Grade 5 | Grade 4 | |||
---|---|---|---|---|

Reading | Math | Reading | Math | |

Class size | -0.410 | -0.185 | -0.098 | 0.095 |

(0.113) | (0.151) | (0.090) | (0.114) | |

Mean score | 74.5 | 67.0 | 72.5 | 68.7 |

SD score | 8.2 | 10.2 | 7.8 | 9.1 |

Obs | 471 | 471 | 415 | 415 |

KAT.TAL.322 Advanced Course in Labour Economics

Nurfatima Jandarova

March 20, 2024

Knowledge/productivity doesn’t rise linearly with years of education.

Production process that takes inputs and develops skills.

Education output of pupil \(i\) in school \(j\) in community \(k\)

\[ q_{ijk} = q(P_i, S_{ij}, C_{ik}) \]

where \(\begin{align}P_i &\quad \text{are pupil characteristics} \\ S_{ij} &\quad \text{are school inputs} \\ C_{ik} &\quad \text{are non-school inputs}\end{align}\)

**Output**

Years of schooling, standardised test scores, noncognitive skills

**Student inputs**

Parental characteristics, family income, family size, genetics, patience, effort

**School inputs**

Teacher characteristics, class sizes, teacher-student ratio, school expenditures, school facilities

**Non-school inputs**

Peers, local economic conditions, national curricula, regulations, certification rules

Static vs

**cumulative**\(\Rightarrow\) levels vs value addedEndogenous allocation of resources by schools

Differences in measured output, multiple outputs

Aggregate policy inputs (curricula, regulation, institutions, etc.)

Other school inputs (selectivity, teacher biases)

Stronger results in lower quality studies

Achievement of student \(i\) in family \(j\) at age \(a\)

\[ q_{ija} = q_a\left(\mathbf{F}_{ij}(a), \mathbf{S}_{ij}(a), \mu_{ij0}, \varepsilon_{ija}\right) \]

\(\mathbf{F}_{ij}(a)\) history of family inputs up to age \(a\)

\(\mathbf{S}_{ij}(a)\) history of school inputs up to age \(a\)

\(\mu_{ij0}\) initial skill endowment

\(\varepsilon_{ija}\) measurement error in output

\(q_a(\cdot)\) age-dependent production function

\(\mathbf{S}_{ij}(a)\) history of school inputs up to age \(a\)

\(\mu_{ij0}\) initial skill endowment

\(\varepsilon_{ija}\) measurement error in output

\(q_a(\cdot)\) age-dependent production function

\[ q_{ija} = q_a(F_{ija}, S_{ija}) + \varepsilon_{ija} \]

Strong assumptions:

- Only current inputs are relevant
**OR**inputs are stable over time - Inputs are uncorrelated with \(\mu_{ij0}\) or \(\varepsilon_{ija}\)

\[ q_{ija} = q_a\left(F_{ija}, S_{ija}, \color{#9a2515}{q_{a-1}\left[F_{ij}(a - 1), S_{ij}(a - 1), \mu_{ij0}, \varepsilon_{ij, a - 1}\right]}, \varepsilon_{ija}\right) \]

Typical empirical estimation assumes linear separability and \(q_a(\cdot) = q(\cdot)\):

\[ q_{ija} = F_{ija} \alpha_F + S_{ija} \alpha_S + \gamma q_{ij, a - 1} + \nu_{ija} \]

Additional assumptions implied:

- Past input effects decay at the same rate \(\gamma\)
- Shocks \(\varepsilon_{ija}\) are serially correlated with persistence \(\gamma\)

Still assume linear separability:

\[ q_{ija} = \sum_{t = 1}^a X_{ijt} \alpha_{a - t + 1}^a + \beta_a \mu_{ij0} + \varepsilon_{ij}(a) \]

Estimation strategies:

- Within-family: \(q_{ija} - q_{i^\prime ja}\) for siblings \(i\) and \(i^\prime\)
- Within-age: \(q_{ija} - q_{ija^\prime}\) for ages \(a\) and \(a^\prime\)

Each with their own caveats

**Non-experimental estimations**

Require strong assumptions

- Some can be relaxed

Require rich data

**(Quasi-)Experimental estimations**

May not recover structural parameters

Ignore general equilibrium

Issues with scaling List (2022)

Meta-analysis of >17,000 twin-analyses (>1,500 **cognitive traits**)

- 47% of variation due to genetic factors
- 18% of variation due to shared environment

Exogenous variation due to court decisions or legislative action

Large variation of spending effects on test scores

Not clear how money was used

Role of differences in regulatory environments

Similar results for participation rates are all positive (mostly significant)

Quasi-experimental variation in Israel: **Maimonides rule**

Rule from Babylonian Talmud, interpreted by Maimonides in XII century:

If there are more than forty [students], two teachers must be appointed

Sharp drops in class sizes with 41, 81, … cohort sizes in schools

**Regression discontinuity design (RDD)**

Maimonides rule: \(f_{sc} = \frac{E_s}{\text{int}\left(\frac{E_s - 1}{40}\right) + 1}\)

**“Fuzzy” RDD**

First stage: \(n_{sc} = X_{sc} \pi_0 + f_{sc} \pi_1 + \xi_{sc}\)

Second stage: \(y_{sc} = X_{s}\beta + n_{sc}\alpha + \eta_s + \mu_c + \epsilon_{sc}\)

Grade 5 | Grade 4 | |||
---|---|---|---|---|

Reading | Math | Reading | Math | |

Class size | -0.410 | -0.185 | -0.098 | 0.095 |

(0.113) | (0.151) | (0.090) | (0.114) | |

Mean score | 74.5 | 67.0 | 72.5 | 68.7 |

SD score | 8.2 | 10.2 | 7.8 | 9.1 |

Obs | 471 | 471 | 415 | 415 |

**Project STAR**: 79 schools, 6323 children in 1985-86 cohort in Tennessee

Randomly assigned students into

small class (13-17 students)

large class (20-25 students)

\[ Y = \alpha + \beta SMALL + X\delta +\varepsilon \]

Randomization means students between classes are on average similar

\(\boldsymbol{\Rightarrow} \color{#9a2515}{\boldsymbol{\beta}}\) **is causal**

Dependent variable | \(SMALL\) | Class quality^{1} |
---|---|---|

Test score percentile (at \(t = 0\)), % | 4.81 (1.05) |
0.662 (0.024) |

College by age 27, % | 1.91 (1.19) |
0.108 (0.053) |

College quality, $ | 119 (96.8) |
9.328 (4.573) |

Wage earnings, $ | 4.09 (327) |
53.44 (24.84) |

2-year pilot program in 2007 among lowest-performing schools in NYC

- 438 eligible schools, 233 offered treatment, 198 accepted, 163 control

Relative rank of schools in each subscore

Bonus sizes:

- $3,000/teacher if 100% target
- $1,500/teacher if 75% target

Instrumental variable approach (LATE = ATT):

\[ \begin{align} Y &= \alpha_2 + \beta_2 X + \pi_2 ~ \text{incentive} + \epsilon \\ \text{incentive} &= \alpha_1 + \beta_1 X + \pi_1 ~ \text{treatment} + \xi \end{align} \]

Elementary | Middle | High | |
---|---|---|---|

English | -0.010 (0.015) |
-0.026 (0.010) |
-0.003 (0.043) |

Math | -0.014 (0.018) |
-0.040 (0.016) |
-0.018 (0.029) |

Science | -0.018 (0.037) |
||

Graduation | -0.053 (0.026) |

Incentive size was too small (\(\approx 4.1\)% of annual salary)

Incentive scheme too complex to nudge a certain behaviour

Bonuses were distributed \(\approx\) equally \(\Rightarrow\) free-riding problem

Incentivising output vs input

Effort of existing teachers vs selection into teaching

Change in teacher pay scheme in Wisconsin in 2011:

- seniority pay (SP):
**collective**scheme based on seniority and quals - flexible pay (FP): bargaining with
**individual**teachers

Main results:

FP \(\uparrow\) salary of high-quality teachers relative to low-quality

high-quality teachers moved to FP districts (low-quality to SP)

teacher effort \(\uparrow\) in FP districts relative to SP

student test scores \(\uparrow 0.06\sigma\) (1/3 of effect of \(\downarrow\) class size by 5)

Prestigious exam schools in Boston and New York

Students from public schools can transfer at 7th or 9th grades

Admission based on test scores, GPA and school preference ranking

Selectivity affects

**peer composition**at either side of the cutoff

Source: Abdulkadiroğlu, Angrist, and Pathak (2014), Figure 2

No effect of peer composition on academic success variables!

Dale and Krueger (2002) study admission into selective colleges in the US

No effect on average earnings

Positive effect on earnings of students from low-income families

Kanninen, Kortelainen, and Tervonen (2023): selective schools in Finland

No effect on high school exit exam score

Positive effect on university enrollment and graduation rates

No impact on income

RCT among schools in remote areas of Istanbul

Carefully designed curriculum promoting **grit** (\(\geq 2\)h/week for 12 weeks)

Treated students are more likely to

- set challenging goals
- exert effort to improve their skills
- accumulate more skills
- have higher standardised test scores

These effects persist 2.5 years after the intervention

Squicciarini (2020): adoption of technical education in France in 1870-1914

- higher resistance in religious areas, led to lower economic development

Machin and McNally (2008): ‘literacy hour’ introduced in UK in 1998/99

highly structured framework for teaching

\(\uparrow\) English and reading skills of primary schoolchildren

Academic achievement is complex function of student, parent, school and non-school inputs

Measuring achievement can also be difficult

Genetic and environmental factors from twin studies almost 50/50

Large variation in school resource effects (from \(\ll 0\) to \(\gg 0\))

- How resources are used?
- Which resources are most effective?

Studies of class size, teacher incentives, peer effects and curricula

Another (often overlooked) step is scaling up to the population

Next: Technological shift and labour markets

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