## _wp10248

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---

### Background on Fiscal Responsibility Laws (FRLs)
- FRLs are enacted as permanent institutional devices to enhance the credibility, predictability, and transparency of fiscal policy.
- FRLs generally combine:
  - procedural rules to strengthen fiscal transparency and budget management, and
  - numerical fiscal rules such as ceilings on fiscal deficits and public debt to impose fiscal discipline.
- FRLs differ from stand-alone numerical fiscal rules; FRLs provide a comprehensive framework in a single piece of legislation.
- New Zealand adopted an FRL in 1994 with a strong emphasis on transparency requirements.
- FRLs have been implemented in several countries in Latin America, Europe, and Asia.

### Research question and motivation
- Main question: Can FRLs be linked to structural breaks in both the level and volatility of fiscal balances?
- Focus: primary fiscal balances (percent of GDP) and fiscal volatility; the paper does not analyze other potential effects of FRLs (accountability, transparency, quality of fiscal policies).
- Sample includes: Argentina, Australia, Brazil, Colombia, Ecuador, New Zealand, Peru, United Kingdom.
- Empirical models control for business and commodity cycles (output gap and country-specific commodity price index, ICP).

### Methodology
- Key econometric approaches used to address unknown break timing:
  - Quandt-Andrews sequential estimation of structural breaks (evaluate Chow statistic over candidate dates; sequentially estimate breakpoints).
  - Markov Switching models (simultaneous estimation of regime-dependent conditional mean and variance; transition probabilities estimated by Maximum Likelihood).
- Conditional mean specification (equation [1]):
  - Surplus_t = a0 + a1 ICP_t + a2 Gap_t + u_t
  - Surplus: primary balance in percent of GDP.
  - Gap: output gap (%) (percentage deviation of real GDP from potential GDP).
  - ICP: country specific commodity price index (log index standardized by z-score).
- Data frequency and transformations:
  - Quarterly data; potential GDP estimated using HP filter with Lambda = 1600.
  - ICP standardized via z-score.
  - New Zealand: overall fiscal balance used instead of primary balance; quarterly series constructed by linear interpolation where necessary.
- Practical exclusion rule for candidate break dates: common practice—every break at least 15 percent of the sample size apart (authors also checked 10 percent and obtained essentially the same results).

### Key findings — overall
- Significant structural breaks in fiscal performance found in several countries, but in most cases these breaks preceded the adoption of the FRL.
- Fiscal volatility declined in most countries for at least some period of time.
- Only in New Zealand did the improvement in fiscal volatility coincide with the introduction of the FRL (volatility break detected in 1994Q2).
- Only in Australia did the FRL introduction correspond exactly to a structural break in the level of primary fiscal balances (FRL date 1998Q2; Chow tests significant).
- For Brazil, Colombia, and the United Kingdom, structural breaks occurred sometime before the introduction of the FRL.
- Conclusion: Difficult to link improvements in fiscal performance directly to FRL adoption; FRLs often appear to have been introduced once fiscal discipline strengthening was already underway.

### Traditional FRL-dummy regressions — selected coefficient estimates (Primary Fiscal Balance, percent of GDP)
- Argentina (FRL date 1999Q4): Constant -1.226** ; Output gap -0.043 ; ICP 1.037** ; FRL dummy -0.895.
- Argentina (alternate; FRL date 2001Q3): Constant -1.577*** ; Output gap -0.040 ; ICP 0.987* ; FRL dummy -0.349.
- Australia (FRL date 1998Q2): Constant -0.056 ; Output gap 0.468*** ; ICP 0.422** ; FRL dummy 1.415***.
- Brazil (FRL date 2000Q2): Constant 1.072*** ; Output gap -0.111** ; ICP 0.252*** ; FRL dummy 1.036***.
- Colombia (FRL dates 2000Q4 and 2003Q3): Constants -1.441*** and -1.349*** ; Output gaps 0.025 and 0.026 ; ICPs 0.703*** and 0.325* ; FRL dummies 0.841*** and 1.208***.
- Ecuador (FRL dates 2002Q4 and 2005Q2): Constants 4.973*** and 4.394*** ; Output gaps 0.046 and -0.060 ; ICPs 0.450 and 1.000 ; FRL dummies -1.420* and -1.939.
- New Zealand (FRL date 1994Q2; overall balance used): Constant 1.033* ; Output gap -0.265 ; ICP -0.778* ; FRL dummy 5.114***.
- Peru (FRL dates 1999Q4 and 2003Q2): Constants 0.319* and -0.022 ; Output gaps 0.033 and 0.100* ; ICPs 1.350*** and 1.150*** ; FRL dummies -0.422* and 0.316.
- United Kingdom (FRL date 1998Q4): Constant 0.977*** ; Output gap 0.476*** ; FRL dummy -0.655.
- Significance notation: * 10%; ** 5%; *** 1%.

### Chow tests at FRL dates — selected statistics (null: no break at specified breakpoints)
- Argentina (1999Q4): F-statistic 0.794, Prob. 0.502; Log likelihood ratio 2.588, Prob. 0.460; Wald 2.383, Prob. 0.497.
- Argentina (2001Q3): F-statistic 1.934, Prob. 0.135; Log likelihood ratio 6.116, Prob. 0.106; Wald 5.801, Prob. 0.122.
- Australia (1998Q2): F-statistic 22.621, Prob. 0.000; Log likelihood ratio 57.365, Prob. 0.000; Wald 67.864, Prob. 0.000.
- Brazil (2000Q2): F-statistic 52.508, Prob. 0.000; Log likelihood ratio 72.775, Prob. 0.000; Wald 157.525, Prob. 0.000.
- Colombia (2000Q4): F-statistic 7.161, Prob. 0.001; Log likelihood ratio 19.952, Prob. 0.000; Wald 21.484, Prob. 0.000.
- Colombia (2003Q3): F-statistic 10.206, Prob. 0.000; Log likelihood ratio 26.588, Prob. 0.000; Wald 30.619, Prob. 0.000.
- Ecuador (2002Q4): F-statistic 12.808, Prob. 0.000; Log likelihood ratio 30.247, Prob. 0.000; Wald 38.424, Prob. 0.000.
- Ecuador (2005Q2): F-statistic 1.308, Prob. 0.288; Log likelihood ratio 4.370, Prob. 0.224; Wald 3.925, Prob. 0.270.
- New Zealand (1994Q2): F-statistic 25.507, Prob. 0.000; Log likelihood ratio 57.720, Prob. 0.000; Wald 76.521, Prob. 0.000.
- Peru (1999Q4): F-statistic 2.565, Prob. 0.066; Log likelihood ratio 8.037, Prob. 0.045; Wald 7.696, Prob. 0.053.
- United Kingdom (1998Q4): F-statistic 3.749, Prob. 0.026; Log likelihood ratio 7.511, Prob. 0.023; Wald 7.498, Prob. 0.024.

### Quandt-Andrews sequential estimation — key stylized results
- Procedure: estimate conditional mean regression, obtain residuals û_t, use û_t^2 to detect volatility breaks sequentially; alternative specification allows breaks in conditional mean first and then tests volatility.
- Volatility findings (selected examples):
  - New Zealand, Peru, United Kingdom: volatility initially increased after first break, then fell after second break.
  - Argentina, Australia, Ecuador: volatility continuously decreasing after each break.
  - Colombia: no change in fiscal volatility detected.
  - Most volatility breaks precede FRL dates; New Zealand exception (volatility break 1994Q2 coincides with FRL).
- Conditional mean breaks (examples):
  - Australia: structural break coincides exactly with FRL adoption date.
  - Colombia: break one quarter before FRL.
  - Brazil and United Kingdom: breaks precede FRL by a few quarters.
  - Peru: traditional FRL-dummy suggested worsening after first FRL, but Quandt-Andrews found no mean break—only volatility break.

### Conditional variance (Model 1) — selected periodized constants and Q-A statistics
- Argentina Period constants: Period 1 (93Q4-95Q3) Constant 40.426** ; Period 2 (96Q1-97Q2) Constant 9.868*** ; Period 3 (97Q4-08Q4) Constant 1.737***.
- Australia Period constants: Period 1 (74Q3-77Q1) Constant 9.806*** ; Period 2 (77Q3-01Q4) Constant 2.369*** ; Period 3 (02Q2-09Q2) Constant 0.870***.
- Brazil Period constants: Period 1 (97Q4-98Q4) Constant 1.865*** ; Period 2 (99Q2-08Q4) Constant 0.103*** ; Period 3 (06Q2-08Q4) Constant 0.804*.
- Sample Quandt-Andrews statistics (examples):
  - Argentina Q-A statistic 46.772, p-value 0.0000 (break dates 1995Q3 and 1997Q3 reported).
  - Australia Q-A statistic 81.437, p-value 0.0000 (break dates 1977Q2 and 2002Q1 reported).
  - Brazil Q-A statistic 301.690, p-value 0.0000 (break date 1999Q1).

### Primary Fiscal Balance — Model 2 (selected periodized coefficients and Q-A statistics)
- Argentina:
  - Period 1 (93Q4-95Q3) Constant 14.624* ; Output gap -0.316 ; ICP -41.467 ; Break date 1995Q4 ; Q-A statistic 29.529, p-value 0.0001.
  - Period 2 (96Q1-02Q3) Constant -3.693*** ; Output gap 0.068*** ; ICP -1.025*** ; Break date 2002Q4 ; Q-A statistic 92.187, p-value 0.0000.
  - Period 3 (03Q1-08Q4) Constant 0.817** ; Output gap 0.324*** ; ICP -1.209***.
- Australia:
  - Period 1 (74Q3-85Q4) Constant -1.637*** ; Period 2 (86Q2-98Q1) Constant 0.333 ; Output gap 0.284* ; Break date 1986Q1 ; Q-A statistic 43.337, p-value 0.0000.
  - Period 3 (98Q3-09Q2) Constant 1.534*** ; Output gap 0.814***.
- Brazil:
  - Period 1 (97Q4-99Q1) Constant 0.599*** ; Output gap -0.098 ; ICP 2.420*** ; Break date 1999Q2 ; Q-A statistic 67.449, p-value 0.0000.
  - Period 2 (99Q3-05Q4) Constant 2.153*** ; Output gap -0.095*** ; ICP 2.686*** ; Break date 2006Q1 ; Q-A statistic 13.378, p-value 0.0969.
  - Period 3 (06Q2-08Q4) Constant 0.684** ; Output gap -0.182** ; Q-A statistic 14.029, p-value 0.0595.
- New Zealand: periodized results use overall fiscal balance; break dates include 1992Q4, 1995Q4, 2002Q4 with Q-A statistic 26.980, p-value 0.0002 (example).

### Markov Switching model — setup and advantages
- Specification:
  - Surplus_t = a0_{S_t} + a1_{S_t} ICP_t + a2_{S_t} Gap_t + ε_t
  - S_t ∈ {1,...,N} is a state; ε_t ~ N(0, Ω_{S_t}) where variance depends on regime.
  - Transition probabilities P(s_t = j | s_{t-1} = i) form an N-state Markov chain; parameters estimated by Maximum Likelihood.
- Advantages:
  - Simultaneous estimation of mean and variance regime shifts.
  - Can detect breaks at consecutive data points.
  - Returns a probability of being in each regime at every date.

### Markov Switching results — regime probabilities and selected parameter estimates
- Regime probabilities (reported):
  - Regime 1 probability: Argentina 0.29 ; Australia 0.48 ; Brazil 0.79 ; Colombia 0.51 ; Ecuador 0.85 ; New Zealand 0.26 ; Peru 0.64 ; United Kingdom 0.40.
  - Regime 2 probability: Argentina 0.71 ; Australia 0.52 ; Brazil 0.21 ; Colombia 0.49 ; Ecuador 0.15 ; New Zealand 0.74 ; Peru 0.36 ; United Kingdom 0.60.
- Selected parameter estimates by regime (preserve reported values):
  - Argentina:
    - Regime 1: Constant 0.977*** ; Output gap -0.182*** ; ICP -0.660*** ; Residuals’ variance 0.022.
    - Regime 2: Constant -3.031*** ; Output gap 0.018 ; ICP 0.704*** ; Residuals’ variance 1.064.
  - Australia:
    - Regime 1: Constant 1.693*** ; Output gap 0.612*** ; ICP 0.192** ; Residuals’ variance 0.573.
    - Regime 2: Constant -1.035*** ; Output gap 0.210*** ; ICP 1.230*** ; Residuals’ variance 1.532.
  - Brazil:
    - Regime 1: Constant 2.078*** ; Output gap -0.063** ; ICP 0.322*** ; Residuals’ variance 0.052.
    - Regime 2: Constant 0.562*** ; Output gap -0.304*** ; ICP 1.279*** ; Residuals’ variance 0.080.
  - New Zealand:
    - Regime 1: Constant 5.376*** ; Output gap 0.820*** ; ICP -1.485*** ; Residuals’ variance 0.202.
    - Regime 2: Constant 2.656*** ; Output gap 0.274 ; ICP -3.636*** ; Residuals’ variance 7.259.
  - United Kingdom:
    - Regime 1: Constant 2.988*** ; Output gap 0.722*** ; Residuals’ variance 0.814.
    - Regime 2: Constant -1.118*** ; Output gap 0.596*** ; Residuals’ variance 2.866.
- Interpretation from figures and probabilities:
  - Developed economies: regime changes tend to track business cycles; State 2 interpreted as “bad regime” (lower primary balances and higher volatility) and probability of State 2 often tracks output gap deterioration.
  - Emerging economies: regime shifts often coincide with consolidations or crises that precede FRL adoption (e.g., Brazil consolidation predates FRL; Argentina captures mid-90s and early-2000s crises).

### Conclusions and policy implications
- Traditional dummy-variable approaches that ignore unknown break timing yield inconsistent and biased estimates when the series contain structural breaks; FRL dummy coefficients may capture unrelated breaks.
- Quandt-Andrews sequential estimation and Markov Switching models produce broadly consistent results: limited empirical evidence that FRLs caused improvements in the level or volatility of primary fiscal balances across the sample.
- Empirical regularity: structural breaks (in level and/or variance) generally occurred before FRL adoption dates in many countries; FRLs often appear to have been adopted once consolidation was already underway.
- FRLs may have functioned to anchor or lock-in earlier consolidation efforts rather than being the primary driver of fiscal improvement.
- Potential additional benefits of FRLs (not tested here) that merit further research:
  - Enhancing transparency and providing guidance in the budget process.
  - Lowering sovereign risk premia and facilitating access to government financing.

### Annex 1 — inconsistent estimation of dummy-variable models in presence of structural breaks (main result)
- True DGP is AR(1) with a true level shift at time 0_t:
  - ttttt uIyy )(1 0 
- If estimation uses a misspecified dummy that places the level shift at a different date 1_t (where 1_t ≠ 0_t and )(),max( 10 TOtt), the OLS estimator for the misspecified dummy coefficient γ̂ need not converge to zero.
- Key asymptotic implication:
  - If )(),max( 10 Tott, then γ̂ →P δ.
  - Interpretation: the estimator γ̂ for a non-existent level shift at the wrong date will asymptotically estimate the true level shift δ (the estimator will generally be different from zero), demonstrating inconsistency of simple dummy-variable estimation when break timing is unknown.

*Source: _wp10248 - Introduction, IMF Working Paper (excerpt).*

### Introduction ...........................................................................................................

### INTRODUCTION

### Background on Fiscal Responsibility Laws (FRLs)
- FRLs are enacted as permanent institutional devices to enhance the credibility, predictability, and transparency of fiscal policy.
- FRLs generally combine:
  - procedural rules to strengthen fiscal transparency and budget management, and
  - numerical fiscal rules such as ceilings on fiscal deficits and public debt to impose fiscal discipline.
- FRLs differ from stand-alone numerical fiscal rules; FRLs provide a comprehensive framework in a single piece of legislation.
- New Zealand adopted an FRL in 1994 with a strong emphasis on transparency requirements.
- FRLs have been implemented in several countries in Latin America, Europe, and Asia.

### Research question and motivation
- Main question: Can FRLs be linked to structural breaks in both the level and volatility of fiscal balances?
- Motivation:
  - Prior literature links the strength of fiscal institutions to better fiscal outcomes, but evidence specifically on FRLs is partial.
  - Fiscal volatility is widely perceived as detrimental to economic growth and welfare; FRLs are often proposed to reduce fiscal volatility.
- The paper focuses on primary fiscal balances and fiscal volatility; it does not analyze other potential effects of FRLs (accountability, transparency, quality of fiscal policies).

### Sample and controls
- Sample includes a wide-ranging set of countries such as Argentina, Australia, Brazil, Colombia, Ecuador, New Zealand, Peru, and the United Kingdom.
- Empirical models control for the effect of business and commodity cycles to capture changes in fiscal performance beyond those explained by economic conditions.

### Methodological challenges and approach
- Traditional econometric approaches to estimate changes in fiscal performance around structural reforms face serious limitations, notably uncertainty about the timing of structural breaks.
  - FRLs may be preceded, accompanied, or followed by complementary reforms; the timing of an FRL's impact is uncertain (e.g., when passed, when legally implemented, or some time before/after).
  - Uncertainty in timing renders traditional structural-break tests biased; the direction of the bias is unknown.
- The paper applies two techniques that account for unknown break timing:
  - the Quandt-Andrews approach to the consistent and sequential estimation of structural breaks; and
  - Markov Switching models.

### Key findings
- Significant structural breaks in fiscal performance were found in several countries, but in most cases these breaks preceded the adoption of the FRL.
- Fiscal volatility declined in most countries for at least some period of time.
- Only in New Zealand did the improvement in fiscal volatility coincide with the introduction of the FRL.
- Only in Australia did the FRL introduction correspond exactly to a structural break in the level of primary fiscal balances.
- For countries such as Brazil, Colombia, and the United Kingdom, structural breaks occurred sometime before the introduction of the FRL.
- Overall conclusion: It is difficult to link improvements in fiscal performance directly to the adoption of an FRL; FRLs often appear to have been introduced once strengthening of fiscal discipline was already underway—likely reflecting political commitment to fiscal prudence that prompted and supported structural reforms, including FRL introduction.

### Literature context and prior findings cited
- Studies linking fiscal institutions to performance include Alesina et al. (1999); Stein et al. (1999); Filc and Scartascini (2005); Von Hagen and Harden (1995); Gleigh (2003); Hallerberg et al. (2007); Alt and Lowry (1994); Poterba (1994); Bohn and Inmann (1996); Kumar et al. (2009).
- Thornton (2009) finds that FRLs have not contributed to improvements in fiscal outcomes using a differences-in-differences approach; this paper notes the importance of correct selection of break dates to avoid estimation bias.
- Evidence that fiscal volatility harms growth: Ramey and Ramey (1995); Fatas and Mihov (2003, 2005); De Ferranti et al. (2000); Perry (2004); Fatas and Mihov (2006).
- Kumar et al. (2009) conclude fiscal rules are often introduced to lock-in earlier consolidation efforts rather than at the beginning of fiscal adjustment processes; Ter-Minassian (2010) and Marcel (2010) suggest fiscal rules may strengthen fiscal discipline in countries with prior trajectories of fiscal responsibility.

### Organization of the paper
- Section II describes traditional approaches to estimating and testing for structural breaks and their drawbacks, and then presents alternative approaches that consider unknown timing of breaks.

*Source: _wp10248 - Introduction, IMF Working Paper (excerpt).*

### Section III discusses the econometric model and data used in the paper. Section IV presents

### _wp10248 - Section III discusses the econometric model and data used in the paper. Section IV presents

### Testing for structural breaks
- Traditional tools:
  - Chow (1960) break test and derivatives are well known but inappropriate when the break timing is unknown because the chi-square critical values used in the standard Chow test are inappropriate.
  - For volatility breaks, Andrews (1993) and Andrews and Ploberger (1994) provide tables of critical values; Hansen (1997) provides a method to calculate the correct p-values.
- Limitations of using a simple FRL dummy:
  - A dummy representing the FRL may be inconsistent if the time series has one or more structural breaks unrelated to the FRL.
  - The FRL dummy can capture effects of other breaks, so the sign and magnitude of the dummy coefficient will vary with the number, magnitude, and direction of structural breaks.
  - These issues persist in panel data models commonly used for fiscal institutions and reforms.
- Approaches for consistent estimation when break timing is unknown:
  - Evaluate the Chow statistic for all possible observations and choose the date that yields the largest value of the Chow test sequence.
  - Quandt-Andrews approach: sequential application of the Chow break test (used in this paper).
  - Markov Switching model: allows simultaneous changes in level and variance and estimates transition probabilities between regimes.
- Practical considerations:
  - Not every sample date can be a candidate break date; researchers impose exclusion criteria (common practice: every break at least 15 percent of the sample size apart from each other and from sample limits; authors also checked 10 percent and obtained essentially the same results).

### Econometric specification and data
- Conditional mean specification (equation [1]):
  - Surplus_t = a0 + a1 ICP_t + a2 Gap_t + u_t
  - Surplus: primary balance in percent of GDP.
  - Gap: output gap (percentage deviation of real GDP from potential GDP).
  - ICP: country specific commodity price index (log index standardized by z-score).
  - u: i.i.d. disturbance; subscript t denotes time index.
- Data frequency and transformations:
  - Quarterly data are used in the analysis (high frequency required for volatility breaks and improves estimator consistency).
  - Potential GDP estimated using a Hodrick-Prescott (HP) filter with Lambda = 1600 (standard for quarterly data).
  - Commodity price index standardized via z-score so mean over entire sample period equals zero.
  - In New Zealand overall fiscal balance used instead of primary balance due to data constraints; quarterly series constructed using linear interpolation from annual accrual data where necessary.
- Sample:
  - Countries: Argentina, Australia, Brazil, Colombia, Ecuador, New Zealand, Peru, United Kingdom.
  - A total of twelve different FRLs analyzed (two for Argentina, Colombia, Ecuador, and Peru where more recent FRLs incorporated important revisions).
  - Data coverage: mostly central government; Brazil uses consolidated public sector; New Zealand and United Kingdom use general government.

### Results — overview
- Section structure:
  - Traditional time series approach with FRL dummy.
  - Quandt-Andrews sequential estimation of structural breaks and Markov Switching models.

### Results — Traditional approach using FRL dummies
- Findings:
  - FRL dummy positive and statistically significant in Australia, Brazil, Colombia, and New Zealand (coefficients suggest effects sizable, with primary fiscal balances increasing by several percentage points of GDP following FRL introduction in some cases).
  - FRL dummy not statistically significant in Argentina and the United Kingdom.
  - In Ecuador and Peru, first FRLs appear to have weakened fiscal balances.
- Caveat:
  - These results are potentially misleading because the FRL dummy may be capturing irregularities or structural breaks in the primary surplus series rather than causal FRL effects.
- Chow break tests around FRL dates:
  - Tests suggest FRL coincided with a structural break in fiscal balances in all countries except Argentina.
  - However, the Chow test is not statistically valid when using an arbitrary break date without accounting for unknown break timing.

### Results — Alternative Approach I: Quandt-Andrews sequential estimation (breaks in level and volatility)
- Model 1 (equations [2] and [3]):
  - Primary regression as in equation [1] to obtain residuals û_t; residuals squared (û_t^2) used as volatility measure in a secondary regression allowing volatility breaks at t0; process repeated sequentially to estimate all volatility breaks.
- Model 2 (equations [4] and [5]):
  - Allows breaks in conditional mean of primary fiscal balance at t1; obtain new residuals v_t from primary regression [4]; v_t^2 used to test for volatility breaks in secondary regression [5].
- Key findings on volatility and mean breaks:
  - Significant volatility breaks found in most countries, generally not coinciding with FRL introduction dates.
  - Examples:
    - New Zealand, Peru, United Kingdom: volatility initially increased after first break, then fell after second break.
    - Argentina, Australia, Ecuador: volatility continuously decreasing after each break.
    - Colombia: no change in fiscal volatility found.
  - Most volatility breaks precede FRL dates; exception: New Zealand volatility break detected in 1994Q2, which corresponds to FRL adoption date.
  - Structural breaks in conditional mean also present in several countries, reinforcing concern that FRL dummies are misleading.
    - Australia: structural break coincides exactly with FRL adoption date.
    - Colombia: break occurs one quarter before FRL.
    - Brazil and United Kingdom: breaks precede FRL by a few quarters (FRLs accompanied consolidation already in place).
  - In Peru, traditional approach suggested lower primary fiscal balances after first FRL, but Quandt-Andrews found no structural break in primary fiscal balance—only in volatility.
- Overall conclusion from Quandt-Andrews:
  - Breaks in level and variance of primary fiscal balance generally preceded FRL adoption dates; limited empirical support that FRLs generally reduced fiscal volatility or made fiscal policy more predictable.

### Results — Alternative Approach II: Markov Switching model
- Model specification (equations [6] and [7]):
  - Surplus_t = a0_{S_t} + a1_{S_t} ICP_t + a2_{S_t} Gap_t + ε_t
  - S_t is a state variable taking N values (N regimes); ε_t ~ N(0, Ω_{S_t}) where variance depends on regime.
  - Transition probabilities P(s_t = j | s_{t-1} = i) form an N-state Markov chain; parameters and Ω_{S_t} estimated by Maximum Likelihood.
- Advantages of Markov Switching:
  - Estimates structural breaks in conditional mean and variance simultaneously.
  - Can handle structural breaks that occur at two successive data points (less dependent on sub-sample degrees of freedom).
  - Returns a probability of being in each regime at every point in time (vs. Quandt-Andrews which assigns probability one over intervals).
- Empirical findings:
  - Results broadly consistent with Quandt-Andrews.
  - Developed countries: regime changes track business cycles without a clear relationship with FRLs.
    - Australia and United Kingdom: probability of being in a different regime tracks output gap fluctuations; large deterioration in output gap tends to transition to State 2 (“bad regime”: lower primary balances and higher volatility).
  - Emerging economies:
    - Brazil: regime shift coincides with consolidation that started before FRL (consistent with Quandt-Andrews).
    - Argentina: regime shifts capture mid-90s and early-2000s crises; a transition to a “good regime” around 2004 as recovery strengthened and output gap closed.
    - Colombia and Peru: FRL adoption does not seem to affect number of transitions to State 2 or probability of being in State 2.
  - Overall: adoption of FRLs does not appear clearly associated with better fiscal outcomes in most countries; often FRLs accompanied a consolidation process already underway.

### Conclusions (Section IV)
- Objective:
  - Evaluate empirically whether FRLs can be linked to changes in fiscal performance using consistent tests for structural breaks.
- Main conclusions:
  - Traditional econometric approaches relying on dummies yield inconsistent and biased estimates when underlying series have structural breaks; dummies may capture time-specific phenomena not contemporaneous to FRLs.
  - Using consistent methods (Quandt-Andrews sequential estimation and Markov Switching models) provides limited empirical evidence linking FRLs to changes in fiscal performance.
  - All sampled countries exhibit one or more structural breaks (in level or variance) of the primary fiscal balance, but generally these breaks did not occur around FRL adoption dates; in several cases breaks preceded FRL adoption.
  - In some cases (Australia, Colombia, New Zealand) timing is reasonably close and FRL adoption seems to have coincided with relative improvement thereafter, but in most cases linking breaks to FRLs is difficult because they occurred years apart.
- Robustness and methodological notes:
  - Quandt-Andrews and Markov Switching results are broadly consistent.
  - Markov Switching can perform simultaneous estimation of mean and volatility regime shifts; Quandt-Andrews requires sufficient observations between breaks but produces sequential change-point estimates.
  - HP filter used for potential GDP with Lambda = 1600 for quarterly data; commodity price index treated as contemporaneous and exogenous due to global determination.

*Source: _wp10248 - Section III discusses the econometric model and data used in the paper. Section IV presents*

### conclusions hold when using the Quandt-Andrews approach to estimate breaks sequentially,

### _wp10248 - conclusions hold when using the Quandt-Andrews approach to estimate breaks sequentially,

### Main conclusions on fiscal responsibility laws (FRLs)
- Using the Quandt-Andrews approach to estimate breaks sequentially or Markov Switching models to detect regime shifts, conclusions are consistent across methods.
- In the developed economies analyzed:
  - Shifts seem to be mainly driven by business cycles.
- In the developing countries in the sample:
  - The fiscal consolidation processes seem to have already been in place before the introduction of the FRLs.
- Overall assessment of FRLs:
  - FRLs may have helped anchor efforts to strengthen fiscal policy, but do not seem to have been the driver of such efforts.
  - Empirical analysis centered on the level and volatility of primary fiscal balances did not show general positive effects of FRLs on those metrics.
  - FRLs could still have positive effects beyond fiscal balances, including:
    - Enhancing transparency and providing guidance in the budget process.
    - Lowering risk sovereign premia and facilitating access to government financing.
  - These additional effects remain areas for further research.

### Data summary (selected metadata from Table 1)
- Countries included (sample excerpts): Argentina, Australia, Brazil, Colombia, Ecuador, New Zealand, Peru, United Kingdom.
- Example FRL adoption dates (as reported):
  - Argentina: 1st FRL date: 1999Q4; 2nd FRL date: 2001Q3.
  - Australia: 1st FRL date: 1998Q2.
  - Brazil: 1st FRL date: 2000Q2.
  - Colombia: 1st FRL date: 2000Q4; 2nd FRL date: 2003Q3.
  - Ecuador: 1st FRL date: 2002Q4; 2nd FRL date: 2005Q2.
  - New Zealand: 1st FRL date: 1994Q2.
  - Peru: 1st FRL date: 1999Q4; 2nd FRL date: 2003Q2.
  - United Kingdom: 1st FRL date: 1998Q4.
- Sample periods and number of observations vary by country (examples preserved in source tables, e.g., Argentina sample period: 93Q4-08Q4, Number of observations: 61; Australia sample period: 74Q3-09Q2, Number of observations: 140).
- For New Zealand, the overall fiscal balance was used due to data constraints; quarterly series were obtained by linear interpolation where necessary.

### Primary Fiscal Balance regressions (Table 2a and 2b) — key coefficients and FRL dummies
- Regression dependent variable: Primary Fiscal Balance (Percent of GDP).
- Selected coefficient estimates (preserve exact values and significance levels as reported):
  - Argentina (Table 2a):
    - Constant: -1.226** ; Output gap: -0.043 ; ICP: 1.037** ; FRL dummy: -0.895 ; FRL date: 1999Q4.
    - Alternate Argentina specification: Constant: -1.577*** ; Output gap: -0.040 ; ICP: 0.987* ; FRL dummy: -0.349 ; FRL date: 2001Q3.
  - Australia: Constant: -0.056 ; Output gap: 0.468*** ; ICP: 0.422** ; FRL dummy: 1.415*** ; FRL date: 1998Q2.
  - Brazil: Constant: 1.072*** ; Output gap: -0.111** ; ICP: 0.252*** ; FRL dummy: 1.036*** ; FRL date: 2000Q2.
  - Colombia (two specifications): Constants: -1.441*** and -1.349*** ; Output gaps: 0.025 and 0.026 ; ICPs: 0.703*** and 0.325* ; FRL dummies: 0.841*** and 1.208*** ; FRL dates: 2000Q4 and 2003Q3.
  - Ecuador (Table 2b): Constants: 4.973*** and 4.394*** ; Output gaps: 0.046 and -0.060 ; ICPs: 0.450 and 1.000 ; FRL dummies: -1.420* and -1.939 ; FRL dates: 2002Q4 and 2005Q2.
  - New Zealand: Constant: 1.033* ; Output gap: -0.265 ; ICP: -0.778* ; FRL dummy: 5.114*** ; FRL date: 1994Q2.
  - Peru (two specifications): Constants: 0.319* and -0.022 ; Output gaps: 0.033 and 0.100* ; ICPs: 1.350*** and 1.150*** ; FRL dummies: -0.422* and 0.316 ; FRL dates: 1999Q4 and 2003Q2.
  - United Kingdom: Constant: 0.977*** ; Output gap: 0.476*** ; ICP: - ; FRL dummy: -0.655 ; FRL date: 1998Q4.
- Significance notation in source: * Significant at the 10% level; ** at the 5% level; *** at the 1% level.

### Structural break tests (Table 3a and 3b — Chow tests)
- Null hypothesis: no breaks at specified breakpoints.
- Selected F-statistics, Log likelihood ratio and Wald statistics and associated p-values (preserve exact reported figures):
  - Argentina (FRL Date 1999Q4): F-statistic 0.794, Prob. 0.502; Log likelihood ratio 2.588, Prob. 0.460; Wald Statistic 2.383, Prob. 0.497.
  - Argentina (FRL Date 2001Q3): F-statistic 1.934, Prob. 0.135; Log likelihood ratio 6.116, Prob. 0.106; Wald Statistic 5.801, Prob. 0.122.
  - Australia (FRL Date 1998Q2): F-statistic 22.621, Prob. 0.000; Log likelihood ratio 57.365, Prob. 0.000; Wald Statistic 67.864, Prob. 0.000.
  - Brazil (FRL Date 2000Q2): F-statistic 52.508, Prob. 0.000; Log likelihood ratio 72.775, Prob. 0.000; Wald Statistic 157.525, Prob. 0.000.
  - Colombia (FRL Date 2000Q4): F-statistic 7.161, Prob. 0.001; Log likelihood ratio 19.952, Prob. 0.000; Wald Statistic 21.484, Prob. 0.000.
  - Colombia (FRL Date 2003Q3): F-statistic 10.206, Prob. 0.000; Log likelihood ratio 26.588, Prob. 0.000; Wald Statistic 30.619, Prob. 0.000.
  - Ecuador (FRL Date 2002Q4): F-statistic 12.808, Prob. 0.000; Log likelihood ratio 30.247, Prob. 0.000; Wald Statistic 38.424, Prob. 0.000.
  - Ecuador (FRL Date 2005Q2): F-statistic 1.308, Prob. 0.288; Log likelihood ratio 4.370, Prob. 0.224; Wald Statistic 3.925, Prob. 0.270.
  - New Zealand (FRL Date 1994Q2): F-statistic 25.507, Prob. 0.000; Log likelihood ratio 57.720, Prob. 0.000; Wald Statistic 76.521, Prob. 0.000.
  - Peru (FRL Date 1999Q4): F-statistic 2.565, Prob. 0.066; Log likelihood ratio 8.037, Prob. 0.045; Wald Statistic 7.696, Prob. 0.053.
  - United Kingdom (FRL Date 1998Q4): F-statistic 3.749, Prob. 0.026; Log likelihood ratio 7.511, Prob. 0.023; Wald Statistic 7.498, Prob. 0.024.
- For New Zealand, the overall fiscal balance was used due to data constraints.

### Conditional variance break analysis (Table 4 — Model 1)
- Dependent variable: Conditional Variance.
- Periodized constants (selected examples preserved exactly as reported):
  - Argentina Period 1 (93Q4-95Q3) Constant: 40.426** ; Period 2 (96Q1-97Q2) Constant: 9.868*** ; Period 3 (97Q4-08Q4) Constant: 1.737***.
  - Australia Period 1 (74Q3-77Q1) Constant: 9.806*** ; Period 2 (77Q3-01Q4) Constant: 2.369*** ; Period 3 (02Q2-09Q2) Constant: 0.870***.
  - Brazil Period 1 (97Q4-98Q4) Constant: 1.865*** ; Period 2 (99Q2-08Q4) Constant: 0.103*** ; Period 3 (06Q2-08Q4) Constant: 0.804*.
  - Colombia Period 1 (99Q1-99Q2) Constant: 18.255 ; Period 2 (99Q4-01Q2) Constant: 5.854** ; Period 3 (01Q4-08Q4) Constant: 0.804*.
  - Ecuador Period 1 (88Q1-92Q4) Constant: 5.751** ; Period 2 (93Q2-94Q3) Constant: 38.152*** ; Period 3 (95Q1-06Q1) Constant: 3.443***.
  - New Zealand Periods and constants reported, with some periods showing very large Q-A statistics.
  - Peru and United Kingdom period constants and break dates are reported (examples: United Kingdom Period 3 constant 4.705***; break dates include 1992Q3, 1993Q1, 1995Q2, 1997Q3, 2000Q4, 2006Q2, 2007Q4).
- Quandt-Andrews (Q-A) statistics and p-values are reported for break dates (examples preserved exactly):
  - Argentina Q-A statistic 46.772, p-value 0.0000 (break date 1995Q3 and 1997Q3 reported).
  - Australia Q-A statistic 81.437, p-value 0.0000 (break date 1977Q2 and 2002Q1 reported).
  - Brazil Q-A statistic 301.690, p-value 0.0000 (break date 1999Q1).
  - Selected additional Q-A statistics and p-values are reported across countries and break dates (see tables for exact multiple entries).

### Primary Fiscal Balance — Model 2 (Table 5)
- Dependent variable: Primary Fiscal Balance in Percent of GDP — Model 2 runs with periodized regimes and coefficients.
- Selected constants, output gap coefficients, ICP coefficients, break dates, Q-A statistics and p-values preserved exactly as reported:
  - Argentina:
    - Period 1 (93Q4-95Q3) Constant 14.624* ; Output gap -0.316 ; ICP -41.467 ; Break date 1995Q4 ; Q-A statistic 29.529, p-value 0.0001.
    - Period 2 (96Q1-02Q3) Constant -3.693*** ; Output gap 0.068*** ; ICP -1.025*** ; Break date 2002Q4 ; Q-A statistic 92.187, p-value 0.0000.
    - Period 3 (03Q1-08Q4) Constant 0.817** ; Output gap 0.324*** ; ICP -1.209***.
  - Australia:
    - Period 1 (74Q3-85Q4) Constant -1.637*** ; Period 2 (86Q2-98Q1) Constant 0.333 ; Output gap 0.284* ; Break date 1986Q1 ; Q-A statistic 43.337, p-value 0.0000.
    - Period 3 (98Q3-09Q2) Constant 1.534*** ; Output gap 0.814***.
  - Brazil:
    - Period 1 (97Q4-99Q1) Constant 0.599*** ; Output gap -0.098 ; ICP 2.420*** ; Break date 1999Q2 ; Q-A statistic 67.449, p-value 0.0000.
    - Period 2 (99Q3-05Q4) Constant 2.153*** ; Output gap -0.095*** ; ICP 2.686*** ; Break date 2006Q1 ; Q-A statistic 13.378, p-value 0.0969.
    - Period 3 (06Q2-08Q4) Constant 0.684** ; Output gap -0.182** ; Q-A statistic 14.029, p-value 0.0595.
  - Colombia:
    - Periods and coefficients reported (examples: Period 1 constant -1.526***; Break date 2003Q2; Q-A statistic 13.914, p-value 0.0493).
  - Ecuador:
    - Period constants and coefficients (examples: Period 1 constant 6.305*** ; ICP 12.110*** ; Break date 2001Q4 ; Q-A statistic 24.644, p-value 0.0004).
  - New Zealand:
    - Periods include use of overall fiscal balance; notable coefficients: Period 2 Output gap 1.031*** ; Period 3 Output gap 2.774*** ; Break dates include 1992Q4, 1995Q4, 2002Q4 with Q-A statistics and p-values preserved (e.g., Q-A statistic 26.980, p-value 0.0002).
  - Peru and United Kingdom: periodized coefficients, break dates and Q-A statistics reported with exact figures (examples include break date 1987Q3 and 1998Q1 for Peru; Q-A statistic 26.824, p-value 0.0001).
- Significance notation: * Significant at the 10% level; ** at the 5% level; *** at the 1% level.

### Markov Switching model results (Table 6) — regime probabilities and parameter estimates
- Dependent variable: Primary Fiscal Balance in Percent of GDP — Markov Switching Model.
- Reported regime probabilities (preserve exact values):
  - Regime 1 probability (per country): Argentina 0.29 ; Australia 0.48 ; Brazil 0.79 ; Colombia 0.51 ; Ecuador 0.85 ; New Zealand 0.26 ; Peru 0.64 ; United Kingdom 0.40.
  - Regime 2 probability (per country): Argentina 0.71 ; Australia 0.52 ; Brazil 0.21 ; Colombia 0.49 ; Ecuador 0.15 ; New Zealand 0.74 ; Peru 0.36 ; United Kingdom 0.60.
- Selected parameter estimates by regime (preserve exact reported values and significance where indicated):
  - Argentina:
    - Regime 1: Constant 0.977*** ; Output gap -0.182*** ; ICP -0.660*** ; Residuals’ variance 0.022.
    - Regime 2: Constant -3.031*** ; Output gap 0.018 ; ICP 0.704*** ; Residuals’ variance 1.064.
  - Australia:
    - Regime 1: Constant 1.693*** ; Output gap 0.612*** ; ICP 0.192** ; Residuals’ variance 0.573.
    - Regime 2: Constant -1.035*** ; Output gap 0.210*** ; ICP 1.230*** ; Residuals’ variance 1.532.
  - Brazil:
    - Regime 1: Constant 2.078*** ; Output gap -0.063** ; ICP 0.322*** ; Residuals’ variance 0.052.
    - Regime 2: Constant 0.562*** ; Output gap -0.304*** ; ICP 1.279*** ; Residuals’ variance 0.080.
  - Colombia:
    - Regime 1: Constant -0.618*** ; Output gap -0.100* ; ICP 1.241*** ; Residuals’ variance 0.438.
    - Regime 2: Constant -1.320*** ; Output gap -0.061* ; ICP 0.867*** ; Residuals’ variance 0.183.
  - Ecuador:
    - Regime 1: Constant 4.855*** ; Output gap -0.176 ; ICP -0.333 ; Residuals’ variance 1.530.
    - Regime 2: Constant -0.403*** ; Output gap -0.767*** ; ICP 2.474*** ; Residuals’ variance 0.073.
  - New Zealand:
    - Regime 1: Constant 5.376*** ; Output gap 0.820*** ; ICP -1.485*** ; Residuals’ variance 0.202.
    - Regime 2: Constant 2.656*** ; Output gap 0.274 ; ICP -3.636*** ; Residuals’ variance 7.259.
  - Peru:
    - Regime 1: Constant 0.400*** ; Output gap 0.121*** ; ICP 1.014*** ; Residuals’ variance 0.059.
    - Regime 2: Constant -0.471*** ; Output gap -0.032 ; ICP 1.751*** ; Residuals’ variance 0.429.
  - United Kingdom:
    - Regime 1: Constant 2.988*** ; Output gap 0.722*** ; ICP - ; Residuals’ variance 0.814.
    - Regime 2: Constant -1.118*** ; Output gap 0.596*** ; ICP - ; Residuals’ variance 2.866.
- FRL dates by country are reported alongside the Markov Switching results (examples preserved as in source).

### Markov Switching figures (Figures 1a and 1b) — description of plotted diagnostics
- Figures display for each country:
  - Left panels: probability of being in State 2 (generally the “bad regime” as described in Table 6) and the output gap.
  - Right panels: probability of being in State 2 and the primary fiscal balance (or overall balance for New Zealand).
  - Dash lines indicate adoption of an FRL.
- Probability scale: 0.0 to 1.0; primary balance and output gap scales vary by country in the figures (examples in source include axes from -12.0 to 8.0, -8.0 to 8.0, etc. as plotted for different countries and time ranges shown).

*Source: Authors’ calculations as presented in the provided IMF working paper excerpt.*

### Annex 1. Inconsistent Estimation of Dummy Variable Models in the Presence of

### Annex 1. Inconsistent Estimation of Dummy Variable Models in the Presence of Structural Breaks

### Model setup (true DGP)
- True data generating process (DGP) is the AR(1) process:
  - ttttt uIyy )(1 0   [1]
  - Parameters:  and .
  - )(A I is the indicator function (1 when event A occurs, 0 otherwise).
  - t u is a sequence of martingale differences with respect to filtration F t.
  - There is a true level shift at time 0 t (denoted by indicator )( 0 tt I  and nonzero ).

### Estimation model (misspecified dummy)
- Model used for estimation is:
  - TtforIyy ttttt ,...,1 )(1 1     [2]
  - The estimated dummy uses time 1 t, where 1 t is different from 0 t and )(),max( 10 TOtt.
  - [2] reflects the belief that the level shift occurred at time 1 t, while in reality it occurred at 0 t.
- Rewriting true DGP and estimation model:
  - True:  t Z tttt uIyy t             ],[ )(1 0  [3]
  - Estimation:  t X tttt t Iyy              ],[ )(1 1  [4]

### OLS estimator representation and decomposition
- OLS estimator of  using model [4]:
  - YXXX   1 )( ˆ  [5]
  - Y )...,( 1  T yy is generated by true DGP in [3] as UZY.
  - Substituting yields:
    - UXXXZXXX     11 )()( ˆ  [6]
- Decomposition details:
  - The term involving U is:
    - (long double-sum expression shown in source)  [reference to decomposition in source]
  - Caceres (2008, Lemma 5.3.1) result:
    - )1()(
      1 p oUXXX  
    - I.e., the U-term vanishes asymptotically (this holds independently of  and ).
  - Hence:
    - )1()(
      ˆ 1 p oZXXX     [7]

### Asymptotic contribution of the misspecified dummy and main finding
- The term    ZXXX 1 )( is given by (expressed as sums in the source):
  - (explicit double/triple sum expression from source showing dependence on  and  and on indicators with ),max( 10 tt T)  [8]
- Implication:
  - Presence of the structural break (indicator )( 0 tt I  and 0 ) implies the estimator ˆ of the coefficient for the ‘non-existent’ level shift at time 1 t will generally be different from zero.
- Special case and asymptotic equivalence:
  - If )(),max( 10 Tott, then from [7] and [8]:
    -  P  ˆ  (in fact  P ˆ ).
  - Interpretation:
    - The estimator ˆ related to the non-existing level shift will be estimating exactly the value of the true level shift , even though the true shift occurred at time 0 t different than 1 t.

*Source: Annex 1 of the provided IMF content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10248.pdf_