ECONMET LEC PRELIMS REVIEW (OWN)

econometrics

use of mathematical methods in describing economic systems

cross-sectional

observes multiple entities at a single point in time

panel/longitudinal data

observes multiple entries over multiple time points

time series 

a single entity over multiple time points 

error term

omitted variables and measures error in dependent variable

least squares

the line best fit minimizes the sum of the squared deviations of the points on the graph from the points on the square line

pooled data

mix of cross sectional and time series data

panel data

follow a microeconomic unit over time

quantitative data

continuous data

qualitative data

categorical data

regressor

independent

regressand

dependent

y=b0+b1x+u

simple regression model

average value of the error term in the population is 0 

assumption of simple regression model

zero conditional mean

assuming expected value of residual is 0, covariance between residual and x variable is also 

Yi=B0+B1xi+ui

OLS

mean/expected value of x, variance, skewness, kurtosis

moment restrictions

beta coefficient of variable x/slope of x

B1

Positive effect in Y

Positive B1

Durbin Watson’s test

auto correlation test

SSE + SSR

SST

R2 Formula

SSE/SST or 1-SSR/SST

Goodness of Fit

R2

High R2/Fitted terms within trendline

x variable explains y very well

B1 near actual value

reliable

Straight line and constant slope

assumption of linearity

1+2xi

sample of linear eq

1B²xi 

Not a linear 

Ui=Yi-E(xi)

Stochastic Error formula

y=B1+B2xi

sample of regression function

B2xi

beta coefficient

y=B1+B2x+u

classical linear regression

e²i=(Yi-Y^i)²

ols regression function

made to ensure that OLS Estimates are BLUE 

CLR assumptions 

linear, unbiased, minimum variance

properties of ols

variance & standard errors

R²

coefficient of determination

square root of R²

correlation coefficient

measures the strength of the relationship between 2 variables

correlation coefficient

can explain the movement of y with respect to x variables

coefficient of determination

multiple linear regression

2 or more independent variables

In(Y) = B0 +B1IN(X)+u

double log function

In(Y)=B0+B1x+u

Semi-log/log lim function

v=B0+B1In(X)+u

vin log 

will increase as more variables are added to the model

R² Multiple regression

takes into account number of variables in the model, and may decrease 

Adjusted R²

Dummy variables/binary variables

takes on the value 0 or 1

Breusch-Pagan Test

doesnt observe the error but can estimate it with the residuals from the OLS regression and will detect any linear forms of heteroskedasticity 

White’s Test

allows for nonlinearities by using squares and cross products of all the x’s 

Ramsey Reset Test

No omitted non-linearity variable