In 2008 all ECB publications feature a motif taken from the €10 banknote.

Recent approaches to development accounting reflect substantial model uncertainty at both the instrument and the development determinant level. Bayesian Model Averaging (BMA) has been proven useful in resolving model uncertainty in economics, and we extend BMA to formally account for model uncertainty in the presence of endogeneity. The new methodology is shown to be highly efficient and to reduce many-instrument bias; in a simulation study we found that IVBMA estimates reduced mean squared error by 60 % over standard IV estimates. We also introduce Bayesian over and under-identification tests that are based on model averaged predictive p-values. This approach is shown to mitigate the reduction in power these tests experience as dimension increases. In a simulation study where the exogeneity of the instrument is compromised we show that the classical Sargan test has a power of 0.2 % while our Bayesian over-identification test has a power of 98 % at detecting the violation of the exogeneity assumption. An application of our method to a prominent development accounting approach leads to new insights regarding the primacy of institutions.

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NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. Macroprudential Research Network This paper presents research conducted within the Macroprudential Research Network (MaRs). The network is composed of economists from the European System of Central Banks (ESCB), i.e. the 27 national central banks of the European Union (EU) and the European Central Bank. The objective of MaRs is to develop core conceptual frameworks, models and/or tools supporting macro-prudential supervision in the EU. The research is carried out in three work streams: 1) Macro-financial models linking financial stability and the performance of the economy; 2) Early warning systems and systemic risk indicators; 3) Assessing contagion risks.

Model uncertainty has become a central focus of policy discussion surrounding the determinants of economic growth. Over 140 regressors have been employed in growth empirics due to the proliferation of several new growth theories in the past two decades. Recently Bayesian model averaging (BMA) has been employed to address model uncertainty and to provide clear policy implications by identifying robust growth determinants. The BMA approaches were, however, limited to linear regression models that abstract from possible dependencies embedded in the covariance structures of growth determinants. The recent empirical growth literature has developed jointness measures to highlight such dependencies. We address model uncertainty and covariate dependencies in a comprehensive Bayesian framework that allows for structural learning in linear regressions and Gaussian graphical models. A common prior specification across the entire comprehensive framework provides consistency. Gaussian graphical models allow for a principled analysis of dependency structures, which allows us to generate a much more parsimonious set of fundamental growth determinants. Our empirics are based on a prominent growth dataset with 41 potential economic factors that has been utilized in numerous previous analyses to account for model uncertainty as well as jointness.

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determi-nants, once both model uncertainty and endogeneity have been jointly addressed.

Institut ekonomických studií Fakulta sociálních věd

Abstract. Bayesian model averaging has increasingly witnessed applications across an array of empirical contexts. However, the dearth of available statistical software which allows one to engage in a model averaging exercise is limited. It is common for consumers of these methods to develop their own code, which has obvious appeal. However, canned statistical software can ameliorate one’s own analysis if they are not intimately familiar with the nuances of computer coding. Moreover, many researchers would prefer user ready software to mitigate the inevitable time costs that arise when hard coding an econometric estimator. To that end, this paper describes the relative merits and attractiveness of several competing packages in the statistical environment R to implement a Bayesian model averaging exercise. 1.

We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct eval-uation of model probabilities is intractable in this setting. We show that by nesting model moves inside the Gibbs sampler, model comparison can be performed via condi-tional Bayes factors, leading to straightforward calculations. This new Gibbs sampler is only slightly more involved than the original algorithm and exhibits no evidence of mixing difficulties. We conclude with a study of two different modeling challenges: incorporating uncertainty into the determinants of macroeconomic growth, and esti-mating a demand function by instrumenting wholesale on retail prices.

Over the past 60 years, a voluminous literature has painstakingly developed theories and associated candidate regressors to motivate Early Warning Signals of economic crises. The hallmark of this literature is the consistency with which selected Early Warning Signals, such as the level of reserves and exchange rate appreciations, are thought to predict different types of crises across countries and time. The diversity of theories motivating Early Warning Signals presents, however, a challenge to empirical implementations. Given that the true model of Early Warning Signals is unknown, omitted variable bias may contaminate estimates and model uncertainty inflates confidence levels when the uncertainty surrounding a particular theory has been ignored. Addressing model uncertainty in Early Warning Signal regressions, we do not find a single regressor that successfully alerts to all dimensions of the 2008 crisis. Instead, distinct sets of Early Warning Signals identify different dimensions of the crisis (Banking, Balance of Payments, Exchange Rate