The slow pace of the recovery from the Great Recession of 2007-2009 has prompted questions about whether the long-run growth rate of GDP in advanced economies is lower now than it has been on average over the past decades, as famously articulated by Robert Gordon and Lawrence Summers (Teulings and Baldwin 2014).

Indeed, evidence of a decline in long-run growth is accumulating. The application of popular statistical tests for structural breaks suggests that evidence in favour of a shift in the mean of US GDP growth has been building up and has recently become significant at the 5% level (Figure 1). The Bai and Perron (1998) test can be used to detect the most likely date at which the break occurred and this is found in the early part of the 2000's.

**Figure 1**. Real-time test statistics of the Nyblom and Bai-Perron Tests

*Note:* The solid gray and blue lines are the values of the test statistics obtained from sequentially re-applying the Nyblom (1989) and Bai and Perron (1998) tests in real time as new National Accounts vintages are being published. In both cases, the sample starts in 1960 and the test is re-applied for every new data release occurring after the beginning of 2000. The dotted line plots the 5% critical value of the test, while the dashed line plots the 10% critical value.

Long run growth projections matter:

- Orphanides (2003) emphasised how real-time misperceptions about the long-run growth of the economy can play a large role in monetary policy mistakes.
- Even small changes in assumptions about the long-run growth rate of output can have large implications on fiscal sustainability calculations.

These points highlight the importance of accurately assessing the current long-run growth rate in a timely manner.

In this respect, Figure 1 also highlights that the strategy of applying conventional tests in real-time is therefore not satisfactory for the purpose of real-time decision making. In fact, the detection of change in the mean of GDP growth can arrive with substantial delay. For instance, the Bai and Perron (1998) test would not detect the early 2000s break at a 5% significance level until the summer of 2014, with almost 15 years of delay!

## Tracking long-run growth in real time

Since the seminal contributions of Evans (2005) and Giannone* et al.* (2008), dynamic factor models (DFMs) have become the standard tool to track GDP. These models can incorporate a large amount of information and of exploit high frequency data to make inference about short-term developments in economic activity.[1]

In a recent paper (Antolin-Diaz *et al*. 2015), we extend this framework by allowing for gradual changes in the mean and the variance of real output growth. By incorporating a large number of economic activity indicators, dynamic factor models are capable of precisely estimating the cyclical comovements in macroeconomic data in a real-time setting. Our extended model exploits this to track changes in the long-run growth rate of GDP in real time, separating them from their cyclical counterpart.

When applied to US data, our model concludes that long-run GDP growth declined meaningfully during the 2000's and currently stands at about 2.25%, almost one percentage point lower than the post-war average. The results are more consistent with a gradual decline rather than a discrete break (Figure 2, panel a)

**Figure 2**. US long-run growth estimate: 1960-2014 (% Annualised growth rate)

(a) Posterior long-run growth estimate vs CBO estimate of potential growth

(b) Filtered estimates of long-run growth vs SPF survey

*Note:* Panel (a) plots the posterior median (solid red), together with the 68% and 90% (dashed blue) posterior credible intervals of long-run GDP growth. The gray circles are the CBO's estimate of potential growth. Shaded areas represent NBER recessions. In Panel (b), the solid gray line is the filtered estimate of the long-run GDP growth rate, using the vintage of National Accounts available as of mid-2014. The blue diamonds represent the real-time mean forecast from the Livingston Survey of Professional Forecasters of the average GDP growth rate for the subsequent 10 years.

Since in-sample results obtained with revised data often underestimate the uncertainty faced by policymakers in real time, we repeat the exercise using real-time vintages of data. By the summer of 2011, the model would have concluded that a significant decline in long-run growth was behind the slow recovery, well before the structural break tests became conclusive. Moreover, explicitly taking into account movements in long-run growth significantly improves the accuracy of both point and density ‘nowcasts’ of US GDP.

## What lies behind the slowdown in long-run growth?

Next, we extend our model in order to disentangle the drivers of secular fluctuations of GDP growth. In our framework, by adding information about aggregate hours worked, long-run growth can be decomposed into the labour productivity and labour input components.

- The results of this decomposition exercise point to a slowdown in labour productivity as the main driver of recent weakness in US GDP growth, in line with the analysis of Fernald (2014).

**Figure 3**. Decomposition of long-run US output growth

*Note:* The figure plots the posterior median (red), together with the 68% and 90% (dashed blue) posterior credible intervals of long-run GDP growth and the posterior median of both long-run labour productivity growth and long-run total hours growth (solid blue and dashed grey lines).

Applying the model to other advanced economies, we provide evidence that the weakening in labour productivity appears to be a global phenomenon.

**Figure 4**. Decomposition for other advanced economies

(a) Long-run labour productivity

(b) Long-run labour input

*Note:* Panel (a) displays the posterior median of long-run labour productivity across advanced economies. Panel (b) plots the corresponding estimates of long-run total hours worked. In both panels, ‘Euro Area’ represents a weighted average of Germany, Italy and France.

Moreover, the results of our decomposition exercise indicate that after using the dynamic factor model to remove business-cycle variation in hours and output, the decline in long-run GDP growth that has been observed in the advanced economies since the early 2000s is according to our model entirely accounted for by a decline in long-run productivity growth. Finally, it is interesting to note for the G7 economies long-run productivity growth appears to converge in the cross-section, with the latest estimates suggesting convergence towards a low growth rate, between 0.5 to 1%.[2]

## Conclusion

Using a state-of-the-art econometric technique we provide evidence for a slowdown in labour productivity as the main driver of weak global growth in recent years, which supports the narrative of Fernald (2014), also for countries other than the US.

We have demonstrated that long-run movements in labour input and labour productivity are an important feature of the data that can be successfully modelled within the dynamic factor model framework. Our econometric framework remains agnostic about the deep structure of the economy. In principle, these low-frequency movements could be influenced both by demand and supply factors. Disentangling the two is a promising avenue for further research.

## Footnotes

[1] See Banbura et al. (2012) for a survey of the literature on nowcasting GDP.

[2] Similar evidence for emerging economies has been recently presented by Pritchett and Summers (2014). Their evidence refers to convergence of overall GDP growth rates, whereas ours indicates that convergence in productivity growth appears to be the dominant source of convergence.

## References:

Antolin-Diaz, J, T Drechsel, I and Petrella (2015), “Following the Trend: Tracking GDP when long-run growth is uncertain”, CEPR Discussion Papers 10272, C.E.P.R. Discussion Papers.

Bai, J and P Perron (1998), “Estimating and testing linear models with multiple structural changes”, *Econometrica*, 66(1):47-68.

Banbura, M, D Giannone, M Modugno, and L Reichlin (2012), “Now-casting and the real-time data flow”, Working Papers ECARES 2012-026, ULB - Universite Libre de Bruxelles.

Evans, M D D (2005), “Where Are We Now? Real-Time Estimates of the Macroeconomy”,* International Journal of Central Banking*, 1(2).

Fernald, J (2014), “Productivity and potential output before, during, and after the great recession”, NBER Macroeconomics Annual 2014, 29.

Giannone, D, L Reichlin, and D Small (2008), “Nowcasting: The real-time informational content of macroeconomic data”, *Journal of Monetary Economics*, 55(4):665-676.

Gordon, R J (2014), “The Demise of U.S. Economic Growth: Restatement, Rebuttal, and Reflections”, NBER Working Papers 19895.

Orphanides, A (2003), “The quest for prosperity without ination”, *Journal of Monetary Economics*, 50(3):633-663.

Pritchett, L and L H Summers (2014), “Asiaphoria Meets Regression to the Mean”, NBER Working Papers 20573.

Summers, L (2014), “Secular stagnation”, IMF Economic Forum: Policy Responses to Crises, speech delivered at the IMF Annual Research Conference, November 8th.

Teuling, C and R Baldwin (2014), “Secular stagnation: Facts, causes, and cures – a new Vox eBook”, VoxEU.org, 10 September.