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Flashcards in Time series Deck (62)
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What are common sources of endogeneity

Omitted variables, Simultaneity, measurement error


What are omitted variables and what are they a source of?

When a statistical model leaves out one or more relevant variables. Omits an independent variable that is correlated with both the dependent variable and one or more of the independent variables. Source of endogeneity


What is simultaneity bias and what can it cause

Where the explanatory variable is jointly determined with the dependent variable (X causes Y, Y causes X). Source of endogeneity. Education determines wages but wages also determine future education


What is measurement error and what can it cause

Difference between a measured quantity and its true value. Source of endogeneity.


2 good examples of omitted variable bias in wage education

Education of individual’s parents,


Example of measurement error in wage education model

Not so much measurement but years does not take into account quality of education


what is a chi squared distribution mean and variance

mean is the degrees of freedom,
variance is the 2 x degrees of freedom


log-level what does β mean

100(β1) is the percentage change in y


log-log what is β

β is the percentage change


level-log what is β



what do you need for unbiased estimates

linear in parameters,
random sampling,
sample variation in explanatory variable,
zero conditional mean (E(u|x)=0)


what does unbiased mean

the sampling distribution of βhat is centred around β


what are the main assumptions for the main properties of OLS in matrix form

data generating process,
random sampling of n observations,
no perfect collinearity: matrix X of full (column) rank, rank k+1,
Zero conditional mean E(u|x1,...,xk)=0


what does --->p(above) and --->d(above) mean

--->p is convergence in probability
--->d is convergence in distribution


what is stationarity

stationary time series is a process whose probability distributions are stable over time


what is significant about the first-order autocovariances for the MA(1) model (yt=εt+αεt-1)

only first-oder autocovariance is nonzero


what is the strong exogeneity eassumption

zero conditional mean assumption E(ut|x)=0, imposes that the error at time t be uncorrelated with each explanatory variable in every time period


what can a model with a lagged dependent variable not satisfy

model with lagged dependent variable cannot satisfy strong exogeneity


what is weakly independent

yt and yt-j are 'almost independent' as j gets large


what is a stable AR(1) process

weakly dependent


what is serial correlation

when homoskedasticity doesn't hold


what happens to OLS in the presence of serial correlation

OLS remains consistent, but becomes inefficient and its standard errors need to be adjusted


what happens to the Gauss-Markov property under serial correlation

Gauss-Markov requires homoskedasticity and serially uncorrelated standard errors, OLS is n longer BLUE in presence of serial correlation


what's the difference between the test for serial correlation and the test for serial correlation without strong exogeneity

Do OLS regression of uthat on x1t,x2t,... and ut-1hat for all t as opposed to just uthat on ut-1hat


how do you adapt the test for serial correlation to tes for higher-order serial correlation (second order ut-2hat)

only need to add ut-2hat (,...ut-qhat) to the equation,
Null: H0:ρ1=ρ2=,...,ρq=0
Then do F test to test joint significance of ρ1 and ρ2 simultaneously


In a random walk yt=θyt-1+et what makes it nonstationary

whenever |θ|>1, process yt has variance that goes to infinity and is nonstationary


where does the term unit root come from

called unit root as comes from the fact that θ=1 in AR(1) so t-1 is the root,
strong memory


when dealing with a unit root how do you transform it

when dealing with a unit root, first differencing turns a unit root process into a weakly dependent process.
It is then integrated of order one or I(1). Also called difference stationary


what does difference stationary mean

when first differencing turns process (for ex a unit root) into a weakly dependent process


what is the order of integration

the number of times the variable has to be differenced to arrive at a weakly dependent process