Financial and Business Cycles in Brazil

Abstract

Financial and Business Cycles in Brazil by Ivo Krznar and Troy Matheson IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.

Towards Macroprudential Stress Testing: Incorporating Macro-Feedback Effects

“… Macro module. This part of the framework is a variant of the models developed in Carabenciov and others (2008) and Krznar and Matheson (2017). This class of models is typically used to understand past economic developments and to produce scenarios and forecasts.…”

“…The macroeconomic model is an extension of the model described in Krznar and Matheson (2017) that incorporates panel credit equations to provide linkages with the stress-testing model. Total credit extended by public and private banks are modelled separately to account for differences in their behavior in Brazil.…”

“…where is common equity tier 1 capital ratio, * is the regulatory capital requirement, and is each bank's historical capital buffer, i.e., the capital buffer each bank has maintained above the regulatory requirement on average over history. The regulatory requirement follows a random walk process: 15 As in Krznar and Matheson (2017), an equation for financial conditions is also included to take into account broader financial shocks (in addition to bank credit) that can affect the corporate sector and economic activity more generally. These financial conditions are also assumed to affect funding spreads and the solvency position of the banks, capturing the link between liquidity and solvency.…”

Seychelles

“…Second, the common factor approach, typically estimated through Principal Components Analysis (PCA), models the variance structure of the financial variables using optimal linear combinations of them. Occasionally, other methods such as common factor analysis using a Kalman filter (Gumata et al, 2012) or semistructural models (Krznar and Matheson, 2017) are employed. The VAR approach has the advantage of linking financial conditions and GDP as the variable of ultimate interest in a system of equations but may present econometric challenges (most notably issues related to degrees of freedom), while the PCA allows for inclusion of ample financial variables, but is, by construction, agnostic about the relationship to output (Ho and Lu, 2013) 2 despite having been found to predict future growth well and occasionally outperforming leading indicators (Gumata et al, 2012).…”

“…Note that the ordering would change based on the software used to estimate the VAR as some software use a lower triangular matrix while others use upper triangular matrix when implementing the Cholesky ordering. This ensures that the response of the variable to a shock would be zero contemporaneously if the response variable is ordered in such a way that it is not affected by the shock variable on impact.4 Put differently, a principal component is a weighted average of the variables where the weights ("loadings") are derived so that the index explains the maximum amount of variation of all included financial variables(Krznar and Matheson, 2017). In practice, only the first few principal components are considered for the FCI, assuming they capture a large share of the variation cumulatively (e.g.…”