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Econometrics Assignment on UK GDP and Tourism Data and Football League Cup Market Probabilities

## Analysis of UK Real GDP and Tourism Data

The file ‘TS CWK 2020 DATA 1.xlsx’ contains the quarterly data on UK real GDP (RGDP, £m, seasonally adjusted) from 1986 Q1 to 2019 Q3; outbound tourist visits from the UK to overseas destinations (UKTOUR), and inbound tourist visits to the UK from overseas (OSVISIT) from 1986 Q1 to 2018 Q4 (both variables in thousands, seasonally adjusted).

a. Given that you may wish to consider elasticities in the analysis of these three variables, transform them accordingly. At this stage, make no assumption regarding the form of analysis you might subsequently perform (i.e. assume both cointegration and an analysis of stationary variables might be feasible). State the transformation you have made.

b. Test the transformed variables for stationarity using the Augmented DickeyFuller (ADF) test with a maximum of 4 Auto-regressive (AR) lags and interpret the test results.

c. Perform any further transformations and tests that are necessary to demonstrate that stationarity in all variables has been achieved. State your transformations and explain how your test results demonstrate stationarity.

d. Model UKTOUR as a function of RGDP using 4 distributed lags (bearing in mindthe transformations to the variables you have already made in [a] and [c]).Test back the lags in this model appropriately (you need only show the output of the first and final model). Show how you calculate the long-run elasticity of UK visits abroad with respect to UK Real GDP and interpret the value.

e. Test the final model in (d) for first-order Autocorrelation and interpret the result.

f. Estimate an Autoregressive Distributed Lag model of UKTOUR adding an appropriate AR lag to the final model of part (d). Show how the long-run elasticity of UK visits abroad with respect to UK Real GDP is calculated and interpret its value.

g. Test the model in (f) for first-order Autocorrelation and comment in relation to the model estimated in (d).

h. Test the model in (f) for functional form mis-specification, normality of the residual and parameter stability (using the QLR test). Interpret these results.  Explain briefly how the QLR test evaluates parameter stability (i.e. what is the concept/procedure for the QLR test).

i. Use the Vector Autoregressive (VAR) lag selection to determine the optimal lag structure for a VAR between the three variables, selecting 4 as the maximal lag structure.

j. Based on this evidence, estimate an appropriate VAR. Interpret the coefficients of the VAR and comment on the nature of Granger Causality between the variables. Does the implied Granger Causality make ‘economic sense’?

## Transformations and Stationarity Testing

k. Use the VAR to forecast total UKTOUR in thousands to 2019 Q4. Tip - you can use the available information 2018.4-2019.3 on RGDP to form this forecast (i.e. you shouldn’t need to forecast RGDP). Note however, that you will need to forecast OSVISITS to form the forecast of UKTOUR.

2. The data ‘TS CWK 2020 DATA 2.xlsx’ contains data on the implied within-game betting market probabilities (in percentages) for Chelsea vs Manchester United (Football League Cup, 30 October 2019). There are two probabilities shown, expressed as the probability of (a) Chelsea winning the game or the match ending in a draw (CH_WIN_DR); (b) Manchester United winning the game (MU_WIN).

The market probabilities are recorded at each minute of the game. There are 106 consecutive minutes of market observation (this includes the 15 minute half-time break in play that occurs at around 45 minutes of play). Probabilities of the two events change as the game unfolds – for example, in the first minute of the game the market believes Man Utd have a 26.2% of winning whilst the alternative of Chelsea winning or a draw is 72%. Man Utd are first to score in the 24th minute and this changes the chances of Man Utd winning to 51.8% and the alternative to 47.2%.

Note – when opening the file in GRETL, specify ‘other’ as the unit of time, set at 1.

a. Assess whether the two variables have properties suitable for investigating cointegration analysis, briefly explaining your answer.

b. Assess whether the two betting probabilities cointegrate, making clear how you arrive at your conclusion. You can use MU_WIN as the dependent.

c. What does the cointegration analysis estimate the long-run effect of changes in the Chelsea win/draw probability on Man Utd’s win-probability to be?

d. Using appropriate transformations to variables, estimate an Error Correction Model for MU_WIN probability. You can start with a contemporaneous term and 1 distributed lag of CH_WIN_DR, one AR term, and an appropriate ECM term. Test the model back accordingly and comment on the final model’s overall explanatory power.

e. Test whether the term on the error correction coefficient is different from a value of -1. You can calculate this manually, showing your working.

f. Interpret the regression coefficients of the ECM and their statistical significance, paying particular attention to the interpretation of the coefficient of the error correction term in context of the test in