Help me solve the following questions step by step....attempt all parts
1.3.7 Exercises 1. We have annual data for the UK economy, for the years 1953-1964, on the percentage change in wages W and the percentage of the labor force unemployed U: W 4.4 5.4 7.1 6.2 4.2 3.1 2.6 3.3 3.8 3.6 4.1 4.4 U 1.5 1.3 1.1 1.2 1.4 2.1 2.2 1.6 1.5 2.0 2.1 1.6 (a) Create a workfile and enter the data (use / quick/empty group (edit series)/). (b) Make a scatterplot of W versus U. Does the relation between them looks linear? What is their correlation? (c) Estimate the regression equation W = o + BU + c. Interpret the estimated value of B. Is U a significant variable? (d) Have a look at the residual series. Do the assumptions HI-H5 seem to be plausible? Make a QQ-plot of the residual series to check for normality. 2. For 25 households we have data (in "households.wfl" ) on their total consumption expenditure (X) and on their food expenditure (F). (a) Estimate the regression equation Y = a + 3X + 6. Predict the value of Y for X = 200 and for X = 1000. (b) Estimate the regression equation log(Y) = o + Blog(X) +c. Predict the value of Y for X = 200 and for X = 1000. (c) Which of the 2 models do you prefer? Make a scatterplot of Y versus X. 3. Ten experts make a prediction f for the economic growth i the EU and ten other3. Ten experts make a prediction for the economic growth in the EU and ten other experts in the US for next year: 34 EU US 2.1 2.6 2.5 2.4 2.3 3.2 1.4 0.8 1.5 1.3 1.5 2.1 2.4 1.6 2.7 3.2 2.8 3.1 1.1 1.4 (a) Test whether the predictions for US and Europe are on average the same. (b) Test for normality of the error terms, given the small sample size. (c) How does your answer change if the 10 experts making predictions are the same? We are interested in knowing whether persons having a loyalty card spend more in a supermarket or not. Take the data in the Eviews le \" ex.wfl\". We have data for 2 supermarkets, and for each of them we have for 20 clients the amount spent (AMOUNT), the size of the household the person belongs to {HHS}, and a binary variable (CARD) indicating whether the person owns a loyalty card or not. Denote my the amount spent by customer i in supermarket j, and 1'\" the personal characteristics of the client (in this case, only consisting of HHS}. The proposed model is: as;- =3$j+j+ECARD+Eiju where of. forj = 1. 2 are xed eects for each supermarket. Our main interest is to know whether 5 is signicant or not. 1. Estimate the parameters of the above model by GL5. Interpret briey the param- eters estimates. (Hint: since the .13 and :5 parameters are supposed to be the same for the 2 supermarkets. it will be necessary to pool the data. You will also need to create yourself the appropriate dummy variables STORE] and STORE? to take the xed effects into account.) 2. We are afraid that there is groupwise heteroscedasticity in the error terms. i.e. Yams\") = of for j = 11 2. (a) Estimate the variances of and 0% using the DLSresiduals. (b) Estimate now the parameters by GL3. Write down an expression for E, the co- variance matrix of the error termsT and show that GLS boils down to Weighted Least Squares (WLS) here. Create the series of weights to be used, and carry out the WLS estimation (in Eviews, take estimation method LS with option Weighted LS). [c] What is the advantage of WLS over OLS? 3. We are also afraid that there might be interaction between the variable CARD and the supermarket. In particular, the effect of the loyality card might differ among 79 different supermarkets. The model becomes now 3;\" = 3's\" + 0:3- + Jj CARD + a\". (a) Estimate the above model by OLS. Do you think there might be interaction? (Hint: creating the variables STORE1*CARD and STORE2*CAHD might be useful.) [b] Test whether the interaction is signicant or not. 4. Economists would say that there is a serious endogeneity problem here. There probably exists a feed-back relation from AMOUNT to CARD. Could you explain why this might be the case? Explain in words why it might indeed be that the error terms are correlated with the variable CARD. 7.5 Homework We are interested in the number of accidents per service month for a sample of ships. The data can be found in the le \"shipsmni\". The endogenous variable is called A00. The explicative variables are: a TYPE: there are 5 types of ships, labeled as ABGD-E or 1-2-345. TYPE is a categorical variable, so 5 dummy variables can be created: TA, TBT TC, TD, TE. a CONSTRUCTION YEAR; the ships are constructed in one of four periods, leading to the dummy variables T6064, Tg, TTU'M, and T7579. I SERVICE: a measure for the amount of service that the ship has already carried out. Questions: 1. Make an histogram of the variable ABC. Comment on its form. Is this the histogram for the conditional or unconditional distribution of ABC? 2. Estimate the Poisson regression model, including all explicative variables and a constant term. (Use estimation method: COUNT integer counting data.) 3. Comment on the coefcient for the variable SERVICE. Is it signicant? 4. Perform a Wald test to test for the joint signicance of the construction year dummy variables. 5. Given a ship of category A, constructed in the period 65-69, with SERVICE=1000. Predict the number of accidents per service month. Also Stimate [a] the probability that no accident will occur for this ship, and {b} the probability that at most one accident will occur. 6. The computer output mentions: \"Convergence achieved after 9 iterations\". What dose this mean? T. What do we learn from the value of \"Probability(LH stat)\"? What is the corre- sponding null hypothesis? 101 3. Estimate now a Negative Binomial Model. EViews reports the log( :12] as the mixture parameter in the estimation output. {a} Compare the estimates of 3 given by the two models. (b) Compare the pseudo R2 values of the two models. 9. Estimate now the Poisson model with only a constant term, so without explicative variables [empty model}. Derive mathematically a formula for this estimate of the constant term (in the empty model}, using the rst order condition of the ML- estimator
