econometrie

causality

specific action leads to specific outcome

cross sectional data

data collected across sample units in a particular time period

time series data

data from a single entity that chnages over time

pooled cross sections

mix of cross section and time series data

panel data

data that combines cross-sectional and time series data, tracking multiple entities over time.

balanced panel

A type of panel data where each entity is observed the same number of times over the same time periods.

outcomes

potential results

probability

proportion of time that outcome occurs in the long run

sample space

set of all outcomes

probability distribution

list of all different outcomes and their probability

cumulative probability distribution

probability that a random variable is less than or equal to a particular value

bernoulli random variable

binary variable

probability density distribution

probability that the random variable falls between 2 particular points

variance

measures spread of a probability distribution

standardization

random variable w mean 0 &variance 1

law of iterated expectations

multivariate normal distribution

joint notmal distribution

marginal distribution

joint probability distribution

bivariate normal distribution

2 random variables are normally distributed

random sampling

selecting sample randomly from population

identically distributed

all of the variables have the same marginal distribution

independently sampled

sample is made randomly

IID

independently and identically distributeed

the law of large numbers

as the size of a sample increases, sample mean will approach the population mean (if IID, large outliers are unlikely)

central limit theorem

the distribution of the sample mean will be well approximated by a normal distribution when n is large

estimators

guesses for the real thing

p-value

the porbability of drawing a statistic adverse to null hypothesis, assuming the hypothesis is correct

type I error

reject true H0

type II error

accept false H0

OLS estimators

chooses the regression coefficients so the estimated regression line is as close as possible to ht eobserved data

R²

the ratio of the sample variance of Y^to the one of Y

ESS

the sum of suared derivations of the predicted value from its average

TSS

the sum of squared derivations of Yi from its average

SER

an estimator of the standard derivation of the regression ui

in sample prediction

the observation for which ther prediction was made is also used in teg regression coefficients

out of sample prediction

prediction for observations not in the estimation sample

Least squares assumptions

mathematical assumptions under which OLS estimates the causal effects

ommited variable bias

bias in the OLS estimator that arises when the regressor is correlated with an omitted variable

2 conditions for omitted variable bias

• X is correlated with the omitted variable

• the omitted variable is a determinant of the dependent variable Y

OLS regression line

straight line constructed using OLS

perfect multicollinearity

if one of the regressors is a perfect linear function of the other regressors

imperfect multicollinearity

2(+) regressors are highly correlated

solutions for multicollinearity

• obtain more information

• introduce nonsample information

• Principal Component Analysis

dummy variable trap

when dummy variables are perfectly collinear, typically from including all categories, leading to multicollinearity in regression

control variable

not the interest of the study, included to not suffer from omitted variable bias

joint hypotheses

imposes two or more restrictions on the general coefficients

F statistic

used to test a join thypothesis about regresison coefficients

restricted regression

H0 is forced to be true

unrestricted regression

alternative hypothesis is allowed to be true

base specification

a core of base set regressors, contains variables of interest

alternative specification

set of control regressors enz

Nonlinear Least Squares

nonlinear functions cannot be estimated by OLS, but can be by nonlinear least squares (consistent, normally distributed in large samples)

Chow test

checks if two groups have different regression lines by testing if their coefficients are the same.

internal validity

statistical inferences about causal effects

external validity

if regression findings can be generalized to population

when are studies internally valid

if the estimated regression coefficients are unbiased & concistent

solution omitted variable bias

• include the variable

• include control variable if they lead to

buest guess model

• predicts outcomes using the most likely values based on available data, often using the mean or most common value

• the buest guess variable us uncorrelated with the error term

what happens w intentional miserporting

the coefficient will be biased

sample selection bias

when certain individuals or groups have a higher chance of being included in the sample due to factors related to the outcome of interest

simultaneous causality

when X and Y are influencing eachother

sources of inconsistency of OLS errors

• improperly handled heteroscadisticy

• correlation of error term across observations (autocorrelations)

solution heteroskadisticity

robust SE

3 requirements of reliable prediction

• data used to estimate prediction en observation for which prediction is to be made are drawn from same distribution (LSA 1)

• list of predictors aim to estimate causal effects

• many predictors —> prove more accurate out of sample

before and after panel data comparisons

if things like cultural impact remain the same, you can see influence of other variable, doesn’t apply when T>2

entity fixed effects regression

method for controlling omitted variables in panel data when the omitted variables vary across entitites but don’t change over time

time fixed regression

fixed regression for time variables

what is the expected value of LPM

Y=1

coefficient in probit model B1

the change in z score associated with 1 unit change in X

nonlinear least squares

OLS but for probit & logit estimators

likelihood function

joint probability function of the data, treated as a function of unknown coefficients

maximum likelihood estimator

consists of the values of the coefficients that maximize the likelihood function

McFadden-R²

goodness-of-fit measure for probit and logit

marginal effects of changes in variables

to interpret the coefficients of probit and logot

odds ratios

represent the probability of a success compared with the probability of a failure in logit model