Introduction
Unemployment, and the impact of economic crises, tend to vary across space as well as time. It is therefore of interest to explore how the unemployment rates of different regions are related. In particular, concerning the UK, London and the south-east of England display persistently lower unemployment rates than other regions of the country. In this exercise you will explore the relationship between the unemployment rate in London and another UK region.
You will apply the time series techniques considered in ECM104 lectures and classes, including unit root tests, diagnostic testing of models, cointegration analysis, and error correction modelling. Koop (2013) discusses these methods (see especially chapters 9, 10, and 11). 2
Data
The data is contained in the Excel file called ‘Regional Unemployment Data (2020) (2)’ available in the Assignments section of the Blackboard site. It contains monthly data for London and eleven other UK regions. These are given in table 1 below.
Table 1: Regions and Variable Names
Region Variable Name
London L
Northern Ireland NI
North East NE
North West NW
Scotland S
Wales W
South West SW
East E
The data also includes a variable Date which provides the year and month of each observation.
The data are in percentage terms, and seasonally adjusted, for the period April 1992 to July 2020 inclusive (340 observations). The last few observations coincide with the onset of the COVID-19 pandemic. The data were obtained from the website of the UK Office for National Statistics (Office for National Statistics, 2020).
For this question, you are required to consider two series, that for London and one for another UK region. The other regional series you must use is determined by the allocation rule given in table 2 below.
Import the data into Stata and identify the series you will use. Set up a monthly time variable based on the variable Date. Use the gen and tsset commands introduced in Stata Exercise 5.3
2 Useful texts including sections on unit root testing and cointegration are Brooks (2003) and Patterson (2000).
3 The commends required are:
gen Month=monthly(Date, "YM") asset Month, monthly
Table 2: Series by Student Number
If the last two digits of your student number are You must use the variables:
00 to 13 L and NI
14 to 27 L and NE
28 to 41 L and W
42 to 55 L and S
56 to 69 L and NW
70 to 84 L and SW
85 to 99 L and E
Questions
1. Ocular Econometrics
a) Provide time series line plots of each of your two unemployment series. (10 marks)
b) Describe the evolution of the series over time commenting especially on any co-movements or changes in behaviour over time and the stationarity or otherwise of the series. (10 marks)
2. Non-Stationarity of Unemployment
Use augmented Dickey-Fuller (ADF) tests with an intercept to determine the order of integration of your two series. Recall that you will have to select an appropriate augmentation order for the tests. This is best done using an information criterion. (8 marks)
3. The Long-Run Relationship Between Unemployment in London and the Other Region
a) Determine if your two unemployment series are cointegrated using the Engle-Granger procedure. (See Stata Exercise 5 for how to do this). Use London as the explanatory variable, not the dependent variable. (8 marks)
b) Comment on the value of the slope coefficient in the cointegrating regression. (8 marks)
c) Save the residuals from the cointegrating regression as RES1 and provide a time series plot of them. Comment any particular characteristics you observe in the graph. (8 marks)
4. The Dynamic Relationship Between Unemployment Rates: Error Correction Models
a) Estimate two error correction models for the relationship between your unemployment series. One should have no additional lags of the differences (equation (1)), the other should include 8 lags of the differences (model (2)).4 Let L represent the unemployment rate in London and OTHER that
4 Remember and error correction model uses the differences of the variables of nterest and the lagged residuals from the cointegrating regression. of your other region. Then the models you should estimate are set out in equations (1) and (2):
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