## 1. FD GMM Estimates of the Fiscal Reaction Function (Content unit: _wp1684)

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---

### Introduction and context
- Need to put national and subnational fiscal positions on a sound footing gained prominence following the Eurozone debt crisis (OECD, 2014; Lledó and Pereira, 2015).
- Fiscal rules have been associated with a greater probability of stabilizing debt (Molnar, 2012).
- Effectiveness of fiscal rules depends on design characteristics such as sufficient flexibility, an institutional mechanism to check deviations from targets, and an unambiguous link between numerical targets and the ultimate objective (Kumar and others, 2009).
- Literature focus:
  - Debate and empirical work mainly on national fiscal rules; subnational fiscal rules literature largely theoretical and qualitative.
  - Empirical assessments often overlook vertical fiscal imbalances (VFIs).

### Definition and mechanisms of vertical fiscal imbalances (VFIs)
- VFIs: occur when there is a gap between own spending (total spending minus transfers paid) and own revenues (total revenues minus transfers received).
- Typical cause: devolution of spending responsibilities outpaces devolution of revenue mandates, leaving subnational governments (SNGs) with limited tax autonomy.
- Two channels by which high VFIs may worsen SNG fiscal outcomes:
  - Common-pool problem (Rodden, 2002): SNGs may fail to internalize full cost of spending mandates when financed from own revenues and a common resource pool, potentially leading to overspending.
  - Moral hazard (Von Hagen and Eichengreen, 1996): Insufficient tax autonomy may generate bailout expectations among SNGs, leading to over-borrowing and soft budget constraints.
- Empirical citations of negative relationship between VFIs and fiscal discipline:
  - Asatryan and others (2012) at the subnational level.
  - Eyraud and Lusinyan (2013) at the general government level.

### Data coverage and sample
- Sample period: 1995 to 2012.
- Countries included (26): Austria, Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, and the United Kingdom.
  - Note: Croatia data available from 2002 (only 11 observations for Croatia).
- Total sample observations reported in summary statistics: The sample has 461 observations.
- Typical regression sample size reported in FD GMM specifications: Number of Observations = 321 (in most FD GMM specifications); 347 in LSDVC reported tables.
- Several figures and series cover 1995–2012 (e.g., "Median Subnational Fiscal Rule Strength in Europe, 1995–2012").

### Empirical model and estimation framework
- Dynamic panel specification (equation (1)):
  - SNPB_it = α SNPB_i,t−1 + β SNFRSI_a,it + γ SNFRSI_a,it * VFI_it + δ X_it + η_i + ρ_t + ε_it, i=1,...,N; t=1,...,T
  - SNPB: sum of primary balances of all SNGs within a country, as percent of GDP.
  - SNFRSI_a: strength index for attribute a of subnational fiscal rules (overall index, statutory base, monitoring and enforcement, non-compliance, media visibility, flexibility).
  - X includes output gap (national output gap as proxy for subnational output gap) and percent of population above the age of 65.
  - VFI: vertical fiscal imbalances.
  - Model includes country fixed effects (η_i) and time fixed effects (ρ_t).
- Primary estimators:
  - First-difference Arellano-Bond (1991) GMM estimator — FD GMM (baseline).
  - Bias corrected Least Squares Dummy Variable — LSDVC (robustness).
- Instrument strategy for FD GMM:
  - Internal instruments: lags t−3 and t−4 of variables.
  - External instruments: dummy for central legislative elections; Herfindahl index of government fragmentation.
  - Instruments collapsed using Roodman’s xtabond2 collapse option.
  - Examples of instrument counts: Instruments = 28 (Table 1), Instruments = 30 (Tables 2, 4, 5), Instruments = 36 (Table 6).
- Rationale:
  - FD GMM addresses dynamic panel bias and reverse causality; external instruments exploit national-level political variables argued exogenous to subnational fiscal shocks.
  - LSDVC corrects small-sample bias but does not address endogeneity; used as robustness.

### Measurement specifics
- VFIs measured as the share of subnational own spending not financed through own revenues.
- Verbati m footnote definition preserved:
  - VFIs are defined as [1− Own Revenue / Own Spending], which can be shown to be equivalent to [1− Revenue Decentralisation / Expenditure Decentralisation (1−GG Deficit)]. Here, own revenue (spending) corresponds to total subnational revenue (spending) minus transfers received by the central government and other public entities (transfer paid to the central government and other public entities). Revenue (expenditure) decentralization corresponds to the share of own revenue (own spending) to general government total revenue (general government total spending). GG deficit is the overall fiscal deficit of the general government as a share of general government total spending.

### Baseline FD GMM high-level results (selected numeric findings)
- General finding: stronger subnational fiscal rules associated with improved subnational primary balances; interaction with VFI shows diminishing effectiveness as VFIs rise.
- Table 1 (FD GMM without interaction) highlights:
  - Lagged dependent variable coefficients ~ 0.101–0.161 (standard errors ~ 0.10–0.13).
  - Overall SNFRSI coefficient: 0.032* (standard error 0.02) — significant at 10% in column (1).
  - Sub-indices (statutory base, monitoring and enforcement, media visibility, flexibility) coefficients ~ 0.029–0.032* (standard error 0.02) — mostly significant at 10%.
  - Non-compliance sub-index: 0.048*** (standard error 0.02) — significant at 1%.
  - Controls:
    - Output Gap: -0.001* to -0.001** (standard errors 0.00).
    - Population > 65: 0.008–0.014 (mostly significant at 10%).
  - Number of Observations = 321; Instruments = 28.
  - Reported m1 and m2 test examples: m1 = -2.02, m2 = 0.16 in column (1).
- Table 2 (FD GMM with SNFRSI * VFI interaction) highlights:
  - Lagged dependent variable coefficients ~ 0.075–0.118 (standard errors ~ 0.08–0.10).
  - Overall SNFRSI: 0.064** (standard error 0.03).
  - Overall*VFI: -0.114* (standard error 0.06).
  - Statutory Base: 0.072**; Statutory Base*VFI: -0.143** (standard error 0.07).
  - Monitoring and Enforcement: 0.056**; Monitoring and Enforcement*VFI: -0.104* (standard error 0.06).
  - Non Compliance: 0.087**; Non Compliance*VFI: -0.136* (standard error 0.07).
  - Media Visibility: 0.062**; Media Visibility*VFI: -0.111* (standard error 0.06).
  - Flexibility: 0.076**; Flexibility*VFI: -0.130** (standard error 0.06).
  - VFI main effect: 0.021–0.031 (mostly not statistically significant).
  - Output Gap: -0.001*** to -0.001** (standard errors 0.00).
  - Population > 65: 0.003–0.009 (some significance at 5%–10%).
  - Number of Observations = 321; Instruments = 30.
- Quantitative interpretation reported:
  - "The estimated SNFRSI regression coefficient implies that a 10 percent increase in the overall SNFRSI would raise subnational primary balance by 0.63 percent of GDP."
  - Marginal effect of SNFRSI on SNPB (∂SNPB/∂SNFRSI) falls as VFI rises; marginal effect becomes negative when VFI > 0.5 (i.e., when the ratio between revenue and expenditure decentralization falls below 0.5).

### Robustness checks (selected numeric highlights)
- LSDVC estimates (Table 3):
  - Coefficients on overall index and attribute sub-indices positive and statistically significant.
  - Interaction terms SNFRSI*VFI remain negative and significant.
  - Point estimates roughly half the size of FD GMM estimates (example: lagged dependent variable = 0.364***; Overall = 0.020*; Overall*VFI = -0.049**).
  - Number of Observations = 347 (bootstrap variance-covariance with 1000 repetitions).
- Alternative dependent variables:
  - Table 4 (Dependent variable = Subnational Overall Balance/GDP): Overall = 0.060**; Overall*VFI = -0.107*.
  - Table 5 (Dependent variable = Subnational Primary Balance as Percent of Subnational Revenue): much larger magnitudes due to normalization by subnational revenue. Examples:
    - Overall = 0.454** (standard error 0.19); Overall*VFI = -0.729** (standard error 0.35).
    - Non Compliance = 0.576***; Non Compliance*VFI = -0.896*.
  - Table 6 (Augmented model adding Expenditure Decentralization, CPI Inflation, Unemployment):
    - Overall = 0.061**; Overall*VFI = -0.115**.
    - Expenditure Decentralization coefficients ~ -0.045 to -0.052 (not significant).
    - CPI Inflation and Unemployment coefficients ~ -0.0001 to -0.0003 (not significant).
    - Instruments = 36; Number of Observations = 321.

### Main empirical findings (concise numeric and qualitative statements)
- Finding 1: Stronger subnational fiscal rules improve subnational fiscal balances.
  - Positive coefficients on overall SNFRSI and most attribute indices across estimators.
  - Example reported interpretation: 10 percent increase in overall SNFRSI → SNPB +0.63 percent of GDP.
  - Non-compliance and flexibility attributes show relatively larger coefficient magnitudes in several specifications.
- Finding 2: Effectiveness of subnational fiscal rules diminishes as VFIs rise.
  - Interaction terms SNFRSI*VFI negative and significant across FD GMM specifications and robust to LSDVC.
  - Marginal effect of SNFRSI on SNPB becomes negative when VFI > 0.5 (i.e., expenditure decentralization more than twice revenue decentralization).
  - VFI main effect generally positive but often insignificantly different from zero in baseline specifications.
- Additional numeric notes:
  - Correlation among attribute indices: correlation coefficients among all attributes are above 0.8; principal component alternative index captures more than 80 percent of variance.

### Theoretical rationale and mechanisms (verbatim concepts)
- Soft budget constraints (SBCs) at the subnational level arise from:
  - Common-pool nature of resources financing subnational spending, preventing SNGs from fully internalizing costs and leading to over-spending and over-borrowing.
  - Moral hazard when central government fails to commit credibly not to bail out SNGs; moral hazard intensifies after a history of bailouts and when SNGs are economically or politically too sensitive to fail.
- Large VFIs undermine SNG fiscal discipline by:
  - Intensifying transfer dependency and common-pool financing, reducing economic and political cost to SNGs of fulfilling spending mandates and inducing overspending.
  - Raising bailout expectations and moral hazard, making it costlier for the central government to commit to a non-bailout policy and harder to enforce fiscal rules.

### Policy-relevant implications and recommendations (as stated)
- Strengthen rule design attributes to increase political cost of reneging:
  - Increase rule coverage to encompass the consolidated public sector.
  - Embed rules in constitutional or high-level legislation (statutory base).
  - Improve monitoring and enforcement (independent bodies, automatic corrective mechanisms, sanctions).
  - Increase media visibility of rules and compliance.
  - Define flexibility carefully (cyclical adjustments and escape clauses) to avoid relaxing nominal targets in bad times; well-defined escape clauses can minimize deviations.
- Address vertical fiscal imbalances:
  - Consider reforms to reduce excessive VFIs; align subnational revenue and expenditure mandates.
  - When VFI > 0.5 (expenditure decentralization more than twice revenue decentralization), subnational fiscal rules may cease to be effective; aligning revenue assignments could be a prerequisite.
- Complementary reform sequencing:
  - Independent reforms to eliminate excessive VFIs are critical in fiscally decentralized countries and federations because high VFIs undermine rule effectiveness even when rules are strong.
- Institutional/PFM preconditions:
  - Sound and uniform subnational PFM procedures: shared medium- and long-term fiscal objectives, shared macroeconomic assumptions, timely in-year fiscal reports and annual accounts with independent external audits, common budget classification and accounting standards.
  - Flaws in the intergovernmental fiscal framework (ill-designed transfer systems, mismatches between revenue and spending responsibilities, unclear or unfunded mandates) can undermine rule effectiveness regardless of rule design.

### Appendix 1 — Data definitions and summary statistics (verbatim variable definitions and selected statistics)
- Key variable definitions (verbatim):
  - Subnational primary balance (SNPB): (Subnational Total Revenue - Subnational Total Expenditure - Subnational Interest Expenditure)/Gross Domestic Product
    - Source: Authors' own consolidation of total revenue and expenditures across local and (when applicable) state or regional governments using non-consolidated fiscal data from Eurostat.
  - Subnational overall balance: (Subnational Total Revenue - Subnational Total Expenditure)/Gross Domestic Product
    - Source: Authors' own consolidation ... using non-consolidated fiscal data from Eurostat.
  - Vertical Fiscal Imbalances (VFIs): 1-(Subnational government own revenue/Subnational government own expenditure)
    - Source: Authors' own consolidation ... using non-consolidated fiscal data from Eurostat.
  - Output Gap: Actual - Potential GDP as percent of Actual GDP
    - Source: World Economic Outlook
  - Population > 65: Percent of population above the age of 65
    - Source: World Development Indicators
  - Expenditure Decentralization: Share of sub-national expenditures in general government expenditures
    - Source: Authors' own consolidation ... using non-consolidated fiscal data from Eurostat.
  - Legislative election dummy: Dummy variable = 1 if national legeslative election held int hat year and zero otherwise
    - Source: Database for Political Institutions (DPI) from Beck et al. (2001)
  - Herfindahl Index of Government Fragmentation: The sum of the squared seat shares of all parties in the government
    - Source: Database for Political Institutions (DPI) from Beck et al. (2001)
- Selected summary statistics (verbatim entries from Table A2):
  - SNPB Overall -0.001640.0069-0.05270.0543 N =     461
    - Between0.0025-0.07140.0034 T =      26
    - Within0.0064-0.04570.0533
  - SNFRSI Overall 0.217070.19430.00001.0000 N =     461
    - Between0.16740.00270.7110 T =      26
    - Within0.1041-0.14520.5363
  - VFIs Overall 0.486150.18092-0.020420.85991 N =     460
    - Between0.145580.205730.70334 T =      26
    - Within0.10999-0.009720.80137
  - Population > 65 Overall 15.624532.126710.835121.1009 N =     461
    - Between1.903511.256818.9956 T =      26
    - Within1.007912.867018.5678
  - Output Gap Overall 0.153023.3668-13.495617.5160 N =     434
    - Between0.9374-2.41522.2387 T =      26
    - Within3.2465-11.401215.6984

### Appendix 2 — The Subnational Fiscal Rule Strength Index (SNFRSI) (construction and scoring)
- Source dataset: European Commission (EC) dataset of domestic fiscal rules (numerical fiscal rules in force since 1990 across EU countries).
- Covered rule types: budget balance rule (BBR), debt rule (DR), expenditure rule (ER), revenue rules (RR).
- Government levels considered: central (CG), regional (RG), local (LG), general government (GG), and social security (SS).
- Attributes collected for each subnational rule and scoring scheme (verbatim):
  - Attribute 1 (a1): Statutory/legal base of the rule (4 constitutional base; 3 legal act; 2 coalition agreement; 1 political commitment)
  - Attribute 2 (a2): Adjustment margin (3 no margin; 2 some constrained margin; 1 complete freedom)
  - Attribute 3 (a3): Nature of the body in charge of monitoring rule compliance (3 independent authority or Parliament; 2 ministry; 1 no regular public monitoring)
  - Attribute 4 (a4): Existence of alert mechanisms (augmented by 1 if real-time monitoring/alert mechanisms exist)
  - Attribute 5 (a5): Nature of the body in charge of enforcing the rule (3 independent authority or Parliament; 2 ministry; 1 no specific body)
  - Attribute 6 (a6): Enforcement mechanisms of the rule (4 automatic correction and sanction mechanisms; 3 automatic correction and possibility of sanctions; 2 obliged to take corrective measures or present proposals; 1 no ex-ante defined actions)
  - Attribute 7 (a7): Existence of Escape Clause (augmented by 1 if escape clauses are foreseen and clearly specified)
  - Attribute 8 (a8): Media visibility of the rule (3 closely monitored by media; 2 high media interest; 1 no/modest interest)
- SNFRSI construction (verbatim equations and description):
  - SNFRSI for each attribute a and rule type j in country i at time t: 푆푁퐹푅푆_푎푗 = ∑_{l∈{LG,RG}} 푤_{l c(j)} × c(j) × 푆_{a l c(j)}
    - a∈{a1...a8}; j∈{BBR,DR,ER,RR}; a and c(j)∈{GG,RG,LG,(RG,LG),(CG,RG,LG)}
    - 푤_{l c(j)} = { 1 if c(j) ∈ {RG} or {LG} ; (G_l / G_{c(j)}) if c(j) ∈ {GG, (RG,LG), (CG,RG,LG)} }
  - Aggregate across rules: 푆푁퐹푅푆_푎 = ∑_j 푆푁퐹푅푆_푎푗
  - Indices for five broad categories (verbatim):
    - 푆푁퐹푅푆_푓푙푒푥푖푏푖푙푖푡푦 = 푆푁퐹푅푆_푎2 + 푆푁퐹푅푆_푎7
    - 푆푁퐹푅푆_푠푡푎푡푢푡표푟푦 푏푎푠푒 = 푆푁퐹푅푆_푎1
    - 푆푁퐹푅푆_푚표푛푖푡표푟푖푛푔 푎푛𝑑 푒푛푓표푟𝑐푒𝑚푒𝑛𝑡 = 푆푁퐹푅푆_푎3 + 푆푁퐹푅푆_푎4 + 푆푁퐹푅푆_푎5
    - 푆푁퐹푅푆_푚푒푑푖푎 푣푖푠푖푏푖푙푖푡𝑦 = 푆푁퐹푅푆_푎8
    - 푆푁퐹푅푆_푛표푛−푐표푚푝푙𝑖푎푛𝑐𝑒 = 푆푁퐹푅푆_푎6

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1684.pdf*

### 1. FD GMM Estimates of the Fiscal Reaction Function ... ................................................................

### _wp1684 - 1. FD GMM Estimates of the Fiscal Reaction Function ... .........................................................................

### Introduction and context
- The need to put national and subnational fiscal positions on a sound footing gained prominence following the Eurozone debt crisis (OECD, 2014; Lledó and Pereira, 2015).
- Fiscal rules have been associated with a greater probability of stabilizing debt (Molnar, 2012).
- Effectiveness of fiscal rules depends on design characteristics such as sufficient flexibility, an institutional mechanism to check deviations from targets, and an unambiguous link between numerical targets and the ultimate objective (Kumar and others, 2009).
- Debate and empirical work have focused mainly on national fiscal rules; the literature on subnational fiscal rules is largely theoretical and qualitative, with empirical assessments often overlooking vertical fiscal imbalances (VFIs).

### Definition and mechanisms of vertical fiscal imbalances (VFIs)
- A vertical fiscal imbalance occurs when there is a gap between own spending (total spending minus transfers paid) and own revenues (total revenues minus transfers received).
- This gap often arises when devolution of spending responsibilities outpaces devolution of revenue mandates, leaving subnational governments (SNGs) with limited tax autonomy to comply with spending obligations.
- Two channels by which high VFIs may worsen SNG fiscal outcomes:
  - Common-pool problem: SNGs may fail to internalize the full cost of fulfilling spending mandates when financed from own revenues and a common resource pool, potentially leading to overspending (Rodden, 2002).
  - Moral hazard: Insufficient tax autonomy may generate bailout expectations among SNGs unable to fulfill spending obligations, leading to over-borrowing and soft budget constraints (Von Hagen and Eichengreen, 1996).
- Empirical evidence citing a negative relationship between VFIs and fiscal discipline:
  - Asatryan and others (2012) find evidence at the subnational level.
  - Eyraud and Lusinyan (2013) find evidence at the general government level.

### Data coverage and temporal scope (as presented)
- Several figures and series cover the period 1995–2012:
  - "Median Subnational Fiscal Rule Strength in Europe, 1995–2012"
  - "Subnational Fiscal Rule Strength in Europe, 1995–2012"
  - "Evolution of Median VFI Level and Subnational Primary Balances, 1995–2012"
  - "Subnational Primary Balances in Europe, 1995–2012"
  - "Mean SN Primary Balance versus SN Fiscal Rules, 1995–2012"
- Appendices listed include:
  - Appendix 1. Data
  - Appendix 2. The Subnational Fiscal Rule Strength Index

### Empirical focus and methods overview (table of contents entries)
- The content unit includes empirical estimations and robustness checks focused on the interaction of VFI and subnational fiscal rules:
  - FD GMM Estimates of the Fiscal Reaction Function
  - FD GMM Estimates of the VFI Impact on the Effectiveness of SNG Fiscal Rules
  - LSDVC Estimates of the VFI Impact on the Effectiveness of SNG Fiscal Rules
  - Robustness Check 1—FD GMM Estimates of the VFI Impact on the Effectiveness of SNG Fiscal Rules
  - Robustness Check 2—FD GMM Estimates of the VFI Impact on the Effectiveness of SNG Fiscal Rules
  - Robustness Check 3—FD GMM Estimates of the VFI Impact on the Effectiveness of SNG Fiscal Rules—Augmented Model

### Key analytical implications (from the presented exposition)
- The presence and magnitude of VFIs are central to understanding the discipline-enhancing effect of subnational fiscal rules.
- High VFIs can undermine subnational fiscal discipline through common-pool and moral hazard channels, suggesting that fiscal-rule design and intergovernmental fiscal frameworks must address VFIs to improve effectiveness.
- Improving the effectiveness of fiscal rules at both national and subnational levels is critical for fiscal consolidation strategies and reforms to EU fiscal governance (Andrle and others, 2015).

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1684.pdf*

### section III.B).

### _wp1684 - section III.B)

### Main contributions and empirical findings
- Main contribution: closes a gap in the empirical literature by evaluating the impact of subnational fiscal rules on fiscal balances and assessing how they operate at varying levels of VFIs.
- Methodological contribution: addresses endogeneity of subnational fiscal rules using national political variables as external instruments in a first difference GMM framework while maintaining a dynamic specification (including a lagged dependent variable). This builds on Foremny (2014) but uses external instruments in FD GMM.
- Key empirical findings:
  - Stronger fiscal rules (larger values for the overall fiscal rule strength index) and better design characteristics (larger values for specific design attribute indices) have a positive effect on subnational primary balances.
  - The disciplining effect of the non-compliance and flexibility attributes appears larger in magnitude than other attributes; the statutory base index also follows closely in several specifications.
  - The interaction between rule strength indices and VFIs is negative and statistically significant across a range of specifications and estimators: the marginal impact of fiscal rules on subnational primary balance falls as VFIs rise.
  - For high levels of VFIs (i.e., if the ratio of revenue to expenditure decentralization falls below the threshold of 0.5), the point estimate of the marginal impact of the strength of subnational rules on subnational primary balance falls below zero; however, the estimate is not statistically different from zero at such high VFI levels, indicating subnational fiscal rules may cease to be effective when VFIs are high.

### Hypotheses tested
- Hypothesis 1: Subnational government fiscal discipline increases with rule strength.
- Hypothesis 2: The effectiveness of stronger subnational fiscal rules in promoting fiscal discipline at the subnational level diminishes as VFIs rise.

### Theoretical rationale and mechanisms
- Soft budget constraints (SBCs) at the subnational level arise from:
  - The common-pool nature of resources financing subnational spending, which prevents SNGs from fully internalizing the cost of public expenditure and leads to over-spending and over-borrowing.
  - Moral hazard when the central government fails to commit credibly not to bail out SNGs; moral hazard intensifies after a history of bailouts and when SNGs are economically or politically too sensitive to fail.
- Large VFIs undermine SNG fiscal discipline through two channels:
  - Intensifying transfer dependency and common-pool financing, reducing the economic and political cost to SNGs of fulfilling spending mandates and inducing overspending.
  - Raising bailout expectations and moral hazard, making it costlier for the central government to commit to a non-bailout policy and harder to enforce fiscal rules.

### Measurement and data highlights
- Sample: 26 European countries, 1995–2012.
- VFIs measured as the share of subnational own spending not financed through own revenues.
- Footnote definition preserved verbatim:
  - VFIs are defined as [1− Own Revenue / Own Spending], which can be shown to be equivalent to [1− Revenue Decentralisation / Expenditure Decentralisation (1−GG Deficit)]. Here, own revenue (spending) corresponds to total subnational revenue (spending) minus transfers received by the central government and other public entities (transfer paid to the central government and other public entities). Revenue (expenditure) decentralization corresponds to the share of own revenue (own spending) to general government total revenue (general government total spending). GG deficit is the overall fiscal deficit of the general government as a share of general government total spending.
- Stylized facts in Europe:
  - Number of subnational rules in the region more than doubled between 1995 and 2012.
  - Most adopted rules were either budget balance or debt rules, usually imposed by the center and adopted alongside national fiscal rules.
  - Median EU SNG primary balance fell from a surplus of 0.2 percent of GDP to a deficit of almost 0.5 percent of GDP in 2009.
  - Median level of VFI rose by almost a third over the last two decades (1995–2012).
  - Median subnational fiscal rule strength increased steadily for the median EU country over the period, except for 2009 when some countries suspended rules in response to the global financial crisis.

### What makes subnational fiscal rules effective (design and institutional preconditions)
- Design attributes that increase rule strength by raising political cost of reneging:
  - Increasing rule coverage to encompass the consolidated public sector limits creative accounting.
  - Legal basis: embedding rules in constitutional or high-level legislation makes them harder to modify.
  - Quality of monitoring and enforcement mechanisms: independent monitoring bodies, automatic corrective mechanisms, and sanctions.
  - Media visibility: high visibility can induce compliance even without strong legal basis or enforcement.
  - Flexibility (cyclical adjustments and escape clauses): ambiguous net effect — can reinforce discipline in good times but relax nominal targets in bad times; well-defined escape clauses may minimize deviations.
- Institutional/PFM preconditions:
  - Sound and uniform subnational PFM procedures: shared medium- and long-term fiscal objectives, shared macroeconomic assumptions, timely in-year fiscal reports and annual accounts with independent external audits, common budget classification and accounting standards.
  - Flaws in the intergovernmental fiscal framework (ill-designed transfer systems, mismatches between revenue and spending responsibilities, unclear or unfunded mandates) can undermine rule effectiveness regardless of rule design.

### Policy-relevant implications from the analysis
- Strengthening the design attributes of subnational fiscal rules (coverage, legal basis, monitoring/enforcement, visibility) can improve subnational primary balances where VFIs are not excessively large.
- However, the intergovernmental fiscal framework—particularly the degree of VFIs—is a crucial determinant of whether subnational fiscal rules succeed in fostering fiscal discipline.
- When VFIs are high (ratio of revenue to expenditure decentralization below 0.5), subnational fiscal rules may become ineffective; policy responses should therefore consider:
  - Reducing VFIs by increasing subnational tax autonomy or restraining access to soft financing.
  - Complementing rule design improvements with reforms to intergovernmental transfers and PFM procedures to align incentives and harden subnational budget constraints.

*Source: _wp1684 - section III.B).*

### Appendix 1 defines all variables used in the empirical analysis and identifies their sources. Data on political

### _wp1684 - Appendix 1 defines all variables used in the empirical analysis and identifies their sources. Data on political

### Empirical model and data
- Dynamic panel specification (equation (1)):
  - SNPB_it = α SNPB_i,t−1 + β SNFRSI_a,it + γ SNFRSI_a,it * VFI_it + δ X_it + η_i + ρ_t + ε_it, i=1,...,N; t=1,...,T
  - SNPB denotes the sum of primary balances of all SNGs within a country, as percent of GDP.
  - SNFRSI_a is the strength index for attribute a of subnational fiscal rules (overall index, statutory base, monitoring and enforcement, non-compliance, media visibility, flexibility).
  - X includes output gap (national output gap as proxy for subnational output gap) and percent of population above the age of 65.
  - VFI denotes vertical fiscal imbalances.
  - Model includes country fixed effects (η_i) and time fixed effects (ρ_t).
- Sample limitation: political institutions data available up to 2012, limiting the sample to this year range.
- Sample size reported in regressions: Number of Observations = 321 (in most FD GMM specifications); 347 in LSDVC reported tables.

### Estimation framework
- Primary estimators:
  - First-difference Arellano-Bond (1991) GMM estimator — FD GMM (baseline).
  - Bias corrected Least Squares Dummy Variable — LSDVC (robustness).
- Instrument strategy for FD GMM:
  - Internal instruments: lags t−3 and t−4 of variables only.
  - External instruments: dummy for central legislative elections; Herfindahl index of government fragmentation.
  - Instruments collapsed using Roodman’s xtabond2 collapse option to limit instrument count.
  - Instruments count examples: Instruments = 28 (Table 1), Instruments = 30 (Tables 2, 4, 5), Instruments = 36 (Table 6).
- Rationale:
  - FD GMM addresses dynamic panel bias and reverse causality; external instruments exploit national-level political variables that influence rule strength but are argued to be exogenous to subnational fiscal shocks.
  - LSDVC corrects small-sample bias but does not address endogeneity; used as a robustness check.

### Baseline FD GMM results (high-level)
- General finding: stronger subnational fiscal rules are associated with improved subnational primary balances; interaction with VFI shows diminishing effectiveness as VFIs rise.
- Table 1 (FD GMM without interaction):
  - Lagged dependent variable coefficients ~ 0.101–0.161 across specifications (standard errors ~ 0.10–0.13).
  - Overall SNFRSI coefficient: 0.032* (standard error 0.02) — significant at 10% in column (1).
  - Sub-indices (statutory base, monitoring and enforcement, media visibility, flexibility) coefficients ~ 0.029–0.032* (standard error 0.02) — mostly significant at 10%.
  - Non-compliance sub-index: 0.048*** (standard error 0.02) — significant at 1%.
  - Controls:
    - Output Gap: -0.001* to -0.001** (standard errors 0.00).
    - Population > 65: 0.008–0.014 (mostly significant at 10%).
  - Number of Observations = 321; Instruments = 28.
  - m1 and m2 tests reported (e.g., m1 = -2.02, m2 = 0.16 in column (1)); Hansen test statistics reported.

- Table 2 (FD GMM with SNFRSI * VFI interaction):
  - Lagged dependent variable coefficients ~ 0.075–0.118 (standard errors ~ 0.08–0.10).
  - Overall SNFRSI: 0.064** (standard error 0.03).
  - Overall*VFI: -0.114* (standard error 0.06).
  - Statutory Base: 0.072**; Statutory Base*VFI: -0.143** (standard error 0.07).
  - Monitoring and Enforcement: 0.056**; Monitoring and Enforcement*VFI: -0.104* (standard error 0.06).
  - Non Compliance: 0.087**; Non Compliance*VFI: -0.136* (standard error 0.07).
  - Media Visibility: 0.062**; Media Visibility*VFI: -0.111* (standard error 0.06).
  - Flexibility: 0.076**; Flexibility*VFI: -0.130** (standard error 0.06).
  - VFI main effect: 0.021–0.031 (mostly not statistically significant).
  - Output Gap: -0.001*** to -0.001** (standard errors 0.00).
  - Population > 65: 0.003–0.009 (some significance at 5%–10%).
  - Number of Observations = 321; Instruments = 30.
- Key quantitative interpretation:
  - "The estimated SNFRSI regression coefficient implies that a 10 percent increase in the overall SNFRSI would raise subnational primary balance by 0.63 percent of GDP."
  - Marginal effect of SNFRSI on SNPB (∂SNPB/∂SNFRSI) falls as VFI rises; marginal effect becomes negative when VFI > 0.5 (i.e., when the ratio between revenue and expenditure decentralization falls below 0.5).

### Robustness checks
- LSDVC estimates (Table 3):
  - Coefficients on overall index and attribute sub-indices positive and statistically significant.
  - Interaction terms SNFRSI*VFI remain negative and significant.
  - Point estimates roughly half the size of FD GMM estimates (example lagged dependent variable = 0.364***; Overall = 0.020*; Overall*VFI = -0.049**).
  - Number of Observations = 347 (bootstrap variance-covariance with 1000 repetitions).
- Alternative dependent variables:
  - Table 4: Dependent variable = Subnational Overall Balance/GDP. Coefficients and signs comparable to baseline; Overall = 0.060**; Overall*VFI = -0.107*.
  - Table 5: Dependent variable = Subnational Primary Balance as Percent of Subnational Revenue. Much larger magnitudes (normalization by subnational revenue). Examples:
    - Overall = 0.454** (standard error 0.19); Overall*VFI = -0.729** (standard error 0.35).
    - Non Compliance = 0.576***; Non Compliance*VFI = -0.896*.
  - Table 6: Augmented model adding Expenditure Decentralization, CPI Inflation, Unemployment:
    - Overall = 0.061**; Overall*VFI = -0.115**.
    - Expenditure Decentralization coefficients ~ -0.045 to -0.052 (not significant).
    - CPI Inflation and Unemployment coefficients ~ -0.0001 to -0.0003 (not significant).
    - Instruments = 36; Number of Observations = 321.

### Interpretation of main findings (numeric and qualitative)
- Finding 1: Stronger subnational fiscal rules improve subnational fiscal balances.
  - Positive coefficients on overall SNFRSI and most attribute indices across estimators.
  - Example: SNFRSI effect — 10 percent increase in overall SNFRSI → SNPB +0.63 percent of GDP.
  - Non-compliance and flexibility attributes show relatively larger coefficient magnitudes in several specifications.
- Finding 2: Effectiveness of subnational fiscal rules diminishes as VFIs rise.
  - Interaction terms SNFRSI*VFI negative and significant across FD GMM specifications and robust to LSDVC.
  - Marginal effect of SNFRSI on SNPB becomes negative when VFI > 0.5 (i.e., expenditure decentralization more than twice revenue decentralization).
  - VFI main effect generally positive but often insignificantly different from zero in baseline specifications.
- Additional quantitative notes:
  - Correlation among attribute indices: correlation coefficients among all attributes are above 0.8; principal component alternative index captures more than 80 percent of variance.

### Policy implications and recommendations (as stated)
- Reforms to strengthen rule design:
  - Address weaknesses in rule design (statutory base, monitoring and enforcement, non-compliance, media visibility, flexibility) to increase discipline-enhancing impact.
- Address vertical fiscal imbalances:
  - Consider reforms to reduce excessive VFIs; align subnational revenue and expenditure mandates.
  - Where expenditure decentralization is more than twice revenue decentralization (VFI > 0.5), subnational fiscal rules may cease to be effective; aligning revenue assignments could be considered a prerequisite for effective rules.
- Complementary reform sequencing:
  - Independent reforms to eliminate excessive VFIs are particularly critical in fiscally decentralized countries and federations, because high VFIs undermine the effectiveness of rules even when those rules are strong.

*Source: _wp1684 - Appendix 1 defines all variables used in the empirical analysis and identifies their sources. Data on political (IMF working paper content provided).*

### Appendix 1. Data

### Appendix 1. Data

### Sample Coverage
- Sample period: 1995 to 2012.
- Countries included (26): Austria, Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, and the United Kingdom.
- Note on Croatia: Data for Croatia is available from 2002 leading to only 11 observations in total for this country.
- Total sample observations: The sample has 461 observations.

### Data Sources and Variable Definitions
- Data compiled from multiple sources; Table A1 defines variables and identifies sources.
- Variables and their definitions (verbatim as in source):
  - Subnational primary balance (SNPB): (Subnational Total Revenue - Subnational Total Expenditure - Subnational Interest Expenditure)/Gross Domestic Product
    - Source: Authors' own consolidation of total revenue and expenditures across local and (when applicable) state or regional governments using non-consolidated fiscal data from Eurostat.
  - Subnational overall balance: (Subnational Total Revenue - Subnational Total Expenditure)/Gross Domestic Product
    - Source: Authors' own consolidation of total revenue and expenditures across local and (when applicable) state or regional governments using non-consolidated fiscal data from Eurostat.
  - Vertical Fiscal Imbalances (VFIs): 1-(Subnational government own revenue/Subnational government own expenditure)
    - Source: Authors' own consolidation of total own revenue and own expenditures across local and (when applicable) state or regional governments using non-consolidated fiscal data from Eurostat.
  - Output Gap: Actual - Potential GDP as percent of Actual GDP
    - Source: World Economic Outlook
  - Population > 65: Percent of population above the age of 65
    - Source: World Development Indicators
  - Expenditure Decentralization: Share of sub-national expenditures in general government expenditures
    - Source: Authors' own consolidation of total expenditures across local and (when applicable) state or regional governments using non-consolidated fiscal data from Eurostat.
  - Unemployment
    - Source: World Economic Outlook
  - Consumer Price Inflation (CPI)
    - Source: World Economic Outlook
  - Legislative election dummy: Dummy variable = 1 if national legeslative election held int hat year and zero otherwise
    - Source: Database for Political Institutions (DPI) from Beck et al. (2001)
  - Herfindahl Index of Government Fragmentation: The sum of the squared seat shares of all parties in the government
    - Source: Database for Political Institutions (DPI) from Beck et al. (2001)

### Summary Statistics (Table A2 — verbatim entries)
- SNPBOverall-0.001640.0069-0.05270.0543N =     461
  - Between0.0025-0.07140.0034T =      26
  - Within0.0064-0.04570.0533
- SNFRSIOverall0.217070.19430.00001.0000N =     461
  - Between0.16740.00270.7110T =      26
  - Within0.1041-0.14520.5363
- VFIsOverall0.486150.18092-0.020420.85991N =     460
  - Between0.145580.205730.70334T =      26
  - Within0.10999-0.009720.80137
- Population > 65Overall15.624532.126710.835121.1009N =     461
  - Between1.903511.256818.9956T =      26
  - Within1.007912.867018.5678
- Output GapOverall0.153023.3668-13.495617.5160N =     434
  - Between0.9374-2.41522.2387T =      26
  - Within3.2465-11.401215.6984
- Overall-1.5316446.558-999.0001.000N =     461
  - Between10.921-55.0301.000T =      26
  - Within45.289-945.50154.499
- Herfindahl Index of Government frgmentation

### Appendix 2 — The Subnational Fiscal Rule Strength Index (SNFRSI)
- Source dataset: European Commission (EC) dataset of domestic fiscal rules (includes numerical fiscal rules in force since 1990 across EU countries).
- Covered rule types: budget balance rule (BBR), debt rule (DR), expenditure rule (ER), revenue rules (RR).
- Government levels considered: central (CG), regional (RG), local (LG), general government (GG), and social security (SS).
- EC dataset provides: overall strength score for each rule and separate scores for rule design attributes.

- Attributes collected for each subnational rule and scoring scheme (verbatim):
  - Attribute 1 (a1): Statutory/legal base of the rule
    - 4 constitutional base
    - 3 the rule is based on a legal act (e.g., Public finance Act, Fiscal Responsibility Law)
    - 2 the rule is based on a coalition agreement or an agreement reached by different general government tiers (and not enshrined in a legal act)
    - 1 political commitment by a given authority (central/local government, minister of finance)
  - Attribute 2 (a2): Adjustment margin
    - 3 there is no margin for adjusting objectives (they are encapsulated in the document underpinning the rule)
    - 2 there is some but constrained margin in setting or adjusting objectives
    - 1 there is complete freedom in setting objectives (the statutory base of the rule merely contains broad principles or the obligation for the government or the relevant authority to set targets)
  - Attribute 3 (a3): Nature of the body in charge of monitoring rule compliance
    - 3 monitoring by an independent authority (Fiscal Council, Court of Auditors or any other Court) or the national Parliament
    - 2 monitoring by the ministry of finance or any other government body
    - 1 no regular public monitoring of the rule (there is no report systematically assessing compliance)
  - Attribute 4 (a4): Existence of alert mechanisms
    - We augmented the score of this sub-criterion by 1 if there is real-time monitoring of compliance with the rule, i.e., if alert mechanisms of the risk of non-respect exist.
  - Attribute 5 (a5): Nature of the body in charge of enforcing the rule
    - 3 enforcement by an independent authority (Fiscal Council or any Court) or the national Parliament
    - 2 enforcement by the ministry of finance or any other government body
    - 1 no specific body in charge of enforcement
  - Attribute 6 (a6): Enforcement mechanisms of the rule
    - 4 there are automatic correction and sanction mechanisms in case of non-compliance
    - 3 there is an automatic correction mechanism in case of non-compliance and the possibility of imposing sanctions
    - 2 the authority responsible is obliged to take corrective measures in case of non-compliance or is obliged to present corrective proposals to Parliament or the relevant authority
    - 1 there are no ex-ante defined actions in case of non-compliance
  - Attribute 7 (a7): Existence of Escape Clause
    - We augmented the score of this variable by 1 if escape clauses are foreseen and clearly specified.
  - Attribute 8 (a8): Media visibility of the rule
    - 3 observance of the rule is closely monitored by the media; non-compliance is likely to trigger public debate
    - 2 high media interest in rule compliance but non-compliance is unlikely to invoke public debate
    - 1 no, or modest interest of the media

- SNFRSI construction (verbatim equations and description):
  - We constructed a SNFRSI for each attribute a and rule type j in country i at time t. We did that by aggregating the product of rule j attribute strength and its coverage over each subnational government levels l to which rule j applies — S_alc(j) and c(j), respectively — weighted by the share of public spending of this government level l (G_l) in the total public spending of all government levels covered by the rule (G_c(j)), as summarized in equation (A2.1).
  - Equation (A2.1):
    - 푆푁퐹푅푆_푎푗 = ∑_{l∈{LG,RG}} 푤_{l c(j)} × c(j) × 푆_{a l c(j)}
    - Where a∈{a1...a8}; j∈{BBR,DR,ER,RR}; a and c(j)∈{GG,RG,LG,(RG,LG),(CG,RG,LG)}
    - And where 푤_{l c(j)} = { 1 if c(j) ∈ {RG} or {LG} ; (G_l / G_{c(j)}) if c(j) ∈ {GG, (RG,LG), (CG,RG,LG)} }
  - An SNFRSI is then computed for each attribute a by aggregating 푆푁퐹푅푆_푎푗 over all rules applicable to subnational governments, as summarized in equation (A2.2).
  - Equation (A2.2):
    - 푆푁퐹푅푆_푎 = ∑_j 푆푁퐹푅푆_푎푗
  - Lastly, SNFRSI indices for five broad categories were calculated as follows (verbatim):
    - 푆푁퐹푅푆_푓푙푒푥푖푏푖푙푖푡푦 = 푆푁퐹푅푆_푎2 + 푆푁퐹푅푆_푎7
    - 푆푁퐹푅푆_푠푡푎푡푢푡표푟푦 푏푎푠푒 = 푆푁퐹푅푆_푎1
    - 푆푁퐹푅푆_푚표푛푖푡표푟푖푛푔 푎푛𝑑 푒푛푓표푟𝑐푒𝑚푒𝑛𝑡 = 푆푁퐹푅푆_푎3 + 푆푁퐹푅푆_푎4 + 푆푁퐹푅푆_푎5
    - 푆푁퐹푅푆_푚푒푑푖푎 푣푖푠푖푏푖푙푖푡푦 = 푆푁퐹푅푆_푎8
    - 푆푁퐹푅푆_푛표푛−푐표푚푝푙𝑖푎푛𝑐푒 = 푆푁퐹푅푆_푎6

*Appendix 1. Data (from _wp1684 - Appendix 1. Data)*

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