PLCY 460 Midtern

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use command

load the stata data file

summarize command

summarize X1 X2 and Y

drop command

delete a variable

regress command

makes a regression

independent variable

variable that possibly influences the value of the dependent variable, X

dependent variable

the outcome of interest dependent on the independent variable, Y

slope coefficient

coefficient that reflects how much the dependent variable increases when the independent variable increases by one, B1

constant/intercept

the point at which a regression line crosses the Y-axis, B0

error term

term associated with unmeasured factors in a regression model, E (epsilon)

i

the observation number

population regression equation

Yi = B0 + B1Xi + Ei

endogenous

when changes in the independent variable are related to factors in the error term (outside factors)

exogenous

when changes in the independent variable are NOT related to factors in the error term

why exogenous > endogenous?

you want to focus on exogenous variables instead of endogenous variables to make reasonable inferences

correlation

measures the extent to which two variables are linearly related to each other

positive correlation

high values of one variable are associated with high values of the other, normally upward trends

negative correlation

high values of one variable are associated with low values of the other, normally downward trends

two challenges of econometrics

randomness and endogeneity

randomization

the process where the value of the independent variable is determined by a rando process, like chance, making the IV uncorrelated with everything

randomized controlled trial

experiment where the treatment of interest is randomized; good because they create exogeneity

treatment group

group that receives treatment of interest

control group

group that does not receive treatment of interest

internal validity

when research findings are not biased

external validity

when research findings can be applied outside of the context in which the experiment was conducted

standard deviation

measured how widely dispersed the values of the observation are

replication

research that can be duplicated based on the information provided at the time of publication using replication files

how to open a Do file

click on window, do file editor, new do-file editor, safe as “assignment.do”

how to load Stata data files

file, open, select file, save command in syntax file "C

tabulate command

produces a frequency table when prompted, must include variable name after

list command

lists out observations, must include variable name after

equal to command

==

not equal to command

!=

if command

limits the data used in analyses

scatter x y command

plotting scatterplot of two variables

fitted value

value of Y predicted by the estimated equation, Yi hat = B0 hat + B1 hat Xi

what do hats mean in equations

hats are estimates

regression line

fitted line from regression

residual

distance between fitted value and actual observed value, E hat = Yi – B0 hat – B1 hat Xi

OLS estimation strategy

minimizing the sum of the squared distances of each data point from the regression line, using calculus to find the solution

OLS formula

∑(i=1)^N▒〖ϵhat= 〗 ∑(i=1)^N▒〖(Yi-B0 hat=B1hat Xi)^2〗

Sampling randomness

variations in estimates seen in a subset of an entire population

Modeled randomness

variation that exits even when observing an entire population

central limit theorem

the average or any random variable follows a normal distribution; histogram should look like a normal distribution

variance

a measure of how much a random variable varied

standard error

the square root of variance

variance of the regression

the variance of the regression measures how well the model explains variation in the dependent variable

homoscedastic

when a random variable has the same variance for all observations

heteroscedastic

when some observations are on average closer to the predicted value than others

goodness of fit

how well a model fits the data, r^2

standard error of regression/goodness of fit

a measure of goodness of fit as the square root of the variance of the regression; σ hat

outliers

observations that are extremely different from the rest of the sample

sample size and outliers

when sample sizes are small, a single outlier can exert considerable influence on OLS coefficient estimates

hypothesis testing

process assessing whether the observed data is or is not consistent with a claim of interest

null hypothesis

a hypothesis of no effect; H0 = B1 = 0

alternative hypothesis

the outcome that is accepted if null hypothesis is rejected

reject null hypothesis

there is sufficient evidence that says that the null hypothesis is false, and the alternative hypothesis is true

fail to reject null hypothesis

there is not enough evidence to prove the null hypothesis is false

type 1 error

rejecting a null hypothesis that is really true

type 2 error

failing to reject a null hypothesis that is actually false

significance level

probability of committing a type 1 error; common is α=0.05

trade off between type 1 and 2 errors

lowering the significance level decreases the probability of making a type 1 error while increasing the probability of making a type 2 error

steps to do a hypothesis test

choose one-sided or two-sided alternative hypothesis; set a significance level α; find a critical value based on the t distribution; use OLS to estimate parameters

confidence interval

range of true values that are most consistent with the observed coefficient estimate

stata commands for hypothesis test

1. display invttail (number of observations – number of parameters, significance level(/2 if two-tailed)) 2. display invnormal (number of observations – number of parameters, significance level(/2 if two-tailed)) 3. Display2*ttail(degrees of freedom, observed t statistics) 4. set obs (possible values) 5. graph twoway

multivariate OLS

OLS with multiple independent variables

multivariate OLS and endogeneity

fights endogeneity by pulling variables from the error term into the estimated equation

ceteris paribus

all else being equal

auxiliary regression

a regression that is not directly the one of interest but yields information helpful in analyzing the equation we really care about

omitted variable bias

bias that results from leaving out a variable that affects the dependent variable and is correlated with the independent variable

measurement error

when a variable is measured inaccurately; has greater effect on the independent variable

attenuation bias

consequence of the omission of the measurement error from the estimated model; grows larger with larger amount of measurement error

multicollinearity

when there are strong linear relationships between independent variables

factors that influence the variance of multivariate estimates

model fit, sample size, variation, multicollinearity

standardized coefficients

the coefficient of an independent variable that has been standardized

standardizing variable formula

〖Variable〗^Standardized=(Variable- (Variable) ̅)/(sd(Variable))

difference of means test

comparing the mean of Y for one group against the mean of Y for another group

dummy variable

either 0 or 1

categorical variables

have two or more categories with no intrinsic ordering

ordinal variables

express rank but not necessarily relative size