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Brazilian stock markets underwent a period of remarkable exuberance between early 2016 and March 2020, only to crash with the global turmoil related to health worries and oil prices. The Ibovespa index tripled its market value between a low point in January 2016 and its maximum in January 2020—by March 12, half those gains had been erased. Narratives about a bubble in Brazilian stocks before the global crash and its subsequent burst are plentiful in specialized media. In this paper, we explore this narrative from within the framework of strict local martingale financial bubbles. A key result in this literature states some financial asset price displays a bubble only if it follows a strict local martingale under the equivalent risk-neutral measure. A diffusion process is a strict local martingale if its volatility increases faster than linearly as its level grows. We first apply a nonparametric method to estimate the volatility function of Ibovespa daily prices, then fit a stochastic volatility model whose parameter values can discriminate the underlying price process as either a true martingale or a strict local martingale. Our results are negative towards the presence of a strict local martingale bubble in the Ibovespa index. Strict local martingale bubbles are related to a positive relationship between returns and volatility which does not seem present in the data at hand. We also performed a comparative analysis of the patterns found for the Ibovespa with the S&P500 index, spot Brent oil and gold prices. Electronic supplementary material The online version of this article (10.1007/s43546-020-00005-w) contains supplementary material, which is available to authorized users.

We apply the data cloning method to estimate a medium-scale dynamic stochastic general equilibrium model. The data cloning algorithm is a numerical method that employs replicas of the original sample to approximate the maximum likelihood estimator as the limit of Bayesian simulation-based estimators. We also analyze the identification properties of the model. We measure the individual identification strength of each parameter by observing the posterior volatility of data cloning estimates and access the identification problem globally through the maximum eigenvalue of the posterior data cloning covariance matrix. Our results corroborate existing evidence suggesting that the DSGE model of Smeets and Wouters is only poorly identified. The model displays weak global identification properties, and many of its parameters seem locally ill-identified.