Module 2: Mathematical Operations and Index Numbers

Question 1

What does aggregation mean?

Answer 1

• It is when you combine multiple numbers to form a single number

Question 2

When do we use aggregation?

Answer 2

• We usually use this with some time series to reduce the frequency: Monthly, quarterly, annual

Question 3

How do we inform our software that our datasets are time series

Answer 3

Usually our datasets have a date column but we need to make sure they understand its for DATES

Question 4

Before formatting our dataset what do we need to understand first about the dataset?

Answer 4

The date conventions (or dates in datasets)

Question 5

What are the two different date conventions that can exists for time series?

Answer 5

1. Flow + stock variables

Question 6

What are ‘flow variables’

Answer 6

• Flow variables are considdered to be the average flow over the period
• This means when we set the exact time of the average flow to the center of the period

Question 7

What are stock variables?

Answer 7

• We consider stock variables to be the total amount at the end of the period
• The exact time for the stock variables is at the end of the hour

Question 8

In Macroeconomics are there many types of stock + flow variables?

Answer 8

YES

Question 9

What’s an example of a flow variable?

Answer 9

Consumption as it accumulates the stock of goods

Question 10

What is the units per measurement for the flow of consumptions

Answer 10

Dollars per month

Question 11

What if we have annual/quarterly for both stock + flow variables?

Answer 11

Stock:
Annual: End of the year –> Dec 31
Quarter: end of the quarter –> March 31

Flow:
Annual: July 1
Quarterly: Feb 15 (first quarter)

Question 12

What’s an exampl of a stock/flow vairbale that is considered neither?

Answer 12

Temperature

Question 13

What is the dates if its neither a flow or stock?

Answer 13

Every time we have a variable that represents an average we set the date to the middle and if its for the total over till the end (stock variable)

Question 14

Can stock variables be averages?

Answer 14

YES stats Canada does it as they publish stats that use the average population

Question 15

How do we define our datasets as time series?

Answer 15

• There might not be a column that has a definite date column (either fix or create one)

Question 16

How to create a monthly time series?

Answer 16

• Add and use the year month date provided and make a column
• Its a monthly time series so we set the date to the middle of the month (flow variable)

Question 17

How to name a table

Answer 17

• Go to ‘design’ and change the ‘table name’

Question 18

How to create an annual time series?

Answer 18

• We create the date column
• However the actual day we set to the middle of the year as its annual flow vraible (july 1)

Question 19

How to add a date column in decimal format

Answer 19

Annual time series
Decimal date = Year + 0.5

Quarterly:
Decimal date = Year + 1/8 + Q-1/4

Monthly:
Decimal date = year + 1/24 + M-1/12

Question 20

What’s a big problem when numbers are saved in text format?

Answer 20

it affects mathematical oerpations so we to change it column by column

Question 21

What should we do if the series are in different units of measurements?

Answer 21

• Make sure to change them into the same units

Question 22

How to change *c to *f?

Answer 22

C = (F-32) *5/9

Question 23

What are growth rates?

Answer 23

Growth rates in this context describes changes in any variable between two periods in percentage form

XT- Express the value of a variable at time T

XT -1 –> expresses the value of the same variable one period in the past
(this is dependent on the time units)

If its monthly previous month and so on

Question 24

What is the equation for the Growth rate?

Answer 24

gt = (Xt - Xt-1 / xt-1)*100

Question 25

For growth rates do you need to only express as a %

Answer 25

No you can keep it as a decima;

Question 26

When we played around with the equation what did we come to learn?

Answer 26

(gt+1 ) = (xt / xt-1)

Question 27

Whats something to keep in mind about mathematical operations with gt?

Answer 27

Never express growth rates in % when doing mathematical operations: use decimal before converting

Question 28

Do growth rates have measurements?

Answer 28

NO

Question 29

Will growth rates in each example be constant?

Answer 29

NO

Question 30

What is the growth rate of a product?

Answer 30

(1+ gx)*(1+gy) -1 = gx + gy –> apporximation

Question 31

Do we wat a higher or smaller growth rate?

Answer 31

Smaller thats why we most likely use the approximation instead of the formula

Question 32

What is the growth rate of ratios?

Answer 32

gt = (1+ gx) / (1+ gy) = gx - gy

Question 33

Can growth rates be negative

Answer 33

Yes so read the question crefully

Question 34

What is the equation for annualized growth rates (monthly data)

Answer 34

gt = (1+ gt)^12 -1

Question 35

What are annualized growth rates?

Answer 35

Its when a monthly growth rate is annualized and calculated over one year

Question 36

What is the equation for annualzied gt (quarterly )

Answer 36

gt = (1+ gt) ^4 -1

Question 37

For any positive/neagtive numbers for log(ab)

Answer 37

log(ab) = Log(a) = Log(B)
Log(a/b) = Log(a) - log (B)

Question 38

How do we express log in

Answer 38

natural (ln)

Question 39

How to interpret the growth rate using log?

Answer 39

Log(xt) - log(xt-1) = log(xt/xt-1) = log(1+gt)

Question 40

What if we want the growth rate of the log (product version)

Answer 40

={ log(xt) - log(xt-1)} + {log(yt) - log(yt-1) = (gx + gy)

Question 41

What is aggregation?

Answer 41

its when we combine multiple numbers to form a single number
- its main usage was to reduce the frequency of a time series
- Converting a monthly –> quarterly

Question 42

How to do aggregation?

Answer 42

• if it’s monthly to quarters you take the first three months and add them up to make 1 quarter –. yearly add everything up

Question 44

When we refer to a variable in anexcel file what do we mean?

Answer 44

• Its when we look by the name of the table followed by the name of the varibake inside the brackets

Ex:
= tempdata[jjA]

Question 44

What are the different logical operators

Answer 44

”>=”
“<”
“<=”
“=”

Question 44

how to take average for 3 months using sum?

Answer 44

=sum(tempdata[@jun] , [@jul] , [@Aug] ) / 3

= sum(tempdata[@[jun] : [Aug] ] ) /3

Question 44

how to use round to find the average of the three months

Answer 44

=round(average([tempdata[@[jun] : [Aug]] , 2)

Question 44

How do we use ‘sumif’/ averageif to find the co2 emission after 1980

Answer 44

=sumif([co2Y[date]] , “>1980” , co2y[co2}

Third argument what we want to sum
First was what we wanted to restrict the observation
Second was the actual restriction

Question 45

How to restrict observations based on a date? (ex: Suppose you want the total CO2 emission before January 15th 1970.

Answer 45

=sumif(co2Y[date] , “<”&DATE(1970, 1 ,15) , co2Y[co2])

Question 46

Can we impose more than one rrestriction? How? Suppose for example that we want the total CO2
emission between January 1st 1980 and March 20th 1995.

Answer 46

=SUMIFS(co2data[Co2], co2data[Date], “<”&DATE(1995, 3, 20), co2data[Date], “>”&DATE(1980,1,1))

1st argument –> the variable used for the operation
Second is the variable for the first criteria
Third –> is the restriction
fourth –> second criteria
fifth –> restriction