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- 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?Exlplain Linear Conditionally Unbiased Estimators and the Gauss–Markov Theorem with its limitations?q7- Which statement is incorrect for statistical independence between X and Y? Select one: a. The occurence of Y has no impact on the probability for the occurence of X b. If X and Y occur jointly, it is purely by chance c. The correlation between X and Y is 0 d. The correlation between X and Y is 1
- 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.With respect to a given product, describe the connection that exists between equalibrium/disequalibrium and prediction. cite an unique exampleDefineIndifference curves usually curve inward
- Given the following data X (consumers of teff) or popn 3 6 8 1 13 13 14 Y ( teff consumption) 8 6 10 12 12 14 20 year 2013 2014 2015 2016 2017 2018 2019 Estimate the regression equation, Y= a+bX, Where Y denotes demand for teff while X is consumers of teff (population) By assuming demand for teff is only affected by its consumers, find the amount demand for teff in the year 2022 if the populations (consumers of teff) are about 18 people? (Hint: use the least square method, parameter a and b can be estimated by solving the two linear equations) SY= na+ bSX SXY=aSX +b Where n is number of years. For example, Estimate the sales for 2012, 2015 and fit a linear regression equation and draw a trend line.ar X Sales (Y) XY X2 year X Sales (Y) XY X2 2002 1 22734 22734 1 2003 2 24731 49462 4 2004 3 31489 94467 9 2005 4 44685 178740 16 2006 5 55319…With Panel Data, if we assume that the individual effects vi are not correlated with the regressors Xit (i.e. E(vi|Xit) = 0), which one of the following statements is correct: The Fixed Effects estimator is not consistent. Both the OLS and the Random Effects estimators are not consistent. The OLS estimator is not consistent, but the Random Effects estimator is consistent. The OLS and the Random Effects estimator are consistent. All of the above. None of the aboveIs the cobb-douglas function concave if a1 +a2 = 1 when
- (Yi, X1i, X2i) satisfy the assumptions of the attachment. You are interestedin β1, the causal effect of X1 on Y. Suppose that X1 and X2 are uncorrelated.You estimate β1 by regressing Y onto X1 (so that X2 is not included in theregression). Does this estimator suffer from omitted variable bias? Explain.1. Why is the existence of a correlation (existence of co-occurrence or association) between and Fnot enough evidencefor us to say that Ycauses Y?2. What is the post hoc, ergo propter hoc fallacy? Give an exampleIn some circumstances, individuals reproduce better when the population size is large, and fail to reproduce when the population size is small (the Allee effect introduced in Exercise 46). Suppose that per capita production is an increasing linear function with λ(0) =−2 and a slope of 0.01. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 100? Is b(t) increasing when b = 300?
