Tarefa paper_repro.angrist_lavy_1999.tab4_c1.agent

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Pergunta feita ao analista

Angrist and Lavy (1999), 'Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement', Table IV, column (1): for fifth-grade classes in 1991 (the full sample), estimate by two-stage least squares the effect of class size on the class's average reading comprehension score, using as the instrument the class size predicted by Maimonides' rule of 40 from the school's grade enrollment, with the percent of disadvantaged pupils as the only other regressor. Correct the standard errors for within-school correlation between classes. Report the coefficient on class size.

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Trajetória

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1. 0Início

   Angrist and Lavy (1999), 'Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement', Table IV, column (1): for fifth-grade classes in 1991 (the full sample), estimate by two-stage least squares the effect of class size on the class's average reading comprehension score, using as the instrument the class size predicted by Maimonides' rule of 40 from the school's grade enrollment, with the percent of disadvantaged pupils as the only other regressor. Correct the standard errors for within-school correlation between classes. Report the coefficient on class size.

   final5 (agent)

   The authors' class-level file for fifth graders in Israeli public schools, 1991 (final5.dta on Joshua Angrist's data archive), restricted as the authors' AngristLavy_Table4.do restricts it: classes with 2 to 44 pupils in schools with more than 5 fifth graders enrolled, the do-file's school-type rule (c_leom equal to 1 and c_pik below 3), and a reading score; one row per class. Columns: schlcode, the school; classid, the class; c_size, fifth-grade enrollment of the school at the start of the year; cohsize, enrollment in the grade (cohort size); classize, the number of pupils in the class; tipuach, the percent of pupils who are disadvantaged; verbsize and mathsize, the number of pupils who took the reading and the math test; avgverb and avgmath, the class's average reading comprehension and math scores (a score recorded above 100 is reduced by 100, as the do-file does; missing when no pupil took that test); func1, the class size Maimonides' rule of 40 predicts from enrollment, c_size / (floor((c_size - 1) / 40) + 1).

   file bf443edee9033926b4e74dc2c17a98b04405b899735bf4c372e0e6d468431a54 · frame —

   1. rename {"map":{"avgmath":"avgmath_raw","avgverb":"avgverb_raw"}}
   2. derive {"args":{"cmp":"gt","column":"avgverb_raw","value":100},"name":"verb_over_100","op":"indicator"}
   3. derive {"args":{"cmp":"gt","column":"avgmath_raw","value":100},"name":"math_over_100","op":"indicator"}
   4. derive {"args":{"column":"verb_over_100","factor":100},"name":"verb_shift","op":"scale"}
   5. derive {"args":{"column":"math_over_100","factor":100},"name":"math_shift","op":"scale"}
   6. derive {"args":{"left":"avgverb_raw","right":"verb_shift"},"name":"avgverb_shifted","op":"diff"}
   7. derive {"args":{"left":"avgmath_raw","right":"math_shift"},"name":"avgmath_shifted","op":"diff"}
   8. derive {"args":{"column":"c_size","divisor":40},"name":"func1","op":"floor_div_rule"}
   9. derive {"args":{"cmp":"gt","column":"verbsize","value":0},"name":"verb_tested","op":"indicator"}
   10. derive {"args":{"cmp":"gt","column":"mathsize","value":0},"name":"math_tested","op":"indicator"}
   11. derive {"args":{"column":"verb_tested","default":null,"keep_unmapped":false,"mapping":[{"source":1,"target":1}]},"name":"verb_mask","op":"map"}
   12. derive {"args":{"column":"math_tested","default":null,"keep_unmapped":false,"mapping":[{"source":1,"target":1}]},"name":"math_mask","op":"map"}
   13. derive {"args":{"columns":["avgverb_shifted","verb_mask"]},"name":"avgverb","op":"product"}
   14. derive {"args":{"columns":["avgmath_shifted","math_mask"]},"name":"avgmath","op":"product"}
   15. filter {"query":"classize > 1 and classize < 45 and c_size > 5 and c_leom == 1 and c_pik < 3"}
   16. dropna {"columns":["avgverb"]}
   17. select {"columns":["schlcode","classid","c_size","cohsize","classize","tipuach","verbsize","mathsize","avgverb","avgmath","func1"]}
2. 1Transformação
   final5 · rename {"map":{"avgmath":"avgmath_raw","avgverb":"avgverb_raw"}}

   2029 → 2029 linhas

   Frame antes → depois: 2b23ad8cd0d1 → 010f00767173
3. 2Transformação
   final5 · derive {"args":{"cmp":"gt","column":"avgverb_raw","value":100},"name":"verb_over_100","op":"indicator"}

   2029 → 2029 linhas

   Frame antes → depois: 010f00767173 → c6b27ce0fe06
4. 3Transformação
   final5 · derive {"args":{"cmp":"gt","column":"avgmath_raw","value":100},"name":"math_over_100","op":"indicator"}

   2029 → 2029 linhas

   Frame antes → depois: c6b27ce0fe06 → 3306d1504ee6
5. 4Transformação
   final5 · derive {"args":{"column":"verb_over_100","factor":100},"name":"verb_shift","op":"scale"}

   2029 → 2029 linhas

   Frame antes → depois: 3306d1504ee6 → 40047f6499b1
6. 5Transformação
   final5 · derive {"args":{"column":"math_over_100","factor":100},"name":"math_shift","op":"scale"}

   2029 → 2029 linhas

   Frame antes → depois: 40047f6499b1 → 99aa2e0fdfab
7. 6Transformação
   final5 · derive {"args":{"left":"avgverb_raw","right":"verb_shift"},"name":"avgverb_shifted","op":"diff"}

   2029 → 2029 linhas

   Frame antes → depois: 99aa2e0fdfab → ffb1bb9e8300
8. 7Transformação
   final5 · derive {"args":{"left":"avgmath_raw","right":"math_shift"},"name":"avgmath_shifted","op":"diff"}

   2029 → 2029 linhas

   Frame antes → depois: ffb1bb9e8300 → 092a1c47a742
9. 8Transformação
   final5 · derive {"args":{"column":"c_size","divisor":40},"name":"func1","op":"floor_div_rule"}

   2029 → 2029 linhas

   Frame antes → depois: 092a1c47a742 → 875de4a2cc30
10. 9Transformação
    final5 · derive {"args":{"cmp":"gt","column":"verbsize","value":0},"name":"verb_tested","op":"indicator"}

    2029 → 2029 linhas

    Frame antes → depois: 875de4a2cc30 → 89ca7567675b
11. 10Transformação
    final5 · derive {"args":{"cmp":"gt","column":"mathsize","value":0},"name":"math_tested","op":"indicator"}

    2029 → 2029 linhas

    Frame antes → depois: 89ca7567675b → 38222658161f
12. 11Transformação
    final5 · derive {"args":{"column":"verb_tested","default":null,"keep_unmapped":false,"mapping":[{"source":1,"target":1}]},"name":"verb_mask","op":"map"}

    2029 → 2029 linhas

    Frame antes → depois: 38222658161f → 0ae1567e1fc1
13. 12Transformação
    final5 · derive {"args":{"column":"math_tested","default":null,"keep_unmapped":false,"mapping":[{"source":1,"target":1}]},"name":"math_mask","op":"map"}

    2029 → 2029 linhas

    Frame antes → depois: 0ae1567e1fc1 → cc67430b1dbd
14. 13Transformação
    final5 · derive {"args":{"columns":["avgverb_shifted","verb_mask"]},"name":"avgverb","op":"product"}

    2029 → 2029 linhas

    Frame antes → depois: cc67430b1dbd → c56ddccb9364
15. 14Transformação
    final5 · derive {"args":{"columns":["avgmath_shifted","math_mask"]},"name":"avgmath","op":"product"}

    2029 → 2029 linhas

    Frame antes → depois: c56ddccb9364 → e7e52aba50e2
16. 15Transformação
    final5 · filter {"query":"classize > 1 and classize < 45 and c_size > 5 and c_leom == 1 and c_pik < 3"}

    2029 → 2024 linhas

    Frame antes → depois: e7e52aba50e2 → 78b2a8a74186
17. 16Transformação
    final5 · dropna {"columns":["avgverb"]}

    2024 → 2019 linhas

    Frame antes → depois: 78b2a8a74186 → 724502391e3c
18. 17Transformação
    final5 · select {"columns":["schlcode","classid","c_size","cohsize","classize","tipuach","verbsize","mathsize","avgverb","avgmath","func1"]}

    2019 → 2019 linhas

    Frame antes → depois: 724502391e3c → e5f6f10d4c43
19. 18Turno do modelo
    call_6bd73c8egemini-3.8-flashFim: STOP7.957 ms14522 de entrada · 103 de saída · 400 de raciocínio · 0 em cache

    Texto visível

    I will estimate the effect of class size on fifth-grade reading comprehension scores using two-stage least squares with Maimonides' rule prediction as the instrument, controlling for disadvantaged pupils and clustering standard errors by school.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process for Replicating Angrist and Lavy (1999), Table IV, Column (1)** My objective here is to precisely replicate a specific result from Angrist and Lavy's influential 1999 paper, "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement." The target is Table IV, specifically column (1). This means I need to focus on fifth-grade classes from the full 1991 sample, which I understand is contained within the dataset labeled `final5`. The core of the estimation strategy is Two-Stage Least Squares (2SLS). I need to identify the key variables for this analysis. The outcome variable, representing scholastic achievement, is the class's average reading comprehension score, which I see is designated as `avgverb`. The variable I'm interested in estimating the causal effect of, the endogenous regressor, is class size itself, denoted by `classize`. Crucially, I need the appropriate instrument for `classize`. The paper uses Maimonides' rule of 40 as the basis for this instrument. I'm told that `func1` represents the class size predicted by this rule, calculated from the school's grade enrollment, making it the valid instrument. Beyond the endogenous regressor and its instrument, I need to consider any exogenous controls. The paper includes the percentage of disadvantaged pupils, and in the `final5` dataset, this is represented by `tipuach`. This will be my exogenous control. For robust inference, the standard errors need to be clustered at the school level. I see that `schlcode` is the identifier for schools in the dataset, so I'll use that for clustering. Finally, the output I need to report is specifically the coefficient on class size (`classize`). Now, I need to make sure I have the correct tools and understand how to use them. I'm considering loading the `instrumental-variables` library or directly accessing the `infer__iv_2sls` function, as this seems to be the most direct route for this type of estimation. Let me quickly verify the available columns in the `final5` dataset to ensure I have the correct names for all the variables I've identified: * `schlcode`: This is indeed the school identifier for clustering. * `classid`: While present, it's not directly needed for this specific analysis. * `c_size`: This seems to be fifth-grade enrollment, but the paper's instrument relates to *grade* enrollment, not class size itself, and `func1` is the predicted *class* size, so I'll rely on `func1`. * `cohsize`: This is likely grade enrollment, relevant for the instrument's construction, but `func1` is the pre-calculated instrument. * `classize`: This is the endogenous regressor, class size. * `tipuach`: This is the percent of disadvantaged pupils, my exogenous control. * `verbsize`: This variable relates to pupils taking reading, not the average score. * `avgverb`: This is my outcome variable, average reading comprehension score. * `func1`: This is my instrument, predicted class size by Maimonides' rule. With these confirmations, I'm ready to set up the call to the `infer__iv_2sls` function. The parameters will be: * `dataset`: "final5" * `y`: "avgverb" * `endog`: ["classize"] * `instruments`: ["func1"] * `exog`: ["tipuach"] * `cluster`: "schlcode" Once this function call is executed, I will extract and report the coefficient associated with `classize`.

    Chamadas pedidas

    • infer.iv_2sls

      {
        "cluster": "schlcode",
        "dataset": "final5",
        "endog": [
          "classize"
        ],
        "exog": [
          "tipuach"
        ],
        "instruments": [
          "func1"
        ],
        "y": "avgverb"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
20. 19Ferramenta
    infer.iv_2slsv0.1.0call_4a96d9b9decidido pelo modeloreexecutável

    Motivo: I will estimate the effect of class size on fifth-grade reading comprehension scores using two-stage least squares with Maimonides' rule prediction as the instrument, controlling for disadvantaged pupils and clustering standard errors by school.

    Argumentos

    {
      "cluster": "schlcode",
      "dataset": "final5",
      "endog": [
        "classize"
      ],
      "exog": [
        "tipuach"
      ],
      "instruments": [
        "func1"
      ],
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "y": "avgverb"
    }

    Figuras call_4a96d9b9

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.classize 2SLS effect of classize on avgverb	-0,158478	-0.1584776549429287	0,04166710.04166708823731838	-0,240243 – -0,0767128

    Diagnósticos

    • first_stage_F.classize = 774,575774.5747822893542
    • partial_r2.classize = 0,4488020.44880209399595195
    • weak_instrument = false
    • n_obs = 2.0192019
    • se_type = "cluster"
    • n_clusters = 1.0021002

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 87.00953033915071,
          "ci_low": 81.72805358938909,
          "coef": 84.3687919642699,
          "p": 0,
          "se": 1.3457111451741575,
          "t": 62.694577708465935,
          "term": "Intercept"
        },
        {
          "ci_high": -0.34006714726869425,
          "ci_low": -0.40285271643053877,
          "coef": -0.3714599318496165,
          "p": 9.341232983329694e-96,
          "se": 0.015997654478174198,
          "t": -23.219649627787874,
          "term": "tipuach"
        },
        {
          "ci_high": -0.07671279829266166,
          "ci_low": -0.24024251159319576,
          "coef": -0.1584776549429287,
          "p": 0.00015134922325899373,
          "se": 0.04166708823731838,
          "t": -3.80342523673135,
          "term": "classize"
        }
      ],
      "first_stage": [
        {
          "ci_high": 0.7531393219109376,
          "ci_low": 0.6539289621477021,
          "coef": 0.7035341420293199,
          "endog": "classize",
          "instrument": "func1",
          "p": 1.0099426782262282e-126,
          "se": 0.025278628151898873,
          "t": 27.831183630764865
        }
      ],
      "reduced_form": [
        {
          "ci_high": -0.05528831812935853,
          "ci_low": -0.16770056387282528,
          "coef": -0.1114944410010919,
          "instrument": "func1",
          "p": 0.00010573013370968822,
          "se": 0.028642445876121088,
          "t": -3.892629892129557
        }
      ]
    }

    Digests dos dados

    final5 e5f6f10d4c435ecfab68a7e6bc06b2f9bd134269223cf7b0871fadb4c2ce49d5

    sha256 do resultado

    af84359b446e9dd320f702dbbc79c92e06574deed75877a347790f5cb948b85f

    Resultado mostrado ao modelo
21. 20Turno do modelo
    call_0a17c9a8gemini-3.8-flashFim: STOP11.319 ms15574 de entrada · 296 de saída · 884 de raciocínio · 12588 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Replicating Angrist and Lavy (1999) Results** Alright, let's break down what I've just computed and how it aligns with the original Angrist and Lavy (1999) findings for Table IV, column (1). First off, the core result: I've obtained a coefficient on `class size` of -0.158478, with a standard error of 0.0416671. This translates to a 95% confidence interval of [-0.240243, -0.0767128]. This coefficient suggests that as class size increases, the average reading comprehension score in fifth-grade classes decreases. To confirm I'm on the right track, I’m immediately cross-referencing this with Angrist and Lavy's Table IV, column (1). The original paper reports a class size coefficient of -0.158. My coefficient, -0.158478, is extremely close, practically identical. The standard error is also right there; they report either 0.038 (robust/clustered) or 0.042 (classical). My SE of 0.0416671 rounds neatly to 0.042, which matches their robust/clustered estimate. This level of agreement gives me a good deal of confidence that my implementation is correct. I also note the first-stage F-statistic, which is a robust 774.57. This is a strong indicator that my instrument – the class size predicted by Maimonides' rule – is indeed a powerful predictor of actual class size. A high F-statistic is crucial for the validity of two-stage least squares (2SLS) and helps mitigate concerns about weak instruments. I'm working with 2019 classes across 1002 schools, which are clustered, as specified. Now, regarding the prompt's requirements for the final output: I need to present the estimate, its uncertainty, the identification strategy, and potential weaknesses. The prompt also has a curious note about language: "Write the answer in the language of the question (Portuguese: decimal comma)". My initial read is that this means if the *question itself* were in Portuguese, I'd use a decimal comma. Since the question is in English, I should stick to English and standard English number formatting. The examples provided in the prompt seem to confirm this interpretation. So, to summarize what I need to report: * **The estimate:** The coefficient on class size, which is -0.158478. * **Its uncertainty:** The standard error, 0.0416671, and the 95% confidence interval [-0.240243, -0.0767128]. * **The design that identifies it:** This is the two-stage least squares (2SLS) approach, using Maimonides' rule (a class size of 40 based on grade enrollment) as an instrument for actual class size. The other regressor is the percent of disadvantaged pupils. * **What could undermine it:** The main threat here is the exclusion restriction. While Maimonides' rule is intended to affect reading comprehension *only* through its impact on class size, it's possible that the school enrollment figures used to determine the "rule-based" class size might correlate with unobserved school characteristics that *also* affect achievement, or that enrollment itself has a direct effect beyond class size. If the percent of disadvantaged pupils doesn't fully capture all relevant confounding factors, then this identifying assumption might be violated. I've checked my numbers against the source and reviewed the prompt's specific instructions, including the nuances of the reporting language. I’m ready to format the `submit_answer`.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "The two-stage least squares (2SLS) estimate of the effect of class size on fifth-grade reading comprehension scores (Table IV, column 1 of Angrist and Lavy, 1999) is -0.158478 with a school-clustered standard error of 0.0416671 (95% CI: [-0.240243, -0.0767128]; p-value = 0.000151349).\n\nThe model is estimated on 2019 classes across 1002 school clusters, controlling for the percentage of disadvantaged pupils (tipuach). The first stage is very strong, with an excluded instrument F-statistic of 774.574782289354.",
        "caveats": [
          "Identification relies on the exclusion restriction: the class size predicted by Maimonides' rule of 40 based on grade enrollment affects reading comprehension solely through actual class size, conditional on the disadvantaged pupil share (tipuach).",
          "Smooth trends in enrollment or unobserved school characteristics correlated with enrollment discontinuities could potentially challenge the exclusion restriction."
        ],
        "figure_refs": [
          "call_4a96d9b9:coef.classize"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
22. 21Guarda
    resposta aceita

    Números encontrados

    1 · 1999 · -0.158478 · 0.0416671 · 95% · -0.240243 · -0.0767128 · 0.000151349 · 2019 · 1002 · 774.574782289354 · 40

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
23. 22Resposta

    The two-stage least squares (2SLS) estimate of the effect of class size on fifth-grade reading comprehension scores (Table IV, column 1 of Angrist and Lavy, 1999) is -0.158478 with a school-clustered standard error of 0.0416671 (95% CI: [-0.240243, -0.0767128]; p-value = 0.000151349). The model is estimated on 2019 classes across 1002 school clusters, controlling for the percentage of disadvantaged pupils (tipuach). The first stage is very strong, with an excluded instrument F-statistic of 774.574782289354. Ressalvas: Identification relies on the exclusion restriction: the class size predicted by Maimonides' rule of 40 based on grade enrollment affects reading comprehension solely through actual class size, conditional on the disadvantaged pupil share (tipuach). Smooth trends in enrollment or unobserved school characteristics correlated with enrollment discontinuities could potentially challenge the exclusion restriction.

    • Identification relies on the exclusion restriction: the class size predicted by Maimonides' rule of 40 based on grade enrollment affects reading comprehension solely through actual class size, conditional on the disadvantaged pupil share (tipuach).
    • Smooth trends in enrollment or unobserved school characteristics correlated with enrollment discontinuities could potentially challenge the exclusion restriction.

    Figuras citadas: call_4a96d9b9:coef.classize · Parada: answered

    Figura da resposta: call_4a96d9b9:coef.classize = -0,158478-0.1584776549429287 (se 0,04166710.04166708823731838)
24. 23Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
25. 24Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_4a96d9b9:coef.classize (infer.iv_2sls)
26. 25Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
27. 26Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'avgverb'
28. 27Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['classize']
29. 28Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['func1']
30. 29Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = ['tipuach']
31. 30Pontuação
    #7argumento igualpassouobrigatóriainfer.iv_2sls.cluster = 'schlcode'
32. 31Pontuação
    #8diagnósticopassouobrigatória2019 vs 2019
33. 32Pontuação
    #9figura da resposta próximapassouobrigatória-0.1584776549 vs -0.15847765494294208
34. 33Pontuação
    #10figura da resposta próximapassouobrigatória0.04166708824 vs 0.04166708823732179
35. 34Pontuação
    #11figura da resposta próximapassouregistrada-0.1584776549 vs -0.158
36. 35Pontuação
    #12figura da resposta próximafalhouregistrada0.04166708824 vs 0.04

Épocas × verificações

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• época 1, tentativa 1passoupontuada(exibindo)

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