Question: London’s congestion charge was introduced in February 2003. A researcher investigated the impact of the congestion charge using multiple linear regression. The variables used in the regression model are as follows. All data are collected in the period from January 2002 to December 2004.

LRSI: Monthly index of retail sales in Central London (Dependent variable)

UKRSI: Monthly UK Retail Sales Index (This variable is used to capture the nationwide retail sales changes)

UNEM: Monthly London Unemployment Index (This variable is used " to capture any other economic trends in London)

Year2003: = 1 in year 2003, 0 otherwise

Year2004: = l in year 2004, 0 otherwise (Year2003 and Year2004 are used to measure the impact of congestion charge on retail sales in the year of implementation and the year after)

Monthi: = 1 in the ith month of each year (i=1, 2, , 12), 0 otherwise (These monthly dummy variables are used to measure seasonal sales trend within a year)

The regression model is specified as follows.

The regression output is summarized in the table below.

1. Interpret the estimated values of \(\beta_{1}\) and \(\beta_{2}\) in the regression output.
2. Based on the coefficient estimates of monthly dummy variables, estimate the seasonal trend of retail sales within any year between 2002 and 2004 (use February as the base period, i.e., the index number in February is 100 ). Which month has the highest retail sales? Which month has the lowest?
3. What is the impact of the congestion charge on retail sales in the year of implementation and the year after?
4. Comment on the use of dummy variables in this analysis. Do you think the coefficient estimates of annual dummy variables can reveal the true relationship between congestion charge and retail sales? Discuss.

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