3.1. Given the assumptions in column 1 of the table, show that the assumptions in column 2 are equivalent to them. Assumptions of the Classical Model (1) (2) E(Y, | X) = B2 + B2X cov (Y, Y) = 0 i i var (Y; | X) = o? E(u| X) = 0 cov (u, u) = 0 i#i var (u|X) = o?
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- (Econmetrics) Q.1 How can you test for general misspecification of model if it would have only (any of) two independent variables?The following scatter plot shows hours of study on the X axis and the final exam score on the Y axis for 21 students in an Econometrics 322 class. The round data points are for economics majors; the square points are for non-majors (and yes, non- majors take econometrics). Score hoursConsider the one-sector Schumpeterian model in discrete time analyzed in the previous exercise, except that now (.) denotes the probability of innovation, and each innovation improves the quality of a machine q to λq, where λ > 1. Suppose that when a new innovation arrives a fraction ϕ of workers employed in the final good production are unable to adapt to this new technology and need to remain unemployed for one time period to “retool.” (a) Define the equilibrium and steady-state (BGP) allocations. [Hint: also specify the number of unemployed workers in equilibrium.] (b) Define the appropriate generalization of the steady state for this economy, and determine the number of unemployed workers in this equilibrium. (c) Show that the economy experiences bursts of unemployment followed by periods of full employment. (d) Show that a decline in ρ increases the average growth rate and the average unemployment rate in the economy.
- You and your research partner want to use Instrumental Variable analysis to write an econometrics paper and find causal estimates. Your partner argues that because the residuals and the instrument are uncorrelated, the exogeneity requirement is satisfied. What do you tell your research partner: a) You agree, the exogeneity requirement is satisfied by construction b) You agree, the exogeneity requirement is satisfied by their demonstration c) You disagree, you would need the results of the White Test to make this conclusion d) You disagree, the exogeneity requirement cannot be tested as we do not observe the error terms e) You cannot make any conclusions with the current informationSuppose that in the model of Myers and Majluf (1984) the parameters take on the following values: λ = 0.60, H = 3, L = 2, I = 1.0, R = 1.25, r = 10 per cent. Use the above data and answer the following questions: (a) Does the model have a separating equilibrium, a pooling equilibrium, or both? (b) Based on your answer to question (a), what is the gain in wealth of the current shareholders of a firm that announces the issuing of new shares to finance the project of investment?Styles 6. The following two regression models are Probit and Logit respectively: Pr(Y=1|X)=(Bo+Bi xXr+Bzx X2) Pr(Y=1|X)=F(Bu + B₁ × Xs + B₂ × X2) (a) what functions do and F represent? (b) How do Probit, and Logit ensure that the predicted probabilities are always between 0 and 1? (c) Sketch a graph of the Y= $(Z) function. (Z on the horizontal axis, Y on the vertical axis) (d) What estimation method is used to estimate the coefficients in a Probit/Logit model? (e) What are the two measures of fit for models with binary dependent variables? Focus 88 B E
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- Question 2. Which of the following models can be estimated (following a suitable transformation if necessary) using ordinary least squares (OLS), where x, y, z are variables and a, B, y are parameters to be estimated? a) y, = e¤x,°e b) y, = a + Byx, + ɛ, c) In(y,)= a + B In(x,)+ɛ, d) y, = a +ßx;z, + ɛ;Suppose we have the following causal model: Ya₁ + ₁ X + u, X + a₂ + B₂Y + v, where E(u) = E(v) = 0, cov(u, v) The best linear prediction of Y given X is: Y = a₁ + ß₁X + error. Similarly, the best linear prediction of Y given X is: X = a* + ß₂Y+ error. Which of the following statements is/are true? 3* = 0 if and only if ₁ = 0 OB₁ B₂ if B₁ = B₂ B = 0 if 3₂ = 0 O B₁ = 0 if B = 0 = : 0. =Problem 2. A researcher is interested in the effect of a US state having access to the ocean (a dummy variable 40) on the density of the population of that state. The density of the population can be affected by many unobserved characteristics of the state including the preferences of the residents, which are hard to measure. To address this, the researcher decides to use panel data with state fixed effects. The researcher collects the data on the population density (PD) and average yearly temperatures (YT) for each year between 2000 and 2012 for each of the US states. The researcher then plans to run a panel data regression: PD BAO BYT + + What is the main problem with this empirical strategy?