Eco4361 Lectures PDF

ECO 4361 Economics of Education Instructor: Dr. Shixuan (Kathy) Li Southern Methodist University Slides author: Dr. Daniel L. Millimet Economics of Education 1 / 319 Introduction Overview De…nition Economics of education encompasses the study of the determinants, provision, and impact of education. Determinants refers to factors a¤ecting the quantity of schooling obtained and the quality of that schooling Provision refers to the structure and …nancing of the market for educational services Impact refers to the private and social returns to schooling Economics of Education 2 / 319 Economic view of education I Private investment F Consumers (students) bear direct costs (tuition, supplies, school expenses, etc.) F Consumers (students) bear indirect costs (foregone income, other opportunity costs) F Consumers (students) reap rewards (better labor market outcomes, better health, etc.) I Social investment F Society bears direct costs (subsidizing education, including both publicly provided education and student loans) F Society bears indirect costs (foregone use of skills/resources, other opportunity costs) F Society reaps rewards (skilled labor force, positive externalities such as health/civics/crime) Notes I Idea that education constitutes an investment dates back to 17th century I Education is heterogeneous... bene…ts and costs may di¤er depending on levels of quantity and quality Economics of Education 3 / 319 Structure of US educational system Economics of Education 4 / 319 Historical goals of US educational system Goals have evolved over time, responded to needs of the era I Determined through the political process I Many original goals from the 19th century remain I List of goals has expanded over time, creating immense pressure King (2008) time line 1920s-1940s 1980s-present 1820s-1840s expansion of HS to community service; teaching common moral, control youth behavior, preparation for global political values; equality reduce youth labor; life- economy; high-stakes of opportunity adjustment education testing 1880s-1920s 1950s-1980s Americanize immigrants; racial and cultural train LF for industrial age; harmony; war on poverty; reforming family life; educating provide food and medical scientists/engineers; care; anticommunism equality of opportunity; career education Economics of Education 5 / 319 Speci…c classes of goals of US educational system Political goals I Create a national culture I Educate the next generation of political leaders I Educate individuals to maintain national security Social goals I Reduce crime through teaching of moral values I Improve quality of family life (through ‘home economics,’now ‘family and consumer sciences’) I Improve diet (through cafeterias and school nutrition programs) I Reduce teenage sexual behavior (through sex ed, extracurricular activities) I Provide ‘secular character education’(2001 NCLB), including caring, citizenship, justice and fairness, respect, responsibility, trustworthiness, and giving Economic goals I Increase stock of ‘human’capital I Provide equality of opportunity I Teach individuals how to learn to adapt to new technology and information post-schooling Economics of Education 6 / 319 “Our progress as a nation can be no swifter than our progress in education.” “The goal of education is the advancement of knowledge and the dissemination of truth.” -JFK “... education should prepare children for jobs, and it should also prepare our children for life.” -GW Bush “The best anti-poverty program is a world-class education.” -B Obama Economics of Education 7 / 319 Introduction Why Public Education? Two key questions 1 Why public education (as opposed to a private market only)? 2 Why subsidize the cost of education? Note: These are two distinct questions! Economics of Education 8 / 319 Purely Private Educational Market Consider what this might look like Demand side of the market I HHs maximize utility, where U depends on education of children F U may directly depend on educ (parents value education intrinsically) F U may indirectly depend on educ (parents value future consumption, welfare of children) I HH maximization problem ! demand curve for years of educ I Assuming diminishing marginal utility, demand curve is downward sloping I Demand curve re‡ects only private bene…ts ! demand curve is a plot of marginal private bene…t (MPB) Economics of Education 9 / 319 Supply side of the market I Suppliers will enter the market if it is pro…table to do so I Assume F PC Market F Perfect information (consumers fully informed about quality) F No production externalities ! MC = MSC F MC is constant Equilibrium I Determined by intersection of supply and demand I Price set to clear the market Economics of Education 10 / 319 Graphical depiction Price ($) p* S=MPC=MSC D=MPB E* Education (years) Implications: Can analyze various changes in D, S I Changes in demand arise due to changes in income, labor market returns to educ, psychic value of educ, etc. I Changes in supply arise due to changes in technology, teacher salaries, other input prices, etc. Economics of Education 11 / 319 Consumption externalities I Consumption externalities arise when private consumption yields positive or negative bene…ts to society I Creates a wedge between MPB and MSB of educ I Creates a market failure since the market cannot address such externalities as HHs only consider private utility when making decisions I Leads to under- (over-)consumption of educ with positive (negative) externalities Price MSB ($) efficient outcome: Eo p* S=MPC=MSC market outcome: E* D=MPB E* Eo Education (years) Economics of Education 12 / 319 What consumption externalities? Economics of Education 13 / 319 Solution to market ine¢ ciency I Under-consumption arises because part of the bene…t to educ is realized by society, but costs are borne fully by HHs I Government should subsidize educ by transferring money (through taxes) to HH to cover portion of the cost related to consumption that bene…ts society (accounting for the distortionary e¤ect of taxes) I Graphical depiction, where s is the amount of the subsidy Price MSB ($) p* S=MPC=MSC p*- s D=MPB E* Eo Education (years) Economics of Education 14 / 319 Publicly provided education Positive consumption externalities justify public subsidy, but not necessarily public provision of educ Public educ may be justi…able if it is ‘easier’to implement when the MSB dominates the MPB such that s = p Price MSB ($) p* S=MPC=MSC D=MPB p*- s Education E* Eo (years) Economics of Education 15 / 319 Public provision of educ may also be justi…ed on other grounds 1 Equality of educational opportunity F Imperfect credit markets represent another possible source of market failure F May impede the poor from borrowing even if sound investment (future HC cannot be used as collateral) 2 Redistribution F Assuming educ is a normal good, children from wealthy HHs will receive more educ F Leads to little intergenerational mobility 3 Parental control F Parents make educ decisions for children, face a trade-o¤ between own consumption and children’s educ F With public loans to parents to pay for private educ, under-consumption may still occur if parents do not receive much utility from children’s welfare 4 Economic and racial segregation F School assignment based on residential location leads to less diversity than free choice F Fully private market is likely to be worse (discussed later) Economics of Education 16 / 319 Potential drawback to publicly provided education: Crowd-out Schools are heterogeneous... in practice, (public and private) schools di¤er in quality Assume I HHs maximize utility U = U (C , E ) where C is all non-educ consumption and E is educ consumption I Public schools o¤er a constant quality I HHs wanting greater school quality must opt for private school I HHs attending private schools forego public subsidy Economics of Education 17 / 319 Graphical depiction C A’,B’ BC (with public school) A indifference curves B BC (no public school) C,C’ E Epub subsidized cost of public school Implications I Public educ crowds out some educ expenditure by HH A, B I Public educ reduces total educ consumption by HH B I HH C is una¤ected I Vouchers can correct this reduction by HH B (discussed later) Economics of Education 18 / 319 Quantity of Education Introduction De…nition Human capital is “the knowledge, skills and competences and other attributes embodied in individuals that are relevant to economic activity” (OECD 2005) Acquire HC through: educ, on-the-job training, training programs, nurtrition, medical care,... Referred to as human capital since it cannot be separated from the individual Here, we focus on investments in educ However, analysis of investments in other types of HC is very similar Economics of Education 19 / 319 Brief US History of Educational Attainment (Goldin 1998) Three key periods 1 Expansion of primary school enrollment (1840-1880s) 2 Expansion of secondary school enrollment (1910-1940s) F Referred to as period of ‘high school movement’ F Expansion fueled by enrollment of students not necessarily intending to continue to college ! led to questioning over role of schools, curriculum F Expansion preceded other comparable countries by several decades 3 Expansion of college (tertiary) enrollment (1960s-present) Important di¤erences along racial, gender lines US fairs well internationally in terms of quantity of educ, but I Reasons for pessimism going forward I Secondary school completion is still an issue Economics of Education 20 / 319 Enrollment Rates Economics of Education 21 / 319 Economics of Education 22 / 319 Economics of Education 23 / 319 Economics of Education 24 / 319 Economics of Education 25 / 319 Educational Attainment Economics of Education 26 / 319 Economics of Education 27 / 319 Educational Attainment: International Comparisons Economics of Education 28 / 319 Economics of Education 29 / 319 Economics of Education 30 / 319 Roadmap 1 Investment decisions I How much? I Compulsory Attendance Laws (CALs) I GED I Over-education 2 Returns to education Economics of Education 31 / 319 Quantity of Education Investment Model Simple Dynamic Optimization Problem Costs of schooling I Direct costs (e.g. tuition, books) I Opportunity costs (e.g. foregone wages) I Psychological costs Bene…ts of schooling I " future wages I Psychological bene…ts Economics of Education 32 / 319 Example: College or no college? Economics of Education 33 / 319 Solution E c T Y (E ) E = arg max DPV = ∑ t + ∑ t t =0 (1 + r ) t =E +1 (1 + r ) where I c = per-period schooling costs I Y (E ) = per-period earnings (dY /dE > 0) I r is the discount rate I T is certain I Educ is uninterrupted Implications I (Work) life expectancy: ∂E /∂T > 0 I Return to educ: ∂E /∂(dY /dE ) > 0 I Discount rate: ∂E /∂r < 0 I Schooling cost: ∂E /∂c < 0 Economics of Education 34 / 319 Educational Attainment: Race/Gender Di¤erences Status dropout rates of 16- to 24-year-olds, by race/ethnicity: 1990 through 2014 Economics of Education 35 / 319 Economics of Education 36 / 319 Economics of Education 37 / 319 Economics of Education 38 / 319 Economics of Education 39 / 319 Economics of Education 40 / 319 Can these di¤erences be explained by the model? Recall, model predicts that educ attainment is increasing with 1 Life expectancy, T 2 Return to education, dY /dE and decreasing with 1 Discount rate, r 2 Schooling cost, c Economics of Education 41 / 319 Life Expectancy Economics of Education 42 / 319 LM Returns to Education: Earnings Economics of Education 43 / 319 Economics of Education 44 / 319 Economics of Education 45 / 319 LM Returns to Education: Employment Economics of Education 46 / 319 Economics of Education 47 / 319 Economics of Education 48 / 319 LM Returns to Education: Lifetime Earnings Economics of Education 49 / 319 Economics of Education 50 / 319 Economics of Education 51 / 319 Discount rates Experimental evidence based on middle school students in Georgia (age 13-14 years) I Castillo et al. (2011) Student o¤ered choices between di¤erent combinations of money today versus future payment Choices yield information on implicit discount rates of students Student make 20 hypothetical choices, but then one is chosen randomly and actual pays in order to induce truthfulness Economics of Education 52 / 319 Economics of Education 53 / 319 Economics of Education 54 / 319 Economics of Education 55 / 319 Schooling costs Economics of Education 56 / 319 Conclusion: I Schooling is no di¤erent than any other investment: costs incurred in SR, bene…ts in the LR I Costs, c, depend also on psychological costs and e¤ort, which may be decreasing in ‘inate’ability (discussed later) I Simple model ignores F Credit market imperfections (HC is not collateral) F Uncertainty (c, dY /dE , T ) F Heterogeneity in costs, returns I Nonetheless, the simple model can perhaps explain much of the variation in schooling across race, gender Economics of Education 57 / 319 Quantity of Education Compulsory Attendance Laws CALs require attendance at school until a certain (biological) age History I 1842: Connecticut banned employment of children < 15 without proof of school attendance for 3+ months per year I 1852: Massachusetts required 8-14 yr olds to attend school 12+ wks per year, with at least 6 wks consecutive I 1873: Massachusetts revised statute to include only 12-14 yr olds, but expanded requirement to 20+ wks per year I 1867-1918: All states adopted some version of a CAL I Texas adopted in 1915, requires attendance from ages 6-18 Economics of Education 58 / 319 Economics of Education 59 / 319 Note: Figures increase to 33 and 21 in 2010. Economics of Education 60 / 319 Current (2013) Economics of Education 61 / 319 Do CALs Matter? Depends on two components 1 Are CALs binding for some individuals? F Answer: Yes, but less today than previously 2 Do CALs a¤ect the educ decisions for individuals even if CALs are non-binding? F Answer: Yes, some evidence that individuals with educ above the CAL increase educ further in response to CALs. Explainable by a signaling model (discussed later). Economics of Education 62 / 319 Are CALs Justi…ed? Economic rationale depends on existence of market failure(s) Possibilities 1 Positive consumption externalities to educ 2 Imperfect information by HHs about the true, private returns to educ Economics of Education 63 / 319 Case 1. Perfect Information I Here, with a full subsidy, individuals only invest to E 0 I This is less than the socially e¢ cient level, Eo I Only way to induce investment to Eo is to mandate Eo ! CALs Price MSB ($) p* S=MPC=MSC D=MPB E* E’Eo Education (years) Economics of Education 64 / 319 “We have one of the highest high school dropout rates of any industrialized nation. And half of the students who begin college never …nish... And dropping out of high school is no longer an option. It’s not just quitting on yourself, it’s quitting on your country – and this country needs and values the talents of every American.” -B Obama (State of the Union, 2009) “When students are not allowed to drop out, they do better. So tonight, I am proposing that every state, every state, requires that all students stay in high school until they graduate or turn 18.” -B Obama (State of the Union, 2012) Economics of Education 65 / 319 Case 2. Imperfect Information I In Case 1, CALs compel individuals to do something that is not in the best interest (i.e., U-maximizing) for the ‘greater good’ I If individuals underestimate private returns to educ, then CALs may compel them to do something in their own interest Price True MPB ($) p* S=MPC=MSC Incorrect MPB E* E’Eo Education (years) Economics of Education 66 / 319 Quantity of Education GED The General Educational Development (GED) program is a major component of the US educ system HS dropouts can take a seven hour battery of tests, covering language arts, social studies, math, and science GED is widely viewed as equivalent to a traditional HS diploma History I Began in 1942 to accomodate veterans that did not complete HS I Periodically revised given changing economic landscape I Revised in 2014, with three levels of passing F GED R Passing Score: at or higher than the minimum needed to demonstrate high school equivalency-level skills and abilities F GED R College Ready: demonstrates the skills and abilities needed to enroll in credit-bearing college courses F GED R College Ready + Credit: may be eligible for up to 10 hours of college credit Economics of Education 67 / 319 Trends: Test Taking & Completion Economics of Education 68 / 319 Economics of Education 69 / 319 Economics of Education 70 / 319 Economics of Education 71 / 319 Counting GEDs as HS grads masks an increase in HS dropouts Counting GEDs as HS dropouts instead would imply that the HS dropout rate for Blacks was roughly the same in 2000 as in 1960 Economics of Education 72 / 319 Trends: Life After the GED Economics of Education 73 / 319 Economics of Education 74 / 319 Economics of Education 75 / 319 But the gains relative to HS dropouts disappear when controlling for inate ability Economics of Education 76 / 319 Economics of Education 77 / 319 Quantity of Education Returns to Education Stylized facts I Corr(educ, Y ) > 0 I Corr(educ, unemployment ) < 0 Human Capital Earnings Function (HCEF) ln(wi ) = α + βEi + εi where β 0.07 ) 7% increase in (expected) wages per year of educ Focus of current research attempts to di¤erentiate between causal e¤ects and correlation Spectrum of explanations Correlation: Causal: Ability Bias, Productivity Signaling Economics of Education 78 / 319 Productivity Hypothesis Causal e¤ect of educ on LM outcomes due to productivity-enhancing e¤ect of educ Educ ) " MPL ) " Y , employment Entire relationship between educ and LM returns is causal Economics of Education 79 / 319 Ability Bias Hypothesis Productivity depends on ‘inate’ability and educ MPL = f (|{z} E ) A , |{z} + + Educ depends on ability and other factors E = g (|{z} X ) A , |{z} + ? Implication I Without holding A …xed, the association between E and Y overstates the causal e¤ect of E by attributing some of the e¤ect of A to E I Plausible that all of the observed association between E and Y may be due to A MPL = f (A) Economics of Education 80 / 319 Graphical depiction slope = observed return to educ Y slope = ‘true’return to educ Y slope = observed return to educ Ahigh Ahigh Alow Alow E E HS college HS college Case I Case II Economics of Education 81 / 319 Signaling Hypothesis (Spence 1973) Goal: Model positive association between E and Y despite educ not a¤ecting productivity Intuition: I Productivity depends on (unobserved to the …rm) ability, A I Schooling ‘signals’ability I For the ‘signal’to have content, Corr(signaling cost, A) < 0 Economics of Education 82 / 319 Setup I Worker productivity unobserved to …rm at time of hire and depends only on ability ! asymmetric information I True productivity only revealed over extended period I If productivity were observed, Y = MPL I Firms have an informed expectation of worker productivity given observed signals I Firms o¤er wages equal to expected productivity given signals Y = E[MPL j Signals] I Signals are alterable by workers, but is costly I Costs are heterogeneous I Workers choose signal to optimize earnings net of signaling costs I An alterable attribute is a potential signal i¤ its associated cost is negatively correlated with MPL Economics of Education 83 / 319 Simpli…ed Model I Two types of workers F High productivity: MPL = AH , fraction p of pop F Low productivity: MPL = AL , fraction 1 p of pop F AH > AL I Signal = years of educ, E I Cost per year F High productivity workers: cH F Low productivity workers: cL F cH < cL Economics of Education 84 / 319 Solution 1. Pooling Equilibrium (PE) I In a PC market, pro…ts, Π, must be zero I Here, there is uncertainty since …rms do not know workers’productivity at time of hiring I Now, PC ! E[Π] = 0 I Implications F All workers paid identically Y = E[MPL ] = p AH + (1 p ) AL F No incentive to obtain educ ! EL = EH = 0 F E¢ cient outcome since no bene…t to E in model F Low ability workers are overpaid; high ability workers underpaid Y 2 (A L , A H ) F Π for any given …rm may be positive or negative due to luck in hiring process, but zero in expectation Economics of Education 85 / 319 Solution 2. Separating Equilibrium (SE) I To alleviate uncertainty, suppose a …rm advertises following compensation schedule e AL if E < E Y = AH if E > E e I Workers optimize; set E = f0, E eg I e For equilibrium to exist, must be that EL = 0 and EH = E F Low productivity worker problem max Y (E ) cL E E F High productivity worker problem max Y (E ) cH E E Economics of Education 86 / 319 Solution 2. SE (cont.) I Implications of SE F Low productivity worker sets E = 0 i¤ AL cL 0 > AH e cL E AH AL ) Ee > cL F e i¤ High productivity worker sets E = E AL cH 0 6 AH e cH E AH AL ) Ee 6 cH F Multiple (possible) values e2 AH AL AH AL E , cL cH i¤ cH < cL F e= Since education does not a¤ect productivity and is costly, E AH AL cL is the most e¢ cient possibility Economics of Education 87 / 319 Notes I Pooling equilbm is socially optimal since educ is not productive I Low productivity workers prefer PE I e is not too high) High productivity workers prefer SE (if E PE SE Low Ability Y = p AH + (1 p ) AL , E = 0 Y = AL , E = 0 High Ability e Y = p AH + (1 p ) AL , E = 0 Y = AH , E = E I In SE, signal serves as a means to circumvent asymmetric info problem I Testable implications 1 Importance of signals fades over time as true productivity is revealed to …rm ! Cov(Y , signals) decreases with job tenure 2 Individuals facing non-binding CALs increase educ further to distinguish themselves from lower ability individuals whose educ is compelled to increase under the CAL Economics of Education 88 / 319 HC vs Signalling Model: Evaluating education policy Recall model for optimal HC investment E c T Y (E ) E = arg max DPV = ∑ t + ∑ t t =0 (1 + r ) t =E +1 (1 + r ) I This implicitly relies on the HC model since earnings depend only on own educ, Y (E ) I Under signalling model, earnings depend on relative educ, Y (E , E i ) Economics of Education 89 / 319 Important implications for the merits of policy proposals regarding free (community) college for all in the US Under HC model, E is unchanged by policy if E CC and will increase for some if E < CC Under Signalling model, E may increase for everyone with E CC and E may decline for those with E 0 (positive MU), U 00 < 0 (diminishing MU) I U > 0 is needed in all periods (due to subsistence cost) I Consumption per period c1 = y1 (1 D )[1 s (r )]` c2 = y2 Dc Economics of Education 115 / 319 Maximum utility with repayment (D = 0) 1 WD =0 = U (y1 [1 s (r )]`) + U (y2 ) 1+r Maximum utility with default (D = 1) 1 WD =1 = U (y1 ) + U (y2 c) 1+r Economics of Education 116 / 319 Default or no default? ? WD = 1 7 WD = 0 as I Default raises c1 , but I Reduces c2 I WD =0 starts out below WD =1 when y1 0 F WD =1 = 0 if y1 = 0 F WD =0 = 0 if y1 [1 s (r )]l I WD =0 increases faster with y1 than WD =1 F MU of consumption is greater after repayment due to lower consumption F Eventually WD =0 > WD =1 as the lower utility due to lower c1 is more than o¤set by higher c2 due to a lack of default penalty I Implication: 9 y1 s.t. D = I(y1 < y1 ) =) default is a strategic response to economic situation Economics of Education 117 / 319 Graphical solution W WD=0 DEFAULT WD=1 REPAY y1* y1 [1-s(r)]l Economics of Education 118 / 319 Extensions: Part I 1 " ` )" y1 since repayment is more costly 2 " s (r ) )# y1 since repayment is less costly 3 " c )# y1 since default becomes more costly 4 # y2 )# y1 since expected MU of c2 increases and, hence, default becomes more costly " `, # s (r ) # y2 , " c Economics of Education 119 / 319 Extensions: Part II I Is it possible to alter loan structure to prevent strategic default? ! Income contingent loans (ICLs) I ICLs F O¤er a form of default insurance F Repayment only due if income exceeds a predetermined threshold F Repayment burden is capped at a certain percentage of income F E¤ectively smoothes consumption by lowering repayment during periods of low income and raising repayment during periods of high income I ICLs are used in some countries: Australia (1989), New Zealand (1991), South Africa (1991), England and Wales (1998), Hungary (2001), Thailand (for 2006 only), South Korea (2009), the Netherlands (revised for 2016) and Malaysia (apparently planned for 2016) Economics of Education 120 / 319 ICL theory I Alter c1 such that it is now given by c 1 = y1 (1 D ) maxf0, minf ϕ(y1 y ), [1 s (r )]`gg where I y = income threshold below which no repayment is required I ϕ = maximum repayment burden Economics of Education 121 / 319 Possible outcome under ICL with well-chosen policy parameters WD=0 W REPAY WD=1 REPAY y1* y1 [1-s(r)]l _ y Economics of Education 122 / 319 US has begun to o¤er Income-Driven Repayment (IDR) plans Student must apply: https://studentaid.ed.gov/sa/repay-loans/understand/plans/income-driven Economics of Education 123 / 319 Economics of Education 124 / 319 Economics of Education 125 / 319 Economics of Education 126 / 319 While IDR plans may reduce default, they imply signi…cant gov’t subsidies Economics of Education 127 / 319 Quality of Education Introduction Focus to this point has been on educ quantity, but now educ quality Here, we will primarily focus on primary and secondary education due to 1 Importance of early life education experiences 2 Lower student mobility at this stage 3 Central to current policy debates 4 Perhaps better data availability Economics of Education 128 / 319 Educ quality is typically proxied by test scores due to data availability, importance, and... lack of a better alternative? Economics of Education 129 / 319 However, test scores are important for economic growth Test scores are also important for individual earnings Di¤erences in cognitive skills explain much of the black-white wage gap in the US Economics of Education 130 / 319 Best available data for US come from the National Assessment of Educational Progress (NAEP) I See http://nces.ed.gov/nationsreportcard/ I Begun in 1969 I Administered to random samples of public and private students I Allows measurement of trends by age-subject, and by state I Administered in math, science, reading, writing, the arts, civics, economics, geography, U.S. history, and technology and engineering literacy (2014) Economics of Education 131 / 319 Trends in Test Scores: US Only Economics of Education 132 / 319 Economics of Education 133 / 319 Economics of Education 134 / 319 Economics of Education 135 / 319 Economics of Education 136 / 319 Economics of Education 137 / 319 Trends in Test Scores: International Comparison Comparisons based on I TIMSS (http://timss.org/) I PIRLS (http://timss.org/) I PISA (http://www.oecd.org/pisa/) Economics of Education 138 / 319 Economics of Education 139 / 319 Economics of Education 140 / 319 Economics of Education 141 / 319 Economics of Education 142 / 319 Economics of Education 143 / 319 Economics of Education 144 / 319 Conclusions: US test scores have stayed relatively constant over time US performance relative to other countries is not stellar Much variation in test score performance across students at a given point in time How does the US improve educ quality??? Economic tools are (perhaps surprisingly) useful in thinking about this question Economics of Education 145 / 319 Quality of Education Educational Production Function The basic building block of economic analyses of educ quality is the educational production function (EPF) I Conceptualize educ quality as a production process F Inputs are various factors determining school ‘quality’ F Outputs are measures of student performance (e.g., test scores) Tech z}|{ Q = f (x1 ,..., xK ) |{z} | {z } Output Inputs Questions: 1 What inputs enter the production function ! x1 ,..., xK 2 What does technology mean here ! f ( ) Similar to traditional …rm production function (inputs ! output), but di¤erences arise due to inputs that may matter (past inputs, family inputs, etc.) Economics of Education 146 / 319 Properties of Production Functions De…nition The marginal product of an input, say MP1 , is the additional output obtained from one more unit of the input. If the production fn is given by Q = f (x1 , x2 ), where Q is output, then ∂f (x1 , x2 ) ∆Q MP1 = > 0. ∂x1 ∆x1 x2 Graphically Q _ f(x1, x2) slope = MP1 x1 production fn Economics of Education 147 / 319 De…nition Diminishing MP refers to the fact that each additional unit of input increases total output by less and less. If the production fn is given by Q = f (x1 , x2 ), then diminishing MP1 implies ∆Q ∂MP1 ∂2 f (x1 , x2 ) ∆ ∆x1 = < 0. ∂x1 ∂x12 ∆x1 x2 Graphically Q _ f(x1, x2) x1 production fn Economics of Education 148 / 319 De…nition Technological improvement refers to a change in the production function such that more output is now obtained for a given level of inputs. If the original production fn is given by Q = f (x1 , x2 ), then technological improvement means the new production fn is given by Q = g (x1 , x2 ), where g (x1 , x2 ) > f (x1 , x2 ) 8x1 , x2 _ Graphically Q g(x1, x2) slope = MP1’ _ f(x1, x2) slope = MP1 x1 production fn Economics of Education 149 / 319 Quality of Education EPF: Inputs (Part I) Starting point: money! Economics of Education 150 / 319 Economics of Education 151 / 319 Economics of Education 152 / 319 Economics of Education 153 / 319 Economics of Education 154 / 319 Economics of Education 155 / 319 Does money matter? Data implies no aggregate correlation between test scores and per pupil expenditures Economics of Education 156 / 319 In line with historical view I Equality of Educational Opportunity (“Coleman Report”, 1966) was a federal gov’t study on racial inequality in education I Concluded there was little association between resources per pupil and student achievement; family background was crucial I Report is widely interpreted (incorrectly) as “resources do not matter” However, not clear from time series correlations that money does not matter or can’t matter 1 How has the increase in resources been allocated: academics, non-academics (support sta¤, litigation, safety, etc.), special education, English Language Learners (ELL), arts/music/sports, etc.? 2 Have other inputs in the EPF eroded over time: income, nutrition, family structure, diability, language, etc.? Economics of Education 157 / 319 Allocations Economics of Education 158 / 319 Demographics Economics of Education 159 / 319 Economics of Education 160 / 319 UNICEF Poverty lines de…ned as a percentage of median income in each country Economics of Education 161 / 319 Economics of Education 162 / 319 Economics of Education 163 / 319 Economics of Education 164 / 319 Economics of Education 165 / 319 Economics of Education 166 / 319 Economics of Education 167 / 319 Aggregate money may not matter, but something does Economics of Education 168 / 319 Quality of Education EPF: Inputs (Part II) Now, let’s go back to the EPF and think about speci…c inputs rather than just money Goals 1 Develop a coherent theoretical framework for modeling student achievement 2 Develop a coherent empirical framework to econometrically test the importance of di¤erent inputs Economics of Education 169 / 319 Theoretical Framework Qg = f (F K , FK , F1 ,..., Fg , PK , P1 ,..., Pg , SK , S1 ,..., Sg , eK , e1 ,..., eg , A) K , 1,..., g represent grade levels P = peer e¤ects K represents the period prior to S = school resources kindergarten entry e = student e¤ort Q = output (test score) A = student inate ability F = family inputs Note: Coleman Report emphasized role of F Economics of Education 170 / 319 Primary implications I Cumulative inputs matter ! di¤erent from …rm production fn F Past inputs, current e¤ort, inate ability, are di¢ cult to observe by researchers I Form of the production fn, f ( ), is unknown Economics of Education 171 / 319 Empirical Framework To overcome the lack of data, most current empirical studies estimate a value-added speci…cation Qg = f (F K , FK ,..., Fg , PK ,..., Pg , SK ,..., Sg , eK ,..., eg , A) Qg 1 = f (F K , FK ,..., Fg 1 , PK ,..., Pg 1 , SK ,..., Sg 1 , eK ,..., eg 1 , A) ) Qg Qg 1 =e f (Fg , Pg , Sg ) which assumes that lagged student achievement, Qg 1 , fully captures all past inputs and that e and A are constant over time Value-added speci…cations require only data on consecutive test scores and current inputs Economics of Education 172 / 319 Interpretation of Empirical Results Before examining the e¤ects of a few key inputs, a short digression I One commonality with …rm production fns is that inputs are potentially substitutable F Has important implications for research and policymakers F Must distinguish between ceteris paribus e¤ects of inputs vs. policy e¤ects De…nition The ceteris paribus e¤ect of an input is the change in output resulting from a change in the input holding all other inputs constant. Analogous to marginal product. De…nition The policy e¤ect of an input is the change in output resulting from a change in the input. Economics of Education 173 / 319 ‘Simple’theoretical illustration Dynamic model Qg = f (Fg , Sg , A) where I Qg = achievement at end of grade g I Fg = family inputs in grade g I Sg = school inputs received by student in grade g I A = student inate ability Economics of Education 174 / 319 HH behavior Fg = F (W , A, Sg Sg ) where I W = family wealth I S g = average school resources I Note: while S g is chosen by parents’school choice, Sg is not; but Sg S g is realized prior to family making its input decisions, Fg School decision rule perhaps Sg = S ( A ) Economics of Education 175 / 319 Total e¤ect of change in Sg on Qg dQg ∂f ( ) ∂f ( ) ∂F ( ) = + dSg ∂Sg ∂Fg ∂ Sg S g | {z } CP E¤ect | {z } Policy E¤ect ) CPE 6= PE unless ∂F ( )/∂(Sg Sg ) = 0 Notes I PE accounts for the fact that other inputs may adjust to compensate or accentuate changes in a given input I Typically, research focuses on CPEs, but PEs are (more?) relevant Economics of Education 176 / 319 Now, turn to discussion speci…c inputs at the forefront of policy discussions 1 Class size 2 Ability tracking 3 Teachers 4 Early childhood programs (pre-K) Economics of Education 177 / 319 Class Size Perhaps the most focused on input by parents, teachers, policymakers Potentially enters the EPF through school resources, S Has fallen signi…cantly in US Economics of Education 178 / 319 Potential bene…ts I Individual attention I Altered instructional techniques I Fewer disciplinary problems I Student engagement Potential costs I Expensive! Opportunity costs? I Reduction in average teacher ‘quality’ Economics of Education 179 / 319 Theoretical model I Setup F EPF Qg = f (..., ng ,..., A ) where ng = Zg /Mg is class size, Z is school enrollment, M is # of teachers F School district maximization problem max Πg = Bene…ts – Costs Mg = φZg Qg wMg = φZg f (..., ng ,..., A ) wMg where φ is the value per unit of student achievement and w is the wage for teachers Economics of Education 180 / 319 Theoretical model (cont.) I Solution ∂Πg ∂Qg = φZg w =0 |{z} ∂Mg ∂Mg | {z } MC MB = φZg MPM g w =0 w ) MPM g = φZg I Add teachers until the MP of the last teacher is equal to w /φZg I Implies ng = Zg /Mg is 1 increasing in teacher costs, w 2 decreasing in value of average student achievement, φZg Economics of Education 181 / 319 Theoretical model (cont.) I Graphical solution Economics of Education 182 / 319 Some evidence that return to smaller classes may be greater for low ability students Economics of Education 183 / 319 Empirical work I Project Star I Class Size Reduction (CSR) mandates F California (1996) ! total cost: over $25 billion; unraveled during the Great Recession F Florida (adopted 2002, implemented fully 2010) ! total cost to date: $24.6 billion I Impacts have been modest due to distinction between CPEs and PEs “In addition to high costs, reducing class size can have unintended consequences. When California reduced class size in 1996, the state found that it did not have enough veteran teachers or classrooms to meet the challenge. Schools were forced to hire new teachers and add portable classrooms to accommodate the state mandate. Schools faced a dilemma: Was it really better to have smaller classes with an inexperienced teacher or larger classes with experienced teachers?... The California experience points to an important lesson. Class size reduction, in and of itself, is not the answer to all the problems in education. In order for a classroom to be e¤ective, it must have a quali…ed teacher and adequate facilities.” (http://www.greatschools.org) Economics of Education 184 / 319 Ability Tracking Tracking is a vague concept, but generally deals with grouping students together according to some criteria (as opposed to random placement in classes) I In primary school, simpler to identify as schools may formally group students by ability level I In secondary school, harder to identify F Formal tracking may exist: “college-bound” versus “vocational training” F Informal tracking may occur by material level (e.g., algebra, pre-calc, or calc; AP vs. non-AP classes) Potentially impacts student achievement through the composition of peers, P, in the classroom Generally viewed as bene…cial to high ability students, harmful to low ability students ! politically contentious issue Empirical analysis is complicated I Track placement within schools that track is obviously correlated with student ability (thus, hard to disentangle e¤ects of tracking and ability) Economics of Education 185 / 319 Theoretical model I Setup F Two types of students: high ability (AH ), low ability (AL ) F Fraction of high ability students is p and 1 p are low ability F EPF Qg = f (..., Pg ,..., A ) where Pg is the average ability of one’s peers, A is one’s own ability, and Qg may depend on Pg I Policy options F Random assignment ! E[Pg ] = p AH + (1 p ) AL F Tracking: PH = AH and PL = AL Economics of Education 186 / 319 Theoretical model (cont.) I Implication: Tracking hurts low ability and helps high ability students I Graphical depiction with concave production fns Economics of Education 187 / 319 Theoretical model (cont.) I Graphical depiction with convex production fns Q f(P,AH) QH,T f(P,AL) QH,R QL,R QL,T AL E[P] AH peer quality (P) I Concave production fn yields the same conclusion, but has a subtle di¤erence: average test score may rise with convexity, but fall with concavity Economics of Education 188 / 319 Empirical evidence I Not overly conclusive I Some evidence that tracking does not a¤ect test scores of high ability, but does bene…t low ability I Why? Low ability su¤er with high ability students (frustration, lack of teacher attention, etc.) I Production fn in this case must be something like this Q QH,R = QH,T f(P,AH) QL,T QL,R f(P,AL) E[P] peer quality (P) AL AH Economics of Education 189 / 319 Teachers Teacher attributes enter the EPF through S Early research focused on observed attributes of teachers such as educ, experience, and salaries Conclusion: Except for the …rst 2-3 yrs of experience, these factors do not a¤ect test scores Economics of Education 190 / 319 Economics of Education 191 / 319 Economics of Education 192 / 319 Lack of correlation between teachers’observed attributes and student test scores contrasts with perception that teachers should matter greatly Current research uses an output-based approach to estimate e¤ects of individual teachers on student test scores I Intuition: Use Qg and Qg 1 to compute the average change achieved by a given teacher’s students 1 nt ∆t = ∑ (Q Qig 1) nt i =1 ig where i indexes students, nt is the class size for teacher t, and ∆t is the average value-added of teacher t I Empirical evidence is striking 1 Distribution of ∆ is highly variable across teachers ! teachers matter and di¤er in quality 2 ∆t is not correlated with observed teacher attributes (e.g., educ, experience) 3 Principals are able to identify high quality teachers in their school Economics of Education 193 / 319 Economics of Education 194 / 319 Economics of Education 195 / 319 Economics of Education 196 / 319 Teacher quality matters in the long-run as well Economics of Education 197 / 319 Economics of Education 198 / 319 Better teachers can close the international test score gap, and especially matter in larger classes Economics of Education 199 / 319 Results lead to new questions regarding recruitment and retention of high quality teachers? Two broad areas of research 1 Occupational licensing 2 Compensation Economics of Education 200 / 319 Occupational licensing... Licensing or screening is one mechanism by which the gov’t can potentially in‡uence the quality of individuals entering a profession Most states require teachers to meet certi…cation requirements either prior to hiring or shortly thereafter I To gain legal permission to teach, individuals are generally required to study full-time for one or two years in an approved education program I Recruiting di¢ culties – especially in urban school districts – has led to hiring of uncerti…ed or alternatively certi…ed teachers I Certi…cation, alternative certi…cation requirements vary by state Motivation is to ensure all teachers meet basic quality threshold Certi…cation may keep out some good teachers Economics of Education 201 / 319 Theoretical model of certi…cation I Setup F Prospective teachers have two occupations to choose among: teaching, non-teaching F wi = wage for individual i in the non-teaching profession F wi also measures the ability of individual i as a teacher F w = …xed wage for teachers F Individuals choose the profession with the higher wage I With certi…cation F States impose a test requirement for entry into teaching F c = cost of taking the test Economics of Education 202 / 319 Theoretical model of certi…cation (cont.) I Implication: Without the testing requirement F Individuals with wi < w enter teaching F Individuals with wi w enter non-teaching Economics of Education 203 / 319 Theoretical model of certi…cation (cont.) I Implication: With perfect testing F Test is “perfect” at measuring teacher quality, then score, s, is given by si = w i and w is the minimum passing score F Individuals with w si = wi < w c enter teaching F Individuals with si = wi < w or si = wi w c enter non-teaching ! Information e¤ect: eliminating low quality teachers ! Discouragement e¤ect: eliminating high quality teachers ! Impact on average quality is ambiguous Economics of Education 204 / 319 Theoretical model of certi…cation (cont.) I Implication: With imperfect testing F Test is “noisy” at measuring teacher quality, then score, s, is given by si = w i + η i , where η is a random assessment error such that E[η i ] = 0 and Corr(wi , η i ) = 0 F Individuals with w si = wi + η i and wi < w c enter teaching F Individuals with si = wi + η i < w or wi w c enter non-teaching ! Ineligibility e¤ect: eliminating quality teachers with a bad η shock ! Eligibility e¤ect: allowing low quality teachers with a good η shock ! Noise necessarily lowers the average quality of teachers relative to perfect measure Economics of Education 205 / 319 Economics of Education 206 / 319 Alternative graphical depiction I A = false positives I B = true negatives I C = false negatives I D = true positives Economics of Education 207 / 319 Economics of Education 208 / 319 Teacher compensation... Screening requirements such as certi…cation place strong requirements on the ability of screeners to identify appropriate screening devices More e¤ective and e¢ cient perhaps to devise a system that incentivizes high quality teachers to self-select into teaching profession Salary structure is most obvious mechanism However, current salary structure does not create the ‘right’incentives I Real teacher salaries have plateaued I Relative teacher salaries have dropped signi…cantly I Teacher unions limit reforms Economics of Education 209 / 319 Teacher compensation data Economics of Education 210 / 319 Economics of Education 211 / 319 Economics of Education 212 / 319 Economics of Education 213 / 319 Economics of Education 214 / 319 Economics of Education 215 / 319 The decline in relative teacher salaries ! decline in traditional ‘ability’ levels of those entering teaching relative to historical patterns However, pattern has reversed some of late Economics of Education 216 / 319 Higher overall salaries may induce more high ability teachers to enter the profession, but it also rewards low ability teachers Performance-related pay (PRP) allows higher salaries only for high ability teachers PRP often advocated as a way to get higher ‘ability’individuals to self-select into teaching PRP compensates workers for outputs (value-added) rather than inputs (time) I PRP discourages low quality teachers from entering the profession I PRP rewards high quality teachers, discourages exit from the profession Trends I 1918: 48% of school districts used merit pay I 1939: 20% I 1953: 4% I 1984: 10% I 1993: 12% I 2010: 3.5% Economics of Education 217 / 319 Data from 2007. Economics of Education 218 / 319 Critiques of PRP for teachers I Measurement ! validity of the value-added approach I Team production makes it di¢ cult I Adverse incentives F Teachers have many objectives, student achievement is only one F Incentives related only to test scores will shift teacher focus away from other dimensions to those that are rewarded F ‘Teaching to the test’ F Incentives for cheating Empirical e¤ects of PRP I E¤ects are fairly mixed I POINT Experiment (Project on Incentives in Teaching) F http://www.rand.org/content/dam/rand/pubs/reprints/2010/RAND_RP1416.pdf I Texas Excellence Initiative (TEI) in DISD F http://tei.dallasisd.org/ Economics of Education 219 / 319 Teacher unions... Role of unions in teaching profession has increased over time Unions are obstacles to many currently debated reforms such as PRP, school choice “THE TEACHER UNIONS HAVE MORE INFLUENCE ON the public schools than any other group in American society. They shape the schools from the bottom up, through collective-bargaining activities so broad in scope that virtually every aspect of the schools is somehow a¤ected. They also shape the schools from the top down, through political activities that give them unrivaled in‡uence over the laws and regulations imposed on public education by government.” -Moe (Education Next, 2001) Economics of Education 220 / 319 Economics of Education 221 / 319 According to Moe (2001), the objectives of teachers’unions typically include 1 Protecting the jobs of all members 2 Preventing uncertainty due to performance-based pay 3 Limiting discretion of principals and administrators 4 Preventing di¤erentiation among teachers 5 Limiting competition between schools 6 Preventing contracting out any part of the educational process 7 Requiring all teachers to join the union As these objectives often con‡ict with the interests of schools and students, unions are not viewed very favorably Economics of Education 222 / 319 Theoretical model I Unions may impact achievement via total resources, S, and the allocation of these resources I E¤ect may be positive or negative F E¢ ciency-enhancing model: Teachers possess the same objective fn as parents, administrators, but possess better information F Rent-seeking model: Teachers possess a di¤erent objective fn, diverting resources to self-serving purposes I In either case, unions may impact the educational production fn via three channels I 1 Budget constraint: total allocation of resources to schools (S ) 2 Input mix: allocation of resources across di¤erent inputs (S1 , S2 ,...) 3 E¢ ciency: returns to di¤erent inputs (MPS1 , MPS2 ,...) Economics of Education 223 / 319 To understand e¤ect of e¤ect of unions, consider how resources are allocated Preliminaries De…nition An iso-achievement curve connects di¤erent combinations of inputs, say S1 and S2 , that yield the same level of test scores. S2 S2 higher test scores Q1 budget Q0 set S1 S1 De…nition The budget constraint connects di¤erent combinations of inputs, say S1 and S2 , that fully utilize available resources. Economics of Education 224 / 319 Maximizing test scores subject to the budget constraint, assuming perfect information, yields the following optimal allocation of resources S2 S2 * Q* S1* S1 Economics of Education 225 / 319 Unions: Rent-seeking model Q2 I A ! B due to " Q Q 1 resources S2 0 I B ! C due to change in input mix due to self-serving preferences.B I C ! D due to S2 *. I e¢ ciency losses Test scores at D A..C D are higher than at A, but opposite is possible S1* S1 Economics of Education 226 / 319 Unions: e¢ ciency-enhancing Q3 model S2 Q 0 I A ! B due to " resources I B ! C due to change in input.. B mix due to S2* A.. D superior C knowledge I C ! D due to e¢ ciency gains I Test scores at D are higher than at A S1* S1 Economics of Education 227 / 319 Empirical e¤ects of teacher unions I Mixed evidence I Do " resources and teacher pay I However, also change input mix in not necessarily a productive way Economics of Education 228 / 319 Early Childhood Programs US has seen a rapid rise in pre-school program participation Enters the EPF though F K Economics of Education 229 / 319 Economics of Education 230 / 319 Three main questions 1 How e¤ective are early childhood programs? 2 How does participation a¤ect behavior of primary schools? 3 Should there exist universal, public pre-K programs? Economics of Education 231 / 319 Program e¤ectiveness I Largest public early childhood program is Head Start F Began in 1965 by LBJ to combat a lack of school readiness among impoverished children prior to K entry F Expanded over time to focus on 3-4 yr olds F Focus is on cognitive and non-cognitive skills, health, nutrition F Evaluations provide some evidence of a long-term impact on student achievement I Recent research suggests that early programs produce much greater, persistent impacts than later interventions I Impacts are largest on low-achieving students Economics of Education 232 / 319 Economics of Education 233 / 319 Economics of Education 234 / 319 Economics of Education 235 / 319 Theoretical model: Program e¤ects on schools I Setup F Three period model F EPFs Q1 = f1 (F 1 ) Q2 = f2 (S 2 , Q 1 ) where Q is end-of-period achievement, F is family resources, and S is school resources F One district containing two schools, A and B F A is more a- uent such that F1A > F1B ! Q1A > Q1B time Pre-K School Adult (Period 1) (Period 2) (Period 3) Economics of Education 236 / 319 Theoretical model (cont.) I School district maximization problem F Must allocate a …xed amount of resources, S 2 , between A and B F Policy options ! Equality: S2A = S2B ! Compensation: S2A < S2B ! Reinforcement: S2A > S2B F Optimal allocation depends on district’s utility fn, U , and EPF, f2 ( ) 8 < Q2A + Q2B ! max average outcomes U= minfQ2A , Q2B g ! max lowest outcome : maxfQ2A , Q2B g ! max highest outcome Economics of Education 237 / 319 Theoretical model (cont.) I Implications F U = minfQ2A , Q2B g ! compensation strategy ! S2A < S2B ! less incentive to invest in F1 , but greater equality F U = maxfQ2A , Q2B g ! reinforcement strategy ! S2A > S2B ! greater incentive to invest in F1 , but greater inequality F U = Q2A + Q2B ! invest in students where the marginal product of S , ∂Q2 /∂S2 , is highest ∂2 Q 2 ∂MPS2 = >0 ! S2A > S2B (reinforcement) ∂S2 ∂Q1 ∂Q1 ∂2 Q 2 ∂MPS2 = 0 Q f(S,Ah) f(S,Am) Qmin f(S,Al) S Economics of Education 262 / 319 Implications I Low and high ability students are ignored ) educational ‘triage’ I Raising Qmin increases (reduces) the number of low (high) ability students that are ignored I Independence between Qmin and distribution of ability at schools provides incentives for teachers, principals to seek out schools with ‘better’distributions since cost of avoiding penalties is smaller Q S* f(S,Amax) Qmin f(S,Amin) S Amin Amax A Economics of Education 263 / 319 Empirical validity? Economics of Education 264 / 319 Economics of Education 265 / 319 Policy implications I To avoid triage, accountability schemes should perhaps be based on continuous measures of test scores ) MBSi > 0 8i I For example, min Ψ I(Q < Qmin ) + ∑i cSi S 1 ,...,S Z where Q is the mean test score in the school and Ψ is the school-level penalty for failure F Now, optimal allocation of e¤ort depends on EPF: Qi = f (Si , Ai ) F Perfect substitutes: all students receive identical S F Complements: S is increasing in A Q Q f(S,Ah) f(S,Ah) f(S,Am) f(S,Am) f(S,Al) f(S,Al) S* S S S*l S*m S*h Economics of Education 266 / 319 Cheating Atlanta, GA ! 178 implicated in scandal; 35 teachers, principals, and administrators (including the superintendent) indicted in March 2013 Washington, D.C. ! 18 teachers cheated in 2012 Birmingham, AL ! investigations after 500+ HS students asked to leave school prior to standardized testing in 2004 Texas ! DMN reported on suspicious test scores across 700 schools in 2004 article; 600 ‘cleared’by completing a survey I El Paso, TX ! low-performing 9th graders held back or encouraged to drop out prior to 10th grade TAKS; Ex-superintendent in federal prison Economics of Education 267 / 319 Quality of Education Market Structure: School Choice Creating strong incentives for public schools to perform via Tiebout choice and accountability schemes seems limited due to 1 Consolidation of public school districts over time 2 Accountability schemes based on single pro…ciency standard Another mechanism to change incentives is to increase school choice Traditional public school system only allows for school choice via residential mobility, which entails large transaction costs Under NCLB, students attending schools deemed “in need of improvement” for 2 consecutive years could transfer to another school in the same district Economics of Education 268 / 319 Relatively new mechanisms to introduce choice include 1 Charter schools 2 Voucher programs Economics of Education 269 / 319 Economics of Education 270 / 319 Quality of Education Market Structure: School Choice (Charter Schools) A relatively new source of school choice that does not require residential mobility comes from charter schools Are public schools I No tuition is charged I Funds allocated based on enrollment, federal aid Began in 1992 in Minnesota Must be approved by government or local school board I Contracts renewable every 3-5 years I Each school must abide by its ‘charter’ I Operate with freedom from many regulations that apply to traditional public schools I Generally o¤er teachers and students more authority Economics of Education 271 / 319 “What do charter schools all have in common? They are independent entities that have received a charter, which is a set of self-written rules (and promises) about how the school will be structured and run. Essentially, they are able to organize a school that’s outside the control of the local school district but still funded by local, state, and federal tax money. This allows charter schools to create free public schools that don’t have to follow the same regulations as district schools. Sometimes this results in a very high-performing school, sometimes not. This approach to education tends to produce a more diverse range of schools than might traditionally be found within school districts.” (http://www.greatschools.org) Economics of Education 272 / 319 Economics of Education 273 / 319 Economics of Education 274 / 319 Economics of Education 275 / 319 Economics of Education 276 / 319 Data from 2007. Economics of Education 277 / 319 Many questions of interest 1 Where do charters enter the market? 2 Who chooses to attend charter schools? 3 What is the e¤ect on public school students? 4 What is the e¤ect of charter school students? Economics of Education 278 / 319 Theoretical Model Framework: Two-stage game I Stage 0: Public school is monopolist, o¤ering quality ) QI I Stage 1: Charter school must decide if to enter and quality ) QC I Stage 2: Public school must decide optimal response if charter school tries to enter the market ) QI Setup I Public school district is the incumbent, sole provider of education ) monopolist I p = price per pupil for schooling, paid by gov’t ) inelastic demand I QI 2 q, q = public school quality I Π = Revenue – Costs = pZ C I C = C (QI , Z ), where Z = # of students; C is increasing in QI and Z I If entrant enters the market, consumers prefer school o¤ering higher Q; if quality is equal, consumers prefer the incumbent Economics of Education 279 / 319 Stage 0 I School district (SD) maximization problem max U (Π, QI ) = Π + V (QI ) = pZ C (QI , Z ) + V (QI ) QI where V represents positive but diminishing MU from quality I Solution ∂V (QI ) ∂C (QI , Z ) MBQ I = MCQ I () = ) QI ∂QI ∂QI I Special case V (QI ) = 0 ) QI = q Economics of Education 280 / 319 Stage 1 I Entrant maximization problem max U (Πc , Qc ) = Πc + V (Qc ) = pc Zc C (Qc , Zc ) + V (Qc ) Qc where F Z c = Z (Q c , Q I ) F pc < p as charter schools receive federal/state funding, but not local property tax revenue I Entrant must choose Qc knowing that incumbent district will respond strategically Economics of Education 281 / 319 Solution: Case I. Unlimited Capacity for Charter School I Entrant can potentially serve all students, Z I If entrant sets Qc > QI , then SD will either 1 Lose all students to charter school, or 2 Adjust QI = Qc to match and charter school will attract no students I If we require the entrant and the SD to earn Π > 0, then entrant will anticipate SD’s response and only enter the market if it is unpro…table for SD to match entrant’s quality I This requires Πc (pc , Qc , Z ) > 0; Π(p, QI , Z ) < 0 which is unlikely since pc < p I Implies no market for entrant; entry does not occur I Monopoly outcome results: QI = QI and all students attend SD Economics of Education 282 / 319 Solution: Case II. Constrained Capacity for Charter School I Entrant can potentially serve only some students, Zmax < Z I Now, if entrant sets Qc > QI , then SD will either 1 Adjust QI = Qc to match and charter school will attract no students 2 Set QI < Qc , losing Zmax to charter school; SD gets Z Zmax I Entry requires value(s) of Qc such that 1 Positive utility for entrant 2 SD’s utility is higher by not matching Qc I This requires CS : pc Zmax C (Qc , Zmax ) + V (Qc ) > 0 SD : p (Z Zmax ) C (QI , Z Zmax ) + V (QI ) > pZ C (Qc , Z ) + V (Qc ) I Second constraint implies C (Qc , Z ) C (QI , Z Zmax ) > pZmax + V (Qc ) V (QI ) > 0 | {z } | {z } cost of matching bene…t of matching Economics of Education 283 / 319 Implications regarding entry by a charter school I Probability of entry is decreasing in p (foregone revenue) I Probability of entry is decreasing in Zmax (foregone students) ! charter schools should be small I Probability of entry is decreasing in SD’s utility from providing quality (warm-glow e¤ect) I Probability of entry is increasing in Qc Revised entrant’s maximization problem max pc Zmax C (Qc , Zmax ) + V (Qc ) Qc subject to < p pc C (Qc , Z ) C (QI , Z Zmax ) > pZmax + V (Qc ) V (QI ) Solution ) Qc (implication regarding charter school quality ) Economics of Education 284 / 319 Stage 2 I Assuming entry by the charter school, SD may still alter its quality I SD maximization problem is now max p (Z Zmax ) C (QI , Z Zmax ) + V (QI ) QI I Recall, monopolist’s solution ∂V (QI ) ∂C (QI , Z ) MBQ I = MCQ I () = ) QI ∂QI ∂QI I Assuming the MC of an additional unit of quality is increasing in student body size, ∂2 C (QI , Z ) >0 ∂QI ∂Z then MCQ I falls due to entry (since student size falls from Z to Z Zmax I To restore MBQ I = MCQ I ! QI < QI < Qc I Special case still holds V (QI ) = 0 ) QI =q Economics of Education 285 / 319 Implication for public school quality C C(QI,Z) slope = MCQ C(QI,Z-Z Cmax) slope = MC’Q slope = MC’ ’Q Q*I Q**I Q Note: MCQ > MC’ ’Q > MC’Q Economics of Education 286 / 319 Conclusion I Competition by charter schools can improve public school quality if entry is successful F However, successful entry implies that public schools do not match charter school quality F Improved quality in public schools only occurs due to reduced marginal cost of improved quality due to fewer students I Unfortunately, the more students charter schools can accommodate, the less likely charter schools can successfully penetrate the market F Implies that charter schools may not yield great improvements in public school quality F Implies should see charter schools in larger, urban areas Economics of Education 287 / 319 Empirical evidence I Growing empirical literature on e¤ects of charter schools on student achievement, mostly focused on charter attendees I Identi…cation based on over-subscribed lotteries I Evidence is mixed; charter schools are heterogeneous F Shortcoming in theoretical model: Model assumes parents know QI , QC I Evidence that charter schools result in greater segregation Economics of Education 288 / 319 Economics of Education 289 / 319 Economics of Education 290 / 319 Economics of Education 291 / 319 Economics of Education 292 / 319 Note: Racial imbalance de…ned as percentage of minority students in school is more than 20% di¤erent than school district as a whole 293 / 319 Quality of Education Market Structure: School Choice (Private Schools) A relatively old source of school choice that does not require residential mobility comes from private schools In contrast to charter schools, private schools charge tuition and many are religiously a¢ liated Economics of Education 294 / 319 Economics of Education 295 / 319 Economics of Education 296 / 319 Impact of competition from private schools may be limited due to cost Moreover, despite the cost of private schools, it is not clear they o¤er higher quality I Test scores higher on average, but causal? I Averages may mask heterogeneity Economics of Education 297 / 319 Theoretical Model Goal: Answer two questions 1 What in‡uences the quality o¤ered by public and private schools? 2 How can inferior private schools co-exist with superior (and free) public schools? Framework: Two-stage game I Stage 0: Public school sets quality ) QG 2 [q, q ] I Stage 1: Private school enters and sets quality and tuition ) Qp 2 [q, q ], p 0 I Stage 2: Students make attendance decisions Economics of Education 298 / 319 Setup I Public school quality determined by majority voting (local elections) I (Single) private school maximizes pro…ts I c is the cost per unit of quality (constant across school types) I Public school is funded by a proportional tax, τ, levied on all HHs I Higher quality requires more student e¤ort, which is decreasing in innate ability I Solution is a set of public and private school qualities and (non-negative) private school tuition that is consistent with majority voting and pro…t maximization I Two possible equilibria 1 Qp > QG 2 Qp < QG Solution obtained via backward induction Economics of Education 299 / 319 Stage 2 I HHs contains parent(s) and a child I Utility maximization problem max U = Y (1 τ) p + w (Q, A) V (e ) where F Y = parental income F τ = tax rate F w = child’s future wage as an adult F Q = QG , Qp F A = child ability F p = cost of school (0 for public schools) F V (e ) = disutility of e¤ort, where e = e (Q, A ) ! ∂e/∂Q > 0 ! ∂e/∂A < 0 Economics of Education 300 / 319 Stage 2 (cont.) I Functional forms wages : w = λ0 + λ1 Q + λ2 A e¤ort : V (e ) = Q/A I Now, substitute these functional forms into U I HH chooses school that maximizes U I Solution depends on relative quality of schools Economics of Education 301 / 319 Stage 2 (cont.) I Case I. Qp > QG F Private school is selected if Up UG ) Up = Y (1 τ) p + λ0 + λ1 Q p + λ2 A Qp /A UG = Y (1 τ ) + λ0 + λ1 Qg + λ2 A Qg /A Qp QG Up UG = p + λ1 (Q p Q G ) A F Choose private school if Qp QG eI Up UG 0)A A p + λ1 (Q p Q G ) F High ability students opt for private school F Ability range of students opting for pirvate school is maximized by setting Qp >> QG Qp QG 1 p A , λ1 p + λ1 (Q p Q G ) A Qp QG Economics of Education 302 / 319 Stage 2 (cont.) I Case II. Qp < QG F Private school is selected if Up UG ) Up = Y (1 τ) p + λ0 + λ1 Q p + λ2 A Qp /A UG = Y (1 τ ) + λ0 + λ1 Qg + λ2 A Qg /A Qp QG Up UG = p + λ1 (Q p Q G ) A F Choose private school if QG Qp e II Up UG 0)A A p + λ1 (Q G Q p ) F Low ability students opt for private school F Ability range of students opting for pirvate school is maximized by setting Qp QG F Pro…t maximization ) Qp = q assuming c is not too high I Case II. Qp < QG F Pro…t maximization ) Qp = q I In either case, Π > 0 Economics of Education 304 / 319 Stage 0 I Given private schools best response, public school quality, QG , and tax rate, τ, are chosen via majority vote I Low ability majority ) q = QG < Qp = q I High ability majority ) q = QG > Qp = q Implications: I When high ability are the majority, there exists a market for low-performing private schools to serve those who cost of e¤ort is too high I When low ability are the majority, there exists a market for high-performing private schools I Regardless, public school quality is una¤ected by the presence of the public school under majority voting F Arises due to no cost of losing students to private schools F Vouchers change this Economics of Education 305 / 319 Voucher Programs Given cost of private schools, competitive e¤ects may be small or even nonexistant Voucher programs amplify the competitive e¤ects of private schools by 1 Making it easier for students to switch to private school 2 Punishing public schools via lower revenue if students switch to private school Similarly, tuition tax credits programs subsidize private school costs De…nition School vouchers, also referred to as opportunity scholarships, are state-funded scholarships that pay for students to attend private school rather than public school. Private schools must meet minimum standards established by legislatures in order to accept voucher recipients. Legislatures also set parameters for student eligibility that typically target subgroups of students. These can be low-income students that meet a speci…ed income threshold, students attending chronically low performing schools, students with disabilities, or students in military families or foster care. Economics of Education 306 / 319 Voucher programs started in 1800s in Maine and Vermont to cover private school costs for rural students without access to a public school Recent voucher programs begun in 1990 13 states + DC currently have voucher programs I http://www.ncsl.org/issues-research/educ/voucher-law-comparison.aspx Milwaukee Public Choice Program I First voucher program, began in 1990 I Originally: HHs with income < 175% of poverty line, who did not attend private school in the previous year were eligible I Limits placed on number of voucher students a private school could take and number of voucher students in total; lottery used if more applicants than seats I Voucher amount set at state per pupil funding in public school I 1998-99: Religious private schools allowed (under Court order) I 2006: 18,000 students took advantage; $100 million reallocated to private schools I 2009: 20,328 students took advantage I 2014-5: Extended to cover entire state Economics of Education 307 / 319 Indiana Choice Scholarship Program I Largest in country in terms of enrollment I Facts F 34,299 participating students (2016-17) F 54 percent of students eligible statewide F 313 participating schools (2016-17) F Average voucher value: $4,024 (2015-16) F Value as a percentage of public school per-student spending: 42 percent Economics of Education 308 / 319 Economics of Education 309 / 319 Data from 2007. Economics of Education 310 / 319 Theoretical Model Vouchers may impact student achievement via four routes 1 Competition induces " QG via F More school resources ! " S F Improved productivity ! f ( ) 2 Private sector may o¤er higher quality, Qp via F Greater productivity than public sector ! di¤erent f ( ) F Better peer quality due to better match ! " P 3 Eliminate ‘crowd out’of educ expenditures due to public educ Economics of Education 311 / 319 Recall simple model of crowd-out from earlier All other A’,B’ spending BC (with public school) A indifference curves B BC (no public school) C,C’ Educational Epub expenditure subsidize

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