Econometrics 7: ARDL and nonstationarity Flashcards
What is an ARDL model?
An autoregressive distributed lag (ARDL) model of y_t is an autoregressive model that also depends on lags of a different series x_t.
Can we estimate a model such as yt = μ + αy_{t-1} + βxt + ε with OLS if ε is temporally dependent?
No, as mean independence will fail.
We can instead use previous lags of y_t as instruments for y_{t-1}, or we could estimate a longer model that removes the endogeneity.
Under what conditions is an ARDL model stable?
In general, we can write an ARDL model as B(L)y_t=α+C(L)x_t+u_t. If B(L) is invertible - that is, the roots of B lie outside the unit circle - we can write y_t in distributed-lag form and it is stable.
What is the contemporaneous multiplier?
The contemporaneous multiplier measures the immediate impact of a change in xt on yt.
What is the total multiplier?
The total multiplier measures the total cumulated effect of changes in x_t on y_t.
What is the mean lag?
The mean lag is the weighted mean of all multipliers.
What is median lag?
The median lag is the number of periods it takes for 50% of the total effect to accumulate.
What is the Error Correction Representation of an ARDL model?
The ECM writes the model only in terms of the first differences of the series, and one term in levels.
Why write models in ECM format?
If the above ECM exists, the variables are cointegrated and α is a consistent estimator of the order of cointegration.
What order of integration are random walks?
Ι(1)
What is the asymptotic distribution of Τ(p̂-p) if ρ =1?
The Dickey-Fuller distribution.
What is a Dickey-Fuller test?
The Dickey-Fuller test is a test for a unit root. In the simplest case, we regress
∆yt ~ θy_t + u with H0: θ = 0 against θ ≠ 0. The null hypothesis corresponds to a unit root.
What is an augmented Dickey-Fuller test? Why would we use it instead of a regular DF test?
The augmented Dickey-Fuller test includes lags of the dependent variable in the initial regression. If the u_t are autocorrelated, the regular DF test will not have the correct standard errors.
What is the KPSS test?
The KPSS test instead tests a null of stationarity against the alternative of a unit root. We estimate a stationary model (under the null) to generate residuals and an estimate of the long-run variance. Then, the KPSS statistic has a well-defined distribution under the null, and divergence under the alternative.
If the true model includes structural breaks, how are the DF and KPSS tests affected?
Both tests are biased towards the nonrejection of a unit root in the presence of structural breaks; that is, stationary models with breaks can be misclassified as nonstationary models with unit roots. Lee, Huang and Shin generalise some of these tests to be robust to this problem.
