Springer Texts in Business and Economics

The back up regressions are given below. These are performed using SAS

a. Dependent Variable: EMP

RootMSE 24.31555 R-square 0.9847

DepMean 587.94141 Adj R-sq 0.9845

C. V. 4.13571

Durbin-Watson D 0.349

(For Number of Obs.) 75

1st Order Autocorrelation 0.788

c. Dependent Variable: RESID

Analysis of Variance

Root MSE 13.44687 R-square 0.6711

DepMean -0.74410 Adj R-sq 0.6666

C. V. -1807.13964

COCHRANE-ORCUTT(1949) METHOD

Dependent Variable: EMP. STAR

Analysis of Variance

d. Prais-Winsten(1954, Yule-Walker) 2-Step Method

Autoreg Procedure Dependent Variable = EMP

Preliminary MSE = 229.5957
Estimates of the Autoregressive Parameters

Lag Coefficient Std Error t Ratio

1 -0.82006318 0.06697949 -12.243497

e. Breusch and Godfrey (1978) LM Test

Dependent Variable: RESID Residual

Analysis of Variance

SAS PROGRAM

Data ORANGE;

Input DATE EMP RGNP;

Cards;

Data ORANGE1; set ORANGE; RGNP_1=LAG(RGNP);

RGNP_2=LAG2(RGNP);

EMP_1=LAG(EMP);

Proc reg data=ORANGE1;

Model EMP=RGNP_1/DW; Output out=OUT1 R=RESID;

Data TEMP; setOUT1; RESID_1=LAG(RESID);

Proc reg data=TEMP;

Model RESID=RESID_1/noint; run;

***** COCHRANE-ORCUTT(1949) METHOD *****;

Data CODATA; set ORANGE1;

EMP_STAR=EMP-0.791403‘'*EMP_1; *** RHO=0.791403 ***;

RGNPSTAR=RGNP_1-0.791403‘'*RGNP_2;

C_STAR=1-0.791403;

Proc reg data=CO_DATA;

Model EMP_STAR=C_STAR RGNPSTAR/noint;

TITLE ‘COCHRANE-ORCUTT(1949) METHOD’;

***** PRAIS-WINSTEN (1954, YULE-WALKER) METHOD *****;

Proc autoreg data=ORANGE1;

Model EMP=RGNP/DW=1 DWPROB LAGDEP NLAG=1 METHOD=YW; TITLE ‘PRAIS-WINSTEN(1954, YULE-WALKER) 2-STEP METHOD’;

****BREUSCH & GODFREY (1978) LM TEST FOR AUTOCORRELATION***;

A**************************************************************************************.

Proc reg data=TEMP;

Model RESID=RESID_1 RGNP_1;

Title ‘BREUSCH AND GODFREY (1978) LM TEST’; run;

5.21 a. Replication of TABLE VIII, Wheeler(2003, p. 90) entitled: County popu­lation Growth Robustness Check. We will only replicate the first and last columns of that table for p = 1 and p = 5.

Forp = 1:

. reg dpopgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logpop, vce(r);

Linear regression Number of obs = 3102

F(9,3092) = 39.69

Prob > F = 0.0000

R-squared = 0.1275

RootMSE = .11041

The higher the proportion of the adult resident population (i. e. of age 25 or older) with a bachelor’s degree or more (collrate); and the higher the proportion of total employment in manufacturing (mfgrate) the higher the County population growth rate (over the period 1980-1990). The unem­ployment rate (ur) and Per capita income (pcinc) have the right sign but are not significant. The higher the share of local government expenditures going to education (educsh) and police protection (polsh), the higher the County population growth rate, whereas the higher the share of local gov­ernment expenditures going to roads and highways (hwsh), the lower is the County population growth rate. Except for (polsh), these local government expenditures shares are significant. The higher the proportion of the resident population that are non-white (nwrate), the lower is the County population growth rate. The larger the size of the county as measured by the log of total resident population (logpop), the higher is the County population growth rate. This is significant.

. test logpop=0;

(1) logpop = 0

F(1,3092) = 17.36 Prob > F = 0.0000

Adding a polynomial of degree 5 in size as measured by logpop, we get for p = 5:

. reg dpopgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logpop logpop2 logpop3 logpop4 logpop5, vce(r);

The results are similar to the p = 1 regression, but we lost the significance of mfgrate and hwsh. The joint test for the fifth degree polynomial in log - pop is significant, but the last term is not, suggesting that the fourth degree polynomial is a good place to stop.

. test (logpop = 0) (logpop2 = 0) (logpop3 = 0) (logpop4 = 0) (logpop5 = 0);

(1) logpop = 0

(2) logpop2 = 0

(3) logpop3 = 0

(4) logpop4 = 0

(5) 7 logpop5 = 0

F(5, 3088) = 25.88 Prob > F = 0.0000

. test logpop5 = 0;

(1) logpop5 = 0 F(1,3088) = 0.01

Prob > F = 0.9127

Replication of TABLE IX, Wheeler(2003, p. 91) entitled: County employ­ment Growth Robustness Check. We will only replicate the first and last columns of that table for p = 1 and p = 5.

For p=1:

. reg dempgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logemp, vce(r);

Linear regression Number of obs = 3102

F(9,3092) = 36.11

Prob > F = 0.0000

R-squared = 0.1108

Root MSE = .13223

The higher the proportion of the adult resident population (i. e. of age 25 or older) with a bachelor’s degree or more (collrate); and the higher the propor­tion of total employment in manufacturing (mfgrate) the higher the County employment growth rate (over the period 1980-1990). The unemployment rate (ur) and Per capita income (pcinc) are not significant. The higher the share of local government expenditures going to education (educsh) and police protection (polsh), the higher the County employment growth rate, whereas the higher the share of local government expenditures going to roads and highways (hwsh), the lower is the County employment growth rate. Except for (educsh), these local government expenditures shares are not significant. The higher the proportion of the resident population that are non-white (nwrate), the lower is the County educsh growth rate. The larger the size of the county as measured by the log of total resident educsh (logemp), the higher is the County employment growth rate. This is significant.

. test logemp = 0;

(1) logemp = 0 F(1,3092) = 7.05

Prob > F = 0.0080

Adding a polynomial of degree 5 in size as measured by logemp, we get for p = 5:

. reg dempgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logemp logemp2 logemp3 logemp4 logemp5, vce(r);

The results are similar to the p = 1 regression, but we lost the significance of mfgrate. The joint test for the fifth degree polynomial in logpop is signif­icant, but the last term is not, suggesting that the fourth degree polynomial is a good place to stop.

. test (logemp = 0) (logemp2 = 0) (logemp3 = 0) (logemp4 = 0) (logemp5 = 0);

(1) logemp = 0

(2) logemp2 = 0

(3) logemp3 = 0

(4) logemp4 = 0

(5) logemp5 = 0

F(5, 3088) = 18.27 Prob > F = 0.0000 . test logemp5 = 0;

(1) logemp5 = 0 F(1,3088) = 1.44

Prob > F = 0.2307

b. Breusch-Pagan test for heteroskedasticity for the specification with a fourth degree polynomial in log(size) in TABLE VIII, Wheeler(2003, p. 90).

. reg dpopgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logpop logpop2 logpop3 logpop4;

Source I SS df MS Number of obs = 3102

................................................................................ F(12,3089) = 48.43

Model 6.84020955 12 .570017462 Prob > F = 0.0000

Residual 36.3559406 3089 .011769485 R-squared = 0.1584

................................................................................ Adj R-squared = 0.1551

Total I 43.1961502 3101 .013929749 Root MSE = .10849

. estat hettest logpop logpop2 logpop3 logpop4, rhs normal;

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance

Variables: logpop logpop2 logpop3 logpop4 collrate mfgrate ur pcinc educsh hwsh polsh nwrate chi2(12) = 589.14 Prob > chi2 = 0.0000

Breusch-Pagan test for heteroskedasticity for the specification with a 4th degree polynomial in log(size) in TABLE IX, Wheeler(2003, p. 91).

. reg dempgr collrate mfgrate ur pcinc educsh hwsh polsh nwrate logemp logemp2 logemp3 logemp4 ;

3102

38.23

0.0000

0.1293

0.1259

.1309

. estat hettest logemp logemp2 logemp3 logemp4, rhs normal;

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance

Variables: logemp logemp2 logemp3 logemp4 collrate mfgrate ur pcinc educsh hwsh polsh nwrate chi2(12) = 425.82 Prob > chi2 = 0.0000

References

Baltagi, B. and Q. Li (1995), “ML Estimation of Linear Regression Model with AR(1) Errors and Two Observations,” Econometric Theory, Solution 93.3.2, 11: 641-642.

Johnston, J. (1984), Econometric Methods, 3rd. Ed., (McGraw-Hill: New York).

Kim, J. H. (1991), “The Heteroscedastic Consequences of an Arbitrary Variance for the Initial Disturbance of an AR(1) Model,” Econometric Theory, Solution 90.3.1, 7: 544-545.

Kmenta, J. (1986), Elements of Econometrics (Macmillan: New York).

Koning, R. H. (1992), “The Bias of the Standard Errors of OLS for an AR(1) Pro­cess with an Arbitrary Variance on the Initial Observations,” Econometric Theory, Solution 92.1.4, 9: 149-150.

CHAPTER 6