Americans For Fair Taxation (AFFT), also known as FairTax.org, is a U.S. politic
ID: 3020217 • Letter: A
Question
Americans For Fair Taxation (AFFT), also known as FairTax.org, is a U.S. political advocacy group dedicated to fundamental tax code replacement. It is made up of volunteers who are working to get the Fair Tax Act (H.R. 25/S. 122) enacted in the United States – a plan to replace all federal payroll and income taxes (both corporate and personal) with a national retail sales tax and monthly tax "prebate" to households of citizens and legal resident aliens. AFFT was founded in 1994 by three Houston businessmen, Jack Trotter, Bob McNair, and Leo Linbeck, Jr., who each pledged $1.5 million as seed money to hire tax experts to identify what they perceived as faults with the current tax system and to determine what American citizens would like to see in tax reform.
Concern over taxation policies stems from the overall impact the current tax structure has on the economy. AFFT argues that a national sales tax is preferable to the tax system currently in place. Data are collected for 14 taxpayers for their reported income, total consumption and the sales tax they paid on those consumption figures. The sales tax will vary depending on the state and city in which the taxpayer lives.
Taxpayer
Income ($000)
Consumption ($000)
Sales Tax ($00)
1
120
111
6.58
2
89
83.1
5.25
3
65
61.5
6.58
4
75
78.2
5.47
5
147
125.8
8.8
6
158
125
8.75
7
65
61.5
4.31
8
47
45.3
3.17
9
58
55.2
3.864
10
109
101.1
7.077
12
115
106.5
7.455
12
87
81.3
5.691
13
35
34.5
2.415
14
74
69.6
4.872
You are to conduct a thorough study examining the relationship among the variables cited in the data set. Your first task is to estimate an OLS model for a consumption function that measures the relationship between consumption and income. The purpose is to determine if changes in a person’s income can explain changes in his or her consumption levels.
Given the emphasis placed on sales taxes by the AFFT, you are concerned about the nature of the relationship between consumption and sales taxes these citizens pay. This requires that you first determine which of these two variables should serve as the dependent variable in the OLS model.
A third regression model involves any relationship between income and sales taxes that might exist. Again, the question arises as to which variable is the dependent variable. It is up to you to make that determination.
Based on the results of the estimated consumption function, what does a 5% hypothesis test for the regression coefficient reveal? If you reject the null hypothesis, provide a 95% confidence interval for the 1 value.
Perform the same tests for the regression coefficient obtained from the model comparing consumption and sales taxes. Set alpha at 1%. How do you interpret the results?
Finally, perform the same tests for the regression coefficient obtained from the model comparing income and sales taxes. Set alpha at 1%. How do you interpret the results?
Taxpayer
Income ($000)
Consumption ($000)
Sales Tax ($00)
1
120
111
6.58
2
89
83.1
5.25
3
65
61.5
6.58
4
75
78.2
5.47
5
147
125.8
8.8
6
158
125
8.75
7
65
61.5
4.31
8
47
45.3
3.17
9
58
55.2
3.864
10
109
101.1
7.077
12
115
106.5
7.455
12
87
81.3
5.691
13
35
34.5
2.415
14
74
69.6
4.872
Explanation / Answer
You are to conduct a thorough study examining the relationship among the variables cited in the data set. Your first task is to estimate an OLS model for a consumption function that measures the relationship between consumption and income. The purpose is to determine if changes in a person’s income can explain changes in his or her consumption levels.
Based on the results of the estimated consumption function, what does a 5% hypothesis test for the regression coefficient reveal? If you reject the null hypothesis, provide a 95% confidence interval for the 1 value
Regression Analysis
r²
0.974
n
14
r
0.987
k
1
Std. Error
4.829
Dep. Var.
Consumption ($000)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
10,620.3930
1
10,620.3930
455.41
6.53E-11
Residual
279.8470
12
23.3206
Total
10,900.2400
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
95% lower
95% upper
Intercept
11.9390
3.5015
3.410
.0052
4.3099
19.5680
Income ($000)
0.7817
0.0366
21.340
6.53E-11
0.7019
0.8615
The regression line is
Consumption = 11.939+0.7817*income
The calculated regression coefficient = 0.7817, t=21.34, P< 0.05.
At 5% hypothesis test for the regression coefficient reveal that the variables are significantly related.
95% confidence interval for the 1 value =(0.7019, 0.8615).
Given the emphasis placed on sales taxes by the AFFT, you are concerned about the nature of the relationship between consumption and sales taxes these citizens pay. This requires that you first determine which of these two variables should serve as the dependent variable in the OLS model.
Perform the same tests for the regression coefficient obtained from the model comparing consumption and sales taxes. Set alpha at 1%. How do you interpret the results?
Dependent variable is sales taxes and independent variable is consumption.
Regression Analysis
r²
0.871
n
14
r
0.934
k
1
Std. Error
0.723
Dep. Var.
Sales Tax ($00)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
42.5759
1
42.5759
81.34
1.08E-06
Residual
6.2810
12
0.5234
Total
48.8569
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
99% lower
99% upper
Intercept
0.6473
0.5963
1.085
.2990
-1.1741
2.4687
Consumption ($000)
0.0625
0.0069
9.019
1.08E-06
0.0413
0.0837
Sales tax = 0.6473+0.0625* consumption
The calculated regression coefficient = 0.0625, t=90.19, P< 0.01.
At 1% hypothesis test for the regression coefficient reveal that the variables are significantly related.
A third regression model involves any relationship between income and sales taxes that might exist. Again, the question arises as to which variable is the dependent variable. It is up to you to make that determination.
Finally, perform the same tests for the regression coefficient obtained from the model comparing income and sales taxes. Set alpha at 1%. How do you interpret the results?
Dependent variable is sales taxes and independent variable is income.
Regression Analysis
r²
0.869
n
14
r
0.932
k
1
Std. Error
0.729
Dep. Var.
Sales Tax ($00)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
42.4795
1
42.4795
79.93
1.18E-06
Residual
6.3774
12
0.5315
Total
48.8569
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
99% lower
99% upper
Intercept
1.3416
0.5286
2.538
.0260
-0.2730
2.9561
Income ($000)
0.0494
0.0055
8.940
1.18E-06
0.0325
0.0663
Sales tax = 1.3416+0.0494* income
The calculated regression coefficient = 0.0494, t=8.94, P< 0.01.
At 1% hypothesis test for the regression coefficient reveal that the variables are significantly related.
Regression Analysis
r²
0.974
n
14
r
0.987
k
1
Std. Error
4.829
Dep. Var.
Consumption ($000)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
10,620.3930
1
10,620.3930
455.41
6.53E-11
Residual
279.8470
12
23.3206
Total
10,900.2400
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
95% lower
95% upper
Intercept
11.9390
3.5015
3.410
.0052
4.3099
19.5680
Income ($000)
0.7817
0.0366
21.340
6.53E-11
0.7019
0.8615
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