Threshold cointegration between inflation and US capacity utilization

ABSTRACT

An analogue to the Phillips curve shows a positive relationship between inflation and capacity utilization. Some recent empirical work has shown that this relationship has broken down when using data after the mid-1980s. We empirically investigate this issue using several threshold error correction models. We find, in the long run, a 1% increase in the rate of inflation leads to approximately a 0.0046% increase in capacity utilization. The asymmetric error correction structure shows that changes in capacity utilization show significant corrective measures only during booms while changes in inflation correct during both phases of the business cycle with the corrections being stronger during recessions. We also find that, in the short run, changes in the inflation rate do Granger cause capacity utilization while changes in capacity utilization do not Granger cause inflation. The Granger causality from inflation to capacity utilization can be interpreted as supporting recent calls made in the popular press by some economists that it may be desirable for the Federal Reserve Bank to try to induce some inflation. However, it is also possible to interpret these Granger causality results as arising because both variables respond to some more fundamental set of variables with the inflation rate simply responding sooner. The lack of Granger causality from capacity utilization to inflation casts doubt on the older view that capacity utilization could be a leading indicator for future inflation.

KEYWORDS:

• Capacity utilization
• inflation
• cointegration
• threshold

JEL CLASSIFICATION:

• E30
• E31
• E32
• E37

Acknowledgements

We would like to thank Giuseppe Cavaliere and Fang Xu for assistance with some of the programming in the article. We would also like to thank a referee for helpful comments on an earlier draft of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Among the numerous Federal Reserve Bank economists’ papers are McElhattan (1978, 1985), Bauer (1990), De Kock and Nadal-Vicens (1996), Corrado and Mattey (1997), Emery and Chang (1997) and Dotsey and Stark (2004).

² Garner (1994), Gordon (1989), Gordon (1994), Cecchetti (1995) and Stock and Watson (1999), Corrado and Mattey (1997), Brayton, Roberts, and Williams (1999) and Nahuis (2003) show that capacity utilization has significant positive relationship with inflation, thus predicting inflation better than the unemployment rate, while Shapiro, Gordon and Summers (1989) show that high-capacity utilization has a small, insignificant and sometimes negative impact on prices. Finn (1995), Aiyagari (1994) and Bansak, Morin and Starr (2007) examined the effects of technological change on capacity utilization, while Gamber and Hung (2001) and Dexterr, Levi and Nault (2005) show that international trade has a significant downward impact on US inflation, which might have obscured the relationship between capacity utilization and inflation in the 1990s.

³ The cointegration literature dates back to Engle and Granger (1987) and has seen many important contributions over the years including Johansen (1988), Johansen and Juilius (1990), Hansen and Seo (2002) and of particular interest to this paper, Enders and Siklos (2001).

⁴ One paper that does investigate cointegration is Mustafa and Rahman (1995) who use traditional cointegration methods. Unlike our results, they did not find a cointegration relationship between capacity utilization and inflation.

⁵ Examples of econometric studies with bounded time series variables are numerous. For example, in their influential paper, Nelson and Plosser (1982) reject the unit root hypothesis of the US unemployment rate and studies which link unemployment rates and other variables are quite commonplace. Several empirical models of the European Monetary System exchange rates have been specified by using cointegrated vector autoregressive (VAR) models without taking account of the presence of a unit root such as Anthony and MacDonald (1998) and Svensson (1993).

⁶ Cavaliere (2005) explains how the concept of I(1) can coexist with the constraints of a bounded process. Further, Cavaliere and Xu (2014) show that the presence of bounds affects the standard unit root tests. Using the now popular, Monte Carlo methods to simulate correct critical values, they show that when bounds are taken into account, the Augmented Dickey–Fuller tests are much less likely to reject the null of a unit root.

⁷ For instance, asymmetric changes in the relationship between capacity utilization and inflation can be associated with the typical Keynesian story. According to this theory, a non-linearity in aggregate supply implies that when the overall resources in the economy are underutilized, firms can increase output without raising the price level because of sticky wages. But when rising aggregate demand pushes output beyond a certain threshold, the increasing marginal cost of resources causes prices to rise. Such an asymmetry was often found in the data from the 1970s and early 1980s where inflation was tame until capacity utilization exceeded a value around 82%.

⁸ We studied both types of capacity utilization data to investigate robustness. However, because the results are largely the same between these two measures, in this paper, we only report the results for total capacity utilization. Results for manufacturing capacity utilization can be obtained from the authors upon request. From this point on, we will frequently leave off the adjective ‘total’ and simply say capacity utilization rather than total capacity utilization.

⁹ By 1% increase in the inflation rate, we mean a calculation of inflation + 1. On the other hand, by a .0046% increase in capacity utilization, we mean a calculation of .0046 × capacity.

¹⁰ For example, on NPR on 7 October 2011, Ken Rogoff is quoted as saying, ‘They need to be willing, in fact actively pursue, letting inflation rise a bit more. That would encourage consumption. It would encourage investment…’, while in The New York Times on 29 October 2011, Christina Romer said, ‘In the current situation, where nominal interest rates are constrained because they can’t go below zero, a small increase in expected inflation could be helpful. It would lower real borrowing costs, and encourage spending on big-ticket items like cars, homes, and business equipment’.

¹¹ The Threshold Autoregressive and Momentum Threshold Autoregressive models were first described by Tong (1983) and Enders and Granger (1998).

¹² These empirical models make use of some standard notations such as α, β, ρ and ε in the different equations. However, these parameters and error terms do differ in the different equations and the subscripts should make things easy to see where each came from.

¹³ The data interval in this table for inflation was 1967:1 to 2013:12.

¹⁴ Standard references for these tests include, Dickey and Fuller (1979), Phillips and Perron (1988) and Kwiatkowski et al. (1992).

¹⁵ Ng and Perron (2001) proposed a class of modified unit root tests that focus on concerns about the low power of the standard unit root tests.

¹⁶ Cavaliere and Xu’s (2014) simulation-based tests are applicable when bounds are known. Based on their arguments, a reasonable range for the bounds can often be inferred from historical observations. We choose the lower and upper bounds of the capacity utilization rate, respectively, at 60% and 90% as the historical data show that the capacity utilization rate never lies beyond this range. See also Herwartz and Xu (2008) for further details.

¹⁷ The desirability of having both ρ_i values negative is motivated by Petrucelli and Woolford (1984), who showed that necessary and sufficient conditions for stationarity are ρ₁ < 0, ρ₂ < 0 and $\left(1+{\rho }_1\right)\left(1+{\rho }_2\right)<1$.

¹⁸ This can be seen on page 169 of Enders and Siklos (2001) where they say, ‘However, as will be shown, the phi statistic is quite useful because it can have substantially more power than the t-max statistic’. It can also be seen in Table 7 of their paper, where they do not even report the t-max statistic values.

¹⁹ This preference for the Φ statistics can also be seen in the literature. For instance, Shen, Chen and Chen (2007) only mention the Φ statistic results and do not mention the t-max results.

²⁰ Here, we use the conventionally Engle and Granger cointegration adjusted ADF statistics rather than a bounded series ADF statistic. We do this because, even though it is reasonable that c_t is bounded, because π_t is not, any linear combination of the two may not be bounded, so the Cavaliere and Xu (2014) adjustment is not needed.

²¹ The critical values for the Φ statistic can be found in Enders and Siklos (2001).