Bridging the Texas GDP Gap, Estimation Details - Southwest Economy, May/June 2007

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Southwest Economy

Issue 3, May/June 2007
Federal Reserve Bank of Dallas

Bridging the Texas GDP Gap
Estimation Details

Table 1

Descriptive Statistics
(First differences of quarterly data, 1980–2005)

	Real State GDP	Final Payroll Employment	Household Employment	Real Earnings
Mean	4852.8	39.7	42.6	2914.3
Median	4520.4	46.6	44.6	2864.5
Std. Dev.	4882.4	43.3	20.0	4010.5
Normalized Std. Dev.	100.6	109.0	47.0	137.6

Table 2

Estimation Strategies for Real State GDP

	Most Recent Quarter	First Quarter	Second Quarter	Third Quarter	Fourth Quarter
July	emp: 0–n lags earn: 1–n lags GDP: 2–n lags	emp: 0–n lags earn: 0–n lags GDP: 1–n lags
October	emp: 0–n lags earn: 1–n lags GDP: 3–n lags	emp: 0–n lags earn: 0–n lags GDP: 1–n lags	emp: 0–n lags earn: 0–n lags GDP: 2–n lags
January	emp: 0–n lags earn: 1–n lags GDP: 4–n lags	emp: 0–n lags earn: 0–n lags GDP: 1–n lags	emp: 0–n lags earn: 0–n lags GDP: 2–n lags	emp: 0–n lags earn: 0–n lags GDP: 3–n lags
April	emp: 0–n lags earn: 1–n lags GDP: 5–n lags	emp: 0–n lags earn: 0–n lags GDP: 1–n lags	emp: 0–n lags earn: 0–n lags GDP: 2–n lags	emp: 0–n lags earn: 0–n lags GDP: 3–n lags	emp: 0–n lags earn: 0–n lags GDP: 4–n lags

We conduct all econometric analysis in first differences because augmented Dickey–Fuller tests show all the series are difference stationary. We use a cointegrating term between real state GDP and real earnings because the Johansen procedures show the two series to be cointegrated.

Table 3A

Bivariate Tests to Project Real State GDP
(July: most recent quarter)

	Model 1	Model 2	Model 3
Payroll Employment	.0056**
Household Employment		.0004**
Real Earnings			.0255*
Real State GDP	.0014**	.0000**	.2106
Optimal Lags	10	10	2
	R² = .50 adj R² = .37	R² = .54 adj R² = .43	R² = .27 adj R² = .24

Table 3B

Multivariate Tests to Project Real State GDP
(July: most recent quarter)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.4625	.0052**		.3702
Household Employment	.1162		.0010**	.1931
Real Earnings		.1257	.1909	.1456
Real State GDP	.0017**	.1278	.4900	.2282
Optimal Lags	9	10	9	10
	R² = .57 adj R² = .40	R² = .59 adj R² = .41	R² = .59 adj R² = .43	R² = .68 adj R² = .45

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 1–n lags for real earnings and 2–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 4A

Bivariate Tests to Project Real State GDP
(October: most recent quarter)

	Model 1	Model 2	Model 3
Payroll Employment	.0001**
Household Employment		.0000**
Real Earnings			.0000**
Real State GDP	.0132*	.0001**	—^H
Optimal Lags	9	10	2
	R² = .44 adj R² = .32	R² = .51 adj R² = .39	R² = .21 adj R² = .20

Table 4B

Multivariate Tests to Project Real State GDP
(October: most recent quarter)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.3736	.0031**		.2619
Household Employment	.0572⁺		.0005**	.1631
Real Earnings		.0088**	.0736⁺	.0518⁺
Real State GDP	.0026**	—^H	.4030	.2029
Optimal Lags	9	2	9	10
	R² = .55 adj R² = .39	R² = .31 adj R² = .28	R² = .59 adj R² = .43	R² = .68 adj R² = .45

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 1–n lags for real earnings and 3–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 5A

Bivariate Tests to Project Real State GDP
(January: most recent quarter)

	Model 1	Model 2	Model 3
Payroll Employment	.0001**
Household Employment		.0000**
Real Earnings			.0000**
Real State GDP	.0067**	.0000**	—^H
Optimal Lags	9	10	2
	R² = .44 adj R² = .33	R² = .50 adj R² = .40	R2 = .21 adj R² = .20

Table 5B

Multivariate Tests to Project Real State GDP
(January: most recent quarter)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.3627	.0031**		.3430
Household Employment	.0535⁺		.0005**	.0893⁺
Real Earnings		.0088**	.0856⁺	.0851⁺
Real State GDP	.0012**	—^H	.3295	.3922
Optimal Lags	9	2	9	9
	R² = .55 adj R² = .40	R² = .32 adj R² = .28	R² = .58 adj R² = .43	R² = .65 adj R² = .45

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 1–n lags for real earnings and 4–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 6A

Bivariate Tests to Project Real State GDP
(April: most recent quarter)

	Model 1	Model 2	Model 3
Payroll Employment	.0000**
Household Employment		.0000**
Real Earnings			.0000**
Real State GDP	.0045**	.0000**	—^H
Optimal Lags	9	10	2
	R² = .43 adj R² = .33	R² = .50 adj R² = .40	R² = .21 adj R² = .20

Table 6B

Multivariate Tests to Project Real State GDP
(April: most recent quarter)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.3865	.0014**		.2935
Household Employment	.0547⁺		.0005**	.1051
Real Earnings		.0279*	.0822⁺	.0680⁺
Real State GDP	.0008**	.0844⁺	.2867	.2430
Optimal Lags	9	10	9	9
	R² = .54 adj R² = .40	R² = .59 adj R² = .42	R² = .58 adj R² = .44	R² = .65 adj R² = .45

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 1–n lags for real earnings and 5–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 7A

Bivariate Tests to Project Real State GDP
(First quarter—employment and earnings are contemporaneous)

	Model 1	Model 2	Model 3
Payroll Employment	.0267*
Household Employment		.0022**
Real Earnings			.0000**
Real State GDP	.0027**	.0000**	—^H
Optimal Lags	10	10	0
	R² = .50 adj R² = .37	R² = .54 adj R² = .42	R² = .50 adj R² = .50

Table 7B

Multivariate Tests to Project Real State GDP
(First quarter—employment and earnings are contemporaneous)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.5418	.1026		.9831
Household Employment	.1237		.0071**	.0330*
Real Earnings		.0000**	.0000**	.0000**
Real State GDP	.0034**	—^H	—^H	—^H
Optimal Lags	9	0	0	0
	R² = .57 adj R² = .40	R² = .52 adj R² = .51	R² = .54 adj R² = .53	R² = .54 adj R² = .53

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 0–n lags for real earnings and 1–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 8A

Bivariate Tests to Project Real State GDP
(Second quarter—employment and earnings are contemporaneous)

	Model 1	Model 2	Model 3
Payroll Employment	.0029**
Household Employment		.0001**
Real Earnings			.0000**
Real State GDP	.0028**	.0000**	—^H
Optimal Lags	9	10	1
	R² = .47 adj R² = .36	R² = .56 adj R² = .45	R² = .53 adj R² = .52

Table 8B

Multvariate Tests to Project Real State GDP
(Second quarter—employment and earnings are contemporaneous)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.4625	.1026		.9831
Household Employment	.1162		.0071**	.0330*
Real Earnings		.0000**	.0000**	.0000**
Real State GDP	.0017**	—^H	—^H	—^H
Optimal Lags	9	0	0	0
	R² = .57 adj R² = .40	R² = .52 adj R² = .51	R² = .54 adj R² = .53	R² = .54 adj R² = .53

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 0–n lags for real earnings and 2–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 9A

Bivariate Tests to Project Real State GDP
(Third quarter—employment and earnings are contemporaneous)

	Model 1	Model 2	Model 3
Payroll Employment	.0001**
Household Employment		.0000**
Real Earnings			.0000**
Real State GDP	.0132*	.0001**	—^H
Optimal Lags	9	10	0
	R² = .44 adj R² = .32	R² = .51 adj R² = .39	R² = .50 adj R² = .50

Table 9B

Multvariate Tests to Project Real State GDP
(Third quarter—employment and earnings are contemporaneous)

	Model 4	Model 5	Model 6	Model 7
Payroll Employment	.3736	.1026		.9831
Household Employment	.0572⁺		.0071**	.0330*
Real Earnings		.0000**	.0000**	.0000**
Real State GDP	.0026**	—^H	—^H	—^H
Optimal Lags	9	0	0	0
	R² = .55 adj R² = .39	R² = .52 adj R² = .51	R² = .54 adj R² = .53	R² = .54 adj R² = .53

NOTE: Tests are conducted in first differences, using 0–n lags for employment, 0–n lags for real earnings and 3–n lags for real Texas GDP. Optimal lag length is determined by the Akaike information criterion. ^HFor an optimal lag length less than or equal to the number of quarters ahead, lagged values of the real state GDP variable are omitted. Reported values are jointly significant, with ⁺significant at better than 10 percent, *significant at better than 5 percent and **significant at better than 1 percent.

Table 10A

Bivariate Tests to Project Real State GDP
(Fourth quarter—employment and earnings are contemporaneous)