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Econometrics uses mathematical and statistical models to develop or test hypotheses in economics. It forecasts the future trends from the data and defines the economic system accordingly. Overall, it evaluates real-world data using statistics and compares the results to specific economic theories. Students take this course to become economists. However, developing a solid understanding of economics takes longer than anticipated. Throughout the academic year, several econometrics assignments are given to students to help them study and develop their knowledge on the subject. However, students face difficulties with econometrics due to complex case studies and research challenges since they're unfamiliar with the abstract statistical methods. Under these circumstances, TutorBin comes forward to eliminate your academic stress. It provides econometrics homework help that helps students in improving their grades.

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Q1:C. d. e. Perform the classical t-tests for all parameters at the 1%, 5% and 10% levels. Also, derive the associated p- values. Test the hypothesis that the above model (1) is reasonable. That is, perform the classical F-test on the joint hypothesis Ho: B₂=0, P3=0 against H₁: at least one is non-zero Perform the test at the 1%, 5% and 10% levels. Comment on the outcome. The sample means of price and sales pc over time is $90.75 and 3001.33, respectively. Estimate the price elasticity of sales. Also, for a 10% increase in the price, predict the percent change of sales./nSee Answer
Q2:Ⓒ Cristina Reiser. All rights reserved. DO NOT SHARE OR DISTRIBUTE. 1. Consider preferences for cookies (on the x-axis) and ice cream bars (on the y-axis) for different people. Draw an indifference curve map with 3 indifference curves on each (label them) for each scenario below. The consumer a. views 2 cookies and an ice cream bar as perfect substitutes b. always eats 2 cookies with one ice cream bar C. likes ice cream bars but doesn't care about cookies (is neutral) d. loves ice cream but hates cookies (hint: cookies are a "bad"). 2. Lavarre's utility function is U (x, y) = x-6y4, where x is the number of units of the x-good and y is the number of units of the y-good. The price of x is $4 and the price of y is $3. Lavarre has $30 to spend on these two goods. What is Lavarre's optimal bundle (use math and a graph to support your answer)? 3. Now, suppose you don't know the prices and income for Lavarre's scenario. Let px be the price of good x, py, be the price of good y, and m be income. a. Use the three steps from lecture to find the demand function for good x, x(px,py, m), and the demand function for good y, y(py,Px, m). You must show your work (e.g., how you derive the tangency condition from the given utility function). (hint: when you come up with your demand function you should be able to plug in the prices and income from (a) and get the same answer!) b. Given the demand functions you determined, calculate and interpret ax ax дрх дру END and ax am 4. Suppose that people derive utility from two goods - housing (H) and all other consumption (C) as measured in dollars. a. Putting housing on the x-axis, illustrate a person's optimal utility-maximizing bundle. As always, be sure to include axes, indifference curves, budget constraint, and labels. b. Now suppose the government agrees to subsidize consumers by paying 50% of their housing cost. How will their budget line change? Show this and the new utility- maximizing bundle. Explain the outcome using concepts from class. 5. There are millions of different scenarios we can apply to the consumer choice model (changing the goods, changing prices, incomes, preferences, etc.) It's actually fun thinking through different scenarios! Using question (4) as a framework, what is a different event (e.g., policy) that could change the optimal bundle of housing and other consumption goods? How would your event change the optimal bundle? Explain.See Answer
Q3:2. Forecasting. For this problem, use file cambridge.dta. The file contains monthly means of daily maximum temperature (variable maxtemp) in Cambridge, from January 1959 up to September 2018. For example, in September 2018, the average maximum daily temperature in Cambridge was 19.9 degrees of Celsius. (a) Make a time series plot of maxtemp. Summarize the behavior of these time series. Plot the correlogram of maxtemp. Comment. (b) Run the regression of maxtemp on the month dummies (don't fall into the dummy variable trap!). How would you interpret the coefficients? Save the residuals from this regression as variable res. (c) Make a time series plot of res. Any signs of global warming? Plot a correlogram of res. Comment. (d) Regress res on variable t, which indexes time, and a constant. Save the residuals as variable res1. Plot a correlogram of res1. Compare with the correlogram of res. Can you explain the difference? (e) Estimate an AR(1) model for res1. Test hypothesis of no AR(1) serial correlation in the errors of this model. (f) Given your estimates in (b-e), what is your forecast of the mean daily maximum temper- ature in Cambridge in February 2018?See Answer
Q4:1. Cochrane-Orcutt. Consider a linear regression model Yt =B₁ + B₂xt + Et. Suppose you have the following data for four time periods: t 1 2 3 4 Yt 0 2 2 0 0 1 2 3 Without using any software, find the Cochrane-Orcutt and Prais-Winsten estimates for ₁ and 3₂. Show your work. Compare the estimates.See Answer
Q5:Question 3 Suppose that you want to study whether the increasing rate of worker's earnings according to the change of age would decrease as the worker gets older, i.e., the null is increasing rate is not affected by the change in age and the alternative is that the increasing rate is negatively affected by an increase in worker's age. To answer the question, agesq need(s) to additionally enter the model in the previous question. The t-test statistic to study the null is -2.15 Question 4 1 pts Question 5 1 pts By using the test statistic in the previous question, draw your conclusion at 5% significance level. 1 pts The variable marst is a categorical variable encoded by six groups: married and spouse present, married and spouse absent, separated, divorced, widowed, and never married. Generate the dummy variable cmarr that takes 1 if an individual is currently married regardless of the presence of her spouse and 0 otherwise. Find the average of cmarr and interpret it. Can you use both cmarr andSee Answer
Q6:There are three dates t = 0, 1, 2 and a continuum of consumers with measure one, each endowed with wealth one. There are two types of consumers: a fraction & is impatient, i.e. their utility is 1 – (1/c₁), where c₁ is consumption at t = 1, and a fraction 1 - a are patient whose utility is 1 – (1/₂), where where ₂ is consumption at t = 2. At t= 0 consumers don't know their type, i.e. it is unknown whether the consumer wishes to consume at date t = 1 or t= 2. At t = 1 all consumers observe their own type, but cannot observe others' types (i.e. type is private information). There are two technologies to manage liquidity. Consumers can invest for one period only (short term technology), in which case the investment will yield r≥ 1. This technology is available at both t = 0 and t = 1. Alternatively, wealth can be invested for two periods (long term technology) at date t = 0, which yields 0 at t = 1, but R > r² at t = 2. The investment in the long-term technology can be liquidated at t = 1, which then yields L < 1. Wealth can also be stored across periods without cost. a) Suppose there is a bank to manage liquidity risk, all consumers deposit their wealth in the bank and the bank maximizes total welfare of its depositors when it chooses , c3, the promised payouts for early (t = 1) and late (t = 2) withdrawals, respectively. I Set up the bank's optimisation problem and derive the first order condition. What does the first order condition tell you about the optimal allocation? Calculate the optimal investment in the long-term technology IB and the optimal allocation c, c III. Does the allocation , always constitute an equilibrium? If not, derive the necessary condition for ² to be an equilibrium and carefully explain your finding. II. IV. Now, suppose the condition that you derived in iii) above does not hold. Derive the feasible (incentive compatible) allocation that maximizes total welfare and can always be supported in an equilibrium. b) Now, suppose there is no financial intermediary to handle liquidity shocks. However, at t = 1 a financial market for bonds opens up and agents trade their wealth at t = 1 for wealth at t = 2 . Each bond pays 1 at t = 2 and its price is pM. Calculate the consumer's optimal investment decision IM at t=0, an expression for the price of the bond M and the consumption levels in the two states , c) Is the bond market allocation efficient? Calculate the price of the bond that would ensure that the market delivers the optimal allocation and discuss what would be needed for this price to clear the market.See Answer
Q7:2. Autocorrelation function. A process yt satisfies Yt = Bo + B₁xt + Et, where xt and et are two independent AR(1) processes 0.5xt-1+ut and Xt = Et = 0.1E-1 + Wt with i.i.d. standard normal ut and wt. Find the autocorrelation function of yt.See Answer
Q8:4. Feasible Generalized Least Squares. Consider the linear regression model price = Bo + B₁lotsize + B₂sqrft + 3bdrms + u, where price is the house price measured in thousands of pounds, lotsize is the size of lot in square feet, sqrft is size of house in square feet, bdrms is the number of bedrooms, and E (u | lotsize, sqrft, bdrms) = 0. An econometrician believes that u² = vexp {0 +1lotsize}, where E (v|lotsize, sqrft, bdrms) = 1. Which assumption(s) of the Gauss-Markov theo- rem are violated? Describe main steps of an asymptotically efficient procedure for estimating Bo, B1, B2, B3.See Answer
Q9:2. Asymptotic variance of OLS and heteroskedasticity robust standard errors. Consider the following regression model: Y₁ = x;ß+Ui, i = 1, ..., , (1) where x₁ = (1, ₁)': ; a dummy variable taking on the value -1 with probability p/2 > 0, the value +1 with probability p/2, and the value 0 with probability 1- p. Assume E (u₂|x;) = 0, and E (u²|x₁) = 2+2₁. Suppose that a random sample (yi, ;), i = 1, ..., n., is available. Let 3 be the OLS estimator of 3. Recall that the asymptotic variance-covariance matrix of 3 is defined as the variance-covariance matrix of the distributional limit of √(-3) as n → ∞o. Find an explicit expression of the asymptotic variance-covariance matrix of 3 in terms of p. How are the heteroskedasticity robust standard errors of the coefficients of 3 related to the matrix you have found?See Answer
Q10:1. Regression modeling and interpretation of results. Jacob Mincer (1958) "Investment in Human Capital and Personal Income Distribution", JPE 66, 281-302 spells a model of education as an investment, where human capital H equals H = AeBeduc where educ is educational attainment, 3 is the return to an investment of the annual earnings amount (that gives you an extra year of education, and so increases human capital), and A includes all other factors influencing human capital. If one unit of H can be rented by a firm at price P, a person with capital H gets wage H x P: log (wage) = log P + Beduc + log A. Using the data on workers' wages, education, experience, etc. from the Stata file wage1.dta (taken from the 1976 Current Population Survey), run a regression of the logarithm of wage on the education and tenure. Interpret and critically assess your results. Pay attention to possible biases.See Answer
Q11:3. F-statistic and regression standard error ô². You are given the following Stata outcome from the regression of the logarithm of wage on the years of education, years of tenure with the current employer, and the dummy that equals 1 for females and 0 for males. Complete the table. That is, replace the "?" by the correct numbers. Show your calculations. tenure female . reg lwage educ Source Model Residual Total lwage edu tenure female cons SS 56.784773 91.5449785 148.329751 Coef. df 3 522 18.9282577 .175373522 525 .28253286 Std. Err. MS .0813537 .0066431 .0216338 .0025882 -.297052 .0374698 .6331253 .0913825 Number of obs F (3, 522) Prob > P R-squared t Adj R-squared Root MSE P>|t| 12.25 0.000 0.000 8.36 -7.93 0.000 6.93 0.000 ? ? .0683033 .0165494 ? ? ? 526 [95% Conf. Interval] 0944042 .0267183 -.3706622 -.2234418 .4536027 .8126479See Answer
Q12:2. Hypothesis testing. You would like to test the null hypothesis Ho: Bo=B1 = 3₂ in the regression Yi = Bo + B₁æi + B₂zi + Ei. Represent this hypothesis in the standard form RB = r, where 3 = (30, 31, 32)'. Suppose that you know that RB-r is distributed as N (0, 1₂) under the null, and that the value of RB - r is (2,-1)', where is the OLS estimator of 3. Test Ho.See Answer
Q13:1. Multicollinearity. Suppose that you postulate a model explaining final exam score in terms of class attendance. Thus, the dependent variable is final exam score, and the key explanatory variable is number of classes attended. To control for student abilities and efforts outside the classroom, you include among the explanatory variables various measures of the student's previous year performance. Someone says, "You cannot hope to learn anything from this exercise because the measures of performance that you included are likely to be highly collinear." What should your response be?See Answer
Q14:The variables in your data set are: • sau: household savings from income during the year (in £10,000s); age: the age of the head of the household at the end of the year (in years); • nchild: the number of children (aged 17 and under) in the household at the end of the year; • inc: household income during the year (in £10,000s); • grad: a dummy variable which equals 1 if the head of the household is a graduate and 0 otherwise; and, • hols: the number of holidays taken by the household during the year. 1. (a) For each of the variables, what is the average, the standard deviation, the minimum value, and the maximum value in your data set? (b) What is the number of observations in your data set? 2. (a) Calculate the correlation coefficient between sav and inc. Is there a strong relationship between these two variables? (b) Construct a graph that plots savings (on the vertical axis) against income (on the hori- zontal axis). Does the visual evidence support your answer in part (a)?See Answer
Q15:#1 Consider the following regression which relates salary and performance for Major League Soccer players. salary =B₁ + B₁games + B₂goals + Bassists + u where salary is the salary paid to a player for the season, games denotes games played, goals is the number of goals scored, and assists is the number of assists scored. The coefficients ₂ and 33 relate to player performance; that is, better players will score more goals and obtain more assists. a) What is the expected sign on B₂? Propose a one-sided hypothesis for this coefficient where the alternative hypothesis is in the expected direction of B₂. b) Propose the hypothesis (both the null and the alternative) that player performance does not matter for the determination of salary. c) Suppose you want to run an F-test for the hypothesis P₁ = 0, B₂ = 0. What is the regression that is run to obtain the SSR of the restricted regression? d) If the error term were heteroskedastic in the regression, would using the usual t-statistic be sufficient to determine statistical significance of a regression parameter? Explain.See Answer
Q16:(d) 12 marks i) Provide an approximate interpretation of 3. ii) Provide an exact interpretation of $3. iii) Is 3 practically significant? Briefly explain. iv) What is the predicted average birth weight of a male child, born to a white mother, who smokes 20 cigarettes per day and who has a family income of $50,000? v) Derive a 95% confidence interval for B3. vi) Comment on the precision of 33 as an estimate of ß3. (2 marks) (2 marks) (2 marks) (2 marks) (2 marks) (2 marks)See Answer
Q17:(c) 10 marks i) Test the joint significance of the regressors white and lfaminc in (3). Conduct the test of joint significance at the 5% significance level. Specify the unrestricted and restricted models. State the null and alternative hypotheses, the form and sampling distribution of the test statistic under the null, the sample and critical values for the test statistic, your decision rule and your conclusion. Place the Eviews output for the restricted model in Appendix (c). ii) Comment on the statement that the race of the mother has no effect on birth weight once we control for family income, the gender of the baby and cigarette consumptions by the mother during pregnancy. (8 marks)See Answer
Q18:(b) 18 marks Assume that E(lbwght white,male, cigs, lfaminc) = Bo + B₁white + B₂male + ß3cigs + ß4lfaminc The associated linear regression equation in error form is given by Ibwght = Bo + B₁white + B₂male + Bacigs + ß4lfaminc + u. i) Estimate (3) by OLS. Report the estimated regression equation in equation form in the main body of your assignment. Report the estimated coefficients and standard errors to three decimal places. Place the Eviews output in Appendix (b). ii) Based on the output obtained when (3) is estimated by OLS, are the regressors in (3) jointly significant? Briefly explain. iii) Based on the reported p-values, are any of the regressors in (3) individually insignificant at the 10% significance level? Briefly explain. iv) Based on the reported p-values, are any of the regressors in (3) individually insignificant at the 5% significance level? Briefly explain. v) Do the estimated coefficients have the expected sign? Briefly explain in two sentences for each estimated coefficient. vi) Evaluate the explanatory power of your model. vii) Interpret 34. viii) Based on the estimated regression equation, what is the most significant influence on the predicted birth weight of a new born infant? Briefly explain. (2) 3 (2 marks) (2 marks) (2 marks) (2 marks) (4 marks) (2 marks) (2 marks) (2 marks)See Answer
Q19:9. (a) Prepare a table reporting the estimates (and corresponding standard errors) from the re- gressions in questions 3(a), 4(a), 6(a), 7(a) and 8(b). In this table, each column should report the results of one regression including the coefficient estimates, the standard errors (robust if necessary), the standard error of the regression and the R². (b) After running all these regressions, which is your preferred model of household savings?See Answer
Q20:7. (a) Fit a multiple linear regression (MLR) of Isav on age, nchild, line, grad and hols, and report the regression results. (b) Which of the regressors are individually significant at the 10% level? And at the 5% level? (c) Carry out a test of the joint significance of the variables age, nchild, grad and hols. Which model do you prefer the SLR model in the previous question, or the MLR model in this question? (d) Carry out a RESET test in the MLR model - is there evidence of functional form mis- specification? (e) Carry out a test for heteroskedasticity in the MLR model - is there evidence of het- eroskedasticity?See Answer

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