Unemployment Rate 3

8/14/2019 Unemployment Rate 3

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Statement of the Problem

This paper studies the relationship between hourly compensation in manufacturing

and unemployment rate in the United States, Canada and the United Kingdom. Since each

country provides only 20 observations, the parameters from the regression may not be valid.

I further study whether the method of pooling data can be applied to this case by using

dummy variable technique to test the difference of intercepts and slopes in each country.

Literature Review

In Branson (1989), the compensation should negatively correlated withunemployment rate because if (inns pay more compensation, labors will have more

incentive to continue working, so unemployment rate is low. But when firms reduce

compensation for labors, unemployment rate will be higher because labors have little

incentive continuing their jobs.

Formulation of General Model:

The linear regression model is set as follows

Yit = 1+ 2 Xit+ Uit (1)

Where Y;t is civilian unemployment rate, and X; t is manufacturing hourly compensat ion

in U.S. dollars (index, 1992 = 100). i denotes country-the United States, Canada and

the United Kingdom and t denotes time period. In this case, i = 3 and t = 20.

Data Sources and Description

I used an annual data from 1980 to 1999 of the United States, Canada and the

United Kingdom. There are 20 observations for each country, so 60 observations in total.

Unemployment Rate and Compensation

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Table 1. Descriptive Statistics


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The data was from Gujarati 2002 (See Appendix) and its descriptive statistics is presented

in here

Histogram and Stats


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Fig: 2: Compensation in UK

Fig:1: Compensation in Canada


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Fig:3: Compensation in USA

Fig:4: Unemployment in Canada


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Fig:5: Unemployment in UK

Fig:6: Unemployment in USA


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Fi :4: Unem lo ment in USA

Graph1. Compensation in Canada


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Graph :2: Compensation in UK


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Graph :5: Unemployment in UK

Graph :6: Unemployment in USA


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Chat 1. Compensation in Canada

Chat :2: Compensation in UK


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Chat 3: Compensation in USA

Chat :4: Unemployment in Canada


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Chat :5: Unemployment in UK

Chat :6: Unemployment in USA


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Model Estimation and Hypothesis Testing

The usual OLS was assigned to estimate equation (1) and 60 observations are

pooled disregarding the space and time dimensions. The results are as follows

= 12.439 - 0.053X (2)

Se (0.818) (0.010)

t (15.202) (-5.424)Rz = 0.3366, d = 0.4806

n=60, df=58


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Clearly, compensation is negatively correlated with unemployment rate as

expected and t statistic is statistically significant but RZ value is quite low. Also

Durbin-Watso n statistic suggests that perhaps there is autocorrelatio n in the data. However`,

there are highly restricted assumption in equation (1) because the differences across each

country's data, such as intercept and slope, are not considered. So, the regression results in

(2) may not capture the different characteristics between the cross-sectional unit. If this is to

be the case, maybe each country's data cannot be pooled


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Table 2. Least Squares Regressions Results

Table 3 ML-ARCHRegressions Results


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One way to take into account the individuality of each country is to let the

intercept and slope coefficients vary across countries. So the fixed effects model (FEM) is

set by using dummy variables as in equation (3) to test whether the intercepts and slope

Cefficients are statistically different.

Yit = 1+ 2D2i+ 3D3i Xit+ 1(D2i Xit)+ 2(D3i Xit)+ Uit (3)

Where D2i = 1 if the observation belongs to Canada, 0 otherwise and D 3i = 1 if the

observation belongs to the United Kingdom, 0 otherwise. Therefore, the United States is

the comparison country. The results of estimating equation (3) are as follows

= 11.524-- 2.181 D2i + 1.029D3i -0.056X;tt + 0.049(D2i Xit)+ 0.009(D3i Xit) (4)

se 1.510 2.173 1.778 0.016 0.025 0.020t (7.627) (-1.004) (0.578) (-3.400) (1.951) (0.463)


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R2 = 0.5582, d = O.6764n = 60, df = 54


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As you can see from the model above, all t statistics of the dummy variables added are

not statistically significant at( 0.05) level of significance suggesting that, the intercepts and

slope coefficients of Canada and the/ United Kingdom are not statistically different

from the United States.

If the comparison country is changed, regression model (3) will yield different

results. Let D2i = 1 if the observation belongs to the United States, 0 otherwise and D3i

= I if the observation belongs to the United

Kingdom

, 0 otherwise; i.e. Canada is a


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Y= 9.342 - 2.181 D2i + 3.211D3 - 0.006X;t- 0.049(D2i Xit) - 0.040(D3i Xit) (5)se (1.561) (2.173) (1.82 (0.019) 0.025) (0.022)

t (5.981) (1.004) (1.76 (-0.341) -0.463) (-1.758)R'= 0.5582, d = 0.6764n = 60, df = 54

Graph :7. Residual, Actual, Fitted


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Then let D2i = 1 if the observation belongs to the United States, 0 otherwise and D3;

-1 if the observation belongs to Canada, 0 otherwise; i.e. the United Kingdom is a

comparison country, the estimation is as follows

Y= 12.554 1.029D2i - 3.211D3i - 0.046Xit - 0.009(D2i Xit t) + 0.040(D3i Xit) (6)se (0.938) (1.778) (1.822) (0.012) (0.020) (0.022)t (-0.578) (-1.762) (-3.847) (-0.463) (1.758)

R2 = 0.5582, d = 0.6764

n = 60, df = 54


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Graph: 8. Pooled Result


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All t statistics for dummy variables in both (5) and (6) are statistically insignificant

as in model (4). It can be concluded that the intercepts and slopes of the three countries

are not statistically different suggesting that they can be pooled. However, the RZ value

from model (2) is very low compared with model (4). To do a formal test whether

model (4) is better, F statistic is calculated as follows

(R2UR-R2R)/q (0 .5582-0.336)/4

F = = =6.771 (7)(1-R2UR)/n-k (1-0.5582)/54

Where q is the number of parameter restrictions. The critical value of F with 4 numerator

df and 54 denominator df is 3.16, so F= 6.7713 exceeds the critical value. This proves that


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Fig:7. Pooled Result


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Appendix

Unenrplolvuent rate (UNEM) and hourly compensation in manufacturing (COMP) in the UnitedStates, Canada and the United Kingdom, 1980-1999

Obs UNEM? COMP?

-US-1980 7.100000 55.600000

-US-1981 7.600000 61.100000

-US-1982 9.700000 6700000

-US-1983 9.600000 68.800000

-US-1984 7.500000 71.200000

-US-1985 7.200000 75.100000

-US-1986 700000 78.500000

-US-1987 6.200000 80.700000

-US-1 988 5.500000 8400000

-US-1989 5.300000 86.600000

-US-1990 5.600000 90.800000

-US-1 991 6.800000 95.600000

-US-1992 7.500000 10000000

-US-1993 6.900000 102.700000

-US-1994 6.100000 105.600000

-US-1995 5.600000 107.900000

-US-1996 5.400000 109.300000

-US-1997 4.900000 111.400000

-US-1998 4.500000 117.300000

-US-1 999 4.000000 123.200000

CAN-1980 7.200000 4900000

-CAN-1981 7.300000 54.100000

-CAN-1982 10.60000 59.60000

-CAN-1983 11.500000 63.900000

-CAN-1984 10.900000 64.300000

_CAN-1985 10.200000 63.500000

-CAN-1 986 9.200000 63.300000

-CAN-1 987 8.400000 6800000

-CAN-1988 7.300000 7600000

-CAN-1989 700000 84.100000

-CAN-1 990 7.700000 91.500000

-CAN-1991 9.800000 100.100000

-CAN-1992 10.600000 10000000

-CAN-1993 10.700000 95.500000


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-CAN-1994 9.400000 91.700000

-CAN-1995 8.500000 93.300000

-CAN-1996 8.700000 93.100000

-CAN-1997 8.200000 94.400000

-CAN-1998 7.500000 90.600000

-CAN-1999 5.700000 91.900000

-UK-1980 7.000000 43.700000

-UK-1981 10.500000 44.100000

-UK-1982 11.300000 42.200000

-UK-1983 11.800000 3900000

-UK-1 984 11.70000 37.200000

_UK-1985 11.200000 3900000

_UK-1986 11.200000 47.800000

_UK-1987 10.300000 60.200000

UK-1988 8.600000 68.300000

UK-1989 7.200000 67.700000

UK-1990 6.900000 81.700000

UK-1991 8.800000 90.500000

UK-19992 10.100000 10000000

UK-1993 10.500000 88.700000

U K-1994 9.700000 92.300000

UK-1995 8.700000 95.900000

UK-1996 8.200000 95.600000

UK-1997 7.000000 103.300000

UK-1998 6.300000 109.800000

UK-1999 6.100000 112.200000


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Unemployment Rate 3

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