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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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