Lecture 1

Question 1

General Keynesian consumption function equation

Answer 1

Y=β₀+β₁x + ε

β₀ is intercept
β₁is MPC
ε is random variable to represent other factors influencing consumption.

Question 2

2 moments

Answer 2

Mean and variance

Question 3

Mean notation

Answer 3

E(x) (expected value) or μ

Question 4

The area under the density function (curve) can be used to find probabilities e.g of income being between A and B.

Question 5

Covariance

Answer 5

Covariance looks at how variables x and Y are associated

Question 6

Can covariance be positive or negative or both?
And what does positive and negative mean

Answer 6

Both
When positive - when X increases Y also increases
When negative - when X increases Y decreases

Question 7

Correlation coefficient

Answer 7

Same as covariance but also shows strength of relationship.

(both dont mean causation between 2 variables!)

Question 8

Correlation values

Answer 8

-1<=p<=1

1 is strong pos
-1 is strong neg
0 is no relationship

E.g income and consumption correlation coefficient would be near 1 as strong positive relationship

Question 9

Normal distribution notation

Answer 9

X~N (μ,σ²)

(Mean and variance)

Question 10

Probability of getting a value of X within 1SD, 2SD, 3SD of the mean in a normal distribution

Answer 10

1SD 68%
2SD 85%
3SD 99.7%

Question 11

Z equation for normal distribution if mean is 0, and SD is 1…

what is this also known as

Answer 11

X-μ / σ ~ N(0,1)

So value - mean / standard deviation
A standard normal!!! A special case of normal distribution.

Question 12

2 main types of data

Answer 12

Cross sectional
Time series

Question 13

Cons of cross sectional data

Answer 13

Costly and time consuming.

Question 14

Sampling distribution of sample mean

Answer 14

X~N (μ,σ²/N)

(the mean of the sample we took is just 1 value from a bunch of possibilities)

Question 15

Central limit theorem

Answer 15

If sample size N is large, then there will be normal distribution

Question 16

So using these estimators like a sample mean require quality data
2 properties of estimators

Answer 16

Unbias and efficiency

Question 17

Unbiasedness

Answer 17

If the estimator E(δ) is centred on δ

E (Xbar) = μ

Question 18

EFFICIEINCY

Answer 18

If the estimator has the smallest variance then it is most efficient.

Question 19

Consistency

Answer 19

As size of the sample increases, the variance of the estimator tends to 0 until density collapses to a single spike at δ

(intuition: variance of sample mean is σ²/n , so as n increases, variance falls smaller and smaller till 0). therefore consistent

Question 20

variance formula

Answer 20

1/(n-1) x (every number squared, - n(xBar²)

xbar is sample mean

Question 21

Practice proof for showing sample mean is unbiased.

+ key to remember

Answer 21

E(X) = μ !!! When replacing each individual E(X₁+X₂+etc)

Question 22

Practice proof of variance of sample mean estimator.

And 2 tips needed to remember

Answer 22

When taking /n out and swapping for 1/n, whenever we remove something from the variance we have to square what we took out!!! So becomes (1/n)²

Then also remember Σvar (Xi) can be written as individual σ².

Question 23

Size of a test

Answer 23

Probability of making a type 1 error (rejecting a true hypothesis)

Question 24

Power of a test

Answer 24

Probability of NOT committing a type 2 error (i.e doing the right thing)