BE

Course: Basic Econometrics

Assignment

Question number: 1, 2, 3, 4

Student number: 1004993

Programme: MSc. in Financial Forecasting and Investment

02 December, 2010

UNIVERSITY OF GLASGOW

Business School

2

Department of Economics

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3

1. (i) Nominal Stock Returns (NSR):

To calculate the Nominal Stock Returns (NSR) of Alleghany Corporation, the below

mentioned formula is used as the data that has been used is in time series data on monthly

basis for the period of January 1980 to December 2009.

is the nominal stock price at time t, and is the nominal stock price at time t-1. It is

mentionable that without the data of previous month of January 1980, it is not possible to

generate the data for February 1980 as NSR shows the change between the two months. To

generate the nominal stock returns (NSR) with time series data, we have used MICROFIT

software. The formulas which have been used in generating the data are as follows:

LS = LOG (S)

DLS = LS – LS (-1)

NSR = DLS * 100

1. (ii) Growth Rate of Industrial Production (GIND):

To generate the growth rate of industrial production (GIND) of Alleghany Corporation, time

series data of level of industrial production (IP) on monthly basis for the period of 1980 to

December 2009 is used. To calculate the series the following formula has been used.

It should be stated that it wasn’t possible to figure out the data for GINP for January 1980 for

the same reason that has been discussed for the previous case. To generate the GIND series of

data, we have used MICROFIT software. The formulas which have been used in generating

the data are as below:

LIP = LOG (IP)

DLIP = LIP – LIP (-1)

GNIP = DLIP * 100

The sample data result for generating NSR and GIND are showed in table 1.

[ Table 1 ]

4

2. Properties of Dataset:

Table 2 represents the statistical measures of monthly nominal stock price (S) of Alleghany

Corporation, nominal short-term interest which is measured by the effective federal funds

rate (FED), the level of industrial production of U.S. (IP), nominal stock return (NSR) and

growth rate of industrial production (GIND) for twenty seven years starting from the year of

1980. Table 3 demonstrates the correlation between the independent and dependant variables

of the models.

[ Table 2]

Graph 1 illustrates the increasing or decreasing pattern of monthly nominal stock price (S) of

Alleghany Corporation, nominal short-term interest (FED), the level of industrial production

of U.S. (IP), nominal stock return (NSR) and growth rate of industrial production (GIND) for

the above mentioned periods.

Location:

Minimum, maximum, mean and median are the statistical measures which are used to know

the location of the given dataset of Alleghany Corporation.

Minimum and Maximum:

Minimum value of nominal stock price (S) of Alleghany Corporation for the period of

February 1880 to December 2009 is 4.8 where as the maximum value of S is 392.19. During

the same period, the maximum growth rate of industrial production (GNIP) is 2.1227%

For the period of February 1880 to December 2009, the maximum of nominal stock returns

(NSR) is 32.1244%.

Mean and Median:

For time series data mean or average do not affect that much in analyzing data. However,

mean of nominal stock price (S) of Alleghany Corporation is 112.90 during the period of

February 1880 to December 2009. After analyzing the dataset, we see that in the very

beginning of the sample period the nominal stock price is very lower than of mean. However,

from the Graph 1, we can say that the nominal stock price tends to increase more on monthly

basis though there is some huge fluctuation in few periods. This fluctuation may arise from

5

economical issues which will be discussed later in this report. Although short term interest

rate is one of the vital issues for this case, still the mean of short term interest rate of 6% do

not imply any consequences for this case.

[ Graph 1,2,3]

The monthly average nominal stock return (NSR) for the Alleghany Corporation is 1.02%.

As the mean is influenced by outliers like maximum and minimum values of NSR, it can be

said that this is not a robust statistical measure. On the other hand, median of NSR is 0.98%

which is less than mean, can reduce the importance to be attached with the outliers.

[ Graph 4]

The median of growth rate of industrial production is 0.209864% whereas the mean of GINP

is 0.1560% which is pretty closer to median. Although, the average growth rate is positive, it

is not as higher as it should have been.

[ Graph 5]

Dispersion:

Range, standard deviation, coefficient of variation and standard error are used to measure the

dispersion of the sample.

Range:

From the table: we can see that the range of S, FED, IP, NSR and GINP are 387.39, 18.98%,

54.1, 0.7724% and 0.0613% respectively. These values can be misleading as the maximum or

minimum values of the variables are turned out to be rare. Thus it does not represent the

entire distribution.

Standard Deviation:

Standard deviation of nominal short term interest rates is 3.7714 shows that the dispersion

from the average is quite low which indicates that the data points tend to be very close to the

mean. As the standard deviation of the FED is quite low, we can say that the rate is not

volatile. From the graph 2, it can be seen that the nominal interest rates is fall as time passes

6

though there is high and low fluctuation in few periods. However, these fluctuations are not

very high.

From the standard deviation of nominal stock returns we can analyze that return on the fund

hasn’t deviated that much that of the expected normal returns. Similarly, standard deviation

of GIND is 0.0071 interprets that though there is positive growth change, it hasn’t affected

the return that much.

Coefficient of Variation:

Nominal short term interest rates’ coefficient of variation of 0.6286 is comparatively lower

than of nominal stock returns of 5.8695. As the FED’s coefficient of variation is higher, it

represents that the risk-return trade off is not better. The higher the coefficient of variation,

the higher is the residuals to the predictive of value of the model and lower the coefficient of

variation the lower is the dispersion. Likewise, the coefficient of GIND is 4.5211.

Standard Error:

The standard error of nominal stock returns is 0.0032 shows that the sample mean has

deviated 0.3167% from the actual mean of the population. We know that standard error is

inversely proportional to the sample size. As the standard error is smaller; we can say that the

statistic has approached near to actual value due to large sample size.

The standard error of the growth rate of industrial production is 0.0004 represents that the

deviation between sample mean and actual mean of the population is only 0.0372. As the

standard error is so small, it shows more representative sample size.

Shape:

In order to know the shape of the curves following statistical measures are used:

Sample Variance:

One of the major dispersion measures is sample variance as it shows a set of data points

around their mean value. The variance of nominal short term interest rate, 14.2236 presents

the volatility of FED. Nominal stock return’s variance is 36.0212 which is quite volatile. On

the other hand the variance for GIND is 0.4971 which indicates the volatility of the GIND is

very lower compared to NSR.

7

Kurtosis:

The kurtosis measure is used to describe the distribution of observed data around the mean

which shows the volatility of volatility. The kurtosis of nominal stock price is very low that is

-0.206182.

If the kurtosis of FED is observed, it can be noticed that it is also quite low and is only

1.6965. Thus, it portrays a chart with skinny tails and a distribution concentrated toward the

mean. Hence, in the figure 1, it can be seen that the shape tends to have a flat top near the

mean rather than a sharp peak.

[ Figure 1]

On the other hand, the kurtosis of nominal stock returns shows a quite higher kurtosis than of

FED. Thus, it tends to have a distinct peak near the mean, decline rather rapidly and have

heavy tails. The histogram showed in figure 2 exhibits the same as discussed.

[ Figure 2]

The kurtosis of industrial production is -1.5170. However, contrary to IP kurtosis the kurtosis

of growth rate of industrial production is higher that is 4.2214.

[ Figure 3]

Skewness:

Skewness is used as a dispersion measure as statistical measure for this case as it describes

asymmetry from the probability distribution of a real valued random variable. The skewness

of FED is 1.0789 that shows a positive value. Hence, it indicates that the tail on right side is

lower than the left side and the bulk of the values lie to the left of the mean. Nominal stock

return’s skewness is -1.1232 which is negative and interprets that the tail on the left side of

the probability density function is longer than the right side and the bulk of the values lie to

the right of the mean. Likewise, the skewness for GIND is -0.935714 which shows negative

value.

8

Correlation between the Variables:

Table 3 shows the correlation between nominal stock price, nominal short term interest rate,

industrial production, nominal stock returns and growth rate of industrial production.

Correlation between nominal stock returns and FED is 0.0230, shows positive relationship.

Thus it can be interpreted as that both the variables move to the same direction. Similarly, the

correlation between NSR and GIND is 0.1082. This positive relation also implies that both

the variables move to same direction. However for both of the correlation, the relationship is

not very strong as both of the values are far from 1.

[Table 3]

Preliminary Analysis of Data:

Before OLS regression analysis, it is important to have preliminary analysis of the dataset.

Thus, to know the best fit for NSR and FED a scattered plot with the best possible regression

line has been created and is showed in graph 6.

[ Graph 6]

3. (i) Using the Ordinary Least Squares (OLS), we can estimate the below mentioned

regression model.

Model 1

In the regression model, nominal stock return (NSR) is dependent variable and nominal short-

term interest rate, measured by effective federal funds rate (FED) is independent variable. To

generate the result using OLS method, MICROFIT software has been used.

[ Figure: 4]

After running the regression, the following nominal stock returns equation is found:

From the equation it can be interpreted that over the monthly period February 1980 to

December 2009, there is positive relationship between nominal stock returns (NSR) and

nominal short term interest rate (FED) as the slope coefficient ( is positive. It interprets

9

that if the nominal short term interest rate goes up by 1%, on average, nominal stock returns

increases by about 0.0366%. Moreover, the value of constant ( indicates that if nominal

short term interest rate is zero, the average nominal stock returns will be about 0.8029%.

From the figure 4, it can be observed that the R2 value is 0.0005290 which is very low and

interprets that only 0.0529% of the variation of nominal stock returns can be explained by

nominal short term interest rate.

3 (ii) To determine whether the estimated slope coefficient ( is significantly

different from zero at the 5% level of significance either through confidence interval

approach or t-test approach, the following hypothesis has been tested at the earlier mentioned

significance level.

Null Hypothesis, : = 0

Alternative Hypothesis, : ≠ 0

From table 1.1, the following data can be observed:

Slope coefficient of FED, = 0.0366

Standard error of FED, =0.0842

Degrees of freedom, df = n-k = 359-2 = 357

Level of Significance, α = 5 %

Confidence Interval Approach:

The confidence interval for 2 can be measured as follows:

2 tα/2

From the t-table (Appendix D, table D.2, Gujarati) it can be found that for 357 degrees of

freedom: tα/2 = t0.05/2 = 1.960. Hence, we can attain the outcome by substituting all the known

values that the 100(1- α) % or 95% confidence interval for 2 is:

2 tα/2 = 0.0366 1.960 (0.0842)

= [ -0.1284, 0.2016 ]

10

Given the confidence coefficient of 95%, in the long run, intervals like (-0.1284, 0.2016)

contains the true value of since 2 under the null hypothesis is zero and it lies within the

confidence interval, we do not reject the null hypothesis at the 5% level of significance.

Therefore, 2 is not statistically different from zero and the finding is not statistically

significant.

t-test Approach:

The t- statistic value can be obtained from figure 4. The following equation also be used to

calculate the t-statistic:

t-statistic, t =

= 0.4347

Critical t- value, = tn-k,α/2

= t357, 0.05/2

=1.960

As, |t| = 0. 4347 < tn-k,α/2 = 1.960, we do not reject the null at the 5% level of significance.

Thus 2 is not statistically different from zero.

Using both the confidence interval approach and t-test approach to test whether the estimate

for 2 is significantly different from zero at the 5% level of significance, same result has been

achieved that is 2 is not statistically different from zero.

3 (iii) As shown in Figure 5, during the period of February 1980 to July 2007, the

constant coefficient ( ) is 1.3900 and slope coefficient of FED (

) is -0.0253.

[ Figure 5 ]

The value of constant indicates that the average value of nominal stock returns is about

1.3900% when the nominal short term interest rate is zero. Moreover, the coefficient of FED

is negative which interprets that when the nominal short term returns increases, the stock

returns decreases, which seem to be a normal phenomenon. When short term interest rate

increases people tend to invest in FED as its risk free. Hence, if nothing else changes, the

stock price tend to drop as the required return is higher. Thus, during the period of February

1980 to July 2007, growth of 1% in FED creates a drop of 0.0253% in nominal stock returns.

11

[ Graph 7, 8 ]

For the period of August 2007 to December 2009, using OLS method it can be seen in the

figure 6 that the constant value coefficient ( ) is -0.9014 and slope coefficient of FED (

) is

-0.2504.

[ Figure 6 ]

can be interpreted as like that if the nominal short term interest rate is zero, nominal stock

returns is -0.9014%. So, it shows that if FED is zero, nominal stock return will be negative.

The slope coefficient of FED for this sub sample model indicates that similar relationship like

previous sub sample model. It indicates 1% increase in FED influences nominal stock returns

to decrease by 0.2504%.

[ Table 4 ]

The correlation between NSR and FED for the period of February 1980- July 2007 is -0.0159

which also indicates that there is negative relationship between NSR and FED. However, the

relationship is not perfectly correlated as it varies from -1. However, when the graph is

observed for the mentioned period it’s been seen that the relationship between the NSR and

FED is not exact as at several points NSR and FED haven’t shown negative relationship.

Moreover, the correlation between NSR and FED during the period of August 2007-

December 2009 is - 0.06057. Likewise the other sub period model, NSR and FED has negative

relationship.

Here, p-value is being used to know whether the null hypothesis would be rejected. If the p-

value associated with the estimate of is evaluated, it can be noticed that p-value is 0.774

which is higher than 0.05 that is level of significance. The higher the p-value, the stronger the

evidence is in favour of the null hypothesis. Thus for the model 1, we do not reject the null at

the 5% level of significance.

If the p-value related with is considered, it can be observed that p-value is 0.755 which is

higher than 0.05 (level of significance). Similarly, for this sub period model, we do not reject

the null at the 5% level of significance.

The R2

of 0.0002519 for the first sub period model indicates that only 0.0252% of the

variation of NSR can be explained by FED. On the other hand, the R2

of 0.0037 for the

12

second sub period model, it interprets as only 0.37% of the variation of the NSR can be

explained by FED. Thus, it can be said that both the model do not have best fitness as the R2

is very lower.

From the above mentioned analysis, it can be said that the recent financial crisis hasn’t

affected that much into the relationship between stock returns and interest rates of Alleghany

Corporation though from their last few years annual report, they have used the recession

period as one of the key indicator for risk in their Financial Report of recent few years.

4. (i) Using the Ordinary Least Squares (OLS), we can estimate the below mentioned

regression model.

NSRt = ß1 + ß2 FED t + ß3 GINDt + μt Model 2

In the regression model, nominal stock returns (NSR) is dependent variable and nominal

short-term interest rate, measured by effective federal funds rate (FED) and growth rate of

industrial production (GIND) are the independent variables. To generate the result using OLS

method, MICROFIT software has been used.

[ Figure: 7]

After running the regression, the following nominal stock returns equation is found:

From the equation it can be interpreted that over the monthly period February 1980 to

December 2009, there is positive relationship between nominal stock returns (NSR) and

nominal short term interest rate (FED) and growth rate of industrial production as the slope

coefficients (ß2,ß3) are positive. The intercept (ß1) of 0.5654 shows that if nominal short term

interest rate and growth rate of industrial product is kept zero, the average nominal stock is

about 0.5654 %. The slope coefficient of FED (ß2) of 0.0516 interprets that if the intercept

and the other slope coefficient is kept zero, a growth of 1% in FED increases the nominal

stock returns by about 0.0516%. Likewise, the slope coefficient of GIND (ß3) of 0.9447

indicates an increase in growth rate of industrial production by 1% increases the nominal

stock returns by 0.9447% while FED and intercept is zero.

13

In order to know the fit of the models mentioned earlier, R2 value is used. In model 1, R

2 is

0.0005290. It shows that 0.0529% of the variation of nominal stock returns can be explained

by independent variable of FED.

On the other hand in model 2, R2, 0.012758 shows a better position than of model 2 as the R

2

is higher in model 2. It interprets that about 1.2758 % of the variation of nominal stock

returns can be explained by the control variables, nominal short term interest rate and growth

rate of industrial production. As the model 2’s R2

is closer to 1, it can be said that

4 (ii) In order to test joint hypothesis, F-statistic is being used and the following

hypothesis has been considered at α = 5%.

Null Hypothesis, :

Alternative Hypothesis, : Not all slope coefficients are simultaneously zero

Figure 7 shows that the value of the F-statistic is 2.3003 for model 2. To know the critical F-

value, (Appendix D, table D.3, Gujarati) is used.

Critical F- value, = F α (k-1, n-k)

= F 0.05(3-1,359-3)

= F 0.05(2,356)

= 3.00

As F-statistic (2.3003) < F-critical (3.00), we do not reject null hypothesis at 5% level of

significance.

Comments:

If any of the dependent or independent variables data is non-stationary for the provided

dataset of Alleghany Corporation, then the results may not be valid at all. If both are non-

stationary, then sometimes the result may be valid (when they are co-integrated), and other

times the result will not be valid. Thus, it’s been assumed that the data is stationary. As the

dataset is time series data autoregressive or moving average nature of the errors should have

been considered. However, it should be considered as a limitation of the report.

14

Tables, Graphs and Figures

Table 1: Generating Data of NSR and GIND D

ate

Nom

inal

Sto

ck

Pric

e of

All

egh

an

y C

orp

, S

Nom

inal

Sh

ort

Term

Inte

rest

Rate

, m

easu

red

by F

ED

, F

ED

Ind

ust

ria

l P

rod

ucti

on

,

IP

LS

=L

OG

(S)

LIP

=L

OG

(IP

)

DL

S=

LS

-LS

(-1)

DL

IP=

LIP

-LIP

(-1)

NS

R=

DL

S*100

GIN

D=

DL

IP*100

31-Jan-80 6.75 13.82 51.7 1.9095 3.9455 *NONE* *NONE* *NONE* *NONE*

29-Feb-80 6.68 14.13 51.5 1.8991 3.9416 -0.0104 -0.0039 -1.0425 -0.3876

31-Mar-80 5.51 17.19 50.5 1.7066 3.9220 -0.1926 -0.0196 -19.2553 -1.9608

30-Apr-80 4.8 17.61 49.2 1.5686 3.8959 -0.1379 -0.0261 -13.7949 -2.6080

30-May-80 5.04 10.98 48.6 1.6174 3.8836 0.0488 -0.0123 4.8790 -1.2270

30-Jun-80 5.97 9.47 48.3 1.7867 3.8774 0.1693 -0.0062 16.9341 -0.6192

31-Jul-80 6.39 9.03 48.5 1.8547 3.8816 0.0680 0.0041 6.7987 0.4132

29-Aug-80 6.49 9.61 49.2 1.8703 3.8959 0.0155 0.0143 1.5528 1.4330

Table 2: Statistical Measures of Dataset, February 1980- December 2009

Sample Period February 1980 to December 2009

Variables Nominal Stock

Price (S)

Nominal

Short-term

Interest Rate

(FED)

Level of

Industrial

Production

(IP)

Nominal

Stock

Returns

(NSR)

Growth Rate

of Industrial

Production

(GIND)

Loca

tion

Minimum 4.800000 0.120000 46.600000 -45.110111 -4.004750

Maximum 392.190000 19.100000 100.700000 32.124404 2.122721

Mean 112.901365 6.000084 73.169638 1.022536 0.155959

Median 68.260000 5.490000 70.900000 0.980157 0.209864

Dis

per

sion

Range 387.390000 18.980000 54.100000 77.234515 6.127471

Standard Deviation 102.012220 3.771415 17.120715 6.001772 0.705099

Coefficient of

variation 0.903550 0.628560 0.233990 5.869500 4.521100

Standard Error 5.383999 0.199048 0.903597 0.316761 0.037214

Shap

e

Sample Variance 10406.492967 14.223572 293.118880 36.021269 0.497164

Kurtosis -0.206182 1.696520 -1.517082 12.570468 4.221496

Skewness 0.911173 1.078916 0.071637 -1.123147 -0.935714

15

Table 3: Correlation between the Variables, February 1980- December 2009

S FED IP NSR GIND

S 1.0000 -0.6252 0.9234 -0.0458 -0.0916

FED -0.6252 1.0000 -0.7081 0.0230 -0.0851

IP 0.9234 -0.7081 1.0000 -0.0692 -0.0347

NSR -0.0458 0.0230 -0.0692 1.0000 0.1082

GIND -0.0916 -0.0851 -0.0347 0.1082 1.0000

Table 4: Correlation between NSR and FED

Period of February 1980- July 2007 -0.01587

Period of August 2007- December 2009 -0.06057

16

Graph 1: Changes in Stock Price of Alleghany Corporation (S), February 1980-

December 2009

Graph 2: Changes in Nominal Short-term Interest Rate, Measured by Effective Federal

Fund Rate (FED), February 1980- December 2009

0

50

100

150

200

250

300

350

400

450

Pri

ce in

Do

llars

Month

0

5

10

15

20

25

Rat

es in

Pe

rcen

tage

Date

17

Graph 3: Changes in Level of Industrial Production (IP), February 1980- December

2009

Graph 4: Changes in Nominal Stock Returns, February 1980- December 2009

0

20

40

60

80

100

120

Un

it

Month

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

Rat

es in

Per

cen

tage

Month

18

Graph 5: Changes in Growth Rate of Industrial Production, February 1980- December

2009

Graph 6: Pre Analysis of Dataset

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

Rat

es

in P

erc

en

tage

Months

19

Graph 7: Relationship between Nominal Short Term Interest Rate (FED) and Nominal

Stock Returns (NSR), February 1980- July 2007

Graph 8: Relationship between Nominal Short Term Interest Rate (FED) and Nominal

Stock Returns (NSR), August 2007- December 2009

-50

-40

-30

-20

-10

0

10

20

30

40

Rat

es

in P

erc

en

tage

MonthFED NSR

-25

-20

-15

-10

-5

0

5

10

15

20

Rat

es in

Pe

rcen

tage

Month

FED NSR

20

Figure 1: Histogram of Nominal Short Term Interest Rate (FED)

Figure 2: Histogram of Nominal Stock Return (NSR)

Figure 3: Histogram of Growth Rate of Industrial Production (GIND)

21

Figure 4: OLS Estimation Output of Model 1 from MICROFIT, February 1980-

December 2009

Ordinary Least Squares Estimation

*************************************************************************

Dependent variable is NSR

359 observations used for estimation from 1980M2 to 2009M12

*************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]

CON .80292 .59650 1.3460[.179]

FED .036602 .084203 .43469[.664]

*************************************************************************

R-Squared .5290E-3 R-Bar-Squared -.0022706

S.E. of Regression 6.0086 F-stat. F(1, 357) .18896[.664]

Mean of Dependent Variable 1.0225 S.D. of Dependent Variable 6.0018

Residual Sum of Squares 12888.8 Equation Log-likelihood -1152.2

Akaike Info. Criterion -1154.2 Schwarz Bayesian Criterion -1158.0

DW-statistic 1.8629

*************************************************************************

Diagnostic Tests

*************************************************************************

* Test Statistics * LM Version * F Version *

*************************************************************************

* * * *

* A:Serial Correlation * CHSQ (12) = 21.6980 [.041] * F (12, 345) = 1.8494 [.040]*

* * * *

* B:Functional Form * CHSQ ( 1) = 4.1061 [.043] * F (1, 356) = 4.1189 [.043]*

* * * *

* C:Normality * CHSQ ( 2) = 2370.6 [.000] * Not applicable *

* * * *

* D:Heteroscedasticity * CHSQ ( 1) = 4.6779 [.031] * F (1, 357) = 4.7133 [.031]*

*************************************************************************

A:Lagrange multiplier test of residual serial correlation

B:Ramsey's RESET test using the square of the fitted values

C:Based on a test of skewness and kurtosis of residuals

D:Based on the regression of squared residuals on squared fitted values

22

Figure 5: OLS Estimation Output for sub period of Model 1 from MICROFIT,

February 1980- July 2007


*************************************************************************


330 observations used for estimation from February 1980 to July 2007

*************************************************************************


CON 1.3900 .64804 2.1450[.033]

FED -.025330 .088116 -.28747[.774]

*************************************************************************

R-Squared .2519E-3 R-Bar-Squared -.0027961

S.E. of Regression 5.8548 F-stat. F(1, 328) .082637[.774]




DW-statistic 1.8408

*************************************************************************

Diagnostic Tests

*************************************************************************


*************************************************************************

* * * *


* * * *

* B:Functional Form * CHSQ ( 1) = 2.4985 [.114] * F ( 1, 327) = 2.4947 [.115]*

* * * *


* * * *

* D:Heteroscedasticity * CHSQ ( 1) = 6.4078 [.011] * F ( 1, 328) = 6.4950 [.011]*

*************************************************************************





23

Figure 6: OLS Estimation Output for sub period of Model 1 from MICROFIT, August

2007- December 2009


*************************************************************************


29 observations used for estimation from August 2007 to December

2009

*************************************************************************


CON -.90141 1.9086 -.47228[.641]

FED -.25039 .79411 -.31531[.755]

*************************************************************************

R-Squared .0036688 R-Bar-Squared -.033232

S.E. of Regression 7.3806 F-stat. F (1, 27) .099423 [.755]

Mean of Dependent Variable -1.3203 S.D. of Dependent Variable 7.2609



DW-statistic 2.2076

*************************************************************************

Diagnostic Tests

*************************************************************************


*************************************************************************

* * * *

* A:Serial Correlation * CHSQ (12) = 11.8369 [.459] * F (12,15) = .86209 [.597]*

* * * *

* B:Functional Form * CHSQ ( 1) = .61686 [.432] * F (1, 26) = .56506 [.459]*

* * * *


* * * *

* D:Heteroscedasticity * CHSQ ( 1) = .93275 [.334] * F (1, 27) = .89728 [.352]*

*************************************************************************





24

Figure 7: OLS Estimation Output of Model 1 from MICROFIT, February 1980- July

2007


**************************************************************************


359 observations used for estimation from February 1980 to December 2009

**************************************************************************


CON .56537 .60436 .93549[.350]

FED .051637 .084109 .61393[.540]

GIND .94473 .44988 2.1000[.036]

**************************************************************************

R-Squared .012758 R-Bar-Squared .0072119

S.E. of Regression 5.9801 F-stat. F (2, 356) 2.3003[.102]


Residual Sum of Squares 12731.1 Equation Log-likelihood 1149.9

Akaike Info. Criterion -1152.9 Schwarz Bayesian Criterion 1158.8

DW-statistic 1.9038

**************************************************************************

Diagnostic Tests

**************************************************************************

* Test Statistics * LM Version * F Version

*

**************************************************************************

* * * *


* * * *

* B:Functional Form * CHSQ ( 1) = .40058 [.527] * F ( 1, 355) = .39655 [.529]*

* * * *


* * * *

* D:Heteroscedasticity * CHSQ ( 1) = 4.8716 [.027] * F ( 1, 357) = 4.9111 [.027]*

**************************************************************************





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