sensitive is population growth. While this variable is a key determinant of growth in the neoclassical growth model, it does not appear to be a robust predictor of growth in a linear model. WEO forecasts also place more weight on foreign direct investment, but the differences are not significant.
LASSOcoefficients (selected variables) for predicting cumulative real GDP growth rates and WEO growth forecasts: all countries
log(GDP per capita), year t-1
I regress real GDP growth rates on the IMF’s growth forecasts and find that IMF forecasts behave similarly to those generated by overfitted models, placing too much weight on observable predictors and underestimating the forces of mean reversion. I identify several such variables that explain forecasts well but are not predictors of actual growth. I show that, at long horizons, IMF forecasts are little better than a forecasting rule that uses no information other than the historical global sample average growth rate (i.e., a constant). Given the large noise component in forecasts, particularly at longer horizons, the paper calls into question the usefulness of judgment-based medium and long-run forecasts for policy analysis, including for debt sustainability assessments, and points to statistical methods to improve forecast accuracy by taking into account the risk of overfitting.
Model selection and forecasting in stress tests can be facilitated using machine learning techniques. These techniques have proved robust in other fields for dealing with the curse of dimensionality, a situation often encountered in applied stress testing. Lasso regressions, in particular, are well suited for building forecasting models when the number of potential covariates is large, and the number of observations is small or roughly equal to the number of covariates. This paper presents a conceptual overview of lasso regressions, explains how they fit in applied stress tests, describes its advantages over other model selection methods, and illustrates their application by constructing forecasting models of sectoral probabilities of default in an advanced emerging market economy.
, bounded by +/- 1 standard deviation lines, vertical axis; upper horizontal axis indicates number of non-zero coefficients associated with a given value of log( λ ). Leftmost discontinuous vertical line corresponds to the MSE of λ -min; rightmost discontinuous vertical line to the MSE of the λ -1se.
Source: Author’s calculations.
Lasso and relaxed lasso, coefficient estimates, λ -min specification
Panel A: Basic Materials
Lasso Number of lags
Relaxed Lasso Number of lags
yields the lassocoefficients β i , k j λ in the i -th equation of the VAR model, where T is the number of observations, and p the number of lags. Note that the coefficients depend on the value of the penalty parameter, λ . The larger the parameter value, the larger the number of coefficients shrinked towards the value of zero.
Typically, k -fold cross-validation serves to choose the penalty parameter. The validation process divides the set of observation into k groups or folds. Each fold
Diebold and Yilmaz (2015) recently introduced variance decomposition networks as tools for quantifying and ranking the systemic risk of individual firms. The nature of these networks and their implied rankings depend on the choice decomposition method. The standard choice is the order invariant generalized forecast error variance decomposition of Pesaran and Shin (1998). The shares of the forecast error variation, however, do not add to unity, making difficult to compare risk ratings and risks contributions at two different points in time. As a solution, this paper suggests using the Lanne-Nyberg (2016) decomposition, which shares the order invariance property. To illustrate the differences between both decomposition methods, I analyzed the global financial system during 2001 – 2016. The analysis shows that different decomposition methods yield substantially different systemic risk and vulnerability rankings. This suggests caution is warranted when using rankings and risk contributions for guiding financial regulation and economic policy.