A first step is to identify variables that can arguably explain the dynamics in GDP growth, which represents the outcome variable in GaR models. Researchers typically rely on a combination of local macroeconomic conditions, local macro-financial conditions, and international macroeconomic conditions. The selection of specific variables will depend, for example, on a country’s risk profile, its economic and financial openness, or the characteristics of financial systems. The following table shows an example of a categorization of variables that can potentially affect GDP growth:

A GaR estimation will typically group these variables in buckets by computing indices. This aggregation can be performed via principal components analysis or, for example, by computing indices such as CEMLA’s Financial Condition Index.

The point estimates from the quantile regressions (QR) can be interpreted as the values of the cumulative distribution function (CDF) of expected GDP growth. The following figure shows how the point estimates from the QR can be ranked to form the shape of a distribution:

The CEMLA GaR Model estimates the distribution (the green line above) by fitting the coefficients from the QR model with a non-parametric approach. In simple, we use a Kernel function and an optimized bandwidth parameter to weight the observations within each bandwidth of GDP growth. This approach allows deriving the expected distribution of GDP growth for a given period and jurisdiction. Since the distribution is obtained from the QR model, it remains being conditional on macrofinancial conditions: changing macrofinancial conditions will likely change the shape of the distribution. The documentation section provides details both on this approach as well as on alternative parametric fitting procedures to translate the results from the QR model into a GDP growth distribution.

Quantile regressions (QR) are used to estimate the relationship between macrofinancial risk and GDP growth. QR estimate the effect of macrofinancial variables on quantiles of the GDP growth distribution (for a given horizon). They provide as many estimated coefficients as quantiles are being estimated.

The diagram above provides an intuition of the QR method. Panel A depicts the (hypothetical) relationship between GDP growth (Y axis) and a financial conditions index (FCI, X axis) for a set of countries in a given quarter. A higher value of FCI indicates tighter macrofinancial conditions. Panel B restricts the sample to GDP-growth observations around a value of 0.5 in the FCI. Here, the red marks represent the five quintiles of the GDP growth distribution for this latter FCI value.

Panel C extends this latter exercise for three different values of the FCI. Panel D adds two lines representing linear regressions at the 80th (blue line) and 20th (red line) percentiles of GDP growth. In this example, a higher FCI has a negative effect on the 20th percentile of the GDP growth distribution, whereas the effect on the 80th percentile is negligible. A higher FCI would therefore shift to the left the left tail of the distribution.

The results from QR are usually reported in plots like the ones depicted above. These plots show the estimated effect of a shift in FCI on each individual quantile of the GDP growth distribution, ranked in the X-axis. The left panel shows that over a one-quarter horizon (h=1), a higher FCI has a negative effect on the lower quantiles of the GDP distribution, increasing the probability of low GDP growth rates. The right panel shows that over an eight-quarters horizon (h=8), higher FCI values have a positive effect on the lower quantiles of the GDP growth distribution.

The main outcome of GaR estimations are expected GDP growth distributions conditional on the stance of macro-financial conditions. Once a distribution is estimated, one can perform counterfactual analyses by evaluating how expected GDP growth distributions shift depending on the stance of macro-financial risk factors.

In this example, a negative shock to macro-financial conditions equal to a one standard deviation shifts the GDP growth distribution to the left (red dashed line). The probability of realizing a negative GDP growth rate increases in a proportion equal to the area identified by the points A, B, and C in the figure. Correspondingly, the model predicts that with a probability of 5% the GDP growth rate will fall below a lower threshold compared to the baseline scenario.

The CEMLA Financial Conditions Index (FCI) measures financial stress by combining data on equity, bond, and foreign exchange markets for each country of the panel. The variables of interest for each market sector are the following:

Equity market: stock market indices (e.g., Bovespa, COLCAP, BVL Peru General Index TR).

Bond market: 10-year government yields.

Real effective exchange rate (REER): weighted average of the exchange rates of foreign currencies against the domestic currency. These exchange rates are weighted according to the share of a trade partner in total net exports. An increase in the REER indicates an appreciation of the local currency vis- `a -vis major trade partners, implying a loss in trade competitiveness.

Each variable is transformed into two stress variables :

   1. A measure of volatility.

Equity market: the realized monthly volatility of daily logarithmic returns of real stock indices.

Bond market: the realized monthly volatility of daily real rate changes.

Foreign exchange market: the logarithmic return between months.

    2. A measure capturing how "bad" the cumulative performance of a variable is (within a rolling time window).

Equity market: gap between the maximum and observed value of the stock index.

Bond market: gap between the minimum and observed value of the spread between the US and domestic yields.

Foreign exchange market: the absolute value of the semiannual change of the REER.

Finally, the country-level FCI index represents the average of the standardized stress variables.

The overall process is schemed in the following diagram:

The four stages are:

a. (yellow section) Data extraction, transformation and loading.

b. (blue section) Creation of stress variables: For each market sector, we construct two stress variables. One variable reflects the volatility of the sector; the other one, the cumulative performance.

c. (red section) Standardization of the stress variables and their aggregation into market sector sub-indices.

d. (green section) Aggregation with the double product via the estimated correlation matrix of the sub-indices.

Considering that the index leaves out many important aspects of financial markets, we include fewer (but relevant) variables than specialized indices in order to get homogeneity and comparability across countries indices in the panel.

It is noteworthy that this methodology allows to capture non-linearity and spillover effects across sectors by the construction of the stress variables (through the realized volatility and the cumulative maximum or minimum values) and the correlation matrix. For additional references, please go to the C-GARP Documentation.

Following this methodology, we present financial conditions index for Mexico (e), as well as the sub-indices (a-c) and their correlations (d) required for its calculation below.

In this example, the dates of the analysis range from the first quarter of 2004 to the last quarter of 2020. This example is intended to show the linkage between the financial stress for each sector and its aggregation into the final index. A tightening in the financial conditions is shown as an increase in the value of the index and sub-indices.

The year 2020 is shaded to highlight the encompassing of the COVID-19 crisis. Note the rise in both the sub-indices and the coupling of the pairwise cross-correlations that result in a spike in the final index.