efficiencies.frontier: Returning Efficiency Estimates
In frontier: Stochastic Frontier Analysis
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
View source: R/efficiencies.frontier.R
Description
This method returns efficiency estimates from stochastic frontier models
estimated with frontier.
Usage
1
2
3
4
Arguments
object
a stochastic frontier model
returned by frontier.
asInData
logical. If TRUE,
the efficiency estimates are returned in the same order
as the corresponding observations in the data set
used for the estimation
(see section ‘value’ below).
logDepVar
logical. Is the dependent variable logged?
minusU
logical. If TRUE (the default),
the efficiencies are calculated by E[exp(-u)],
i.e. Farrel-type efficiencies are returned for input-oriented models,
Shepard-type efficiencies are returned for output-oriented models,
and the returned efficiency estimates have values
between zero and one,
where a one indicates a fully efficient firm
and a zero indicates a fully inefficient firm.
If FALSE,
the efficiencies are calculated by E[exp(u)],
i.e. Shepard-type efficiencies are returned for input-oriented models,
Farrell-type efficiencies are returned for output-oriented models,
and the returned efficiency estimates have values larger than
or equal to one,
where a one indicates a fully efficient firm
and plus infinity indicates a fully inefficient firm.
farrell
logical. This argument is only kept for backward compatibility
and will be removed in the future.
margEff
logical. If TRUE, the marginal effects
of the z variables (of an Efficiency Effects Frontier, EEF)
on the efficiency measure are returned as an ‘attribute’
to the returned object (i.e. the efficiency estimates).
These marginal effects are calculated by the formula derived in
Olsen and Henningsen (2011),
which was slightly adjusted for the differing model specifications.
Currently, this feature is implemented only for models
with logged dependent variables.
newdata
an optional data frame from which the values
of explanatory variables and the dependent variable are taken
to calculate the efficiency estimates.
If this argument is NULL (the default),
the efficiency estimates are calculated for the observations
that were used in the estimation.
...
currently ignored.
Value
If argument asInData is FALSE (default),
a matrix of efficiency estimates is returned,
where each row corresponds to a firm (cross-section unit)
and each column corresponds to a time period
(only if efficiency estimates differ between time periods).
If argument asInData is TRUE,
a vector of efficiency estimates is returned,
where the efficiency estimates are in the same order
as the corresponding observations in the data set
used for the estimation.
If argument margEff is TRUE,
and the model is an Efficiency Effects Frontier (EFF)
with z variables,
and the dependent variable is logged,
the returned efficiency estimates have an attribute "margEff"
that contains the marginal effects of the z variables
on the efficiency measure.
If the dependent variable is logged,
the marginal effect of the kth z variable on the efficiency is
\frac{\partial E[ \exp( - κ \, u ) ]}{\partial z_{kit}}
= \frac{ δ_{k} ( 1 - γ )
\exp ≤ft( - κ \, \bar{μ}_{it}
+ \frac{1}{2} \bar{σ}^{2} \right) }{
Φ ≤ft( \frac{\bar{μ}_{it}}{ \bar{σ} } \right) }
\cdot ≤ft( \frac{ φ ≤ft( -κ \, \bar{σ}
+ \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) }{ \bar{σ} }
- \frac{ Φ ≤ft( -κ \, \bar{σ}
+ \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) \,
φ ≤ft( \frac{ \bar{μ}_{it} }{ \bar{σ} } \right)}{
\bar{σ} \,
Φ ≤ft( \frac{ \bar{μ}_{it} }{ \bar{σ}}\right) }
- κ \, Φ ≤ft( -κ \, \bar{σ}
+ \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) \right),
where
\bar{μ}_{it}
= ( 1 - γ ) \, z_{it} ' δ
- τ \, γ \, ε_{it},
\bar{σ}^{2}
= γ \, ( 1 - γ ) \, σ^{2},
κ = 1 in case of Farrell efficiencies
(i.e. efficiencies have values between between 0 and 1),
whereas κ = -1 otherwise
(i.e. efficiencies have values larger than 1),
and τ = 1 if inefficiency decreases the dependent variable,
whereas τ = -1 otherwise
(see Olsen and Henningsen 2011).
If argument asInData is FALSE,
this attribute is a 3-dimensional array,
where the first dimension represents the individual firm,
the second deminsion represents the time period,
and the third dimension represents the z variables.
In contrast, if argument asInData is TRUE,
this attribute is a matrix,
where the rows represent the observations
and the columns represent the z variables.
Author(s)
Arne Henningsen
References
Olsen, Jakob Vesterlund and Arne Henningsen (2011):
Investment utilization and farm efficiency in Danish agriculture.
FOI working paper 2011/13, Institute of Food and Resource Economics,
University of Copenhagen,
http://EconPapers.repec.org/RePEc:foi:wpaper:2011_13.
See Also
sfa, summary.frontier,
and efficiencies.
Examples
1
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3
4
5
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8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
# rice producers in the Philippines (panel data)
data( "riceProdPhil" )
library( "plm" )
riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )
# Error Components Frontier (Battese & Coelli 1992), no time effect
rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
data = riceProdPhil )
efficiencies( rice )
riceProdPhil$efficiencies <- efficiencies( rice, asInData = TRUE )
# efficiency of an 'average' farm
efficiencies( rice,
newdata = data.frame( t( colMeans( riceProdPhil[ , -c(1,2) ] ) ) ) )
# Error Components Frontier (Battese & Coelli 1992), with time effect
riceTime <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
data = riceProdPhil, timeEffect = TRUE )
efficiencies( riceTime )
riceProdPhil$efficienciesTime <- efficiencies( riceTime, asInData = TRUE )
# Technical Efficiency Effects Frontier (Battese & Coelli 1995)
rice2 <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
EDYRS + BANRAT - 1, data = riceProdPhil )
eff <- efficiencies( rice2, margEff = TRUE )
attr( eff, "margEff" ) # marginal effects
Example output
Loading required package: micEcon
If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/
Loading required package: lmtest
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Please cite the 'frontier' package as:
Tim Coelli and Arne Henningsen (2013). frontier: Stochastic Frontier Analysis. R package version 1.1. http://CRAN.R-Project.org/package=frontier.
If you have questions, suggestions, or comments regarding the 'frontier' package, please use a forum or 'tracker' at frontier's R-Forge site:
https://r-forge.r-project.org/projects/frontier/
Loading required package: Formula
efficiency
1 0.7348838
2 0.9335358
3 0.7356669
4 0.9047961
5 0.8646110
6 0.8084379
7 0.9231276
8 0.8150041
9 0.8722820
10 0.8539424
11 0.6021630
12 0.9491698
13 0.7820029
14 0.8703560
15 0.7123153
16 0.9058007
17 0.8788236
18 0.9238596
19 0.8586420
20 0.9046036
21 0.8014665
22 0.8277730
23 0.7080684
24 0.7073893
25 0.8363073
26 0.8557391
27 0.8002148
28 0.9382601
29 0.7072642
30 0.6075254
31 0.9152860
32 0.8476270
33 0.8877271
34 0.4978360
35 0.9083843
36 0.6955584
37 0.9265961
38 0.9333733
39 0.7423341
40 0.6689979
41 0.9361506
42 0.8994492
43 0.7249107
efficiency
1 0.7348838
2 0.9335358
3 0.7356669
4 0.9047961
5 0.8646110
6 0.8084379
7 0.9231276
8 0.8150041
9 0.8722820
10 0.8539424
11 0.6021630
12 0.9491698
13 0.7820029
14 0.8703560
15 0.7123153
16 0.9058007
17 0.8788236
18 0.9238596
19 0.8586420
20 0.9046036
21 0.8014665
22 0.8277730
23 0.7080684
24 0.7073893
25 0.8363073
26 0.8557391
27 0.8002148
28 0.9382601
29 0.7072642
30 0.6075254
31 0.9152860
32 0.8476270
33 0.8877271
34 0.4978360
35 0.9083843
36 0.6955584
37 0.9265961
38 0.9333733
39 0.7423341
40 0.6689979
41 0.9361506
42 0.8994492
43 0.7249107
1 2 3 4 5 6 7
1 0.7036591 0.7176992 0.7312209 0.7442280 0.7567260 0.7687222 0.7802252
2 0.9152460 0.9197825 0.9240924 0.9281853 0.9320704 0.9357570 0.9392540
3 0.6930843 0.7075251 0.7214433 0.7348415 0.7477240 0.7600971 0.7719686
4 0.8863269 0.8923068 0.8979991 0.9034148 0.9085646 0.9134594 0.9181097
5 0.8305840 0.8392249 0.8474790 0.8553577 0.8628730 0.8700370 0.8768620
6 0.7799158 0.7908320 0.8012919 0.8113056 0.8208841 0.8300389 0.8387821
7 0.9163653 0.9208451 0.9251007 0.9291417 0.9329773 0.9366168 0.9400687
8 0.7952759 0.8055177 0.8153220 0.8246997 0.8336622 0.8422212 0.8503893
9 0.8440482 0.8520610 0.8597087 0.8670030 0.8739557 0.8805789 0.8868845
10 0.8228167 0.8318156 0.8404157 0.8486284 0.8564656 0.8639395 0.8710623
11 0.5276153 0.5470780 0.5661066 0.5846728 0.6027530 0.6203276 0.6373816
12 0.9387675 0.9420962 0.9452531 0.9482460 0.9510825 0.9537701 0.9563159
13 0.7381054 0.7507832 0.7629639 0.7746549 0.7858647 0.7966029 0.8068802
14 0.8315627 0.8401583 0.8483685 0.8562050 0.8636796 0.8708045 0.8775918
15 0.6820662 0.6969153 0.7112388 0.7250375 0.7383147 0.7510756 0.7633270
16 0.8748583 0.8813986 0.8876290 0.8935607 0.8992050 0.9045731 0.9096759
17 0.8458582 0.8537858 0.8613514 0.8685666 0.8754433 0.8819934 0.8882289
18 0.9084840 0.9133620 0.9179985 0.9224035 0.9265867 0.9305577 0.9343259
19 0.8372931 0.8456222 0.8535751 0.8611635 0.8683992 0.8752943 0.8818610
20 0.8895082 0.8953315 0.9008735 0.9061452 0.9111572 0.9159201 0.9204443
21 0.7378206 0.7505100 0.7627021 0.7744042 0.7856249 0.7963736 0.8066613
22 0.8104189 0.8199825 0.8291291 0.8378701 0.8462170 0.8541820 0.8617775
23 0.6607368 0.6763490 0.6914329 0.7059865 0.7200102 0.7335070 0.7464815
24 0.6719749 0.6871897 0.7018769 0.7160362 0.7296695 0.7427811 0.7553767
25 0.8097515 0.8193453 0.8285211 0.8372903 0.8456645 0.8536559 0.8612767
26 0.8241086 0.8330483 0.8415910 0.8497483 0.8575321 0.8649545 0.8720279
27 0.7627839 0.7744354 0.7856121 0.7963230 0.8065783 0.8163889 0.8257664
28 0.9293251 0.9331426 0.9367656 0.9402028 0.9434625 0.9465530 0.9494821
29 0.6527008 0.6685908 0.6839528 0.6987835 0.7130823 0.7268510 0.7400936
30 0.5662764 0.5847947 0.6028316 0.6203675 0.6373869 0.6538782 0.6698331
31 0.8994373 0.9047683 0.9098385 0.9146583 0.9192381 0.9235878 0.9277173
32 0.8050218 0.8148286 0.8242109 0.8331799 0.8417471 0.8499246 0.8577247
33 0.8641915 0.8712472 0.8779729 0.8843803 0.8904808 0.8962861 0.9018076
34 0.4112413 0.4325334 0.4536340 0.4744858 0.4950372 0.5152417 0.5350581
35 0.8922470 0.8979350 0.9033474 0.9084948 0.9133878 0.9180370 0.9224525
36 0.6300435 0.6466875 0.6628078 0.6783975 0.6934525 0.7079717 0.7219563
37 0.9222721 0.9264512 0.9304195 0.9341861 0.9377600 0.9411497 0.9443639
38 0.9174599 0.9218841 0.9260866 0.9300768 0.9338641 0.9374573 0.9408652
39 0.6728266 0.6880108 0.7026676 0.7167967 0.7304002 0.7434823 0.7560490
40 0.6098523 0.6271302 0.6438932 0.6601304 0.6758345 0.6910013 0.7056294
41 0.9155355 0.9200574 0.9243532 0.9284326 0.9323050 0.9359794 0.9394647
42 0.8881516 0.8940418 0.8996480 0.9049811 0.9100519 0.9148711 0.9194490
43 0.6326719 0.6492307 0.6652650 0.6807684 0.6957372 0.7101705 0.7240701
8
1 0.7912447
2 0.9425699
3 0.7833477
4 0.9225257
5 0.8833602
6 0.8471261
7 0.9433418
8 0.8581789
9 0.8928845
10 0.8778466
11 0.6539034
12 0.9587266
13 0.8167083
14 0.8840540
15 0.7750774
16 0.9145245
17 0.8941617
18 0.9379003
19 0.8881113
20 0.9247400
21 0.8164993
22 0.8690161
23 0.7589404
24 0.7674640
25 0.8685397
26 0.8787647
27 0.8347232
28 0.9522574
29 0.7528158
30 0.6852465
31 0.9316363
32 0.8651602
33 0.9070566
34 0.5544504
35 0.9266445
36 0.7354098
37 0.9474104
38 0.9440964
39 0.7681080
40 0.7197198
41 0.9427696
42 0.9237961
43 0.7374396
, , Z_EDYRS
1 2 3 4 5
1 0.0015141075 0.0018748843 0.0014338949 0.0018565976 0.0018775870
2 0.0016621628 0.0011788353 0.0010456460 0.0005896525 0.0006734038
3 0.0014585178 0.0018644616 0.0018271448 0.0019818070 0.0017231825
4 0.0009846104 0.0019720588 0.0003133005 0.0008890440 0.0011226468
5 0.0012469637 0.0015098999 0.0012632628 0.0010721278 0.0018908266
6 0.0007534912 0.0019196687 0.0013046308 0.0019611551 0.0015597168
7 0.0008653043 0.0006426711 0.0008616376 0.0005634276 0.0012024682
8 0.0010159852 0.0011180063 0.0019817550 0.0013621971 0.0013952756
9 0.0014608851 0.0010079595 0.0011610526 0.0016201660 0.0014905412
10 0.0017520562 0.0018959534 0.0009127320 0.0008181538 0.0018399783
11 0.0012241237 0.0012620448 0.0018036418 0.0018614046 0.0016936418
12 0.0008888603 0.0015756076 0.0016669902 0.0003810151 0.0019480626
13 0.0012253698 0.0019816308 0.0013009946 0.0019578375 0.0018712539
14 0.0015613173 0.0018975172 0.0014751381 0.0011100169 0.0010722268
15 0.0017961180 0.0018424656 0.0019668973 0.0014419725 0.0015338821
16 0.0016877451 0.0009760373 0.0015580019 0.0011276668 0.0008347424
17 0.0018862237 0.0013226156 0.0010274893 0.0004963296 0.0003655444
18 0.0007583000 0.0011799311 0.0008562169 0.0009967072 0.0010737627
19 0.0009542183 0.0006071018 0.0011653493 0.0014279838 0.0012326128
20 0.0011354951 0.0009117224 0.0009228813 0.0012100605 0.0010511221
21 0.0019639738 0.0017114555 0.0007457202 0.0017970942 0.0015982909
22 0.0008118010 0.0016312697 0.0007546924 0.0006645077 0.0018756256
23 0.0018553314 0.0019706697 0.0014345555 0.0015916296 0.0016706845
24 0.0018026852 0.0019692275 0.0010924817 0.0015018516 0.0013807573
25 0.0017517300 0.0010816911 0.0010352920 0.0008404301 0.0016598878
26 0.0016765701 0.0019783681 0.0011015000 0.0019693574 0.0009304259
27 0.0017988276 0.0013631903 0.0011587304 0.0018458076 0.0019800822
28 0.0009132237 0.0006632061 0.0006396114 0.0012499868 0.0010763934
29 0.0018327501 0.0018907666 0.0017918336 0.0008122518 0.0017984818
30 0.0019667994 0.0018902121 0.0019517180 0.0015131451 0.0016767383
31 0.0002994025 0.0019754227 0.0006214450 0.0017728467 0.0007783518
32 0.0015010724 0.0015702096 0.0008265229 0.0010834765 0.0016145323
33 0.0014807670 0.0015534334 0.0015064494 0.0012082662 0.0007398880
34 0.0010771385 0.0010903457 0.0016697864 0.0019307372 0.0012924200
35 0.0008728765 0.0006827890 0.0009293306 0.0010830148 0.0019792740
36 0.0012853716 0.0019767675 0.0019316677 0.0019642537 0.0019699785
37 0.0006077181 0.0006692920 0.0005219998 0.0006718313 0.0012912313
38 0.0006307439 0.0011854821 0.0008936768 0.0008181167 0.0019814242
39 0.0017990761 0.0014059166 0.0019031293 0.0012646755 0.0005977668
40 0.0018513343 0.0016688898 0.0019818450 0.0019742034 0.0019682190
41 0.0012901689 0.0005615152 0.0005942352 0.0006926856 0.0018635619
42 0.0003675504 0.0006611971 0.0007848537 0.0013632262 0.0019068692
43 0.0011333888 0.0010452650 0.0019680231 0.0019807556 0.0013143763
6 7 8
1 0.0017569784 0.0015661458 0.0010143924
2 0.0005686120 0.0015184924 0.0003545019
3 0.0010928662 0.0014665836 0.0010180168
4 0.0017352208 0.0017462446 0.0015227635
5 0.0014334398 0.0016207366 0.0009682922
6 0.0011949175 0.0019565455 0.0017317910
7 0.0016242850 0.0018104169 0.0008025713
8 0.0019814739 0.0018026416 0.0011362714
9 0.0018486764 0.0013288247 0.0007579606
10 0.0008383400 0.0018400334 0.0008407799
11 0.0017445894 0.0013484638 0.0018197537
12 0.0005430227 0.0007909056 0.0004445086
13 0.0017046332 0.0016471293 0.0011202762
14 0.0012911456 0.0007347367 0.0010343855
15 0.0014339797 0.0011423296 0.0019502457
16 0.0006595668 0.0006801905 0.0007280954
17 0.0005326911 0.0019325894 0.0007321784
18 0.0011164551 0.0013702594 0.0005197660
19 0.0008528085 0.0012634672 0.0003943996
20 0.0014635380 0.0016859250 0.0008023613
21 0.0006126377 0.0008253271 0.0015265778
22 0.0019487688 0.0019617892 0.0015413864
23 0.0016036909 0.0014711374 0.0015391197
24 0.0017934069 0.0017667741 0.0015450038
25 0.0019793672 0.0018608797 0.0005237168
26 0.0009913574 0.0016044984 0.0008314211
27 0.0012685165 0.0019029508 0.0007594243
28 0.0013288632 0.0010519229 0.0007139303
29 0.0010740767 0.0019774654 0.0011769169
30 0.0018172607 0.0019730120 0.0004598761
31 0.0005955656 0.0015708716 0.0002304060
32 0.0017187681 0.0019617991 0.0001574054
33 0.0009918826 0.0019719173 0.0005519880
34 0.0018581066 0.0017009436 0.0017140299
35 0.0016789546 0.0010934404 0.0005754204
36 0.0019378465 0.0018012173 0.0010001661
37 0.0011819680 0.0017851906 0.0011897999
38 0.0006573525 0.0010787676 0.0002586127
39 0.0008794896 0.0019539664 0.0017552250
40 0.0019778564 0.0016034038 0.0012068133
41 0.0003443047 0.0014644377 0.0003200081
42 0.0016195915 0.0018663807 0.0008856472
43 0.0005648518 0.0015616731 0.0005131718
, , Z_BANRAT
1 2 3 4 5 6
1 0.036652887 0.04538642 0.034711136 0.044943747 0.045451851 0.042532207
2 0.040236949 0.02853676 0.025312566 0.014274063 0.016301480 0.013764724
3 0.035307197 0.04513412 0.044230765 0.047974766 0.041714091 0.026455652
4 0.023835040 0.04773878 0.007584248 0.021521609 0.027176569 0.042005509
5 0.030185983 0.03655103 0.030580543 0.025953628 0.045772349 0.034700118
6 0.018240204 0.04647055 0.031581962 0.047474832 0.037756979 0.028926068
7 0.020946930 0.01555752 0.020858168 0.013639223 0.029108853 0.039320019
8 0.024594550 0.02706424 0.047973505 0.032975504 0.033776254 0.047966701
9 0.035364504 0.02440027 0.028106282 0.039220308 0.036082405 0.044751994
10 0.042413053 0.04589646 0.022095039 0.019805528 0.044541433 0.020294188
11 0.029633081 0.03055106 0.043661816 0.045060114 0.040998980 0.042232299
12 0.021517163 0.03814166 0.040353809 0.009223457 0.047157895 0.013145268
13 0.029663247 0.04797050 0.031493939 0.047394520 0.045298542 0.041265056
14 0.037795724 0.04593431 0.035709533 0.026870831 0.025956024 0.031255520
15 0.043479683 0.04460165 0.047613837 0.034906674 0.037131584 0.034713188
16 0.040856235 0.02362751 0.037715465 0.027298091 0.020207099 0.015966520
17 0.045660924 0.03201733 0.024873036 0.012014942 0.008848948 0.012895165
18 0.018356613 0.02856328 0.020726945 0.024127877 0.025993204 0.027026685
19 0.023099322 0.01469647 0.028210294 0.034568042 0.029838580 0.020644435
20 0.027487595 0.02207060 0.022340730 0.029292644 0.025445130 0.035428723
21 0.047543065 0.04143021 0.018052087 0.043503315 0.038690766 0.014830479
22 0.019651742 0.03948910 0.018269280 0.016086127 0.045404369 0.047174991
23 0.044913095 0.04770516 0.034727126 0.038529511 0.040443240 0.038821487
24 0.043638659 0.04767025 0.026446346 0.036356204 0.033424802 0.043414052
25 0.042405157 0.02618513 0.025061921 0.020344785 0.040181878 0.047915704
26 0.040585716 0.04789152 0.026664657 0.047673390 0.022523365 0.023998370
27 0.043545274 0.03299955 0.028050067 0.044682548 0.047933010 0.030707723
28 0.022106942 0.01605462 0.015483448 0.030259164 0.026056886 0.032168571
29 0.044366456 0.04577090 0.043375966 0.019662656 0.043536905 0.026000805
30 0.047611467 0.04575747 0.047246384 0.036629590 0.040589787 0.043991496
31 0.007247812 0.04782022 0.015043684 0.042916339 0.018842019 0.014417205
32 0.036337341 0.03801099 0.020008125 0.026228351 0.039083930 0.041607228
33 0.035845796 0.03760487 0.036467504 0.029249208 0.017910904 0.024011084
34 0.026074924 0.02639464 0.040421498 0.046738489 0.031286370 0.044980276
35 0.021130235 0.01652867 0.022496850 0.026217174 0.047913447 0.040643439
36 0.031115745 0.04785277 0.046761013 0.047549842 0.047688426 0.046910586
37 0.014711389 0.01620194 0.012636357 0.016263414 0.031257593 0.028612594
38 0.015268787 0.02869766 0.021633758 0.019804631 0.047965499 0.015912917
39 0.043551291 0.03403385 0.046070167 0.030614742 0.014470492 0.021290320
40 0.044816336 0.04039980 0.047975685 0.047790700 0.047645832 0.047879130
41 0.031231876 0.01359293 0.014385000 0.016768247 0.045112337 0.008334785
42 0.008897507 0.01600599 0.018999413 0.033000416 0.046160702 0.039206402
43 0.027436607 0.02530334 0.047641091 0.047949312 0.031817877 0.013673698
7 8
1 0.03791261 0.024555992
2 0.03675904 0.008581636
3 0.03550245 0.024643730
4 0.04227237 0.036862429
5 0.03923412 0.023440017
6 0.04736325 0.041922480
7 0.04382582 0.019428313
8 0.04363760 0.027506389
9 0.03216764 0.018348397
10 0.04454277 0.020353253
11 0.03264305 0.044051846
12 0.01914592 0.010760481
13 0.03987303 0.027119183
14 0.01778620 0.025039976
15 0.02765304 0.047210741
16 0.01646577 0.017625432
17 0.04678333 0.017724272
18 0.03317067 0.012582281
19 0.03058549 0.009547462
20 0.04081218 0.019423231
21 0.01997918 0.036954765
22 0.04749018 0.037313245
23 0.03561269 0.037258373
24 0.04276934 0.037400813
25 0.04504741 0.012677921
26 0.03884103 0.020126698
27 0.04606585 0.018383830
28 0.02546451 0.017282530
29 0.04786967 0.028490318
30 0.04776186 0.011132491
31 0.03802701 0.005577573
32 0.04749042 0.003810404
33 0.04773536 0.013362298
34 0.04117574 0.041492528
35 0.02646955 0.013929539
36 0.04360312 0.024211608
37 0.04321516 0.028802184
38 0.02611436 0.006260389
39 0.04730081 0.042489761
40 0.03881454 0.029214039
41 0.03545050 0.007746623
42 0.04518057 0.021439381
43 0.03780434 0.012422652
frontier documentation built on July 14, 2020, 3:01 a.m.
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Description Usage Arguments Value Author(s) References See Also Examples
View source: R/efficiencies.frontier.R
Description
This method returns efficiency estimates from stochastic frontier models
estimated with frontier.
Usage
1 2 3 4 |
Arguments
object |
a stochastic frontier model
returned by |
asInData |
logical. If |
logDepVar |
logical. Is the dependent variable logged? |
minusU |
logical. If |
farrell |
logical. This argument is only kept for backward compatibility and will be removed in the future. |
margEff |
logical. If |
newdata |
an optional data frame from which the values
of explanatory variables and the dependent variable are taken
to calculate the efficiency estimates.
If this argument is |
... |
currently ignored. |
Value
If argument asInData is FALSE (default),
a matrix of efficiency estimates is returned,
where each row corresponds to a firm (cross-section unit)
and each column corresponds to a time period
(only if efficiency estimates differ between time periods).
If argument asInData is TRUE,
a vector of efficiency estimates is returned,
where the efficiency estimates are in the same order
as the corresponding observations in the data set
used for the estimation.
If argument margEff is TRUE,
and the model is an Efficiency Effects Frontier (EFF)
with z variables,
and the dependent variable is logged,
the returned efficiency estimates have an attribute "margEff"
that contains the marginal effects of the z variables
on the efficiency measure.
If the dependent variable is logged, the marginal effect of the kth z variable on the efficiency is
\frac{\partial E[ \exp( - κ \, u ) ]}{\partial z_{kit}} = \frac{ δ_{k} ( 1 - γ ) \exp ≤ft( - κ \, \bar{μ}_{it} + \frac{1}{2} \bar{σ}^{2} \right) }{ Φ ≤ft( \frac{\bar{μ}_{it}}{ \bar{σ} } \right) }
\cdot ≤ft( \frac{ φ ≤ft( -κ \, \bar{σ} + \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) }{ \bar{σ} } - \frac{ Φ ≤ft( -κ \, \bar{σ} + \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) \, φ ≤ft( \frac{ \bar{μ}_{it} }{ \bar{σ} } \right)}{ \bar{σ} \, Φ ≤ft( \frac{ \bar{μ}_{it} }{ \bar{σ}}\right) } - κ \, Φ ≤ft( -κ \, \bar{σ} + \frac{ \bar{μ}_{it} }{ \bar{σ} } \right) \right),
where
\bar{μ}_{it} = ( 1 - γ ) \, z_{it} ' δ - τ \, γ \, ε_{it},
\bar{σ}^{2} = γ \, ( 1 - γ ) \, σ^{2},
κ = 1 in case of Farrell efficiencies (i.e. efficiencies have values between between 0 and 1), whereas κ = -1 otherwise (i.e. efficiencies have values larger than 1), and τ = 1 if inefficiency decreases the dependent variable, whereas τ = -1 otherwise (see Olsen and Henningsen 2011).
If argument asInData is FALSE,
this attribute is a 3-dimensional array,
where the first dimension represents the individual firm,
the second deminsion represents the time period,
and the third dimension represents the z variables.
In contrast, if argument asInData is TRUE,
this attribute is a matrix,
where the rows represent the observations
and the columns represent the z variables.
Author(s)
Arne Henningsen
References
Olsen, Jakob Vesterlund and Arne Henningsen (2011): Investment utilization and farm efficiency in Danish agriculture. FOI working paper 2011/13, Institute of Food and Resource Economics, University of Copenhagen, http://EconPapers.repec.org/RePEc:foi:wpaper:2011_13.
See Also
sfa, summary.frontier,
and efficiencies.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | # rice producers in the Philippines (panel data)
data( "riceProdPhil" )
library( "plm" )
riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )
# Error Components Frontier (Battese & Coelli 1992), no time effect
rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
data = riceProdPhil )
efficiencies( rice )
riceProdPhil$efficiencies <- efficiencies( rice, asInData = TRUE )
# efficiency of an 'average' farm
efficiencies( rice,
newdata = data.frame( t( colMeans( riceProdPhil[ , -c(1,2) ] ) ) ) )
# Error Components Frontier (Battese & Coelli 1992), with time effect
riceTime <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
data = riceProdPhil, timeEffect = TRUE )
efficiencies( riceTime )
riceProdPhil$efficienciesTime <- efficiencies( riceTime, asInData = TRUE )
# Technical Efficiency Effects Frontier (Battese & Coelli 1995)
rice2 <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
EDYRS + BANRAT - 1, data = riceProdPhil )
eff <- efficiencies( rice2, margEff = TRUE )
attr( eff, "margEff" ) # marginal effects
|
Example output
Loading required package: micEcon
If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/
Loading required package: lmtest
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Please cite the 'frontier' package as:
Tim Coelli and Arne Henningsen (2013). frontier: Stochastic Frontier Analysis. R package version 1.1. http://CRAN.R-Project.org/package=frontier.
If you have questions, suggestions, or comments regarding the 'frontier' package, please use a forum or 'tracker' at frontier's R-Forge site:
https://r-forge.r-project.org/projects/frontier/
Loading required package: Formula
efficiency
1 0.7348838
2 0.9335358
3 0.7356669
4 0.9047961
5 0.8646110
6 0.8084379
7 0.9231276
8 0.8150041
9 0.8722820
10 0.8539424
11 0.6021630
12 0.9491698
13 0.7820029
14 0.8703560
15 0.7123153
16 0.9058007
17 0.8788236
18 0.9238596
19 0.8586420
20 0.9046036
21 0.8014665
22 0.8277730
23 0.7080684
24 0.7073893
25 0.8363073
26 0.8557391
27 0.8002148
28 0.9382601
29 0.7072642
30 0.6075254
31 0.9152860
32 0.8476270
33 0.8877271
34 0.4978360
35 0.9083843
36 0.6955584
37 0.9265961
38 0.9333733
39 0.7423341
40 0.6689979
41 0.9361506
42 0.8994492
43 0.7249107
efficiency
1 0.7348838
2 0.9335358
3 0.7356669
4 0.9047961
5 0.8646110
6 0.8084379
7 0.9231276
8 0.8150041
9 0.8722820
10 0.8539424
11 0.6021630
12 0.9491698
13 0.7820029
14 0.8703560
15 0.7123153
16 0.9058007
17 0.8788236
18 0.9238596
19 0.8586420
20 0.9046036
21 0.8014665
22 0.8277730
23 0.7080684
24 0.7073893
25 0.8363073
26 0.8557391
27 0.8002148
28 0.9382601
29 0.7072642
30 0.6075254
31 0.9152860
32 0.8476270
33 0.8877271
34 0.4978360
35 0.9083843
36 0.6955584
37 0.9265961
38 0.9333733
39 0.7423341
40 0.6689979
41 0.9361506
42 0.8994492
43 0.7249107
1 2 3 4 5 6 7
1 0.7036591 0.7176992 0.7312209 0.7442280 0.7567260 0.7687222 0.7802252
2 0.9152460 0.9197825 0.9240924 0.9281853 0.9320704 0.9357570 0.9392540
3 0.6930843 0.7075251 0.7214433 0.7348415 0.7477240 0.7600971 0.7719686
4 0.8863269 0.8923068 0.8979991 0.9034148 0.9085646 0.9134594 0.9181097
5 0.8305840 0.8392249 0.8474790 0.8553577 0.8628730 0.8700370 0.8768620
6 0.7799158 0.7908320 0.8012919 0.8113056 0.8208841 0.8300389 0.8387821
7 0.9163653 0.9208451 0.9251007 0.9291417 0.9329773 0.9366168 0.9400687
8 0.7952759 0.8055177 0.8153220 0.8246997 0.8336622 0.8422212 0.8503893
9 0.8440482 0.8520610 0.8597087 0.8670030 0.8739557 0.8805789 0.8868845
10 0.8228167 0.8318156 0.8404157 0.8486284 0.8564656 0.8639395 0.8710623
11 0.5276153 0.5470780 0.5661066 0.5846728 0.6027530 0.6203276 0.6373816
12 0.9387675 0.9420962 0.9452531 0.9482460 0.9510825 0.9537701 0.9563159
13 0.7381054 0.7507832 0.7629639 0.7746549 0.7858647 0.7966029 0.8068802
14 0.8315627 0.8401583 0.8483685 0.8562050 0.8636796 0.8708045 0.8775918
15 0.6820662 0.6969153 0.7112388 0.7250375 0.7383147 0.7510756 0.7633270
16 0.8748583 0.8813986 0.8876290 0.8935607 0.8992050 0.9045731 0.9096759
17 0.8458582 0.8537858 0.8613514 0.8685666 0.8754433 0.8819934 0.8882289
18 0.9084840 0.9133620 0.9179985 0.9224035 0.9265867 0.9305577 0.9343259
19 0.8372931 0.8456222 0.8535751 0.8611635 0.8683992 0.8752943 0.8818610
20 0.8895082 0.8953315 0.9008735 0.9061452 0.9111572 0.9159201 0.9204443
21 0.7378206 0.7505100 0.7627021 0.7744042 0.7856249 0.7963736 0.8066613
22 0.8104189 0.8199825 0.8291291 0.8378701 0.8462170 0.8541820 0.8617775
23 0.6607368 0.6763490 0.6914329 0.7059865 0.7200102 0.7335070 0.7464815
24 0.6719749 0.6871897 0.7018769 0.7160362 0.7296695 0.7427811 0.7553767
25 0.8097515 0.8193453 0.8285211 0.8372903 0.8456645 0.8536559 0.8612767
26 0.8241086 0.8330483 0.8415910 0.8497483 0.8575321 0.8649545 0.8720279
27 0.7627839 0.7744354 0.7856121 0.7963230 0.8065783 0.8163889 0.8257664
28 0.9293251 0.9331426 0.9367656 0.9402028 0.9434625 0.9465530 0.9494821
29 0.6527008 0.6685908 0.6839528 0.6987835 0.7130823 0.7268510 0.7400936
30 0.5662764 0.5847947 0.6028316 0.6203675 0.6373869 0.6538782 0.6698331
31 0.8994373 0.9047683 0.9098385 0.9146583 0.9192381 0.9235878 0.9277173
32 0.8050218 0.8148286 0.8242109 0.8331799 0.8417471 0.8499246 0.8577247
33 0.8641915 0.8712472 0.8779729 0.8843803 0.8904808 0.8962861 0.9018076
34 0.4112413 0.4325334 0.4536340 0.4744858 0.4950372 0.5152417 0.5350581
35 0.8922470 0.8979350 0.9033474 0.9084948 0.9133878 0.9180370 0.9224525
36 0.6300435 0.6466875 0.6628078 0.6783975 0.6934525 0.7079717 0.7219563
37 0.9222721 0.9264512 0.9304195 0.9341861 0.9377600 0.9411497 0.9443639
38 0.9174599 0.9218841 0.9260866 0.9300768 0.9338641 0.9374573 0.9408652
39 0.6728266 0.6880108 0.7026676 0.7167967 0.7304002 0.7434823 0.7560490
40 0.6098523 0.6271302 0.6438932 0.6601304 0.6758345 0.6910013 0.7056294
41 0.9155355 0.9200574 0.9243532 0.9284326 0.9323050 0.9359794 0.9394647
42 0.8881516 0.8940418 0.8996480 0.9049811 0.9100519 0.9148711 0.9194490
43 0.6326719 0.6492307 0.6652650 0.6807684 0.6957372 0.7101705 0.7240701
8
1 0.7912447
2 0.9425699
3 0.7833477
4 0.9225257
5 0.8833602
6 0.8471261
7 0.9433418
8 0.8581789
9 0.8928845
10 0.8778466
11 0.6539034
12 0.9587266
13 0.8167083
14 0.8840540
15 0.7750774
16 0.9145245
17 0.8941617
18 0.9379003
19 0.8881113
20 0.9247400
21 0.8164993
22 0.8690161
23 0.7589404
24 0.7674640
25 0.8685397
26 0.8787647
27 0.8347232
28 0.9522574
29 0.7528158
30 0.6852465
31 0.9316363
32 0.8651602
33 0.9070566
34 0.5544504
35 0.9266445
36 0.7354098
37 0.9474104
38 0.9440964
39 0.7681080
40 0.7197198
41 0.9427696
42 0.9237961
43 0.7374396
, , Z_EDYRS
1 2 3 4 5
1 0.0015141075 0.0018748843 0.0014338949 0.0018565976 0.0018775870
2 0.0016621628 0.0011788353 0.0010456460 0.0005896525 0.0006734038
3 0.0014585178 0.0018644616 0.0018271448 0.0019818070 0.0017231825
4 0.0009846104 0.0019720588 0.0003133005 0.0008890440 0.0011226468
5 0.0012469637 0.0015098999 0.0012632628 0.0010721278 0.0018908266
6 0.0007534912 0.0019196687 0.0013046308 0.0019611551 0.0015597168
7 0.0008653043 0.0006426711 0.0008616376 0.0005634276 0.0012024682
8 0.0010159852 0.0011180063 0.0019817550 0.0013621971 0.0013952756
9 0.0014608851 0.0010079595 0.0011610526 0.0016201660 0.0014905412
10 0.0017520562 0.0018959534 0.0009127320 0.0008181538 0.0018399783
11 0.0012241237 0.0012620448 0.0018036418 0.0018614046 0.0016936418
12 0.0008888603 0.0015756076 0.0016669902 0.0003810151 0.0019480626
13 0.0012253698 0.0019816308 0.0013009946 0.0019578375 0.0018712539
14 0.0015613173 0.0018975172 0.0014751381 0.0011100169 0.0010722268
15 0.0017961180 0.0018424656 0.0019668973 0.0014419725 0.0015338821
16 0.0016877451 0.0009760373 0.0015580019 0.0011276668 0.0008347424
17 0.0018862237 0.0013226156 0.0010274893 0.0004963296 0.0003655444
18 0.0007583000 0.0011799311 0.0008562169 0.0009967072 0.0010737627
19 0.0009542183 0.0006071018 0.0011653493 0.0014279838 0.0012326128
20 0.0011354951 0.0009117224 0.0009228813 0.0012100605 0.0010511221
21 0.0019639738 0.0017114555 0.0007457202 0.0017970942 0.0015982909
22 0.0008118010 0.0016312697 0.0007546924 0.0006645077 0.0018756256
23 0.0018553314 0.0019706697 0.0014345555 0.0015916296 0.0016706845
24 0.0018026852 0.0019692275 0.0010924817 0.0015018516 0.0013807573
25 0.0017517300 0.0010816911 0.0010352920 0.0008404301 0.0016598878
26 0.0016765701 0.0019783681 0.0011015000 0.0019693574 0.0009304259
27 0.0017988276 0.0013631903 0.0011587304 0.0018458076 0.0019800822
28 0.0009132237 0.0006632061 0.0006396114 0.0012499868 0.0010763934
29 0.0018327501 0.0018907666 0.0017918336 0.0008122518 0.0017984818
30 0.0019667994 0.0018902121 0.0019517180 0.0015131451 0.0016767383
31 0.0002994025 0.0019754227 0.0006214450 0.0017728467 0.0007783518
32 0.0015010724 0.0015702096 0.0008265229 0.0010834765 0.0016145323
33 0.0014807670 0.0015534334 0.0015064494 0.0012082662 0.0007398880
34 0.0010771385 0.0010903457 0.0016697864 0.0019307372 0.0012924200
35 0.0008728765 0.0006827890 0.0009293306 0.0010830148 0.0019792740
36 0.0012853716 0.0019767675 0.0019316677 0.0019642537 0.0019699785
37 0.0006077181 0.0006692920 0.0005219998 0.0006718313 0.0012912313
38 0.0006307439 0.0011854821 0.0008936768 0.0008181167 0.0019814242
39 0.0017990761 0.0014059166 0.0019031293 0.0012646755 0.0005977668
40 0.0018513343 0.0016688898 0.0019818450 0.0019742034 0.0019682190
41 0.0012901689 0.0005615152 0.0005942352 0.0006926856 0.0018635619
42 0.0003675504 0.0006611971 0.0007848537 0.0013632262 0.0019068692
43 0.0011333888 0.0010452650 0.0019680231 0.0019807556 0.0013143763
6 7 8
1 0.0017569784 0.0015661458 0.0010143924
2 0.0005686120 0.0015184924 0.0003545019
3 0.0010928662 0.0014665836 0.0010180168
4 0.0017352208 0.0017462446 0.0015227635
5 0.0014334398 0.0016207366 0.0009682922
6 0.0011949175 0.0019565455 0.0017317910
7 0.0016242850 0.0018104169 0.0008025713
8 0.0019814739 0.0018026416 0.0011362714
9 0.0018486764 0.0013288247 0.0007579606
10 0.0008383400 0.0018400334 0.0008407799
11 0.0017445894 0.0013484638 0.0018197537
12 0.0005430227 0.0007909056 0.0004445086
13 0.0017046332 0.0016471293 0.0011202762
14 0.0012911456 0.0007347367 0.0010343855
15 0.0014339797 0.0011423296 0.0019502457
16 0.0006595668 0.0006801905 0.0007280954
17 0.0005326911 0.0019325894 0.0007321784
18 0.0011164551 0.0013702594 0.0005197660
19 0.0008528085 0.0012634672 0.0003943996
20 0.0014635380 0.0016859250 0.0008023613
21 0.0006126377 0.0008253271 0.0015265778
22 0.0019487688 0.0019617892 0.0015413864
23 0.0016036909 0.0014711374 0.0015391197
24 0.0017934069 0.0017667741 0.0015450038
25 0.0019793672 0.0018608797 0.0005237168
26 0.0009913574 0.0016044984 0.0008314211
27 0.0012685165 0.0019029508 0.0007594243
28 0.0013288632 0.0010519229 0.0007139303
29 0.0010740767 0.0019774654 0.0011769169
30 0.0018172607 0.0019730120 0.0004598761
31 0.0005955656 0.0015708716 0.0002304060
32 0.0017187681 0.0019617991 0.0001574054
33 0.0009918826 0.0019719173 0.0005519880
34 0.0018581066 0.0017009436 0.0017140299
35 0.0016789546 0.0010934404 0.0005754204
36 0.0019378465 0.0018012173 0.0010001661
37 0.0011819680 0.0017851906 0.0011897999
38 0.0006573525 0.0010787676 0.0002586127
39 0.0008794896 0.0019539664 0.0017552250
40 0.0019778564 0.0016034038 0.0012068133
41 0.0003443047 0.0014644377 0.0003200081
42 0.0016195915 0.0018663807 0.0008856472
43 0.0005648518 0.0015616731 0.0005131718
, , Z_BANRAT
1 2 3 4 5 6
1 0.036652887 0.04538642 0.034711136 0.044943747 0.045451851 0.042532207
2 0.040236949 0.02853676 0.025312566 0.014274063 0.016301480 0.013764724
3 0.035307197 0.04513412 0.044230765 0.047974766 0.041714091 0.026455652
4 0.023835040 0.04773878 0.007584248 0.021521609 0.027176569 0.042005509
5 0.030185983 0.03655103 0.030580543 0.025953628 0.045772349 0.034700118
6 0.018240204 0.04647055 0.031581962 0.047474832 0.037756979 0.028926068
7 0.020946930 0.01555752 0.020858168 0.013639223 0.029108853 0.039320019
8 0.024594550 0.02706424 0.047973505 0.032975504 0.033776254 0.047966701
9 0.035364504 0.02440027 0.028106282 0.039220308 0.036082405 0.044751994
10 0.042413053 0.04589646 0.022095039 0.019805528 0.044541433 0.020294188
11 0.029633081 0.03055106 0.043661816 0.045060114 0.040998980 0.042232299
12 0.021517163 0.03814166 0.040353809 0.009223457 0.047157895 0.013145268
13 0.029663247 0.04797050 0.031493939 0.047394520 0.045298542 0.041265056
14 0.037795724 0.04593431 0.035709533 0.026870831 0.025956024 0.031255520
15 0.043479683 0.04460165 0.047613837 0.034906674 0.037131584 0.034713188
16 0.040856235 0.02362751 0.037715465 0.027298091 0.020207099 0.015966520
17 0.045660924 0.03201733 0.024873036 0.012014942 0.008848948 0.012895165
18 0.018356613 0.02856328 0.020726945 0.024127877 0.025993204 0.027026685
19 0.023099322 0.01469647 0.028210294 0.034568042 0.029838580 0.020644435
20 0.027487595 0.02207060 0.022340730 0.029292644 0.025445130 0.035428723
21 0.047543065 0.04143021 0.018052087 0.043503315 0.038690766 0.014830479
22 0.019651742 0.03948910 0.018269280 0.016086127 0.045404369 0.047174991
23 0.044913095 0.04770516 0.034727126 0.038529511 0.040443240 0.038821487
24 0.043638659 0.04767025 0.026446346 0.036356204 0.033424802 0.043414052
25 0.042405157 0.02618513 0.025061921 0.020344785 0.040181878 0.047915704
26 0.040585716 0.04789152 0.026664657 0.047673390 0.022523365 0.023998370
27 0.043545274 0.03299955 0.028050067 0.044682548 0.047933010 0.030707723
28 0.022106942 0.01605462 0.015483448 0.030259164 0.026056886 0.032168571
29 0.044366456 0.04577090 0.043375966 0.019662656 0.043536905 0.026000805
30 0.047611467 0.04575747 0.047246384 0.036629590 0.040589787 0.043991496
31 0.007247812 0.04782022 0.015043684 0.042916339 0.018842019 0.014417205
32 0.036337341 0.03801099 0.020008125 0.026228351 0.039083930 0.041607228
33 0.035845796 0.03760487 0.036467504 0.029249208 0.017910904 0.024011084
34 0.026074924 0.02639464 0.040421498 0.046738489 0.031286370 0.044980276
35 0.021130235 0.01652867 0.022496850 0.026217174 0.047913447 0.040643439
36 0.031115745 0.04785277 0.046761013 0.047549842 0.047688426 0.046910586
37 0.014711389 0.01620194 0.012636357 0.016263414 0.031257593 0.028612594
38 0.015268787 0.02869766 0.021633758 0.019804631 0.047965499 0.015912917
39 0.043551291 0.03403385 0.046070167 0.030614742 0.014470492 0.021290320
40 0.044816336 0.04039980 0.047975685 0.047790700 0.047645832 0.047879130
41 0.031231876 0.01359293 0.014385000 0.016768247 0.045112337 0.008334785
42 0.008897507 0.01600599 0.018999413 0.033000416 0.046160702 0.039206402
43 0.027436607 0.02530334 0.047641091 0.047949312 0.031817877 0.013673698
7 8
1 0.03791261 0.024555992
2 0.03675904 0.008581636
3 0.03550245 0.024643730
4 0.04227237 0.036862429
5 0.03923412 0.023440017
6 0.04736325 0.041922480
7 0.04382582 0.019428313
8 0.04363760 0.027506389
9 0.03216764 0.018348397
10 0.04454277 0.020353253
11 0.03264305 0.044051846
12 0.01914592 0.010760481
13 0.03987303 0.027119183
14 0.01778620 0.025039976
15 0.02765304 0.047210741
16 0.01646577 0.017625432
17 0.04678333 0.017724272
18 0.03317067 0.012582281
19 0.03058549 0.009547462
20 0.04081218 0.019423231
21 0.01997918 0.036954765
22 0.04749018 0.037313245
23 0.03561269 0.037258373
24 0.04276934 0.037400813
25 0.04504741 0.012677921
26 0.03884103 0.020126698
27 0.04606585 0.018383830
28 0.02546451 0.017282530
29 0.04786967 0.028490318
30 0.04776186 0.011132491
31 0.03802701 0.005577573
32 0.04749042 0.003810404
33 0.04773536 0.013362298
34 0.04117574 0.041492528
35 0.02646955 0.013929539
36 0.04360312 0.024211608
37 0.04321516 0.028802184
38 0.02611436 0.006260389
39 0.04730081 0.042489761
40 0.03881454 0.029214039
41 0.03545050 0.007746623
42 0.04518057 0.021439381
43 0.03780434 0.012422652
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