Question 1

In a study to investigate regional bias a web-scraped sample of online hotel reviews is taken. The data thus consists of multiple ratings from each hotel but only one rating from each reviewer. A generalised linear mixed model is then fitted to this data to see if the probability a survey respondent gives a high score depends on the region.

(a) Explain why the mixed effects term is needed.

[3 marks]

The R code for this model is shown below and the output generated is shown in Table 1.

high<-1*(rating>3)

medium<-1*(rating==3)

low<-1*(rating<3)

yhigh<-cbind(high, 1-high)

high1<-glmmPQL(yhigh~region, random=~1|product, family=binomial)

Coefficient	Estimate	Estimated Standard Error
Intercept London North East and Yorkshire North West Scotland South South West Wales West Midlands	1.0760804 -0.2214280 -0.0109988 0.0102060 0.0811167 -0.0064580 0.0426359 0.0589384 0.0020951	0.09293285 0.06144537 0.06057182 0.06014998 0.06892505 0.06077871 0.07024479 0.07794753 0.06645689

Table 1: R output for Question 1

(b) Using Table 1 is there any evidence of a regional effect?

[5 marks]

(c) Using the results in Table 1 estimate the probability that respondents in each region give a high score.

[5 marks]

An additional generalised linear mixed model is fitted to this data. The R code for this model is shown below and the output generated is shown in Table 2.

high2<-glmmPQL(yhigh~region, random=~1|product, family=binomial(link=probit))

Coefficient	Estimate	Estimated Standard Error
Intercept London North East and Yorkshire North West Scotland South South West Wales West Midlands	0.6562287 -0.1352726 -0.0073310 0.0022180 0.0467937 -0.0056253 0.0231553 0.0340817 0.0001860	0.05468946 0.03636635 0.03578405 0.03545799 0.04072884 0.03574069 0.04126953 0.04580647 0.03915476

Table 2: Additional R output for Question 1

(d) Using Table 2 is there any evidence of a regional effect?

[5 marks]

(e) Using the results in Table 2 estimate the probability that respondents in each region give a high score.

[5 marks]

(f) Comment on the results in parts (c) and (e).

[2 marks]

Question 2

(a) List the stylised empirical facts of financial time series.

[11 marks]

(b) To what extent do you expect cryptocurrency prices to obey similar patterns

[2 marks]

Log-returns for Ripple are analysed in R. The code used is shown below and the output is shown in Table 3.

>RippleData<-read.table(“E:RippleData.txt”)

>ncol(RippleData)

[1] 4

>price<-RippleData[,4]

> price<-rev(price)

> length(price)

[1] 2385

> logreturn<-log(price[-1])-log(price[-2385])

>a1<-garch(logreturn-mean(logreturn))

>summary(a1)

Coefficient	Estimate	Estimated Standard Error
a0	3.634e-04	1.453e-05
a1	3.366e-01	1.652e-02
b1	6.413e-01	1.261e-02

Table 3: R output for Question 2

(c) Does Table 3 give any evidence of the ARCH effect?

[4 marks]

(d) Does Table 3 give any evidence of the GARCH effect?

[4 marks]

(e) Why might it be possible, in this context, to improve upon this classical formulation of this model with conditional normal distributions?

[2 marks]

(f) In the light of observations in part (e) what are the implications for how well cryptocurrencies like Ripple could serve as a “genuine currency”?

[2 marks]

Question 3

Discuss, with examples, what historical experiences of currency debasement and asset price bubbles can teach us about the development of Bitcoin and cryptocurrencies.

[25 marks]

Question 4

What is meant by the Oxford Blockchain Framework? How might this framework be used to analyse potential Blockchain applications to education and government?

[25 marks]