## wp1736r

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### Introduction and research questions
- Core questions examined for England during the fiscal consolidation of 2010–14:
  - (i) Has public sector efficiency or productivity at the sub-regional level improved or weakened in England during the fiscal consolidation of 2010–14?
  - (ii) What has been the pattern across different sectors and sub-regions?
  - (iii) Have sub-regions with lower initial levels of efficiency experienced stronger gains, implying some catch up in efficiency levels?
  - (iv) Were deeper cuts in public spending associated with stronger efficiency gains?
  - (v) Has there been any relationship between changes in public sector efficiency and labor productivity across sub-regions?
  - (vi) What are the determinants of sub-regional variation in public sector service efficiency?
- Rationale and case selection:
  - Efficiency gains can limit adverse impacts of spending cuts; the UK’s centrally financed public spending provides an “exogenous” shock across regions.
  - Geographic scope: nine NUTS1 regions of England listed; Greater London excluded. Analysis combines NUTS1 spending (excluding Greater London → eight regions) with sectoral outputs at NUTS2 (28 sub-regions, Greater London excluded).

### Data, inputs, outputs, and methodological approach
- Periods compared:
  - Pre-crisis: 2003–07; Post-crisis: 2010–14. Years 2008–09 excluded.
- Main inputs and outputs by sector:
  - Education:
    - Input = Real public expenditure on education per pupil (lagged one year in robustness checks).
    - Controls = Private spending on education; education attainment by income level per head; pupil-to-teacher ratio/class size.
    - Output = High school (GCSE) achievement (5 or more A*-C including English and Maths).
  - Health:
    - Input = Real public expenditure on health per head (lagged two years in robustness checks).
    - Controls = Ratio of population over 65 (age-structure), prevalence of obesity, private health spending, mother's smoking status at delivery.
    - Output = Life expectancy at age 65 years (alternative: HALE/life expectancy at birth used in robustness).
  - Economic services:
    - Input = Real public expenditure on economic services normalized by lagged population.
    - Controls = Lagged stock of capital.
    - Output = Number of active enterprises (alternative: labor productivity used in robustness).
- Main methodology:
  - Baseline: Data Envelopment Analysis (DEA), output-oriented, constant returns to scale (CRS); variable returns to scale (VRS) also estimated (no material change).
  - Complementary parametric Stochastic Frontier Analysis (SFA) estimated via Cobb-Douglas functions and maximum likelihood for robustness.
  - Second-stage multivariate truncated regressions (fixed effects) of SFA efficiency scores to estimate determinants; 58 observations (28 sub-regions × 2 periods averages plus averages).

### Stylized facts: spending, outputs, and productivity
- Spending changes (change reported 2003–07 → 2010–14, percent or per head/pupil terms as in tables):
  - "Public health inputs or spending per head actually increased sharply across all English regions without exception post-crisis" (Figure 3).
  - Education spending per pupil "declined sharply" (Figure 3), particularly in the North.
  - Public spending on economic services showed "more sub-regional variation, with small cuts in some regions and small increases in others" (Figure 3).
  - Caveat: "The increases in real health spending could be overestimated if health sector deflators have not been adjusted concomitantly with rising health care costs."
- Output changes:
  - Outputs did not decline proportionally with spending cuts; "rather all outputs improved post crisis":
    - Life expectancy increased marginally.
    - GCSE achievement improved sharply (noted measurement issues: Department of Education "points to GCSE score inflation").
    - Number of enterprises expanded a little.
- Regional examples (Table A.1 and A.2 selected):
  - North East: Education 1.80 → 1.41 (Change: -22); Health 2.03 → 2.65 (Change: 31); Economic services 2.02 → 1.95 (Change: -4).
  - North East outputs: Education 38 → 58 (Change: 53); Health 18 → 19 (Change: 7); Economic services 6 → 6 (Change: 8).
  - England average excl. London (Table A.5): Pre-crisis Education 0.894, Health 0.896, Economy 0.462, Combined 0.751 → Post-crisis Education 0.947, Health 0.911, Economy 0.463, Combined 0.774 (Change post-crisis: 3.63).

### Baseline empirical findings (DEA and aggregated results)
- Overall:
  - "Despite large public spending cuts, overall efficiency improved post crisis."
- Sectoral pattern:
  - Education: efficiency improved most notably—sector saw deepest cuts.
  - Health: efficiency improved despite spending increases.
  - Economic services: efficiency deteriorated slightly; economic services display the widest and most persistent disparities.
- Sub-regional variation:
  - Examples: Tees Valley and Durham (UKC1) improved post-crisis; Devon (UKK4) deteriorated post-crisis.
  - "The lower quartile of efficiency, however, remains a northern-county phenomenon."
- Selected aggregated regional DEA results (Table A.5 examples):
  - North East (UKC): Pre-crisis Combined 0.54 → Post-crisis Combined 0.62 (Change post-crisis: 14.1).
  - North West (UKD): Pre-crisis Combined 0.70 → Post-crisis Combined 0.73 (Change post-crisis: 3.9).
  - Yorkshire and the Humber (UKE): Pre-crisis Combined 0.69 → Post-crisis Combined 0.72 (Change post-crisis: 4.0).
  - England average excl. London: Combined 0.751 → Post-crisis Combined 0.774 (Change post-crisis: 3.63).

### Convergence and simple bivariate regression evidence
- Convergence:
  - "Sub-regions with the weakest pre-crisis levels in public sector efficiency converged the most."
- Bivariate regressions (Change in efficiency on Initial efficiency; number of observations = 29):
  - Change in efficiency (Education) on Initial efficiency (Education): coefficient = -1.366*** (0.174), adj. R-sq = 0.721.
  - Change in efficiency (Health) on Initial efficiency (Health): coefficient = -0.168*** (0.0171), adj. R-sq = 0.835.
  - Change in efficiency (Economic Services) on Initial efficiency (Economic services): coefficient = -0.212* (0.171), adj. R-sq = 0.265.
  - Change in efficiency (Simple Average) on Initial efficiency (Simple Average): coefficient = -0.391** (0.126), adj. R-sq = 0.702.
  - Significance notation: * p<0.10, ** p<0.05, *** p<0.01.

### Relationship between spending cuts and efficiency gains (bivariate)
- Regressions of percentage change in efficiency on percentage change in public spending (number of observations = 29):
  - Education sector: Change in efficiency regressed on change in education spending per pupil: coefficient = -0.733** (0.301), adj. R-sq = 0.512.
    - Interpretation: "Deeper education spending cuts are associated with large public sector efficiency gains in that sector."
  - Health sector: coefficient = 0.116 (0.298), adj. R-sq = 0.344 (insignificant).
    - Source interpretation: "The increase in spending in the health sector actually led to efficiency increases—although the coefficient is also insignificant."
  - Economic services: coefficient = -1.102 (0.789), adj. R-sq = 0.167 (insignificant).
  - Simple average (three sectors): coefficient = -1.701 (1.077), adj. R-sq = 0.453 (insignificant).

### Public sector efficiency and labor productivity
- Visual and regression evidence:
  - "Sub-regions that have improved their level of public sector efficiency or productivity in the post-crisis period also tend to have higher labor productivity growth" (examples: Merseyside, Greater Manchester, Northumberland and Tyne and Wear, West and South Yorkshire, Derbyshire and Nottinghamshire and the West Midlands).
  - Regression of change in sub-regional efficiency on labor productivity growth: coefficient statistically significant at the 5 percent level (exact coefficient value not provided in the excerpt).
  - Caution: "Association does not imply causality."

### Robustness checks: alternative specifications and SFA
- Alternative DEA specifications:
  - Input-oriented DEA and VRS estimated with "similar results."
  - Weighted DEA (weights = average sectoral shares at NUTS1) produces similar sub-region ranking.
- Alternative inputs, outputs, and lags (Section IV.B and summarized):
  - Education: pupil-to-teacher ratio included; spending lagged one year; higher-order lags insignificant; DEA scores similar to baseline.
  - Health: output alternative HALE; spending lagged two years; private health spending and mother's smoking included; DEA ranking unchanged.
  - Economic services: alternative output labor productivity; spending lagged two years; some changes in ranking but post-crisis changes similar in order/magnitude.
- Reported robustness bivariate statistics (Table 6 and Table 7; Number of observations = 29):
  - Table 6 (Change in efficiency vs Initial efficiency level):
    - Education: coefficient = -1.343*** (0.121), adj. R-sq = 0.710
    - Health: coefficient = -0.211** (0.0141), adj. R-sq = 0.913
    - Economic services: coefficient = -1.143** (0.026), adj. R-sq = 0.353
    - Weighted Average: coefficient = -0.677** (0.117), adj. R-sq = 0.790
  - Table 7 (Change in efficiency vs Change in spending):
    - Education (per pupil): coefficient = -0.728*** (0.301), adj. R-sq = 0.548
    - Health (per person): coefficient = 0.166*** (0.268), adj. R-sq = 0.484
    - Economic services (per person): coefficient = -1.301* (0.801), adj. R-sq = 0.378
    - Weighted Average: coefficient = -1.789** (1.078), adj. R-sq = 0.484
- Stochastic Frontier Analysis (SFA):
  - SFA efficiency scores are smaller in size than baseline DEA scores but rankings and magnitude of post-crisis change are "highly and significantly correlated" with DEA results.
  - SFA displays more variation (greater distance from the frontier) and is used for second-stage determinants analysis.

### Second-stage multivariate truncated regressions — determinants of SFA efficiency scores
- Setup:
  - Dependent variable: SFA efficiency scores (bounded 0–1).
  - Observations: 58 (28 sub-regions × 2 period-averages plus averages).
  - Fixed effects included; standard errors reported; significance: * p<0.10, ** p<0.05, *** p<0.01.
- Selected coefficient estimates (Table 8; standard errors in parentheses):
  - Education (column (1)):
    - Income per capita: 0.012*** (0.001)
    - Private spending on education: 1.132*** (0.206)
    - Education attainment: 2.412*** (0.214)
    - Teacher to pupil ratio: 0.024** (0.002)
    - Population density: 1.362* (0.171)
    - Smoking status: 0.000 (0.001)
    - Prevalence of obesity: 0.000 (0.001)
    - Capital stock: -0.001 (0.001)
    - Active enterprises: 0.012*** (0.022)
  - Health (column (2)):
    - Income per capita: 0.000 (0.001)
    - Private spending on health: 0.020 (0.266)
    - Education attainment: 3.101*** (0.311)
    - Population density: 1.561*** (0.180)
    - Capital stock: -0.001* (0.001)
  - Economic Services (column (3)):
    - Income per capita: 0.001 (0.001)
    - Education attainment: 3.001*** (0.300)
    - Population density: 1.542*** (0.181)
    - Active enterprises: 0.012*** (0.022)
  - Weighted Average (column (4)):
    - Income per capita: 0.000 (0.001)
    - Education attainment: 3.000*** (0.311)
    - Population density: 1.442*** (0.172)
    - Capital stock: -0.001* (0.001)
- Interpretation of key determinants:
  - Education attainment: positive, large, and statistically significant across sectors — explains substantial sub-regional variation in efficiency.
  - Population density: positive, large, and statistically significant — denser areas have higher spending efficiency.
  - Private spending on education: positive and large (education) — private spending around GCSE year matters for attainment.
  - Pupil-to-teacher ratio: positive and statistically significant for secondary education — consistent with smaller class sizes associated with more efficient public spending on high school education.
  - Capital stock: small, negative sign in some regressions; limited explanatory role, possible measurement error.
  - Smoking status and obesity: small and statistically insignificant for health efficiency.

### Distributional findings and sectoral dispersion
- Dispersion changes post-crisis:
  - Educational services: sub-regional variation in efficiency narrowed by 44 percent post crisis.
  - Health services: variation narrowed by 11 percent post crisis.
  - Economic services: variation remained widest and persisted post crisis (limited change).
- Regional narrowing:
  - Northern counties with lower initial efficiency levels made the largest efficiency gains post crisis, narrowing regional disparities across England; nonetheless the lower quartile remains concentrated in northern counties.

### Policy implications and conclusions
- Main conclusions:
  - Despite large public spending cuts (notably in education), overall public sector efficiency improved post crisis; education experienced the largest efficiency gains.
  - Northern counties converged the most from lower initial efficiency levels.
  - Economic affairs display the widest and most persistent disparities.
  - Improvements in measured outputs (including GCSE and life expectancy) occurred despite cuts in some inputs—interpretation includes potential trimming of "excess fat," technological improvements, sectoral reforms, employment patterns, and incentives from fiscal devolution.
- Policy recommendations:
  - Consider devolving spending powers first to sub-regions that delivered the largest efficiency improvements; if improvements persist, consider granting revenue-generation powers next.
  - Use benchmarking as an incentive tool for sub-regions with deteriorations.
  - Reforms to increase sub-regional connectivity (reduce transportation costs), raise education attainment, address class size, and consider private spending complementarities to help narrow sub-regional disparities.
- Caveats and suggested further research:
  - Output measures have limitations (e.g., GCSE score inflation, slow-moving health outputs); quality of outputs not measured.
  - Long-term impacts of spending cuts (e.g., primary education effects) may take years to materialize.
  - Endogeneity of public spending not fully resolved in robustness checks; two-stage and instrumented approaches suggested.
  - Association between public sector efficiency gains and labor productivity growth does not imply causality; further micro-level sub-regional research recommended.

*Source: wp1736r - References (pdf).*

### References .............................................................................................................

### wp1736r - References .............................................................................................................

### Introduction and research questions
- This paper examines sub-regional public sector efficiency/productivity in England during the fiscal consolidation of 2010–14, asking:
  - (i) Has public sector efficiency or productivity at the sub-regional level improved or weakened in England during the fiscal consolidation of 2010–14?
  - (ii) What has been the pattern across different sectors and sub-regions?
  - (iii) Have sub-regions with lower initial levels of efficiency experienced stronger gains, implying some catch up in efficiency levels?
  - (iv) Were deeper cuts in public spending associated with stronger efficiency gains?
  - (v) Has there been any relationship between changes in public sector efficiency and labor productivity across sub-regions?
  - (vi) What are the determinants of sub-regional variation in public sector service efficiency?

### Motivation and case selection
- Rationale:
  - Efficiency gains can limit adverse impacts of spending cuts; little evidence exists on how large “exogenous” fiscal consolidation episodes affect sub-regional public sector efficiency.
  - The study links public sector efficiency to broader economic productivity and performance (Evans and Rauch, 1999; Afonso et al. 2003; Kibblewhite, 2011).
- Why the United Kingdom:
  - The UK undertook a sizable fiscal consolidation to reduce public debt after the global financial crisis.
  - Majority of public spending in the UK is centrally financed, providing an “exogenous” shock across regions.
  - The paper focuses on sub-regional performance because fiscal decentralization discussions are conducted at that level.
- Geographic scope and units:
  - The nine NUTS1 regions of England are listed; Greater London is excluded as a common outlier practice.
  - Analysis combines official public spending data at the English regional (NUTS1) level (excluding Greater London, leaving eight regions) and sectoral output measures at the sub-regional (28 NUTS2 sub-regions or “counties”, Greater London sub-regions excluded) level to estimate a sub-regional index of public efficiency.
- Methodological references and related approaches:
  - The approach is related to Simar and Wilson (2007), Giordano and Tommasino (2013), and Giordano et al. (2015).
  - Official spending data are only available at the regional NUTS1 level; no within-region variation in spending is assumed.

### Stylized facts: spending, outputs, and productivity
- Cross-country and sub-regional spending context:
  - Public and sub-regional spending in the UK are well below those of large EU and OECD economies (Figure 1).
  - Government expenditure in the UK is below the European average and significantly below most comparator economies; this trend became more pronounced following the crisis and could continue given the need for medium-term fiscal consolidation and the large current account deficit.
- Sectoral inputs and outputs examined:
  - Inputs: real education public spending per pupil, health and economic service expenditure per head.
  - Outputs (achievements): high school education attainment proxied by GCSE scores, life expectancy at the age of 65 years, and the number of private enterprises created.
  - Change periods: averages of pre-crisis (2003–07) and post-crisis (2010–14), changes reported in percent; spending in real £s per head or pupil.
- Caveats on output proxies and timing:
  - Cuts in primary education spending post-crisis may take years to affect GCSE scores; more intermediate results (Key Stage 2) are not examined due to data constraints.
  - No distinction between private and state schools or pupils due to data limits.
  - Health outputs such as hospital waiting lists or numbers of surgeries are preferable but unavailable at the sub-regional level; life expectancy is slow-moving and may require longer horizon analysis.
  - Quality adjustments of services are not studied at the sub-regional level.

### Empirical first-cut findings (from Figures 2 and 3)
- Correlations and visual patterns between pre- and post-crisis changes (2003–07 vs. 2010–14):
  - Changes in spending per pupil and high school education attainment (change in GCSE scores) are strongly and negatively correlated (Figure 2, first left panel).
  - Changes in spending per pupil and estimated efficiency are strongly and negatively correlated (Figure 2, first right panel).
  - Changes in health spending per head and health output (change in life expectancy at 65) are positively correlated (Figure 2, second left panel).
  - Changes in health spending per head and estimated efficiency are positively correlated (Figure 2, second right panel).
  - For economic services (proxied by change in number of private enterprises), the picture is less definitive: some positive correlation between inputs and outputs (Figure 2, third left panel) and negative correlation between efficiency and inputs; underestimated regional transportation spending may influence results (annex).
- Regional aggregate observation:
  - Despite substantial spending-led consolidation and cuts across most categories in England, education spending per pupil fell most dramatically, while achievement (in the outputs used) rose across all sectors, including education (Figure 3).

### Data, robustness, and related material noted in content
- Periods and aggregates:
  - Pre-crisis period: 2003–07; post-crisis period: 2010–14.
  - Spending data source: HM Treasury’s “Public Expenditure by Country, Region and Function” Chapter 9, Table 9.15 (data appendix).
- Robustness and alternative measures:
  - Section IV.B examines alternative outputs and robustness checks where data permit.
  - Annexes and tables listed include robustness exercises (e.g., alternative public sector efficiency indicators, VRS, weighted DEA scores, NUTS1 aggregation) and detailed figures and tables of results (listed in the Figures and Tables inventory).
- Limitations explicitly acknowledged:
  - Official national-accounts’ government sector output and productivity estimates differ from microeconomic measures of public sector performance and cannot be used interchangeably (Atkinson, 2005).
  - The paper does not present data nor study the efficiency of devolved spending responsibilities or local-level spending; those are outside the scope.

*Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1736r.pdf*

### annex Tables A.1 and A.2). The following findings, aggregated to the regional NUTS1 level,

### wp1736r - annex Tables A.1 and A.2). The following findings, aggregated to the regional NUTS1 level, emerge

### Major empirical findings
- Public spending changes (post-crisis):
  - "Public health inputs or spending per head actually increased sharply across all English regions without exception post-crisis" (Figure 3, yellow striped-bars).  
  - Education spending per pupil "declined sharply" (Figure 3, orange striped-bars), particularly in the North.  
  - Public spending on economic services showed "more sub-regional variation, with small cuts in some regions and small increases in others" (Figure 3, green striped-bars).
  - Caveat: "The increases in real health spending could be overestimated if health sector deflators have not been adjusted concomitantly with rising health care costs."

- Output changes (post-crisis):
  - Outputs did not decline proportionally with spending cuts; "rather all outputs improved post crisis":
    - Life expectancy increased marginally (health output).
    - GCSE achievement improved sharply (education output), most notably in the North and Midlands.
    - Number of enterprises expanded a little (economic services output), most notably in the East of England.
  - Note: Department of Education "points to GCSE score inflation, in part attributed to measurement issues rather than a change in education output." Quality measures are not fully captured.

- Interpretation:
  - "Despite large spending cuts, actual output (at least in terms of 'quantities' measured here) has not suffered—rather it seems that excess fat in public spending has been trimmed."
  - Other drivers likely contributed to output improvements: technological improvements, sector-specific reforms, incentives from fiscal decentralization, and employment patterns (employment in education and health did not decline as sharply as in other OECD economies).

### Empirical strategy and data
- Objective: estimate an index of public productivity/efficiency at the sub-regional English level (excluding London) for sectors: education, health, economic affairs (including transport and housing).
- Periods compared: pre-crisis (2003–07) vs. post-crisis (2010–14). Years 2008–09 excluded.
- Methodology:
  - Data Envelopment Analysis (DEA) output-oriented model with constant returns to scale as baseline; variable returns to scale also estimated (no material change).
  - "Three separate production processes are estimated for each sector."
  - Inputs, controls, and outputs (as specified in the paper):
    - Education: Input = Real public expenditure on education per pupil; Controls = Private spending on education and education attainment by income level per head; Output = High school (GCSE) achievement.
    - Health: Input = Real public expenditure on health per head; Controls = Adjusted for population’s age structure (ratio of population over 65) and prevalence of obesity; Output = Life expectancy at the age of 65 years.
    - Economy: Input = Real public expenditure on economic services normalized by lagged population size; Controls = Lagged stock of capital; Output = Number of active enterprises.
  - Second-stage regressions include sub-regional controls (private spending, income per capita, population density and age profile, capital stocks).
  - Complementary parametric stochastic frontier analysis (SFA) conducted as robustness.

### Baseline DEA findings (efficiency)
- Overall result: "Despite large public spending cuts, overall efficiency improved post crisis."
- Sectoral pattern:
  - Efficiency improved most notably in the education sector (which saw the deepest cuts).
  - Health saw efficiency improvements despite spending increases.
  - Economic services efficiency deteriorated slightly.
- Sub-regional variation:
  - Examples: Tees Valley and Durham (UKC1) improved post-crisis; Devon (UKK4) deteriorated post-crisis.
  - "The lower quartile of efficiency, however, remains a northern-county phenomenon."
- England average (excl. London) reported DEA combined indices (as presented in the source):
  - England average (exl. London) 2 0.8820.9160.5230.7780.9280.9300.5210.796

- Table 1 (selected interpretation): A DEA score of one implies an efficient county; higher values imply higher efficiency.

### Convergence and regression evidence
- Convergence:
  - "Sub-regions with the weakest pre-crisis levels in public sector efficiency converged the most."
  - Regression evidence (bivariate regressions of change in efficiency on initial efficiency level; all regressions: number of observations = 29):
    - Change in efficiency (Education) on Initial efficiency (Education): coefficient = -1.366*** (0.174), adj. R-sq = 0.721.
    - Change in efficiency (Health) on Initial efficiency (Health): coefficient = -0.168*** (0.0171), adj. R-sq = 0.835.
    - Change in efficiency (Economic Services) on Initial efficiency (Economic services): coefficient = -0.212* (0.171), adj. R-sq = 0.265.
    - Change in efficiency (Simple Average) on Initial efficiency (Simple Average): coefficient = -0.391** (0.126), adj. R-sq = 0.702.
  - Significance notation in source: * p<0.10, ** p<0.05, *** p<0.01.

- Relationship between spending cuts and efficiency gains:
  - Bivariate regressions of percentage change in efficiency on percentage change in public spending (number of observations = 29):
    - Education sector: Change in efficiency regressed on change in education spending per pupil: coefficient = -0.733** (0.301), adj. R-sq = 0.512.
      - Interpretation in source: "Deeper education spending cuts are associated with large public sector efficiency gains in that sector."
    - Health sector: coefficient = 0.116 (0.298), adj. R-sq = 0.344 (insignificant).
    - Economic services: coefficient = -1.102 (0.789), adj. R-sq = 0.167 (insignificant).
    - Simple average (three sectors): coefficient = -1.701 (1.077), adj. R-sq = 0.453 (insignificant).
  - Source interpretation: "The increase in spending in the health sector actually led to efficiency increases—although the coefficient is also insignificant," and "other factors have raised efficiency in the health sector (other than public spending)."

### Public sector efficiency and labor productivity
- Visual and regression evidence suggest correlation:
  - "Sub-regions that have improved their level of public sector efficiency or productivity in the post-crisis period also tend to have higher labor productivity growth" (examples: Merseyside, Greater Manchester, Northumberland and Tyne and Wear, West and South Yorkshire, Derbyshire and Nottinghamshire and the West Midlands).
  - Regression of change in sub-regional efficiency on labor productivity growth: coefficient statistically significant at the 5 percent level (source notes statistical significance but not the exact coefficient value in the excerpt).
  - Caution: "Association does not imply causality."

### Distributional/dispersion findings
- Sectoral disparities narrowed post crisis:
  - Educational services: sub-regional variation in efficiency narrowed markedly post crisis (by 44 percent).
  - Health services: variation narrowed post crisis (by 11 percent).
  - Economic services: variation remained widest and persisted post crisis (limited change), "likely the result of limited infrastructural spending in the post crisis period."

### Robustness checks (overview)
- Weighted DEA: DEA efficiency scores weighted by sectoral shares of public spending at the NUTS1 level (weights = average shares for full sample, Table 4) produce a similar ranking of sub-region efficiency (Table 5).
- Alternative outputs and controls examined (Section IV.B) depending on data availability; lags in public spending explored.
- Complementary SFA employed to address endogeneity concerns, particularly in the education sector.
- Alternative DEA specifications: input-oriented DEA and variable returns to scale technologies estimated with "similar results."

*Source: wp1736r - annex Tables A.1 and A.2). The following findings, aggregated to the regional NUTS1 level, emerge (PDF chapter/section).*

### Section III holding.

### Section III holding

### B. Alternative inputs, outputs and control variables
- Purpose: Assess robustness of baseline DEA results using alternative/additional specifications of outputs, control variables, and lags in public spending.
- Education sector
  - Additional control: pupil to teacher ratios (or class size when unavailable).
  - Spending lag: education spending is lagged one year.
  - Rationale: relatively strong contemporaneous effects of public spending on achievement in the state school system, and in poorer sub-regions in particular (Jackson et al. 2016).
  - Empirical result: education sector coefficients using higher order lags of public spending in Tables 6 and 7 were insignificant albeit similar in magnitude and sign.
  - DEA outcome: resultant DEA scores for the education sector do not vary significantly from those shown in the baseline (Table 5).
- Health sector
  - Output: life expectancy at birth (HALE) used instead of life expectancy at age 65.
  - Spending lag: health spending is lagged two years to reflect non-contemporaneous dynamics.
  - Additional controls (inputs): private spending on health from household surveys, and mother's smoking status at time of delivery.
  - Caveat: output still suffers from earlier-noted limitations; results should be interpreted with caution.
  - DEA outcome: sub-regional ranking for the health sector and post-crisis changes do not alter (Table 5).
- Public economic services sector
  - Alternative output: labor productivity used instead of number of enterprises created.
  - Spending lag: lagged two years.
  - Empirical result: some changes in sub-regional ranking occurred, but post-crisis changes remain in the same order or magnitude as baseline (Table 5).
- Overall robustness conclusions
  - Baseline result that sub-regions with the weakest levels of public sector efficiency converged the most still holds when using these alternatives.
  - Coefficients display the same sign, similar magnitudes, with slightly more statistical significance and larger R-square (Table 6).
  - Re-estimating regression of percentage change in efficiency on percentage change in public spending shows coefficients slightly larger, gaining statistical significance and larger R-square (Table 7).
  - Remaining issue: endogeneity of public spending is not resolved in these checks; next section addresses it with a two-stage regression framework.

Key reported robustness statistics (preserving values exactly):
- Table 6: Bivariate regression results (Change in efficiency vs Initial efficiency level), Number of observations = 29
  - Education: coefficient = -1.343*** (0.121), adj. R-sq = 0.710
  - Health: coefficient = -0.211** (0.0141), adj. R-sq = 0.913
  - Economic services: coefficient = -1.143** (0.026), adj. R-sq = 0.353
  - Weighted Average: coefficient = -0.677** (0.117), adj. R-sq = 0.790
- Table 7: Bivariate regression results (Change in efficiency vs Change in spending), Number of observations = 29
  - Education (per pupil): coefficient = -0.728*** (0.301), adj. R-sq = 0.548
  - Health (per person): coefficient = 0.166*** (0.268), adj. R-sq = 0.484
  - Economic services (per person): coefficient = -1.301* (0.801), adj. R-sq = 0.378
  - Weighted Average: coefficient = -1.789** (1.078), adj. R-sq = 0.484

Notes on data and controls:
- Education spending is lagged one year (two lags were insignificant). NUTS2 teacher-pupil ratios included as a control (data available since 2006).
- Health: private health spending added as control from household surveys; mother's smoking status at time of delivery included (data available since 2006); HALE is the output.
- Economic services: spending lagged two years (one year lags were insignificant); output = labor productivity.

### C. Stochastic frontier analysis — First-stage analysis
- Motivation: DEA's limitation in fully controlling for heterogeneity (differences in development or income) motivates a parametric stochastic frontier analysis (SFA) for robustness.
- Advantages of parametric SFA over DEA:
  - Can control for a larger number of variables that influence each public sector output.
  - More limited sensitivity to outliers.
  - Relevant for within-country analyses where heterogeneity and outliers matter (e.g., exclusion of Greater London).
- Methodological overview:
  - SFA assumes a production frontier (here a Cobb-Douglas production function) enveloping input-output pairs.
  - The regression model uses a composite error term: an idiosyncratic (normally distributed) disturbance capturing measurement error, plus a one-sided disturbance representing inefficiency.
- Implementation details:
  - Two SFA cross-sections estimated using Cobb-Douglas production functions for each sector and for each of the pre- and post-crisis sub-sample averages (identical to baseline DEA sub-samples).
  - Estimation by maximum likelihood.
  - First step: regression of each sector’s outputs on its lagged inputs to estimate SFA efficiency scores.
  - Inputs and outputs used in SFA are precisely those introduced in Section B (“alternative inputs and outputs” described on pages 23-27).

*Source: wp1736r - Section III holding.*

### 25. As can be seen from the results of the SFA cross-sectional estimation (Figure 8),

### 25. As can be seen from the results of the SFA cross-sectional estimation (Figure 8)

### Robustness: SFA vs DEA; Convergence of weaker NUTS2 sub-regions
- SFA cross-sectional estimated sub-regional efficiency scores are smaller in size than baseline DEA scores but:
  - Their ranking and magnitude of change post crisis (convergence) are highly and significantly correlated with those estimated in the baseline DEA (for both simple and weighted average scores).
  - There is more variation in the SFA sub-regional scores (i.e., greater distance from the frontier).

### Second-stage analysis: purpose and setup
- Objective: estimate determinants (covariates) of sub-regional public sector spending efficiency for education, health, economic services, and the weighted overall sectoral average.
- Motivation: partly address public spending endogeneity (e.g., via lags in public spending and instruments).
- Interpretation: SFA efficiency scores represent how much output (e.g., GCSE achievement) a sub-region could achieve at given pre- or post-crisis spending if it were as efficient as the most efficient sub-region in England during the same periods.
- Estimation approach:
  - A multivariate truncated regression with fixed effects is run because SFA efficiency scores are bounded between zero and one.
  - All estimated SFA scores during pre- and post-crisis periods (28 sub-regions and their average × 2-period averages, total 58 observations) are included on the left-hand side.
  - Control variables plus a fixed effect per sub-region per period-average are on the right-hand side.

### Table 8: Multivariate truncated regression results (coefficients as reported)
- Dependent variable: SFA efficiency scores.
- Number of observations: 58 (for each regression).
- Fixed effects: yes (for each regression).
- Standard errors in parentheses. Significance: * p<0.10, ** p<0.05, *** p<0.01.

- Education (column (1)):
  - Income per capita: 0.012***
    - (0.001)
  - Private spending on education: 1.132***
    - (0.206)
  - Education attainment: 2.412***
    - (0.214)
  - Teacher to pupil ratio: 0.024**
    - (0.002)
  - Population density: 1.362*
    - (0.171)
  - Smoking status: 0.000
    - (0.001)
  - Prevelance of obesity: 0.000
    - (0.001)
  - Capital stock: -0.001
    - (0.001)
  - Active enterprises: 0.012***
    - (0.022)

- Health (column (2)):
  - Income per capita: 0.000
    - (0.001)
  - Private spending on health: 0.020
    - (0.266)
  - Education attainment: 3.101***
    - (0.311)
  - Population density: 1.561***
    - (0.180)
  - Capital stock: -0.001*
    - (0.001)

- Economic Services (column (3)):
  - Income per capita: 0.001
    - (0.001)
  - Education attainment: 3.001***
    - (0.300)
  - Population density: 1.542***
    - (0.181)
  - Active enterprises: 0.012***
    - (0.022)

- Weighted Average (column (4)):
  - Income per capita: 0.000
    - (0.001)
  - Education attainment: 3.000***
    - (0.311)
  - Population density: 1.442***
    - (0.172)
  - Capital stock: -0.001*
    - (0.001)

### Interpretation of key regressors (findings)
- Income per capita
  - Positive but small; statistically significant only in education.
  - Insignificant in health—interpreted as the NHS contributing to improved sub-regional health outputs irrespective of private disposable incomes.
- Private spending on education and health
  - Education: positive and large (statistically significant) — private spending around GCSE year matters for attainment and explains sub-regional variation.
  - Health: positive but small and statistically insignificant.
- Education attainment
  - Coefficients positive, large, and statistically significant across sectors — education attainment explains a large fraction of sub-regional variation in efficiency scores.
- Pupil-to-teacher ratio
  - Positive, small, and statistically significant for secondary education — consistent with smaller class sizes associated with more efficient public spending on high school education.
- Population density
  - Positive, large, and statistically significant for all sectors — denser (more connected/urban) areas exhibit higher spending efficiency.
- Smoking status at delivery; Prevalence of obesity
  - For health: coefficients positive but small and statistically insignificant — not important in explaining variation in public health spending efficiency.
- Capital stock
  - For economic services and weighted average: coefficient small, does not display expected positive sign, only statistically significant for the weighted average — may reflect measurement error (input likely underestimated).
- Number of active enterprises
  - For economic services: coefficient positive, large, and statistically significant — more firms associated with higher public economic service efficiency.

### Overall determinants ranking
- Most important determinant: education attainment.
- Followed by: population density (proxy for urbanization/connectivity).
- Then: private spending on high school education and class size.

### Conclusions and policy implications
- Despite large public spending cuts (notably in education), overall public sector efficiency improved post crisis; larger cuts yielded higher efficiency improvements across sub-regions, notably in education, although the lower quartile remains a northern-county phenomenon.
- Northern counties, despite lower initial efficiency levels, made the largest efficiency gains post crisis, narrowing regional disparities across England.
- Sectoral disparities:
  - Economic affairs: widest disparities and broadly unchanged post-crisis.
  - Education and health: disparities narrowed markedly (education following spending cuts; health following spending increases).
- Policy implications:
  - Consider devolving spending powers first to sub-regions that delivered the largest efficiency improvements; if improvements persist, consider granting revenue-generation powers next.
  - For sub-regions with deteriorations, benchmarking could be used as an incentive to improve future performance.
  - Reforms to increase sub-regional connectivity (reduce transportation costs), raise education attainment, and address class size and private spending on education could help narrow sub-regional disparities in public sector productivity.
- Caveats and further research:
  - Results may be influenced by technological improvements, sector reforms, stable employment, and incentives from fiscal devolution.
  - Output measures chosen have shortcomings; additional sub-regional data (e.g., Key Stage 2 results, hospital waiting lists) would improve analysis.
  - Quality of outputs has not been measured.
  - Long-term impacts of spending cuts (especially on health and the effect of cuts in primary education on later attainment) may take years to materialize.
  - Post-crisis changes in public sector efficiency are associated with changes in post-crisis sub-regional labor productivity, but the relationship may involve lags and other factors contributing to the UK’s weak “productivity puzzle”; further micro-level sub-regional research is recommended.

*Source: wp1736r - 25. As can be seen from the results of the SFA cross-sectional estimation (Figure 8).*

### References

### References

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### Appendix mention
- The document includes an APPENDIX: "The NUTS2 statistical classification of the United Kingdom, including all its regions."

### Data and sources

- Real public spending by NUTS1: central government, local government and public corporations. Source: Her Majesty’s Treasury, “Public Expenditure by Country, Region and Function” Chapter 9. November 2015.
- Real sectoral NUTS1 spending on economic affairs, transport and housing: sum of HMT budget chapters including Public and common services; Public order and safety; Economic affairs including enterprise and economic development, science and technology, employment policies, agriculture, fisheries and forestry, transport; Environment protection; and Recreation, culture and religion. Note: much of rail and air transport spending cannot be apportioned regionally and is likely an underestimate. Source: Her Majesty’s Treasury, “Public Expenditure by Country, Region and Function” Chapter 9. November 2015.
- Real NUTS1 private spending on public services (e.g., education and health): household survey. Source: Office of National Statistics.
- Real gross disposable income: available by NUTS1 and 2. Source: Office of National Statistics.
- Number of pupils: school-level aggregated up to NUTS2 using ONS Geography and GIS & Mapping’s keys. Source: Department of Education.
- Education achievement: GCSE of 5 or more A*-C grades at GCSE or equivalent, including English and Maths, at Key Stage 4 as a percentage of the number of pupils at the end of KS4. Historically consistent Level 2 attainment is used. Aggregation weighted by number of pupils to NUTS2. Source: Department for Education.
- Pupil teacher ratio for secondary: available at NUTS1; where missing, spliced with change in secondary class size at local school level and aggregated up to NUTS1 using ONS keys. Source: Department of Education.
- Population at NUTS2: Total resident population (midyear population estimates). Methodology notes on inclusion of armed forces and students; reflects new migration methodology. Source: Office of National Statistics.
- Life expectancy at birth and at age 65: derived from the NUTS2 Annual Population Survey (APS). Source: Office for National Statistics.
- Population age structure (ratio of population over 65) and density: NUTS2 APS and EuroStat Population Database. Source: Office for National Statistics and http://ec.europa.eu/eurostat/statistics-explained/index.php/Population_statistics_at_regional_level
- Number of active enterprises: defined as enterprises with turnover or employment at any time in the reference period. Data augmented by splicing with growth rates from the ORBIS firm level database by Bureau van Dijk, aggregated up to NUTS2 via matching of city postcodes. Source: Office for National Statistics.
- Regional Gross Fixed Capital Formation and initial stock of capital for transport and housing: provided at NUTS2 with industry breakdown. Source: Office for National Statistics.
- Labor productivity at NUTS2: measured as the change in real output per worker between 2010-14 and 2003-07. Source: Office for National Statistics.
- Smoking status at time of delivery and prevalence of obesity: Public Health of England, www.phoutcomes.info at the NUTS2 level.

### Tables — Selected key statistics and findings

- Table A.1. Real public spending pre- and post-crisis (Per head for health and economy and per pupil for eduction) — change (2003-07) to (2010-14), selected regional examples:
  - North East: Education 1.80 → 1.41 (Change: -22), Health 2.03 → 2.65 (Change: 31), Economic services 2.02 → 1.95 (Change: -4)
  - North West: Education 1.74 → 1.32 (Change: -24), Health 1.60 → 2.02 (Change: 27), Economic services 1.58 → 1.61 (Change: 1)
  - South East: Education 1.44 → 1.33 (Change: -7), Health 1.33 → 1.70 (Change: 27), Economic services 1.21 → 1.20 (Change: -1)
  - Note: "Author's estimates based on official and indexed UK data. 1 Aggregated up from NUTS-2 or 3 to NUTS-1 level."

- Table A.2. Outputs pre- and post-crisis (Per head for health and economy and per pupil for eduction) — selected regional examples:
  - North East: Education 38 → 58 (Change: 53), Health 18 → 19 (Change: 7), Economic services 6 → 6 (Change: 8)
  - North West: Education 46 → 58 (Change: 27), Health 18 → 19 (Change: 6), Economic services 16 → 17 (Change: 4)
  - South East: Education 50 → 60 (Change: 21), Health 19 → 20 (Change: 5), Economic services 36 → 38 (Change: 6)
  - Note: "Author's estimates based on official UK data. 1 Aggregated up from NUTS-2 or 3 to NUTS-1 level."

- Table A.3. Robustness: Alternative Public Sector Efficiency Indicators (constant returns to scale, output-oriented DEA)
  - England average pre-crisis: 0.791
  - England average post-crisis: 0.796
  - Individual NUTS2 examples (Pre-crisis → Post-crisis shown in table for Education, Health, Economy, Combined Input-oriented Efficiency Index): examples include Lincolnshire UKF3 (1.00, 0.96, 1.00, 0.98 → 0.96, 0.97, 1.00, 0.97), Kent UKJ4 (0.94, 0.95, 1.00, 0.96 → 0.95, 0.97, 1.00, 0.97).

- Table A.4. Robustness: Alternative Public Sector Efficiency Scores Using a Variable Returns Technology
  - England average pre-crisis: 0.939
  - England average post-crisis: 0.947
  - Table reports scale (irs/drs) and component efficiency scores for Education, Health, Economy for many NUTS2 regions (examples: Essex UKH3 combined efficiency entries include 0.93 pre- and 0.93 post-crisis under various scale specifications).

- Table A.5. Public Sector Efficiency Indicators Aggregated to the Regional NUTS1 Level (Constant returns to scale and output oriented-DEA analysis)
  - North East (UKC): Pre-crisis Education 0.80, Health 0.68, Economy 0.14, Combined 0.54 → Post-crisis Education 0.96, Health 0.72, Economy 0.17, Combined 0.62 (Change post-crisis: 14.1)
  - North West (UKD): Pre-crisis Combined 0.70 → Post-crisis Combined 0.73 (Change post-crisis: 3.9)
  - Yorkshire and the Humber (UKE): Pre-crisis Combined 0.69 → Post-crisis Combined 0.72 (Change post-crisis: 4.0)
  - England average excl. London: Pre-crisis Education 0.894, Health 0.896, Economy 0.462, Combined 0.751 → Post-crisis Education 0.947, Health 0.911, Economy 0.463, Combined 0.774 (Change post-crisis: 3.63)
  - Note: "Pre- and post-crisis refer to the average of 2003-07 and 2010-14, respectively."

*Source: wp1736r - References (pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1736r.pdf_