Econometrics Assignment

Instructions: Show and explain your work for all questions. Always state null and alternative hypotheses in any hypothesis test, include the appropriate test statistic and critical value, then indicate what your calculated test statistic relative to the critical value indicates.

Show and explain your work, don't just assert or provide only regression output. Explain the results from any regression output you include. Simple yes, no, or providing only number answers to these questions will not suffice (what calculations were made to arrive at numbers, why, and interpret results, do they make sense in terms of hypotheses, etc.). Unless otherwise specified, test hypotheses at the .05 level of significance. Be clear and concise, extraneous material will be counted against you (e.g., I will not choose between multiple answers you may provide). Cite any references you use, and programming that you use (e.g., SAS, STATA, R, etc.) and include the code.

Submit your work on Blackboard (.pdf or Word file, no macros) for all problems by end of day, Dec 23, 2016. Include your name in the file names, e.g., if I were submitting the file would be named PatrickE1final.

1. The data in file "E1 F16 Final Problem 1 data.xls" was generated according to the following process:

y_t = β x_t² + e_t
x_t = π z_t + v_t,

where

β = π = z = 1 for all observations and (e_t, v_t) are joint normal with zero means, unit

variances, and correlation 0.8. Now that you know the data generating process, your task is to determine the best estimator using the 200 generated data observations provided.

The primary objective here is to obtain unbiased (and/or consistent) and efficient estimates for β. Begin by estimating the model

y_t = β x_t² + e_t

using OLS and interpret the results. Is OLS valid for this data generating process? Why or why not? Test and explain.

Provide an alternative estimator and compare these results to your OLS results. Why is your alternative estimator appropriate for this data generating process? Provide a test and explain the results.

Be sure to provide and explain tests that address bias (and/or inconsistency) and efficiency in supporting your choice of an estimator.

2. After collecting the data in file "E1 f16 final q2.xlsx", a forecaster plans on initially estimating the following model

y = β₀ + _i=1∑⁸ β_i X_i + β₉ (X₅ * X₇) + e,

then dropping all of the X variables that are not significant at the 0.05 level, and re-estimating the resulting model to use in forecasting y. Follow this plan and interpret the results from each of the estimated models. Are there potential errors in the model? Assess the models in terms of bias and/or consistency, and efficiency of the estimates. Provide tests and explain the results.

Assess the models in terms of forecasting.

Is there a better alternative forecasting model? If so, why would this model be preferred to either of the above models. If not, explain why either or both of the above models are adequate.

Explain the role of nonsample information in specifying and estimating models in this context. How may nonsample information be useful in obtaining unbiased/consistent and efficient estimates? Explain in the context of the above model.

Attachment:- Data_Files.rar