Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied when a) Zi is independent of (Yi, Xi, Wi)? b) Zi=Wi? c) Wi is1 for all i? d) Zi=Xi?
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Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied when
a) Zi is independent of (Yi, Xi, Wi)?
b) Zi=Wi?
c) Wi is1 for all i?
d) Zi=Xi?
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- 1.1 Which of the following is NOT a good reason for including a disturbance term in a regression equation?/ A. To allow for random influences on the dependent variable/ B. To allow for errors in the measurement of the dependent variable/ C. It captures omitted determinants of the dependent variable D. To allow for the non-zero mean of the dependent variable/ 1.2 Consider the equation Y = B1 + B2X2 + u. A null hypothesis of H0: B2 = 0 means that/ A. X2 has no effect on the expected value of Y / B. B2 has no effect on the expected value of Y/ C. X2 has no effect on the expected value of B2 / D. Y has no effect on the expected value of X2/ 1.3 The OLS residuals in the multiple regression model/ A. can be calculated by subtracting the fitted values from the actual values / B. are zero because the predicted values are another name for forecasted values / C. are typically the same as the population regression function errors / D. cannot be calculated because there…"In the regression model InY=b0+b1*InX+u, the coefficient b1 is interpreted as" O the intercept O A covariance O A regressor O An elasticity10. Residual analysis Consider a regression of y on several independent variables, and the resulting predicted values of the dependent variable. The residual for the ith observation Consider a data set for a large sample of professional basketball players. Each observation contains the salary, as well as various performance statistics such as points, rebounds, and assists for each player. Suppose a regression of salary on all performance statistics is run, and the residuals are obtained. The player with the lowest (most negative) resid represents which of the following? (Assume the regression reasonably predicts salaries in most cases.) The most fairly paid player relative to her on-court performance The most overpaid player relative to her on-court performance The highest-paid player, regardless of her on-court performance The most underpaid player relative to her on-court performance
- Discuss the FIVE (5) importance of adding error term in the regression model.1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearityConsider a linear causal model Ya+BX+yW+u, with cov(X, W) > 0. Suppose we do not observe the variable W and have to omit it from the regression, then O OLS is expected to be larger than 3 in large samples. BOLS is expected to be equal to 3 in large samples. OLS is expected to be smaller than 3 in large samples. Since we do not know whether X and u are correlated and the sign of y, there is not enough information to compare OLS and B.
- Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1The OLS estimators of the coefficients in multiple regression will have omitted variable bias: a. i only if an omitted determinant of b. if an omitted variable is correlated with at least one of the regressors, even though it is not a determinant of the dependent variable. C. only if the omitted variable is not normally distributed. d. if an omitted determinant of is a continuous variable. Y; i is correlated with at least one of the regressors. e. if the degree of freedom is less than 50.If we run a regression where y (bankruptcy) = f (factors potentially predicting bankruptcy), what is the dependent variable?
- 1. Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = 0 + 1educ + u, where u is the unobserved error. (a) What kinds of factors are contained in u? Are these likely to be correlated with level of education? (b) Will a simple regression analysis uncover the ceteris paribus eect of education on fertility? Explain.(a) Interpret the elasticity of cigarette consumption with respect to prices. (b) Does this regression model return the expected sign for this relationship? Explain. (c) Is the independent variable's coefficient statistically significant at a = 0.05? Explain. (d) As you have noticed, both the dependent and independent variables are defined in logs. Does this fact violate the linearity portion of CLRM Assumption I? Explain your answer. (e) A Shapiro-Wilk test on this model's residuals returns a p-value of 0.5329. Given this fact, is CLRM Assumption VII satisfied? Explain.Consider the regression model Y₁ = BX; +u; Where u; and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß = Show that ẞ is a linear function of Y₁, Y2,..., Yn. where Y and X are the sample means of Y; and X;, respectively. Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2,..., Xn) = 1 -B (X ₁ + X 2 + ... + Xn) Х answer these part correctly + ... + Y) +X₂+ ... + Xn) = B 2. E (B|×₁, ×2,..., Xn) = E | (X1, X2,..., Xn) BX; ☑ BX BY