Econometric Exam free essay sample

The demand for roses was estimated using quarterly figures for the period 1971 (3rd quarter) to 1975 (2nd quarter). Two models were estimated and the following results were obtained: Y = Quantity of roses sold (dozens) X2 = Average wholesale price of roses ($ per dozen) X3 = Average wholesale price of carnations ($ per dozen) X4 = Average weekly family disposable income ($ per week) X5 = Time (1971. 3 = 1 and 1975. 2 = 16) ln = natural logarithm The standard errors are given in parentheses. A. ln Yt = 0. 627 1. 273 ln X2t + 0. 937 ln X3t + 1. 713 ln X4t 0. 182 ln X5t (0. 327) (0. 659) (1. 201) (0. 28) R2 = 77. 8%D. W. = 1. 78N = 16 B. ln Yt = 10. 462 1. 39 ln X2t (0. 307) R2 = 59. 5%D. W. = 1. 495N = 16 Correlation matrix: | ln X2| ln X3| ln X4| ln X5| ln X2| 1. 0000| -. 7219| . 3160| -. 7792| ln X3| -. 7219| 1. 0000| -. 1716| . 5521| ln X4| . 3160| -. 1716| 1. 0000| -. 6765| ln X5| -. 7792| . 5521| -. 6765| 1. 0000| a) How would you interpret the coefficients of ln X2, ln X3 and ln X4 in model A? What sign would you expect these coefficients to have? Do the results concur with your expectation? b) Are these coefficients statistically significant? c) Use the results of Model A to test the following hypotheses: ) The demand for roses is price elastic ii) Carnations are substitute goods for roses iii) Roses are a luxury good (demand increases more than proportionally as income rises) d) Are the results of (b) and (c) in accordance with your expectations? If any of the tests are statistically insignificant, give a suggestion as to what may be the reason. e) Do you detect the presence of multicollinearity in the data? Explain. f) Do you detect the presence of serial correlation? Explain g) Do the variables X3, X4 and X5 contribute significantly to the analysis? Test the joint significance of these variables. ) Starting from model B, assuming that at the time point of January, 1973, there was a disaster that heavily affected the quantity of roses produced. Suggest a model to check if we have to use two different models for the data before and after the disaster. (Using dummy variable). Problem 2: Two large US corporations, General Electric and Westinghouse, compete with each other and produce many similar products. In order to investigate whether they have similar investment strategies, we estimate the following model using pooled time series data for the period 1935 to 1954 for the two firms: INVt = 1 + 2DVt + 3Vt + 4DV*Vt + 5Kt + 6DV*Kt + ut(1) whereINV = gross investment in plant and equipment V = value of the firm = value of common and preferred stock K = stock of capital DV = 0 if General Electric (observations 1 to 20) = 1 if Westinghouse (observations 21 to 40) All three continuous variables are measured in millions of 1947 dollars. Pooling the data yields 40 observations with which to estimate the parameters of the investment function. However, pooling is valid only if the regression parameters are the same for both firms. In order to test this ypothesis, intercept and slope dummy variables are included in the model. Dependent Variable: INV| Method: Least Squares| | Sample: 1 40| Included observations: 40| Variable| Coefficient| Std. Error| t-Statistic| Prob. | C| -9. 956306| 23. 62636| -0. 421407| 0. 6761| DV| 9. 446916| 28. 80535| 0. 327957| 0. 7450| V| 0. 026551| 0. 011722| 2. 265064| 0. 0300| DV*V| 0. 026343| 0. 034353| 0. 766838| 0. 4485| K| 0. 151694| 0. 0193 56| 7. 836865| 0. 0000| DV*K| -0. 059287| 0. 116946| -0. 506962| 0. 6155| R-squared| 0. 827840| Mean dependent var| 72. 59075| Adjusted R-squared| 0. 802523| S. D. dependent var| 47. 24981| S. E. of regression| 20. 99707| Akaike info criterion| 9. 064124| Sum squared resid| 14989. 82| Schwarz criterion| 9. 317456| Log likelihood| -175. 2825| F-statistic| 32. 69818| Durbin-Watson stat| 1. 121571| Prob(F-statistic)| 0. 000000| (a) Interpret all the coefficient estimates, stating whether the signs are as you would expect, and comment on the statistical significance of the individual coefficients. (b) Comment on the overall fit and statistical significance of the model. (c) The Jarque-Bera statistic is 7. 77 and its p-value is 0. 02. What can you conclude about the distribution of the disturbance term? Why is this test important? (d) On the basis of the above results, is pooling the data from the two firms appropriate? Explain. (e) An alternative way of testing whether pooling the data is appropriate, without using dummy variables, is to use the Chow breakpoint test. Referring to table below, briefly discuss how the test works and whether the results are consistent with the earlier model (which includes dummy variables). Chow Breakpoint Test: 21 | F-statistic| 1. 189433| Probability| 0. 328351| Log likelihood ratio| 3. 992003| Probability| 0. 62329| (f) Explain the results and implications of the following Ramsey RESET test. (Note that the dummy variables have been omitted from the original model). Ramsey RESET Test:| F-statistic| 0. 000200| Probability| 0. 988806| Log likelihood ratio| 0. 000219| Probability| 0. 988189| | | | | | Test Equation:| Dependent Variable: INV| Method: Least Squares| Date: 05/15/02 Time : 13:07| Sample: 1 40| Included observations: 40| Variable| Coefficient| Std. Error| t-Statistic| Prob. | C| 17. 81458| 8. 199161| 2. 172732| 0. 0365| V| 0. 015226| 0. 006706| 2. 270632| 0. 0293| K| 0. 144467| 0. 065596| 2. 02383| 0. 0341| FITTED^2| -2. 87E-05| 0. 002028| -0. 014128| 0. 9888| R-squared| 0. 809773| Mean dependent var| 72. 59075| Adjusted R-squared| 0. 793921| S. D. dependent var| 47. 24981| S. E. of regression| 21. 44950| Akaike info criterion| 9. 063919| Sum squared resid| 16562. 91| Schwarz criterion| 9. 232807| Log likelihood| -177. 2784| F-statistic| 51. 08255| Durbin-Watson stat| 1. 106556| Prob(F-statistic)| 0. 000000| Note: We can have similar questions using results from eviews to check for autocorrelation and heteroscedasticity (Breusch Godfrey test and White test).