Question

1.Assume you collected a quarterly sales data (in millions of dollars) over a four-year period from the first quarter 2016 to the fourth quarter 2019, and computed the seasonal index for each quarter. If the values of the actual sales and deseasonalised sales were 162 and 158.68, respectively, in the second quarter of 2016, what is the (normalised) seasonal index for the second quarter? Round your answer to two decimal places.

2.

Assume you collected data representing the number of full-time employed males ('000) without access to paid leave entitlements in Australia from 1992 to 2007, and fitted a third-order autoregressive model. What number of degrees of freedom do you use if you test the appropriateness of the fitted model.

3.

The following are prices and consumption quantities for three commodities in 2009 and 2019:

Commodity	2009		2019
	Price	Quantity	Price	Quantity
A	$2	15	$5	17
B	$32	4	$28	3
C	$5	20	$7	15

Based on the above information, calculate the Laspeyres aggregate price index for 2019 using 2009 as the base year. Round your final answer to two decimal places.

Answer 1

Part 1:

Seasonal index = Actual sales / Deseasonalised sales x 100

Seasonal index = 162 / 158.68 x 100

Seasonal index = 102.09


Part 2:

"Degrees of Freedom" means the maximum number of logically independent values that have the freedom to vary, in the data sample."

The degrees of freedom (for example) for a set of three numbers is two. If you wanted to find a confidence interval for a sample, degrees of freedom is n – 1. “N' can also be the number of classes or categories.


Part 3:

Remember the table given in the question has got disarrayed. I have put it right, to the best of my ability, as below:

Commodity	2009	2019
Price P0	Quantity Q0	Price P1	Quantity Q1
A	$               2.00	15	$       5.00	17
B	$            32.00	4	$    28.00	3
C	$               5.00	20	$       7.00	15

Now, we know that as per Laspeyre's method:

Now, let us find out the required variables as below:

Commodity	2009	2019	P1Q0	P0Q0
Price P0	Quantity Q0	Price P1	Quantity Q1
A	$               2.00	15	$       5.00	17	$              75.00	$     30.00
B	$            32.00	4	$    28.00	3	$           112.00	$   128.00
C	$               5.00	20	$       7.00	15	$           140.00	$   100.00
				Sum	$           327.00	$   258.00

Now, after putting the values in formula, we get:

P01 = 327 / 258 * 100
P01 = 126.74

Aggregate price index for 2019 using 2009 as the base year = 126.74