Leaving School VA on the Table: Ainsworth, Dehejia, Pop-Eleches & Urquiola (2023)

What this is. The core results, the model, and the method from the paper in condensed form: enough to know what it found and how. To replicate or extend, read the full source at doi.org/10.1257/aer.20210949.

TL;DR

Romanian households leave roughly one standard deviation of academic value added (VA) unexploited when choosing among high school tracks. Two candidate explanations are examined: households may lack information about which schools add the most academic value, or they may have genuine preferences for other school characteristics. The authors conduct a clustered information RCT - distributing VA rankings at baseline survey sessions - and find the treatment raises the VA of assigned tracks mostly for low-achieving students who were rejected by their top baseline choices (0.12 SD for low-achieving students overall; 0.20 SD for low-achieving students ineligible for their two top choices). For the full ineligible group, the estimate is 0.18 SD. A rank-ordered logit estimated on household preference rankings reveals that preferences for curricular focus are much stronger than those for academic VA; the peer-quality coefficient is similar in size to the VA coefficient. Counterfactual simulations imply that fully correcting information would close only 17-25 percent of the VA gap for low-achieving students; preferences for other school traits account for 83 percent of the remaining gap.

Core results

Magnitudes and significance are as reported; * / ** / *** = 10% / 5% / 1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Households choose tracks at the 67th percentile of VA in their feasible sets; the mean potential gain from switching to the highest-VA option is 1 standard deviation	Table 4, Panel B-C, p. 1062	Mean percentile rank = 67.1 (all students); potential increase = 1.01 SD = 12 pp baccalaureate pass probability (2019 SD)
R2	VA and selectivity are positively correlated for less- and moderately-selective tracks but negatively correlated for the most selective third	Table 3, Figure 1, p. 1060	Overall correlation = 0.562 (SE 0.005); most selective third: coefficient = -0.243 (SE 0.024)
R3	Households’ VA beliefs are substantially inaccurate: scores are off by 1.1 within-town quintiles on average and explain only 17 percent of the variation in true VA	Tables 5-6, p. 1064	Mean absolute error = 1.13 quintiles; R-squared on true VA quintile = 0.17 (VA); 0.33 (selectivity)
R4	The information treatment raises the VA of assigned tracks by 0.05 SD for all students (10%) and 0.12 SD for low-achieving students (5%); no significant effect for high-achieving students	Table 7, p. 1066	All: 0.048 SD (SE 0.025)*; low-achieving: 0.121 SD (SE 0.049)**; high-achieving: -0.002 SD (insig.)
R5	Among students ineligible for their two top baseline choices, the treatment raises VA by 0.18 SD = 2.21 pp baccalaureate probability (1%)	Table 8, p. 1067	0.184 SD (SE 0.065)*** for the full ineligible group; near-zero for those eligible for either of their two top baseline choices. Among low-achieving students in the ineligible group, the effect is 0.204 SD (SE 0.069), or 2.45 pp (Table 9, p. 1068).
R6	Fully correcting beliefs raises VA by 0.13-0.20 SD for low-achievers (17-25% of potential) and 0.10-0.23 SD for high-achievers (11-24%), across four model specifications	Table 14, p. 1078	Change in VA: 0.13-0.20 SD (low-achieving); 0.10-0.23 SD (high-achieving); share of potential increase 17-25% (low) and 11-24% (high)
R7	Households have much stronger preferences for curricular focus (beta = 0.93) than for academic VA (beta = 0.34) or peer quality (beta = 0.34); 83 percent of unexploited VA under accurate beliefs is due to preferences	Table 13, col. 1, p. 1074; Table 15, col. 5, p. 1079	All rank-ordered logit coefficients sig. at 1%; R-squared = 0.33; 83% of VA left on table under accurate beliefs is attributable to preferences for curricular focus, peer quality, and other traits
R8	Households come closer to maximizing track selectivity than value added	Table 4, Panels B-C, p. 1062	Mean chosen-track selectivity rank = 81.0th percentile; potential selectivity increase = 0.32 SD, compared with a 1.01 SD potential increase in value added
R9	Belief accuracy varies by achievement and favored tracks are overestimated	Tables 5-6, p. 1064; text p. 1065	VA belief errors: 1.19 quintiles for low-achieving and 1.09 for high-achieving households; VA-score R-squared = 0.12 and 0.20, respectively; favored-track VA overestimation = 0.64 and 0.63 quintiles
R10	Treatment effects among students missing their top choices are concentrated among low-achieving students	Table 9, p. 1068	Ineligible students: low-achieving effect = 0.204 SD (SE 0.069, 1% level); high-achieving = -0.023 SD (SE 0.123, insignificant); eligible low-achieving = 0.035 SD (SE 0.058)
R11	Information changes curricular track choice but produces little change in other track traits	Table 10, p. 1068	Among students ineligible for both top choices, technical-track attendance falls 0.069 (SE 0.033); effects on selectivity = 0.006 (SE 0.050), peer SES = -0.009 (SE 0.052), and location quality = 0.073 (SE 0.086)
R12	Information improves accuracy for less-preferred tracks, not the top two	Table 11, p. 1070	Treatment effect on absolute VA-belief error = -0.055 quintiles overall (SE 0.034, insignificant), -0.101 for tracks below the top two (SE 0.045), and -0.181 below the top five (SE 0.063)
R13	Information raises the association between VA and preference ranks for less-preferred tracks	Table 12, p. 1071	Treatment interaction = 0.049 overall (SE 0.026), 0.062 for tracks below the top two (SE 0.023), and -0.072 for the top two (SE 0.103)
R14	In the horse race, households value college and wage VA more than baccalaureate-pass VA	Table 13, col. 5, p. 1074	VA-college = 0.347 (SE 0.082); VA-wages = 0.320 (SE 0.069); VA-pass = 0.013 (SE 0.083); teacher quality = -0.026 (SE 0.080)
R15	Preference counterfactuals leave substantial value added unused even with accurate beliefs	Table 15, p. 1079	Mean residual potential VA gain = 0.44 SD with VA and curricular focus only, 0.57 SD adding peer quality, and 0.69 SD with all attributes
R16	The paper’s alternative value-added measures track the main measure closely	Text p. 1055	Main track-year pass-probability measure has correlation above 0.9 with each alternative value-added measure
R17	Value-added estimates are reported to match RD causal effects at track admissions cutoffs	Text p. 1055	The article says all measures closely match the RD causal effects; no numeric RD estimates are reported in the article text
R18	The local linear forest predicts most of the variation in value added out of sample	Text p. 1055	Out-of-sample model predicts almost 80% of the variation in tracks’ true value added
R19	The authors find no evidence that treatment effects are smaller in towns with more study-school coverage	Text p. 1066	No evidence of informational spillovers is reported; no numerical estimate is printed in the article
R20	Experimental treatment and control groups pass the reported joint balance test	Text p. 1058	Joint test p-value = 0.722; none of the individual balance differences is statistically significant
R21	Households value college and wage value added when those outcomes enter separately	Table 13, cols. 2-4, p. 1074	VA-college = 0.519 (SE 0.073) and VA-wages = 0.485 (SE 0.064), both significant at 1%; teacher quality = 0.180 (SE 0.088), significant at 5%

Overall (paper’s conclusion). Both information and preferences play a role in explaining why households leave VA on the table. Providing information raises the VA of tracks for some students, but only for low-achieving students who were rejected by their top choices. Even fully correcting information would leave most of the VA gap in place because households have strong preferences for curricular focus and peer quality that cause them to forego schools with high VA. Simply making VA information available is unlikely to close the gap.

Theory / model

The paper has no formal equilibrium model; it investigates two candidate explanations empirically. The preference structure is specified as a linear expected utility function over quality scores (p. 1073, eq. 4):

$$U_{ij} = \sum_{q} \beta_q \cdot s_{ij}^q + \epsilon_{ij} \tag{4}$$

where $U_{ij}$ is household $i$‘s expected utility from track $j$, $s_{ij}^q$ is the household’s baseline survey score for track $j$ on quality dimension $q$ (location, peer quality, VA on the baccalaureate, curricular focus, siblings and friends; scale 1 to 5), $\beta_q$ is the preference weight, and $\epsilon_{ij}$ follows a Type I extreme value distribution. The model assumes households rank tracks by expected utility and that the serial dictatorship mechanism is incentive compatible, so submitted rankings truthfully reveal preferences.

Value added $V_{jt}$ is a track-year effect on the probability of passing the baccalaureate exam, estimated via selection-on-observables (Rothstein 2010). The measures are validated against regression discontinuity estimates at track admissions cutoffs following Angrist, Hull, Pathak, and Walters (2017): school-specific RD cutoffs (the minimum transition score for admission) generate quasi-random variation in track attendance, and the paper shows that all VA measures closely match the resulting causal estimates. For cohorts without baccalaureate data (2015-2017, 2019), VA is extended via local linear forests (Athey et al. 2019), which explain almost 80 percent of the variation in true VA out of sample.

The counterfactual comparison asks what track choices would look like if households had accurate VA beliefs. Two predicted VA values are compared for each student:

• $V_{i,IS}$: weighted-average VA across the feasible set using the preference model with inaccurate (baseline survey) scores for VA
• $V_{i,AS}$: the same but replacing inaccurate VA scores with within-town quintiles of measured VA

The difference $V_{i,AS} - V_{i,IS}$ estimates the effect of accurate beliefs, holding preferences constant.

For inaccurate scores, the paper predicts value added as the preference-probability-weighted mean across the student’s feasible set (Section VB, p. 1076):

$$V_{i,IS} \equiv \sum_{j \in \mathcal{J}_i^e} \text{std}(V_{jt}) \cdot \frac{\exp\!\left[\sum_q \hat{\beta}_q \cdot \tilde{s}_{ij}^q\right]}{\sum_{k \in \mathcal{J}_i^e} \exp\!\left[\sum_q \hat{\beta}_q \cdot \tilde{s}_{ik}^q\right]}$$

The accurate-beliefs version uses the same formula but replaces the inaccurate VA score with the measured within-town VA quintile. The simulation holds each household’s feasible set fixed.

Identification. Sections II-III are purely descriptive (selection-on-observables): they document the VA gap and the accuracy of households’ beliefs without claiming causal identification. Section IV is identified by the clustered RCT (randomization at the middle school level, within matched pairs). Section V (preference estimation) is identified by within-town variation in quality scores and track choice under the rank-ordered logit.

Method

Three methodological components produce the paper’s results.

Information experiment. Middle schools were assigned to treatment or control by a matched-pair clustered randomization. At the end of the baseline survey session, all schools received a flyer with links to government admissions websites; treatment schools additionally received a ranking of the town’s high school tracks by VA. The main treatment effect equation (eq. 1, p. 1065) is:

$$\text{std}(V_i) = \eta_0 + \eta_1 \cdot T_i + \eta_X' \cdot \mathbf{X}_i + \eta_i \tag{1}$$

where $\text{std}(V_i)$ is the standardized VA of student $i$‘s assigned track, $T_i$ is the treatment indicator, and $\mathbf{X}_i$ includes the VA of the track to which the student would have been assigned based on the baseline preference ranking (equal to the VA of the highest-ranked feasible track, set to zero if no feasible track was ranked) and an indicator for whether the student ranked a feasible track. Standard errors are clustered by middle school treatment-control pairs (78 clusters).

The treatment effect on the accuracy of VA beliefs is estimated via:

$$\left|\text{quint}(V_{jt}) - s_{iV_j,\text{fs}}\right| = \eta_0 + \eta_1 \cdot T_i + \eta_X' \cdot \mathbf{X}_{ij} + \eta_{ij} \tag{2}$$

where $\text{quint}(V_{jt})$ is the within-town quintile of measured VA and $s_{iV_j,\text{fs}}$ is the follow-up-survey quality score for track $j$ (p. 1069, eq. 2). The effect of treatment on the association between preference ranks and VA is estimated via:

$$\text{ppr}_{ij,\text{fs}} = \bigl(\delta_1 + \delta_2 \cdot T_i\bigr) \cdot \text{pr}(V_{jt}) + \bigl(\delta_{X,1} + \delta_{X,2} \cdot T_i\bigr)' \cdot \mathbf{X}_{ij} + \delta_{ij} \tag{3}$$

where $\text{ppr}_{ij,\text{fs}}$ is the follow-up-survey percentile preference rank of track $j$ and $\text{pr}(V_{jt})$ is the within-town VA percentile rank (p. 1070, eq. 3). The coefficient of interest is $\delta_2$, which measures how treatment changed the association between VA and preference ranks.

Rank-ordered logit for preference estimation. Building on Fack, Grenet, and He (2019) for preference estimation in centralized choice mechanisms, and the heterogeneous-beliefs framework of Kapor, Neilson, and Zimmerman (2020), the preference weights $\beta_q$ are estimated by maximizing the log-likelihood of the top-two baseline track choices (eq. 5, p. 1073):

$$\Pr\!\left(r_{i1}, r_{i2} \mid \mathcal{J}_i, \{s_{ij}^q\}_{q,j}\right) = \prod_{l=1}^{2} \frac{\exp\!\left(\sum_q \beta_q \cdot s_{i r_{il}}^q\right)}{\sum_{k \in \mathcal{J}_i \setminus \{r_{im}:m<l\}} \exp\!\left(\sum_q \beta_q \cdot s_{ik}^q\right)} \tag{5}$$

Here $\mathcal{J}_i$ is the set of all tracks in household $i$‘s town (the feasible choice set) and the product runs over the first two ranked choices. The denominator at stage $l$ excludes all tracks already ranked. Missing quality scores are imputed via a random forest. Standard errors are clustered by middle school.

The method builds on the registry terms randomized-survey-experiment, panel-regression, regression-discontinuity-design, and rank-ordered-logit. The preference-constraint channel uses the registry mechanism multidimensional-preferences alongside information-asymmetry.

Empirical specifications

Value added and selectivity (R2). Table 3 reports student-weighted regressions of standardized track-year value added on standardized minimum transition score, written out from Section II (p. 1060):

$$\text{std}(V_{jt}) = \alpha + \beta\,\text{std}(\text{MTS}_{jt}) + \varepsilon_{jt}$$

The paper splits this specification by yearly selectivity tercile. Standard errors are clustered by town-year; the regressions have no fixed effects specified in the main-text description. The all-town sample has 5,969 town-years, 57,521 track-years, and 2,162,736 students; the survey-town sample has 720 town-years, 11,253 track-years, and 424,508 students. Regressions are weighted by student counts (Table 3, p. 1060).

Feasible-choice gaps (R1, R8). For each student, the chosen-track percentile is its rank by value added or selectivity within the eligible tracks divided by the number of feasible tracks. The potential gain is the feasible-set maximum less the value at the assigned track. Table 4 reports these descriptive statistics by achievement group, without a regression or standard-error estimate (p. 1062). Two percent of students in the full sample have only one feasible track.

Belief accuracy and heterogeneity (R3, R9). Table 5 calculates mean absolute error and mean signed bias between the household score and the within-town quintile of measured value added; Table 6 estimates the score-to-quintile relationship. Written out from the description of Table 6 (pp. 1064-1065):

$$\text{quint}(V_{jt}) = \alpha + \beta_V s_{ij}^{V} + \varepsilon_{ij}, \qquad \text{quint}(\text{MTS}_{jt-1}) = \alpha + \beta_P s_{ij}^{PQ} + \varepsilon_{ij}$$

These are separate regressions for all, low-achieving, and high-achieving households. Standard errors are clustered by middle school; no fixed effects are specified. The full sample has 17,460 student-track observations and 188 clusters (Table 6, p. 1064).

Randomized information effects on assignment and track traits (R4, R5, R10, R11). The printed estimating equation (1) is:

$$\text{std}(V_i) = \eta_0 + \eta_1 T_i + \eta_X' X_i + \eta_i \tag{1}$$

The controls are an indicator for ranking a feasible track at baseline and the value added of the highest-ranked feasible baseline track, set to zero when none was ranked (footnote 27, p. 1065). The intent-to-treat sample has 2,692 assigned students in 170 middle schools and 78 matched-pair clusters; subgroup estimates split by achievement, eligibility for the two highest-ranked baseline tracks, gender, and mother’s schooling (Tables 7-9, pp. 1066-1068). Table 10 applies the same equation to other track attributes, with the baseline-assigned track’s value for the relevant outcome and an indicator for no feasible ranked track as controls (p. 1068). Standard errors are clustered by randomized middle-school pair. No fixed effects are specified in the printed equation.

Information effects on beliefs and preference ranks (R12, R13). The printed absolute-error regression (2) is:

$$\left|\text{quint}(V_{jt}) - s_{iV_j,\text{fs}}\right| = \eta_0 + \eta_1 T_i + \eta_X' X_{ij} + \eta_{ij} \tag{2}$$

Here the outcome is the absolute difference between measured within-town VA quintile and follow-up score. Controls include indicators for the baseline absolute score difference; estimates use 1,525 students, 4,970 student-tracks, and 76 treatment-control-pair clusters. The preference-rank regression (3) is:

$$\text{ppr}_{ij,\text{fs}} = (\delta_1 + \delta_2 T_i)\,\text{pr}(V_{jt}) + (\delta_{X,1} + \delta_{X,2}T_i)'X_{ij} + \delta_{ij} \tag{3}$$

The controls include indicators for baseline track-rank position interacted with treatment. Estimates use 1,533 students, 20,029 student-tracks, and 76 pair clusters. Both regressions report standard errors clustered by middle-school treatment-control pair; no fixed effects are specified in the equations (Tables 11-12, pp. 1070-1071).

Preference estimates (R7, R14). Utility equation (4) and the rank-ordered-logit probability (5) appear in Section V (pp. 1073-1074). The likelihood uses the first two baseline choices from 1,170 students in experimental middle schools; standard errors are clustered by middle school (150 clusters). Columns vary the VA dimension and include a horse race across all measured attributes (Table 13, p. 1074). This is a discrete-choice likelihood, so the paper does not specify fixed effects for it.

Counterfactual information and preference mechanisms (R6, R15). For each student and belief scenario, the preference model weights standardized track VA by predicted track-choice probabilities. The formula for inaccurate scores is displayed in Theory / model; accurate scores replace the VA scores by measured within-town quintiles (Section VB, p. 1076). Table 14 reports four belief/model specifications for 997 low-achieving and 1,680 high-achieving students (p. 1078). Table 15 sets selected preference coefficients to zero to test each trait’s contribution to the residual gap; it reports mean potential VA gains in SD units for the same sample (p. 1079). These are simulated counterfactuals, not regressions, so no fixed effects or standard errors are reported.

Datasets used

Dataset	Role in paper	Wiki page
Romanian Ministry of Education administrative microdata (2004-2017, 2019 cohorts)	Track-year VA estimation; student demographics, transition scores, middle school GPA, assigned tracks, baccalaureate performance; 2,162,736 students	no page yet
Baseline survey of parents (194 middle schools, 48 towns, 3,898 students, 2019)	Households’ quality scores for tracks on eight dimensions, intended preference rankings, student characteristics; primary data collected by the authors	no page yet (primary data, collected by authors)
Endline (follow-up) survey of parents (2019)	Final submitted preference rankings; post-intervention quality scores for tracks	no page yet (primary data, collected by authors)

Sample: baccalaureate outcomes available for 2004-2014 cohorts; machine-learning VA extension covers 2015-2017 and 2019. Survey and experiment conducted in 2019 in 48 towns selected for moderate size (7-28 tracks) and VA forecastability. Experimental sample (after removing schools that withdrew permission): 2,692 assigned students in 170 middle schools, 45 towns.

When to read the full paper

Read the source if you are: (i) estimating or validating school value added in a serial dictatorship setting, including the RD validation approach following Angrist, Hull, Pathak, and Walters (2017) (Sections I-II); (ii) studying how information provision affects school or college choices and want a rigorous mechanism decomposition separating information from preferences, building on Hastings and Weinstein (2008) (Section IV); (iii) estimating rank-ordered logit preference weights for multidimensional product quality in a centralized choice mechanism, extending Fack, Grenet, and He (2019) (Section V); or (iv) running simulation-based counterfactuals to separate information and preference constraints on household choices, in the spirit of Kapor, Neilson, and Zimmerman (2020). The Tables 13-15 combination (preference estimation, simulation, and decomposition by quality dimension) is particularly citable. The prior question of whether parents value school effectiveness is studied for New York City by Abdulkadiroğlu, Pathak, and Walters (2020); this paper provides complementary evidence for Romania with the additional advantage of observing the full feasible choice set.

Attribution and rights

Source: peer-reviewed, American Economic Review 113(4), April 2023. AEA open access policy applies to 2023 publications; specific Creative Commons variant not confirmed from Crossref (license field returned empty) or PDF in this session. The initial distillation was extracted by an LLM (claude-sonnet-4-6) on 2026-06-24; the page was updated by gpt-6-luna on 2026-10-04. It is not human-verified or independently reproduced. Replication data: doi.org/10.3886/E181263V1.

Ainsworth, Robert, Rajeev Dehejia, Cristian Pop-Eleches, and Miguel Urquiola. “Why Do Households Leave School Value Added on the Table? The Roles of Information and Preferences.” American Economic Review 113, no. 4 (April 2023): 1049-1082. DOI: 10.1257/aer.20210949. Distilled extract only; redistribution of the verbatim PDF not authorized in this session.