The empirical results reported in this study are obtained by estimating the following baseline regression equation using school-level panel data that varies by school and time:

(Education Outcomes)sy= β01 ln?(spending per pupil)sy2 (% free or reduced lunch)sy3 ln(grade enrollment)sy + γsysy.

The variables are denoted with school and time subscripts indicating that a particular variable is for school s in year y. The main predictor variable of academic outcomes is constructed as the natural logarithm of annual school-level total spending divided by annual school-level total student enrollment. The purpose of transforming spending per pupil into natural logarithms is to make the relationship between academic outcomes and spending per pupil linear, since it is possible that the statistical relationship between these two variables is nonlinear. In addition, academic outcomes are further modeled as functions of the percentage of students eligible for a free or reduced-price lunch and the number of students enrolled in a specific grade level.

Different measures of education outcomes represent the dependent variables in the equation. These outcomes are measures of performances of for all students who took the MEAP subject tests for grades three through eight, MME and ACT subject tests in grade 11 and the high school graduation rates of all students.

β0 is the constant term, εsy is the error term, αy is a year effect and γs is a school fixed effect. These fixed-effects terms are included in the regression equation to account for the effects of predictor variables on academic outcomes that are omitted in the regression equation. For example, measures of school quality and economic conditions for the state of Michigan are not included in the regression equation, but they have an impact on academic outcomes and so are accounted for via the fixed-effect terms. The fixed-effects terms remove both the school-specific means and year-specific means from the variables in the equation.

Finally, the equation is estimated considering that the schools are grouped into districts. If the error terms for different schools within a given district are correlated, then this could lead to relatively small standard errors being estimated and, therefore, misleading statistical inferences. Therefore, to control for this statistical issue, the estimated standard errors in the regression equation are clustered at the district level.

As is standard in reporting statistical results, a figure with one asterisk signifies statistical significance at a 90 percent level of confidence, two asterisks at a 95 percent level of confidence and three asterisks at a 99 percent level of confidence.

Academic Indicator                       Grade
MEAP: Math 3 4 5 6 7 8
Coefficient Estimate
Spending per pupil 1.297 0.505 2.514 -0.714 0.574* 0.243
-0.908 -1.596 -1.739 -0.447 -0.346 -0.432
Pct FRL 4.962 7.11 5.338 -1.841 -1.925** -1.892**
-4.383 -6.416 -4.935 -1.537 -0.912 -0.882
Grade enrollment -8.949*** -1.696 -14.89*** -10.14*** -13.00*** -9.504***
-2.128 -5.23 -3.022 -2.515 -2.499 -2.465
Additional Information
N 6,626 6,434 5,327 1,896 2,274 2,256
Adjusted R-squared 0.89 0.91 0.884 0.889 0.908 0.908

Grade
MEAP: Reading 3 4 5 6 7 8
Coefficient Estimate
Spending per pupil 0.894 0.035 1.419 0.514 0.386 -0.249
-0.952 -1.638 -1.324 -0.4 -0.513 -0.381
Pct FRL 6.758 6.832 6.471 -0.924 -2.799** -1.972**
-4.733 -6.586 -4.881 -1.349 -1.403 -0.775
Grade enrollment -8.747*** -2.336 -9.735*** -6.001*** -12.06*** -6.674***
-2.196 -5.11 -2.564 -1.848 -2.776 -1.926
Additional Information
N 6,628 6,435 5,328 1,896 2,274 2,256
Adjusted R-squared 0.892 0.907 0.883 0.892 0.865 0.896

Grade
MEAP: Science 5 8
Coefficient Estimate
Spending per pupil 2.013 -0.143
-1.43 -0.511
Pct FRL 4.486 -2.614***
-4.394 -0.829
Grade enrollment -13.46*** -8.318***
-2.904 -2.207
Additional Information
N 5,327 2,256
Adjusted R-squared 0.9 0.909

Subject
MME Math Reading Science Social Studies Writing
Coefficient Estimate
Spending per pupil 0.46 -0.535 0.304 0.559 0.259
-1.221 -0.876 -1.111 -0.501 -1.131
Pct FRL -1.323 -1.966* -1.386 0.213 -1.425
-1.165 -1.179 -1.189 -0.622 -1.343
Grade enrollment -11.05*** -4.274* -7.020** -2.139 -3.943
-2.237 -2.501 -2.784 -1.733 -2.792
Additional Information
N 3,096 3,102 3,101 3,101 3,108
Adjusted R-squared 0.919 0.908 0.923 0.928 0.912

Test
ACT Composite English Math Reading Science Writing
Coefficient Estimate
Spending per pupil 0.0027 0.0091 0.0084 -0.049 0.031 0.064
-0.074 -0.102 -0.074 -0.1 -0.081 -0.041
Pct FRL -0.105 -0.117 -0.041 -0.029 -0.170* -0.092
-0.095 -0.126 -0.076 -0.124 -0.102 -0.084
Grade enrollment -0.711*** -0.804*** -0.814*** -0.748*** -0.482* -0.221
-0.215 -0.282 -0.162 -0.274 -0.254 -0.186
Additional Information
N 3,562 3,562 3,562 3,562 3,562 2,557
Adjusted R-squared 0.952 0.935 0.952 0.931 0.937 0.865

Graduation Rate 4-year 5-year 6-year
Coefficient Estimate
Spending per pupil 0.58 0.042 0.494
-0.7 -0.687 -0.758
Pct FRL 1.627 1.493 0.938
-0.988 -1.103 -1.288
Grade enrollment -9.997** -3.09 3.251
-3.924 -2.751 -3.53
Additional Information
N 3,880 3,364 2,802
Adjusted R-squared 0.909 0.925 0.917

The graphics below include scatterplots of regression results. The x-axis displays a school’s change in per-pupil spending and the y-axis shows a school’s change in average scale scores. If school spending were positively correlated in a statistically significant way to student achievement, the blots on these graphs would appear to follow a line slopping upwards from the bottom left to the upper right. The results, however, show much more vertical lines, suggesting that the amount of money that schools spend have little correlation to how well students perform.

Graphic 4: MEAP Reading Test Results, Grades 3-5, 2008-2013

MEAP reading elem

Graphic 5:  MEAP Reading Test Results, Grades 6-8, 2008-2013

MEAP reading middle

Graphic 6: MEAP Math Test Results, Grades 3-5, 2008-2013

MEAP math elem

Graphic 7: MEAP Math Test Results, Grades 6-8, 2008-2013

MEAP math middle

Graphic 8: MEAP Science Test Results, Grades 5 and 8, 2008-2013

MEAP science

Graphic 9: MME Test Results by Subject, 11th Grade, 2008-2013

MME

Graphic 10: ACT Test Results by Subject, 11th Grade, 2007-2013

ACT

Graphic 11: Graduation Rates, 2007-2013

grad