Here Y=a0+a1x+e and y=b0+b1x+b2x+u
si a1 be biased so y(a1x+e) =y(b1+b2+u)
Here there is unbiased but few actually are, suggests a new study. In the study, Mohsen Javdani and Ha-Joon Chang examine how ideology influences views held by 2,425 economists from 19 countries. They conduct an online experiment where participants were asked to evaluate statements on a range of topics including inequality, the role of government and the free market. Each statement was attributed randomly to a mainstream economist or a less-mainstream economist with a different ideology. In addition, a few statements did not have an attributed source.
While over 80% of the participants said that a statement should be evaluated for its content and not for its source, this did not translate into their evaluations. The authors find that participants were more likely to agree with a statement if it came from a mainstream source than from a non-mainstream or unattributed source.
(6)Suppose that we estimate the model: y = ap + a2 +e, when the true model...
a. Suppose we propose the model E(Y)-Ao + β when the true model is E(X) = A-+ βίζί + β2 If we use observations of Y at x = (-1, 0, 1), in oder to estimate A) and A of the proposed model find EBo and EB
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
2. Given the following model: Y, = B. +X;B, + Mi a. Suppose we estimate the model ignoring the constant term. Show that the resulting estimator (call it ß, ) is biased. b. Derive the variance
Question 1 (4 points] 1. [1 point] Suppose the regression model is logarithmic: log(Y) = B1 + B2 log(X) +u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 2. (1 point] Suppose the regression model is semi-logarithmic: log(Y) = Bi + B2X + u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 3. [1 point] Suppose the regression model has quadratic term: Y = Bi+B2X + B3 X2 +u. The...
3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2 and consider a problem of regressing y on two (qualitative) variables x\, xz. Data y (Income) x (Gender) X2 (Management Status) obs no. Female None 2 Male None 3 Female Yes 4 Male Yes Y4 To handle the qualitative variables x\, x2, we define dummy variables z1, 22 as Male for for 1, 1, T2= Yes Z1= Z2= -1 for for 1 1 =...
Suppose the true model is given by y = β0 + β1x1 + β2 x2 + u , if we estimate the following models: (I) y = β0 + β1x1 + β2 x2 + β3x3 + u (II) y = β0 + β1x1 + u what are the consequences?
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2 59 Can you estimate βο, βι, and β2? Why or why not?
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2...
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 + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (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 βί-1-- ie1 (2) Find E(%) in terms...