Tarefa paper_repro.angrist_krueger_1991.tab5_c2.design

Veredito

Pergunta feita ao analista

Is the earnings gain from schooling causal? For men born in the United States in 1930-1939, observed in the 1980 Census, estimate the causal effect of a year of education on log weekly earnings, using a source of variation in schooling that is unrelated to ability or family background.

Valores esperados e de onde vêm

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

   Is the earnings gain from schooling causal? For men born in the United States in 1930-1939, observed in the 1980 Census, estimate the causal effect of a year of education on log weekly earnings, using a source of variation in schooling that is unrelated to ability or family background.

   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_532cba81gemini-3.8-flashFim: STOP7.451 ms15100 de entrada · 19 de saída · 300 de raciocínio · 0 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on the Earnings Gain from Schooling** Ah, so the core of the user's query is whether the observed correlation between education and earnings is truly causal. They're specifically asking about men born in the US between 1930 and 1939, as observed in the 1980 Census. The crucial element here is identifying a source of variation in schooling that is *exogenous* to both ability and family background. This immediately brings to mind the seminal work of Angrist and Krueger (1991) – this is precisely the problem their paper tackles! Now, let's examine the data at hand. I see a dataset named `asciiqob` with a substantial number of observations – over 329,000. This is promising. The key variables are laid out: `lwklywge` for the log of weekly earnings in 1979, and `educ` for years of education. The demographic information includes `yob` (year of birth, thankfully within the target range of 1930-1939) and `qob` (quarter of birth), along with `pob` (state of birth). The presence of indicator variables like `yob_30` to `yob_39` and `qtr_1` to `qtr_4`, and particularly the interaction terms `qtr1_yob30` to `qtr3_yob39`, signals that the data is structured to facilitate the kind of instrumental variable (IV) analysis often employed in this context. These interactions are particularly interesting, as they are likely intended to capture the "natural experiment" that Angrist and Krueger famously used. Regarding the methodology, the user's prompt explicitly points towards using instrumental variables or at least a strategy focused on achieving exogeneity. The "skills" mentioned – `instrumental-variables` or `choose-identification-strategy` – are exactly what I'd be looking to employ. Given the data structure, especially the quarter of birth indicators and their interactions with year of birth, the most probable strategy is to use quarter of birth as an instrument for education. The logic, as Angrist and Krueger established, is that the compulsory schooling laws often meant individuals were more likely to complete certain grade levels if their birthday fell in a particular quarter, leading to variations in schooling attainment that are plausibly unrelated to underlying ability or family endowments. Therefore, I would plan to use an instrumental variable approach, leveraging quarter of birth (or combinations thereof) to isolate the exogenous variation in education and then estimate its causal impact on log weekly earnings.

    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_ff2107b2gemini-3.8-flashFim: STOP16.310 ms15887 de entrada · 108 de saída · 1202 de raciocínio · 0 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Estimating the Causal Effect of Education on Earnings** My primary objective is to answer the user's question: "Is the earnings gain from schooling causal? For men born in the United States in 1930-1939, observed in the 1980 Census, estimate the causal effect of a year of education on log weekly earnings, using a source of variation in schooling that is unrelated to ability or family background." This requires me to move beyond simple OLS and employ instrumental variables (IV) estimation, specifically Two-Stage Least Squares (2SLS), as per the established literature, particularly Angrist & Krueger (1991). First, I need to establish what constitutes a "standard" or "classic" specification in this context. I'm immediately drawn to Angrist & Krueger (1991) and their seminal work on this topic. My immediate impulse is to consult their tables, specifically looking for specifications relevant to the 1930-1939 birth cohort. I recall that they often present results in tables like Table IV or Table V. Digging into these tables (or recalling their structure), I see they typically compare OLS estimates with 2SLS estimates. For the OLS component, I anticipate seeing models that regress log weekly earnings on education, potentially with controls for year of birth dummies, or sometimes without any controls, or with state of birth and year of birth interactions. This serves as a crucial benchmark. For the IV approach, the key lies in identifying valid instruments. Angrist & Krueger famously used quarter of birth (QOB) dummies as instruments for education. So, I'm looking for specifications using `qtr_1`, `qtr_2`, `qtr_3` (with `qtr_4` as the omitted category) as instruments. They also explored interacting these QOB dummies with year of birth dummies, creating instruments like `qtr1_yob30` through `qtr3_yob39`. This interaction provides a richer set of instruments. Before I dive into the actual estimation, I need to understand what instruments and control variables are available in the `asciiqob` dataset that I'll be using. The dataset description lists: * `lwklywge` (log weekly earnings) - my dependent variable. * `educ` (education) - my endogenous variable of interest. * `yob` (year of birth) - a demographic variable. * `qob` (quarter of birth) - the basis for my instruments. * `pob` (place of birth) - potentially a control. * `yob_30` through `yob_39` - year of birth dummies for the 1930-1939 cohort. * `qtr_1` through `qtr_4` - quarter of birth dummies. * `qtr1_yob30` through `qtr3_yob39` - interaction terms between quarter of birth and year of birth dummies. These are numerous (30 in total). Now, I need to map this understanding to the specific estimation steps. I need to be clear about the exact specifications used in Angrist & Krueger (1991), particularly for the 1930-1939 cohort (which is likely Table V in their paper). Let's break down the Angrist & Krueger (AK91) Table V specifications more precisely: * **Column (1):** Likely an OLS model. This could be just `educ` on `lwklywge`, or `educ` and `yob` dummies on `lwklywge`. * **Column (2):** A 2SLS model where `educ` is instrumented by the three quarter of birth dummies (`qtr_1`, `qtr_2`, `qtr_3`). Crucially, I need to check if Year of Birth (YOB) dummies are *not* included as exogenous controls in this specific specification. * **Column (3):** This would be an OLS regression with `educ` and the nine YOB dummies (`yob_31` through `yob_39`) as covariates. * **Column (4):** This is where it gets interesting for 2SLS. If YOB dummies are included as exogenous controls, what are the instruments? * Option 1: The three basic QOB dummies (`qtr_1`, `qtr_2`, `qtr_3`) are used as instruments. This would mean we have 9 exogenous YOB controls and 3 instruments, leading to an overidentified model with 9 - 3 = 6 degrees of freedom for the overidentification test. * Option 2: The full set of interaction terms are used as instruments. If YOB dummies are already in the model, then the instruments would be the interactions `qtr1_yob30` to `qtr3_yob39` (excluding interactions with `qtr4` and `yob_30` as they are collinear with the included controls). This would give us 30 instruments. This brings me to the practical execution. I need to use the `infer.ols` function to get the OLS benchmark first, to see the uncorrected estimates. Then, I'll move to `infer.iv_2sls`. For `infer.iv_2sls`, I need to carefully define the `instruments` and `exog` (exogenous variables) arguments. Let's consider the key specifications I want to replicate: * **Specification A (Similar to AK91 Table V, Column 2):** * `endog = ['educ']` * `instruments = ['qtr_1', 'qtr_2', 'qtr_3']` * `exog = []` (or only a constant). This means I'm not controlling for YOB directly in the second stage, relying solely on QOB as instruments. This might be a specification to check, but AK91 typically *does* control for YOB, as age is a major determinant of earnings. The rationale here is that QOB might affect schooling, and schooling affects earnings, but if YOB is omitted, QOB might be correlated with age/cohort effects that also affect earnings. * **Specification B (More aligned with AK91 Table V, Column 4):** * `endog = ['educ']` * `instruments = ['qtr_1', 'qtr_2', 'qtr_3']` * `exog = ['yob_31', 'yob_32', 'yob_33', 'yob_34', 'yob_35', 'yob_36', 'yob_37', 'yob_38', 'yob_39']`. This seems like a plausible interpretation of using basic QOB dummies as instruments when YOB dummies are included as controls. I have 9 YOB dummies and 3 QOB instruments. * **Specification C (Using interaction instruments, also relevant to AK91):** * `endog = ['educ']` * `instruments = [f'qtr{q}_yob{y}' for q in [1,2,3] for y in range(30, 40)]`. This is a list of 30 interaction terms. * `exog = ['yob_31', 'yob_32', 'yob_33', 'yob_34', 'yob_35', 'yob_36', 'yob_37', 'yob_38', 'yob_39']`. In this case, the interaction terms are the instruments. Since the interaction terms implicitly include the YOB effects (e.g., `qtr1_yob30` is `qtr_1` interacted with `yob_30`), and I'm already including `yob_31` to `yob_39`, I need to be careful about perfect collinearity. AK91 likely uses *all* 30 interaction terms as instruments and includes *all* 10 YOB dummies as controls (or some variation that avoids collinearity). If I include `yob_31` to `yob_39` as `exog`, then the instruments should be `qtr1_yob30` to `qtr3_yob39`. This setup would yield 30 instruments. Before I run anything, I should confirm the structure of the available interaction terms. The dataset description gives `qtr1_yob30` to `qtr3_yob39`. This means 3 quarters * 10 years = 30 interaction variables. My plan is to: 1. Run `infer.ols` to get the baseline OLS estimate. 2. Run `infer.iv_2sls` using the basic QOB dummies as instruments, *without* YOB controls in the second stage (to see if it's significantly different, though this might not be the most standard AK spec). 3. Run `infer.iv_2sls` using the basic QOB dummies as instruments, *with* YOB dummies (`yob_31` to `yob_39`) in the second stage. 4. Run `infer.iv_2sls` using the interaction terms (`qtr1_yob30` to `qtr3_yob39`) as instruments, with YOB dummies (`yob_31` to `yob_39`) in the second stage. This systematic approach will allow me to compare the different specifications and identify the one that best reflects the "standard" Angrist & Krueger approach for this cohort, providing the causal estimate requested by the user. I'm particularly keen to see how the estimated coefficient for education changes across these specifications and whether the results are robust. I also need to ensure I'm using the correct columns from the dataset description for each specification. I should probably start by checking the structure of `infer.ols` and `infer.iv_2sls` to make sure I'm passing the arguments correctly.

    Chamadas pedidas

    • infer.ols

      {
        "controls": [
          "yob_31",
          "yob_32",
          "yob_33",
          "yob_34",
          "yob_35",
          "yob_36",
          "yob_37",
          "yob_38",
          "yob_39"
        ],
        "dataset": "asciiqob",
        "x": [
          "educ"
        ],
        "y": "lwklywge"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
37. 36Ferramenta
    infer.olsv0.1.0call_bc18c14cdecidido pelo modeloreexecutável

    Argumentos

    {
      "cluster": null,
      "controls": [
        "yob_31",
        "yob_32",
        "yob_33",
        "yob_34",
        "yob_35",
        "yob_36",
        "yob_37",
        "yob_38",
        "yob_39"
      ],
      "dataset": "asciiqob",
      "fe": [],
      "intercept": true,
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "weights": null,
      "x": [
        "educ"
      ],
      "y": "lwklywge"
    }

    Figuras call_bc18c14c

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ Coefficient on educ in the regression of lwklywge	0,071081	0.07108104582881641	0,0003814630.0003814625508367558	0,0703334 – 0,0718287

    Diagnósticos

    • n_obs = 329.509329509
    • k = 1111
    • r2 = 0,1177450.1177450558150579
    • df_resid = 329.498329498
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 5.029144685452213,
          "ci_low": 5.005551888466924,
          "coef": 5.017348286959568,
          "p": 0,
          "se": 0.006018659145412517,
          "t": 833.632236971559,
          "term": "Intercept"
        },
        {
          "ci_high": 0.07182870143631512,
          "ci_low": 0.07033339022131771,
          "coef": 0.07108104582881641,
          "p": 0,
          "se": 0.0003814625508367558,
          "t": 186.33820193593536,
          "term": "educ"
        },
        {
          "ci_high": 0.003654620736688567,
          "ci_low": -0.016429530675149365,
          "coef": -0.006387454969230398,
          "p": 0.21251673705979898,
          "se": 0.005123583339783002,
          "t": -1.2466772853354082,
          "term": "yob_31"
        },
        {
          "ci_high": -0.004936408269283734,
          "ci_low": -0.024740341078769944,
          "coef": -0.01483837467402684,
          "p": 0.003313502501579154,
          "se": 0.0050520979514752686,
          "t": -2.9370718494667885,
          "term": "yob_32"
        },
        {
          "ci_high": -0.007649142847665968,
          "ci_low": -0.027517182480641292,
          "coef": -0.01758316266415363,
          "p": 0.0005221965936430843,
          "se": 0.005068451973413265,
          "t": -3.469138655429054,
          "term": "yob_33"
        },
        {
          "ci_high": -0.01107757207221368,
          "ci_low": -0.03092094348614214,
          "coef": -0.02099925777917791,
          "p": 0.000033506495111181844,
          "se": 0.005062158967871783,
          "t": -4.148280982966908,
          "term": "yob_34"
        },
        {
          "ci_high": -0.0230174487192081,
          "ci_low": -0.04277190720234062,
          "coef": -0.03289467796077436,
          "p": 6.701791425159347e-11,
          "se": 0.00503947676429863,
          "t": -6.527399470082185,
          "term": "yob_35"
        },
        {
          "ci_high": -0.022039173219305555,
          "ci_low": -0.04152236982602252,
          "coef": -0.031780771522664036,
          "p": 1.616407884888965e-10,
          "se": 0.004970276288648868,
          "t": -6.394165973276991,
          "term": "yob_36"
        },
        {
          "ci_high": -0.027119059880288888,
          "ci_low": -0.046305169173626246,
          "coef": -0.036712114526957565,
          "p": 6.363280681430232e-14,
          "se": 0.004894487594465081,
          "t": -7.500706420928182,
          "term": "yob_37"
        },
        {
          "ci_high": -0.027372029567121557,
          "ci_low": -0.046408888465939484,
          "coef": -0.03689045901653052,
          "p": 3.056658926334681e-14,
          "se": 0.004856412954459875,
          "t": -7.5962360207964315,
          "term": "yob_38"
        },
        {
          "ci_high": -0.03869036675333921,
          "ci_low": -0.05763688568608099,
          "coef": -0.0481636262197101,
          "p": 2.1893242141006344e-23,
          "se": 0.004833366705922259,
          "t": -9.964819379563288,
          "term": "yob_39"
        }
      ]
    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    f630f35c29091e5858d52e4f44c9bdca0203ec5e6a8494d51f626e992f3e6852

    Resultado mostrado ao modelo
38. 37Turno do modelo
    call_5207f47fgemini-3.8-flashFim: STOP5.325 ms18083 de entrada · 137 de saída · 118 de raciocínio · 12933 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Testing `infer.iv_2sls`** Alright, the next logical step in my analysis is to rigorously test the `infer.iv_2sls` function. I've outlined two distinct approaches to explore the instrumental variable strategy. First, I want to investigate a baseline scenario. This will involve using a relatively simple set of instruments: the three quarter-of-birth (QOB) dummies (`qtr_1`, `qtr_2`, `qtr_3`). These will serve as my instrumental variables. For the exogenous variables in this first stage, I'll include the year-of-birth (YOB) dummies. This setup represents a clear and interpretable starting point to understand the basic performance of the function with a standard IV approach. However, I'm also keenly interested in exploring a more complex and potentially more powerful set of instruments. So, my second option will involve a considerably more granular approach. Instead of just the QOB dummies, I plan to create and utilize a set of thirty interaction terms. Specifically, these will be the product of the QOB dummies and the YOB dummies, covering a range of birth years. The idea here is to generate a richer set of instruments that might capture finer-grained variation in the treatment variable. Again, the YOB dummies will be treated as exogenous variables in this second scenario. My objective is to run both of these instrumental variable (IV) regressions and then meticulously compare the results. I'll be looking at the output from both options to understand how the choice of instruments, particularly the complexity and the inclusion of interactions, impacts the estimated coefficients, their standard errors, and overall model fit. This comparison will be crucial in determining the most appropriate and robust IV strategy for my research question.

    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": [
          "qtr_1",
          "qtr_2",
          "qtr_3"
        ],
        "y": "lwklywge"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
39. 38Ferramenta
    infer.iv_2slsv0.1.0call_a351b6d5decidido pelo modeloreexecutável

    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": [
        "qtr_1",
        "qtr_2",
        "qtr_3"
      ],
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "y": "lwklywge"
    }

    Figuras call_a351b6d5

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ 2SLS effect of educ on lwklywge	0,105252	0.10525237815751685	0,02011580.02011579728531004	0,065826 – 0,144679

    Diagnósticos

    • first_stage_F.educ = 32,323332.323288104300566
    • partial_r2.educ = 0,0002937190.00029371857750060126
    • weak_instrument = false
    • overid_p = 0,1960030.19600265324202926
    • sargan = 3,259253.2592541657882292
    • sargan_df = 22
    • n_obs = 329.509329509
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 5.082866109981523,
          "ci_low": 4.100612223144528,
          "coef": 4.591739166563025,
          "p": 5.74579460219554e-75,
          "se": 0.2505786551215099,
          "t": 18.324542305235106,
          "term": "Intercept"
        },
        {
          "ci_high": 0.00046245642403975815,
          "ci_low": -0.02268798014618407,
          "coef": -0.011112761861072155,
          "p": 0.059882279143252934,
          "se": 0.005905810441659455,
          "t": -1.8816658561681867,
          "term": "yob_31"
        },
        {
          "ci_high": -0.008681765621735137,
          "ci_low": -0.033091144633599454,
          "coef": -0.020886455127667295,
          "p": 0.0007960659231866866,
          "se": 0.006226973949515358,
          "t": -3.3541902209648518,
          "term": "yob_32"
        },
        {
          "ci_high": -0.011891115732719344,
          "ci_low": -0.03923828535662553,
          "coef": -0.02556470054467244,
          "p": 0.0002479159813543451,
          "se": 0.006976421348460814,
          "t": -3.6644433109408876,
          "term": "yob_33"
        },
        {
          "ci_high": -0.015527940653515027,
          "ci_low": -0.044617024308172964,
          "coef": -0.030072482480843998,
          "p": 0.00005069312606073804,
          "se": 0.007420793705763074,
          "t": -4.052461727576305,
          "term": "yob_34"
        },
        {
          "ci_high": -0.0277445671873654,
          "ci_low": -0.060527447529103814,
          "coef": -0.04413600735823461,
          "p": 1.3106356698122568e-7,
          "se": 0.008363102632756931,
          "t": -5.277468099621419,
          "term": "yob_35"
        },
        {
          "ci_high": -0.02677826029236713,
          "ci_low": -0.06323787211695024,
          "coef": -0.045008066204658685,
          "p": 0.000001305355442369753,
          "se": 0.009301058127319439,
          "t": -4.839026440707773,
          "term": "yob_36"
        },
        {
          "ci_high": -0.03181299019275943,
          "ci_low": -0.07232702934973442,
          "coef": -0.05207000977124693,
          "p": 4.705656467818668e-7,
          "se": 0.01033536602047542,
          "t": -5.038042162037696,
          "term": "yob_37"
        },
        {
          "ci_high": -0.03197831488277511,
          "ci_low": -0.07839094765670915,
          "coef": -0.05518463126974213,
          "p": 0.0000031508670927774516,
          "se": 0.011840131413061958,
          "t": -4.660812396800156,
          "term": "yob_38"
        },
        {
          "ci_high": -0.04312648769533238,
          "ci_low": -0.09247379690150752,
          "coef": -0.06780014229841995,
          "p": 7.218929243788692e-8,
          "se": 0.01258878436670489,
          "t": -5.38575769696551,
          "term": "yob_39"
        },
        {
          "ci_high": 0.14467876118431428,
          "ci_low": 0.06582599513071943,
          "coef": 0.10525237815751685,
          "p": 1.674936656455949e-7,
          "se": 0.02011579728531004,
          "t": 5.232324459462489,
          "term": "educ"
        }
      ],
      "first_stage": [
        {
          "ci_high": -0.11671629993733762,
          "ci_low": -0.18027625115413287,
          "coef": -0.14849627554573525,
          "endog": "educ",
          "instrument": "qtr_1",
          "p": 5.3043008822118475e-20,
          "se": 0.016214511653829953,
          "t": -9.158232990054909
        },
        {
          "ci_high": -0.05978063596555019,
          "ci_low": -0.12385116052866832,
          "coef": -0.09181589824710926,
          "endog": "educ",
          "instrument": "qtr_2",
          "p": 1.9395078512512426e-8,
          "se": 0.016344761871389904,
          "t": -5.617450958880292
        },
        {
          "ci_high": -0.004636100871815506,
          "ci_low": -0.06668323710982477,
          "coef": -0.03565966899082014,
          "endog": "educ",
          "instrument": "qtr_3",
          "p": 0.02426829109668617,
          "se": 0.015828583791488673,
          "t": -2.252865414908124
        }
      ],
      "reduced_form": [
        {
          "ci_high": -0.0069361271421543025,
          "ci_low": -0.02014201226181339,
          "coef": -0.013539069701983847,
          "instrument": "qtr_1",
          "p": 0.00005849771705180587,
          "se": 0.003368897774032123,
          "t": -4.018842544390826
        },
        {
          "ci_high": -0.00233300403587223,
          "ci_low": -0.01564455906755098,
          "coef": -0.008988781551711606,
          "instrument": "qtr_2",
          "p": 0.008121647148358259,
          "se": 0.003395854780560619,
          "t": -2.6469864386331783
        },
        {
          "ci_high": 0.007933121954108552,
          "ci_low": -0.004992850374464482,
          "coef": 0.0014701357898220348,
          "instrument": "qtr_3",
          "p": 0.6557169151421668,
          "se": 0.003297490399950917,
          "t": 0.44583474446018634
        }
      ]
    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    37726a938472189830bd5c3b8934c4d21723aad9d2633856651ecfc78797753c

    Resultado mostrado ao modelo
40. 39Turno do modelo
    call_886c6ce5gemini-3.8-flashFim: STOP10.005 ms19795 de entrada · 446 de saída · 695 de raciocínio · 16155 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **Reflections on Instrumental Variable Estimation and Instrument Validity** Alright, I've just run a first pass with a specific set of instruments: `qtr_1`, `qtr_2`, `qtr_3` as my instruments, and `yob_31` through `yob_39` as exogenous controls. The initial results look promising, particularly regarding instrument strength. The first-stage F-statistic came in at a robust 32.32, comfortably exceeding the commonly cited threshold of 10, so I'm confident these aren't weak instruments. Looking at the first-stage coefficients themselves, I see that `qtr_1` has the largest negative impact (-0.148 with a t-statistic of -9.16), followed by `qtr_2` (-0.092, t = -5.62), and then `qtr_3` (-0.036, t = -2.25). This aligns with my understanding of the compulsory schooling laws: children born earlier in the year are more likely to turn 16 and be able to leave school before the end of the academic year, leading to less schooling, and this effect is captured by these quarter dummies relative to the fourth quarter. Crucially, the Sargan test for overidentifying restrictions passed. With a p-value of 0.196 and a Sargan statistic of 3.259 (with 2 degrees of freedom), I can't reject the null hypothesis, meaning my instruments are likely valid and uncorrelated with the error term. This is a significant finding for the credibility of the subsequent 2SLS estimate. The 2SLS estimate for `educ` is 0.105252, with a standard error of 0.0201158, resulting in a 95% confidence interval of [0.065826, 0.144679]. This estimate is notably different from the OLS estimate, which was 0.071081 with a much smaller standard error of 0.000381463. The widening of the confidence interval and the shift in the point estimate further underscore the necessity of using instrumental variables here, likely due to endogeneity issues in the OLS model. Now, my next step is to explore a more complex instrument set. I want to replicate the approach seen in Table V, column (6) of AK91, which involves a larger set of 30 instruments: the interaction terms between the quarters (`qtr1` to `qtr3`) and year of birth dummies (`yob30` to `yob39`). I'm curious to see if this richer set of instruments yields a significantly different result, or if the simpler, 3-instrument specification I just ran proves to be a cleaner and more interpretable benchmark. This will be a valuable comparison to understand the sensitivity of my results to the instrument set.

    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
41. 40Ferramenta
    infer.iv_2slsv0.1.0call_2f284f63decidido pelo modeloreexecutável

    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_2f284f63

    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,
          "se": 0.005805799252958204,
          "t": -3.1055734196477376,
          "term": "yob_32"
        },
        {
          "ci_high": -0.009370023577531679,
          "ci_low": -0.03422104383269585,
          "coef": -0.021795533705113765,
          "p": 0.0005861498599969342,
          "se": 0.006339639188386165,
          "t": -3.437976997972039,
          "term": "yob_33"
        },
        {
          "ci_high": -0.012727148691280315,
          "ci_low": -0.03884841569027313,
          "coef": -0.025787782190776723,
          "p": 0.00010890217206636189,
          "se": 0.006663686489197591,
          "t": -3.8698972757168177,
          "term": "yob_34"
        },
        {
          "ci_high": -0.024408474064822112,
          "ci_low": -0.053246427350637913,
          "coef": -0.03882745070773001,
          "p": 1.308161141707517e-7,
          "se": 0.007356728894284171,
          "t": -5.277814537640105,
          "term": "yob_35"
        },
        {
          "ci_high": -0.02300740608131808,
          "ci_low": -0.05451592575803326,
          "coef": -0.03876166591967567,
          "p": 0.0000014197631631827207,
          "se": 0.008038005846823553,
          "t": -4.822298796285828,
          "term": "yob_36"
        },
        {
          "ci_high": -0.02755235902664934,
          "ci_low": -0.06208256880418383,
          "coef": -0.044817463915416585,
          "p": 3.624905305278879e-7,
          "se": 0.008808856491248577,
          "t": -5.087773192802248,
          "term": "yob_37"
        },
        {
          "ci_high": -0.02705661445312191,
          "ci_low": -0.06603432692958938,
          "coef": -0.046545470691355645,
          "p": 0.000002855604593003383,
          "se": 0.00994344018685156,
          "t": -4.681022846891944,
          "term": "yob_38"
        },
        {
          "ci_high": -0.03791390525396447,
          "ci_low": -0.07914025293106855,
          "coef": -0.05852707909251651,
          "p": 2.624228397532098e-8,
          "se": 0.010517080049197979,
          "t": -5.56495517945399,
          "term": "yob_39"
        },
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    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    395d128f6dd46da7a74a6b556fc9fddcc1b21d2bfa2fb3b581eac645a4ac63c3

    Resultado mostrado ao modelo
42. 41Turno do modelo
    call_7ae23ecegemini-3.8-flashFim: STOP6.253 ms23652 de entrada · 62 de saída · 359 de raciocínio · 19479 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thoughts on Instrument Strength and Specification Choice** This is absolutely fascinating and strikes me as incredibly relevant to the modern econometrics literature, particularly the foundational work by Bound, Jaeger, and Baker (1995). Looking at these results, the core of their critique becomes vividly clear. When I employed the 30 instruments, specifically the `qtr*yob` interactions, the first-stage F-statistic plummeted to a mere 4.80. This immediately triggers a "weak instrument" flag, as it falls well below the conventional threshold of 10. This is precisely the weak instruments problem that Bound, Jaeger, and Baker (1995) highlighted in their seminal paper when discussing specifications with a large number of interaction instruments like this! The power of the instruments to explain the endogenous variable is severely compromised. However, the situation is dramatically different when I consider a more parsimonious specification. By using just the three quarter-of-birth dummies (`qtr_1`, `qtr_2`, `qtr_3`) in conjunction with the year-of-birth dummies (`yob_31` to `yob_39`), the picture changes entirely. Here, the first-stage F-statistic is a robust 32.32, comfortably above the 10 threshold, indicating that these instruments are far from weak. Furthermore, this stronger instrument set yields a 2SLS estimate of 0.105252 with a standard error of 0.0201158, giving me a 95% confidence interval of [0.065826, 0.144679]. This contrasts with the OLS estimate, which is 0.071081 with a much smaller standard error of 0.000381463, and a tight 95% confidence interval of [0.0703334, 0.0718287]. The divergence between the OLS and 2SLS estimates in the weak instrument case, and their closer alignment in the stronger instrument case, is a key takeaway. This leads me to pause and consider an important alternative: what about the specification without year-of-birth controls? I need to go back and check what Table V, column 2 of AK91 presents. I recall it uses just the QOB dummies and education, but importantly, without the YOB controls. It's crucial to see how that particular specification performs in terms of instrument strength and the resulting estimates. This comparison will be essential for a complete understanding of the sensitivity of the results to model specification.

    Chamadas pedidas

    • infer.iv_2sls

      {
        "dataset": "asciiqob",
        "endog": [
          "educ"
        ],
        "instruments": [
          "qtr_1",
          "qtr_2",
          "qtr_3"
        ],
        "y": "lwklywge"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
43. 42Ferramenta
    infer.iv_2slsv0.1.0call_5b14fc79decidido pelo modeloreexecutável

    Argumentos

    {
      "cluster": null,
      "dataset": "asciiqob",
      "endog": [
        "educ"
      ],
      "exog": [],
      "instruments": [
        "qtr_1",
        "qtr_2",
        "qtr_3"
      ],
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "y": "lwklywge"
    }

    Figuras call_5b14fc79

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ 2SLS effect of educ on lwklywge	0,102598	0.10259759780305362	0,01952810.0195281199249531	0,064323 – 0,140872

    Diagnósticos

    • first_stage_F.educ = 34,054534.05446223068362
    • partial_r2.educ = 0,0003095450.0003095454300584555
    • weak_instrument = false
    • overid_p = 0,2409410.24094086749252064
    • sargan = 2,846412.8464074773990133
    • sargan_df = 22
    • n_obs = 329.509329509
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 5.078570401649435,
          "ci_low": 4.100992695815059,
          "coef": 4.589781548732247,
          "p": 1.3232393599861455e-75,
          "se": 0.24938573429129893,
          "t": 18.40434683152758,
          "term": "Intercept"
        },
        {
          "ci_high": 0.1408721501340934,
          "ci_low": 0.06432304547201384,
          "coef": 0.10259759780305362,
          "p": 1.49053404439943e-7,
          "se": 0.0195281199249531,
          "t": 5.253838986924392,
          "term": "educ"
        }
      ],
      "first_stage": [
        {
          "ci_high": -0.11953932292536562,
          "ci_low": -0.18319261003975784,
          "coef": -0.15136596648256173,
          "endog": "educ",
          "instrument": "qtr_1",
          "p": 1.1535108273634481e-20,
          "se": 0.016238322183477785,
          "t": -9.321527481242736
        },
        {
          "ci_high": -0.06263883247926916,
          "ci_low": -0.12679343093195433,
          "coef": -0.09471613170561174,
          "endog": "educ",
          "instrument": "qtr_2",
          "p": 7.15921262227449e-9,
          "se": 0.01636620960916253,
          "t": -5.787297973538446
        },
        {
          "ci_high": -0.002959522306265897,
          "ci_low": -0.06507635694601437,
          "coef": -0.03401793962614013,
          "endog": "educ",
          "instrument": "qtr_3",
          "p": 0.031815138234071054,
          "se": 0.015846364259010662,
          "t": -2.1467346749142555
        }
      ],
      "reduced_form": [
        {
          "ci_high": -0.006887544854790142,
          "ci_low": -0.020091501041267466,
          "coef": -0.013489522948028805,
          "instrument": "qtr_1",
          "p": 0.00006210447873063894,
          "se": 0.003368405692344279,
          "t": -4.004720387062588
        },
        {
          "ci_high": -0.002294021287008126,
          "ci_low": -0.015605029903326604,
          "coef": -0.008949525595167365,
          "instrument": "qtr_2",
          "p": 0.008400877931648018,
          "se": 0.0033957153871784318,
          "t": -2.635534659046825
        },
        {
          "ci_high": 0.007898890636734233,
          "ci_low": -0.0050273453197783825,
          "coef": 0.0014357726584779257,
          "instrument": "qtr_3",
          "p": 0.6632688618940527,
          "se": 0.0032975576532959256,
          "t": 0.4354048691287819
        }
      ]
    }

    Digests dos dados

    asciiqob 654074d5953a60c49422fd28f157a9ede3a844493e1280ba284d386a05958cf7

    sha256 do resultado

    665218c00ab7ab0e1483a270b1b8ffd2de6c99a307e3f0b2cf042b7eeb73c66e

    Resultado mostrado ao modelo
44. 43Turno do modelo
    call_dcc7cde5gemini-3.8-flashFim: STOP4.060 ms24932 de entrada · 43 de saída · 88 de raciocínio · 22750 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Transforming Coefficients** As an expert in this domain, I recognize the critical need for precise and interpretable results. My current task involves analyzing the impact of education on some outcome, and I've calculated a coefficient for education. However, I've noticed that the outcome variable is logged. This immediately flags a potential issue with how I'm presenting the coefficient. The standard interpretation of a coefficient in a linear regression model assumes that both the independent and dependent variables are in their original scale. When the dependent variable is logged, a one-unit change in the independent variable is no longer directly associated with a one-unit change in the dependent variable. Instead, it's associated with a percentage change in the dependent variable. I recall a specific recommendation from the `instrumental-variables` skill, which is highly relevant here. The guidance is explicit: "If the outcome is in logs, restate the coefficient as a percent with `core.scale_effect`, never by hand." This is a crucial instruction, as manually calculating this percentage can be prone to error and may not perfectly align with the underlying statistical assumptions or best practices. Therefore, my immediate next step is to apply the `core.scale_effect` function to the coefficient of education. I'll be calling this function specifically on `call_a351b6d5:coef.educ` to ensure I'm transforming the correct value. This will allow me to present the effect of education as a percentage, making it much more intuitive and directly interpretable for my audience, who, like me, expect rigorous and well-communicated findings. This step is essential for ensuring the clarity and validity of my analysis.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_a351b6d5:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
45. 44Ferramenta
    core.scale_effectv0.1.0call_0dc26894decidido pelo modeloreexecutável

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_a351b6d5:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_0dc26894

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): 2SLS effect of educ on lwklywge	11,0991 %	11.099096482926587	—	6,80409 – 15,5668

    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

    ace1c48c853959839082532717b3f4ebb1267ba59abbacfe744ae6b40c4c5f78

    Resultado mostrado ao modelo
46. 45Turno do modelo
    call_92cc1091gemini-3.8-flashFim: STOP3.438 ms25184 de entrada · 42 de saída · 44 de raciocínio · 22746 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Scaling OLS Coefficients for Comparison** My current objective is to facilitate a direct, percentage-based comparison between Ordinary Least Squares (OLS) and Instrumental Variables (IV) estimates for the effect of education. To achieve this, I've identified the OLS coefficient for `educ` (specifically, `call_bc18c14c:coef.educ`) and I've decided that I need to apply the `core.scale_effect` function to it. This step is crucial because it will transform the OLS coefficient into a percentage change, allowing for a meaningful side-by-side analysis with the corresponding IV estimate, which I anticipate will also be (or I will ensure it is) presented in percentage terms. By scaling the OLS coefficient, I'm essentially bringing it to the same unit of interpretation as the IV estimate, thereby enhancing the clarity and interpretability of my results. This is a standard practice when one wants to understand the *magnitude* of an effect relative to the baseline, and it's particularly important when comparing different estimation strategies that might inherently produce coefficients in different units or scales.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_bc18c14c:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
47. 46Ferramenta
    core.scale_effectv0.1.0call_6b2add4edecidido pelo modeloreexecutável

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_bc18c14c:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_6b2add4e

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): Coefficient on educ in the regression of lwklywge	7,36682 %	7.366823867457449	—	7,28658 – 7,44713

    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

    7ac98c78302cfbbf93f167b537f4b496086c4ede3e7e39ea98d96bfd3b31465d

    Resultado mostrado ao modelo
48. 47Turno do modelo
    call_0f87fbebgemini-3.8-flashFim: STOP5.121 ms25389 de entrada · 18 de saída · 28 de raciocínio · 22734 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Loading "reporting-numbers"** Alright, my immediate next step, after considering what's come before, is to verify the integrity and adherence to established protocols for the `reporting-numbers` skill. I need to meticulously examine `load_skill("reporting-numbers")` to ensure that every rule governing the generation of our final output has been strictly observed. This isn't just a perfunctory check; it's a deep dive to confirm that the underlying mechanisms of this particular skill are functioning precisely as intended and in complete alignment with our established best practices for crafting comprehensive and accurate responses.

    Chamadas pedidas

    • load_skill (meta-ferramenta)

      {
        "name": "reporting-numbers"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
49. 48Habilidade
    reporting-numbersTexto da habilidade
50. 49Turno do modelo
    call_9b1f8855gemini-3.8-flashFim: STOP4.635 ms25871 de entrada · 77 de saída · 23 de raciocínio · 22800 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process Regarding Calculating the Difference Between IV and OLS Estimates via `calc.combine`** Right, so the immediate question I'm grappling with is whether we should proceed with calculating the difference between Instrumental Variables (IV) and Ordinary Least Squares (OLS) estimates, specifically utilizing the `calc.combine` function. My mind is going through the implications and necessity of this particular computation. On one hand, I understand the value of comparing these two estimation methods. The discrepancy between IV and OLS estimates is often a crucial diagnostic tool. It directly speaks to the presence or absence of endogeneity in our model. If the estimates diverge significantly, it's a strong signal that our independent variables are correlated with the error term, and thus, OLS is likely producing biased results. The IV approach, by design, aims to address this endogeneity by using instruments that are correlated with the endogenous regressors but not with the error term. So, quantifying that difference is, in principle, a very informative step. The mention of `calc.combine` brings a specific implementation into focus. I need to consider what this function actually *does*. Does it inherently provide the most robust or efficient way to calculate this difference? What are its underlying assumptions? Is it designed for this exact purpose, or is it a more general-purpose tool that *can* be bent to this task? I'm thinking about the computational overhead, the potential for numerical instability, and whether it aligns with our existing analytical framework or if it introduces a new dependency or complexity that might not be entirely justified. My internal calculus is weighing the analytical gain against the practical implementation. If `calc.combine` offers a straightforward, accurate, and efficient way to get this difference, then it's a clear path forward. It could streamline our workflow and provide a readily interpretable metric. However, if it's a kludge, or if there are better-suited methods already at our disposal or that we could easily develop, then I need to question its inclusion. I'm also considering the context of the broader project. Is this difference *the* key output we're looking for, or is it a secondary consideration? The emphasis I place on this calculation will depend on its centrality to our overall research question. Ultimately, my decision will hinge on whether `calc.combine` is the optimal tool for the job, providing a clear, reliable, and meaningful quantification of the IV-OLS estimate difference that serves our analytical goals without introducing unnecessary complications.

    Chamadas pedidas

    • calc.combine

      {
        "a": "call_a351b6d5:coef.educ",
        "b": "call_bc18c14c:coef.educ",
        "label": "Diferença entre estimativa IV e MQO",
        "op": "difference",
        "unit": "pontos de log"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
51. 50Ferramenta
    calc.combinev0.1.0call_aee801dcdecidido pelo modeloreexecutável

    Argumentos

    {
      "a": "call_a351b6d5:coef.educ",
      "b": "call_bc18c14c:coef.educ",
      "label": "Diferença entre estimativa IV e MQO",
      "op": "difference",
      "unit": "pontos de log"
    }

    Figuras call_aee801dc

    Chave	Valor	Valor bruto	Erro-padrão	IC
    result Diferença entre estimativa IV e MQO	0,0341713 pontos de log	0.03417133232870044	—	—

    • no uncertainty is propagated: the result carries no standard error

    Digests dos dados

    sha256 do resultado

    9b6e1ec2a1e90f2231ed4e6d43bfb1f5c2c0c0aff568b38a5efaf4178843c128

    Resultado mostrado ao modelo
52. 51Turno do modelo
    call_33687900gemini-3.8-flashFim: STOP20.869 ms26014 de entrada · 923 de saída · 1595 de raciocínio · 22778 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Estimating the Causal Effect of Education on Earnings** My core objective was to rigorously determine if the observed earnings gains from education are truly causal for a specific cohort of men in the United States, using the 1980 Census data. The fundamental challenge, as I see it, is the potential for omitted variable bias. Individuals with higher innate ability or more advantageous family backgrounds are likely to both achieve higher levels of education *and* earn more, irrespective of the education itself. This means a simple Ordinary Least Squares (OLS) regression would likely overstate the causal return to schooling. To tackle this, I needed an instrumental variable (IV) – a source of variation in education that is correlated with educational attainment but *uncorrelated* with ability or family background. The brilliant insight of Angrist and Krueger (1991) comes to mind here: quarter of birth. The logic is that compulsory schooling laws, which typically require individuals to remain in school until a certain age (around 16), create a discontinuity. Those born earlier in the calendar year start school at a younger age relative to their age peers. Consequently, when they reach the compulsory school-leaving age, they will have completed fewer years of schooling than those born later in the year, who started school closer to their compulsory age and thus had more time in the system. This variation in schooling, driven solely by the timing of school entry due to birth quarter and compulsory attendance laws, should be exogenous with respect to individual ability or upbringing. So, my identification strategy hinges on using quarter of birth as an instrument for years of education. I included year-of-birth indicators as controls to account for any cohort-specific trends in earnings that might coincide with age. Now, let's examine the diagnostics and the actual estimates. First, the **instrument relevance** is crucial. I checked the first stage results. The Wald F-statistic for the excluded instruments is a robust 32.32 (using heteroskedasticity-consistent standard errors). This is well above any conventional threshold, indicating that I have strong instruments and am not suffering from the "weak instrument" problem. The coefficients of the first stage confirm the mechanism: individuals born in earlier quarters of the year systematically completed fewer years of education. Specifically, compared to those born in the fourth quarter (the base category), those born in the first quarter had 0.148 fewer years of schooling (t = -9.16), the second quarter had 0.092 fewer (t = -5.62), and the third quarter had 0.036 fewer (t = -2.25). This provides strong support for the instrument's predictive power. Next, I considered the **overidentifying restrictions**. While I only needed three instruments (the three quarter-of-birth dummies), the Sargan test allows me to assess the validity of these instruments under a more general specification. The test yielded a statistic of 3.259 with 2 degrees of freedom, and a p-value of 0.196. Critically, I *do not* reject the null hypothesis that the instruments are valid. This is a good sign that the chosen instruments are not correlated with the error term in the second stage. Moving to the **causal estimate** using Two-Stage Least Squares (2SLS), I found a coefficient on `educ` of 0.01053 (standard error 0.0201) for the log of weekly earnings. When I scale this effect, it suggests that an additional year of education leads to an approximately 11.10% increase in weekly earnings. This estimate falls within the 95% confidence interval of [6.80%, 15.57%]. It's imperative to compare this with the OLS estimate. A simple OLS regression, even with cohort controls, yields a coefficient of 0.0711 (standard error 0.0004) for `educ`, translating to a 7.37% increase in weekly earnings per year of schooling (95% CI: [7.29%, 7.45%]). The difference between the IV estimate (0.1053) and the OLS estimate (0.0711) is 0.0342 log points. The fact that the IV estimate is not only statistically significant but also comparable to, and indeed slightly higher than, the OLS estimate suggests that the observed earnings gain from education is indeed causal. The OLS estimate likely captures some of the ability bias, but the IV result, by isolating exogenous variation, confirms a substantial causal return. However, I must acknowledge some important **caveats**. The IV estimate represents a Local Average Treatment Effect (LATE). It specifically captures the return to education for "compliers" – those individuals whose schooling decisions were directly influenced by the quarter-of-birth mechanism and compulsory attendance laws. These might be individuals who would have left school precisely upon reaching the minimum legal age. Their returns to education could differ from those who would have pursued more schooling regardless of these laws. Furthermore, I must assume that quarter of birth doesn't directly impact earnings through other channels, such as biological effects of birth season on health or early development that then independently influence earnings. I also noted that using a more extensive set of instruments (interactions of quarter of birth with year of birth) can lead to weak instrument problems, reinforcing the choice of the more parsimonious specification with just the three quarter dummies. In summary, my analysis strongly supports a causal interpretation of the earnings premium associated with education, with a robust estimate of around 11% per additional year of schooling for the affected subpopulation.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Sim, os ganhos salariais da escolaridade são causais. Utilizando o trimestre de nascimento como variável instrumental para contornar o viés de habilidade e antecedentes familiares (Angrist & Krueger, 1991), estima-se que cada ano adicional de escolaridade aumenta o log do salário semanal em 0,1053 (erro padrão de 0,0201; IC 95%: [0,0658, 0,1447]), o que corresponde a um aumento salarial de 11,10% por ano de estudo (IC 95%: [6,80%, 15,57%]).\n\nPrincipais elementos da estratégia empírica:\n1. **Identificação e Mecanismo**: As leis de frequência escolar compulsória exigem que os estudantes permaneçam na escola até uma idade mínima (tipicamente 16 anos). Como as crianças nascidas no início do ano ingressam na escola mais velhas, atingem a idade legal de evasão tendo completado menos anos de estudo do que as nascidas no final do ano. A variação no trimestre de nascimento gera, portanto, um quase-experimento exógeno de escolaridade.\n2. **Primeiro Estágio**: No modelo com controles de ano de nascimento (1930 a 1939) e 3 instrumentos de trimestre de nascimento (tendo o 4º trimestre como referência), o instrumento é forte, com estatística F de 32,32 (acima do limiar convencional). Homens nascidos no 1º trimestre completam em média 0,148 ano a menos de estudo (t = -9,16), os do 2º trimestre completam 0,092 ano a menos (t = -5,62) e os do 3º trimestre 0,036 ano a menos (t = -2,25).\n3. **Validade dos Instrumentos**: O teste de sobreidentificação de Sargan apresenta estatística de 3,259 (2 graus de liberdade, p = 0,196), não rejeitando a validade dos instrumentos.\n4. **Comparação com MQO**: A regressão por Mínimos Quadrados Ordinários (MQO) indica um coeficiente de 0,0711 (erro padrão de 0,0004; IC 95%: [0,0703, 0,0718]), equivalente a um ganho de 7,37% (IC 95%: [7,29%, 7,45%]). A estimativa de variáveis instrumentais é 0,0342 pontos de log superior à de MQO, confirmando que a associação positiva observada entre estudo e salários não decorre de viés de seleção ou de habilidade.",
        "caveats": [
          "A estimativa de variáveis instrumentais representa um Efeito Médio Local de Tratamento (LATE) restrito aos 'compliers' — indivíduos cuja escolaridade foi diretamente alterada pela idade mínima de frequência compulsória (geralmente nos anos finais do ensino fundamental ou médio), podendo não se aplicar a transições para o ensino superior.",
          "A restrição de exclusão assume que a estação de nascimento afeta o salário no longo prazo exclusivamente por meio da educação, sem impactos diretos independentes decorrentes de fatores de saúde infantil no nascimento ou idade relativa na turma.",
          "Especificações superidentificadas com muitas interações (ex.: 30 instrumentos interagindo trimestre e ano de nascimento) sofrem do problema de instrumentos fracos apontado por Bound, Jaeger e Baker (1995), com F de primeiro estágio caindo para 4,80; por isso, a especificação mais parcimoniosa com 3 instrumentos de trimestre é a preferida."
        ],
        "figure_refs": [
          "call_a351b6d5:coef.educ",
          "call_0dc26894:effect",
          "call_bc18c14c:coef.educ",
          "call_6b2add4e:effect",
          "call_aee801dc:result"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
53. 52Guarda
    resposta recusada

    Números encontrados

    1991 · 0,1053 · 0,0201 · 95% · 0,0658 · 0,1447 · 11,10% · 95% · 6,80% · 15,57% · 1 · 16 · 2 · 1930 · 1939 · 3 · 32,32 · 0,148 · -9,16 · 0,092 · -5,62 · 0,036 · -2,25 · 3 · 3,259 · 2 · 0,196 · 4 · 0,0711 · 0,0004 · 95% · 0,0703 · 0,0718 · 7,37% · 95% · 7,29% · 7,45% · 0,0342 · 30 · 1995 · 4,80 · 3

    Sem lastro

    0,092 · 30

    Não citados

    —

    0 nova(s) tentativa(s) restante(s)
54. 53Turno do modelo
    call_9ae94316gemini-3.8-flashFim: STOP16.799 ms28618 de entrada · 797 de saída · 1146 de raciocínio · 23171 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Refining the Numerical Presentation** I've been presented with an error report flagging "unbacked_numbers: ['0,092', '30']". This means I need to be exceptionally careful about how I present numerical data to ensure it aligns precisely with what's provided by the tools or the original question, avoiding any ambiguity from rounding or implicit assumptions. First, let's dissect the "0,092" issue. I see it corresponds to a rounded value of `coef: -0.0918159` from the first stage table. The checker's demand for "exact digits or the numbers stated by tools / figures" is crucial here. My takeaway is to avoid quoting rounded numbers from intermediate tables unless they are explicitly requested or presented as such. It's far safer to either quote the exact figure as provided by a specific tool output or to omit it if it’s a rounded representation that could cause confusion. Next, the "30" flag. This number appears to have been derived from phrases like "30 instrumentos interagindo..." and "1930 a 1939". While "1930" is from the question, the standalone "30" as a count of instruments needs scrutiny. The principle remains: any number I present must be strictly verifiable against either the `figures` or `diagnostics` provided by the tools, or directly from the question's context. To implement this, I've meticulously gone through all the tool outputs available to me. For `call_a351b6d5`, I've noted the precise figures: * `coef.educ` = 0.105252 (with its confidence interval [0.065826, 0.144679] and standard error 0.0201158). * Diagnostics: `first_stage_F.educ` = 32.3232881043006, `overid_p` = 0.196002653242029, `sargan` = 3.25925416578823, `sargan_df` = 2, and `n_obs` = 329509. For `call_0dc26894`, the key figure is: * `effect` = 11.0991 (with its confidence interval [6.80409, 15.5668]). For `call_bc18c14c`, I have: * `coef.educ` = 0.071081 (with its confidence interval [0.0703334, 0.0718287] and standard error 0.000381463). For `call_6b2add4e`, the figure is: * `effect` = 7.36682 (with its confidence interval [7.28658, 7.44713]). For `call_aee801dc`, the single result is: * `result` = 0.0341713. And for `call_2f284f63`, I have a diagnostic: * `first_stage_F.educ` = 4.80075023866826. Furthermore, I've re-examined the numbers in the original question: "men born in the United States in 1930-1939, observed in the 1980 Census". This clearly gives me "1930-1939" and "1980" as figures directly from the source. Based on this, I've established a clear rule for myself: I must avoid presenting any numbers that aren't directly extractable from these tool outputs or the question itself. This means I will not write out phrases like "16 anos", "3 instrumentos", "30 instrumentos", "0,092", "0,148", or "0,036" unless they are exact matches to the tool's `figures` or `diagnostics`, or part of the question's specific phrasing. For concepts like minimum legal age or birth quarters, I should use descriptive words rather than approximated numbers. My final verification step involves comparing every single digit in my generated answer against these verified sources to ensure absolute precision. So, the numbers I am cleared to cite are: * For the 2SLS estimate: 0.105252, with a standard error of 0.0201158 and a 95% confidence interval of [0.065826, 0.144679]. * For the 2SLS percentage effect: 11.0991% (with a 95% confidence interval of [6.80409%, 15.5668%]). * For the OLS estimate: 0.071081, with a standard error of 0.000381463 and a 95% confidence interval of [0.0703334, 0.0718287]. * For the OLS percentage effect: 7.36682% (with a 95% confidence interval of [7.28658%, 7.44713%]). * For the difference between the estimates: 0.0341713. * For the first-stage F-statistic: 32.323288 (from `call_a351b6d5`) and 4.80075 (from `call_2f284f63` in the context of caveats). * For the Sargan statistic: 3.259254, with a p-value of 0.196002 and 2 degrees of freedom. * And, as established from the question: the years 1930-1939 and the 1980 Census. I will now proceed to construct my response, adhering strictly to these verified numerical values.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Sim, os retornos salariais da educação são causais. Utilizando o trimestre de nascimento como instrumento para lidar com a endogeneidade da escolaridade decorrente de habilidades e histórico familiar (estratégia de Angrist & Krueger), estima-se que cada ano adicional de estudo aumenta o log do salário semanal em 0,105252 (erro padrão de 0,0201158; IC 95%: [0,065826; 0,144679]), o que equivale a um ganho salarial de 11,0991% por ano de estudo (IC 95%: [6,80409%; 15,5668%]).\n\nAspectos centrais da identificação:\n1. **Mecanismo e primeiro estágio**: As leis de frequência escolar compulsória exigem frequência escolar até uma idade mínima. Indivíduos nascidos no início do ano entram na escola com idade cronológica mais avançada e atingem a idade legal para abandonar os estudos tendo cursado menos anos de escolaridade formal. No modelo controlando por efeitos de ano de nascimento (coortes de 1930-1939 do Censo de 1980), o primeiro estágio apresenta estatística F de 32,323288, superando o limiar de instrumentos fracos.\n2. **Sobreidentificação**: O teste de Sargan para a validade dos instrumentos resulta em estatística de 3,259254 (2 graus de liberdade; valor-p de 0,196002), não rejeitando a hipótese nula de restrições de exclusão válidas.\n3. **Comparação com MQO**: A regressão de MQO com os mesmos controles de ano de nascimento reporta um coeficiente de 0,071081 (erro padrão de 0,000381463; IC 95%: [0,0703334; 0,0718287]), ou 7,36682% (IC 95%: [7,28658%; 7,44713%]). A estimativa por variáveis instrumentais excede o MQO em 0,0341713 pontos de log, evidenciando que o efeito da escolaridade sobre a renda não decorre meramente de viés de habilidade ou antecedentes socioeconômicos.",
        "caveats": [
          "A estimativa por variáveis instrumentais identifica o Efeito Médio Local de Tratamento (LATE) entre os 'compliers' — indivíduos induzidos a permanecer mais tempo na escola pelas leis de escolaridade compulsória —, cujos retornos podem diferir dos retornos ao ensino universitário.",
          "A validade da exclusão exige que o trimestre de nascimento afete os salários exclusivamente por meio dos anos de escolaridade acumulados, sem efeitos diretos sobre a produtividade no mercado de trabalho.",
          "Modelos com instrumentos adicionais formados por interações completas de trimestre e ano de nascimento apresentam estatística F de primeiro estágio de 4,80075, incorrendo em problemas de instrumentos fracos."
        ],
        "figure_refs": [
          "call_a351b6d5:coef.educ",
          "call_0dc26894:effect",
          "call_bc18c14c:coef.educ",
          "call_6b2add4e:effect",
          "call_aee801dc:result"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
55. 54Guarda
    resposta aceita

    Números encontrados

    0,105252 · 0,0201158 · 95% · 0,065826 · 0,144679 · 11,0991% · 95% · 6,80409% · 15,5668% · 1 · 1930 · 1939 · 1980 · 32,323288 · 2 · 3,259254 · 2 · 0,196002 · 3 · 0,071081 · 0,000381463 · 95% · 0,0703334 · 0,0718287 · 7,36682% · 95% · 7,28658% · 7,44713% · 0,0341713 · 4,80075

    Sem lastro

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    Não citados

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    0 nova(s) tentativa(s) restante(s)
56. 55Resposta

    Sim, os retornos salariais da educação são causais. Utilizando o trimestre de nascimento como instrumento para lidar com a endogeneidade da escolaridade decorrente de habilidades e histórico familiar (estratégia de Angrist & Krueger), estima-se que cada ano adicional de estudo aumenta o log do salário semanal em 0,105252 (erro padrão de 0,0201158; IC 95%: [0,065826; 0,144679]), o que equivale a um ganho salarial de 11,0991% por ano de estudo (IC 95%: [6,80409%; 15,5668%]). Aspectos centrais da identificação: 1. **Mecanismo e primeiro estágio**: As leis de frequência escolar compulsória exigem frequência escolar até uma idade mínima. Indivíduos nascidos no início do ano entram na escola com idade cronológica mais avançada e atingem a idade legal para abandonar os estudos tendo cursado menos anos de escolaridade formal. No modelo controlando por efeitos de ano de nascimento (coortes de 1930-1939 do Censo de 1980), o primeiro estágio apresenta estatística F de 32,323288, superando o limiar de instrumentos fracos. 2. **Sobreidentificação**: O teste de Sargan para a validade dos instrumentos resulta em estatística de 3,259254 (2 graus de liberdade; valor-p de 0,196002), não rejeitando a hipótese nula de restrições de exclusão válidas. 3. **Comparação com MQO**: A regressão de MQO com os mesmos controles de ano de nascimento reporta um coeficiente de 0,071081 (erro padrão de 0,000381463; IC 95%: [0,0703334; 0,0718287]), ou 7,36682% (IC 95%: [7,28658%; 7,44713%]). A estimativa por variáveis instrumentais excede o MQO em 0,0341713 pontos de log, evidenciando que o efeito da escolaridade sobre a renda não decorre meramente de viés de habilidade ou antecedentes socioeconômicos. Ressalvas: A estimativa por variáveis instrumentais identifica o Efeito Médio Local de Tratamento (LATE) entre os 'compliers' — indivíduos induzidos a permanecer mais tempo na escola pelas leis de escolaridade compulsória —, cujos retornos podem diferir dos retornos ao ensino universitário. A validade da exclusão exige que o trimestre de nascimento afete os salários exclusivamente por meio dos anos de escolaridade acumulados, sem efeitos diretos sobre a produtividade no mercado de trabalho. Modelos com instrumentos adicionais formados por interações completas de trimestre e ano de nascimento apresentam estatística F de primeiro estágio de 4,80075, incorrendo em problemas de instrumentos fracos.

    • A estimativa por variáveis instrumentais identifica o Efeito Médio Local de Tratamento (LATE) entre os 'compliers' — indivíduos induzidos a permanecer mais tempo na escola pelas leis de escolaridade compulsória —, cujos retornos podem diferir dos retornos ao ensino universitário.
    • A validade da exclusão exige que o trimestre de nascimento afete os salários exclusivamente por meio dos anos de escolaridade acumulados, sem efeitos diretos sobre a produtividade no mercado de trabalho.
    • Modelos com instrumentos adicionais formados por interações completas de trimestre e ano de nascimento apresentam estatística F de primeiro estágio de 4,80075, incorrendo em problemas de instrumentos fracos.

    Figuras citadas: call_a351b6d5:coef.educ, call_0dc26894:effect, call_bc18c14c:coef.educ, call_6b2add4e:effect, call_aee801dc:result · Parada: answered

    Figura da resposta: call_a351b6d5:coef.educ = 0,1052520.10525237815751685 (se 0,02011580.02011579728531004)
57. 56Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
58. 57Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_a351b6d5:coef.educ (infer.iv_2sls)
59. 58Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
60. 59Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwklywge'
61. 60Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog[0] = 'educ'
62. 61Pontuação
    #5argumento igualpassouregistradainfer.iv_2sls.y = 'lwklywge'
63. 62Pontuação
    #6argumento igualpassouregistradainfer.iv_2sls.endog = ['educ']
64. 63Pontuação
    #7argumento igualfalhouregistradainfer.iv_2sls.instruments = ['qtr_1', 'qtr_2', 'qtr_3']
65. 64Pontuação
    #8diagnósticopassouregistrada329509 vs 329509
66. 65Pontuação
    #9figura da resposta próximafalhouregistrada0.1052523782 vs 0.08911545635601215
67. 66Pontuação
    #10figura da resposta próximafalhouregistrada0.02011579729 vs 0.016110089092885405
68. 67Pontuação
    #11figura da resposta próximafalhouregistrada0.1052523782 vs 0.0891
69. 68Pontuação
    #12figura da resposta próximafalhouregistrada0.02011579729 vs 0.0161

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