Consider the following unobserved effects model: Yit =B₁xit1 +...+ ßkitk + ai + Uit You plan on using fixed effects to estimate the model. Suppose you have a panel data set consisting of 10 individuals over 6 years. However, you are missing the last 3 years of data for the third, ż = 3, individual in your data set. Your panel data set has total observations. Suppose the reason individual i is missing data for certain time periods (called attrition) is correlated with the idiosyncratic error, uit. Recall that a; is assumed to be uncorrelated with the idiosyncratic error, uit. This correlation cause the fixed effects estimators to be biased.

Consider the following unobserved effects model: Yit =B₁xit1 +...+ ßkitk + ai + Uit You plan on using fixed effects to estimate the model. Suppose you have a panel data set consisting of 10 individuals over 6 years. However, you are missing the last 3 years of data for the third, ż = 3, individual in your data set. Your panel data set has total observations. Suppose the reason individual i is missing data for certain time periods (called attrition) is correlated with the idiosyncratic error, uit. Recall that a; is assumed to be uncorrelated with the idiosyncratic error, uit. This correlation cause the fixed effects estimators to be biased.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4A: Problems In Applying The Linear Regression Model

Section: Chapter Questions

Problem 5E

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Consider the following unobserved effects model: Yit =B₁ it1 + ... +ßkxitk + ai + Uit You plan on using fixed effects to estimate the model. Suppose you have a panel data set consisting of 10 individuals over 6 years. However, you are missing the last 3 years of data for the third, ż = 3, individual in your data set. Your panel data set has total observations. Suppose the reason individual i is missing data for certain time periods (called attrition) is correlated with the idiosyncratic error, uit. Recall that a; is assumed to be uncorrelated with the idiosyncratic error, Uit. This correlation cause the fixed effects estimators to be biased.
Consider the binary variable version of the fixed effects model with an additional regressor, D1; that is, let Yit = β0 + β1Xit + γ1D1i + γ2D2i +...+ γnDni + ui.a) Suppose that n = 3. Show that the binary regressors and the “constant” regressor areperfectly multicollinear; that is, express one of the variables D1i , D2i, D3i, and X0it as aperfect linear function of the others, where X0it = 1 for all i,t.b) Show the result in (a) for general n.c) What will happen if you try to estimate the coefficients of the regression by OLS?
When estimating the equation: i Acrimerate =B+B Aunemployment + Au, i 0 The estimate of B, is only causal if there is no correlation between Acrimerate; 1 True False and Au; i
A justification for job training programs is that they improve worker productivity. Suppose that you are asked to evaluate whethe r more job training makes workers more productive. However, rather than having data on individual workers, you have access to data on manufacturing firms in Ohio. In particular, for each firm, you have information on hours of job training per worker (training) and number of nondefective items produced per worker hour (output).(iv) If you find a positive correlation between output and training, would you have convincingly established that job training makes workers more productive? Explain.
et R2unrestricted and R2restricted be 0.54 and 0.30 respectively. The difference between the unrestricted and the restricted model is that you have imposed two restrictions. The number of regressors in the unrestricted model is 5. There are 500 observations. The F-statistic (under the assumption of homoskedasticity) in this case is 1. 4.61 2. 8.01 3. 98.5 4. 128.9
Fixed effects model with three time periods Consider the following general fixed effects model for use with a panel data set with three time periods (T = 3): yir = 51 +82 d2: +63 d31 + ẞ1x11 + ... + ẞkxisk + Vit where, for t=1, 2, 3, and time period 1 is the base year: yir = value of dependent variable y for i, in year t, in pounds d2, 1 in the second time period (t = 2), and 0 otherwise d3, =1 in the third time period (t = 3), and 0 otherwise Xirl,..., Xink value of explanatory variables for individual i at time f Vir = composite error consisting of the unobserved, time-constant effect (a) and the idiosyncratic error (uir) If there are 106 cross-sectional units in your balanced panel data set, then the total number of observations you have in your data set is For the first time period (1), the intercept is Which of the following would cause pooled OLS estimation of the model to yield biased and consistent estimators? Check all that apply. Measurement error in any explanatory variable…
Comment on why there exists a trade-off between variance and bias of of OLS estimators when considering the choice of including a particular explanatory variable in your underlying model. Please keep your answer precise.
Describe the Probabilistic Analysis?
The model initial setup is• The number of vacancies posted in the economy during a particular month is v = 100.• There were initially u = 225 unemployed workers at the beginning of the month.• Suppose that the average wage is 0.6 relative to their productivity. Unemployed workersreceive benefits that are half the wage, i.e., b = 0.3 relative to productivity.• Suppose that the number of matches between firms and workers are given by thefollowing matching functionsM = Au^0.5v^0.5• Suppose that 45 workers were able to find a job by the end of the month.Answer the following questions.a) What is the monthly job finding rate?b) What is the probability that an average vacancy is filled in a month?c) What is the job creation cost, k?d) What is the value of A?e) Explain how introducing a searching cost to this model would affect the queue length,the number of vacancy and unemployment rate, and wage.
6. Assume we draw a random sample (ri, Yi) : i = 1, ..., N from a certain population and estimate the following linear model via OLS: aAEb4jalF: OLS? Which not? Why? y = Bo + B1r1 + u (i) E[ûr1] = 0 (ii) E[r1û] = 0 hold by construction of (iii) E[ù] = 0 ialF: id:KaAEftb4jalF:
As a manager of a small software retailing company, you are concerned with projected profit next year. While profit can be determined as the difference between sales and maintenance cost, or in symbols, P = S - M, where P is profit, S is sales, and M is maintenance cost including technical support. It is argues that when sales goes up so does maintenance cost because the cost of technical support will go up. Further, it is measured that the correlation between S and M is 0.8. Now given the figure that sales next year is expected to be $300 thousand with standard deviation of $4 thousand and maintenance cost is expected to be $150 thousand with standard deviation of $6 thousand, what would be the expected profit and its standard deviation you will include in your report?
You are studying the effects of smoking by pregnant women on rates of asthma in their children. You collect data on the number of cigarettes smoked per day and whether or not the child developed asthma by the age of two. The data is below: Smoked 1-5 cigarettes per day --- 9.2% developed asthma Smoked 6-10 cigarettes per day --- 10.3% developed asthma Smoked 11-20 cigarettes per day -- 25% developed asthma Smoked 21-40 cigarettes per day --- 34.8% developed asthma Smoked 41-60 cigarettes per day --- 38.4% developed asthma In order to study the relationship between the number of cigarettes smoked by pregnant women per day and the percentage of their children developed asthma by the age of two using statistical knowledge, we convert the above data into the following format and see if we can obtain an adequate fit using linear regression. Average number of cigarettes smoked per day 3 8 Percentage of children developed asthma What is the value of the correlation coefficient? Г 15-5 30.5…