Model Averaging and its Use in Economics

Steel, Mark F. J. (2017): Model Averaging and its Use in Economics.

Abstract

The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal response to model uncertainty in a Bayesian framework, and most of the paper deals with Bayesian model averaging. The important role of the prior assumptions in these Bayesian procedures is highlighted. In addition, frequentist model averaging methods are also discussed. Numerical methods to implement these methods are explained, and I point the reader to some freely available computational resources. The main focus is on uncertainty regarding the choice of covariates in normal linear regression models, but the paper also covers other, more challenging, settings, with particular emphasis on sampling models commonly used in economics. Applications of model averaging in economics are reviewed and discussed in a wide range of areas, among which growth economics, production modelling, finance and forecasting macroeconomic quantities.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian methods; Model uncertainty; Normal linear model; Prior specification; Robustness
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C20 - General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O47 - Empirical Studies of Economic Growth ; Aggregate Productivity ; Cross-Country Output Convergence

References

Acemoglu, D., S. Johnson, and J. Robinson (2001). The colonial origins of comparative development: An empirical investigation. American Economic Review 91, 1369–1401.

Adler, K. and C. Grisse (2017). Thousands of BEERs: Take your pick. Review of International Economics 25, 1078–104.

Aijun, Y., X. Ju, Y. Hongqiang, and L. Jinguan (2018). Sparse Bayesian variable selection in probit model for forecasting U.S. recessions using a large set of predictors. Computational Economics 51, 1123–38.

Albert, J. H. and S. Chib (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88, 669–79.

Albouy, D. (2012). The colonial origins of comparative development: An empirical investigation: Comment. American Economic Review 102, 3059–3076.

Alvarez, J. and M. Arellano (2003). The time series and cross-section asymptotics of dynamic panel data estimators. Econometrica 71, 1121–59.

Amini, S. and C. Parmeter (2011). Bayesian model averaging in R. Journal of Economic and Social Measurement 36, 253–87.

Amini, S. M. and C. F. Parmeter (2012). Comparison of model averaging techniques: Assessing growth determinants. Journal of Applied Econometrics 27, 870–76.

Arin, K. and E. Braunfels (2018). The resource curse revisited: A Bayesian model averaging approach. Energy Economics 70, 170–8.

Asatryan, Z. and L. Feld (2015). Revisiting the link between growth and federalism: A Bayesian model averaging approach. Journal of Comparative Economics 43, 772–81.

Atchad´e, Y. and J. Rosenthal (2005). On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11, 815–28.

Barbieri, M. and J. Berger (2004). Optimal predictive model selection. Annals of Statistics 32, 870–97.

Barro, R. (1991). Economic growth in a cross section of countries. Quarterly Journal of Economics 106, 407–44.

Barto´n, K. (2016). MuMIn - R package for model selection and multi-model inference. http: //mumin.r-forge.r-project.org/.

Bates, J. and C. Granger (1969). The combination of forecasts. Operations Research Quarterly 20, 451–68.

Bayarri, M.-J., J. Berger, A. Forte, and G. Garc´ıa-Donato (2012). Criteria for Bayesian model choice with application to variable selection. Annals of Statistics 40, 1550–77.

Bencivelli, L., M. Marcellino, and G. Moretti (2017). Forecasting economic activity by Bayesian bridge model averaging. Empirical Economics 53, 21–40.

Benjamini, Y. and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B 57, 289–300.

Berger, J., G. Garc´ıa-Donato, M. Mart´ınez-Beneito, and V. Pe˜na (2016). Bayesian variable selection in high dimensional problems without assumptions on prior model probabilities. arXiv 1607.02993v1.

Berger, J. and L. Pericchi (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91, 109–22.

Berger, J. and L. Pericchi (2001). Objective Bayesian methods for model selection: Introduction and comparison. In P. Lahiri (Ed.), Model Selection, Institute of Mathematical Statistics Lecture Notes - Monograph Series 38, Beachwood, OH: IMS, pp. 135–207.

Bernardi, M. and L. Catania (2018). The model confidence set package for R. International Journal of Computational Economics and Econometrics 8, 144–158.

Bernardo, J. and A. Smith (1994). Bayesian Theory. Chichester: Wiley.

Bła˙zejowski, M., P. Kufel, and J. Kwiatkowski (2018). Model simplification and variable selection: A replication of the UK inflation model by Hendry (2001). MPRA Papers 88745.

Bła˙zejowski, M. and J. Kwiatkowski (2015). Bayesian model averaging and jointness measures for gretl. Gretl Working Paper 2, Torun School of Banking.

Bła˙zejowski, M. and J. Kwiatkowski (2018). Bayesian averaging of classical estimates (BACE) for gretl. Gretl Working Paper 6, Universit`a Politecnica delle Marche.

Brock,W. and S. Durlauf (2001). Growth empirics and reality. World Bank Economic Review 15, 229–72.

Brock, W. and S. Durlauf (2015). On sturdy policy evaluation. Journal of Legal Studies 44, S447–73.

Brock, W., S. Durlauf, and K. West (2003). Policy evaluation in uncertain economic environments. Brookings Papers of Economic Activity 1, 235–322 (with discussion).

Brown, P., M. Vannucci, and T. Fearn (1998). Bayesian wavelength selection in multicomponent analysis. Journal of Chemometrics 12, 173–82.

Brown, P. J., T. Fearn, and M. Vannucci (1999). The choice of variables in multivariate regression: A non-conjugate Bayesian decision theory approach. Biometrika 86, 635–48.

Buckland, S., K. Burnham, and N. Augustin (1997). Model selection: an integral part of inference. Biometrics 53, 603–18.

Burnham, K. and D. Anderson (2002). Model selection and multimodel inference: a practical information-theoretic approach (2nd ed.). New York: Springet.

Camarero, M., A. Forte, G. Garc´ıa-Donato, Y. Mendoza, and J. Ordo˜nez (2015). Variable selection in the analysis of energy consumption-growth nexus. Energy Economics 52, 2017–16.

Castillo, I., J. Schmidt-Hieber, and A. van der Vaart (2015). Bayesian linear regression with sparse priors. Annals of Statistics 43, 1986–2018.

Catania, L. and M. Bernardi (2017). MCS: Model confidence set procedure, R package. https: //cran.r-project.org/web/packages/MCS.

Catania, L. and N. Nonejad (2017). eDMA: Dynamic model averaging with grid search, R package. https://cran.r-project.org/web/packages/eDMA.

Catania, L. and N. Nonejad (2018). Dynamic model averaging for practitioners in economics and finance: The eDMA package. Journal of Statistical Software 84.

Charitidou, E., D. Fouskakis, and I. Ntzoufras (2018). Objective Bayesian transformation and variable selection using default Bayes factors. Statistics and Computing 28, 579–94.

Chatfield, C. (1995). Model uncertainty, data mining and statistical inference. Journal of the Royal Statistical Society, Series A 158, 419–66 (with discussion).

Chen, H., A. Mirestean, and C. G. Tsangarides (2018). Bayesian model averaging for dynamic panels with an application to a trade gravity model. Econometric Reviews 37, 777–805.

Chen, M. and J. Ibrahim (2003). Conjugate priors for generalized linear models. Statistica Sinica 13, 461–76.

Chen, R.-B., Y.-C. Chen, C.-H. Chu, and K.-J. Lee (2017). On the determinants of the 2008 financial crisis: A Bayesian approach to the selection of groups and variables. Studies in Nonlinear Dynamics & Econometrics 21, article 20160107.

Cheng, X. and B. Hansen (2015). Forecasting with factor-augmented regression: A frequentist model averaging approach. Journal of Econometrics 186, 280–93.

Chib, S. (1995). Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90, 1313–1321.

Chib, S. (2011). Introduction to simulation and MCMC methods. In J. Geweke, G. Koop, and H. van Dijk (Eds.), The Oxford Handbook of Bayesian Econometrics, Oxford: Oxford University Press, pp. 183–217.

Chipman, H., M. Hamada, and C. Wu (1997). A Bayesian variable selection approach for analyzing designed experiments with complex aliasing. Technometrics 39, 372–81.

Christensen, G. and E. Miguel (2018). Transparency, reproducibility, and the credibility of economics research. Journal of Economic Literature 56, 920–80.

Christofides, C., T. Eicher, and C. Papageorgiou (2016). Did established early warning signals predict the 2008 crises? European Economic Review 81, 103–114. Special issue on “Model Uncertainty in Economics”.

Ciccone, A. and M. Jaroci´nski (2010). Determinants of economic growth: Will data tell? American Economic Journal: Macroeconomics 2, 222–46.

Claeskens, G., C. Croux, and J. van Kerckhoven (2006). Variable selection for logistic regression using a prediction-focused information criterion. Biometrics 62, 972–9.

Claeskens, G. and N. Hjort (2003). The focused information criterion. Journal of the American Statistical Association 98, 900–45 (with discussion).

Claeskens, G., J. Magnus, A. Vasnev, and W. Wang (2015). The forecast combination puzzle: A simple theoretical explanation. International Journal of Forecasting 32, 754–62.

Clyde, M. (2017). BAS: Bayesian adaptive sampling for Bayesian model averaging, R package version 1.4.3. https://cran.r-project.org/web/packages/BAS.

Clyde, M. and E. George (2004). Model uncertainty. Statistical Science 19, 81–94.

Clyde, M., J. Ghosh, and M. Littman (2011). Bayesian adaptive sampling for variable selection and model averaging. Journal of Computational and Graphical Statistics 20, 80–101.

Clyde, M. and E. Iversen (2013). Bayesian model averaging in the M-open framework. In P. Damien, P. Dellaportas, N. Polson, and D. Stephens (Eds.), Bayesian Theory and Applications, Oxford: Oxford University Press, pp. 483–98.

Cogley, T. and T. Sargent (2005). The conquest of US inflation: Learning and robustness to model uncertainty. Review of Economic Dynamics 8, 528–63.

Cohen, J., K. Moeltner, J. Reichl, and M. Schmidthaler (2016). An empirical analysis of local opposition to new transmission lines across the EU-27. The Energy Journal 37, 59–82.

Cordero, J., M. Mu˜niz, and C. Polo (2016). The determinants of cognitive and non-cognitive educational outcomes: empirical evidence in Spain using a Bayesian approach. Applied Economics 48, 3355–72.

Crespo Cuaresma, J. (2011). How different is Africa? a comment on Masanjala and Papageorgiou. Journal of Applied Econometrics 26, 1041–47.

Crespo Cuaresma, J., G. Doppelhofer, F. Huber, and P. Piribauer (2018). Human capital accumulation and long-term income growth projections for European regions. Journal of Regional Science 58, 81–99.

Crespo Cuaresma, J. and M. Feldkircher (2013). Spatial filtering, model uncertainty and the speed of income convergence in Europe. Journal of Applied Econometrics 28, 720–741.

Crespo Cuaresma, J., B. Gr¨un, P. Hofmarcher, S. Humer, and M. Moser (2016). Unveiling covariate inclusion structures in economic growth regressions using latent class analysis. European Economic Review 81, 189–202. Special issue on “Model Uncertainty in Economics”.

Cui, W. and E. George (2008). Empirical Bayes vs. fully Bayes variable selection. Journal of Statistical Planning and Inference 138, 888–900.

Dasgupta, A., R. Leon-Gonzalez, and A. Shortland (2011). Regionality revisited: An examination of the direction of spread of currency crises. Journal of International Money and Finance 30, 831–48.

Daude, C., A. Nagengast, and J. Perea (2016). Productive capabilities: An empirical analysis of their drivers. The Journal of International Trade & Economic Development 25, 504–35.

De Luca, G., J. R. Magnus, and F. Peracchi (2018). Weighted-average least squares estimation of generalized linear models. Journal of Econometrics 204, 1–17.

Dearmon, J. and T. Smith (2016). Gaussian process regression and Bayesian model averaging: An alternative approach to modeling spatial phenomena. Geographical Analysis 48, 82–111.

Deckers, T. and C. Hanck (2014). Variable selection in cross-section regressions: Comparisons and extensions. Oxford Bulletin of Economics and Statistics 76, 841–73.

Desbordes, R., G. Koop, and V. Vicard (2018). One size does not fit all... panel data: Bayesian model averaging and data poolability. Economic Modelling 75, 364–76.

Devereux, J. and G. Dwyer (2016). What determines output losses after banking crises? Journal of International Money and Finance 69, 69–94.

DiCiccio, D., R. Kass, A. Raftery, and L. Wasserman (1997). Computing Bayes factors by combining simulation and asymptotic approximations. Journal of the American Statistical Association 92, 903–15.

Diebold, F. (1991). A note on Bayesian forecast combinatton procedures. In A. Westlund and P. Hackl (Eds.), Economic structural change: Analysis and forecasting, New York: Springer Verlag, pp. 225–32.

Diebold, F. and P. Pauly (1990). The use of prior information in forecast combination. International Journal of Forecasting 6, 503–8.

Diebold, F. and G. Rudebusch (1989). Long memory and persistence in aggregate output. Journal of Monetary Economics 24, 189–209.

Domingos, P. (2000). Bayesian averaging of classifiers and the overfitting problem. In Proceedings of the Seventeenth International Conference on Machine Learning, Stanford, CA, pp. 223–30.

Doppelhofer, G., O.-P. Moe Hansen, and M.Weeks (2016). Determinants of long-term economic growth redux: A measurement error model averaging (MEMA) approach. Working paper 19/16, Norwegian School of Economics.

Doppelhofer, G. and M. Weeks (2009). Jointness of growth determinants. Journal of Applied Econometrics 24, 209–44.

Doppelhofer, G. and M. Weeks (2011). Robust growth determinants. Working Paper in Economics 1117, University of Cambridge.

Dormann, C. F., J. M. Calabrese, G. Guillera-Arroita, E. Matechou, V. Bahn, K. Barto´n, C. M. Beale, S. Ciuti, J. Elith, K. Gerstner, J. Guelat, P. Keil, J. J. Lahoz-Monfort, L. J. Pollock, B. Reineking, D. R. Roberts, B. Schr¨oder,W. Thuiller, D. I.Warton, B. A.Wintle, S. N.Wood, R. O. W˜A 1 4 est, and F. Hartig (2018). Model averaging in ecology: a review of Bayesian, information-theoretic, and tactical approaches for predictive inference. Ecological Monographs, forthcoming.

Drachal, K. (2016). Forecasting spot oil price in a dynamic model averaging framework - have the determinants changed over time? Energy Economics 60, 35–46.

Draper, D. (1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society, Series B 57, 45–97 (with discussion).

Draper, D. and D. Fouskakis (2000). A case study of stochastic optimization in health policy: Problem formulation and preliminary results. Journal of Global Optimization 18, 399–416.

Ductor, L. and D. Leiva-Leon (2016). Dynamics of global business cycle interdependence. Journal of International Economics 102, 110–27.

Dupuis, J. and C. Robert (2003). Variable selection in qualitative models via an entropic explanatory power. Journal of Statistical Planning and Inference 111, 77–94.

Durlauf, S. (2018). Institutions, development and growth: Where does evidence stand? Working Paper WP18/04.1, Economic Development & Institutions.

Durlauf, S., C. Fu, and S. Navarro (2012). Assumptions matter: Model uncertainty and the deterrent effect of capital punishment. American Economic Review: Papers and Proceedings 102, 487–92.

Durlauf, S., A. Kourtellos, and C. Tan (2008). Are any growth theories robust? Economic Journal 118, 329–46.

Durlauf, S., A. Kourtellos, and C. Tan (2012). Is God in the details? a reexamination of the role of religion in economic growth. Journal of Applied Econometrics 27, 1059–75.

Eicher, T. and M. Newiak (2013). Intellectual property rights as development determinants. Canadian Journal of Economics 46, 4–22.

Eicher, T., C. Papageorgiou, and A. Raftery (2011). Default priors and predictive performance in Bayesian model averaging, with application to growth determinants. Journal of Applied Econometrics 26, 30–55.

Eicher, T. S. and D. J. Kuenzel (2016). The elusive effects of trade on growth: Export diversity and economic take-off. Canadian Journal of Economics 49, 264–295.

Eklund, J. and S. Karlsson (2007). Forecast combination and model averaging using predictive measures. Econometric Reviews 26, 329–63.

Fan, J. and R. Li (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96, 1348–60.

Feldkircher, M. (2014). The determinants of vulnerability to the global financial crisis 2008 to 2009: Credit growth and other sources of risk. Journal of International Money and Finance 43, 19–49.

Feldkircher, M., R. Horvath, and M. Rusnak (2014). Exchange market pressures during the financial crisis: A Bayesian model averaging evidence. Journal of International Money and Finance 40, 21–41.

Feldkircher, M. and F. Huber (2016). The international transmission of US shocks - evidence from Bayesian global vector autoregressions. European Economic Review 81, 167–88. Special issue on “Model Uncertainty in Economics”.

Feldkircher, M. and S. Zeugner (2009). Benchmark priors revisited: On adaptive shrinkage and the supermodel effect in Bayesian model averaging. Working Paper 09/202, IMF.

Feldkircher, M. and S. Zeugner (2012). The impact of data revisions on the robustness of growth determinants: A note on ‘determinants of economic growth. will data tell’? Journal of Applied Econometrics 27, 686–94.

Feldkircher, M. and S. Zeugner (2014). R-package BMS: Bayesian Model Averaging in R. http://bms.zeugner.eu.

Fern´andez, C., E. Ley, and M. Steel (2001a). Benchmark priors for Bayesian model averaging. Journal of Econometrics 100, 381–427.

Fern´andez, C., E. Ley, and M. Steel (2001b). Model uncertainty in cross-country growth regressions. Journal of Applied Econometrics 16, 563–76.

Forte, A., G. Garc´ıa-Donato, and M. Steel (2018). Methods and tools for Bayesian variable selection and model averaging in normal linear regression. International Statistical Review 86, 237–58.

Foster, D. and E. George (1994). The risk inflation criterion for multiple regression. Annals of Statistics 22, 1947–75.

Fouskakis, D. and I. Ntzoufras (2016a). Limiting behavior of the Jeffreys power-expectedposterior Bayes factor in Gaussian linear models. Brazilian Journal of Probability and Statistics 30, 299–320.

Fouskakis, D. and I. Ntzoufras (2016b). Power-conditional-expected priors: Using g-priors with random imaginary data for variable selection. Journal of Computational and Graphical Statistics 25, 647–64.

Fragoso, T., W. Bertoli, and F. Louzada (2018). Bayesian model averaging: A systematic review and conceptual classification. International Statistical Review 86, 1–28.

Frankel, J. (2012). The natural resource curse: A survey of diagnoses and some prescriptions. In R. Arezki, C. Pattillo, M. Quintyn, and M. Zhu (Eds.), Commodity Price Volatility and Inclusive Growth in Low-Income Countries, Washington, D.C.: International Monetary Fund, pp. 7–34.

Frankel, J. and D. Romer (1999). Does trade cause growth? American Economic Review 89, 379–399.

Frankel, J. and G. Saravelos (2012). Can leading indicators assess country vulnerability? Evidence from the 2008-09 global financial crisis. Journal of International Economics 87, 216–31.

Furnival, G. and R. Wilson (1974). Regressions by leaps and bounds. Technometrics 16, 499– 511.

Garc´ıa-Donato, G. and A. Forte (2015). BayesVarSel: Bayes factors, model choice and variable selection in linear models, R package version 1.6.1. http://CRAN.R-project.org/ package=BayesVarSel.

Garc´ıa-Donato, G. and A. Forte (2018). Bayesian testing, variable selection and model averaging in linear models using R with BayesVarSel. R Journal 10, 155–74.

Garc´ıa-Donato, G. and M. Mart´ınez-Beneito (2013). On sampling strategies in Bayesian variable selection problems with large model spaces. Journal of the American Statistical Association 108, 340–52.

Garratt, A., K. Lee, M. Pesaran, and Y. Shin (2003). Forecasting uncertainties in macroeconometric modelling: An application to the UK economy. Journal of the American Statistical Association 98, 829–38.

Gelfand, A. and S. Ghosh (1998). Model choice: A minimum posterior predictive loss approach. Biometrika 85, 1–11.

George, E. (1999a). Comment on “Bayesian model averaging: A tutorial” by J. Hoeting, D. Madigan, A. Raftery and C. Volinksy. Statistical Science 14, 409–12. George, E. (1999b). Discussion of “Bayesian model averaging and model search strategies” by M. Clyde. In J. Bernardo, J. Berger, A. Dawid, and A. Smith (Eds.), Bayesian Statistics 6, Oxford: Oxford University Press, pp. 175–7.

George, E. (2010). Dilution priors: Compensating for model space redundancy. In J. Berger, T. Cai, and I. Johnstone (Eds.), Borrowing Strength: Theory Powering Applications, Institute of Mathematical Statistics - Collections, Vol. 6, Beachwood, OH: IMS, pp. 158–65.

George, E. and D. Foster (2000). Calibration and empirical Bayes variable selection. Biometrika 87, 731–47.

George, E. and R. McCulloch (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association 88, 881–89.

George, E. and R. McCulloch (1997). Approaches for Bayesian variable selection. Statistica Sinica 7, 339–73.

George, E., D. Sun, and S. Ni (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics 142, 553–80.

Geweke, J. and G. Amisano (2011). Optimal prediction pools. Journal of Econometrics 164, 130–41.

Ghosh, J. and A. Ghattas (2015). Bayesian variable selection under collinearity. The American Statistician 69, 165–73.

Giannone, D., M. Lenza, and G. Primiceri (2018). Economic predictions with big data: The illusion of sparsity. Staff Reports 847, Federal Reserve Bank of New York.

Giannone, D., M. Lenza, and L. Reichlin (2011). Market freedom and the global recession. IMF Economic Review 59, 111–35.

Gneiting, T. and A. Raftery (2007). Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association 102, 359–78.

Good, I. (1952). Rational decisions. Journal of the Royal Statistical Society. B 14, 107–114.

Granger, C. (1989). Combining forecasts - twenty years later. Journal of Forecasting 8, 167–73.

Gravestock, I. and D. Saban´es Bov´e (2017). glmBfp: Bayesian fractional polynomials for GLMs, R package version 0.0-51. https://cran.r-project.org/package=glmBfp.

Griffin, J., K. Łatuszy´nski, and M. Steel (2017). In search of lost (mixing) time: Adaptive MCMC schemes for Bayesian variable selection with very large p. ArXiv 1708.05678, University of Warwick.

Griffin, J. and M. Steel (2008). Flexible mixture modelling of stochastic frontiers. Journal of Productivity Analysis 29, 33–50.

Hall, S. and J. Mitchell (2007). Combining density forecasts. International Journal of Forecasting 23, 1–13.

Hanck, C. (2016). I just ran two trillion regressions. Economics Bulletin 36, 2017–42.

Hansen, B. (2000). Sample splitting and threshold estimation. Econometrica 68, 575–603.

Hansen, B. (2007). Least squares model averaging. Econometrica 75, 1175–89.

Hansen, B. and J. Racine (2012). Jackknife model averaging. Journal of Econometrics 157, 38–46.

Hansen, L. and T. Sargent (2014). Uncertainty Within Economic Models, Volume 6 of World Scientific Series in Economic Theory. Singapore: World Scientific.

Hansen, M. H. and B. Yu (2001). Model selection and the principle of minimum description length. Journal of the American Statistical Association 96, 746–74.

Hansen, P., A. Lunde, and J. Nason (2011). The model confidence set. Econometrica 79, 453–97.

Hartwell, C. (2016). The institutional basis of efficiency in resource-rich countries. Economic Systems 40, 519–38.

Hastie, T., R. Tibshirani, and J. Friedman (2009). The Elements of Statistical Learning. New York: Springer.

Hauser, M., B. P¨otscher, and E. Reschenhofer (1999). Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures. Empirical Economics 24, 243–69.

Havranek, T., R. Horvath, Z. Irsova, and M. Rusnak (2015). Cross-country heterogeneity in intertemporal substitution. Journal of International Economics 96, 100–18.

Havranek, T., Z. Irsova, and O. Zeynalova (2018). Tuition fees and university enrolment: A meta-regression analysis. Oxford Bulletin of Economics and Statistics 80, 1145–84.

Havranek, T., M. Rusnak, and A. Sokolova (2017). Habit formation in consumption: A metaanalysis. European Economic Review 95, 142–67.

Havranek, T. and A. Sokolova (2016). Do consumers really follow a rule of thumb? three thousand estimates from 130 studies say “probably not”. Working Paper 8/2016, Czech National Bank.

Henderson, D. and C. Parmeter (2016). Model averaging over nonparametric estimators. In G. Gonz´alez-Rivera, R. Carter Hill, and T.-H. Lee (Eds.), Essays in Honor of Aman Ullah, Advances in Econometrics, Vol. 36, Emerald Group Publishing Limited, pp. 539–60.

Hendry, D. (2001). Modelling UK inflation, 1875-1991. Journal of Applied Econometrics 16, 255–75.

Hendry, D. and H.-M. Krolzig (2005). he properties of automatic gets modelling. Economic Journal 115, C32–61.

Hendry, D. H. and H.-M. Krolzig (2004). We ran one regression. Oxford Bulletin of Economics and Statistics 66, 799–810.

Hern´andez, B., A. Raftery, S. Pennington, and A. Parnell (2018). Bayesian additive regression trees using Bayesian model averaging. Statistics and Computing 28, 869–90.

Hjort, N. and G. Claeskens (2003). Frequentist model average estimators. Journal of the American Statistical Association 98, 879–99.

Ho, T. (2015). Looking for a needle in a haystack: Revisiting the cross-country causes of the 2008-9 crisis by Bayesian model averaging. Economica 82, 813–40.

Hoeting, J., D. Madigan, A. Raftery, and C. Volinksy (1999). Bayesian model averaging: A tutorial. Statistical Science 14, 382–417 (with discussion).

Hoeting, J., A. Raftery, and D. Madigan (1996). A method for simultaneous variable selection and outlier identification in linear regression. Computational Statistics and Data Analysis 22, 251–70.

Hoeting, J., A. Raftery, and D. Madigan (2002). A method for simultaneous variable and transformation selection in linear regression. Journal of Computational and Graphical Statistics 11, 485–507.

Hofmarcher, P., J. Crespo Cuaresma, B. Gr¨un, S. Humer, and M. Moser (2018). Bivariate jointness measures in Bayesian model averaging: Solving the conundrum. Journal of Macroeconomics 57, 150–65.

Hoogerheide, L., R. Kleijn, F. Ravazzolo, H. van Dijk, and M. Verbeek (2010). Forecast accuracy and economic gains from Bayesian model averaging using time-varying weights. Journal of Forecasting 29, 251–69.

Hoover, K. and S. Perez (1999). Data mining reconsidered: encompassing and the general-tospecific approach to specification search. Econometrics Journal 2, 167–91.

Hortas-Rico, M. and V. Rios (2016). The drivers of income inequality in cities: A spatial Bayesian Model Averaging approach. Estudios sobre la Econom´ıa Espa˜nola 2016/26, FEDEA.

Horvath, R., E. Horvatova, and M. Siranova (2017). Financial development, rule of law and wealth inequality: Bayesian model averaging evidence. Discussion Paper 12/2017, Bank of Finland Institute for Economies in Transition.

Ibrahim, J. and M.-H. Chen (2000). Power prior distributions for regression models. Statistical Science 15, 46–60.

Iyke, B. (2015). Macro determinants of the real exchange rate in a small open small island economy: Evidence from mauritius via bma. MPRA Paper 68968.

Jeffreys, H. (1961). Theory of Probability (3rd ed.). Oxford University Press.

Jetter, M. and C. Parmeter (2018). Sorting through global corruption determinants: Institutions and education matter - not culture. World Development 109, 279–94.

Jetter, M. and A. Ram´ırex Hassan (2015). Want export diversification? educate the kids first. Economic Inquiry 53, 1765–82.

Jovanovic, B. (2017). Growth forecast errors and government investment and consumption multipliers. International Review of Applied Economics 31, 83–107.

Kapetanios, G., J. Mitchell, S. Price, and N. Fawcett (2015). Generalised density forecast combinations. Journal of Econometrics 188, 150–65.

Kapetanios, G. and F. Papailias (2018). Big data & macroeconomic nowcasting: Methodological review. Discussion Paper 2018-12, Economic Statistics Centre of Excellence.

Karl, A. and A. Lenkoski (2012). Instrumental variables Bayesian model averaging via conditional Bayes factors. Technical Report arXiv: 1202.5846v3, Heidelberg University.

Kass, R. and A. Raftery (1995). Bayes factors. Journal of the American Statistical Association 90, 773–795.

Kass, R. and L. Wasserman (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association 90, 928– 34.

Kiviet, J. (1995). On bias, inconsistency, and efficiency of various estimators in dynamic panel data models. Journal of Econometrics 68, 53–78.

Koop, G. (2003). Bayesian Econometrics. Chichester: Wiley. 92

Koop, G. (2017). Bayesian methods for empirical macroeconomics with big data. Review of Economic Analysis 9, 33–56.

Koop, G. and D. Korobilis (2012). Forecasting inflation using dynamic model averaging. International Economic Review 53, 867–86.

Koop, G. and D. Korobilis (2016). Model uncertainty in panel vector autoregressive models. European Economic Review 81, 115–131. Special issue on “Model Uncertainty in Economics”.

Koop, G., R. Leon-Gonzalez, and R. Strachan (2012). Bayesian model averaging in the instrumental variable regression model. Journal of Econometrics 171, 237–50.

Koop, G., E. Ley, J. Osiewalski, and M. Steel (1997). Bayesian analysis of long memory and persistence using ARFIMA models. Journal of Econometrics 76, 149–69.

Korobilis, D. (2018). Machine learning macroeconometrics: A primer. Working Paper 36: 07- 2018, University of Essex.

Kourtellos, A., C. Marr, and C. Tan (2016). Robust determinants of intergenerational mobility in the land of opportunity. European Economic Review 81, 132–47. Special issue on “Model Uncertainty in Economics”.

Kourtellos, A. and C. Tsangarides (2015). Robust correlates of growth spells: Do inequality and redistribution matter? Working Paper 15-20, The Rimini Centre for Economic Analysis.

Lamnisos, D., J. E. Griffin, and M. F. J. Steel (2009). Transdimensional sampling algorithms for Bayesian variable selection in classification problems with many more variables than observations. Journal of Computational and Graphical Statistics 18, 592–612.

Lamnisos, D., J. E. Griffin, and M. F. J. Steel (2013). Adaptive Monte Carlo for Bayesian Variable Selection in Regression Models. Journal of Computational and Graphical Statistics 22, 729– 48.

Lanzafame, M. (2016). Potential growth in Asia and its determinants: An empirical investigation. Asian Development Review 33, 1–27.

Leamer, E. (1978). Specification Searches: Ad Hoc Inference with Nonexperimental Data. New York: Wiley.

Leamer, E. (1983). Let’s take the con out of econometrics. American Economic Review 73, 31–43.

Leamer, E. (1985). Sensitivity analyses would help. American Economic Review 75, 308–13.

Leamer, E. (2016a). S-values and Bayesian weighted all-subsets regressions. European Economic Review 81, 15–31. Special issue on “Model Uncertainty in Economics”.

Leamer, E. (2016b). S-values: Conventional context-minimal measures of the sturdiness of regression coefficients. Journal of Econometrics 193, 147–61.

Lee, K.-J. and Y.-C. Chen (2018). Of needles and haystacks: revisiting growth determinants by robust Bayesian variable selection. Empirical Economics 54, 1517–47.

Leeper, E., C. Sims, and T. Zha (1996). What does monetary policy do? Brookings Papers on Economic Activity 2, 1–78 (with discussion).

Lenkoski, A., T. Eicher, and A. Raftery (2014). Two-stage Bayesian model averaging in endogenous variable models. Econometric Reviews 33, 122–51.

Lenkoski, A., A. Karl, and A. Neudecker (2014). ivbma: Bayesian instrumental variable estimation and model determination via conditional bayes factors, R package. https: //cran.r-project.org/web/packages/ivbma.

Le´on-Gonz´alez, R. and D. Montolio (2015). Endogeneity and panel data in growth regressions: A Bayesian model averaging approach. Journal of Macroeconomics 46, 23–39.

LeSage, J. (2014). Spatial econometric panel data model specification: a bayesian approach. Spatial Statistics 9, 122–45.

LeSage, J. (2015). Software for bayesian cross section and panel spatial model comparison. Journal of Geographical Systems 17, 297–310.

LeSage, J. P. and O. Parent (2007). Bayesian model averaging for spatial econometric models. Geographical Analysis 39, 241–67.

Levine, R. and D. Renelt (1992). A sensitivity analysis of cross-country growth regressions. American Economic Review 82, 942–63.

Ley, E. and M. Steel (2007). Jointness in Bayesian variable selection with applications to growth regression. Journal of Macroeconomics 29, 476–93.

Ley, E. and M. Steel (2009a). Comments on ’Jointness of growth determinants’. Journal of Applied Econometrics 24, 248–51.

Ley, E. and M. Steel (2009b). On the effect of prior assumptions in Bayesian model averaging with applications to growth regression. Journal of Applied Econometrics 24, 651–74.

Ley, E. and M. Steel (2012). Mixtures of g-priors for Bayesian model averaging with economic applications. Journal of Econometrics 171, 251–66.

Li, C., Q. Li, J. Racine, and D. Zhang (2018). Optimal model averaging of varying coefficient models. Statistica Sinica.

Li, K.-C. (1987). Asymptotic optimality for cp, cl, cross-validation and generalized crossvalidation: Discrete index set. Annals of Statistics 15, 958–75.

Li, Y. and M. Clyde (2017). Mixtures of g-priors in generalized linear models. Journal of the American Statistical Association, forthcoming.

Liang, F., R. Paulo, G. Molina, M. Clyde, and J. Berger (2008). Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association 103, 410–23.

Liang, F. and W. Wong (2000). Evolutionary Monte Carlo: Applications to cp model sampling and change point problem. Statistica Sinica 10, 317–42.

Lindley, D. (1968). The choice of variables in multiple regression (with discussion). Journal of the Royal Statistical Society Ser. B, 30, 31–66.

Liu, C.-A. (2015). Distribution theory of the least squares averaging estimator. Journal of Econometrics 186, 142–59.

Liu, Q., R. Okui, and A. Yoshimura (2016). Generalized least squares model averaging. Econometric Reviews 35, 1692–752.

Ly´ocsa, v., P. Moln´ar, and N. Todorova (2017). Volatility forecasting of non-ferrous metal futures: Covariances, covariates or combinations? Journal of International Financial Markets, Institutions & Money 51, 228–47.

Madigan, D., J. Gavrin, and A. Raftery (1995). Eliciting prior information to enhance the predictive perfromance of Bayesian graphical models. Communications in Statistics, Theory and Methods 24, 2271–92.

Madigan, D. and A. Raftery (1994). Model selection and accounting for model uncertainty in graphical models using Occam’s window. Journal of the American Statistical Association 89, 1535–46.

Madigan, D. and J. York (1995). Bayesian graphical models for discrete data. International Statistical Review 63, 215–32.

Magnus, J. and G. De Luca (2011). Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues. Stata Journal 11, 518–44.

Magnus, J. and G. De Luca (2016). Weighted-average least squares (WALS): A survey. Journal of Economic Surveys 30, 117–48.

Magnus, J. andW.Wang (2014). Concept-based bayesian model averaging and growth empirics. Oxford Bulletin Of Economics And Statistics 76, 874–97.

Magnus, J. R., O. Powell, and P. Pr¨ufer (2010). A comparison of two model averaging techniques with an application to growth empirics. Journal of Econometrics 154, 139–53.

Magnus, J. R., A. T. Wan, and X. Zhang (2011). Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market. Computational Statistics and Data Analysis 55, 1331–41.

Makieła, K. and J. Osiewalski (2018). Cost efficiency analysis of electricity distribution sector under model uncertainty. The Energy Journal 39, 31–56.

Man, G. (2015). Competition and the growth of nations: International evidence from Bayesian model averaging. Economic Modelling 51, 491–501.

Man, G. (2018). Critical appraisal of jointness concepts in Bayesian model averaging: Evidence from life sciences, sociology, and other scientific fields. Journal of Applied Statistics 45, 845– 67.

Marinacci, M. (2015). Model uncertainty. Journal of the European Economic Association 13, 1022–1100.

Maruyama, Y. and E. George (2011). Fully Bayes factors with a generalized g-prior. Annals of Statistics 39, 2740–2765.

Masanjala, W. and C. Papageorgiou (2008). Rough and lonely road to prosperity: a reexamination of the sources of growth in Africa using Bayesian model averaging. Journal of Applied Econometrics 23, 671–82.

Mazerolle, M. (2017). AICcmodavg - model selection and multimodel inference based on (q)aic(c), R package. https://cran.r-project.org/web/packages/ AICcmodavg.

McCullagh, P. and J. A. Nelder (1989). Generalized Linear Models. Chapman and Hall.

McKenzie, T. (2016). Technological change and productivity in the rail industry: A Bayesian approach. Technical report, University of Oregon. Meng, X. and W. Wong (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica 6, 831–860.

Miloschewski, A. (2016). Model uncertainty and the endogeneity problem. 9-month PhD progress report, University of Warwick.

Min, C.-K. and A. Zellner (1993). Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates. Journal of Econometrics 56, 89–118.

Min, X. and D. Sun (2016). Bayesian model selection for a linear model with grouped covariates. Annals of the Institute of Statistical Mathematics 68, 877–903.

Mirestean, A. and C. G. Tsangarides (2016). Growth determinants revisited using limitedinformation Bayesian model averaging. Journal of Applied Econometrics 31, 106–32.

Moral-Benito, E. (2012). Determinants of economic growth: a Bayesian panel data approach. Review of Economics and Statistics 94, 566–79.

Moral-Benito, E. (2013). Likelihood-based estimation of dynamic panels with predetermined regressors. Journal of Business and Economic Statistics 31, 451–72.

Moral-Benito, E. (2015). Model averaging in economics: An overview. Journal of Economic Surveys 29, 46–75.

Moral-Benito, E. (2016). Growth empirics in panel data under model uncertainty and weak exogeneity. Journal of Applied Econometrics 31, 584–602.

Moral-Benito, E. and O. Roehn (2016). The impact of financial regulation on current account balances. European Economic Review 81, 148–66. Special issue on “Model Uncertainty in Economics”.

Moreno, E., J. Gir´on, and G. Casella (2015). Posterior model consistency in variable selection as the model dimension grows. Statistical Science 30, 228–41.

Morey, R. D., J. N. Rouder, and T. Jamil (2015). BayesFactor: Computation of Bayes factors for common designs, R package version 0.9.11-1. http://CRAN.R-project.org/ package=BayesFactor.

Moser, M. and P. Hofmarcher (2014). Model priors revisited: Interaction terms in BMA growth applications. Journal of Applied Econometrics 29, 344–47.

Mukhopadhyay, M. and T. Samanta (2017). A mixture of g-priors for variable selection when the number of regressors grows with the sample size. Test 26, 377–404.

Mukhopadhyay, M., T. Samanta, and A. Chakrabarti (2015). On consistency and optimality of Bayesian variable selection based on g-prior in normal linear regression models. Annals of the Institute of Statistical Mathematics 67, 963–997.

Ng, A., M. Ibrahim, and A. Mirakhor (2016). Does trust contribute to stock market development? Economic Modelling 52, 239–50.

Nott, D. and R. Kohn (2005). Adaptive sampling for Bayesian variable selection. Biometrika 92, 747–63.

Oberdabernig, D., S. Humer, and J. Crespo Cuaresma (2018). Democracy, geography and model uncertainty. Scottish Journal of Political Economy 65, 154–85.

Onorante, L. and A. E. Raftery (2016). Dynamic model averaging in large model spaces using dynamic Occam’s window. European Economic Review 81, 2–14. Special issue on “Model Uncertainty in Economics”.

Osiewalski, J. and M. Steel (1993). Una perspectiva bayesiana en selecci´on de modelos. Cuadernos Economicos 55, 327–51. Original English version “A Bayesian perspective on model selection” at http://www.cyfronet.krakow.pl/˜eeosiewa/pubo.htm.

Ouysse, R. (2016). Bayesian model averaging and principal component regression forecasts in a data rich environment. International Journal of Forecasting 32, 763–87.

Papageorgiou, C. (2011). How to use interaction terms in BMA: reply to Crespo Cuaresma’s comment on Masanjala and Papageorgiou (2008). Journal of Applied Econometrics 26, 1048– 50.

Parmeter, C., A. Wan, and X. Zhang (2016). Model averaging estimators for the stochastic frontier model. Economics Working Paper 2016-09, University of Miami.

Pelster, M. and J. Vilsmeier (2018). The determinants of CDS spreads: evidence from the model space. Review of Derivatives Research 21, 63–118.

P´erez, J. and J. Berger (2002). Expected-posterior prior distributions for model selection. Biometrika 89, 491–511.

Perrakis, K., D. Fouskakis, and I. Ntzoufras (2015). Variations of the power-conditionalexpected- posterior prior for Bayesian variable selection in generalized linear models. ArXiv 1508.00793, Athens University of Economics and Business.

Perrakis, K. and I. Ntzoufras (2018). Bayesian variable selection using the hyper-g prior in WinBUGS. WIREs Computational Statistics, e1442. https://doi.org/10.1002/wics.1442.

Pham, T. (2017). Impacts of globalization on the informal sector: Empirical evidence from developing countries. Economic Modelling 62, 207–18.

Philips, A. (2016). Seeing the forest through the trees: a meta-analysis of political budget cycles. Public Choice 168, 313–41.

Piironen, J. and A. Vehtari (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing 27, 711–35.

Piribauer, P. (2016). Heterogeneity in spatial growth clusters. Empirical Economics 51, 659–80.

Piribauer, P. and J. Crespo Cuaresma (2016). Bayesian variable selection in spatial autoregressive models. Spatial Economic Analysis 11, 457–79.

Puy, D. (2016). Mutual funds flows and the geography of contagion. Journal of International Money and Finance 60, 73–93.

Raftery, A. (1995). Bayesian model selection in social research. Sociological Methodology 25, 111–63.

Raftery, A. (1996). Approximate Bayes factors and accounting for model uncertainty in generalised linear models. Biometrika 83, 251–66.

Raftery, A., T. Gneiting, F. Balabdaoui, and M. Polakowski (2005). Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133, 1155–74.

Raftery, A., J. Hoeting, C. Volinsky, I. Painter, and K. Yeung (2010). Bayesian model averaging. R package vs. 3.13. http://CRAN.R-project.org/package=BMA.

Raftery, A., D. Madigan, and J. Hoeting (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association 92, 179–91.

Raftery, A. and Y. Zheng (2003). Discussion: Performance of Bayesian model averaging. Journal of the American Statistical Association 98, 931–8.

Raftery, A. E., M. K´arn´y, and P. Ettler (2010). Online prediction under model uncertainty via dynamic model averaging: Application to a cold rolling mill. Technometrics 52, 52–66.

Ribeiro, P. (2017). Selecting exchange rate fundamentals by bootstrap. International Journal of Forecasting 33, 894–914.

Robert, C. (2007). The Bayesian choice: from decision-theoretic foundations to computational implementation (2nd ed.). Springer.

Robert, C. and G. Casella (2004). Monte Carlo Statistical Methods. New York: Springer.

Rockey, J. and J. Temple (2016). Growth econometrics for agnostics and true believers. European Economic Review 81, 86–102. Special issue on “Model Uncertainty in Economics”.

Rodrik, D., A. Subramanian, and F. Trebbi (2004). Institutions rule: the primacy of insitutions over geography and integration in economic development. Journal of Economic Growth 9, 131–165.

Rose, A. and M. Spiegel (2011). Cross-country causes and consequences of the crisis: An update. European Economic Review 55, 309–24.

Rossell, D., J. D. Cook, D. Telesca, and P. Roebuck (2014). mombf: Moment and inverse moment Bayes factors, R package version 1.5.9. http://CRAN.R-project.org/package= mombf.

Rossell, D. and D. Telesca (2017). Nonlocal priors for high-dimensional estimation. Journal of the American Statistical Association 112, 254–65.

Rossi, P. E., G. Allenby, and R. McCulloch (2006). Bayesian Statistics and Marketing. New York: Wiley.

Russell, N., T. Murphy, and A. Raftery (2015). Bayesian model averaging in model-based clustering and density estimation. Technical Report arXiv: 1506.09035, University ofWashington.

Saban´es Bov´e, D. (2011). hyper-g priors for GAM selection, R package. https://r-forge. r-project.org/projects/hypergsplines/.

Saban´es Bov´e, D. and L. Held (2011a). Bayesian fractional polynomials. Statistics and Computing 29, 309–24.

Saban´es Bov´e, D. and L. Held (2011b). Hyper-g priors for generalized linear models. Bayesian Analysis 6, 387–410.

Saban´es Bov´e, D., L. Held, and G. Kauermann (2015). Objective Bayesian model selection in generalised additive models with penalised splines. Journal of Computational and Graphical Statistics 24, 394–415.

Sachs, J. and A. Warner (2001). The curse of natural resources. European Economic Review 45, 827–38.

Sala-i-Martin, X. (1997). I just ran two million regressions. American Economic Review 87(2), 178–83.

Sala-i-Martin, X., G. Doppelhofer, and R. Miller (2004). Determinants of long-term growth: A Bayesian averaging of classical estimates (BACE) approach. American Economic Review 94, 813–35.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461–4.

Scott, J. and J. Berger (2010). Bayes and empirical Bayes multiplicity adjustment in the variableselection problem. Annals of Statistics 38, 2587–619.

Shao, J. (1997). An asymptotic theory for linear model selection. Statistica Sinica 7, 221–64.

Shi, J. (2016). Bayesian model averaging under regime switching with application to cyclical macro variable forecasting. Journal of Forecasting 35, 250–62.

Sickles, R. (2005). Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings. Journal of Econometrics 126, 305– 34.

Smith, J. and K. Wallis (2009). A simple explanation of the forecast combination puzzle. Oxford Bulletin of Economics and Statistics 71, 331–55.

Som, A., C. Hans, and S. MacEachern (2015). Bayesian modeling with mixtures of block g priors. Technical report, Dept. of Statistics, Ohio State University.

Sparks, D., K. Khare, and M. Ghosh (2015). Necessary and sufficient conditions for highdimensional posterior consistency under g-priors. Bayesian Analysis 10, 627–664.

Spiegelhalter, D., N. Best, B. Carlin, and A. van der Linde (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B 64, 583–640.

Stock, J. and M. Watson (2004). Combination forecasts of output growth in a seven-country data set. Journal of Forecasting 23, 405–30.

Stock, J. and M. Watson (2006). Forecasting with many predictors. In C. G. G. Elliott and A. Timmermann (Eds.), Handbook of Economic Forecasting, pp. 515–54. Elsevier.

Strachan, R. and H. van Dijk (2013). Evidence on features of a DSGE business cycle model from Bayesian model averaging. International Economic Review 54, 385–402.

Strachan, R. W. (2009). Comment on ’jointness of growth determinants’ by Gernot Doppelhofer and Melvyn Weeks. Journal of Applied Econometrics 24, 245–47.

Strawderman, W. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Annals of Mathematical Statistics 42, 385–8.

Temple, J. (2000). Growth regressions and what the textbooks don’t tell you. Bulletin of Economic Research 52, 181–205.

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58, 267–88.

Tobias, J. and M. Li (2004). Returns to schooling and Bayesian model averaging; a union of two literatures. Journal of Economic Surveys 18, 153–80.

Traczynski, J. (2017). Firm default prediction: A Bayesian model-averaging approach. Journal Of Financial And Quantitative Analysis 52, 1211–45.

Tsangarides, C. G. (2004). A Bayesian approach to model uncertainty. Working Paper 04/68, IMF.

Tu, Y. (2018). Entropy-based model averaging estimation of nonparametric models. Guanghua School of Management and Center for Statistical Science, Peking University.

Ullah, A. and H. Wang (2013). Parametric and nonparametric frequentist model selection and model averaging. Econometrics 1, 157–79.

Vallejos, C. and M. Steel (2017). Bayesian survival modelling of university outcomes. Journal of the Royal Statistical Society, A 180, 613–31.

van den Broeck, J., G. Koop, J. Osiewalski, and M. Steel (1994). Stochastic frontier models: a Bayesian perspective. Journal of Econometrics 61, 273–303.

van der Maas, J. (2014). Forecasting inflation using time-varying Bayesian model averaging. Statistica Neerlandica 68, 149–82.

Varian, H. (2014). Big data: New tricks for econometrics. Journal of Economic Perspectives 28, 3–28.

Vaˇs´ıˇcek, B., D. ˇ Zigraiov´a, M. Hoeberichts, R. Vermeulen, K. ˇSm´ıdkov´a, and J. de Haan (2017). Leading indicators of financial stress: New evidence. Journal of Financial Stability 28, 240– 57.

Verdinelli, I. and L. Wasserman (1995). Computing Bayes factors by using a generalization of the Savage-Dickey density ratio. Journal of the American Statistical Association 90, 614–618.

Villa, C. and J. Lee (2016). Model prior distribution for variable selection in linear regression models. Discussion paper, University of Kent.

Villa, C. and S. Walker (2015). An objective Bayesian criterion to determine model prior probabilities. Scandinavian Journal of Statistics 42, 947–66.

Volinsky, C., D. Madigan, A. Raftery, and R. Kronmal (1997). Bayesian model averaging in proportional hazards model: Predicting the risk of a stroke. Applied Statistics 46, 443–8.

Wagner, M. and J. Hlouskova (2015). Growth regressions, principal components augmented regressions and frequentist model averaging. Jahrb¨ucher fur National¨okonomie und Statistik 235, 642–62.

Wallis, K. (2005). Combining density and interval forecasts: A modest proposal. Oxford Bulletin of Economics and Statistics 67, 983–94.

Wang, H., X. Zhang, and G. Zou (2009). Frequentist model averaging estimation: A review. Journal of Systems Science and Complexity 22, 732–48.

Wang, H. and S. Zhou (2013). Interval estimation by frequentist model averaging. Communications in Statistics: Theory and Methods 42, 4342–56.

Wang, M. (2017). Mixtures of g-priors for analysis of variance models with a diverging number of parameters. Bayesian Analysis 12, 511–32.

Wang, M. and Y. Maruyama (2016). Consistency of Bayes factor for nonnested model selection when the model dimension grows. Bernoulli 22, 2080–100.

Watson, P. and S. Deller (2017). Economic diversity, unemployment and the Great Recession. The Quarterly Review of Economics and Finance 64, 1–11.

Wei, Y. and Y. Cao (2017). Forecasting house prices using dynamic model averaging approach: Evidence from China. Economic Modelling 61, 147–55.

W¨olfel, K. and C. Weber (2017). Searching for the Fed’s reaction function. Empirical Economics 52, 191–227.

Womack, A., C. Fuentes, and D. Taylor-Rodriguez (2015). Model space priors for objective sparse Bayesian regression. arXiv 1511.04745v1.

Wright, J. (2008). Bayesian model averaging and exchange rate forecasts. Journal of Econometrics 146, 329–41.

Wu, H., M. Ferreira, and M. Gompper (2016). Consistency of hyper-g-prior-based Bayesian variable selection for generalized linear models. Brazilian Journal of Probability and Statistics 30, 691–709.

Xiang, R., M. Ghosh, and K. Khare (2016). Consistency of Bayes factors under hyper g-priors with growing model size. Journal of Statistical Planning and Inference 173, 64 – 86.

Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: Wiley.

Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel and A. Zellner (Eds.), Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, Amsterdam: North-Holland, pp. 233–43.

Zellner, A. and A. Siow (1980). Posterior odds ratios for selected regression hypotheses (with discussion). In J. Bernardo, M. DeGroot, D. Lindley, and A. Smith (Eds.), Bayesian Statistics, Valencia: University Press, pp. 585–603.

Zeugner, S. and M. Feldkircher (2015). Bayesian model averaging employing fixed and flexible priors: The BMS package for R. Journal of Statistical Software 68.

Zhang, H., X. Huang, J. Gan, W. Karmaus, and T. Sabo-Attwood (2016). A two-component g-prior for variable selection. Bayesian Analysis 11, 353–80.

Zhang, X., Z. Lu, and G. Zou (2013). Adaptively combined forecasting for discrete response time series. Journal of Econometrics 176, 80–91.

Zhang, X. and W. Wang (2018). Optimal model averaging estimation for partially linear models. Statistica Sinica, forthcoming.

Zhang, X., D. Yu, G. Zou, and H. Liang (2016). Optimal model averaging estimation for generalized linear models and generalized linear mixed- effects models. Journal of the American Statistical Association 111, 1775–90.

Zhu, R., A. Wan, X. Zhang, and G. Zou (2018). A Mallows- type model averaging estimator for the varying-coefficient partially linear model. Journal of the American Statistical Association, forthcoming.

Zigraiova, D. and T. Havranek (2016). Bank competition and financial stability: Much ado about nothing? Journal of Economic Surveys 30, 944–81.

Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101, 1418–29.