Comments on the Exercises in "The Practice of Econometrics" (1991) by Clint Cummins 11/24/1998 This is an accumulated list of comments, based on my working all the exercises in TSP (over a long period of time). Most of the comments just point out minor typos in the book. Others suggest possible extensions to the exercises. It may seem at first glance that there are lots of minor errors in the book. However, there are also a huge number of things which are correct in the book. I think on balance the error rate is actually fairly small. Other books that tackle a similar range of complicated material also contain a similar number of errors; it is part of the risk taken for covering interesting material. The exercises are identified in the same way as the TSP filenames, with Chapter number, an e, and then the Exercise number, and usually a final letter to identify the part of the Exercise. For example, 3e1 is Chapter 3, Exercise 1. 4e3c is Chapter 4, Exercise 3, part (c). 2e1-10. The data for MOTOR (Motorola) is from 76:1 to 85:12, unlike the other 16 companies, which are from 78:1 to 87:12 . It would be best to fix the data for Motorola; otherwise it can't be used in 1987 like many exercises require. 2e8e. Text mislabels alternative hypotheses null hypotheses. Correct: null: January is the same, alt: January is different null: January is the same, alt: January is better 3e1,2,7,10. TIO2 file: variable names in file not consistent with exercise: File: UCOST, PROD, CUM. Exercise: UCOSTT, PRODT, CUMT. It's probably best to change the data file to agree with the exercise names, which is what we did for the TSP databanks. 3e4b. SE for Beta(y) is .0174 (not .175) 3e5f. The coef of Beta(yy) does depend on the base of logarithms used, because the factor log(10) enters it twice and no longer cancels. 4e3c. It's easier to just add LNWORDS to the equation and do a t-test. 4e4. s**2 = .051 , s = .225 . 4e4a. The names of PRICE and SPEED for the original data are OLDPR and OLDSP. 4e6a. Better way with D(1954)? (Better for a) 4e6b. Better way with D(1954)? (harder for b). 4e7a. DISPERSE <= 0 for 10 observations (remove from sample for all regressions). 5e1a. Botched geometric vs. arithmetic mean (correct first 2 sentences) 5e1c. What is the definition of geometric standard deviation? Is it exp(a.s.d.)? 5e4c. Extension: Standard errors for EX*(i), using ANALYZ. (This sort of extension is done routinely in most exercises where elasticities or any function of coefficients is computed). 5e5c. Extension: Standard errors and t-stats for wage differentials. 5e8c. 17 cross products (nonwh*hist = 0, so it doesn't count). Also need ed*ex, ed*exsq, ex*exsq. df = 29 . P-value = .208 . 6e2b. h > rho_hat , not h > rho . 6e3a. ... estimate Eq. (6.41) for equipment --> structures 6e3b. Table 6.8 (not 6.7) 6e3c. ... but for investment in structures --> equipment rather than in equipment --> structures 6e4a. make FJ starting in 52:1, so that lags will exist in 56:1 6e6. p.288, second paragraph. (Q) not (q) . 6e8b. instruments for Y(t), not I(t). 6e9. LKE, LKS are not defined for 86:4, because KELAG(+1) doesn't exist. 6e10a. 56:1 - 81:4 data, not 86:4 7e2b. 74-84, not 73-84 7e2c. Entire 1951-1984 --> 1952-1984 Pre-OPEC 1951-1973 --> 1952-1973 Does logarthmic --> logarithmic 7e6b. Durbin-Watson *can* be used. It is not inappropriate, especially in small samples. It is biased towards 2, so its P-value is biased away from zero. This merely makes it a more conservative test. You can definitely use it when it rejects rho=0; it would be unwise to use it to accept rho=0, though. 7e6c. Durbin's h can be calculated just fine for this equation. 7e6c. Use 1953-1984, not 1953-1985. 7e6e. Local minimum is rho=.70 . 7e8b. OK to use 52,73 (no data is lost). 8e1f. LPR --> LPRI 8e1g. LPR --> LPRI Use LQTYFIT from (e) 8e7f. Redefine F = F/100 to convert from percentage to fraction. 9e5a. p.464 (9.32) j .ne. i (instead of j .ne. 1) p.499 the IZEF estimates of GL given in "note 11" are not the correct ML estimates. They yield a LogL of 394.165, while the real ML estimates yield a LogL of 397.792. p.464 if we use the estimates from "note 11", the own Allen elasticities given under (9.30) are correct, but the cross Allen elasticites are incorrect. They appear to be calculated from (9.29) with (PiPJ)**(1/2) instead of (PiPj)**(-1/2) . Extension: it is possible to calculate standard errors for all elasticites. 9e5b. It is easier to use an LDL' decomposition or eigenvalues (instead of all the submatrix determinants) to check if the matrix of Allen elasticities is negative semi definite. 10e1d. The OLS-AR(1) estimates in Table 10.3 were computed using Cochrane-Orcutt. They can also be computed using ML or GLS. 10e1e. (including footnote 86). These are not the instruments that Fair suggests. Fair suggests adding the lagged dependent and lagged RHS variables as instruments. The book suggests adding the lagged original instruments -- this is not the same. This also affects footnote 83 on p.552. 10e5b. The Durbin-Watson statistic is OK for rejecting rho=0 (not OK for accepting rho=0, though). See the comment above to 7e6b. 10e6. In (10.70), C --> CN . 10e8a. The book's FIML estimates in Table 10.3 are incorrect (I don't know why -- the model looks right). Correct estimates are given by Calzolari and Panattoni, Econometrica (1988) p.702. You should get a Log Likelihood of -83.3238 at the correct estimates. 10e8c. The ML Restricted Reduce Form coefficients in Table 10.4 are incorrect (due to incorrect FIML estimates). LogL should be -83.3238, as above. 10e9a. The diagonal of Jacobian for Klein-I is not unity. (You have to substitute in the identities before taking the derivatives). 10e9b. det(Jacobian) for Klein(1953) is 1-A1, not unity. Same comment as 10e9a for identities. Below (10.65'), C --> CN . 10e9c. estimate (10.63) first, not (10.62). 10e9f. det(Jacobian) is not unity, but Jacobian is triangular. Note: if (10.75) is used instead of (10.62), then the Jacobian is unity, and IZEF coincides with FIML. This demonstrates that IZEF is sensitive to the normalization of which variable is on the LHS, while FIML is invariant to normalization. p.625 in (11.45a), change X(i)** theta to b*X(i)** theta . the expression [.] is ambiguous. 11e1d. WA2 is for immediate use; AX2 for later use. sample LFPR *mean* of 428/753 (not 425/753) f(P) = normal *density* function, corresponding to cumulative distribution function result of P = NORM(CNORMI(P)) in TSP notation 11e4a. LWW --> LWW1, also include PRIN. It helps in many of these exercises to use LWW1 when it says LWW, because LWW1 = LWW when LWW is non-missing. 11e4d. 1 percent change in wage, not 1 dollar change in wage. 11e5b. H(i) --> WHRS(i) 11e6e. The Olsen(1980) model is not identified when the RHS variables in the Probit and OLS equations are the same. It requires an exclusion restriction for identification.