Tarefa paper_repro.angrist_krueger_1991.tab5_c2.agent

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Pergunta feita ao analista

Angrist and Krueger (1991), 'Does Compulsory School Attendance Affect Schooling and Earnings?', Table V, column (2): for men born in 1930-1939 in the 1980 Census, estimate by two-stage least squares the return to education, the effect of years of education on the log of weekly earnings. Use as instruments a full set of quarter-of-birth times year-of-birth interactions (each of the first three quarters of birth interacted with each of the ten years of birth), and include nine year-of-birth dummies and an intercept as the only other regressors. Report the coefficient on years of education.

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Verificações

Caminho de referência e caminho do agente

A chamada de referência ao lado da chamada que deu a resposta, argumento por argumento.

Trajetória

Cada evento na ordem em que aconteceu: turnos do modelo, chamadas de ferramentas, guardas, transformações e pontuação.

1. 0Início

   Angrist and Krueger (1991), 'Does Compulsory School Attendance Affect Schooling and Earnings?', Table V, column (2): for men born in 1930-1939 in the 1980 Census, estimate by two-stage least squares the return to education, the effect of years of education on the log of weekly earnings. Use as instruments a full set of quarter-of-birth times year-of-birth interactions (each of the first three quarters of birth interacted with each of the ten years of birth), and include nine year-of-birth dummies and an intercept as the only other regressors. Report the coefficient on years of education.

   asciiqob (agent)

   Joshua Angrist's minimal extract of the 1980 Census used by Angrist and Krueger (1991), 'Does Compulsory School Attendance Affect Schooling and Earnings?' (asciiqob.txt in asciiqob.zip): one row per man born in the United States in 1930-1939, from the 5 percent public-use sample of the 1980 Census (329,509 rows). Columns: lwklywge, the log of weekly earnings in 1979; educ, years of education; yob, year of birth (30 for 1930 to 39 for 1939); qob, quarter of birth (1 to 4); pob, state of birth (census code). Added by the declared transforms: yob_30 to yob_39, one indicator per year of birth; qtr_1 to qtr_4, one indicator per quarter of birth; and qtr1_yob30 to qtr3_yob39, thirty columns, each the product of the indicator for quarter of birth 1, 2 or 3 and the indicator for one year of birth (qtr2_yob35 is 1 for men born in the second quarter of 1935).

   file 0b6c505e52fd6c9f6194c356c91688acf2f8937b5023a84e754e942c9a2f2dcc · frame —

   1. dummies {"column":"yob","drop_first":false,"prefix":"yob"}
   2. dummies {"column":"qob","drop_first":false,"prefix":"qtr"}
   3. derive {"args":{"columns":["qtr_1","yob_30"]},"name":"qtr1_yob30","op":"interaction"}
   4. derive {"args":{"columns":["qtr_1","yob_31"]},"name":"qtr1_yob31","op":"interaction"}
   5. derive {"args":{"columns":["qtr_1","yob_32"]},"name":"qtr1_yob32","op":"interaction"}
   6. derive {"args":{"columns":["qtr_1","yob_33"]},"name":"qtr1_yob33","op":"interaction"}
   7. derive {"args":{"columns":["qtr_1","yob_34"]},"name":"qtr1_yob34","op":"interaction"}
   8. derive {"args":{"columns":["qtr_1","yob_35"]},"name":"qtr1_yob35","op":"interaction"}
   9. derive {"args":{"columns":["qtr_1","yob_36"]},"name":"qtr1_yob36","op":"interaction"}
   10. derive {"args":{"columns":["qtr_1","yob_37"]},"name":"qtr1_yob37","op":"interaction"}
   11. derive {"args":{"columns":["qtr_1","yob_38"]},"name":"qtr1_yob38","op":"interaction"}
   12. derive {"args":{"columns":["qtr_1","yob_39"]},"name":"qtr1_yob39","op":"interaction"}
   13. derive {"args":{"columns":["qtr_2","yob_30"]},"name":"qtr2_yob30","op":"interaction"}
   14. derive {"args":{"columns":["qtr_2","yob_31"]},"name":"qtr2_yob31","op":"interaction"}
   15. derive {"args":{"columns":["qtr_2","yob_32"]},"name":"qtr2_yob32","op":"interaction"}
   16. derive {"args":{"columns":["qtr_2","yob_33"]},"name":"qtr2_yob33","op":"interaction"}
   17. derive {"args":{"columns":["qtr_2","yob_34"]},"name":"qtr2_yob34","op":"interaction"}
   18. derive {"args":{"columns":["qtr_2","yob_35"]},"name":"qtr2_yob35","op":"interaction"}
   19. derive {"args":{"columns":["qtr_2","yob_36"]},"name":"qtr2_yob36","op":"interaction"}
   20. derive {"args":{"columns":["qtr_2","yob_37"]},"name":"qtr2_yob37","op":"interaction"}
   21. derive {"args":{"columns":["qtr_2","yob_38"]},"name":"qtr2_yob38","op":"interaction"}
   22. derive {"args":{"columns":["qtr_2","yob_39"]},"name":"qtr2_yob39","op":"interaction"}
   23. derive {"args":{"columns":["qtr_3","yob_30"]},"name":"qtr3_yob30","op":"interaction"}
   24. derive {"args":{"columns":["qtr_3","yob_31"]},"name":"qtr3_yob31","op":"interaction"}
   25. derive {"args":{"columns":["qtr_3","yob_32"]},"name":"qtr3_yob32","op":"interaction"}
   26. derive {"args":{"columns":["qtr_3","yob_33"]},"name":"qtr3_yob33","op":"interaction"}
   27. derive {"args":{"columns":["qtr_3","yob_34"]},"name":"qtr3_yob34","op":"interaction"}
   28. derive {"args":{"columns":["qtr_3","yob_35"]},"name":"qtr3_yob35","op":"interaction"}
   29. derive {"args":{"columns":["qtr_3","yob_36"]},"name":"qtr3_yob36","op":"interaction"}
   30. derive {"args":{"columns":["qtr_3","yob_37"]},"name":"qtr3_yob37","op":"interaction"}
   31. derive {"args":{"columns":["qtr_3","yob_38"]},"name":"qtr3_yob38","op":"interaction"}
   32. derive {"args":{"columns":["qtr_3","yob_39"]},"name":"qtr3_yob39","op":"interaction"}
2. 1Transformação
   asciiqob · dummies {"column":"yob","drop_first":false,"prefix":"yob"}

   329509 → 329509 linhas

   Frame antes → depois: 845a36d4dcec → d4b277b4997b
3. 2Transformação
   asciiqob · dummies {"column":"qob","drop_first":false,"prefix":"qtr"}

   329509 → 329509 linhas

   Frame antes → depois: d4b277b4997b → 2c53c053bf00
4. 3Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_30"]},"name":"qtr1_yob30","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: 2c53c053bf00 → cf52bf944241
5. 4Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_31"]},"name":"qtr1_yob31","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: cf52bf944241 → c572825a7957
6. 5Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_32"]},"name":"qtr1_yob32","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: c572825a7957 → f423f0515e53
7. 6Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_33"]},"name":"qtr1_yob33","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: f423f0515e53 → 53a56d68c9d1
8. 7Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_34"]},"name":"qtr1_yob34","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: 53a56d68c9d1 → 4a3cff9083bb
9. 8Transformação
   asciiqob · derive {"args":{"columns":["qtr_1","yob_35"]},"name":"qtr1_yob35","op":"interaction"}

   329509 → 329509 linhas

   Frame antes → depois: 4a3cff9083bb → 373b8fd4038e
10. 9Transformação
    asciiqob · derive {"args":{"columns":["qtr_1","yob_36"]},"name":"qtr1_yob36","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 373b8fd4038e → e7e4772d7f72
11. 10Transformação
    asciiqob · derive {"args":{"columns":["qtr_1","yob_37"]},"name":"qtr1_yob37","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: e7e4772d7f72 → 493704cb4202
12. 11Transformação
    asciiqob · derive {"args":{"columns":["qtr_1","yob_38"]},"name":"qtr1_yob38","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 493704cb4202 → 459fa0f19579
13. 12Transformação
    asciiqob · derive {"args":{"columns":["qtr_1","yob_39"]},"name":"qtr1_yob39","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 459fa0f19579 → 85c2fdc43e1d
14. 13Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_30"]},"name":"qtr2_yob30","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 85c2fdc43e1d → 221b8d8c4186
15. 14Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_31"]},"name":"qtr2_yob31","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 221b8d8c4186 → 318603958de3
16. 15Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_32"]},"name":"qtr2_yob32","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 318603958de3 → 069525d0a1fe
17. 16Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_33"]},"name":"qtr2_yob33","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 069525d0a1fe → 64ef72351a15
18. 17Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_34"]},"name":"qtr2_yob34","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 64ef72351a15 → 0c272ae20586
19. 18Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_35"]},"name":"qtr2_yob35","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 0c272ae20586 → 7856b1936015
20. 19Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_36"]},"name":"qtr2_yob36","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 7856b1936015 → 06252be82053
21. 20Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_37"]},"name":"qtr2_yob37","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 06252be82053 → 4a442f63e865
22. 21Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_38"]},"name":"qtr2_yob38","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 4a442f63e865 → 1a895d8e4ad2
23. 22Transformação
    asciiqob · derive {"args":{"columns":["qtr_2","yob_39"]},"name":"qtr2_yob39","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 1a895d8e4ad2 → 7fd62953f64c
24. 23Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_30"]},"name":"qtr3_yob30","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 7fd62953f64c → fbb95e831358
25. 24Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_31"]},"name":"qtr3_yob31","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: fbb95e831358 → 3c39c77165ba
26. 25Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_32"]},"name":"qtr3_yob32","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 3c39c77165ba → 7e4ccc705689
27. 26Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_33"]},"name":"qtr3_yob33","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 7e4ccc705689 → e14e138d365d
28. 27Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_34"]},"name":"qtr3_yob34","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: e14e138d365d → efea1aed1a08
29. 28Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_35"]},"name":"qtr3_yob35","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: efea1aed1a08 → 889c869c49df
30. 29Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_36"]},"name":"qtr3_yob36","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 889c869c49df → 4690bc1fd2a9
31. 30Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_37"]},"name":"qtr3_yob37","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 4690bc1fd2a9 → 73cf0a1d91c6
32. 31Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_38"]},"name":"qtr3_yob38","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: 73cf0a1d91c6 → adbbeec74207
33. 32Transformação
    asciiqob · derive {"args":{"columns":["qtr_3","yob_39"]},"name":"qtr3_yob39","op":"interaction"}

    329509 → 329509 linhas

    Frame antes → depois: adbbeec74207 → 654074d5953a
34. 33Turno do modelo
    call_8d54518agemini-3.8-flashFim: STOP6.828 ms15175 de entrada · 42 de saída · 351 de raciocínio · 0 em cache

    Texto visível

    I will load the instrumental variables skill to review the recommended procedure for two-stage least squares estimation and diagnostic reporting.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process for Replicating Angrist and Krueger (1991), Table V, Column (2)** My primary objective is to meticulously reproduce the results presented in Table V, column (2) of the seminal Angrist and Krueger (1991) paper. This means I need to precisely replicate their empirical setup using the specified dataset and econometric methodology. First and foremost, I've identified the core components of this replication. The dataset is crucial: it's the `asciiqob` dataset, containing observations for men born between 1930 and 1939, as drawn from the 1980 Census. The sample size is substantial, N = 329,509. The estimation strategy is Two-Stage Least Squares (2SLS), a standard approach for addressing endogeneity. The outcome variable I'll be working with is `lwklywge`, representing the logarithm of weekly earnings. The key endogenous regressor, the one whose causal impact on earnings we're interested in isolating, is `educ` – years of education. Now, the heart of any instrumental variables (IV) estimation lies in the choice of instruments. For this specific replication, Angrist and Krueger employed a comprehensive set of interaction terms between quarter of birth and year of birth. Specifically, they used the first three quarters of birth, each interacted with each of the ten years of birth (1930-1939). This yields a total of 30 distinct instruments. I'll need to ensure these are correctly constructed and included in the model. These instruments are: `qtr1_yob30` through `qtr1_yob39`, `qtr2_yob30` through `qtr2_yob39`, and `qtr3_yob30` through `qtr3_yob39`. In addition to the instruments, the model also incorporates exogenous regressors. This includes a set of nine year-of-birth dummy variables. I need to be careful about the base category. Based on the standard presentation of Table V, column (2) in the original paper, it's likely that either 1930 is omitted, or one of the other years is. I'll need to confirm this specific convention. Crucially, an intercept term is also included. Before proceeding with the actual implementation, I need to consider the available tools and the necessary skills. I'll need to access functionality for instrumental variables estimation, specifically 2SLS. I'll check if a dedicated `instrumental-variables` skill is available, or if I can leverage a more general function like `infer__iv_2sls`. This ensures I have the right computational machinery to perform the required regressions.

    Chamadas pedidas

    • load_skill (meta-ferramenta)

      {
        "name": "instrumental-variables"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
35. 34Habilidade
    instrumental-variablesTexto da habilidade
36. 35Turno do modelo
    call_4f455df4gemini-3.8-flashFim: STOP15.042 ms16036 de entrada · 516 de saída · 1038 de raciocínio · 12791 em cache

    Texto visível

    I will estimate the 2SLS specification from Table V, column (2) of Angrist and Krueger (1991), regressing log weekly earnings on years of education, instrumented by 30 quarter-of-birth × year-of-birth interactions, with 9 year-of-birth dummies and an intercept.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Approaching the Instrumental Variables Regression** My primary goal here is to perform an instrumental variables (IV) regression to estimate the coefficient on years of education, using a specific set of instruments and controls as outlined in the prompt. I need to ensure I'm correctly identifying and implementing these components within the `infer.iv_2sls` function. First, I'm examining the available columns in the `asciiqob` dataset. The prompt specifies using "a full set of quarter-of-birth times year-of-birth interactions" as instruments. The dataset description confirms the existence of `yob_30` to `yob_39` and `qtr1_yob30` to `qtr3_yob39`. It seems the latter group, totaling 30 columns (3 quarters * 10 years of birth), directly corresponds to the required interaction terms. I'll need to select all of these as my instruments. Next, I need to consider the other regressors. The prompt states to "include nine year-of-birth dummies and an intercept as the only other regressors." This is a standard way to control for year-of-birth effects when the full set of year-of-birth dummies might create perfect multicollinearity with other variables or the intercept. The common practice is to omit one year-of-birth dummy to serve as the reference category. I see columns `yob_30` through `yob_39` available. The prompt doesn't explicitly state *which* nine dummies to include, but it's a crucial detail for setting up the regression. However, I'm recalling a fundamental econometric principle: the choice of the omitted year dummy category will *not* affect the estimated coefficient on `educ` in a 2SLS regression. The set of all year-of-birth dummies (plus an intercept) spans the same space regardless of which dummy is left out. Therefore, I can confidently select any nine unique year dummies from the available ten, along with the intercept. For simplicity and consistency with typical presentation, I'll likely use `yob_31` through `yob_39` and implicitly include the intercept in the `infer.iv_2sls` call. Now, I'm thinking about the standard errors. The prompt asks to "Report the coefficient on years of education," but doesn't specify the standard error type. The `infer.iv_2sls` function has a `se` parameter which defaults to `'HC1'` (Huber-White robust standard errors), but also allows for `'classical'` (homoskedastic) standard errors. I'm recalling that the *point estimate* of the coefficient on `educ` in a 2SLS regression is invariant to the choice of standard error estimator. The difference lies solely in the standard error calculation itself. Given that the prompt doesn't mandate a specific type, and robust standard errors are often preferred in practice to account for potential heteroskedasticity, I'll likely stick with the default `'HC1'`. If the specific paper being referenced (implicitly Angrist-Krueger 1991, as mentioned) used classical standard errors, that would be a reason to switch, but the prompt doesn't require that level of adherence for the standard errors, only the variables. For now, I'll assume the default is acceptable. Finally, I'll assemble the list of instruments and exogenous regressors. The instruments will be all 30 `qtrX_yobYY` columns. The exogenous regressors will be the intercept (implicitly handled by `infer.iv_2sls`) and the nine year-of-birth dummies (e.g., `yob_31` to `yob_39`). With these components identified, I'm ready to call the `infer.iv_2sls` function. I'll pass the `asciiqob` dataset, specify the endogenous variable (presumably `educ`), the exogenous variables (the year dummies), the instruments (the quarter-year-of-birth interactions), and then extract the coefficient on `educ` from the results.

    Chamadas pedidas

    • infer.iv_2sls

      {
        "dataset": "asciiqob",
        "endog": [
          "educ"
        ],
        "exog": [
          "yob_31",
          "yob_32",
          "yob_33",
          "yob_34",
          "yob_35",
          "yob_36",
          "yob_37",
          "yob_38",
          "yob_39"
        ],
        "instruments": [
          "qtr1_yob30",
          "qtr1_yob31",
          "qtr1_yob32",
          "qtr1_yob33",
          "qtr1_yob34",
          "qtr1_yob35",
          "qtr1_yob36",
          "qtr1_yob37",
          "qtr1_yob38",
          "qtr1_yob39",
          "qtr2_yob30",
          "qtr2_yob31",
          "qtr2_yob32",
          "qtr2_yob33",
          "qtr2_yob34",
          "qtr2_yob35",
          "qtr2_yob36",
          "qtr2_yob37",
          "qtr2_yob38",
          "qtr2_yob39",
          "qtr3_yob30",
          "qtr3_yob31",
          "qtr3_yob32",
          "qtr3_yob33",
          "qtr3_yob34",
          "qtr3_yob35",
          "qtr3_yob36",
          "qtr3_yob37",
          "qtr3_yob38",
          "qtr3_yob39"
        ],
        "y": "lwklywge"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
37. 36Ferramenta
    infer.iv_2slsv0.1.0call_1b43c76ddecidido pelo modeloreexecutável

    Motivo: I will estimate the 2SLS specification from Table V, column (2) of Angrist and Krueger (1991), regressing log weekly earnings on years of education, instrumented by 30 quarter-of-birth × year-of-birth interactions, with 9 year-of-birth dummies and an intercept.

    Argumentos

    {
      "cluster": null,
      "dataset": "asciiqob",
      "endog": [
        "educ"
      ],
      "exog": [
        "yob_31",
        "yob_32",
        "yob_33",
        "yob_34",
        "yob_35",
        "yob_36",
        "yob_37",
        "yob_38",
        "yob_39"
      ],
      "instruments": [
        "qtr1_yob30",
        "qtr1_yob31",
        "qtr1_yob32",
        "qtr1_yob33",
        "qtr1_yob34",
        "qtr1_yob35",
        "qtr1_yob36",
        "qtr1_yob37",
        "qtr1_yob38",
        "qtr1_yob39",
        "qtr2_yob30",
        "qtr2_yob31",
        "qtr2_yob32",
        "qtr2_yob33",
        "qtr2_yob34",
        "qtr2_yob35",
        "qtr2_yob36",
        "qtr2_yob37",
        "qtr2_yob38",
        "qtr2_yob39",
        "qtr3_yob30",
        "qtr3_yob31",
        "qtr3_yob32",
        "qtr3_yob33",
        "qtr3_yob34",
        "qtr3_yob35",
        "qtr3_yob36",
        "qtr3_yob37",
        "qtr3_yob38",
        "qtr3_yob39"
      ],
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "y": "lwklywge"
    }

    Figuras call_1b43c76d

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ 2SLS effect of educ on lwklywge	0,0891155	0.08911545635102291	0,01621230.016212302230258307	0,0573398 – 0,120891

    Diagnósticos

    • first_stage_F.educ = 4,800754.800750238668263
    • partial_r2.educ = 0,0004466170.0004466165850589565
    • weak_instrument = true
    • overid_p = 0,6552610.6552608024510715
    • sargan = 25,439425.43938765476591
    • sargan_df = 2929
    • n_obs = 329.509329509
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 5.188576692239491,
          "ci_low": 4.39687725189862,
          "coef": 4.7927269720690555,
          "p": 2.2375964419139252e-124,
          "se": 0.20196711225026592,
          "t": 23.73023468360624,
          "term": "Intercept"
        },
        {
          "ci_high": 0.002124706859193375,
          "ci_low": -0.019887313707599635,
          "coef": -0.00888130342420313,
          "p": 0.11374202067728985,
          "se": 0.005615393926203265,
          "t": -1.5815993572169644,
          "term": "yob_31"
        },
        {
          "ci_high": -0.006651136602639713,
          "ci_low": -0.02940953507695567,
          "coef": -0.01803033583979769,
          "p": 0.001899265750293312,
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        {
          "ci_high": 0.030078065875940613,
          "ci_low": -0.012967026908212676,
          "coef": 0.008555519483863969,
          "instrument": "qtr3_yob33",
          "p": 0.4359116333000104,
          "se": 0.010981052455469894,
          "t": 0.7791165299098707
        },
        {
          "ci_high": 0.019321105775201224,
          "ci_low": -0.022307960050448123,
          "coef": -0.0014934271376234483,
          "instrument": "qtr3_yob34",
          "p": 0.8881651269700763,
          "se": 0.010619815777745373,
          "t": -0.14062646366738657
        },
        {
          "ci_high": 0.03302397887679615,
          "ci_low": -0.008740384470877854,
          "coef": 0.012141797202959149,
          "instrument": "qtr3_yob35",
          "p": 0.25444905516540295,
          "se": 0.010654330959159847,
          "t": 1.13961141713178
        },
        {
          "ci_high": 0.022388926350049767,
          "ci_low": -0.017769829394362713,
          "coef": 0.0023095484778435276,
          "instrument": "qtr3_yob36",
          "p": 0.8216389373948503,
          "se": 0.010244731161042861,
          "t": 0.22543768514160087
        },
        {
          "ci_high": 0.02227285720828177,
          "ci_low": -0.01639078733570695,
          "coef": 0.002941034936287412,
          "instrument": "qtr3_yob37",
          "p": 0.7655667251197893,
          "se": 0.009863319635205519,
          "t": 0.29817901528709106
        },
        {
          "ci_high": 0.015125078719663256,
          "ci_low": -0.023457308012806936,
          "coef": -0.004166114646571841,
          "instrument": "qtr3_yob38",
          "p": 0.6720954836737745,
          "se": 0.009842590296900313,
          "t": -0.4232742114526354
        },
        {
          "ci_high": 0.0012202727934319153,
          "ci_low": -0.036461935599071446,
          "coef": -0.017620831402819767,
          "instrument": "qtr3_yob39",
          "p": 0.06679891233440349,
          "se": 0.009612949589188968,
          "t": -1.8330306675733243
        }
      ]
    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    768cb8aeb9c396dd8f8a99662a2ec7aa3574b2680fb5e8899a8d0fa32e68724c

    Resultado mostrado ao modelo
38. 37Turno do modelo
    call_19201befgemini-3.8-flashFim: STOP7.277 ms20306 de entrada · 478 de saída · 121 de raciocínio · 16181 em cache

    Texto visível

    I will run the same specification with classical homoskedastic standard errors as reported in the original 1991 paper.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process** I'm currently focused on replicating a specific result from Angrist & Krueger's (1991) seminal paper. My immediate goal is to verify that my implementation of the instrumental variables (IV) two-stage least squares (2SLS) estimation aligns with their reported findings, particularly regarding the standard error calculation. To achieve this, I'm planning to run my `infer__iv_2sls` function with the `se="classical"` option. This setting is crucial because it should mirror the "classical" standard error that Angrist & Krueger themselves reported. I want to see if this yields the same diagnostic outcomes as their published results. Specifically, I'm looking at Table V, column (2) of their paper. The coefficient reported there is 0.0891 (or variations like 0.089 or 0.0891), with a standard error of approximately 0.0161. My intention is to run my `infer__iv_2sls` with `se="classical"` and then meticulously compare the coefficient and, more importantly, the calculated standard error against these benchmark values. If the numbers match, it will provide strong confirmation that my standard error estimation methodology is consistent with theirs for this specific approach.

    Chamadas pedidas

    • infer.iv_2sls

      {
        "dataset": "asciiqob",
        "endog": [
          "educ"
        ],
        "exog": [
          "yob_31",
          "yob_32",
          "yob_33",
          "yob_34",
          "yob_35",
          "yob_36",
          "yob_37",
          "yob_38",
          "yob_39"
        ],
        "instruments": [
          "qtr1_yob30",
          "qtr1_yob31",
          "qtr1_yob32",
          "qtr1_yob33",
          "qtr1_yob34",
          "qtr1_yob35",
          "qtr1_yob36",
          "qtr1_yob37",
          "qtr1_yob38",
          "qtr1_yob39",
          "qtr2_yob30",
          "qtr2_yob31",
          "qtr2_yob32",
          "qtr2_yob33",
          "qtr2_yob34",
          "qtr2_yob35",
          "qtr2_yob36",
          "qtr2_yob37",
          "qtr2_yob38",
          "qtr2_yob39",
          "qtr3_yob30",
          "qtr3_yob31",
          "qtr3_yob32",
          "qtr3_yob33",
          "qtr3_yob34",
          "qtr3_yob35",
          "qtr3_yob36",
          "qtr3_yob37",
          "qtr3_yob38",
          "qtr3_yob39"
        ],
        "se": "classical",
        "y": "lwklywge"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
39. 38Ferramenta
    infer.iv_2slsv0.1.0call_549a6c8adecidido pelo modeloreexecutável

    Motivo: I will run the same specification with classical homoskedastic standard errors as reported in the original 1991 paper.

    Argumentos

    {
      "cluster": null,
      "dataset": "asciiqob",
      "endog": [
        "educ"
      ],
      "exog": [
        "yob_31",
        "yob_32",
        "yob_33",
        "yob_34",
        "yob_35",
        "yob_36",
        "yob_37",
        "yob_38",
        "yob_39"
      ],
      "instruments": [
        "qtr1_yob30",
        "qtr1_yob31",
        "qtr1_yob32",
        "qtr1_yob33",
        "qtr1_yob34",
        "qtr1_yob35",
        "qtr1_yob36",
        "qtr1_yob37",
        "qtr1_yob38",
        "qtr1_yob39",
        "qtr2_yob30",
        "qtr2_yob31",
        "qtr2_yob32",
        "qtr2_yob33",
        "qtr2_yob34",
        "qtr2_yob35",
        "qtr2_yob36",
        "qtr2_yob37",
        "qtr2_yob38",
        "qtr2_yob39",
        "qtr3_yob30",
        "qtr3_yob31",
        "qtr3_yob32",
        "qtr3_yob33",
        "qtr3_yob34",
        "qtr3_yob35",
        "qtr3_yob36",
        "qtr3_yob37",
        "qtr3_yob38",
        "qtr3_yob39"
      ],
      "level": 0.95,
      "se": "classical",
      "subset": null,
      "y": "lwklywge"
    }

    Figuras call_549a6c8a

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ 2SLS effect of educ on lwklywge	0,0891155	0.08911545635102291	0,01611010.01611008909298044	0,0575401 – 0,120691

    Diagnósticos

    • first_stage_F.educ = 4,907074.907068900451316
    • partial_r2.educ = 0,0004466170.0004466165850589565
    • weak_instrument = true
    • overid_p = 0,6552610.6552608024510715
    • sargan = 25,439425.43938765476591
    • sargan_df = 2929
    • n_obs = 329.509329509
    • se_type = "classical"
    • n_clusters = —

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 5.186061841131547,
          "ci_low": 4.399392103006564,
          "coef": 4.7927269720690555,
          "p": 6.040569096975984e-126,
          "se": 0.2006840060861588,
          "t": 23.881957837793085,
          "term": "Intercept"
        },
        {
          "ci_high": 0.001956062336237083,
          "ci_low": -0.019718669184643343,
          "coef": -0.00888130342420313,
          "p": 0.10822846091416162,
          "se": 0.005529349537227467,
          "t": -1.6062112486121476,
          "term": "yob_31"
        },
        {
          "ci_high": -0.006760330000213135,
          "ci_low": -0.029300341679382245,
          "coef": -0.01803033583979769,
          "p": 0.0017148126415292937,
          "se": 0.005750087516758911,
          "t": -3.135662855086535,
          "term": "yob_32"
        },
        {
          "ci_high": -0.00944662520809413,
          "ci_low": -0.0341444422021334,
          "coef": -0.021795533705113765,
          "p": 0.0005416434347180716,
          "se": 0.006300556149217415,
          "t": -3.459303145456606,
          "term": "yob_33"
        },
        {
          "ci_high": -0.012883412786730393,
          "ci_low": -0.03869215159482305,
          "coef": -0.025787782190776723,
          "p": 0.0000897653155635818,
          "se": 0.006583958737734576,
          "t": -3.91675938717226,
          "term": "yob_34"
        },
        {
          "ci_high": -0.024585319187546528,
          "ci_low": -0.0530695822279135,
          "coef": -0.03882745070773001,
          "p": 9.130500506333137e-8,
          "se": 0.007266500464321365,
          "t": -5.343349374072626,
          "term": "yob_35"
        },
        {
          "ci_high": -0.02312606971718504,
          "ci_low": -0.0543972621221663,
          "coef": -0.03876166591967567,
          "p": 0.0000011809573418822942,
          "se": 0.00797746228535571,
          "t": -4.858896793637089,
          "term": "yob_36"
        },
        {
          "ci_high": -0.02765243345125555,
          "ci_low": -0.06198249437957762,
          "coef": -0.044817463915416585,
          "p": 3.098911059021082e-7,
          "se": 0.00875779736067973,
          "t": -5.117435591354915,
          "term": "yob_37"
        },
        {
          "ci_high": -0.027119821725232984,
          "ci_low": -0.0659711196574783,
          "coef": -0.046545470691355645,
          "p": 0.00000265082563555943,
          "se": 0.009911191104507902,
          "t": -4.696253982045144,
          "term": "yob_38"
        },
        {
          "ci_high": -0.038030675805034206,
          "ci_low": -0.07902348237999882,
          "coef": -0.05852707909251651,
          "p": 2.1869436357519675e-8,
          "se": 0.010457502361520765,
          "t": -5.596659419162235,
          "term": "yob_39"
        },
        {
          "ci_high": 0.12069076674846455,
          "ci_low": 0.05754014595358128,
          "coef": 0.08911545635102291,
          "p": 3.174631768574158e-8,
          "se": 0.01611008909298044,
          "t": 5.53165509120944,
          "term": "educ"
        }
      ],
      "first_stage": [
        {
          "ci_high": -0.24423101623566612,
          "ci_low": -0.44430994826211034,
          "coef": -0.34427048224888823,
          "endog": "educ",
          "instrument": "qtr1_yob30",
          "p": 1.5334104885064538e-11,
          "se": 0.05104129427328395,
          "t": -6.744940291004462
        },
        {
          "ci_high": 0.033299970254182215,
          "ci_low": -0.17667020336252406,
          "coef": -0.07168511655417092,
          "endog": "educ",
          "instrument": "qtr1_yob31",
          "p": 0.1808020027801256,
          "se": 0.053564607285920295,
          "t": -1.3382925813592903
        },
        {
          "ci_high": -0.09210161848062393,
          "ci_low": -0.2942591678209045,
          "coef": -0.1931803931507642,
          "endog": "educ",
          "instrument": "qtr1_yob32",
          "p": 0.00017979988812768732,
          "se": 0.051571561587900765,
          "t": -3.7458705379998882
        },
        {
          "ci_high": 0.08420754559397836,
          "ci_low": -0.12236226572556544,
          "coef": -0.019077360065793546,
          "endog": "educ",
          "instrument": "qtr1_yob33",
          "p": 0.7173382253017206,
          "se": 0.05269715517146024,
          "t": -0.36201878457616393
        },
        {
          "ci_high": -0.048588906785980907,
          "ci_low": -0.2526220347339264,
          "coef": -0.15060547075995367,
          "endog": "educ",
          "instrument": "qtr1_yob34",
          "p": 0.0038102951969120062,
          "se": 0.05205003255271905,
          "t": -2.8934750541685528
        },
        {
          "ci_high": -0.0671419542379034,
          "ci_low": -0.2703229693553745,
          "coef": -0.16873246179663892,
          "endog": "educ",
          "instrument": "qtr1_yob35",
          "p": 0.0011327157087520413,
          "se": 0.051832653634840076,
          "t": -3.2553313396870527
        },
        {
          "ci_high": -0.08391769441428754,
          "ci_low": -0.28602847196448133,
          "coef": -0.18497308318938444,
          "endog": "educ",
          "instrument": "qtr1_yob36",
          "p": 0.0003338397919255675,
          "se": 0.05155962983338105,
          "t": -3.587556462044808
        },
        {
          "ci_high": -0.03889071440462097,
          "ci_low": -0.23848230110235066,
          "coef": -0.13868650775348582,
          "endog": "educ",
          "instrument": "qtr1_yob37",
          "p": 0.006454332685703103,
          "se": 0.05091696965757508,
          "t": -2.7237777245223977
        },
        {
          "ci_high": 0.005983711115710694,
          "ci_low": -0.1888927726749878,
          "coef": -0.09145453077963855,
          "endog": "educ",
          "instrument": "qtr1_yob38",
          "p": 0.0658265939096934,
          "se": 0.04971411959950506,
          "t": -1.8396087774739363
        },
        {
          "ci_high": -0.016570143818319144,
          "ci_low": -0.21051088292704784,
          "coef": -0.11354051337268349,
          "endog": "educ",
          "instrument": "qtr1_yob39",
          "p": 0.021740170944314765,
          "se": 0.04947540571197407,
          "t": -2.2948879698666995
        },
        {
          "ci_high": -0.09622064831729046,
          "ci_low": -0.29629373328457786,
          "coef": -0.19625719080093418,
          "endog": "educ",
          "instrument": "qtr2_yob30",
          "p": 0.00012048696764356094,
          "se": 0.05103980265463109,
          "t": -3.845179263896053
        },
        {
          "ci_high": 0.023937774923538532,
          "ci_low": -0.18608624341831842,
          "coef": -0.08107423424738995,
          "endog": "educ",
          "instrument": "qtr2_yob31",
          "p": 0.13023226414762015,
          "se": 0.05357834338713618,
          "t": -1.5131903885414897
        },
        {
          "ci_high": -0.014849005578585206,
          "ci_low": -0.22017659422596847,
          "coef": -0.11751279990227684,
          "endog": "educ",
          "instrument": "qtr2_yob32",
          "p": 0.02486808810947719,
          "se": 0.052380256973731394,
          "t": -2.2434559639753067
        },
        {
          "ci_high": 0.04655037022906353,
          "ci_low": -0.16167160957613086,
          "coef": -0.05756061967353366,
          "endog": "educ",
          "instrument": "qtr2_yob33",
          "p": 0.2785323866266002,
          "se": 0.05311863292032183,
          "t": -1.0836238906952824
        },
        {
          "ci_high": 0.032766768058846873,
          "ci_low": -0.172568878949373,
          "coef": -0.06990105544526307,
          "endog": "educ",
          "instrument": "qtr2_yob34",
          "p": 0.18206060751178457,
          "se": 0.05238231270824905,
          "t": -1.3344400396100724
        },
        {
          "ci_high": 0.07885479305818224,
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          "coef": -0.022713509999253693,
          "endog": "educ",
          "instrument": "qtr2_yob35",
          "p": 0.6611659885450735,
          "se": 0.051821324641092,
          "t": -0.4383043111414966
        },
        {
          "ci_high": -0.0151123411276117,
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          "coef": -0.11693892685580198,
          "endog": "educ",
          "instrument": "qtr2_yob36",
          "p": 0.024395349632846453,
          "se": 0.051953103451285974,
          "t": -2.2508554655536646
        },
        {
          "ci_high": -0.027122489144994266,
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          "coef": -0.1269336996980037,
          "endog": "educ",
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          "p": 0.01268273276767146,
          "se": 0.05092483569370037,
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        },
        {
          "ci_high": 0.07561511674872554,
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          "coef": -0.022468322367477252,
          "endog": "educ",
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          "p": 0.6534481306224874,
          "se": 0.05004330669462148,
          "t": -0.4489775726569261
        },
        {
          "ci_high": -0.005827556820412402,
          "ci_low": -0.2004333242480552,
          "coef": -0.1031304405342338,
          "endog": "educ",
          "instrument": "qtr2_yob39",
          "p": 0.03776952239052892,
          "se": 0.04964505828749499,
          "t": -2.077355613866026
        },
        {
          "ci_high": -0.03370087482664842,
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          "coef": -0.1328158200124509,
          "endog": "educ",
          "instrument": "qtr3_yob30",
          "p": 0.008629813299591315,
          "se": 0.050569593038814455,
          "t": -2.6263968529568498
        },
        {
          "ci_high": 0.178488330584879,
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          "coef": 0.07459723418003177,
          "endog": "educ",
          "instrument": "qtr3_yob31",
          "p": 0.15933229029808862,
          "se": 0.05300644071083968,
          "t": 1.4073239625156877
        },
        {
          "ci_high": 0.034241620103155374,
          "ci_low": -0.16756473077573358,
          "coef": -0.0666615553362891,
          "endog": "educ",
          "instrument": "qtr3_yob32",
          "p": 0.19537202922363325,
          "se": 0.05148196882651075,
          "t": -1.294852486332294
        },
        {
          "ci_high": 0.1652995161455748,
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          "coef": 0.06168436673114571,
          "endog": "educ",
          "instrument": "qtr3_yob33",
          "p": 0.24328643630285893,
          "se": 0.05286564936015516,
          "t": 1.1668137529326787
        },
        {
          "ci_high": 0.010053401807841214,
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          "endog": "educ",
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          "p": 0.07795572238863695,
          "se": 0.05095668777353743,
          "t": -1.7626781062185026
        },
        {
          "ci_high": 0.14097507283865626,
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          "endog": "educ",
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          "t": 0.8236111987951312
        },
        {
          "ci_high": 0.058144540332962985,
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          "endog": "educ",
          "instrument": "qtr3_yob36",
          "p": 0.41249689060608113,
          "se": 0.05098329490544019,
          "t": -0.8195085991997627
        },
        {
          "ci_high": 0.08810327213981045,
          "ci_low": -0.10572224710236602,
          "coef": -0.008809487481277793,
          "endog": "educ",
          "instrument": "qtr3_yob37",
          "p": 0.8585944794466438,
          "se": 0.04944601245674596,
          "t": -0.17816375969617562
        },
        {
          "ci_high": 0.05212658174332847,
          "ci_low": -0.13928127409497137,
          "coef": -0.043577346175821444,
          "endog": "educ",
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      "reduced_form": [
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        {
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        {
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        {
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        {
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        {
          "ci_high": 0.03126161351027988,
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        },
        {
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        },
        {
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        },
        {
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        },
        {
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        },
        {
          "ci_high": 0.0055814213051183885,
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        },
        {
          "ci_high": 0.015254995937529048,
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          "p": 0.6250018913918476,
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        },
        {
          "ci_high": 0.017080795119365826,
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        },
        {
          "ci_high": 0.01554767415892478,
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          "p": 0.6339657235995096,
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        },
        {
          "ci_high": 0.02212342849393739,
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        {
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        },
        {
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        {
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        },
        {
          "ci_high": 0.03270937771658598,
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          "t": 1.1570428828202637
        },
        {
          "ci_high": 0.02301443511475677,
          "ci_low": -0.018395338159069716,
          "coef": 0.0023095484778435276,
          "instrument": "qtr3_yob36",
          "p": 0.8269407082709517,
          "se": 0.01056387297779055,
          "t": 0.2186270587216558
        },
        {
          "ci_high": 0.023021613966401906,
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          "coef": 0.002941034936287412,
          "instrument": "qtr3_yob37",
          "p": 0.7740660749328558,
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          "t": 0.28706063306858076
        },
        {
          "ci_high": 0.01566399127123229,
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          "instrument": "qtr3_yob38",
          "p": 0.6805074687639181,
          "se": 0.010117549722698986,
          "t": -0.4117711067161898
        },
        {
          "ci_high": 0.0019509568391933435,
          "ci_low": -0.03719261964483288,
          "coef": -0.017620831402819767,
          "instrument": "qtr3_yob39",
          "p": 0.07763242078595264,
          "se": 0.009985753052529859,
          "t": -1.7645971525758475
        }
      ]
    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    0b1e9309b12495566d8e2e71c7c81982ad38ff73f6930e19b3837090d40b211e

    Resultado mostrado ao modelo
40. 39Turno do modelo
    call_d08de59bgemini-3.8-flashFim: STOP7.573 ms23598 de entrada · 65 de saída · 479 de raciocínio · 19405 em cache

    Texto visível

    I will convert the log-point coefficient to a percentage return to provide both the direct coefficient and its interpretation.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process Regarding the Angrist & Krueger (1991) Analysis** Okay, let's break down what I'm seeing here with this Angrist and Krueger (1991) replication. My primary goal is to accurately reproduce the coefficient on `educ` as requested by the user, while also performing the necessary diagnostic checks. First, I'm comparing the results from two different methods of calculating standard errors: HC1 and the classical approach. It's reassuring to see that both `call_1b43c76d` (HC1) and `call_549a6c8a` (classical) are yielding the *exact same coefficient* for `educ`: 0.0891155, which I can confidently round to 0.0891. This consistency is a good sign. When I look at the standard errors themselves, the classical SE is reported as 0.0161101. This aligns perfectly with Angrist & Krueger's Table V, column (2), where they report 0.0891 with an SE of 0.0161. The HC1 SE, at 0.0162123, is very close, which is also expected. Now, for the crucial diagnostics. The first-stage F-statistic is a key indicator of instrument strength. I'm seeing values of 4.80 for HC1 and 4.91 for the classical method. Both of these are significantly below the commonly cited threshold of 10. This immediately flags a potential weak instrument issue, which is a point I recall Bound, Jaeger, and Baker (1995) later emphasized. This is something I need to be aware of and potentially mention. The Sargan test results are also important for assessing the validity of overidentifying restrictions, if applicable. I have a Sargan test statistic of 25.439 with 29 degrees of freedom, resulting in a p-value of 0.65526. This p-value is quite high, suggesting that I *cannot reject* the null hypothesis that the instruments are valid. This is a positive finding, indicating that the overidentifying restrictions are not violated. Finally, I've confirmed the number of observations used in the analysis is 329,509, which is a substantial dataset. Before I finalize the output, I'm pausing to carefully re-read the user's original request. They specifically asked to "Report the coefficient on years of education." They did *not* ask for any percentage conversion or a scaled effect. Therefore, my immediate inclination is to report the raw coefficient. However, a brief thought crosses my mind: should I also consider running `core.scale_effect`? The prompt is very direct about reporting *the coefficient*. If the user had asked for the "percentage return to education" or something similar, then `core.scale_effect` with `log_points_to_percent` would be essential. But given the precise wording, directly reporting the coefficient seems the most faithful approach to the request. I'll stick to that unless there's a strong implicit reason to do otherwise, which I don't see here.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_549a6c8a:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
41. 40Ferramenta
    core.scale_effectv0.1.0call_532e1fd2decidido pelo modeloreexecutável

    Motivo: I will convert the log-point coefficient to a percentage return to provide both the direct coefficient and its interpretation.

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_549a6c8a:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_532e1fd2

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): 2SLS effect of educ on lwklywge	9,32069 %	9.32068667160387	—	5,92278 – 12,8276

    Diagnósticos

    • transform = "log_points_to_percent"

    • the standard error is not carried: a percent effect is a nonlinear function of b, so only the interval, transformed endpoint by endpoint, keeps its meaning

    Digests dos dados

    sha256 do resultado

    b16637f7ef98b5ec950d21f059baee33144e62432a1d8a39ab063f3f31fd2d65

    Resultado mostrado ao modelo
42. 41Turno do modelo
    call_ced3189cgemini-3.8-flashFim: STOP3.894 ms24263 de entrada · 37 de saída · 19 de raciocínio · 19472 em cache

    Texto visível

    I will load the reporting-numbers skill to verify formatting and guidelines for presenting figures and caveats.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process** Okay, first things first, I need to double-check the `reporting-numbers` skill. My primary goal here is to ensure we're adhering to all the established rules. It's a crucial step, a sort of quality control for myself, to guarantee I'm operating within the expected parameters and meeting all requirements before I proceed further with generating the output.

    Chamadas pedidas

    • load_skill (meta-ferramenta)

      {
        "name": "reporting-numbers"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
43. 42Habilidade
    reporting-numbersTexto da habilidade
44. 43Turno do modelo
    call_ea6b6968gemini-3.8-flashFim: STOP26.405 ms24755 de entrada · 401 de saída · 2754 de raciocínio · 22789 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Estimating the Return to Education** I've been tasked with estimating the return to education, specifically the effect of years of education on the log of weekly earnings for men born between 1930 and 1939, using data from the 1980 Census. The method specified is two-stage least squares (2SLS), with a particular set of instruments: quarter-of-birth interacted with year-of-birth (specifically, the first three quarters interacted with each of the ten years of birth), along with nine year-of-birth dummies and an intercept as controls. My primary objective is to report the coefficient on years of education. First, I need to extract the core coefficient estimate and its associated uncertainty. From the tool output, I see the coefficient on `educ` is approximately **0.0891**. The standard error, using the classical method, is **0.0161**, with a 95% confidence interval ranging from **0.0575** to **0.1207**. If I consider the robust (HC1) standard errors, the SE is **0.0162**, and the CI is **[0.0573, 0.1209]**. Given the prompt asks for a single estimate and its uncertainty, I should prioritize the classical estimates unless there's a strong reason otherwise, or present both if clarity allows. For a concise summary, the classical estimate and CI are usually sufficient. Next, I need to consider the diagnostic tests that speak to the validity and reliability of this 2SLS estimation. The most critical diagnostic here is the strength of the instruments. The first-stage F-statistic is a key indicator. I see the classical F-statistic is **4.91**, and the HC1 version is **4.80**. This is significantly below the commonly accepted threshold of 10 for weak instruments. This is a major concern because weak instruments can lead to biased estimates that tend towards the Ordinary Least Squares (OLS) estimates, and they render the standard errors and confidence intervals unreliable. This is a point I absolutely must highlight. I recall the seminal work by Bound, Jaeger, and Baker (1995) on this very issue. Another diagnostic is the Sargan test of overidentifying restrictions. This test is relevant because I have more instruments (30) than endogenous variables (1, which is `educ`). The Sargan test's p-value is **0.655**, based on a statistic of **25.44** with **29** degrees of freedom. A high p-value (typically above 0.05 or 0.10) suggests that the instruments are not jointly statistically significantly different from zero in the second stage, which is a good sign – it means the instruments are not being rejected by the data. This test seems fine. Finally, the number of observations is **329,509** men. This is a very large sample, which is generally a positive for any estimation, but it doesn't overcome the problem of weak instruments. The prompt also specifies the language of the answer. It states, "Write the answer in the language of the question (Portuguese: decimal comma)". Since the question is in English, my natural interpretation is to write the answer in English. The parenthetical "(Portuguese: decimal comma)" seems to be an instruction for when the question itself is in Portuguese – in that case, I would use a decimal comma. Here, I will use standard English notation with a decimal point. I need to ensure all numbers are reported as they appear in the tool outputs and that I avoid quoting rule-of-thumb thresholds as numbers. For instance, instead of saying "below 10," I'll say "below the conventional threshold." Given these considerations, my summary should include: 1. The estimated coefficient on years of education and its uncertainty. 2. The identification strategy (2SLS with specified instruments). 3. A clear statement about what could undermine the conclusion, specifically the weak instruments issue. 4. The figure references, which are `call_549a6c8a:coef.educ` and potentially others if they represent the same coefficient. I have all the necessary components and a clear understanding of the caveats. I'm ready to compile the answer.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "In Table V, column (2) of Angrist and Krueger (1991), the two-stage least squares (2SLS) estimate of the return to education—the coefficient on years of education (`educ`) in the regression of log weekly earnings (`lwklywge`)—is 0.0891155 (classical standard error of 0.0161101; 95% CI: [0.0575401, 0.120691]). With heteroskedasticity-robust standard errors (HC1), the standard error is 0.0162123 (95% CI: [0.0573398, 0.120891]).\n\nThe specification uses 30 quarter-of-birth × year-of-birth interaction instruments and controls for 9 year-of-birth dummies and an intercept, on a sample of 329509 men born in 1930-1939 from the 1980 Census.",
        "caveats": [
          "The first-stage F-statistic on the excluded instruments is 4.90706890045132 (classical) / 4.80075023866826 (HC1), which is below the conventional threshold, signaling weak instruments that bias 2SLS toward OLS and distort hypothesis testing.",
          "Identification rests on the exclusion restriction that quarter of birth affects adult weekly earnings only through its effect on compulsory school attendance."
        ],
        "figure_refs": [
          "call_549a6c8a:coef.educ",
          "call_1b43c76d:coef.educ"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
45. 44Guarda
    resposta recusada

    Números encontrados

    2 · 1991 · 0.0891155 · 0.0161101 · 95% · 0.0575401 · 0.120691 · 0.0162123 · 95% · 0.0573398 · 0.120891 · 30 · 9 · 329509 · 1930 · 1939 · 1980 · 4.90706890045132 · 4.80075023866826

    Sem lastro

    30

    Não citados

    —

    0 nova(s) tentativa(s) restante(s)
46. 45Turno do modelo
    call_05b685b9gemini-3.8-flashFim: STOP13.568 ms27996 de entrada · 401 de saída · 621 de raciocínio · 23311 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **Eureka! I've cracked it!** My initial thought process was thrown off by this pesky validation error – it flagged "30" when I'd written "30 quarter-of-birth...". At first, I was confused because I thought the question explicitly mentioned "thirty". But then, a lightbulb moment! I realized the question stated "each of the first three quarters of birth interacted with each of the ten years of birth," not the digit "30." My interpretation of generating 30 interaction instruments was a misstep based on a too-literal reading of my own initial phrasing. To fix this, I explored two options. The first was to remove the number "30" entirely and rephrase it to something like "the quarter-of-birth × year-of-birth interaction instruments" or simply "the full set of interaction instruments." This seemed promising, especially when I checked my output and found that no tool had actually reported a result of 30 (the `sargan_df` was 29). This confirmed that removing the arbitrary "30" was the correct course of action. Then, I meticulously went through every other number in my response and the accompanying caveats. I cross-referenced each one against the original question and the specific outputs from my tools. This thorough check was crucial to ensure I wasn't making any other unbacked claims. I confirmed that numbers like 1991, 2, 0.0891155, 0.0161101, 0.0575401, 0.120691, 0.0162123, 0.0573398, 0.120891, 9, 329509, 1930, 1939, and 1980 were all either present in the question or directly derived from my tool outputs (coefficients, standard errors, confidence intervals, observation counts, diagnostic statistics like `first_stage_F.educ`). Having verified that "30" was the sole extraneous number and that all others were properly substantiated, I felt confident in proceeding with the resubmission. It's always the subtle nuances that trip you up, isn't it? This experience has reinforced the importance of re-reading and questioning my own initial interpretations, even when they seem straightforward.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "In Table V, column (2) of Angrist and Krueger (1991), the two-stage least squares (2SLS) estimate of the return to education—the coefficient on years of education (`educ`) in the regression of log weekly earnings (`lwklywge`)—is 0.0891155 (classical standard error of 0.0161101; 95% CI: [0.0575401, 0.120691]). With heteroskedasticity-robust standard errors (HC1), the standard error is 0.0162123 (95% CI: [0.0573398, 0.120891]).\n\nThe specification uses the full set of quarter-of-birth × year-of-birth interactions as instruments and controls for nine year-of-birth dummies and an intercept, on the sample of 329509 men born in 1930-1939 from the 1980 Census.",
        "caveats": [
          "The first-stage F-statistic on the excluded instruments is 4.90706890045132 (classical) / 4.80075023866826 (HC1), which is below the conventional threshold, indicating weak instruments that bias 2SLS toward OLS and distort hypothesis testing.",
          "Identification relies on the exclusion restriction that quarter of birth affects adult weekly earnings only through its effect on educational attainment."
        ],
        "figure_refs": [
          "call_549a6c8a:coef.educ",
          "call_1b43c76d:coef.educ"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
47. 46Guarda
    resposta aceita

    Números encontrados

    2 · 1991 · 0.0891155 · 0.0161101 · 95% · 0.0575401 · 0.120691 · 0.0162123 · 95% · 0.0573398 · 0.120891 · 329509 · 1930 · 1939 · 1980 · 4.90706890045132 · 4.80075023866826

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48. 47Resposta

    In Table V, column (2) of Angrist and Krueger (1991), the two-stage least squares (2SLS) estimate of the return to education—the coefficient on years of education (`educ`) in the regression of log weekly earnings (`lwklywge`)—is 0.0891155 (classical standard error of 0.0161101; 95% CI: [0.0575401, 0.120691]). With heteroskedasticity-robust standard errors (HC1), the standard error is 0.0162123 (95% CI: [0.0573398, 0.120891]). The specification uses the full set of quarter-of-birth × year-of-birth interactions as instruments and controls for nine year-of-birth dummies and an intercept, on the sample of 329509 men born in 1930-1939 from the 1980 Census. Ressalvas: The first-stage F-statistic on the excluded instruments is 4.90706890045132 (classical) / 4.80075023866826 (HC1), which is below the conventional threshold, indicating weak instruments that bias 2SLS toward OLS and distort hypothesis testing. Identification relies on the exclusion restriction that quarter of birth affects adult weekly earnings only through its effect on educational attainment.

    • The first-stage F-statistic on the excluded instruments is 4.90706890045132 (classical) / 4.80075023866826 (HC1), which is below the conventional threshold, indicating weak instruments that bias 2SLS toward OLS and distort hypothesis testing.
    • Identification relies on the exclusion restriction that quarter of birth affects adult weekly earnings only through its effect on educational attainment.

    Figuras citadas: call_549a6c8a:coef.educ, call_1b43c76d:coef.educ · Parada: answered

    Figura da resposta: call_549a6c8a:coef.educ = 0,08911550.08911545635102291 (se 0,01611010.01611008909298044)
49. 48Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
50. 49Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_549a6c8a:coef.educ (infer.iv_2sls)
51. 50Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
52. 51Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwklywge'
53. 52Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['educ']
54. 53Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['qtr1_yob30', 'qtr1_yob31', 'qtr1_yob32', 'qtr1_yob33', 'qtr1_yob34', 'qtr1_yob35', 'qtr1_yob36', 'qtr1_yob37', 'qtr1_yob38', 'qtr1_yob39', 'qtr2_yob30', 'qtr2_yob31', 'qtr2_yob32', 'qtr2_yob33', 'qtr2_yob34', 'qtr2_yob35', 'qtr2_yob36', 'qtr2_yob37', 'qtr2_yob38', 'qtr2_yob39', 'qtr3_yob30', 'qtr3_yob31', 'qtr3_yob32', 'qtr3_yob33', 'qtr3_yob34', 'qtr3_yob35', 'qtr3_yob36', 'qtr3_yob37', 'qtr3_yob38', 'qtr3_yob39']
55. 54Pontuação
    #6diagnósticopassouobrigatória329509 vs 329509
56. 55Pontuação
    #7figura da resposta próximapassouobrigatória0.08911545635 vs 0.08911545635601215
57. 56Pontuação
    #8figura da resposta próximapassouregistrada0.01611008909 vs 0.016110089092885405
58. 57Pontuação
    #9figura da resposta próximapassouregistrada0.08911545635 vs 0.0891
59. 58Pontuação
    #10figura da resposta próximapassouregistrada0.01611008909 vs 0.0161

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