Question 1

Which of the following best describes the distributed lag regression model used to estimate dynamic causal effects in time series data?

Accepted Answer

A model where Y is regressed on current and past values of X, capturing the effect of X over multiple periods.

Question 2

In the context of the orange juice example, what is the immediate effect of an additional freezing degree day on the price of orange juice concentrate, according to Equation (16.2)?

Accepted Answer

0.47% increase in price

Question 3

Which assumption is necessary for OLS estimation of dynamic causal effects in the distributed lag model to be consistent?

Accepted Answer

Exogeneity: $$E(u_t | X_t, X_{t-1}, X_{t-2}, ... ) = 0$$

Question 4

Suppose you estimate a distributed lag regression with autocorrelated errors. Why are HAC (heteroskedasticity- and autocorrelation-consistent) standard errors necessary?

Accepted Answer

Because HAC standard errors provide consistent estimates of the variance when errors are serially correlated or heteroskedastic.

Question 5

What is the formula for the h-period cumulative dynamic multiplier in a distributed lag model?

Accepted Answer

$$\$$beta_1$$ + \$$beta_2$$ + \cdots + \beta_{h+1}$$

Question 6

In the distributed lag model $$Y_t = \$$beta_0$$ + \$$beta_1$$ X_t + \$$beta_2$$ X_{t-1} + \cdots + \beta_{r+1} X_{t-r} + u_t$$, what does the coefficient $$\$$beta_2$$ represent?

Accepted Answer

The effect of a unit change in $$X_{t-1} on$$ $$Y_t$$, or equivalently, the effect of a unit change in $$X_t on$$ $$Y_{t+1}.$$

Question 7

A researcher wants to estimate the effect of U.S. income on Australian exports using a distributed lag model. Why is U.S. income plausibly exogenous in this context?

Accepted Answer

Because the Australian economy is much smaller than the U.S. economy, so feedback effects are negligible.

Question 8

Which of the following is NOT a distributed lag model assumption as summarized in Key Concept 16.2?

Accepted Answer

There is perfect multicollinearity among regressors.

Question 9

If the error term in a distributed lag regression is serially correlated, what is the effect on OLS coefficient estimates and their standard errors?

Accepted Answer

OLS coefficient estimates remain consistent, but standard errors are inconsistent unless HAC corrections are used.

Question 10

In the orange juice example, why is the weather (number of freezing degree days) considered exogenous but not strictly exogenous?

Accepted Answer

Because traders use forecasts of future weather, making the error term correlated with future values of FDD.

Question 11

Suppose you estimate a distributed lag regression of orange juice price changes on freezing degree days and find that the cumulative dynamic multiplier after 6 months is 0.90%. What does this value represent?

Accepted Answer

The total effect of a unit increase in freezing degree days on orange juice prices over the first 6 months.

Question 12

Which formula is used to determine the truncation parameter m for Newey–West HAC standard errors?

Accepted Answer

$$m = 0.75 T$$^{1/3}$$

Question 13

Why are ADL and GLS estimation methods not appropriate for estimating dynamic causal effects in the orange juice example?

Accepted Answer

Because the weather is exogenous but not strictly exogenous, so the error term may be correlated with future values of FDD.

Question 14

In the context of time series regression, what is meant by 'stationarity' as an assumption for the distributed lag model?

Accepted Answer

The distribution of the variables does not change over time, and their joint distribution is stable.

Question 15

A QLR (Quandt likelihood ratio) test is used in time series regression to:

Accepted Answer

Test for the stability of regression coefficients over time, indicating possible structural breaks.

Question 16

Which of the following statements about the relationship between forecasting and estimating dynamic causal effects is correct?

Accepted Answer

Forecasting uses predictors that may be correlated with future outcomes, but estimating dynamic causal effects requires exogeneity to interpret coefficients causally.

Question 17

In the ADL model $$Y_t = \$$alpha_0$$ + \$$phi_1$$ Y_{t-1} + \$$delta_0$$ X_t + \$$delta_1$$ X_{t-1} + \$$delta_2$$ X_{t-2} + 	ilde{u}_t$$, what is the main advantage of using OLS to estimate this model when X is strictly exogenous?

Accepted Answer

The error term $$	ilde{u}_t is $$serially uncorrelated, so usual OLS standard errors are valid.

Question 18

If you observe that the cumulative dynamic multiplier for a freeze in Florida is much larger and more persistent in the 1950s than in the 1990s, what is a plausible explanation based on the study materials?

Accepted Answer

Orange juice prices became less sensitive to freezes because orange groves migrated south, reducing exposure to frost.

Question 19

Which of the following is a correct interpretation of strict exogeneity in time series regression?

Accepted Answer

The error term has mean zero given past, present, and future values of X: $$E(u_t | ..., X_{t+2}, X_{t+1}, X_t, X_{t-1}, ...) = 0$$

Estimation of Dynamic Causal Effects in Time Series Regression

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