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# Statistical test

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Unfortunately, we did not find any support for the additional variables presented in section 6.9, for this period.

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∆USDGBP chi2 252.85

Breusch-Pagan test for heteroscedasticity Prob > chi2 0.0000

∆GBPEUR chi2 0.98

Breusch-Pagan test for heteroscedasticity Prob > chi2 0.3227

Table 4: Breusch-Pagan test statistic, period 1

7.2.4 Autocorrelation of residuals

To ensure that there is zero autocorrelation between the residuals, the Breusch-Godfrey test for autocorrelation was performed. The test statistics for both models are presented in Table 5.

∆USDGBP chi2 5.313

Breusch-Godfrey test for autocorrelation Prob > chi2 0.0212

∆GBPEUR chi2 1.314

Breusch- Godfrey test for autocorrelation Prob > chi2 0.2516

Table 5: Breusch-Godfrey test statistic, period 1

As mention in section 5.1.3, a rejection of the null hypothesis indicates that the residuals in the models are assumed to be correlated. For both models the null hypothesis is rejected, thus our model contains autocorrelation of the residuals. Implementing the modified standard error by Newey-West, we are able to adjust the model for autocorrelation.

7.2.5 Multicollinearity

Lets first look at the model in Equation 16, ΔUSDGBP. The correlation matrix in Table 6 show that the correlations between the independent variables. The highest correlation is between the CDS for the UK and the broad dollar index with a correlation of 0.3462. This is far off being considered high, especially since financial data can often correlate to a large extent, while still being independent of each other. The additional VIF test is presented in Table 7, shows that all variables are under the critical value of 10 as well with a low mean of 1.16. The correlation matrix and the VIF test statistic indicate that the model for ΔUSDGBP has no evidence for multicollinearity. It is noteworthy that no variables were excluded because of high correlations and/or high VIF values.

CDS 10Y YIELD Broad dollar LIBOR-OIS

UK GERMANY index GBP

CDS UK 1.0000

10Y yield, Germany -0.3341 1.0000

Broad dollar index 0.3462 -0.3257 1.0000

LIBOR-OIS GBP 0.1020 -0.0844 0.0363 1.0000

Table 6: Correlation matrix for ΔUSDGBP, period 1

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Variable VIF 1/VIF

CDS UK 1.22 0.8197

Broad dollar index 1.20 0.8333 10Y yield, Germany 1.20 0.8333 LIBOR-OIS GBP 1.01 0.9901

Mean VIF 1.16

Table 7: VIF test results for ΔUSDGBP, period 1

For the ΔGBPEUR model presented in Equation 17, we document similar values as the tables above. For the correlation matrix in Table 8, the highest correlation is between CDS for the UK and the broad dollar index with a correlation of 0.3462. To ensure that the model has no multicollinearity, the VIF test has been carried out and is presented in Table 9. The VIF test shows promising results with test results ranging from 1.02 to 1.22 and a mean of 1.14. This indicates further that our model for ΔGBPEUR does not show evidence of multicollinearity. Related to the ΔUSDGBP model, no variables were rejected based on high correlation and/or high VIF values.

LIBOR-OIS LIBOR-OIS CDS 10Y YIELD Broad dollar

GBP EUR UK GERMANY index

LIBOR-OIS GBP 1.0000

LIBOR-OIS EUR 0.0706 1.0000

CDS UK 0.1020 0.1182 1.0000

10Y yield, GER -0.0844 0.1929 -0.3341 1.0000

Broad dollar index 0.0363 0.1383 0.3462 -0.3257 1.0000

Table 8: Correlation matrix for ΔGBPEUR, period 1

Variable VIF 1/VIF

10Y yield, GER 1.22 0.8197

CDS UK 1.22 0.8197

Broad dollar index 1.21 0.8264 LIBOR-OIS GBP 1.05 0.9524 LIBOR-OIS EUR 1.02 0.9804

Mean VIF 1.14

Table 9: VIF test results for ΔGBPEU, period 1.

Page 63 of 86 7.2.6 Exogeneity

The exogeneity is important to draw the right conclusion on the results, as an incorrect causality does not give an understanding of what we actually want to understand. The LIBOR-OIS spread is assumed to be independent for the basis, as the spread captures the risk premium of a set of panel banks. The risk premia likely stem from the banks’ fundamentals such as the balance sheet, leverage and exposure, rather than due to the basis movements. The same goes for the CDS spreads which are likely to affect the basis, but not the other way around, as the basis itself does not affect any risk measures. The funding gap, however, is not that easy to assume, as there is plausible that there exists some feedback effect. Though it is likely that the main effect is from the funding gap to the basis with a plausible feedback effect of market participants using the spread to achieve cheaper funding. Here we assume that the condition holds, as it has been used in Borio et al. 2018 paper. The broad dollar index could also be affected by the basis, as larger arbitrage opportunities could affect the spot strength of the USD, but due to the large transaction volume in USD, this seems very unlikely to have a significant effect that would make our findings invalid. The end of the year effect is assumed to be caused by financial regulations and assumed to be exogen. On the topic of the additional variables, we believe that the EPU index would also be a one-way causality, as the basis is unlikely to affect the monetary policy uncertainty in analyst forecasts and the media. The S&P500 variable is dependent on the performance in the equity market and the uncertainty tied to the index, and is therefore assumed to be exogen.

We conclude that all of the variables presented are exogen and exercise primarily a one-way causality, as it is illogical for the majority of the variables to have a causality the other way around to a significant degree. What further supports this conclusion, is that several research papers have used these variables, and we assume that they have tested for the exogeneity.

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### 8 Empirical Results – 2015-2019

This chapter will look into the sample period of 01/01/2015 – 01/03/2019. With variables express different characteristics through the whole sample, a key objective will be to investigate if the variables exercise the same explanatory power for the given ΔBasis model for USDGBP and GBPEUR as it did in section 7. Another objective will be to determine if the variables found to be significant in the previous models still are, and if any other variables show promising results. Throughout the sample period, Brexit has been a key political event after voting to leave the EU in June 2016. It is plausible that Brexit can help explain a part of the CIP deviations for this sample, as the event has introduced a lot of uncertainty to the UK economy. Two new variables will also be introduced and tested.

The chapter is divided into three parts: In the first part, looks at Brexit and how the CIP for USDGBP and GBPEUR has developed through the period. The second part covers the new models and also include the regression results which will be compared to both the previous sample period and the research papers.

Finally, the statistical test results of the regression models will be presented.

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