Data Overview

In order to undertake a meaningful comparison with previous studies such as NP (1992), Perron (1989), ZA (1992), Narayan (2010), Narayan and Smyth (2008), Narayan and Wong (2009), and Narayan (2008), the univariate structural break analysis includes 25 Macroeconomic and Financial Time (MEFT) series. To account for the impact of data frequencies, the data series is composed of 12 monthly and 13 quarterly series. Additionally, this research includes 12 MEFT data series more than what has been studied previously. The time series variables are obtained from IFS, EUROSTAT, OECD, the ONS, and the BoE databases. In order to reduce the effect of trends, the series are converted to natural logarithm. The variables are provided in Table 4.1A (see Appendix). Among the MEFT series, 13 of them are similar to the series initially used by NP (1982) for the U.S. and in subsequent studies that examined the time series properties. The 16 MEFT series are similar to what was used by Narayan and Popp (2013) for Australia. The time span was determined by the availability of data. For the majority of the series, it ranges from 1960 to 2014 with a wider coverage of the UK monetary policy regimes and the macroeconomic structural changes.

To describe the basic features of the time series properties, the variables are examined using summary statistics. The order of integration is determined based on the unit root test to ensure univariate stationary process and enable valid inference (El-Shazly, 2016). The univariate time series properties of each MEFT series are presented in Table 4.2A (see Appendix). First, based on the mean and standard deviation reported in column two and three, respectively, the coefficient of variance is the highest for LRINV (33.26), followed by LSNLPS, LSNLPS, LRCON, LINV, LIIP and LHP. This probably implies that these series are amongst the most volatile and are expected to have the highest number of significant structural break(s). On the other hand, the least volatile MEFT series are likely to include LLTIR (0.64), LIBR (1.54), LST90R, LEXR, LSPR and LMHE. Second, the statistics on skewness, kurtosis and J-B reveal that the MEFT series are non-normal. Figure 4.1A presents an inspection of the plots that reveals two features worth highlighting as they have implications for the econometric modelling. First, it can be noticed that almost all of the MEFT series have a positive trend for most of the period. However, from early 1970s, 2006 and 2008, the trend shows a negative (downward) movement. These changes could be attributed to the oil price crisis and the recent GFC. Second, some obvious structural breaks can also be noticed in many of the MEFT series, which motivates further investigation of the time series in order to determine how valid these structural breaks are. The empirical investigation identifies the SBs and test its statistical significance before extracting them to conduct unit root tests so that the power of the test improves (see Perron, 1989; Nelson and Murray, 2000; Narayan, 2008; Narayan and Papp, 2010; Narayan and Wong, 2009; and ZA, 1992, among others).

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Assuming structural consistency, it is a standard practice to verify the stationarity property of MEFT series before explaining their properties. Following the data description, the order of integration is determined using the ADF unit root test as a benchmark⁶² before allowing structural breaks. The ADF test developed by Dickey and Fuller (1979, 1981) and Said and Dickey (1984) is based on the statistics obtained from applying the Ordinary Least Square (OLS) method. Following the standard ADF test for a unit root in 𝑦_𝑖𝑡 for MEFT series (𝑖), at time 𝑡, allowing for a drift and a linear deterministic trend is represented as follows:

𝑀𝐸𝐹𝑇_𝑖𝑡 = 𝜇_𝑖+ 𝛽_𝑖𝑡 + 𝜔_𝑖𝑀𝐸𝐹𝑇_𝑖𝑡−1+ ∑ 𝑐_𝑖Δ𝑀𝐸𝐹𝑇_{𝑖𝑡−𝑗}+ 𝜀_𝑖𝑡

𝑘

𝑗=1

(4.10) where 𝑀𝐸𝐹𝑇_𝑖𝑡 = natural log of the MEFT series/variable 𝑖 at time 𝑡 = time trend:

Δ𝑀𝐸𝐹𝑇_𝑡−𝑖 = 𝑀𝐸𝐹𝑇_𝑡−𝑖− 𝑀𝐸𝐹𝑇_{𝑡−𝑖−1}; 𝜀_𝑖𝑡 ∼ 𝑖. 𝑖. 𝑑 (0, 𝜎²).

in Equation (4.10), 𝑀𝐸𝐹𝑇_𝑖𝑡 represents the MEFT series 𝑖 at time 𝑡. ∆𝑀𝐸𝐹𝑇_𝑡−1 is the lagged first differences of the dependent variable, included to accommodate data for serial correlation in the error term 𝜀_𝑡. The equation examines the null-hypothesis of a unit root against the alternative that the variable is stationary around a constant, a trend, and both constant and trend. 𝜀_𝑖𝑡 is a white noise (serially uncorrelated sequence) disturbance term with variance 𝜎², and 𝑡 = 1, … , 𝑇 is an index of time. Following the standard practice in the real output unit root literature; the study includes a linear deterministic trend in Equation (4.10) (as in Rapach and Wohar, 2004). The 𝜔_𝑖𝑀𝐸𝐹𝑇_𝑖𝑡−1 term on the right hand side of Equation (4.10) allows for serial correlation and ensures the disturbance term is white noise (Smyth and Inder, 2004). The lag length (𝑘) is selected using the information-based method, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC). The null hypothesis is 𝜔_𝑖 = 0, as in Equation (4.10), implying that there is a unit root (a random walk) in 𝑀𝐸𝐹𝑇_𝑖𝑡. The alternative hypothesis is that 𝜔_𝑖 < 0, which implies that 𝑦_𝑖𝑡 is stationary around a linear deterministic trend. When the series is characterised by a unit root, it is considered as strongly dependent or highly persistent because it is highly autocorrelated with its own lags and the contribution of temporary shocks permanently built in it.

The 𝜏 − 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠, 𝜏 =^𝜔−1_𝑠𝑒

𝜔 is used to test the unit-root null hypothesis. Since 𝜏 does not have the usual property of 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 − 𝑡 distribution, the test procedure uses the critical values tabulated in Fuller (1976: Table 8.5.2, p373)⁶³. The lagged first difference terms are included in the equation to

62 As in ZA and BP approaches developed based on the traditional ADF test, using ADF as a benchmark allows the analysis to follow the sequential developments in both approaches and permits comparison with previous findings.

63 Mean of the distribution is equal to zero, the variance is equal to 𝑣/( 𝑣 -2), where 𝑣 is the degree of freedom and 𝑣 ≥ 2, unlike the normal distribution, the variance is always greater than 1, although close to 1 for high degrees of freedom.

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take care of possible correlation in the residuals and the number of such lags needs to be an increasing function of the sample size 𝑇, at a controlled rate 𝑇¹³ to whiten the residuals (Said and Dickey, 1984). Since the time lag structure is different for each data series, it is desirable to estimate the optimal time lag by setting the maximum lag 𝑘_𝑀𝐴𝑋 as 2 years (standard short-run period). The optimal lag structure is estimated based on Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC), setting 𝑘_𝑀𝐴𝑋 = 8 for quarterly series and 𝑘_𝑀𝐴𝑋 = 24 for monthly series.

The ADF test results, reported in Table 4.3A (see Appendix), show that the unit root null is not rejected for all of the MEFT series at all levels of significance, except for manufacturing hourly earnings (LMHE) at 10% sig. level. This suggests that a long-run relationship may exist in the univariate time series, which implies that all MEFT series are characterised by the presence of persistent shocks. It is well established in the applied econometrics literature that the failure of the ADF model to reject the unit root null hypothesis is largely due to its inability to cater for structural breaks (BP, 2006). One of the potential problems with time series regression models is that the estimated parameters may change over time. This necessitates testing for structural changes (El-Shazly, 2016). The results are consistent with previous studies. The random walk hypothesis implies that random shocks have permanent effects on the long-run level and fluctuations are highly persistent. This suggests that most of the UK MEFT series are considered as nonstationary stochastic process rather than stationary fluctuations as a drift and around a deterministic trend. When structural breaks are correctly accounted, it becomes a source of power to reject the null hypothesis in unit root testing (Narayan and Liu, 2013). This fact shows that it is necessary for a macroeconomic model to contain a variable that expresses a structural break to obtain stronger evidence of the stationarity property of the series under investigation (Matsuki and Sugimoto, 2013).

NP (1982) also obtain similar results for the 14 U.S. macroeconomic variables over the period 1909 to 1970. Their null hypothesis is not rejected for 13 of the 14 series. They conclude that these series behave more like a random walk than like transitory deviations from steadily growing trend.

The following sections investigate the presence of SBs in the MEFT series and identify break points that correspond to known economic events. The research combines the ZA and BP algorithms to the same data series. To accommodate the structural breaks in the MEFT series and for a robustness check, the investigation is carried out based on the ZA one time break, the BP (2003a) double maximum, and the sequential algorithms.

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