3- Transformation of Data

Question 1

Why we take logs for given data?

Answer 1

• It compresses data sets so outliers are less of a problem.
• So we do not have to throw away valuable data because observations are outliers.
• Taking logs doesn’t rule out the problem of outliers it just reduces the size of the problem.
• To log-linearise the variable where needed.

Question 2

Cobb-Douglass (C-D) Production Function

Answer 2

Y = AK^a L^b
Y- real output for a country
K- real capital stock
L- labour (employment or no. workers employed by a company).
a (alpha)- capital elasticity
b (beta)- labour elasticity
A- technical progress- if positive technical progress, if negative technical regress.

Question 3

What does capital elasticity measure?

Answer 3

The percentage change in 𝑌 following a marginal change in 𝐾 (capital).

Question 4

What does labour elasticity measure?

Answer 4

The percentage change in 𝑌 following a marginal change in L.

Question 5

Why we take logs of the C-D production function

Answer 5

• We cannot estimate the multiplicative form of the Cobb- Douglas production function above using regression analysis.
• The second reason why we take log⁡ is therefore to transform the multiplicative equation into a log⁡-linear additive equation that we can estimate using regression analysis.
• An estimate of this additive equation will give us the estimate of average technical change across the sample and the estimates of the average labour and capital elasticities across the sample

Question 6

C-D production function once logs of both sides are taken

Answer 6

lnY= lnA + alnK + blnL
y= a + ak + bl

Question 7

Extension of C-D production function

Answer 7

• The traditional form of the Cobb-Douglass production function can be extended to include other inputs in additional to capital (K) and labour (L).
• These other inputs may be human capital, (H), which we take to be measured by academic achievement or number of years of education, energy usage, (E), material usage, (M), and/or health of the labour, (D), which measured by life expectancy so on..

Question 8

Growth Rate function

Answer 8

100 x (Present-past/ past)

Question 9

Growth sequence equation which grows by 10%

Answer 9

Yt= 1.10Y(t-1)

Question 10

Inflation growth rate equation

Answer 10

𝑔𝑡=100×(𝑃_𝑡−𝑃_(𝑡−1))/𝑃_(𝑡−1)
= 100 x (new-old)/old

Question 11

Inflation growth rate equation after log linearising

Answer 11

100(𝑙𝑛𝑃_𝑡−𝑙𝑛𝑃_(𝑡−1))

Question 12

Why we log-linearise extremely volatile inflation rates?

Answer 12

• Makes it smoother and less volatile

Question 13

Inflation key rules/tips

Answer 13

• Falling inflation does not mean falling prices.

Question 14

How is inflation calculated?

Answer 14

• The main measure of inflation is the consumer price index (CPI)
• CPI is a weighted price index. Changes in weights reflect shifts in the spending patterns of households in the economy as measured by the Family Expenditure Survey.

Question 15

How to work out price index of inflation

Answer 15

Sum of (price x weight) / sum of the weights

Question 16

Phillips Curve

Answer 16

Implies that there is a trade-off between inflation and unemployment: to get inflation low, unemployment has to be high and vice versa.

Question 17

How to convert raw growth rates into ln growth rates

Answer 17

1. Ln all raw growth rates
2. (New-old) x 100

Question 18

Components of time series data

Answer 18

• Trend
• Seasonal
• Irregular
  Y= T + S + I

Question 19

Seasonal component of time series data

Answer 19

Regular, short term, annual cycle

Question 20

Irregular component of time series data

Answer 20

What is left over after the trend and seasonal components have been ‘taken out’.

Question 21

Aim of decomposing time series data

Answer 21

Technique that attempts to find the main trends within time series.

Question 22

Why is seasonally adjusted data useful?

Answer 22

• Useful for understanding reasons for unemployment.
  E.g. monthly unemployment data are usually seasonally adjusted in order to highlight variation due to the underlying state of the economy rather than the seasonal variation.

Question 23

Issues with decomposition of time series data

Answer 23

It doesn’t work well with random events, or multiple cycles.

Question 24

Moving average (MA)

Answer 24

• An indicator often used in technical analysis.
• An average of any subset of numbers.
• Equal weighted, centred moving average for time series.

Question 25

Moving average equation

Answer 25

〖𝑀𝐴〗𝑡 3= (𝑥(𝑡−1)+𝑥_𝑡+𝑥_(𝑡+1))/ 3

Question 26

Reason for calculating the moving average of any time series data?

Answer 26

• Help smooth out the data by creating a constantly updated average value.
• Helpful for forecasting long-term trends.

Question 27

Index number equation

Answer 27

100 x (observed value/ base value)

Question 28

Data issues when calculating index numbers

Answer 28

• One problem when monitoring an index over time is that the base sometimes changes which causes the data to jump.
• When the base year changes old index values cannot be compared to new index value as they have different base years. You can solve this problem by chaining the data.

Question 29

Laspeyres Price Index (LPI)

Answer 29

𝟏𝟎𝟎×(∑(𝑷_𝒕×𝑸_𝒃𝒂𝒔𝒆)〗)/(∑(𝑷_𝒃𝒂𝒔𝒆×𝑸_𝒃𝒂𝒔𝒆))

Question 30

Disadvantages of LPI

Answer 30

• Adjusting the base will change the base expenditure and the price relatives which will cause the index value to change.
• Possibly a bigger problem with the Laspeyres Price Index is that as the price relatives change over time we would expect quantities to change but the index does not permit quantities to change i.e. unchanging base quantities.
• This may mean the index quickly becomes unrepresentative over time and needs to be rebased with more recent quantities.

Question 31

Paasche Price Index (PPI)

Answer 31

𝟏𝟎𝟎×(∑(𝑷_𝒕×𝑸_𝒕)〗)/(∑(𝑷_𝒃𝒂𝒔𝒆×𝑸_𝒕))
The Paasche Price Index is a price index used to measure the general price level and cost of living in the economy and calculate inflation.

Question 32

Disadvatages of PPI

Answer 32

• Data on current weightings (i.e., quantities for each item) can be difficult to obtain
• Costlier than using a LPI
• Tends to understate the changes in price because the index already reflects changes in consumption patterns when consumers respond to price changes

Question 33

LPI vs PPI

Answer 33

• The PPI values are in general smaller than the LPI values which is to be expected as consumption of energy involves switching to the cheapest fuels.
• The PPI can pick up the switching because it uses current weights.
• The PPI values are more difficult to calculate

Question 34

Fisher Price Index (FPI)

Answer 34

• Geometric average of LPI and PPI
• Corrects the positive bias (upward bias) in the LPI, corrects the negative bias (downward bias) in the PPI.
• 𝐹𝑃𝐼=√(𝐿𝑃𝐼×𝑃𝑃𝐼)

Question 35

Deflator equation

Answer 35

𝑅𝑒𝑎𝑙 𝐺𝐷𝑃=(𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝐺𝐷𝑃)/(𝐺𝐷𝑃 𝐷𝑒𝑓𝑙𝑎𝑡𝑜𝑟)×100