Presented by John Buckell on 4th July 2014 at the 8th North American Productivity Workshop in Ottawa, Canada. The work is coauthored with Dr Andrew Smith and Phill Wheat at ITS, Roberta Longo from the Academic Unit of Health Economics and David Holland from Keele Universwww.its.leeds.ac.uk/people/j.buckell

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Regional variation in health care system performance: A
dual-level efficiency approach applied to NHS pathology in
England
John Buckell1,2, Andrew Smith2,3, Phill Wheat2, Roberta Longo1, David Holland4
1. Academic Unit of Health Economics University of Leeds
2. Institute for Transport Studies, University of Leeds
3. Leeds University Business School, University of Leeds
4. Keele Benchmarking Unit, Keele University

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Outline: Regional Performance
1. Motivation
2. Methods
3. Data and Results
4. Interpretation of Mundlak group mean variables and model selection

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1. Motivation – why are we interested in regional performance?
(a) Policy interest: (i) expenditure savings (NHS, 2010; 2013) and (ii)
regional inequalities (horizontal equity) (Marmot et al. 2010; NHS 2013)
(b) Literature gap: no regional performance measure per se
Apply a dual-level model to pathology services in the NHS in England

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2. Methods
• Dual-level stochastic frontier (Smith and Wheat, 2012) (DLSF)
• Upper level (SHA): Central
management, configuration of
laboratories
• Lower level (laboratories):
Local management, degree of
autonomy, local conditions
Where does inefficiency reside within the organisation?
Then, regional inefficiency is simply the product of the SHA (upper tier) and laboratory
(lower tier) inefficiency

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DLSF based on a simple cost SF:
𝑐𝑖𝑙 = 𝛼 + 𝑓 𝑋𝑖𝑙; 𝛽 + 𝑢𝑖𝑙 + 𝑣𝑖𝑙
Where c are costs, x are regressors, u is inefficiency and v is noise.
Can decompose uil into SHA- and laboratory-specific components:
𝑢𝑖𝑙 = 𝜇𝑖 + 𝜏𝑖𝑙
Then, we can construct our regional measure as:
𝑢𝑖 = 𝜇𝑖.
1
𝑁𝑖
𝑙=1
𝑁
(𝑤𝑙. 𝜏𝑙)
For estimation, we use the two-stage RE FGLS/SF procedure outlined in Smith and
Wheat (2012)

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Unobservable heterogeneity: Mundlak transform
Following Mundlak (1978) and Farsi et al. (2005), it is possible to partition a fixed
effect into two components: one which is correlated with the regressors, and one
which varies randomly,
𝛼𝑖 = 𝑋𝑖𝑙′𝜌 + 𝛿𝑖𝑙
If it is assumed that the UOH is correlated with the regressors, then delta
represents inefficiency.
By averaging over SHA,
𝛼𝑖 = 𝑋𝑖′𝜌 + 𝛿𝑖
And we can then add group means of Xs directly into the regression and estimate
RE FGLS
𝑪𝒊𝒍 = 𝑿𝒊
′
𝝆 + 𝜹𝒊 + 𝒇 𝑿𝒊𝒍; 𝜷 + 𝝉𝒊𝒍 + 𝒗𝒊𝒍

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Strategy
• First, compare DL models to single level models
• Second, compare Mundlak-adjusted model to non-
adjusted model
• Third, discuss interpretation and model selection

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3. Data and Results
• We use pathology benchmarking data from Keele University combined with
labour force survey data and NHS trust data
• 57 laboratories, 10 SHAs, 5 years (unbalanced panel)
• Costs and wage data are adjusted using the consumer prices index
Variable Mean S.D. Min Max
Operating costs (adjusted) 3617320 2058358 963875 11741895
Number of tests 5037362 2990846 1380384 30199502
Number of requests 714125 465535 191078 4423531
Input prices (Labour) (adjusted) 24551 4160 15834 49955

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Results: DLSF vs single level (SL) models
DLSF versus single level models
• Parameter estimates similar between models
• Parameter estimates match theory and previous work (Buckell et al., 2013; Gutacker et al.,
2013)
• Inefficiency is detected at both levels of the DLSF
Dual-level (stage 1) Single-level SHA SF Single-level laboratory SF
Variable
Constant (-)5.275 (1.74)*** (-)5.275 (1.74)*** 2.315 (2.831)
OUTPUT 0.857 (0.043)*** 0.857 (0.043)*** 0.506 (0.043)***
INPUT PRICES 0.775 (0.157)*** 0.775 (0.157)*** 0.484 (0.289)*
TESTS:REQUESTS 0.520 (0.070)*** 0.520 (0.070)*** 0.284 (0.054)***
TIME 0.009 (0.013) 0.009 (0.013) 0.017 (0.010)*
METROPOLITAN 0.193 (0.050)*** 0.193 (0.050)*** 0.202 (0.111)*
FOUNDATION (-)0.084 (0.044)* (-)0.084 (0.044)* (-) 0.055 (0.082)
TEACHING 0.013 (0.042) 0.013 (0.042) 0.079 (0.078)
Moulton-Randolph 3.11 3.11
Lambda 3.24***
Lambda (2nd stage) 1.58***

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Mean CE SHA Mean CE LAB Mean CE Region
SHA-level frontier 0.795 n/a 0.795
LAB-level frontier n/a 0.699 0.699
DLSF 0.795 0.809 0.643
• Single level SHA SF model cannot measure inefficiency at lower
(laboratory) level
• Single level laboratory SF cannot disentangle laboratory and SHA
inefficiency; ascribes both levels’ performances to lower level
• Both single level models underestimate inefficiency at regional level
(in keeping with Smith and Wheat, 2012)

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DLSF with Mundlak vs. DLSF without Mundlak
• Lower level estimates are identical for both models (because we have removed SHA-
specific effects in the first stage)
• Significantly different estimates with/without Mundlak transform applied
• Ranking of SHAs/regions sensitive to transformation
SHA
Dual-level SF (Mundlak) Dual-level SF
SHA CE Laboratory CE (weighted) Regional CE SHA CE Laboratory CE (weighted) Regional CE
1 0.973 0.793 0.772 0.908 0.793 0.612
2 0.976 0.830 0.810 1.000 0.830 0.673
3 0.966 0.784 0.757 0.795 0.784 0.594
4 0.974 0.809 0.788 0.789 0.809 0.638
5 0.973 0.821 0.798 0.658 0.821 0.655
6 0.969 0.793 0.769 0.714 0.793 0.610
7 0.968 0.832 0.806 0.719 0.832 0.671
8 0.952 0.774 0.737 0.808 0.774 0.570
9 0.969 0.823 0.797 0.780 0.823 0.656
10 1.000 0.784 0.784 0.781 0.784 0.615
Avg. 0.972 0.804 0.781 0.795 0.804 0.629
s.e. 0.012 0.021 0.023 0.098 0.021 0.034

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4. Interpretation of Mundlak group mean variables
Interpretation of Mundlak (group mean) variables
Literature appears divided on the issue
• Earlier applications ascribed interpretation of the variables as the
realisation of unobservable heterogeneity (Farsi et al., 2005a; Farsi et al.,
2005b; Farsi et al., 2007)
• Later, papers seemed not to comment on the interpretation of the group
means (Abdulai et al., 2007; Last et al., 2010; Titus et al., 2012;
Emvalomatis 2012; Menagaki, 2013)
• Recent papers have explicitly stated that these variables have no meaning
(Hunt et al., 2012 – citing Baltagi, 2006)
Does ‘meaning’ refer to elasticity or to the decomposition of inefficiency?

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Results: Mundlak transform
DLSF with Mundlak retrieves within estimates
Dual-level RE Mundlak Dual level FE
Variable
Constant No constant
OUTPUT 0.852 (0.042)*** 0.852 (0.045)***
INPUT PRICES 0.910 (0.163)*** 0.910 (0.175)***
TESTS:REQUESTS 0.522 (0.067)*** 0.522 (0.072)***
TIME 0.007 (0.013) 0.007 (0.013)
METROPOLITAN 0.187 (0.048)*** 0.187 (0.052)***
FOUNDATION (-)0.074 (0.043)* (-)0.074 (0.046)
TEACHING 0.029 (0.040) 0.029 (0.043)
REQBAR 0.637 (0.346)*
INPBAR (-)0.132 (0.338)
TESBAR 0.812 (0.737)
YEABAR 0.095 (0.107)
AREBAR 0.107 (0.160)
FOUBAR (-)0.507 (0.276)*
TEABAR 1.151 (0.395)***
Wu test (Wald Chi-squared) 29.57***

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Thank You