Lecture 1

Question 1

Define Econometrics

Answer 1

Econometrics is the quantitative analysis (numbers) of actual economic phenomena (economic events)

It can also be defined as: the application of statistical methods to economic models

Question 2

What is important to remember about economic data?

Answer 2

Economics is a non-experimental science (difficult to establish cause and effect as a result as there are so many factors at play - unlike physics, chemistry etc where extraneous variables are closely controlled to establish cause and effect)

As a result, the data is described as being weak/noisy etc and … the empirical evidence provided by econometrics is frequently inconclusive in that it struggles to establish cause and effect (confirming that a certain factor/factors cause economic phenomena/events)

Question 3

What does Econometrics involve?

Answer 3

It may involve:
- developing statistical methods to estimate economic relationships
- testing economic theories
- evaluating economic policies
- forecasting future path of economic variables e.g. GDP, inflation etc (one of the most important applications of econometrics)

Question 4

Give an example of the use of econometrics in a practical, real life situation

Answer 4

A University needs to estimate how much enrolment will fall by a £100 increase in tuition fees per semester and … predict whether its tuition revenue will rise or fall

Question 5

State the econometric methodology in detail including the differences when investigating time-series, cross-sectional and panel data

Answer 5

1) Statement of theory or hypothesis (what you are investigating)
2) Specification of the mathematical model of the theory
3) Specification of the econometric model of the theory (normally same mathematical model but written with the inclusion of an error term or disturbance denoted by an epsilon)
4) Collect data (now the subscript, small letter(s) in front of each variable of the model, will vary depending on what type of data is used - note that the subscript is only put in front of the dependent, independent and extraneous variables (which is denoted by epsilon) and not any stand alone beta’s): time-series data will have subscript t for time, cross-sectional data will have subscript i for individual and panel data will have subscript it denoting both data for several individuals over time
5) Estimate the parameters of the econometric model (at this point you substitute values in for your beta(s) and denote your dependent variable (being measured typically left of equals sign alone) using its same symbol e.g. C but this time with a hat ^ on top of it which indicates that it is an estimation of the dependent variable
6) Conduct hypothesis testing (statistical test) to determine whether the data sufficiently supports the hypothesis/theory
7) Conduct forecasting or a prediction (I assume given that your hypothesis is statistically sound - so your hypothesis is true that’s when you can start using your model to make predictions and forecasts)
8) Use the model for control or policy purposes - basically just future use of model

Question 6

What do we try to do using our econometric model and the data found from our sample?

Answer 6

Make an inference about the real world

Question 7

Briefly state and describe the difference between the 2 types of statistics

Answer 7

1) Descriptive statistics
2) Inferential statistics

Descriptive statistics describe/summarise features from sample data whereas inferential statistics use the sample data to make predictions about the population

Question 8

How important is data?

Answer 8

Data is extremely important in economics - it is described as being the ‘new oil’ - once converted into information it can be extremely useful for several purposes e.g. in making informed investment and policy decisions

Question 9

In how many ways (that we look at in this module) can data be generated?

Answer 9

We look at 3 ways

Question 10

What are the ways (that we look at in this module) can data be generated?

Answer 10

1) Experimental data
2) Quasi-experimental data
3) Observational data

Question 11

Describe experimental data

Answer 11

• Involves control (receive no treatment - potentially using a placebo e.g. sugar tablets) and treatment/experimental groups - participants/subjects are randomly assigned to either the control or treatment group
• highly controlled laboratory conditions - typical of experiments in sciences like physics and chemistry (all variables and potential variables both exogenous/independent and endogenous/dependent are closely controlled so that only the independent variables have an effect on the dependent variable being measured/studied and no others)
• economics data may be collected experimentally but it can be difficult to show the affect of real world economic events and reactions in a lab - it is very difficult to predict what the effect of certain policies would be for example

Question 12

Describe Quasi-experimental data

Answer 12

• here the main difference is that subjects aren’t randomly assigned to either the control or treatment group but instead they are assigned based on some criteria
• like experimental data, they aim to establish cause and effect between independent (exogenous) and dependent (endogenous) variables

Question 13

Describe observational data

Answer 13

• this type of data is typical of social sciences like economics as it is often quite difficult to collect data in economics in a laboratory due to the immense number of factors at play and their unpredictable effect on the system
• here there is no control group as it is quite difficult to only observe yet somehow control which subjects receive treatment and which don’t
• there is also no assignment criteria here as there is no control group - all subjects that are observed are in the experimental/treatment group regardless of any criteria

Question 14

What are exogenous and endogenous variables?

Answer 14

Exogenous (external) variables are the independent variables (being manipulated to see the affect on the dependent/endogenous variables) of a model - their cause is external to the model and their role is to explain other (dependent/endogenous variables and the outcomes of a model)

Endogenous (internal) variables, as mentioned above, are the dependent variables of a model which are measured and the effect on which is considered the outcome of the model - the effect on the endogenous variable is caused by its relationship with the independent variables of the model and potentially, if any, the extraneous variables of a model

Question 15

How many types of dataset are there?

Answer 15

3 types

Question 16

State the types of dataset

Answer 16

1) Cross-section data
2) Time-series data
3) Panel data

Question 17

What is cross-section data?

Answer 17

• several sample units recorded in same, particular time period
• e.g. income by counties in California during 2006 or high school graduation rates by state in 2006

Question 18

What is time-series data?

Answer 18

• same sample unit over different discrete (e.g. daily, monthly, annual, decades etc) time periods
• e.g. annual price of wheat in U.K from 1880 to 2007

Question 19

What is panel data?

Answer 19

• several sample units/individuals (when tracking individuals micro-units probably a more fit description) tracked over time (so essentially combination of cross-section and time-series data)
• e.g. US DofE (department of education) has several (… cross sectional) on-going surveys in which the same students are tracked over time (… time-series) from when they were in the 8th grade to their mid-twenties
  The British Household Panel Study follows several households from the UK over time

Question 20

What is the difference between micro
and macro data?

Answer 20

The difference between the two is the level of aggregation (how clustered the data is):
- micro data is collected on individual economic decision making units e.g. individuals, household or firms
- macro data pools or aggregates (combines/brings together) the data from all these individual economic decision making units (individuals, households and firms) at the local, state or national level

Question 21

What is a stock and flow variable respectively and therefore the difference between the two?

Answer 21

Stock variable - measures an asset at a particular point in time e.g. quantity of crude oil held by BP on April 1st 2006
Flow variable - measures transactions occurring over a time interval e.g. consumption of gasoline during the last quarter of 2018

Question 22

How many main types of outcomes can you have?

Answer 22

2 main types

Question 23

What are the main types of outcomes you can have?

Answer 23

1) Quantitative outcomes
2) Qualitative outcomes

Question 24

What are quantitative outcomes?

Answer 24

Outcomes which can be expressed as numbers e.g. price, income or some transformation of them like real prices and income per capita etc

Question 25

What are qualitative outcomes?

Answer 25

Outcomes which can be expressed in words rather than numbers e.g. whether a consumer did or did not make a purchase

Question 26

What are the ways in which statistical inference can be carried out?

Answer 26

1) estimating economic parameters e.g. elasticities using econometric methods (parameters would be value of beta values in front of each independent variable)
2) predicting economic outcomes for next 10 years using present econometric data e.g. enrolment is universities in the next 10 years
3) testing economic hypotheses e.g. whether newspaper advertising is better than store displays to increase sales
(Steps 5, 6 and 7 of econometric methodology - on cards before)

Question 27

Does correlation imply causation?

Answer 27

No it does not

Economic theory provides and possesses the extra assumptions needed to make econometric model to be interpreted as causal (it is only when you negate or make other variables constant, can you pin point the effect of one independent variable on the dependent variable)

Question 28

If X is a discrete random variable with probability function f(X), what is the expected value defined as?

Answer 28

E(X) = sum of sign with k above it and j=1 below it then followed by Xj (j in subscript) f(Xj) (again j in subscript)
… it would be E(X) = sum of sign with k on top and j=1 underneath Xjf(Xj)

Question 29

Assuming that X is a discrete random variable with probability function f(X), BUT this time X = -1, 0, 2 and probabilities p(X) = 1/8, 1/2, 3/8. Now calculate the expected value.

Answer 29

Remember E(X) = sum of sign with k on top and j=1 underneath Xjf(Xj)
…
E(X) = (-11/8) + (01/2) + (2*3/8) = 5/8

Question 30

If X is a continuous variable then what is the expected value defined as?

Answer 30

E(X) = integral s swish sign with infinity as upper limit and negative infinity as lower limit followed by Xf(X) dX

NOTE infinity signs appear on right side of s swish at the top of the sign and bottom of the sign

Question 31

What are the properties of the expected value?

Answer 31

1) for any constant c: E(c) = c - in words this means that for any constant c the expected value of c is equal to c
2) for any constants a and b: E (aX + b) = aE(X) + b

Question 32

Assume there are 2 random variables X1 and X2 with E(X1) = 25 and E(X2) = 30. Calculate E(5X1 + 2X2).

Answer 32

In words: assume there are 2 random variables X1 and X2 with the expected value of X1 equal to 25 and the expected value of X2 equal to 30. Calculate the expected value of five X1 plus two X2.

E(5X1 + 2X2) = 5E(X1) + 2E(X2)
If E(X1) = 25 and E(X2) = 30 then 525 = 125 plus 230 = 60 … total expected value is equal to 185

Question 33

What is variance denoted as?

Answer 33

Variance is denoted as sigma squared

Question 34

Define variance

Answer 34

The variance (sigma squared) is defined as the squared deviation from the population mean mu (weird u shape)

Question 35

How would you write the variance in terms of its expected value?

Answer 35

variance (sigma squared) = E [(X - mu)^2] = E(X^2) - mu^2

Question 36

What are the properties of the variance?

Answer 36

1) Var(c) = 0 - means that the variance of any constant c is equal to 0
2) for any random variable X and constants a and b: Var(aX + b) = a^2Var(X) - because Var (b) = 0 from first property above

Question 37

Define the standard deviation

Answer 37

Standard deviation is defined as the squared root of the variance: SD(X) = root of sigma^2 = sigma

Question 38

If X and Y denote two random variables, what is the covariance between X and Y defined as?

Answer 38

Cov (X,Y) = E[(X - E(X))(Y - E(Y))]
= 2 sum of signs, first one with lowercase x underneath and the second with lowercase y underneath and then: (x - E(X))(y - E(Y))f(x,y)

Question 39

What is the correlation coefficient p defined as?

Answer 39

p (lowercase rho symbol) = Cov (X,Y) / square root of Var(X)Var(Y)

Question 40

Variance of a linear function of random variables:

Consider the following function: Z = aX + bY

What is the variance of Z in expected value form?

Answer 40

Var (Z) = Var (aX + bY) = a^2Var(X) + b^2Var(Y) + 2abCov(X,Y)

If X and Y and not correlated, then Cov (X,Y) = 0 which … implies that:
Var (aX + bY) = a^2Var(X) + b^2Var(Y)