Lecture 1 Flashcards
Define Econometrics
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
What is important to remember about economic data?
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)
What does Econometrics involve?
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)
Give an example of the use of econometrics in a practical, real life situation
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
State the econometric methodology in detail including the differences when investigating time-series, cross-sectional and panel data
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
What do we try to do using our econometric model and the data found from our sample?
Make an inference about the real world
Briefly state and describe the difference between the 2 types of statistics
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
How important is data?
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
In how many ways (that we look at in this module) can data be generated?
We look at 3 ways
What are the ways (that we look at in this module) can data be generated?
1) Experimental data
2) Quasi-experimental data
3) Observational data
Describe experimental data
- 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
Describe Quasi-experimental data
- 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
Describe observational data
- 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
What are exogenous and endogenous variables?
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
How many types of dataset are there?
3 types
State the types of dataset
1) Cross-section data
2) Time-series data
3) Panel data
What is cross-section data?
- 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
What is time-series data?
- 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
What is panel data?
- 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
What is the difference between micro
and macro data?
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
What is a stock and flow variable respectively and therefore the difference between the two?
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
How many main types of outcomes can you have?
2 main types
What are the main types of outcomes you can have?
1) Quantitative outcomes
2) Qualitative outcomes
What are quantitative outcomes?
Outcomes which can be expressed as numbers e.g. price, income or some transformation of them like real prices and income per capita etc
What are qualitative outcomes?
Outcomes which can be expressed in words rather than numbers e.g. whether a consumer did or did not make a purchase
What are the ways in which statistical inference can be carried out?
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)
Does correlation imply causation?
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)
If X is a discrete random variable with probability function f(X), what is the expected value defined as?
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)
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.
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
If X is a continuous variable then what is the expected value defined as?
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
What are the properties of the expected value?
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
Assume there are 2 random variables X1 and X2 with E(X1) = 25 and E(X2) = 30. Calculate E(5X1 + 2X2).
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
What is variance denoted as?
Variance is denoted as sigma squared
Define variance
The variance (sigma squared) is defined as the squared deviation from the population mean mu (weird u shape)
How would you write the variance in terms of its expected value?
variance (sigma squared) = E [(X - mu)^2] = E(X^2) - mu^2
What are the properties of the variance?
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
Define the standard deviation
Standard deviation is defined as the squared root of the variance: SD(X) = root of sigma^2 = sigma
If X and Y denote two random variables, what is the covariance between X and Y defined as?
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)
What is the correlation coefficient p defined as?
p (lowercase rho symbol) = Cov (X,Y) / square root of Var(X)Var(Y)
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?
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)
