3- Transformation of Data Flashcards
Why we take logs for given data?
- 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 doesnβt rule out the problem of outliers it just reduces the size of the problem.
- To log-linearise the variable where needed.
Cobb-Douglass (C-D) Production Function
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.
What does capital elasticity measure?
The percentage change in π following a marginal change in πΎ (capital).
What does labour elasticity measure?
The percentage change in π following a marginal change in L.
Why we take logs of the C-D production function
- We cannot estimate the multiplicative form of the Cobb- Douglas production function above using regression analysis.
- The second reason why we take logβ‘ is therefore to transform the multiplicative equation into a logβ‘-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
C-D production function once logs of both sides are taken
lnY= lnA + alnK + blnL
y= a + ak + bl
Extension of C-D production function
- 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..
Growth Rate function
100 x (Present-past/ past)
Growth sequence equation which grows by 10%
Yt= 1.10Y(t-1)
Inflation growth rate equation
ππ‘=100Γ(π_π‘βπ_(π‘β1))/π_(π‘β1)
= 100 x (new-old)/old
Inflation growth rate equation after log linearising
100(πππ_π‘βπππ_(π‘β1))
Why we log-linearise extremely volatile inflation rates?
- Makes it smoother and less volatile
Inflation key rules/tips
- Falling inflation does not mean falling prices.
How is inflation calculated?
- 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.
How to work out price index of inflation
Sum of (price x weight) / sum of the weights
Phillips Curve
Implies that there is a trade-off between inflation and unemployment: to get inflation low, unemployment has to be high and vice versa.
How to convert raw growth rates into ln growth rates
- Ln all raw growth rates
- (New-old) x 100
Components of time series data
- Trend
- Seasonal
- Irregular
Y= T + S + I
Seasonal component of time series data
Regular, short term, annual cycle
Irregular component of time series data
What is left over after the trend and seasonal components have been βtaken outβ.
Aim of decomposing time series data
Technique that attempts to find the main trends within time series.
Why is seasonally adjusted data useful?
- 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.
Issues with decomposition of time series data
It doesnβt work well with random events, or multiple cycles.
Moving average (MA)
- An indicator often used in technical analysis.
- An average of any subset of numbers.
- Equal weighted, centred moving average for time series.