Chat with AIExam 5: Sample Exam for Chapters 12-16
Briefly identify the following in words or equations as appropriate:
(a) Problems with ad hoc distributed lags
(b) Unconditional forecasting
(c) Moving-average process
(d) How to test for serial correlation in a dynamic model
(e) Difference-in-differences estimator
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Answered by Examlex AI Copilot(a) Problems with ad hoc distributed lags:
Ad hoc distributed lag models are used to estimate the effect of a variable over time. However, they have several problems:
- Specification Bias: Without a strong theoretical basis, the choice of lag length and form is arbitrary, which can lead to incorrect specifications.
- Multicollinearity: Lagged variables are often highly correlated with each other, which can make estimates of their coefficients imprecise and unstable.
- Omitted Variable Bias: If the lag structure does not adequately capture the true relationship, the model may omit relevant variables, leading to biased estimates.
(b) Unconditional forecasting:
Unconditional forecasting refers to making predictions about future values of a variable without conditioning on the current or past values of other variables. It is based on the assumption that the future values of the variable are determined by its own history and not by any external or contemporaneous influences.
(c) Moving-average process:
A moving-average (MA) process is a time series model where the current value of a series is defined as a linear combination of past error terms. An MA(q) process has the form:
X_t = μ + ε_t + θ_1ε_{t-1} + θ_2ε_{t-2} + ... + θ_qε_{t-q}
where μ is the mean of the series, ε_t is the error term at time t, and θ_1, ..., θ_q are the parameters of the model.
(d) How to test for serial correlation in a dynamic model:
To test for serial correlation (also known as autocorrelation) in a dynamic model, one can use the Durbin-Watson test or the Breusch-Godfrey test. The Durbin-Watson test is suitable for models with no lagged dependent variables, while the Breusch-Godfrey test is more general and can be used even when lagged dependent variables are present.
(e) Difference-in-differences estimator:
The difference-in-differences (DiD) estimator is a quasi-experimental technique used in econometrics to estimate causal effects. It compares the changes in outcomes over time between a group that is exposed to some treatment or intervention (the treatment group) and a group that is not (the control group). The estimator is calculated as follows:
(Difference in post-treatment outcome between treatment and control group) - (Difference in pre-treatment outcome between treatment and control group)
This method helps to control for unobserved factors that may be correlated with the treatment and the outcome, assuming that these factors do not change over time.
Suppose you've been hired by your school's admissions department to help them decide whether to change admissions procedures. You are given the files of all of the students in the last graduating class (including those students who didn't graduate) and told to build a model to explain why some admitted students graduate and others don't.
(a) Specify the functional form you would use in building such a model and carefully explain why that form is appropriate.
(b) Specify the independent variables you would include in the equation and briefly explain how they apply to the dependent variable in question.
(c) Carefully explain the meaning of the coefficient of your first independent variable.
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VerifiedThe appropriate functional form is the logit because of the problems with the linear probability model outlined in Section 13.1. The key to choosing independent variables is the type of variable suggested; some students will misunderstand the disaggregate nature of the variables required by such a study and will suggest variables that are constant for all observations in the dataset. Each coefficient tells the impact of a one-unit change in the independent variable in question (holding constant all the other independent variables in the equation) on the log of the odds that the person graduated. his or her
You have been hired to forecast GDP (Y) for the Caribbean island of Tabasco. Tabasco has domestic food (F) and shelter (S) industries, a tourist (T) industry, and an export (X) industry.
All tourists come from the United States, while the exports are split between Mexico and the
United States. Investment is virtually zero, and government expenditures (G) can be considered to be exogenously determined. Imports (I) are a function of GDP. Thus the structural equations for
a simultaneous model of the Tabascan economy would look something like:
Y = F + S + T + X + G - I
F = fF (Y, ?)
S = fS (Y, ?)
T = fT (USGNP, ?)
X = fX (USGNP, MEXICOGNP, ?)
I =fI (Y, ?)
G = exogenous
(a) Develop a theory for Tabasco's economy. Then choose which predetermined variables you would like to add to the simultaneous system and specify to which of the five stochastic structural equations (see question marks) you would like to add them. Explain your reasoning.
(b) Comment on the identification properties of each of the five stochastic equations in the system you outlined in your answer to part (a) above.
(c) How should the coefficients of the system be estimated?
(d) What technique would you use to forecast Tabasco's GNP? Why?
(35) VerifiedOK, OK, we know this will be hard to grade, since each answer will be different depending on
the exact variables and equations added, but this question tends to work well. The student will be forced to apply the identification, estimation, and forecasting techniques to a system of his or her own choosing in much the same way he or she will have to in his or her work later on.
The key to the questions on estimation and forecasting have to do with the size and importance of the feedback loops (as compared to exogenous factors in determining GDP). In this case, there is a good chance that the most accurate forecast of Tabasco's GDP would be based on a "simplified reduced-form" equation that included only USGNP and MEXICOGNP as explanatory variables.
Virtually all of Chapter 14 is spent discussing the violation of the assumption that the error term is independent of the explanatory variables.
(a) Under what circumstances might that assumption be violated?
(b) What would the violation of that assumption be likely to cause?
(c) What general technique is used to rid the equation of this problem? Specifically, how does
it work?
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