## wp18101

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### Introduction: context, motivation, and contributions
- Context and motivation
  - A prolonged period of sluggish productivity and income growth in advanced economies has led to renewed calls for structural reforms, notably in labor and product markets.
  - Structural reforms are difficult to implement; theory is unsettled and empirical evidence is limited and inconsistent.
  - Paper argues political-economy uncertainty reflects:
    - Fundamental model uncertainty on the selection of covariates.
    - Reform measurement issues arising from existing indicator-based approaches.
- Contributions and significance
  - Empirical:
    - Constructs a "narrative" dataset of major reforms in four areas: product market regulation (PMR) in network industries; EPL for regular workers; EPL for temporary workers; unemployment benefit systems.
    - Dataset covers 26 advanced economies over 1970-2013 and identifies exact timing and content of reforms.
    - Synthesizes and compares existing hypotheses on reform drivers.
  - Methodological:
    - Adapts Bayesian averaging of maximum likelihood estimates (BAMLE) to binary logit models.
    - First to apply BAMLE to binary logit in the political-economy literature on structural reforms and addresses pervasive model uncertainty.

### Reform identification and narrative dataset
- Identification procedure (Romer and Romer–style narrative approach)
  - For each country-year, all legislative and regulatory actions mentioned in OECD Economic Surveys are recorded.
  - Major liberalizing measures are identified if they meet at least one of three criteria:
    - (i) narrative criterion based on OECD staff’s judgement on the significance of the reform at the time of adoption;
    - (ii) mentioned again in subsequent Economic Surveys;
    - (iii) magnitude of the change in the corresponding OECD indicator, when available.
  - Each reform’s timing is precisely identified and content carefully documented.
- Stylized facts from the narrative dataset
  - Major liberalizing reforms have been more frequent in product markets than in labor markets in recent decades.
  - Product market reforms were most frequent in telecoms and airlines.
  - In labor markets, major changes in EPL have been more common than major changes in unemployment benefit systems.
  - Liberalizing reforms were predominantly implemented during the 1990s and the 2000s; product market reforms clustered around the late 1990s and early 2000s; labor market liberalization began more gradually in the 1980s.
  - Reform reversals are extremely rare and are ignored in the analysis.
  - Geographic distribution: EU countries took more actions on average than non-EU countries; southern European countries (e.g. Portugal, Spain) undertook many significant actions easing EPL.

### Data coverage and key descriptive statistics
- Coverage: 26 advanced countries, annual data over 1970-2013.
- Sample sizes used in the four BAMLE exercises:
  - product market reforms: 841 observations.
  - employment protection legislation reforms: 685 observations (EPL indicators limit sample).
  - unemployment benefit reforms: 799 observations.
- Selected descriptive statistics (as reported)
  - Reform database (narrative)
    - product market reforms: obs. 841; mean 0.05; st.dev 0.22; min 0; max 1.
    - labor market reforms (regular contracts): obs. 841; mean 0.04; st.dev 0.19; min 0; max 1.
    - labor market reforms (temporary contracts): obs. 841; mean 0.04; st.dev 0.20; min 0; max 1.
    - unemployment benefit reforms: obs. 836*; mean 0.03; st.dev 0.18; min 0; max 1.
  - Business conditions
    - GDP growth (growth rate): obs. 841; mean 2.41; st.dev 2.67; min -9.28; max 12.44.
    - unemployment (lag(rate)): obs. 841; mean 6.63; st.dev 3.66; min 0.18; max 27.47.
    - deep recession (years in lowest 20% of GDP growth): obs. 841; mean 0.32; st.dev 0.71; min 0; max 5.
    - crisis (dummy): obs. 841; mean 0.11; st.dev 0.31; min 0; max 1.
  - Structural features and regulation indicators
    - openness (lag((exp + imp)/GDP)): obs. 841; mean 0.76; st.dev 0.61; min 0.11; max 4.43.
    - old age dependency Ratio: obs. 841; mean 14.18; st.dev 2.97; min 4.13; max 25.01.
    - gini coefficient (net): obs. 841; mean 28.41; st.dev 4.07; min 19.70; max 37.80.
    - government debt in % of GDP: obs. 841; mean 0.58; st.dev 0.341; min 0.023; max 2.38.
    - reg. index: product markets (lag(level); used for PMR): obs. 841*; mean 3.66; st.dev 1.42; min 0.79; max 5.98.
    - reg. index: labor (regular contracts) (lag(level); used for EPL regular): obs. 685*; mean 2.14; st.dev 0.93; min 0.26; max 5.
    - reg. index: labor (temporary contracts) (lag(level); used for EPL temporary): obs. 685*; mean 1.86; st.dev 1.34; min 0.25; max 5.38.
    - reg. index: gross replacement rate (lag(level); used for unemployment benefits): obs. 799*; mean 28.64; st.dev 13.27; min 0.35; max 64.94.
  - External and political variables (selected)
    - EU accession (dummy t-3 : t-1; excluded for EPL regular): obs. 841; mean 0.02; st.dev 0.15; min 0; max 1.
    - EU directives (count t-3 : t-1; used for PMR): obs. 841; mean 0.80; st.dev 1.05; min 0; max 3.
    - exec r.l.c (cont) right: 1, center: 2, left: 3: obs. 841; mean 1.92; st.dev 0.91; min 1; max 3.
    - union density (%): obs. 841; mean 38.34; st.dev 21.77; min 7.54; max 99.07.
    - months to election: obs. 841; mean 23.55; st.dev 13.79; min 1; max 58.

### Methodology: BAMLE adaptation, sampling, and estimation details
- Model uncertainty and sampling
  - Model space size is 2^K variable combinations; estimation of all models infeasible.
  - Implemented Markov Chain Monte Carlo Model Composition (MC^3) per Madigan, York, and Allard (1995); candidate models drawn from neighborhood (current model, deletions of one variable, additions of one variable).
  - Candidate model M^* accepted with probability α(M,M^*) = min{ f(y|M^*) P(M^*) / [ f(y|M) P(M) ], 1 } (Equation (7)).
  - To reduce starting-model influence, first 1% of estimated models are discarded as burn-in.
  - MC^3 increases draws from regions with relatively high posterior probability; the Markov chain forms the model space used in BAMLE.
- BAMLE for logit models
  - Underlying latent variable model: y* = xβ + e, with y = B(y* > 0) and errors e standard logistic.
  - P(y_it = 1 | x) = Λ(x_it β) = exp(xβ) / (1 + exp(xβ)). (Equation (8))
  - Use average partial effects (APE) rather than log odds ratios:
    - APE estimator: β̂_j^APE = β̂_j N^{-1} ∑_{i=1}^{N} g(x_i β̂).
  - Model weights based on BIC: BIC = −2(l) + ln(N_j) k^*, with convention to use total number of observations for N_j.
  - Observations reduced to a balanced panel across variables to keep N_j consistent across models.
  - BAMLE outputs: posterior inclusion probability (PIP), posterior means and standard deviations conditional on inclusion, and APEs multiplied by 100 (interpretable as percentage point effects).
- Application and computation specifics
  - BAMLE applied to four reform indicators: PMR; EPL regular contracts; EPL temporary contracts; unemployment benefit generosity.
  - Binomial beta priors with m = 4 used unless otherwise noted.
  - MC^3 algorithm runs: one million iterations for each reform area; figures and distributions based on all unique models visited (1 million runs each).
  - Posterior inclusion probability thresholds for robustness:
    - Robustly correlated variables: PIP > 0.154.
    - Still relatively robust variables: 0.154 > PIP > 0.077.

### Main empirical findings (summary)
- Crisis‑induces‑reform hypothesis
  - Reforms across all areas tend to occur during periods of high unemployment, low growth, or recessions/crises.
  - Economic significance example: an increase of 10 percentage points in unemployment is associated with an increase in the probability to undertake a major EPL reform for regular contracts of about 5 percentage points (about twice the average probability in the sample).
  - Distributions of the APE for unemployment across the four reform areas are centered on positive means with little density in the negative space.
- Regulation stringency and scope for reform
  - APEs for regulation indicators are positive across reform areas: reforms more likely when lagged regulation is more stringent (greater scope for reform).
  - Regulation indicator often shows pip = 1 (always included) in BAMLE results.
- External pressure and EU influence
  - Reforms in PMR and EPL (temporary contracts) are more likely when other countries undertake reforms (international spillovers).
  - EU accession and competition-relevant EU directives have been important factors behind product market deregulation.
  - Example product-market estimates: int. spillovers post.mean 0.988 post.se 0.277 pip 0.998; EU directives (pmr) post.mean 1.741 post.se 1.047 pip 0.196.
- Political factors and heterogeneity
  - Political factors generally show little robust evidence except for EPL regular-worker reforms:
    - Likelihood of regular EPL deregulation is lower under higher union density and left-leaning governments.
    - No robust ideological bias overall; exec left not robustly associated with reforms in most areas except for regular EPL in some specifications.
  - Political business cycle effects appear less important than commonly assumed.
- Structural heterogeneity
  - Aging (old age dependency) is associated with a higher likelihood of PMR and temporary EPL reforms in some specifications.

### Representative posterior estimates (selected entries preserved exactly)
- Product market reforms (baseline Logit examples from Annex A2.1)
  - gdp growth: post.mean -0.488 post.se 0.341 pip 0.069.
  - unemployment: post.mean 0.366 post.se 0.172 pip 0.184.
  - deep recession: post.mean -1.575 post.se 1.707 pip 0.037.
  - crisis: post.mean 2.499 post.se 3.304 pip 0.038.
  - government debt: post.mean 4.609 post.se 1.919 pip 0.293.
  - regulation indicator: post.mean 2.181 post.se 0.653 pip 1.
  - int. spillovers: post.mean 0.988 post.se 0.277 pip 0.998.
  - EU accession: post.mean 9.651 post.se 6.749 pip 0.134.
- Temporary EPL reforms (baseline Logit examples from Annex A2.2)
  - gdp growth: post.mean -0.298 post.se 0.382 pip 0.045.
  - unemployment: post.mean 0.298 post.se 0.216 pip 0.071.
  - deep recession: post.mean 2.516 post.se 0.922 pip 0.924.
  - regulation indicator: post.mean 2.670 post.se 0.645 pip 1.
  - momentum domestic packaging: post.mean 3.235 post.se 1.054 pip 0.968.
- Unemployment benefit reforms (baseline Logit examples from Annex A2.3)
  - gdp growth: post.mean 0.323 post.se 0.262 pip 0.059.
  - unemployment: post.mean 0.292 post.se 0.172 pip 0.125.
  - regulation indicator: post.mean 0.124 post.se 0.058 pip 1.
  - EU accession: post.mean 3.709 post.se 6.622 pip 0.037.
  - exec r.l.c (cont): post.mean 0.711 post.se 0.839 pip 0.034.

### Robustness checks and sensitivity analyses
- Estimator choices
  - Alternative estimators tested: BAMLE with country and time fixed effects (Moral-Benito, 2012) and a linear probability model (LPM) version of BAMLE.
  - Results robust across estimators: unemployment rate remains the most robust correlate of regular EPL reforms.
  - Demeaning country/time data changes ordering: when level information of unemployment is neglected by demeaning, GDP growth shows higher pip and remains negative; indicates two economic-condition aspects drive regular EPL reforms (unemployment level and cyclical weakness via GDP growth).
- Multicollinearity
  - Addressed by restricting model space so variables in predefined exclusion sets are never included together (at most one variable from each set per model).
  - Restriction sets include groups such as (GDP growth, deep recession, unemployment, crisis) and (two Gini coefficients).
  - Empirical results largely unaffected by exclusion-set adjustments; BAMLE found robust to multicollinearity concerns.
  - Example pip changes baseline -> restricted for EPL regular: gdp growth 0.069 -> 0.047; unemployment 0.184 -> 0.141; deep recession 0.037 -> 0.008; int. spillovers 0.998 -> 1.000; regulation indicator 1 -> 1.
- Prior specification (model-size hyperparameter m)
  - Sensitivity tested for m = 1; m = K/2; m = K.
  - Top pips for regular EPL under Panel 1 (m=1): regulation indicator 1; unemployment 0.988; elections next year 0.578; exec left 0.518; union density 0.254; exec r.l.c (cont) 0.207; gdp growth 0.193; taylor rate 0.156; years left in office 0.148; years spent in office 0.115.
  - Posterior model sizes consistently moderate (~six to seven variables) despite extreme prior changes; posterior dominated by data rather than prior.
- Summary of robustness conclusions
  - Crisis-induces-reform hypothesis confirmed across all four reform areas.
  - Economic-condition indicators:
    - Product market deregulation and unemployment benefit cuts: associated with periods of high unemployment.
    - Temporary EPL reform: mostly passed during deep recessions.
    - Regular EPL reforms: enacted under high unemployment and weak GDP growth.
  - Other robust drivers: scope for deregulation (regulation indicator) and international pressure (int. spillovers) for some reform areas.
  - Political drivers: some political variables robustly associated with EPL regular reforms (e.g., exec left, union density), but little support for a broad ideological bias or a strong political business cycle effect across reform areas.
  - Methodological takeaway: BAMLE tailored to binary logit models combined with a narrative reform-identification database provides a robust framework to test many candidate reform drivers simultaneously.

### Annex findings: MC^3 algorithm properties and posterior model-size behavior
- Convergence and model-size behavior
  - When forced to start at the maximum model size, MC^3 converges within 200 iterations to models typically between two and seven variables.
  - Required burn-in around 200 iterations; first 1% of estimated models discarded in main runs.
  - Posterior distribution of model size (EPL regular contracts) looks reasonably Gaussian with mean 3.4 and peaks at a model size of 3–4 variables.
  - Across reform areas:
    - Product Market Reforms: posterior peaks at a model size of 3–4 variables.
    - EPL temporary contracts: posterior peaks at 4–5 variables.
    - Unemployment Benefits: posterior peaks at 1–2 variables.
- Posterior summaries and tables
  - BAMLE tables report posterior mean conditional on inclusion (post.mean), posterior standard error conditional on inclusion (post.se), and posterior inclusion probability (pip) across estimators (Logit baseline; LPM; demeaned Logit).
  - Several variables show very high pips (e.g., regulation indicator pip 1; int. spillovers pip 0.998 in product market reforms), indicating strong posterior support for inclusion.

*Source: wp18101 — IMF Working Paper (selected sections: Introduction; Section 3 and 3.2; 4.3 Sampling; 5.2 Robustness checks; Annexes).*

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

### Introduction

### Context and motivation
- A prolonged period of sluggish productivity and income growth in advanced economies has led to renewed calls for structural reforms, notably in labor and product markets.
- Structural reforms are difficult to implement; theory is unsettled and empirical evidence is limited and inconsistent.
- The paper argues that uncertainty in the political economy of reforms reflects:
  - Fundamental model uncertainty on the selection of covariates.
  - Reform measurement issues arising from existing indicator-based approaches.

### Reform identification and data issues
- Common approaches infer reforms indirectly (e.g., collapse in inflation) or use structural policy indicators (IMF, OECD, World Bank, Fraser Institute) with diverse rules to identify reforms (first differences, standard deviation criteria, predefined absolute changes, structural break tests).
- These approaches involve value judgments about what constitutes a reform versus a minor policy action and often fail to identify the exact timing of reform implementation, increasing measurement error and risking misleading inferences.
- This study uses a newly constructed "narrative" dataset of major reforms in four areas:
  - product market regulation (PMR) in network industries,
  - EPL for regular workers,
  - EPL for temporary workers,
  - unemployment benefit systems.
- The narrative dataset covers 26 advanced economies over four decades and identifies the exact timing and nature of reforms, minimizing the need for assumptions linking reforms to indicator movements.

### Methodological approach: addressing model uncertainty
- The paper adapts Bayesian averaging of maximum likelihood estimates (BAMLE) to binary logit models explaining structural reforms.
- BAMLE allows comparison of robustness of a large number of potential reform drivers across the entire model space, addressing variable selection uncertainty.
- The authors claim to be the first to adapt the BAMLE methodology to binary logit models and the first to apply such model averaging in the political economy literature on structural reforms.

### Main empirical findings
- Evidence supports some form of the crisis-induces-reform hypothesis across all four reform areas:
  - High unemployment, recession and/or an open economic crisis tend to be associated with a greater likelihood of reform.
  - The effect is economically significant: an increase of 10 percentage points in unemployment is associated with an increase in the probability to undertake a major EPL reform for regular contract of about 5 percentage points — that is, about twice the average probability in the sample.
- Outside pressure increases the likelihood of reform in certain areas:
  - Reforms are more likely when other countries also undertake them.
  - Formal pressure matters; many product market reforms in EU countries have occurred during accession processes and via competition-relevant EU directives.
- Political factors:
  - Generally little robust evidence for an important role of political factors in driving reforms.
  - EPL for regular workers is an exception: reforms in this area tend to occur under right-leaning governments, consistent with theories on entrenched interests blocking reforms.
  - The political business cycle seems less important than commonly assumed.
  - No robust evidence of an ideological bias overall—no robust difference between left- and right-of-center governments’ propensity to undertake reform (with the EPL regular exception noted above).

### Contributions and significance
- Empirical:
  - Synthesizes and compares existing hypotheses regarding reform drivers using a dataset that identifies major labor and product market reforms via a narrative approach.
  - Provides evidence on the economic significance of macroeconomic distress and external pressure as drivers of reform.
- Methodological:
  - Tackles pervasive model uncertainty in the political economy of reforms by applying BAMLE to binary logit models.
  - Expands the model averaging literature with an application and adaptation of BAMLE to binary choice settings.

*Source: wp18101 - Introduction*

### Section 3 introduces our database of major labor and product market reforms as well as the other

### wp18101 - Section 3 introduces our database of major labor and product market reforms as well as the other

### Model uncertainty and political-economy drivers of structural reform
- Theoretical and empirical literature emphasizes six broad categories of potential drivers of reforms:
  - business conditions, with particular emphasis on the role of crises;
  - macroeconomic (monetary and fiscal) policies;
  - structural features of the domestic economy (e.g. size, trade openness, demographics, income inequality; stringency of existing regulations, and thereby need and scope for reform);
  - external factors, including formal and informal international pressure on the domestic economy to undertake reform;
  - political factors, including ideology, structural features of the political system, and conjunctural features (e.g. political cycles and crises);
  - reform packaging, sequencing and momentum, and the role of reform strategies in overcoming resistance to reform.
- Key theoretical expectations and empirical ambiguities documented:
  - Crisis effects: theory suggests non-linear impact where acute crisis matters disproportionately; empirical literature yields mixed support for “crisis-induces-reform” depending on crisis type and reform area.
  - Macroeconomic policy effects: accommodative fiscal and monetary policies may increase reform likelihood through compensation of losers and bringing forward gains, but fiscal consolidation may erode political capital and hinder reforms. Competing “TINA” argument posits reforms may be necessary when monetary policy autonomy is lost.
  - Structural features: small open economies may be more amenable to reform; demographic aging and high inequality have ambiguous effects; stringency of regulation has ambiguous influence because reform losers may form powerful opposition.
  - International pressure and learning: formal institutions (e.g. European Union membership) and informal peer learning can promote reforms; empirical evidence on spillovers is broadly positive but mixed.
  - Political factors: timing effects (political cycle, re-election concerns, timing within term) and political structure (fractionalization, partisan orientation) produce mixed empirical findings; extreme political crises can be influential.
  - Reform strategies: packaging and sequencing (e.g., combining wage-lowering reforms with wage-raising reforms; deregulating product markets first) can increase the chance of adoption and generate reform momentum or cascades.

### Coverage choices, omissions, and empirical goals
- Sample and focus:
  - Analysis focuses on advanced economies and aims to shed light on the relative importance of the various hypotheses and their robustness to model specification.
- Exclusions due to sample and focus:
  - The role of conditionality under adjustment programs is not covered because such programs are rare events in the sample.
  - Democracy effects are not tested because the vast majority of OECD countries score very high on the usual Polity IV index.
  - Specificities of transition economies are not addressed in depth; the sample incorporates only one transition economy.
- Empirical objective:
  - To evaluate relative importance of candidate drivers of labor and product market reform and test robustness to model specification.

### Reform identification and data: narrative database
- Dataset characteristics:
  - A newly constructed “narrative” dataset of major reforms covering four areas: PMR in network industries, EPL for regular workers, EPL for temporary workers, and unemployment benefit systems.
  - Coverage: 26 advanced countries and each year over 1970-2013.
- Identification procedure (Romer and Romer–style narrative approach):
  - For each country-year, all legislative and regulatory actions mentioned in OECD Economic Surveys are recorded.
  - Major liberalizing measures are identified if they meet at least one of three criteria:
    - (i) a narrative criterion based on OECD staff’s judgement on the significance of the reform at the time of adoption;
    - (ii) whether the reform is mentioned again in subsequent Economic Surveys (as opposed to only once when adopted);
    - (iii) the magnitude of the change in the corresponding OECD indicator, when available.
  - Each reform’s timing is precisely identified and its content carefully documented.
  - The approach aims to minimize value judgements and measurement error and eliminates the need for assumptions on the relation between structural reforms and regulation indicators.

### Stylized facts from the narrative dataset
- Relative frequency and timing:
  - Major liberalizing reforms have been more frequent in product markets than in labor markets in recent decades.
  - Major product market reforms were most frequent in telecoms and airlines.
  - In labor markets, major changes in EPL have been more common than major changes in unemployment benefit systems.
  - Liberalizing reforms were predominantly implemented during the 1990s and the 2000s; product market reforms clustered around the late 1990s and early 2000s, while labor market liberalization was more gradual beginning in the 1980s.
- Other observed features:
  - Reform reversals are extremely rare events in practice and are ignored in the analysis.
  - For unemployment benefit systems, several countries increased or maintained generosity during the 1970s and early 1980s before reducing it later; reforms affected replacement rates and duration roughly equally.
  - Geographic distribution:
    - EU countries took more actions on average than non-EU countries, reflecting greater scope for action.
    - In labor markets, southern European countries (e.g. Portugal, Spain) undertook many significant actions, particularly easing EPL for both regular and temporary workers.

*Source: wp18101 - Section 3 introduces our database of major labor and product market reforms as well as the other (PDF).*

### 3.2 Other data sources

### 3.2 Other data sources

### Overview
- Aim: provide a synthesis and comparison of commonly cited studies on structural reforms using the most commonly employed data sources wherever available.
- Lags employed rule out some simultaneity concerns but do not claim causal inference; objective is to establish relative robustness of covariates claimed to drive reforms.
- Table 1 presents descriptive statistics for all variables used in the analysis; constructions and sources are reviewed below.
- Sample notes: In the four BAMLE exercises the sample is limited and reduced to available data for the relevant regulation indicator. Results: product market reforms based on 841 observations, reforms of employment protection legislation on 685 observations, and unemployment benefit reforms on 799 observations.

### Table 1 — Selected descriptive statistics (variable construction, obs., mean, st.dev, min, max, source)
- Reform database (narrative database)
  - product market reforms: obs. 841; mean 0.05; st.dev 0.22; min 0; max 1; source: Duval, Furceri, Hu, Jalles, and Nguyen (2018)
  - labor market reforms (regular contracts): obs. 841; mean 0.04; st.dev 0.19; min 0; max 1; source: Duval, Furceri, Hu, Jalles, and Nguyen (2018)
  - labor market reforms (temporary contracts): obs. 841; mean 0.04; st.dev 0.20; min 0; max 1; source: Duval, Furceri, Hu, Jalles, and Nguyen (2018)
  - unemployment benefit reforms: obs. 836*; mean 0.03; st.dev 0.18; min 0; max 1; source: Duval, Furceri, Hu, Jalles, and Nguyen (2018)
- Business conditions
  - GDP growth (growth rate): obs. 841; mean 2.41; st.dev 2.67; min -9.28; max 12.44; source: IMF WEO
  - unemployment (lag(rate)): obs. 841; mean 6.63; st.dev 3.66; min 0.18; max 27.47; source: IMF WEO
  - deep recession (count variable: years in lowest 20% of GDP growth): obs. 841; mean 0.32; st.dev 0.71; min 0; max 5; source: based on GDP growth
  - crisis (dummy (Bank, Currency and/or Sov. debt crisis/restructuring)): obs. 841; mean 0.11; st.dev 0.31; min 0; max 1; source: Valencia and Laeven (2012)
- Macroeconomic policies
  - exchange rate regime (1(loose) : 15(tight)): obs. 841; mean 7.30; st.dev 4.37; min 1; max 14; source: Ilzetzki, Reinhart, and Rogoff (2017)
  - taylor rate (lag(residual of regressing 3 months interest rate on the cpi rate and cyclical gdp)): obs. 841; mean 0.09; st.dev 3.19; min -17.23; max 8.91; source: based on IMF data
- Structural features of the economy
  - openness (lag((exp + imp)/GDP)): obs. 841; mean 0.76; st.dev 0.61; min 0.11; max 4.43; source: based on IMF Data
  - old age dependency Ratio: obs. 841; mean 14.18; st.dev 2.97; min 4.13; max 25.01; source: World Bank
  - gini coefficient (net) (based on net income): obs. 841; mean 28.41; st.dev 4.07; min 19.70; max 37.80; source: IMF (Standardized World Income Inequality Database)
  - gini coefficient (market) (based on gross income): obs. 841; mean 44.63; st.dev 4.81; min 32.10; max 56.60; source: IMF (Standardized World Income Inequality Database)
  - government debt in % of GDP: obs. 841; mean 0.58; st.dev 0.341; min 0.023; max 2.38; source: IMF
  - reg. index: product markets (lag(level); used for PMR): obs. 841*; mean 3.66; st.dev 1.42; min 0.79; max 5.98; source: OECD
  - reg. index: labor (regular contracts) (lag(level); used for EPL regular): obs. 685*; mean 2.14; st.dev 0.93; min 0.26; max 5; source: OECD
  - reg. index: labor (temporary contracts) (lag(level); used for EPL temporary): obs. 685*; mean 1.86; st.dev 1.34; min 0.25; max 5.38; source: OECD
  - reg. index: gross replacement rate (lag(level); used for unempl. benefits over 5-year spell): obs. 799*; mean 28.64; st.dev 13.27; min 0.35; max 64.94; source: OECD
- External factors
  - EU accession (dummy based on accession year (t-3 : t-1); excluded for EPL regular): obs. 841; mean 0.02; st.dev 0.15; min 0; max 1; source: manually constructed
  - EU directives (count (t-3 : t-1); used for PMR): obs. 841; mean 0.80; st.dev 1.05; min 0; max 3; source: Bouis, Duval, and Eugster (2016)
  - int. spillovers (adds reforms in same area in other countries (t-3 : t-1)): source: Duval, Furceri, Jalles, and Nguyen (2018)
- Political factors (including ideology, structural features of the political system and conjunctural features)
  - exec r.l.c (cont) right: 1, center: 2, left: 3: obs. 841; mean 1.92; st.dev 0.91; min 1; max 3; source: DPI
  - exec left Dummy: obs. 841; mean 0.37; st.dev 0.48; min 0; max 1; source: DPI
  - union density (% of employees with right to bargain): obs. 841; mean 38.34; st.dev 21.77; min 7.54; max 99.07; source: OECD
  - centralization gov. (sum of squared seat share of all gvt parties): obs. 841; mean 0.71; st.dev 0.27; min 0.18; max 1; source: DPI
  - vote share gov. in %: obs. 841; mean 47.70; st.dev 13.32; min 0; max 84.42; source: DPI
  - gov. controls all houses (Dummy): obs. 841; mean 0.21; st.dev 0.408; min 0; max 1; source: DPI
  - months to election (count of months left): obs. 841; mean 23.55; st.dev 13.79; min 1; max 58; source: Gupta, Liu, and Mulas-Granados (2016)
  - elections next year (Dummy): obs. 841; mean 0.29; st.dev 0.45; min 0; max 1; source: based on months to elections
  - years left in term (Count): obs. 841; mean 1.68; st.dev 1.241; min 0; max 4; source: DPI
  - years executive spent in office (Count): obs. 841; mean 3.86; st.dev 2.91; min 1; max 18; source: DPI
  - momentum domestic packaging (adds reforms in same country but other areas (t-3 : t-1)): source: Duval, Furceri, Hu, Jalles and Nguyen (2018)

- Note on asterisks: * indicates sample is limited by and reduced to available data for the relevant regulation indicator. All variables are then reduced to these dimensions.

### Business conditions and economic crises (construction and sources)
- GDP growth: actual annual rate of real GDP growth in the current year; source: IMF World Economic Outlook database.
- Unemployment rate: enters with a lag; source: IMF and OECD data.
- Deep recession: counts years in which GDP growth is in its lowest 20% across the panel dataset; robustness: similar results obtained for cut offs at 10% and 15%.
- Crisis variable: equals 1 if there was either a currency crisis, a sovereign debt crisis, or a sovereign debt restructuring in the last three years; source: Valencia and Laeven (2012).

### Macroeconomic policies (construction)
- Exchange rate regimes: continuous variable from Ilzetzki, Reinhart, and Rogoff (2017).
- Taylor rate (monetary policy stance): constructed as the residual from a regression of the short-term interest rate on the CPI inflation rate and the cyclical component of GDP (HP detrended); all variables from IMF World Economic Outlook database.

### Structural features of the domestic economy (construction)
- Trade openness: first lag of (exports + imports)/GDP; source: IMF WEO.
- Old age dependency ratio: population above 65 relative to working age population, in percent; source: World Bank Development Indicators.
- Inequality: Gini coefficients based on net and gross income from the Standardized World Income Inequality Database.
- Government debt: percent of GDP; source: IMF WEO.
- Existing regulation stringency: lag and initial sample value of OECD indicators for PMR, EPL (permanent and temporary contracts), and gross replacement rate of unemployment benefits over a five-year unemployment spell. The first lag of these indicators is included as the only variable in every specification for the corresponding reform area (one indicator per reform as indicated in Table 1).

### External factors (construction)
- EMU accession dummy: constructed based on date of accession to the monetary union, acting in t-1:t-3; omitted for EPL regular contracts; included for the other three reform areas.
- EU directives in product markets: number of single market directives in t-3 to t-1; source: Bouis, Duval, and Eugster (2016) based on European Commission historical list. Used only for product market reforms.
- International spillovers (peer pressure): total number of reforms in the same field in other countries in the sample over the last three years (t-1:t-3).

### Political factors (construction)
- Government ideology: continuous variable right (0) to left (2) through center (1) and a separate dummy for leftwing governments; source: Database of Political Institutions (DPI).
- Union density: share of workforce unionized; source: OECD.
- Centralization: squared parliamentary seat share of all government parties.
- Vote share of government, dummy for controlling all houses, years in office, years left in term: source: DPI.
- Months left until next legislative election: detailed data from Gupta, Liu, and Mulas-Granados (2016), extended manually where necessary.
- Elections next year dummy: equals 1 if next election scheduled in less than 12 months.

### Domestic packaging (construction)
- Explanatory variable: occurrence of reforms in the other 3 fields in the same country to test for reform packages and facilitation of implementation.
- Window for measuring domestic packaging: t-2 : t+2; robustness: results robust to window t-1 : t+1.

*Italic source attribution: IMF Working Paper — content from section "3.2 Other data sources" of wp18101 (source PDF: wp18101 - 3.2 Other data sources).*

### 4.3 Sampling

### 4.3 Sampling

### Sampling algorithm and rationale
- The model space size is 2^K possible variable combinations, making estimation of all models infeasible and motivating a sampling algorithm.
- Implemented a Markov Chain Monte Carlo Model Composition (MC^3) routine as introduced by Madigan, York, and Allard (1995) and described following Koop (2003).
- MC^3 moves through model space by comparing a current model M to a candidate model M^* drawn from M's neighborhood: M, all models deleting one variable from M, and all models adding one variable to M.
- Candidate model M^* is accepted with probability α(M,M^*) equal to the posterior odds if these are smaller than unity:
  - Equation (7): α(M,M^*) = min{ f(y|M^*) P(M^*) / [ f(y|M) P(M) ], 1 }.
- Because a (weak) prior on the model space is used, the posterior odds do not reduce to the Bayes factor.
- The Markov chain produced by MC^3 forms the model space used in the BAMLE exercise.

### Starting values, burn-in, and convergence
- A starting model M is necessary; example: starting at the maximum model including all 26 variables used to investigate product market reforms.
- If the prior on model size is m=4, the full 26-variable model is very unlikely; algorithm quickly converges to smaller model sizes (Annex A1).
- To reduce influence of the starting model, the first 1% of all estimated models are discarded as a 'burn-in' sample and not included in results.
- The burn-in sample is described as "very generous" and results are robust to different starting models.
- Rationale: MC^3 increases draws from regions where posterior probability is relatively high, decreasing the number of estimated models to be averaged and avoiding the infeasible task of estimating the entire 2^K model space.

### BAMLE in logit models (application and measures)
- Underlying latent variable model: y* = xβ + e, with y = B(y* > 0) and errors e following a standard logistic distribution.
  - Equation (8): P(y_it = 1 | x) = Λ(x_it β) = exp(xβ) / (1 + exp(xβ)).
- Use average partial effects (APE) rather than log odds ratios because APEs are comparable across models:
  - APE estimator: β̂_j^APE = β̂_j N^{-1} ∑_{i=1}^{N} g(x_i β̂), preserving the form as in the source.
- Model weights for BAMLE are based on the BIC:
  - BIC = −2(l) + ln(N_j) k^*, where l is maximized likelihood of model M_j, k^* is number of parameters, and N_j total observations.
- Two BIC-related researcher choices and resolutions:
  - Whether N_j should be number of countries or total number of observations: the authors follow convention and use total number of observations (assume independence across countries).
  - To keep N_j consistent across models with differing available data, observations are reduced to a balanced panel across variables: the panel is unbalanced across countries but balanced across variables.
- BAMLE outputs reported include the posterior inclusion probability (PIP), posterior means and standard deviations conditional on inclusion, and APEs multiplied by 100 (interpretable as percentage point effects).

### Application details and computation
- BAMLE applied to logit models of likelihood of major labor and product market reforms across four reform indicators: PMR, EPL (regular contracts), EPL (temporary contracts), and unemployment benefit generosity (replacement rate and duration).
- Results are based on binomial beta priors with m=4 as outlined in the methodological section.
- MC^3 algorithm runs: one million iterations for each reform area; figures and distributions are based on all unique models visited by the algorithm (1 million runs each).
- Posterior inclusion probability thresholds used to classify robustness:
  - Robustly correlated variables: PIP > 0.154 (dark grey in table).
  - Still relatively robust variables: 0.154 > PIP > 0.077 (light grey in table).

### Main empirical findings (summary of results presented)
- Common macroeconomic drivers:
  - Reforms across all areas tend to occur during periods of high unemployment, low growth, or recessions/crises, supporting the crisis-induces-reform hypothesis.
  - Economic significance example: an increase of 10 percentage points in unemployment is associated with an increase in the probability to undertake a major regular EPL reform of about 5 percentage points (about twice the average probability in the sample).
  - Distributions of the APE for unemployment across the four reform areas are centered on positive means with little density in the negative space; product market and regular EPL reforms show reasonably Gaussian APE distributions; temporary EPL APE distribution is more spread but still right of zero.
- Regulation and scope for reform:
  - Average partial effects for regulation indicators are positive across reform areas, indicating reforms are more likely when (lagged) regulation is more stringent (i.e., when more scope for reform exists).
- External pressure and EU influences:
  - Reforms in PMR and EPL (temporary contracts) are more likely when other countries also undertake reforms (int. spillovers).
  - EU accession and competition-relevant EU directives have been important factors behind product market deregulation.
- Political and structural heterogeneity:
  - Political factors are significant for EPL regular-worker reforms but not for other areas:
    - Likelihood of regular EPL deregulation is lower under higher union density and left-leaning governments.
    - No robust evidence for a broader ideological bias between left- and right-of-center governments' propensity to undertake reform.
  - Political business cycle effects appear generally less important than commonly assumed.
  - Aging (old age dependency) is associated with a higher likelihood of PMR and temporary EPL reforms, possibly because retirees reap gains but do not bear potential costs (e.g., greater job insecurity).

*Source: wp18101 - 4.3 Sampling (excerpt).*

### 5.2 Robustness checks

### 5.2 Robustness checks

### Different model choices
- Methods applied:
  - BAMLE methodology with country and time fixed effects (Moral-Benito, 2012).
  - Linear probability model (LPM) version of BAMLE.
- Rationale for main-specification choice:
  - Model averaging aims to infer relationships without imposing much structure.
  - In a logit set-up, including country (time) fixed effects would drop countries (times) where a given reform never occurred.
- Key empirical comparisons (regular EPL reforms; full results for other reform areas in Annex 2):
  - Baseline: pooled logit (Columns 1–3 in Table 3).
  - LPM: Columns 4–6 in Table 3; posterior means directly derived from estimates (average partial effects not required).
    - Finding: Little impact on results; unemployment rate remains the most robust correlate of regular EPL reforms.
  - Logit with country and time demeaned data: Columns 7–9 in Table 3.
    - Limitation: international spillovers cannot be included since demeaned spillover variables are identical across countries.
    - Effect ordering change: when level information of unemployment is neglected, GDP growth shows a higher pip and remains negative — implying two economic-condition aspects drive regular EPL reforms:
      - structurally poor labor market performance (unemployment level),
      - weak business cycle conditions (GDP growth).

- Representative coefficient/pattern excerpts from the (excerpted) Table 3:
  - gdp growth: -0.111, -0.117, -0.175, -0.437 (values shown in table excerpt).
  - unemployment: +0.839, +0.942, +0.083, +0.086 (values shown in table excerpt).
  - deep recession: +0.086, +0.159, +0.133, +0.139.
  - Other listed coefficients (excerpted): crisis +0.040/+0.017/+0.023/+0.028; exchange rate +0.032/+0.050/+0.016/+0.029; taylor rate -0.083/-0.094/+0.023/+0.017.
- Overall conclusion for estimator robustness:
  - Except for the unemployment rate (affected by demeaning for clear reasons), results are surprisingly consistent across estimator choices (pooled logit, LPM, demeaned logit/LPM).

### Addressing multicollinearity
- Concern: several explanatory variables are strongly correlated (e.g., unemployment and interest rate spreads both increase during recessions).
- Strategy: alter BAMLE to restrict model space so that variables in predefined exclusion sets are never included together in the same model; still use results for all variables.
- Restriction sets (at most one variable from each set per model):
  - GDP growth, deep recession, unemployment, crisis
  - The two Gini coefficients (net and market)
  - Continuous ideology variable and dummy for leftwing executive
  - Government vote share and government party majority in all houses
  - Number of months to elections, close elections, years left in office, years executive has already been in office
- Algorithmic procedure:
  - Start with a model using the maximum number of variables, then discard all but one randomly drawn variable from each restriction set.
  - Updating proceeds as before for smaller/identical models.
  - When moving to a larger model, restrict draws to variables that do not violate restriction sets.
- Empirical result (Table 4 comparison):
  - Posterior inclusion probabilities (pips) shown for baseline vs restricted BAMLE.
  - Key findings remain largely unaffected by the exclusion-set adjustment.
  - Interpretation: BAMLE is highly robust even to multicollinearity concerns.
- Selected pip comparisons (excerpt from Table 4 columns baseline vs restricted for EPL regular and other reform areas; values shown in table excerpt):
  - gdp growth: 0.069 -> 0.047 (baseline -> restricted; first reform area column)
  - unemployment: 0.184 -> 0.141
  - deep recession: 0.037 -> 0.008
  - int. spillovers: 0.998 -> 1.000 (strong inclusion in baseline and restricted for some reform areas)
  - government debt: 0.293 -> 0.239
  - regulation indicator: 1 -> 1 (always included)

### Changing prior specifications (model size hyperparameter m)
- Sensitivity tested for three extreme prior choices for m (regular EPL reforms; other reform areas show same message):
  - Panel 1: prior m = 1
  - Panel 2: prior m = K/2
  - Panel 3: prior m = K
- Table 5 findings (top 10 variables by pip under each prior):
  - Panel 1 (prior: m=1) top pips:
    - regulation indicator 1
    - unemployment 0.988
    - elections next year 0.578
    - exec left 0.518
    - union density 0.254
    - exec r.l.c (cont) 0.207
    - gdp growth 0.193
    - taylor rate 0.156
    - years left in office 0.148
    - years spent in office 0.115
  - Panel 2 (prior: m=K/2) top pips:
    - regulation indicator 1
    - unemployment 0.930
    - elections next year 0.301
    - exec left 0.278
    - union density 0.194
    - exec r.l.c (cont) 0.151
    - gdp growth 0.102
    - taylor rate 0.094
    - deep recession 0.090
    - years left in office 0.079
  - Panel 3 (prior: m=K) top pips (excerpt matches Panel 1 ordering for many):
    - regulation indicator 1
    - unemployment 0.988
    - elections next year 0.578
    - exec left 0.518
    - union density 0.254
    - exec r.l.c (cont) 0.207
    - gdp growth 0.193
    - taylor rate 0.156
    - years left in office 0.148
    - years spent in office 0.115
- Posterior model size behavior (Figure 6):
  - Despite dramatic shifts in the prior mode across panels, the posterior consistently indicates relatively moderate model sizes of around six to seven variables.
  - Conclusion: the posterior model size is dominated by the data rather than the prior; results robust to hyperparameter m choices.

### Key robustness conclusions (synthesis across checks)
- Crisis-induces-reform hypothesis confirmed across all four reform areas analyzed.
- Economic-condition indicators:
  - Product market deregulation and unemployment benefit cuts: mostly associated with periods of high unemployment.
  - Temporary EPL reform: mostly passed during deep recessions.
  - Regular EPL reforms: enacted under all variants of weak economic conditions (unemployment level and cyclical weakness via GDP growth).
- Other robust drivers:
  - Scope for deregulation and international pressure (PMR) are robust predictors for some reform areas.
  - A few political factors are robustly associated with reforms of EPL for regular contracts (e.g., exec left, elections next year have nontrivial pips in some specifications).
- Non-robust or weak findings:
  - Limited support for the it-takes-a-Nixon-to-go-to-China hypothesis: political orientation of the executive is not a robust driver for most reform areas (except regular EPL reforms).
  - Little support for a strong political business cycle effect: timing of elections has at most a minor effect on the likelihood of reform.
- Methodological takeaway:
  - BAMLE tailored to binary logit models, combined with a narrative reform-identification database, offers a robust framework to test a large set of potential reform drivers simultaneously.
  - BAMLE results are robust across estimator choices (logit vs LPM), inclusion of fixed effects (with caveats on dropped information), exclusion-set rules to address multicollinearity, and extreme prior model-size choices.

*Source: IMF Working Paper — section 5.2 "Robustness checks", wp18101*

### Annex 1. Properties of the Sampling Algorithm

### Annex 1. Properties of the Sampling Algorithm

### Algorithm convergence and model-size behavior
- When forced to start at the maximum model size, the MC3 algorithm converges within 200 iterations to a region of reasonable model sizes.
- Convergent region: models within a range between two and seven variables per model.
- Required burn in: around 200 iterations.
- The algorithm does not converge to a single model size; model uncertainty remains high and a single "best" model cannot be selected.
- Implication: using a model averaging estimator is important to investigate correlations with structural reforms.

### Posterior distribution of model size (EPL regular contracts)
- Posterior distribution of model size looks reasonably Gaussian with a mean of 3.4.
- For EPL regular contracts (as used in Figure 3), the posterior updates belief to a smaller mean model size than the proposed four variables.
- Posterior peaks at a model size of 3-4 variables (mode not the smallest model), indicating the data is informative as intended by Ley and Steel (2009).

### Posterior model-size results across reform areas
- Product Market Reforms:
  - Posterior again peaks at a model size of 3-4 variables and looks reasonably Gaussian.
- EPL temporary contracts:
  - Posterior peaks at a model size of 4-5 variables and looks reasonably Gaussian.
- Unemployment Benefits:
  - Posterior peaks at a model size of 1-2 variables, indicating the data is not able to distinguish well-fitting models as strongly as in other reform areas.

### Notes on figures and experiment setup
- Panel 1 shows the initial 1000 replications and convergence toward a mean slightly below 4 variables, while not converging to a single model (fundamental model uncertainty).
- Panel 2 compares the prior on the model space (random inclusion probability with mean model size four) with the posterior produced by the algorithm (posterior peaks at 3-4 variables).
- All reported convergence and posterior results are based on runs of the MC3 algorithm with structural reforms (EPL regular contracts, product markets, EPL temporary contracts, unemployment benefits) on the left-hand side of the logit model.

---

### Annex 2. BAMLE Results for Different Estimations

### General description of tables A2.1–A2.3
- Tables report posterior means conditional on inclusion (post.mean), standard errors conditional on inclusion (post.se), and posterior inclusion probabilities (pip) from the BAMLE exercise across different estimators.
- First three result columns: baseline results based on Logit models.
- Columns 4–6: same exercise based on a linear probability model.
- Columns 7–9: Logit models run on time and individually demeaned data (pooled/time and year demeaned/pooled variations noted).

### Selected illustrative estimates and posterior inclusion probabilities (preserve exact figures as reported)
- From Table A2.1 (Product market reforms, mixed estimator columns shown in the source):
  - gdp growth: post.mean -0.488 post.se 0.341 pip 0.069 (baseline Logit column shown)
  - unemployment: post.mean 0.366 post.se 0.172 pip 0.184 (baseline Logit)
  - deep recession: post.mean -1.575 post.se 1.707 pip 0.037
  - crisis: post.mean 2.499 post.se 3.304 pip 0.038
  - openness: post.mean -2.439 post.se 1.533 pip 0.093
  - government debt: post.mean 4.609 post.se 1.919 pip 0.293
  - regulation indicator: post.mean 2.181 post.se 0.653 pip 1 (shown as 1 in table)
  - int. spillovers: post.mean 0.988 post.se 0.277 pip 0.998
  - EU accession: post.mean 9.651 post.se 6.749 pip 0.134
  - EU directives (pmr): post.mean 1.741 post.se 1.047 pip 0.196
- From Table A2.2 (Temporary EPL reforms, baseline Logit column examples):
  - gdp growth: post.mean -0.298 post.se 0.382 pip 0.045
  - unemployment: post.mean 0.298 post.se 0.216 pip 0.071
  - deep recession: post.mean 2.516 post.se 0.922 pip 0.924
  - regulation indicator: post.mean 2.670 post.se 0.645 pip 1 (shown as 1 in table)
  - momentum domestic packaging: post.mean 3.235 post.se 1.054 pip 0.968
- From Table A2.3 (Unemployment benefit reforms, baseline Logit column examples):
  - gdp growth: post.mean 0.323 post.se 0.262 pip 0.059
  - unemployment: post.mean 0.292 post.se 0.172 pip 0.125
  - government debt: post.mean 1.382 post.se 1.610 pip 0.038
  - regulation indicator: post.mean 0.124 post.se 0.058 pip 1 (shown as 1 in table)
  - EU accession: post.mean 3.709 post.se 6.622 pip 0.037
  - exec r.l.c (cont): post.mean 0.711 post.se 0.839 pip 0.034

### Interpretation emphasis
- The BAMLE tables show variation in posterior means, posterior standard errors, and posterior inclusion probabilities across model specifications (Logit vs linear probability model vs demeaned data).
- Several variables show very high pip values (e.g., regulation indicator with pip 1 and int. spillovers with pip 0.998 in product market reforms), indicating strong posterior support for inclusion across estimators in those cases.
- Other variables show low pips and large standard errors, reflecting uncertainty and sensitivity to estimator choice and data transformations.

---

### Annex 3. Robustness of Results to the Choice of Priors

### Prior scenarios examined
- Panel 1: prior with m = 1 (lower extreme).
- Panel 2: prior with m = K/2 (half the available variables).
- Panel 3: prior with m = K (maximum number of variables).

### Key robustness findings (top variables by pip under different priors)
- Product Market Reforms (selected entries shown exactly as in source):
  - regulation indicator: pip 1 (all priors)
  - int. spillovers: pip 1.000 (all priors)
  - government debt: pip 0.224 (panel 1), 0.372 (panel 2), 0.509 (panel 3)
  - unemployment: pip 0.148 (panel 1), 0.236 (panel 2), 0.385 (panel 3)
  - EU directives (pmr): pip 0.137 (panel 1), 0.289 (panel 2), 0.596 (panel 3)
  - EU accession: pip 0.092 (panel 1), 0.148 (panel 2), 0.301 (panel 3)
  - openness, exchange rate, gdp growth, old age dep.: pips vary across panels (exact figures presented in the source).
- EPL temporary contracts (selected entries):
  - regulation indicator: pip 1 across panels.
  - domestic packaging: pip 0.970 (panel 1), 0.986 (panel 2), 0.999 (panel 3)
  - deep recession: pip 0.919 (panel 1), 0.966 (panel 2), 0.996 (panel 3)
  - int. spillovers: pip 0.651 (panel 1), 0.789 (panel 2), 0.930 (panel 3)
  - taylor rate, old age dep., and others show increasing pips as prior m increases.
- Unemployment Benefits (selected entries):
  - regulation indicator: pip 1 across priors.
  - gdp growth: pip 0.032 (panel 1), 0.107 (panel 2), 0.171 (panel 3)
  - unemployment: pip 0.075 (panel 1), 0.223 (panel 2), 0.569 (panel 3)
  - deep recession and crisis: low to moderate pips that increase with more permissive priors.
  - exchange rate, taylor rate, openness, old age dep., gini (net): pips vary by prior choice.

### Visualization note
- Figure A3.1 presents prior (empty framed bars) and posterior (grey bars) model sizes for the three prior choices (m = 1, m = K/2, m = K) across reform areas (product markets; EPL temporary contracts; unemployment benefits).
- Results are consistent with Figure 7 and illustrate how posterior model-size distributions respond to extreme prior choices.

*Source: wp18101 - Annex 1. Properties of the Sampling Algorithm (selected annex material).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18101.pdf_