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Suppose we wish to estimate the effect of the federally funded school lunch program on student performance. The file MEAP93.xls contains data on 408 high schools in Australia for the year 1993.

  • math10: percentage of tenth graders at a high school receiving a passing scoreon a standardized mathematics exam.
  • expend: expenditures per student (in dollars).
  • lnchprg: percentage of students who are eligible for the federal free lunch
  • enrol: number of student enrolment which measures school size
  • Consider a regression model

Estimate the model using Eviews and write down the fitted equation (including the sample size, t-statistic, and R-squared). 

(b) Test the overall validity of the regression model at the 5% significance level.

(c) Does the lunch program increase student performance? Test the hypothesis at the 5% level.

(d) Based on the regression output, if expend increase by 10% what is the estimated percentage point change in math10, holding lnchprg and enroll constant.

(e) Now run the simple regression of math10 on lnchprg such that

 

Compare the Eviews output with that from part (a). Which model will you choose? Why? [Hint: should we use R2 or adjusted R2 for model comparison?]

Suppose a researcher wants to analysis the short-term interest rate, and she develops a model given by

where is the three-month T-bill rate, is the annual inflation rate based on the consumer price index (CPI), and is the federal budget surplus or deficit as a percentage of GDP. He collects the yearly data for the period from 1960 to 2016 (57 observations) from the Federal Reserve Economic Data. They are in the Excel file Interest_rate.xlsx.

  • Plot the three variables in a line graph using Eviews and comment on the dynamics (any co-movement between interest rate and the other two variables).
  • Estimate the regression model using Eviews and provide the output.
  • What does the coefficient of determination tell you?
  • Interpret the coefficients ?B1and ?B2 . Do the signs of the estimated coefficients agree with standard economic intuition?
  • Conduct a test of H0: there is no second order serial correlation in the errors of this model at the 5% significance level.
  • Re-estimate the equation with Newy-West standard errors and provide the Eviews output. Compare the serial correlation consistent estimation with output from Part (b).
  • Test the null hypothesis that a one percent increase in the annual inflation rate leads to a one percent increase in the short-term interest rate on average at the 5% level.

In the file pubexp.xls there are data on public expenditure on education (EE), gross domestic product (GDP), and population (P) for 34 countries in the year 1980. It is hypothesized that per capita expenditure on education is linearly related to per capita GDP. That is

 

Import the data into Eviews.

  • It is suspected that . Why might the suspicion 

may be heteroskedastic with a variance related to about heteroskedasticity be reasonable?

  • Draw a scatter plot between x and y using Eviews and comment on the graph (what is the expected relationship and any evidence of heteroskedasticity). Hint: To generate variable x using Eviews, click Genr, type in x=GDP/P in the box.
  • Run the OLS regression and provide the Eviews output. Does the sign of the slope coefficient make sense? Explain.
  • Test for the existence of heteroskedasticity using a White test (assuming a 5% level of significance).
  • Re-estimate the equation with White consistent standard errors and provide the Eviews output. Compare the heteroskedasticity consistent estimation with output from part (c).

Model Estimation with Eviews

a.

The regression output is given as

Dependent Variable: MATH10

Method: Least Squares

Date: 06/08/18   Time: 13:07

Sample: 1 408

Included observations: 408

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-23.13766

24.99323

-0.925757

0.3551

LOG(EXPEND)

7.746062

3.041386

2.546885

0.0112

LNCHPRG

-0.323927

0.036319

-8.918835

0.0000

LOG(ENROL)

-1.255435

0.581173

-2.160175

0.0313

R-squared

0.189291

    Mean dependent var

24.10686

Adjusted R-squared

0.183271

    S.D. dependent var

10.49361

S.E. of regression

9.483400

    Akaike info criterion

7.346718

Sum squared resid

36333.69

    Schwarz criterion

7.386044

Log likelihood

-1494.731

    Hannan-Quinn criter.

7.362280

F-statistic

31.44310

    Durbin-Watson stat

1.906937

Prob(F-statistic)

0.000000

 
From the regression result, the fitted equation is obtained as

 

The overall significance of the model can be tested to examine overall significance of the model.

Null hypothesis: Coefficients of all the independent variables are zero

Alternative hypothesis: At least one of the coefficients is significantly different from zero.

The significant p value F statistics from the regression model is obtained as 0.00. The p value is less than the significant value of 0.05. This indicates rejection of null hypothesis of neither of coefficients are statistically significant. The result thus suggests that the model has overall significance.

As obtained from the regression result the coefficient of lunch program is -0.32. The negative coefficient indicates an inverse relation between lunch program and percentage of tenth grade on a standardized math exam. This implies with increase in lunch program obtained grades of the students decreases. P value of the coefficient is 0.0000. As the p value is smaller than the level of significance 0.05, the null hypothesis of no significant relation between lunch-program and students’ performance is rejected at 5% level of significance. Therefore, lunch-program fails to increase performance of the student rather it influences student performance negatively.

The coefficient of log(expend) is 7.74. This indicates a 10% increase in expend will increase math10 by (7.74* 10) = 77.4 percent.

Dependent Variable: MATH10

Method: Least Squares

Date: 06/08/18   Time: 14:22

Sample: 1 408

Included observations: 408

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

32.14271

0.997582

32.22061

0.0000

LNCHPRG

-0.318864

0.034839

-9.152422

0.0000

R-squared

0.171034

    Mean dependent var

24.10686

Adjusted R-squared

0.168992

    S.D. dependent var

10.49361

S.E. of regression

9.565938

    Akaike info criterion

7.359184

Sum squared resid

37151.91

    Schwarz criterion

7.378847

Log likelihood

-1499.274

    Hannan-Quinn criter.

7.366965

F-statistic

83.76683

    Durbin-Watson stat

1.907745

Prob(F-statistic)

0.000000


In both the model, the variable lunch program is negative and statistically significant. The magnitude of the coefficient in both the model is equivalent to -0.32. For the model in part (a) the value of adjusted R square is 0.18. In the new model, the R square value is 0.16. The R square value indicates goodness of fit of the model. This explains how much variation in the dependent variable is explained by the independent variable. Higher the R square value better is fitted model. In terms of R square value, model 1 is more acceptable as compared to model 2.

a.

 

Figure 1: Line plot of T-bill rate, inflation rate and federal budget balance

As shown from the figure above, interest rate and inflation rate moves in the same direction. Movement of interest rate follows the movement of inflation indicating a positive association between them. In most of the times, interest rate is above inflation rate. The variable federal budget does not show any clear co-movement with Treasury bill interest rate.  

Testing Overall Validity of Regression Model

The regression output for the concerned regression model is given as

Dependent Variable: I3

Method: Least Squares

Date: 06/08/18   Time: 12:04

Sample: 1960 2016

Included observations: 57

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

2.056980

0.556708

3.694899

0.0005

INF

0.817576

0.096280

8.491619

0.0000

DEF

0.190321

0.115244

1.651455

0.1045

R-squared

0.590980

    Mean dependent var

4.687295

Adjusted R-squared

0.575831

    S.D. dependent var

3.109814

S.E. of regression

2.025369

    Akaike info criterion

4.300576

Sum squared resid

221.5143

    Schwarz criterion

4.408105

Log likelihood

-119.5664

    Hannan-Quinn criter.

4.342366

F-statistic

39.01139

    Durbin-Watson stat

0.444886

Prob(F-statistic)

0.000000


Estimated regression equation

 

Value of R square gives coefficient of determination. It indicates how much of the variation in dependent variable can be explained by the independent variables. In the present model, the R square value is given as 0.59. This implies inflation and balance in federal budget can together explain 59 percent variation in interest rate.

The value of inflation coefficient is 0.82. This implies there is a positive relation between rate of inflation and 3 months T-bill rate. That is as inflation increases return to 3 months T-bill rate increases. The p value of the coefficient is 0.00. P value less than the level of significance value 0.05 indicates rejection of null hypothesis of no significant relation between inflation and interest on T-bill rate. The coefficient of federal budget is 0.19. The positive co-efficient indicates that federal budget positively influences interest on T-bill rate. P value of the coefficient 0.10. The value is greater than significance level of 0.05. As the p value is greater than significant value, null hypothesis of no significant relation between T–bill rate and budget surplus is rejected.

Inflation and expected inflation affect the interest rate on Treasury bill. The period of high inflation is generally associated with a high interest rate. From the regression result, a positive significant relation is obtained between inflation and 3 months T-bill rate. The sign of inflation coefficient is thus consistent with standard economic intuition. The federal budget deficit is associated with an inflationary pressure. In presence budget deficit, central bank purchases securities issued by the government. This raises growth of monetary base crating inflationary pressure. This has a positive impact on interest rate. The variable budget deficit though is not statistically significant but it has the expected sign.

Test of serial autocorrelation

Hypothesis

Null hypothesis: There is no second order serial autocorrelation in the model at 5% level of significance

Alternative hypothesis: There exists a second order serial autocorrelation in the model at 5% level of significance.

Auxiliary regression

The auxiliary regression regress current values of residuals on all the explanatory variables and is related with lagged residual terms. The Breusch- Godfrey test statistics is given as (T – p)*R2 , where T is the number of observation and p is the number of lagged residual terms. The test statistics follows a chi-square distribution with p degrees of freedom.

Effect of Lunch Program on Student Performance

Decision rule

The null hypothesis is rejected if P value of the Breusch-Godfrey test statistics is less than 0.05.

Conclusion

From the test result, p value of the LM statistics is obtained as 0.0000. As the p value is less than 0.05, the null hypothesis of no second order serial autocorrelation exists in the model is rejected. This implies the model has the problem of second order autocorrelation.

Breusch-Godfrey Serial Correlation LM Test:

F-statistic

39.78589

    Prob. F(2,52)

0.0000

Obs*R-squared

34.47237

    Prob. Chi-Square(2)

0.0000

Test Equation:

Dependent Variable: RESID

Method: Least Squares

Date: 06/08/18   Time: 12:50

Sample: 1960 2016

Included observations: 57

Presample missing value lagged residuals set to zero.

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-0.148451

0.357065

-0.415752

0.6793

INF

0.003478

0.061905

0.056180

0.9554

DEF

-0.040788

0.074426

-0.548033

0.5860

RESID(-1)

0.738955

0.140036

5.276884

0.0000

RESID(-2)

0.062394

0.140898

0.442831

0.6597

R-squared

0.604778

    Mean dependent var

-7.64E-16

Adjusted R-squared

0.574377

    S.D. dependent var

1.988872

S.E. of regression

1.297536

    Akaike info criterion

3.442443

Sum squared resid

87.54723

    Schwarz criterion

3.621658

Log likelihood

-93.10962

    Hannan-Quinn criter.

3.512092

F-statistic

19.89295

    Durbin-Watson stat

1.995246

Prob(F-statistic)

0.000000

Newy-West standard error estimation model

Dependent Variable: I3

Method: Least Squares

Date: 06/10/18   Time: 10:12

Sample: 1960 2016

Included observations: 57

HAC standard errors & covariance (Bartlett kernel, Newey-West fixed

        bandwidth = 4.0000)

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

2.056980

0.525294

3.915866

0.0003

INF

0.817576

0.129667

6.305189

0.0000

DEF

0.190321

0.178272

1.067589

0.2905

R-squared

0.590980

    Mean dependent var

4.687295

Adjusted R-squared

0.575831

    S.D. dependent var

3.109814

S.E. of regression

2.025369

    Akaike info criterion

4.300576

Sum squared resid

221.5143

    Schwarz criterion

4.408105

Log likelihood

-119.5664

    Hannan-Quinn criter.

4.342366

F-statistic

39.01139

    Durbin-Watson stat

0.444886

Prob(F-statistic)

0.000000

    Wald F-statistic

21.38973

Prob(Wald F-statistic)

0.000000


The result of Newy-West standard error consistent model gives exactly same result as that obtained in part (b).Part g

Dependent Variable: I3

Method: Least Squares

Date: 06/08/18   Time: 13:02

Sample: 1960 2016

Included observations: 57

HAC standard errors & covariance (Bartlett kernel, Newey-West fixed

        bandwidth = 4.0000)

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

1.522099

0.677918

2.245255

0.0288

INF

0.832006

0.131128

6.345005

0.0000

R-squared

0.570322

    Mean dependent var

4.687295

Adjusted R-squared

0.562510

    S.D. dependent var

3.109814

S.E. of regression

2.056927

    Akaike info criterion

4.314760

Sum squared resid

232.7021

    Schwarz criterion

4.386446

Log likelihood

-120.9707

    Hannan-Quinn criter.

4.342620

F-statistic

73.00279

    Durbin-Watson stat

0.421116

Prob(F-statistic)

0.000000

    Wald F-statistic

40.25909

Prob(Wald F-statistic)

0.000000


From the estimated regression result, the coefficient of inflation is obtained as 0.83. This means 1 percent increases in inflation rate increases return on T-bill rate by 0.8%. For 1 percent increase in inflation rate to cause a 1 percent increase in interest rate, the two variables need to be perfectly correlated that is having R square value equals to 1. From the regression coefficient and value of R square, the null hypothesis that 1 percent increase in inflation leads to a 1 percent increase in interest rate is rejected.

a.

The suspicion about heteroskadascity is reasonable as countries with a higher per capita GDP have access to a large amount of money to distribute. The people with a higher average income enjoy a higher flexibility regarding their spending on education. Countries with smaller per capita GDP has limited option for budget and hence, spending on education tend to vary less.

 

Figure 2: Scatter plot between x and y

The scatter plot between X and Y reveals that there exists a linear relationship between X and Y. This indicates presence of heteroskedasticity that is non-constant variance of error terms. In presence of heteroskadascity, variation in Y differs depending on the variation in X.  From the scatter plot it is seen that small values of X leads to small scatter in Y while large values are associated with large scatter in Y.

The output OLS regression is given as follows

Dependent Variable: Y

Method: Least Squares

Date: 06/08/18   Time: 15:27

Sample: 1 34

Included observations: 34

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-0.124573

0.048523

-2.567308

0.0151

X

0.073173

0.005179

14.12755

0.0000

R-squared

0.861823

    Mean dependent var

0.476735

Adjusted R-squared

0.857505

    S.D. dependent var

0.359903

S.E. of regression

0.135858

    Akaike info criterion

-1.097394

Sum squared resid

0.590635

    Schwarz criterion

-1.007608

Log likelihood

20.65569

    Hannan-Quinn criter.

-1.066774

F-statistic

199.5875

    Durbin-Watson stat

1.774258

Prob(F-statistic)

0.000000


The coefficient of X is obtained as 0.07. The positive coefficient indicates a positive association between per capita education and per capita GDP. That is an increase in per capita GDP leads to an increase in per capita expenditure on education. With 10% increase in per capita GDP expenditure on education increases by 0.7 percent.  P value of the coefficient is 0.00.  As the p value is less than significance value of 0.05, it can be said that the coefficient is statistically valid.  This means average income increase, people have more income to spend on education ad hence, expenditure on education increases.

Test of Heteroskedasticity: White test

Hypothesis

Null hypothesis: Variances for errors are equal

Alternative hypothesis: Variance of errors are not equal

In order to test constant variance auxiliary regression analysis is undertaken. The auxiliary regression regress squares of residuals from the original regression on a set of regressors containing regressors of the original model with their squares and cross product. One can then inspect R square value. The Lagrange multiplier test statistics is obtained as product of sample size and R square value.

 

The obtained test statistics follows a chi-square distribution with (P-1) degrees of freedom. P is the number of parameters in the auxiliary regression.

The null hypothesis is rejected if the p value of the chi square statistics is less than significance value of 0.05.

Conclusion

From the result of White test, p value of the chi-square statistics is 0.0000. As the p value is less than significance value of 0.05, the null hypothesis of homoskadastiity of error variance is rejected implying presence of hetetroskadascity in the model.

Heteroskedasticity Test: White

F-statistic

6.423121

    Prob. F(2,31)

0.0046

Obs*R-squared

9.961452

    Prob. Chi-Square(2)

0.0069

Scaled explained SS

11.90755

    Prob. Chi-Square(2)

0.0026

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 06/11/18   Time: 12:27

Sample: 1 34

Included observations: 34

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.017677

0.016112

1.097134

0.2810

X^2

0.000484

0.000264

1.834593

0.0762

X

-0.005206

0.004548

-1.144759

0.2611

R-squared

0.292984

    Mean dependent var

0.017372

Adjusted R-squared

0.247370

    S.D. dependent var

0.028968

S.E. of regression

0.025131

    Akaike info criterion

-4.445344

Sum squared resid

0.019578

    Schwarz criterion

-4.310665

Log likelihood

78.57084

    Hannan-Quinn criter.

-4.399414

F-statistic

6.423121

    Durbin-Watson stat

2.210357

Prob(F-statistic)

0.004636

White consistent standard error

Dependent Variable: Y

Method: Least Squares

Date: 06/08/18   Time: 15:48

Sample: 1 34

Included observations: 34

White heteroskedasticity-consistent standard errors & covariance

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-0.124573

0.040414

-3.082420

0.0042

X

0.073173

0.006212

11.78005

0.0000

R-squared

0.861823

    Mean dependent var

0.476735

Adjusted R-squared

0.857505

    S.D. dependent var

0.359903

S.E. of regression

0.135858

    Akaike info criterion

-1.097394

Sum squared resid

0.590635

    Schwarz criterion

-1.007608

Log likelihood

20.65569

    Hannan-Quinn criter.

-1.066774

F-statistic

199.5875

    Durbin-Watson stat

1.774258

Prob(F-statistic)

0.000000

    Wald F-statistic

138.7696

Prob(Wald F-statistic)

0.000000

The White consistent standard error model gives the same result as that obtained from heteroskadasticity consistent output in part (c).

Confidence interval

Coefficient Confidence Intervals

Date: 06/11/18   Time: 15:27

Sample: 1 34

Included observations: 34

90% CI

Variable

Coefficient

Low

High

C

-0.124573

-0.193030

-0.056116

X

 0.073173

 0.062651

 0.083695

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My Assignment Help. (2020). Estimating The Effect Of Federally Funded School Lunch Program On Student Performance Using MEAP93 Data Essay.. Retrieved from https://myassignmenthelp.com/free-samples/econ634-econometrics-and-business-statistics/lunch-program-on-student-performance.html.

"Estimating The Effect Of Federally Funded School Lunch Program On Student Performance Using MEAP93 Data Essay.." My Assignment Help, 2020, https://myassignmenthelp.com/free-samples/econ634-econometrics-and-business-statistics/lunch-program-on-student-performance.html.

My Assignment Help (2020) Estimating The Effect Of Federally Funded School Lunch Program On Student Performance Using MEAP93 Data Essay. [Online]. Available from: https://myassignmenthelp.com/free-samples/econ634-econometrics-and-business-statistics/lunch-program-on-student-performance.html
[Accessed 23 June 2024].

My Assignment Help. 'Estimating The Effect Of Federally Funded School Lunch Program On Student Performance Using MEAP93 Data Essay.' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/econ634-econometrics-and-business-statistics/lunch-program-on-student-performance.html> accessed 23 June 2024.

My Assignment Help. Estimating The Effect Of Federally Funded School Lunch Program On Student Performance Using MEAP93 Data Essay. [Internet]. My Assignment Help. 2020 [cited 23 June 2024]. Available from: https://myassignmenthelp.com/free-samples/econ634-econometrics-and-business-statistics/lunch-program-on-student-performance.html.

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