As of the March meeting, the median FOMC member reckons that real US GDP will grow at 6.5 percent in 2021. The reason that the Fed upgraded its forecast from 4.2 percent in December is threefold. First, the progress of the vaccination campaign and the attendant ‘revenge consumption’ expected of Americans. Second, the $1.9 trillion fiscal package passed by Congress that will put a lot of disposable income in the hands of financially-constrained consumers. Last but not the least, the upgrade reflects the Fed’s new reaction function. The Powell Fed is now committed to an empirical stance. And given that there is still considerable slack in the global production system, the best informed don’t expect inflation to rise on a sustained basis. The Fed is therefore prepared to run the economy really hot to deliver broad-based growth — in order to contain ‘the threat from below’ revealed by 2016. Beyond the fact that monetary policy is expected to remain accommodative, the dramatically improved outlook for the US economy is not due to improved financial conditions. This idea motivates the general thrust of the argument that follows.
Tobias Adrian and coworkers at the IMF and the NY Fed have produced a series of recent papers on ‘growth-at-risk’. The main idea is to capture the effect of financial conditions on growth vulnerability. Basically, tighter financial conditions increase the probability that output growth would disappoint. The question is how one can capture this risk. The ‘growth-at-risk’ research agenda builds on an early effort in this direction in a classic paper by Adrian, Shin and Moench in 2010 on the “macro risk premium.”
In their 2019 paper titled “Vulnerable Growth,” Adrian, Boyarchenko and Giannone outline an interesting strategy. The idea is to model the conditional distribution of future RGDP growth as a function of economic and financial variables. In practice, Adrian et al. (2019) carry out quantile regressions of quarterly growth on lagged growth and lagged NFCI — the Chicago Fed’s aggregate of one hundred financial stress indicators — for the 5th, 25th, 75th, and 95th percent quantiles. Then they match these quantiles to the theoretical quantiles of the skew-t distribution — a highly flexible four-parameter family of distributions that admits both fat tails and skew and includes the Student’s t-distribution and the normal distribution as special cases. This allows them to obtain these gorgeous surface graphs of the conditional distribution of RGDP:
In later papers, the NFCI would be replaced by more sophisticated metrics of financial conditions and the parametric approach would be replaced by a fully-nonparametric one. In their 2020 paper, “Multimodality in Macro-Financial Dynamics,” the same authors would show that the non-parametric density estimator reveals the existence of a hidden mode. Usually, the forecast density of real GDP growth is Gaussian. But when financial conditions deteriorate, an additional bad mode appears and the conditional density becomes bimodal. In very recent work with other coworkers, “Macrofinancial Feedback, Bank Stress Testing and Capital Surcharges,” Adrian shows how to quantify the causal impact of shocks to bank capital on the conditional distribution of financial conditions and output growth. The Fed can use this technology to calibrate a countercyclical capital buffer, that it has had the authority to impose on systemically important banks for a decade but has chosen not to so far.
In private correspondence, Adrian suggested that, ideally, we want to pin down the term-structure of conditional density of GDP growth. For then we can better manage not only the risk of poor economic performance in the next quarter, but over the next few quarters. This is important because both monetary policy and the financial accelerator work with lags. In what follows, I take a stab at this problem.
My basic idea is that sophisticated observers, above all, financial intermediaries, have a lot of information in real time about growth prospects. In particular, professional forecasts incorporate information on developments that is not fully reflected in recent trends in growth — such as vaccination programs and innovations in fiscal policy and political economy. So we propose to reorient the strategy in Adrian et al. (2019) as follows: instead of modeling conditional growth quantiles as a function of lagged growth and financial conditions, we model conditional growth densities as a function of professional growth forecasts and financial conditions. This is equivalent to saying that the prior density that financial conditions modify is not recent trend growth but forward-looking projections that incorporate all sorts of information about the macroeconomic trajectory.
We proceed as follows. We obtain mean real GDP growth forecasts for the next five quarters from the Philadelphia Fed’s Survey of Professional Forecasters. We obtain realized real GDP growth from FRED. We then compute forecast errors over five quarterly horizons as the difference between the two. We then model the forecast errors as a function of financial conditions. Following Adrian et al. (2019), we run quantile regressions of forecast errors on the (first-differenced) NFCI, the Chicago Fed’s composite indicator of financial stress. We then obtain skew-t densities by choosing the parameters that minimize the Euclidean distance between the theoretical quantiles and the fitted quantiles for each quarter and forecast horizon.
We report t-statistics by selected quantiles and forecast horizons for four different subsamples. The full sample is potentially confounded by the shock of the pandemic in 2020 and the considerable inflation and uncertainly over inflation in the 1970s and early-1980s. The bottom table excludes both and is probably the most reliable. We therefore use the parameter estimates from the most restricted sample to obtain the time-varying quantiles by forecast horizon.
The estimates in the bottom panel show that tighter financial conditions, as captured by the NFCI, predict negative forecast errors over the 1 quarter horizon. This means that when financial conditions tighten, GDP immediately surprises on the downside. Interestingly, tighter financial conditions predict positive forecast errors over the 4 and 5 quarter horizons. This is a robust pattern that holds across samples. It likely reflects the Fed’s reaction function: the Fed responds to tighter financial conditions with monetary accommodation, which results in positive surprises in growth after a one-year lag.
We obtain the forecast error quantiles by quarter and forecast horizon as a function of NFCI. We then use Jonathan Berrisch’s implementation of the skew-t densities, and choose parameters to minimize the Euclidean distance between the theoretical quantiles and the fitted quantiles (5th, 25th, 75th, and 95th, following Adrian). The next graph displays the optimized parameters of the skew-t density over the one quarter horizon. Of particular interest are the values of the skew parameter, nu. The distribution is parameterized such that values of nu lower than one imply a negatively skewed density. An extremely negatively skewed density obtains with the Lehman bankruptcy in 2008.
The next graph displays the parameters over the 5-quarter horizon. In contrast to the previous graph, forecast errors over the 5-quarter horizon around the GFC are positively-skewed. This reflects the extraordinary policy response of the authorities. Professional forecasters were positively surprised by the GDP numbers in 2009.
The next figure displays the conditional forecast error densities over the one quarter horizon. We find that professional forecasters, who are basically financial intermediaries, have often been positively surprised over the past three decades. Growth forecasts have often been too conservative — particularly during recoveries. This is a surprising result given that market-based intermediaries are infamous for a bullish bias. In normal times, however, professional forecasts are largely unbiased.
The next figure displays the conditional forecast error densities over the 5-quarter horizon. These are more evenly distributed, although forecasters were positively surprised by the GDP numbers in 2011. Contrasting the two density graphs reveals that forecast errors are less concentrated around zero over longer horizons. There is much more variation. This shows that the predictive accuracy of informed investors decays over the horizon — an expected result.
This technology only goes so far. While it allows us to get a handle on the term-structure of conditional growth density, it appears that the skew-t distribution is not sufficiently flexible enough to capture the hidden, bad mode revealed by the fully non-parametric approach.
The basic message here is straightforward. Output growth is influenced by extra-economic developments, productivity shocks, fiscal and monetary policy innovations, and shifts in the electoral landscape and political economy. All these non-financial factors cannot be directly captured by a tractable number of variables in macroeconomic modeling. However, using forward-looking estimates of real output growth allows us to parsimoniously incorporate a lot of this information available to intermediaries in real time. It can thus help us avoid ascribing too much influence to financial conditions and give us a tighter handle on the causal channel between financial conditions and growth risk.
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You can find the code to replicate this exercise on my GitHub.
Hey, do you have code for this exercise? Thanks!