Show that ๐๐ and ๐ข๐s are correlated and that the OLS estimator of ๐ฝ1 is inconsistent. How would you estimate ๐ฝ0,๐ฝ1 and ๐พ0?
1.Consider a product market with a supply function ๐๐๐๐๐ ๐ =๐ฝ๐ฝ0+๐ฝ๐ฝ1๐๐๐๐+๐ข๐ข๐๐ ๐ ๐ , a demand function ๐๐๐๐๐๐=๐พ๐พ0+๐ข๐ข๐๐๐๐, and a market equilibrium condition ๐๐๐๐๐ ๐ =๐๐๐๐๐๐, where ๐ข๐ข๐๐ ๐ ๐ and ๐ข๐ข๐๐๐๐ are mutually independent i.i.d. random variables, both with a mean of zero.
ย (i) Show that ๐๐๐๐ and ๐ข๐ข๐๐ ๐ ๐ are correlated and that the OLS estimator of ๐ฝ๐ฝ1 is inconsistent. (ii ) How would you estimateย ๐ฝ๐ฝ0,๐ฝ๐ฝ1 and ๐พ๐พ0.ย
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Show that ๐๐ and ๐ข๐s are correlated and that the OLS estimator of ๐ฝ1 is inconsistent. How would you estimate ๐ฝ0,๐ฝ1 and ๐พ0?
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we ca...
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + ฮฒฮฏฯ + u and we estimate an OLS regression model through the origin: Y-ฮฒยกXHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the ฮฒฮฏ-1-- ie1 (2) Find E(%) in terms...
Q1 a) Explain what it means that the ordinary least squares regression estimator is a linear...
Q1 a) Explain what it means that the ordinary least squares regression estimator is a linear estimator, paying specific attention to how it implies independent variables interact with each other. b) Give two examples of models where the parameters of interest cannot be directly estimated using OLS regression because of nonlinear relationships between them. c) What is the minimum set of conditions necessary for the OLS estimator to be the most efficient unbiased estimator (BLUE) of a parameter? List each...
Please provide your answer with a detailed description on how you came to that answer please!...
Please provide your answer with a detailed description on how you
came to that answer please!
ECN 702 Econometrics II HW2 Due: Jan 29 1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the x term as in Assume cov (X,, U,)s 0, E [Xn]-O and E [x?J-1. Is hisher estimate consistent for Anf not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where...
can you help with these questions and briefly explain how you got to the answer. it...
can you help with these questions and briefly explain
how you got to the answer. it would be a big help thank for your
time.
Question 1 Suppose that the conditional variance is var(WXi) = (x), where i is a constant and h is a known function. The WLS estimator: O A. is the estimator obtained by first dividing the dependent variable and regressor by h and then regressing this modified dependent variable on the modified regressor using OLS. O...
I. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
I. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) = 0, E [Xa] = 0 and E [x7-1. Is his/her estimate consistent for ฮฒ? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E (uiX]-0. It was discovered that we observe X, with a measurement error w instead of the real value...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for ฮฒ? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Problem 3 Consider the linear MMSE estimator to the case where our estimation of a random variable Y is based on ob...
Problem 3 Consider the linear MMSE estimator to the case where our estimation of a random variable Y is based on observations of multiple random variables, say XXX. Then, our linear MMSE estimator can be e written in the following fom: (a) Show that the optimal values of aa,a.a for the linear LMSE estimator is given as where E(X, a, Cxx is an covariance matrix of X,,X,...Xv and cxy is a cross-correlation vector, which is defined as E(x,r EtXyY (b)...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population model );-po +ax, + ฮฒ2W, + u, a. What does it imply about the population that u, has a zero conditional mean? b. Let u be correlated with W, but not with X,. What can we say about the estimate d, in the case where Wi is included and when it is not included? c. What are the assumptions made for OLS estimiation? What...
Show all working clearly. Thank you. 1. In this question, X is a continuous random variable...
Show all working clearly. Thank you.
1. In this question, X is a continuous random variable with density function (x)a otherwise where ? is an unknown parameter which is strictly positive. You wish to estimate ? using observations X1 , . โฆx" of an independent random sample XIโฆยทX" from X Write down the likelihood function L(a), simplifying your answer as much as possi- ble 2 marks] i) Show that the derivative of the log likelihood function (a) is 4 marks]...
#2 can you please go through the steps of how you got this Consider the simple...
#2
can you please go through the steps of how you got this
Consider the simple linear regression model yi-Xiรl + ฮฒ0 + Ei, where the errors โฌ1, โฌn are i.i.d. random variables with E[c]-0, var(G) ฯ2, i 1, , n. Solve either one of the questions below. 1. Let h be the least squares estimator for ฮฒ1- Show that Bi is the best linear unbiased estimator for ฮฒ1. (Note: you can read the proof in wikipedia, but you cannot...
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + ฮฒฮฏฯ + u and we estimate an OLS regression model through the origin: Y-ฮฒยกXHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the ฮฒฮฏ-1-- ie1 (2) Find E(%) in terms...
Please provide your answer with a detailed description on how you
came to that answer please!
ECN 702 Econometrics II HW2 Due: Jan 29 1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the x term as in Assume cov (X,, U,)s 0, E [Xn]-O and E [x?J-1. Is hisher estimate consistent for Anf not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where...
can you help with these questions and briefly explain
how you got to the answer. it would be a big help thank for your
time.
Question 1 Suppose that the conditional variance is var(WXi) = (x), where i is a constant and h is a known function. The WLS estimator: O A. is the estimator obtained by first dividing the dependent variable and regressor by h and then regressing this modified dependent variable on the modified regressor using OLS. O...
I. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) = 0, E [Xa] = 0 and E [x7-1. Is his/her estimate consistent for ฮฒ? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E (uiX]-0. It was discovered that we observe X, with a measurement error w instead of the real value...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for ฮฒ? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Problem 3 Consider the linear MMSE estimator to the case where our estimation of a random variable Y is based on observations of multiple random variables, say XXX. Then, our linear MMSE estimator can be e written in the following fom: (a) Show that the optimal values of aa,a.a for the linear LMSE estimator is given as where E(X, a, Cxx is an covariance matrix of X,,X,...Xv and cxy is a cross-correlation vector, which is defined as E(x,r EtXyY (b)...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population model );-po +ax, + ฮฒ2W, + u, a. What does it imply about the population that u, has a zero conditional mean? b. Let u be correlated with W, but not with X,. What can we say about the estimate d, in the case where Wi is included and when it is not included? c. What are the assumptions made for OLS estimiation? What...
Show all working clearly. Thank you.
1. In this question, X is a continuous random variable with density function (x)a otherwise where ? is an unknown parameter which is strictly positive. You wish to estimate ? using observations X1 , . โฆx" of an independent random sample XIโฆยทX" from X Write down the likelihood function L(a), simplifying your answer as much as possi- ble 2 marks] i) Show that the derivative of the log likelihood function (a) is 4 marks]...
#2
can you please go through the steps of how you got this
Consider the simple linear regression model yi-Xiรl + ฮฒ0 + Ei, where the errors โฌ1, โฌn are i.i.d. random variables with E[c]-0, var(G) ฯ2, i 1, , n. Solve either one of the questions below. 1. Let h be the least squares estimator for ฮฒ1- Show that Bi is the best linear unbiased estimator for ฮฒ1. (Note: you can read the proof in wikipedia, but you cannot...
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