Ask Question, Ask an Expert


Ask Microeconomics Expert

Suppose time-series data has been generated according to the following process:

yt =  α+ Φyt-1 + ut,      ut =  εt +   ρεt-1 ,

where εt is independent white noise. Our main interest is consistent estimation of Φ from realizations on yt.

1) Provide conditions for this process to be stationary.

2) From hereonout, assume the process is stationary. Will OLS generally provide you with consistent point estimates of Φ? Can you give conditions under which it will? Provide the asymptotic distribution of OLS under these assumptions.

3) ARMA processes are generally estimated by ML. Do you have enough information to set up the (marginal or conditional) likelihood function?

4) Show that

E[yt-j(yt - α - Φyt-1)] = 0; j ≥  2,


5) Use the moment conditions under problem 4 to derive a consistent GMM estimator of (α,Φ). Does it require knowledge of the distribution of  εt? Note that we discussed asymptotic properties of GMM estimators assuming a fixed amount of moments.

6) Given your answer to the previous problem, derive a lower bound on the variance of your estimator.

7) Suppose that you are uncertain about the model specification above. Moreover, you fear that ut might have the structure

ut =  εt + ρεt-1 + δt-2;

which is an MA(2) if δ ≠ 0. Can your estimation framework from above (problems 5 and 6) be used to test the null hypothesis that δ = 0? If yes, show how.

8) To convince yourself that your estimator is consistent, try it on simulated data (use Matlab or R, say). You can experiment with the number of moments to investigate the effect on the bias and the coverage of confidence intervals.

Microeconomics, Economics

  • Category:- Microeconomics
  • Reference No.:- M91932

Have any Question? 

Related Questions in Microeconomics

Economics assignment1 multiple product pricinganswer the

Economics Assignment 1. Multiple Product Pricing: Answer the following about the pricing of multiple products: a. Icarus Medical Supplies produces adhesives that are used to reassemble broken bones. Pindrop Medical Produ ...

Econ discussionwith everything discussed with this course

Econ discussion With everything discussed with this course, first watch How we can make the world a better place by 2030. Then, offer your considerations as to whether this could work or not. Within your response, provid ...

You are an economic consultant and encounter a firm with

You are an economic consultant and encounter a firm with the following data: Quantity of Labor Fixed Costs Variable Costs Total Costs Quantity Marginal Costs 5 $150 20 6 $150 28 7 $150 34 8 $150 38 The wage rate is $8 pe ...

Question 1consider the market for a course of antibiotics

Question 1. Consider the market for a course of antibiotics. Suppose the supply of antibiotics follows P = 5 + 2Qs and the demand follows P = 20 - 2Q D . Here, Q represents antibiotics, denominated in millions of units. ...

1 please prove that two indifferent curve cannot cross each

1. Please prove that two indifferent curve cannot cross each other. 2. Please solve the following maximization problem u = √x 1 + x 2 max√x 1 + x 2 , st, p 1 x 1 + p 2 x 2 ≤ m 3. a. When prices are (p 1 , p 2 ) = (1, 2) ...

Assignmentteamworkhow does effective teamwork look how is

Assignment Teamwork How does effective teamwork look? How is teamwork displayed in your life as it relates to your current role? Why is teamwork a necessity for organizations? Does this help or hurt an organization if te ...

Mcdonalds and the hindu culturein many ways mcdonalds

McDonald's and the Hindu Culture In many ways, McDonald's Corporation has written the book on global expansion. Every day, on average, somewhere around the world 4.2 new McDonald's restaurants are opened. By 2003, the co ...

Assignmentwe often have difficulty understanding how our

Assignment We often have difficulty understanding how our own customs and traditions could be viewed any way other than as right. In that regard, cultural relativism (viewing a custom from the other culture's perspective ...

Exam set 1 amp 2set-11 which of the following statements is

Exam SET 1 & 2 SET-1 1. Which of the following statements is true about a downward-sloping demand curve that is a straight line? The slope and the elasticity are the same at all points. The slope remains the same, but el ...

1 a explain in clear language the economic inefficiency

1. a) Explain in clear language the economic inefficiency associated with adverse selection. b) The ACA (aka Obamacare) included an insurance mandate, which forces everyone to purchase insurance or face a penalty. Under ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro