A new approach to quantifying risks: the Quantile-MIDAS model
We have developed a new approach to nowcasting GDP growth, drawing on the existing mixed-frequency data sampling (MIDAS) models used at the Bank, with some enhancements. As the name suggests, the Quantile-MIDAS model merges the MIDAS approach with quantile regression, popularised as ‘GDP-at-risk’ models.
Quantile regression, which is increasingly used to quantify risks around the economic outlook, focuses on specific points in the distribution (eg, the 10th percentile). By doing so for multiple quantiles, our model reveals the broader shape of the distribution of possible future outcomes for UK GDP. A similar approach has been used at the Bank previously to estimate Inflation-at-Risk. Combining this with MIDAS techniques allows for the use of higher-frequency data, such as monthly, or even weekly indicators, by directly mapping them to the target variable without adjusting for different frequencies and helping to prevent information loss. This is a novel approach to quantile forecasting for GDP and enables us to exploit the information in the higher-frequency data across the full distribution. As a result, our framework can also provide insights on the determinants of growth at different quantiles of the distribution.
Specifically, we predict quarterly UK GDP growth one quarter ahead across five quantiles corresponding to the 10th, 25th, 50th, 75th and 90th percentiles. Similar to our standard MIDAS approach, the model separately estimates nowcasts from soft indicators (eg, business surveys, sentiment indices) and hard indicators (eg, monthly GDP (MGDP) data) before combining them. This two-stage process ensures that the model leverages the strengths of both types of data, resulting in a more robust and accurate nowcast.
Dynamic indicators and adaptive weighting
For our model, we have selected a range of soft indicators based on two criteria: those available at a higher frequency than GDP and those that capture movements across the full GDP distribution. Specifically, this includes measures of systemic risk, the Economic Policy Uncertainty (EPU) Index, UK house approvals, S&P Global Purchasing Managers Index (PMI) balances for output and employment and ONS retail sales.
We summarise the steer from the different indicators into a single nowcast by weighting them using the quantile combination model by Aastveit et al (2024). We adopt this approach as it allows us to consider the possibility that one indicator can be more useful than another to measure specific risks across quantiles and over time. The quantile combination approach allows us to consider forecast accuracy at the quantile level. For instance, if one indicator is more accurate in predicting the mean of the distribution while performing poorly in the tails, this combination scheme accounts for this heterogeneity and draws insights from each indicator’s contribution to the overall nowcast.
Importantly, we find that the time-varying nature of the weights is important to achieving accurate results. In our model, there is considerable variation in the weights over time. In particular, the results show that the weight on MGDP data has gradually increased over the past few years, which we believe reflects the increasingly volatile nature of monthly output data, which can lead to swings in quarterly estimates.
Looking at GDP through the lens of the model
The quantile nowcasts only show specific points in the distribution. To visualise the balance of risks and how these evolve over time, in Chart 1 we map the full distribution profile of our one quarter ahead GDP nowcasts from the Quantile-MIDAS model for 2024. In this chart, we compare the nowcasts to the ONS first estimate of GDP in each quarter (shown in the vertical lines). Firstly, we find that the model can accurately map shifts in UK activity, shown by the movement of the whole distribution leftward over the course of the year. This chart also shows us that the model can accurately predict GDP outturns, as in Q2, when the modal forecast was tightly concentrated around 0.6%, which in the event was in line with the published data (orange lines).
Secondly, and more importantly for our assessment of risk, the results show us that the risk profile changes over time: not only in shifts in the median or the overall uncertainty (ie, in the width of the distribution) but also on the skewness, giving us a full picture of the changes in risk profile. Looking at the most recent data, we find that the Quantile-MIDAS model reveals a significant increase in uncertainty around GDP growth prospects since the first half of 2024. This period has been marked by several economic events, including geopolitical tensions and the UK Autumn Budget 2024, which may have generated additional uncertainties around the economic outlook. The model’s ability to capture these dynamics is evident in the widening distribution of possible future growth outcomes, indicating heightened risks, particularly on the downside.
Chart 1: Density plots of GDP nowcasts, compared to their respective outturns
Footnotes
- Note: One quarter ahead probability distributions for GDP outcomes are fitted from Quantile-MIDAS outputs to a skew-t distribution.
- Sources: Bank of England mortgage approvals, ECB Composite Index of Systemic Stress, Economic Policy Uncertainty Index, ONS MGDP, ONS retail sales and S&P Global PMIs.
Our dynamic risk profile allows policymakers to see how the distribution of potential outcomes flexibly includes new information. For example, as can be seen in Chart 2, during the recent period of increased uncertainty, we find that monthly output data (MGDP in the chart) accounts for around one third of the fall in the 25th quantile nowcast since September. Survey indicators of activity, such as the employment and near-term output PMIs, and our uncertainty measure (EPU in the chart) have also contributed sizeable drags on this quantile nowcast over this period. However, the weakness has been broad-based with all indicators pointing to a higher likelihood of weaker growth outcomes. The ability to determine where in the economy the risk is stemming from is an important feature of the model.
Chart 2: Contributions to the one quarter ahead quantile forecast for GDP growth
Footnotes
- Sources: Bank of England mortgage approvals, ECB Composite Index of Systemic Stress, Economic Policy Uncertainty Index, ONS MGDP, ONS retail sales and S&P Global PMIs.
Conclusion
Our model contributes to the way central banks address uncertainty by providing a systematic framework to assess the level and drivers of risks around the outlook for UK activity. Moving forward, by understanding the full distribution of potential outcomes, policymakers can better prepare for a range of scenarios, from mild slowdowns to more severe economic downturns, helping to navigate the complexities of modern economic landscapes.
This post was prepared with the help of Giulia Mantoan and Jessica Verlander.
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