Growth-at-Risk: A Framework for Assessing Economic Vulnerability

Abbrevations

GaR: The Growth-at-Risk; GDP: Gross Domestic Product; VaR: Value-at-Risk; GARCH: Generalized Autoregressive Conditional Heteroskedasticity; NFCI: National Financial Conditions Index; FCI: Financial Conditions Index; GIV: Granular Instrumental Variables; IMF: International Monetary Fund; LDA: Linear Discriminant Analysis; SRI: Systemic Risk Indicator; MPI: Macroprudential Policy Indicator; CLI: Composite Leading Indicator; OLS: Ordinary Least Squares; RIR: Real Interest Rate; KDE: Kernel Density Estimation; BERT: Barbados Economic Recovery and Transformation.

Introduction

The concept of Growth at Risk (GaR) has emerged as a valuable tool in economic analysis, especially for assessing vulnerability to future downturns. GaR shifts focus from point forecasts of economic growth to the entire distribution of possible outcomes. It emphasizes the link between financial conditions and downside risks. Unlike traditional forecasts, GaR quantifies the probability and severity of potential negative growth scenarios. GaR also originated as an extension of value-at-risk (VaR) models. It estimates the expected distribution of GDP growth based on financial market conditions and other macroeconomic factors. Thus, GaR models link financial conditions with anticipated GDP growth to assess real-sector implications of systemic risk.

GaR offers policymakers valuable insights by enabling them to comprehensively assess economic risks. By quantifying the likelihood of downside scenarios, GaR helps them implement preemptive measures to mitigate potential downturns. Policymakers can use the framework in macroprudential policy to assess financial vulnerabilities and guide regulatory actions. Overall, GaR research advances economic analysis. By incorporating financial conditions and the entire growth distribution, GaR provides a more robust framework for assessing economic vulnerability and informing policy decisions.

This study examined three main approaches for multivariate GaR. First, copula-based models estimate marginal distributions using methods such as kernel density estimation. Researchers then select a copula function, such as the Gaussian or Clayton copula, to model the dependence structure of the variables. They use the joint distribution to simulate future scenarios for all variables. Second, GaR models with stochastic volatility capture dynamic interactions. These models track time-varying volatility using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and forecast future values for all variables, accounting for volatility changes. Thirdly, the quantile regression approach addresses the limitations of linear regression, by enabling researchers to explore how changes in macrofinancial conditions affect different quantiles of the GDP growth distribution.

With the GaR model, we seek to determine the probability that GDP growth will fall below a given threshold for four (4) Caribbean economies: The Bahamas, Barbados, Jamaica, and Trinidad and Tobago. We also extend the model to simulate macroeconomic shocks and scenarios, and then calculate their impact on the probability that growth falls below the threshold. Following the introduction, Section II investigates pertinent literature. Section III gives an overview of the selected countries’ economic performance. Section IV discusses the methodology and analyzes results. Section V summarizes the findings and concludes the paper.

Literature Review

The GaR Methodology was introduced by Tobias Adrian, Nina Boyarchenko, and Domenico Giannone in their 2019 paper, “Vulnerable Growth” [1, 2]. The paper models the entire distribution of future real GDP growth as a function of current financial and economic conditions and evaluates financial risks to economic growth in the United States. To assess economic and financial conditions, Adrian et al. used real GDP growth data from the Bureau of Economic Analysis and the National Financial Conditions Index (NFCI). The authors then employed semi-parametric quantile regressions to estimate the distribution. This approach describes the conditional relationship between future GDP growth and current financial and economic conditions. A skewed-t distribution was fitted to the quantile regression to smooth the results and derive a probability density function. The results indicated a nonlinear relationship between financial conditions and economic growth. The authors found that deteriorating financial conditions resulted in higher conditional volatility and a lower conditional mean of GDP growth. Adrian et al. also noted that upside growth risks were lower in most periods, while downside risks increased as financial conditions tightened. Measures of downside risk moved in line with financial conditions. Upside risk measures were more stable, meaning that lower quantiles depend more on current financial conditions for future GDP growth than upper quantiles. To verify these findings, Adrian et al. used both a fully parametric and a non-parametric approach. Both methods produced consistent results, confirming that the findings were robust and not dependent on their two- step method.

In an extension of the previous paper, Adrian, et al. [1] estimated the term structure of the predicted distribution of GDP growth for 11 advanced economies. The authors examined whether high GaR could occur in the near term due to loose financial conditions and whether it would be sustained. The panel quantile regression model used financial conditions, credit-to-GDP growth, the credit boom indicator, initial output growth, and inflation.

These variables helped derive the future distribution of GDP growth. Local projections were used to estimate the dynamic responses of GDP growth moments over 1 to 12 quarters. This allowed the authors to explore the progression of downside risk over time. Adrian et al. constructed a Financial Conditions Index (FCI) for each country in the panel. The FCI included up to 17 price-based variables, including short-term interbank risk spreads, corporate bond spreads, and stock return volatility. Estimates for the FCI were obtained using a vector autoregression model. This model varied over time due to changes in variable interactions and differences in data availability. The results showed that financial conditions had a greater effect on the lower fifth percentile of the growth distribution than on the median. This echoed a key finding in Vulnerable Growth. The term structure developed, showed that downside risks to growth are small in the near term with loose initial financial conditions, but increase in later quarters. When loose financial conditions combined with a credit boom, the authors noted a substantial adverse effect on the fifth percentile after quarter five, but no impact on the median. Adrian et al. also used the granular instrumental variables (GIV) approach to create a new instrument for financial conditions outside the FCI. This tested whether endogeneity bias between financial factors and GDP growth could explain their findings. The GIV results showed that the concern was unwarranted.

Since the introduction of the GaR approach, several authors have explored the concept in depth and evaluated its benefits for assessing growth risks. Further, policy institutions such as the International Monetary Fund (IMF)

have adopted the technique to monitor risks across countries. For example, Prasad [3] indicated that the GaR analysis was beneficial to policy-makers, as it could enhance their macro-financial surveillance activities. The reason is that the methodology focused on the entire growth distribution, which encompassed upside and downside risks to future economic growth, compared to the traditional point forecast used to guide policy decisions. Access to the complete distribution might encourage policy-makers to create and implement policies geared towards reducing risks to growth beforehand, compared to those that optimise outcomes under central scenarios [3, 4]. Further, it provided a framework for assessing the key drivers of future economic growth, which varied across the distribution of growth [5, 6, 7, 8, 9]. Lastly, the authors noted that GaR analysis could help gauge the impact of systemic risk on future GDP growth, thereby aiding the guidance and implementation of macro-prudential policies that protect financial stability and positively impact GaR [10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. However, Adrian, et al. [1] suggested that policy- makers might want to consider the inter-temporal trade- offs arising from their policy decisions, given their findings on the term structure of Growth-At-Risk. Moreover, when applying the GaR framework to country-specific data for risk measurement and macro-prudential policy implementation, a proper understanding of cross-country heterogeneity was needed, particularly for panel models. This was because a nation’s structural characteristics played an important role in shaping cross-country variations in GaR across risk indicators and time horizons [11].

Raluca [15] examined the potential impact of the GaR analysis on macro-prudential policy in Indonesia under different stress scenarios. The first step involved sorting 26 macro-financial variables into the categories of financial conditions (FINC), macrofinancial vulnerabilities (MAF), or other relevant factors (OTH), using factor analysis. The minimal residual method (MINRES) was used to determine which variables contributed most to the variability in the original series. Once determined, the author built a composite index for each partition, which was used to account for changes in financial conditions observed within each partition over time. This was followed by applying the quantile regression approach to the sample’s quarterly data, conditional on the partitions as mentioned above and a proxy for macroprudential policy. The GDP growth rate was included as a control variable. Findings showed that the materialisation of risk under three scenarios had significant benefits for improving the Growth-At-Risk contingent on the nature of their underlying vulnerabilities.

O’Brien, et al. [17] of the Central Bank of Ireland used the GaR framework to assess the likelihood and severity of future weak economic growth in Ireland, given current financial conditions and vulnerabilities. Results indicated that adverse growth outcomes in Ireland were most likely to occur during periods when threats to financial stability were rising. Further, near-term tail risks were heavily impacted by prevailing financial market conditions, while medium-horizon risks were more dependent on systemic financial vulnerabilities. The author’s analysis also suggested that structural features of Ireland’s economy increased the country’s susceptibility to weak growth outcomes.

Drenkovska, et al. [9], in a discussion paper published by the Bank of Slovenia, utilised the GaR approach to examine the connection between macro-financial conditions and economic activity in Slovenia. Following the three-step GaR procedure proposed by Prasad [3], the author developed, for analysis purposes, a financial conditions indicator (FCI) that aggregated metrics of financial stress and volatility from multiple financial markets. Moreover, the FCI included simpler metrics on yields and price indices that were regularly featured in policy debates or had been found to have good leading properties in other literature. In an effort to improve the quality of their regressions, the authors used Linear Discriminant Analysis (LDA) as a data reduction technique to extract common trends from relevant macro- financial events and remove idiosyncratic noise. Further, data reduction lowered the number of parameters needed for their estimations. Drenkovsak, et al. [9] also included the Domestic Systemic Risk Indicator (SRI) proposed by Lang, et al. [14] in their analysis, along with a macroprudential policy indicator (MPI) and a composite leading indicator (CLI). Results from the author’s baseline scenario supported the view that macro-financial conditions contained predictive signals of increased risks at the tails of the future GDP growth distribution. Further, estimates showed that the FCI represented downside risks to growth across all projection horizons.

At the same time, the SRI had the most significant adverse effects on the tail of the growth distribution around 8-12 quarters ahead. The negative coefficients on both indicators also indicated that higher systemic risk and financial stress are associated with lower GDP growth at the 10th percentile of the growth distribution, leading to lower growth forecasts for the distribution’s tail. In addition, the scenario analysis exercise showed that loose financial conditions were associated with sizeable leverage build-ups and higher short- term future growth. However, build-ups in leverage over time increased risks to medium-term growth in the Slovenian data; the same conclusion was reached by O’Brien, et al. [17] in Irish Data. Moreover, similar results from Lang, et al. [13] revealed that financial stress and vulnerability indicators contained information on growth-at-risk in the short term. In contrast, vulnerability indicators held information about GaR over the medium term [2, 9, 11, 12, 17]. Researchers also proposed modifications to the traditional growth-at-risk to improve the reliability and performance of GaR models, with a focus on assessing the impact of the COVID-19 pandemic on economic growth.

Chicana, et al. [8] modified the growth-at-risk framework by incorporating several model validation techniques to determine which forecasting density from their quantile regression results had the best predictive power for Peruvian data, adding a step to the methodology proposed by Prasad [3], which was used to build their GaR model. The authors utilised Schmidt, et al. [19] quantile-spacing approach to obtain a large sample of data from the estimated GDP growth quantiles, which were then fit to a broad set of probability distributions for interpolation. Findings indicated that macro-financial factors had heterogeneous effects on the distribution of future GDP growth across quantiles at different horizons.

Further, the negative impact of external financial conditions was more pronounced in the lower distribution quantile, consistent with the literature on GaR. After evaluating their models, the authors found that nonparametric density fitting via Kernel Density Estimation (KDE) and mixed normal density fitting produced the best density forecasts for Peruvian data. After establishing a reliable methodology for the GaR model, Chicana, et al. [8] proceeded with their counterfactual to evaluate the “Reactiva Peru” program sponsored by the government. The results of their estimations showed that the policy reduced the impact of the COVID-19 shock on the economy, as it would have had lower expected future growth and higher macro-financial risks if it had not been implemented [22, 23, 24, 25].

Mihail Yanchev [26] created an enhanced GaR Model, known as DeepGar, by proposing improvements to Adrian, et al. ’s [2] approach. The first enhancement consisted of generating quantiles simultaneously to alleviate the quantile-crossing problem. This was followed by introducing a quantile-crossing loss into the tilted loss function to prevent the above-mentioned problem further. Thirdly, the author used an artificial neural network implemented with the TensorFlow library to model non-linear relationships between the predictors and the target variable. The last change to the original procedure involved combining the above steps into a single model, which was optimised by minimising the tilted absolute loss and the least-squares loss. The author compared their deep-growth-at-risk model to a benchmark similar to Adrian, et al. [2] procedure and found that their proposed model outperformed the benchmark in predicting the adverse effects of the COVID-19 pandemic on GDP for the countries of interest (Bulgaria, Lithuania, Estonia, and Romania). It also performed better when modelling the recession caused by the unexpected shock of the global pandemic.

Methodology and Results Analysis

In the GaR application, the first step was to identify relevant macrofinancial variables that could explain the dynamics of GDP growth in the selected countries. Most studies consider three buckets of variables that could potentially explain GDP growth prospects: Local Macroeconomic Conditions, Local Macrofinancial Conditions, and International Macroeconomic Conditions. Therefore, in applying the methodology used by Busch, et al. [5], this study was conducted for selected Caribbean economies. The countries included in the study were The Bahamas, Jamaica, Barbados, and Trinidad & Tobago. It should be noted that the selection of variables was based on an initial qualitative assessment of relevant factors that impact GDP growth in the selected group of countries over the period 2000 to 2022. However, due to data availability constraints, other variables, such as credit-to-GDP and a financial conditions index, could not be used.

Table 5 presents the variables used in GaR applications and the categorisation of relevant GDP risk factors in this study. The bucket of local macroeconomic conditions includes GDP growth and inflation. The second bucket shifts the focus to macrofinancial conditions specific to the selected countries. The study used the interest rate differentials as a proxy for capturing trends in the credit market for The Bahamas and the selected group of countries.

The next step in the process, after selecting the relevant macrofinancial risk factors, was to estimate the relationship between these risk factors and GDP growth using quantile regressions. Quantile regressions, which can be viewed as a generalisation of ordinary least squares (OLS) estimations, were used to explore heterogeneous responses across the distribution of GDP growth, examining whether the left tail is more sensitive to macrofinancial conditions.

Policy Implications and Conclusion

Overall, the study revealed that weaker financial conditions are associated with a higher probability of experiencing negative economic growth. In addition, the impact of financial conditions on growth is asymmetric, with a more substantial influence on the lower tail (downside risks) than on the upper tail. The asymmetry suggests a potential trade-off: more relaxed financial conditions may boost short-term growth but heighten vulnerability to future downturns. Country-specific factors, such as financial depth and government effectiveness, can influence the sensitivity of growth to financial risks.

Further, the study showed that, across different levels of macroeconomic shocks, the probability of growth falling below the 2.0% threshold varied by shock size and simulation. Larger shock sizes generally increase the probability that GDP growth will fall below the threshold.

The results are well in line with similar studies conducted. According to Maran [15], early tightening of macroprudential policy would reduce downside (tail) risks to GDP growth by increasing the financial system’s resilience in the medium to long term. The results have several implications for policy-makers, as they dictate how the macro-prudential stance should be adjusted in response to certain macro-financial risks. Various studies support the view that the timing of macroprudential policy is relevant and affects the distribution of GDP growth. Therefore, Galàn [12] recommended tightening the macro-prudential stance when financial conditions become very loose, and the macro- economic environment is strong. Maran [15] also suggested tightening the macro-prudential stance when macro- financial vulnerabilities are sizeable within an expansionary economic environment or when the macro-economic environment improves substantially, as this could lead to the accumulation of macro-financial vulnerabilities in the mid-to-long term, which could negatively impact economic growth [3].

It is evident that the GaR framework can support countries’ macroprudential and macrofinancial policy implementation. The GaR framework has proven it can provide an analytical framework for quantifying the severity of systemic risk based on the current level of macrofinancial vulnerabilities.

Conflict of Interest: The authors declare no conflict of interest. Disclaimer: The views within this paper reflect the thoughts and opinions of the authors and do not represent the views of the Central Bank of The Bahamas.