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70 Table 4.10 Data on Housing Starts in Canada (1954-4 to 1982-4 Quarterly)" | | | | | | | | 54-4 | 28.73 | 101.8 | 3.92 | 66-2 | 29.11 | 185.8 | 2.73 | 55-1 | 29.83 | 103.3 | 4.25 | | 29.83 | 191.0 | 2.44 | | 31.22 | 107.4 | 4.42 | | 32.95 | 186.9 | 2.38 | | 32.61 | 113.7 | 4.63 | 67-1 | 30.04 | 190.3 | 2.29 | | 30.47 | 110.8 | 4.90 | | 43.53 | 193.5 | 2.14 | 56-1 | 31.34 | 117.2 | 4.63 | | 42.41 | 194.5 | 2.13 | | 32.42 | 118.3 | 5.16 | | 35.87 | 194.0 | 2.39 | | 30.56 | 116.8 | 4.64 | 68-1 | 46.34 | 197.4 | 2.83 | | 22.01 | 121.7 | 4.09 | | 48.37 | 202.6 | 2.70 | 57-1 | 17.75 | 122.8 | 3.12 | | 42.49 | 208.0 | 2.40 | | 29.41 | 122.5 | 2.79 | | 51.00 | 209.1 | 2.53 | | 28.76 | 118.8 | 2.96 | 69-1 | 66.32 | 211.7 | 2.93 | | 30.39 | 121.8 | 3.47 | | 54.51 | 213.2 | 3.42 | 58-1 | 36.67 | 121.5 | 3.71 | | 47.52 | 218.1 | 4.06 | | 41.27 | 124.2 | 3.38 | | 41.58 | 218.0 | 4.09 | | 36.18 | 123.2 | 3.04 | 70-1 | 40.85 | 218.3 | 4.25 | | 37.46 | 127.7 | 3.07 | | 34.54 | 220.4 | 3.77 | 59-1 | 32.99 | 127.2 | 3.42 | | 44.43 | 222.4 | 3.29 | | 32.49 | 128.8 | 4.52 | | 60.78 | 221.7 | 3.62 | | 32.98 | 128.4 | 4.87 | 71-1 | 49.18 | 227.8 | 3.36 | | 33.32 | 131.5 | 4.59 | | 55.81 | 233.3 | 3.76 | 60-1 | 21.95 | 133.4 | 4.41 | | 57.23 | 239.8 | 2.97 | | 23.54 | 130.5 | 4.52 | | 59.27 | 242.0 | 2.02 | | 27.05 | 133.3 | 4.54 | 72-1 | 62.12 | 243.8 | 1.93 | | 27.34 | 133.8 | 4.55 | | 62.08 | 250.5 | 1.68 | 61-1 | 31.90 | 132.5 | 4.54 | | 60.51 | 249.2 | 1.60 | | 29.88 | 137.1 | 4.36 | | 57.25 | 257.7 | 1.05 | | 30.07 | 135.1 | 4.47 | 73-1 | 62.39 | 264.7 | 0.88 | | 27.39 | 141.5 | 4.45 | | 68.25 | 267.2 | 1.65 | 62-1 | 30.58 | 143.3 | 4.34 | | 65.32 | 267.0 | 1.92 | | 31.97 | 143.3 | 4.05 | | 62.45 | 278.1 | 1.46 | | 31.53 | 148.4 | 4.38 | 74-1 | 68.48 | 280.6 | 1.21 | | 28.36 | 148.2 | 3.96 | | 62.68 | 279.6 | 2.34 | 63-1 | 31.94 | 148.2 | 3.72 | | 50.43 | 274.5 | 2.50 | | 32.78 | 150.1 | 3.63 | | 40.33 | 281.5 | 1.37 | | 34.97 | 157.1 | 3.84 | 75-1 | 37.28 | 278.9 | -0.96 | | 39.12 | 157.7 | 3.85 | | 51.37 | 280.4 | -1.23 | 64-1 | 42.82 | 160.7 | 3.75 | | 60.49 | 282.7 | -0.09 | | 32.84 | 162.2 | 3.69 | | 67.14 | 286.8 | 0.78 | | 37.40 | 165.2 | 3.81 | 76-1 | 66.58 | 294.4 | 1.42 | | 46.10 | 166.6 | 3.90 | | 70.57 | 298.9 | 1.87 | 65-1 | 40.63 | 169.9 | 3.68 | | 64.94 | 299.0 | 2.54 | | 38.23 | 172.4 | 3.47 | | 63.81 | 299.0 | 2.88 | | 39.63 | 177.0 | 3.34 | 77-1 | 53.48 | 301.3 | 2.36 | | 40.38 | 179.0 | 3.28 | | 61.83 | 302.5 | 1.65 | 66-1 | 41.12 | 183.4 | 3.17 | | 61.79 | 304.9 | 0.71 |
Table 4.10 (Cont.) | | | | | | | | 77-4 | 59.81 | 307.9 | 0.54 | 80-3 | 41.39 | | 2.69 | 78-1 | 69.51 | 310.5 | 0.59 | | 40.57 | 332.6 | 4.97 | | 50.31 | 312.7 | 1.62 | 81-1 | 39.14 | 332.0 | 7.53 | | 55.22 | 318.4 | 2.28 | | 53.69 | 338.5 | 8.56 | | 53.05 | 318.9 | 4.00 | | 47.06 | 338.3 | 11.37 | 79-1 | 46.19 | 322.5 | 4.28 | | 33.87 | 335.5 | 8.00 | | 48.53 | 322.3 | 3.73 | 82-1 | 40.71 | 319.8 | 6.27 | | 48.29 | 324.6 | 3.85 | | 28.61 | 320.9 | 7.41 | | 49.24 | 328.1 | 5.85 | | 25.43 | 322.4 | 6.26 | 80-1 | 38.24 | 325.6 | 6.00 | | 32.20 | 316.6 | 3.12 | | 35.33 | 321.3 | 5.26 | | | | |
"T, year and quarter; HS, housing starts; y, gross national expenditures (in 1971 $); RR, estimated real interest rate. Source: R. Davidson and J. G. MacKinnon, "Testing Linear and Log-Linear Regressions Against Box-Cox Alternatives," Canadian Journal of Economics, August 1985, Table 5, pp. 515-516. Data on HS and have been rounded to four-digit numbers. Table 4.11 Wages, Benefits, Unemployment, and Net National Product: United Kingdom, 1920-1938 Year | Weekly Wages, W(s.) | Weekly Benefits, is.) | Unemployment Rate (%) | BenefitsI Wages | NNP, e° (£ million at 1938 factor cost) | 1920 | 73.8 | 11.3 | | 0.15 | 3426 | 1921 | 70.6 | 16.83 | 17.0 | 0.24 | 3242 | 1922 | 59.1 | 22.00 | 14.3 | 0.37 | 3384 | 1923 | 55.5 | 22.00 | 11.7 | 0.40 | 3514 | 1924 | 56.0 | 23.67 | 10.3 | 0.42 | 3622 | 1925 | 56.4 | 27.00 | 11.3 | 0.48 | 3840 | 1926 | 55.8 | 27.00 | 12.5 | . 0.48 | 3656 | 1927 | 56.2 | 27.00 | | 0.48 | 3937 | 1928 | 55.7 | 27.67 | 10.8 | 0.50 | 4003 | 1929 | 55.8 | 28.00 | 10.4 | 0.50 | 4097 | 1930 | 55.7 | 29.50 | 16.1 | 0.53 | 4082 | 1931 | 54.9 | 29.54 | 21.3 | 0.54 | 3832 | 1932 | 54.0 | 27.25 | 22.1 | 0.50 | 3828 | 1933 | 53.7 | 27.25 | 19.9 | 0.51 | 3899 | 1934 | 54.3 | 28.6 | 16.7 | 0.53 | 4196 | 1935 | 55.0 | 30.3 | 15.5 | 0.55 | 4365 | 1936 | 56.1 | 32.00 | 13.1 | 0.57 | 4498 | 1937 | 57.2 | 32.00 | 10.8 | 0.56 | 4665 | 1938 | 58.9 | 32.75 | 12.9 | 0.56 | 4807 |
°NNP, net national product; s., shilling =
Heteroskedasticity 5.1 Introduction 5.2 Detection of Heteroskedasticity 5.3 Consequences of Heteroskedasticity 5.4 Solutions to the Heteroskedasticity Problem 5.5 Heteroskedasticity and the Use of Deflators *5.6 Testing the Linear Versus Log-Linear Functional Form Summary Exercises Appendix to Chapter 5 5.1 Introduction One of the assumptions we have made until now is that the errors u, in the regression equation have a common variance cr. This is known as the homo-skedasticity assumption. If the errors do not have a constant variance we say they are heteroskedastic. There are sesveral questions we might want to ask if the errors do not have a constant variance. These are: 1. How do we detect this problem? 2. What are the consequences on the properties of the least squares estimators, and what are the consequences on the estimated standard errors if we use OLS? 3. What are the solutions to this problem?
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