Lecture 1 Flashcards

1
Q

General Keynesian consumption function equation

A

Y=β₀+β₁x + ε

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

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2
Q

2 moments

A

Mean and variance

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3
Q

Mean notation

A

E(x) (expected value) or μ

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4
Q

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

A
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5
Q

Covariance

A

Covariance looks at how variables x and Y are associated

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6
Q

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

A

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

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7
Q

Correlation coefficient

A

Same as covariance but also shows strength of relationship.

(both dont mean causation between 2 variables!)

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8
Q

Correlation values

A

-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

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9
Q

Normal distribution notation

A

X~N (μ,σ²)

(Mean and variance)

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10
Q

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

A

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

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11
Q

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

what is this also known as

A

X-μ / σ ~ N(0,1)

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

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12
Q

2 main types of data

A

Cross sectional
Time series

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13
Q

Cons of cross sectional data

A

Costly and time consuming.

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14
Q

Sampling distribution of sample mean

A

X~N (μ,σ²/N)

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

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15
Q

Central limit theorem

A

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

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16
Q

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

A

Unbias and efficiency

17
Q

Unbiasedness

A

If the estimator E(δ) is centred on δ

E (Xbar) = μ

18
Q

EFFICIEINCY

A

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

19
Q

Consistency

A

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

20
Q

variance formula

A

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

xbar is sample mean

21
Q

Practice proof for showing sample mean is unbiased.

+ key to remember

A

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

22
Q

Practice proof of variance of sample mean estimator.

And 2 tips needed to remember

A

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.

23
Q

Size of a test

A

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

24
Q

Power of a test

A

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