exogenous case
  • Endogeneity is quantified in terms of correlation
    of Q(i) with u(i)

43
A Simulation Experiment
Conclusion Omitted variable problem does not
make the bias worse.
Write a Comment
User Comments (0)
About PowerShow.com