#### By Gary Koop, Stuart McIntyre, James Mitchell, and Aubrey Poon

Economics 101 teaches us that there are different ways of measuring gross domestic product (GDP), via the income approach (GDPI), the production approach (GDPP) and the expenditure approach (GDPE). In principal, the aggregate estimates from these approaches should equal each other.

But, in practice, they differ due to various reasons including measurement errors; and statistics producers take different approaches to communicating and/or *reconciling* these contrasting measures. Reconciling involves combining the contrasting estimates to arrive at a single estimate of GDP.

There is a long-standing academic literature that explores different ways of reconciling contrasting estimates of GDP using statistical (econometric) models. A recent application by the Federal Reserve Bank of Philadelphia produces a reconciled quarterly estimate of United States (US) GDP using the model outlined in Aruoba, Diebold, Nalewaik, Schorfheide and Song (2016), hereafter ADNSS. Their quarterly estimate of “true” GDP growth is known as GDPplus. GDPplus combines the income and expenditure side measures of GDP (GDPI and GDPE), which are published separately in the US via a model that views them as noisy indicators of “true”, but latent, GDP.

**Our work**

In our discussion paper , we extend ADNSS to the monthly frequency. This is important as the US, unlike the UK, does not produce an official monthly measure of GDP. Instead, we exploit the fact that many indicators of economic activity in the US are available at the monthly frequency. But given that GDP itself, on both the income and expenditure sides, is measured in the US at the quarterly frequency only, we accordingly develop a ‘mixed-frequency’ econometric model. This mixed-frequency model lets us reconcile the quarterly GDPE and quarterly GDPI estimates along with the monthly indicators, and thereby produce monthly estimates of true GDP and its uncertainty.

There already exist some unofficial estimates of monthly GDP in the US, most notably the popular Federal Reserve Bank of Chicago measure developed in the model of Brave, Butters and Kelley (2019). But this is a measure of GDPE, rather than “true” GDP as in ADNSS (2016), since the model of Brave, Butters and Kelley (2019) uses GDPE data only.

In our paper, we build on this work to reconcile the income and expenditure side estimates of GDP and produce a measure of reconciled ‘true’ US GDP at the monthly frequency. In doing so, like ADNSS, we treat GDPI and GDPE as ‘noisy’ measures of underlying ‘true’ GDP.

We use the mixed-frequency data reconciliation model to produce reconciled historical estimates of monthly GDP in the US dating back to 1960. We illustrate how the new monthly data contribute to a better understanding of US business cycles.

We refer readers looking for discussion of various technical aspects of our work to the discussion paper.

**Why does data reconciliation matter?**

Reconciling different estimates of GDP is not just a dry statistical issue. Our understanding of what is happening in the economy can depend on which measure of GDP – say GDPE or GDPI – we consult.

For example, while the quarterly annualised growth rate of real GDPI in the US turned negative 3% in 2007Q3, GDPE was still growing robustly (at an annualised rate of more than 2%).

In a similar way, it is clear that having indicators of GDP itself at the monthly frequency is important to policymakers and others trying to track and understand developments in the US economy. Albeit this raises the challenge of timeliness versus accuracy highlighted through subsequent revisions.

For example, the NBER Business Cycle Dating Committee on their home page write: *“Because the BEA figures for real GDP [GDPE] and real GDI [GDPI ] are only available quarterly, the committee considers a variety of monthly indicators to determine the months of peaks and troughs.”*

Our *reconciled* estimates of GDP at the monthly frequency provide a single measure of activity in the economy as a ‘whole’. Effectively, our methods provide a formal means of aggregating a wide-range of monthly indicators that capture specific aspects of economic activity, to represent the whole of GDP.

**What do we find?**

Figure 1 plots historical estimates of monthly GDPI, GDPE and reconciled GDP from our mixed-frequency model. We also overlay the NBER recession dates as grey shaded bars. It can be seen that the three lines tend to follow each other with reconciled GDP tending to lie between the estimates of GDPE and GDPI, but there are some exceptions to this pattern. GDPE and GDPI do not contribute equally to “true” GDP, with GDPI explaining more of its variation.

We can use our mixed-frequency model to produce recession probability estimates from its density estimates of monthly GDP. These probability estimates can be compared to independent estimates produced by Professor Jeremy Piger (click here).

The recessionary signals from our model align well both with the NBER recession dates and with Piger’s estimates. Importantly, though, the strength of the recessionary signal varies depending on whether one consults reconciled GDP, GDPI or GDPE. The recessionary probabilities based on reconclied GDP, GDPI and GDPE often differ, with false signals most evident when one consults GDPI or GDPE alone. In other words, reconciling the information in the two proxies of GDP, via our model, provides improved recessionary signals.

In the paper, we also provide a case study illustrating the use of our model over the period of the global financial crisis. This confirms that in “real-time”, acknowledging the staggered release of data, our model is able to provide informative real-time estimates of the probability of recession. We also discuss the performance of our model in light of the COVID-19 pandemic and its extreme GDP outturns. Reassuringly, we find that our historical estimates of monthly GDP are largely unaffected.

The methods that we develop could be applied in a range of context internationally, and could also extended to sub-national (regional) applications where different measures are often available, including in the UK.

**Conclusions**

In our paper we develop an econometric method for producing reconciled historical estimates of monthly GDP in the US. We illustrate empirically how these estimates are useful in understanding historical US business cycles as well as in tracking recession probabilities.

Our model provides the higher frequency insight into economic activity that policymakers seek, while also addressing challenges that can emerge when different measures of GDP provide contrasting assessments of economic activity.

**References**

Aruoba, S., Diebold, F., Nalewaik, J., Schorfheide, F. and Song, D. (2016). Improving GDP measurement: A measurement-error perspective. Journal of Econometrics, 191, 384-397.

Brave, S., Butters, R. and Kelley, D. (2019). A new _big data_ index of U.S. economic activity. Economic Perspectives, Federal Reserve Bank of Chicago, 43. Available at https://www.chicagofed.org/publications/economic-perspectives/2019/1

Gary Koop is a Professor of Economics at the University of Strathclyde

Stuart McIntyre is Head of Research at the Fraser of Allander Institute & a Senior Lecturer at the Department of Economics at the University of Strathclyde

James Mitchell is a Professor of Economic Modelling and Forecasting at the University of Warwick

Aubrey Poon is a Research Associate at the University of Strathclyde

*ESCoE blogs are published to further debate. Any views expressed are solely those of the author(s) and so cannot be taken to represent those of the ESCoE, its partner institutions or the Office for National Statistics*.