To test our hypothesis, we follow standard econometric procedure. We first establish whether the variables (log GVA per employee, log UK import share, and log import to GDP ratio for goods and services) are stationary using the Augmented Dickey-Fuller (ADF) and Phillips and Perron (1988) unit root tests. We then establish whether the series are cointegrated using the Johansen (1991) test. Finally, given that the variables are non-stationary and there is one and only one cointegrating relationship between them, we perform the test for Granger causality by fitting a Vector Error Correction Model (VECM) to the time-series variables employed for this analysis, using the Engle and Granger (1987) two-step approach. Econometric identification of a causal relationship requires both Granger
15Austria, Finland and Sweden in 1995, Cyprus, the Czech Republic, Estonia, Hungary, Latvia,
Lithuania, Malta, Poland, Slovakia and Slovenia in 2004, Bulgaria and Romania in 2007 and Croatia in 2013.
16From 2004 to 2014, on average, 86% of UK imports from the European Union are from countries
3.3. Econometric Analysis 61 causality and a driver of changes in the independent variable that is exogenous to changes in the dependent variable. Thus, we can consider the causal relationship to be identified in the empirical regressions if we find evidence in favour of Granger causality in our empirical regressions, given that we have already shown that changes in the import share in services were exogenous to changes in productivity. The time series variables are as follows: PROD TS, IS S and IM S, where PROD TS denotes the natural logarithm of UK productivity in tradeable services, IS S denotes the natural logarithm of the European Union’s share of UK imports in services, and IM S denotes the natural logarithm of UK import to GDP ratio in services17.
Unit Root Tests
The results of the unit root test for services data, according to both the ADF and the Phillips-Perron tests show that all variables are non-stationary at the 5% significance level, and that the first difference of these variables are stationary at the 5% significance level, as reported in the Table A1 in Appendix A.1. We therefore confirm that all the time series are integrated processes of order one, I(1), and proceed with cointegration tests.
Cointegration Tests
Given that all the time series are I(1), some of these time series may exhibit long-run cointegrating relationships with each other. To test for the presence of long-run cointegrating relationships we employ the Johansen (1991) test. The results of the Johansen (1991) test show that there is one and only one cointegrating relationship for services, as presented in Table A2 in Appendix A.2. Given this result, we next use the Engle and Granger (1987) two-step approach to estimate the VECM, rather than the Johansen (1991) methodology, to avoid the larger loss of degrees of freedom associated with the Johansen (1991) methodology.
17For the analysis of tradeable goods presented in Appendix A.4, the time series variables are
PROD TG, IS G and IM G where PROD TG denotes the natural logarithm of UK productivity in tradeable goods, IS G denotes the natural logarithm of the European Union’s share of UK imports in goods, and IM G denotes the natural logarithm of UK import to GDP ratio in goods.
The use of the Engle and Granger (1987) two-step approach to VECM estimation, in our case requires the assumption that there exists a long-run relationship between productivity and at least one of the right hand side variables. If no such long-run relationship exists, then the estimated coefficients in our VECM below will be spurious. The existing literature shows that there is a long-run relationship between productivity and the import to GDP ratio, for example, Macdonald (1994), Bernard et al. (2006b) and Bloom et al. (2016), therefore we can be confident that the assumption necessary for the Engle and Granger (1987) two-step approach holds18.
Vector Error Correction Model
Our Johansen (1991) test results for cointegration suggest that our three services time-series variables have a cointegration rank of one. The optimal lag length was identified using the Schwartz Information Criterion and the Hannan-Quinn Criterion, and was found under both these criteria to be one (see Appendix A.3 for results). The first step in the Engle and Granger (1987) approach to VECMs is the estimation of the long-run relationship:
P ROD T St = 8.4057+ (0.3631)∗∗∗ 0.9982IS St+ (0.2226)∗∗∗ 0.9877IM St+ (0.03765)∗∗∗ θSt. (3.3.1)
Rearranging, we obtain the estimated residual equation:
c
θSt= P ROD T St− 8.4057 − 0.9982IS St− 0.9877.IM St (3.3.2)
We run the Cointegration ADF (CADF) and Phillips-Perron (1988) tests on the time series of the estimated long-run relationship residual ( [θSt−1) to determine
18Peseran and Shin (2002) showed that, in a VECM, the system of cointegrating equations
is exactly identified if the number of restrictions on the cointegrating equations is exactly equal to the number of cointegrating vectors squared. If there are more restrictions than the number of cointegrating vectors squared, then the system is over-identified, whereas if there are fewer restrictions than the number of cointegrating vectors squared, the system is under-identified. In our case, the restriction on the cointegrating equation exactly identifies the system, as the number of restrictions is equal to the number of cointegrating vectors squared, ie, one, and thus we next proceed to estimating the full VECM.
3.3. Econometric Analysis 63 whether these deviations from long-run equilibrium are stationary. If they are, then we can argue that equation (1) estimates a long-run cointegrating relationship for services. The results of the CADF and Phillips-Perron tests are presented in Table 3.3:
Table 3.3: CADF and Phillips-Perron Unit Root Test Results
Variable CADF Test Phillips-Perron Test
[
θS
t−1-3.351** [0]
-3.351**
Notes: The figures in brackets denote the optimal lag length, determined using the Schwarz Information Criteria. Significant at or below ** 1% and * 5% significance.
Given that the optimal lag length, determined using the SIC is zero for services, the CADF and the Phillips-Perron tests are identical. We find that [θSt−1 is stationary
at the 1% significance level. These results mean that the long-run relationship estimated in equation (3.3.1) is the long-run cointegrating relationship for services. We next proceed to undertake the second step of the two-step Engle and Granger (1987) approach, namely the estimation of the full VECM. The estimated VECM for tradeable services is as follows:
∆P ROD T St = η1+δ11θS[t−1+δ21∆P ROD T St−1+δ31∆IS St−1+δ41∆IM St−1+1t,
(3.3.3)