Does real U.K. GDP have a unit root? Evidence from a multi-century perspective

ABSTRACT

We employ linear and nonlinear unit-root tests to examine the stationarity of five multi-century historical U.K. series of real output compiled by the Bank of England. Three series span 1270 to 2016 and two series span 1700 to 2016. These datasets represent the longest span of historical real output data available and, thus, provide the environment for which unit-root tests are most powerful. A key feature of our test is its simultaneous allowance for two types of nonlinearity: time-dependent (structural breaks) nonlinearity and state-dependent (asymmetric adjustment) nonlinearity. The key finding of the test, contrary to what other more popular nonlinear unit-root tests suggest, provides strong evidence that the main structure of the five series is a stationary process characterized by an asymmetric nonlinear adjustment and a permanent break affecting both the intercept and the trend. A major policy implication of this finding is fiscal and/or monetary stabilization policies have only temporary effects on the output levels of the United Kingdom.

KEYWORDS:

• Unit root
• time-dependence
• nonlinearity
• state-dependence
• Fourier function

JEL CLASSIFICATION:

• C12
• C22
• O52

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Other researchers independently propose slightly different versions of the Omay et al. (2014, 2018) tests. Two, in particular, warrant mention. First, Chen and Xie (2015) develop the Leybourne et al. (1998) version of the AESTAR test and examine current account sustainability. Second, Ranjbar et al. (2018) develop the Fourier version of the AESTAR test and reexamine real interest rate parity for 12 OECD countries. An important difference between our paper and these two other papers relates to the critical-value problem. That is, Omay, et al. (2018) obtain convergent critical values (see Tables 1 and 2, Omay et al. 2018), whereas Chen and Xie (2015) and Ranjbar et al. (2018) obtain divergent critical values (see Table 1, Chen and Xie, 2015, and Table 1, Ranjbar et al. 2018). Unlike Chen and Xie (2015) and Ranjbar et al. (2018), we apply the Simplex method to compute critical values for the Leybourne et al. (1998) type of detrending. Omay and Emirmahmutoğlu (2017) show that the Genetic and Simplex methods are the appropriate optimizing algorithms for the Leybourne et al. (1998) type of unit-root testing.

² We also computed the critical values for T = 2500. We report them for additional information. They are, respectively, −4.42, −3.86, and −3.56 for the 1%, 5%, and 10% significance level, respectively.

³ For further details, see Luukkonen, Saikkonen, and Terasvirta (1988).

⁴ In Equation (13), we assume that the transition variable is not one of the elements in . If this is not the case, we drop the term from the auxiliary regression.

⁵ As Kapetanios, Shin, and Snell (2003) indicate, the ADF test is still powerful in some form of ESTAR nonlinearity. Therefore, the test results that are obtained as stationarity may be found for this reason..