Week 1

Question 1

Population

Answer 1

A large group, or repeated process, that we are studying.

Question 2

Sample space

Answer 2

Collection of all possible samples. Uncertainty about which sample is drawn. The probability function P(x

Question 3

Random variable

Answer 3

Describes a feature of the random sample. Formally, a rule that assigns a number to each possible sample.

Question 4

Variance

Answer 4

Measures the spread of the distribution and also how accurate the prediction is.

Question 5

Covariance

Answer 5

Measures how different variables move together - either in same direction, positive, or in opposite directions, negative. Or not correlated at all.

Question 6

Exprectation

Answer 6

The expected value of a random variable is always the average of it.

Question 7

Random sampling

Answer 7

A recipe for picking out points from the population at random and for recording their characteristics.

Question 8

Realized sample

Answer 8

Recorded characteristics of the sample, a dataset with numbers.

Question 9

Estimand, estimator, estimate

Answer 9

The estimand is the population feature that we try to infer using an estimator (rule) that gives us an estimate of the estimand.

Question 10

Method of moments

Answer 10

Strategy for constructing an estimator by replacing population quantities by sample analogues.

Question 11

Linear regression model (OLS-1):

Answer 11

Functional form. Assumption that the m (the regression curve) takes a functional form of a linear model with k regressors and excluded variables U. This means that it is linear in the coefficients, the betas, but can still have nonlinear variables in the x’s.

Question 12

Regression curve

Answer 12

Rule that describes how the regressors contribute to the outcome. It is pinned down by k+1 parameters (coefficients)

Question 13

Marginal effect

Answer 13

The causal effects that we want to compute. If we change on regressor by one (infinitesimal) unit and keep everything else constant (ceteris paribus), we get the marginal effect.

Question 14

Conditional expectation

Answer 14

A recipe that tells us how to construct, for each state of the world, a “best” prediction of a rv by using the info contained in other rv’s.

Question 15

Exogeneity assumption (OLS-2)

Answer 15

The regressors are not informative about the level of the U. The m gives the conditional expectation of the Y given the regressors. Cov(Xj, U)=0

Question 16

Observational data

Answer 16

Data collected by observing economic agents in real world. The observed regressors can themselves be the product of economic behaviour.

Question 17

Randomized controlled trial

Answer 17

At least partially artificial environment in which the econometrician assigns regressor values to the economic agents they are studying. This will play out the role that U can have on the outcome, for ex the mathematical ability (U) that affect study time (x1) is not affecting the outcome if you divide into treatment group and control group randomly.

Question 18

Observational equivalence

Answer 18

Two models with different sets of coefficients have the same regression function, i.e. transform regressors into outcomes in the same way. Cannot say which one is the best one…

Question 19

Full rank assumption (OLS-3):

Answer 19

We cannot find a model that is observationally equivalent to the true model, but is describes by a different set of coefficients.

Question 20

Variance decomposition

Answer 20

After a regression we can, at the sample level, decompose the total variation in outcomes into variation that is due to regressors (explained part) and in the estimated unobserved component (unexplained part).

Question 21

R^2

Answer 21

This measures how well our model predicts the outcome, in fact it is measuring how much of the variance that is described in the model. A high value is good because then our model is a good model for predicting Y.

Question 22

If the regressors have no predictive power of Y…

Answer 22

Then you should continue estimating Y with E(Y) instead of making use of the x’s in a conditional expectation. They are statistically independent we say.