The steady downward trend of real interest rates worldwide over the last 30 years has raised the issue of whether the natural rate – defined by Wicksell (1898) as the marginal productivity of capital – has fallen in tandem. Blanchard et al. (2014) conclude that the factors that led to low real interest rates are unlikely to be reversed, and that the natural rate may remain low as well. Borio and Disyatat (2014) go even further and argue that low interest rates validate themselves, suggesting that the natural rate would fall as a result.

There are several channels through which this causality can run. One channel for which the literature has found increasing evidence is the impact of low real rates on resource allocation, which affects total factor productivity (TFP) growth, one of the key drivers of the natural rate. Barnett et al. (2014) report an inefficient allocation of resources in the low interest rate environment across sectors in the UK, where less efficient firms continued operating. Cette et al. (2016) come to similar conclusions for countries in southern Europe, where TFP growth in the manufacturing sectors has been affected by a decline in the interest rate. For Japan, where low interest rates have been common since the early 1990s, Caballero et al. (2008) find that undercapitalised Japanese banks kept on lending to insolvent borrowers (zombies). This kept less productive firms alive and reduced aggregate TFP growth. Schivardi et al. (2017) also investigate the effects of undercapitalised banks on TFP in Italy and find that it adversely affects aggregate TFP dispersion, but only in the presence of a large fraction of zombie firms.

## Modelling framework

In a recent article, we present new evidence on the link between real interest rates and the natural rate for seven OECD countries (Hoeberichts and Van den End 2018). We test for the causal effect running from the real rate to the natural rate by extending the model of Laubach and Williams (2003) with the real interest rate (*r*) as determinant for the natural rate (*r**). In the model of Laubach and Williams, the growth rate of potential output (*g _{t}*) determines the natural rate of interest (

*r**). Because we allow

*g*to also be affected by the real rate (

_{t}*r*),

_{t}*r** can be affected by the real interest rate as well. The sign and the size of the effect of the real rate are captured by the coefficient

*α*. If

_{r}*α*is negative, the potential output curve is downward-sloping, as in Figure 1, panel A of Figure 1. If

_{r }*α*is positive, the potential output curve is upward-sloping, as panel B of Figure 1.

_{r }**Figure 1** Determinants of the natural rate

A. Coefficient α with negative sign

B. Coefficient α with positive sign

To test for the effect of the real rate on the natural rate, coefficient is estimated with a vector autoregression model, together with coefficient β.This direct effect has not yet been investigated empirically in the literature, which might be related to the fact that the natural and the real interest rate have a different (time) dimension and can only be measured by approximation. Our proxy for r*is the expected long-term economic growth rate, taken from Consensus Economics. Inflation expectations 5 to 10 years ahead are used to infer the ex-ante real interest rate (r) five to ten years ahead.

## New evidence

To identify the interaction effect between* r* and *r**, we control for technology shocks, terms of trade shocks, and demand shocks in the vector autoregression models. Moreover, in robustness tests we control for other potential drivers of* r**, such as population growth and financial shocks. The simulation outcomes provide evidence for a significant effect running from the real rate to the natural rate, which is statistically significant for Japan in all model specifications, for Canada, France, the UK, and Germany in some specifications, and not significant for the US and Italy. This result confirms that low real rates can lead to a decline of *r** through lowering potential output growth. The response is quite persistent and substantial in economic terms; a negative (positive) shock to *r* by 1 percentage point leads to a decline (increase) in *r** by 0.27 percentage points in Japan and 0.16 percentage points in France, one year later (at t-2, when the response peaks) (see upper-right panels in Figure 2).

**Figure 2** Impulse responses

A. Japan

B. France

Note: Response of variable to a 1 standard deviation shock in other variable, 95% confidence bands.

Our results lend support to concerns that a prolonged period of low real interest rates can adversely affect the real economy. It can undermine potential economic growth through real and financial channels, for instance through misallocation of capital by weak banks (Andrews and Petroulakis 2017). This is confirmed for Japan, where we find a significant link between the real rate and the natural rate (Figure 2.A, upper-right panel). It illustrates the dynamics in the country over the last 15 years between the ultra-low real rates and weak economic growth.

For Japan and France (and to a lesser extent, Canada and the UK) we also find a significant effect running from the natural rate to the real rate, see lower-left panels in Figure 2. A channel for this causality is that expected returns (i.e. the ex-ante real rate) on investments will be lowered if potential output growth (and so the natural rate) declines. This refers to the indicator function of the real interest rate, which can be influenced by expectations of potential output growth through an information channel.

## Policy conclusions

From the model results we infer two policy conclusions. First, expansionary monetary policy may become less effective over time, since by reducing real interest rates, this policy may also affect the natural rate. This diminishes the effective degree of monetary policy accommodation provided to the economy, which depends on the difference between natural and real rate. Second, raising the natural rate will be more effective in avoiding secular stagnation than a policy aimed at reducing the real rate, for instance by lifting inflation expectations. The latter may even be counterproductive in the sense that it reduces real rates and long-term potential growth.

Potential growth – and thereby the natural rate – can be raised by structural reforms in labour, product, and financial markets, which will unleash new dynamics in the economy. The positive growth effects of structural reforms are quantified by Jimeno et al. (2014) amongst others. They show that creating a more dynamic business environment can boost investment and thereby economic growth. Moreover, addressing problems in the banking sector, for instance through swift recapitalisation, is important to limit the risk of resource misallocation through the bank lending channel.

## References

Andrews, D and F Petroulakis (2017), “Breaking the shackles: Zombie firms, weak banks and depressed restructuring in Europe”, OECD Working Paper, 1433.

Barnett, A, B Broadbent, A Chiu, J Franklin, and H Miller ( 2014), “Impaired capital reallocation and productivity”, *National Institute Economic Review*, 228.

Blanchard, O, D Furceri and A Pescatori (2014), “A prolonged period of low real interest rates?”, in C Teulings and R Baldwin (eds), *Secular Stagnation: Facts, Causes and Cures,* CEPR Press.

Borio, C and P Disyatat (2014), “Low interest rates and secular stagnation: Is debt a missing link?”, VoxEU.org, 25 June.

Caballero, R, T Hoshi and A Kashyap (2008), “Zombie lending and depressed restructuring in Japan”, *American Economic Review *98(5): 1943–77.

Cette, G, J Fernald and B Mojon (2016), “The pre-Great Recession slowdown in productivity”, *European Economic Review *88(C): 3–20.

Hoeberichts, M M and J W Van den End (2018), “Low real rates as driver of secular stagnation: Empirical assessment [5]", *Japan and the World Economy*, forthcoming.

Jimeno, J F, F Smets and J Yiangou (2014), “Secular stagnation: A view from the Eurozone”, in C Teulings and R Baldwin (eds), *Secular Stagnation: Facts, Causes and Cures,* CEPR Press.

Laubach, T and J C Williams (2003), “Measuring the natural rate of interest”, *Review of Economics and Statistics* 85(4): 1063–1070.

Rachel, L and T D Smith (2015), “Secular drivers of the global real interest rate”, Bank of England, Staff Working Paper571.

Schivardi, F, E Sette and G Tabellini (2017), “Credit misallocation during the European financial crisis”, VoxEU.org, 18 July.

Wicksell, K (1898), *Geldzins und Güterpreise,* Verlag Gustav Fischer.