Tarefa paper_repro.mroz_1987.ex15_1.agent

Veredito

Pergunta feita ao analista

Wooldridge, Introductory Econometrics (7th edition), Example 15.1, equation (15.17), using Mroz's (1987) data on married women: among the women who worked in 1975 (those with an observed wage), estimate by instrumental variables the return to education in a simple regression of the log hourly wage on years of schooling and an intercept, using the father's years of schooling as the instrument. Report the coefficient on years of schooling.

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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

   Wooldridge, Introductory Econometrics (7th edition), Example 15.1, equation (15.17), using Mroz's (1987) data on married women: among the women who worked in 1975 (those with an observed wage), estimate by instrumental variables the return to education in a simple regression of the log hourly wage on years of schooling and an intercept, using the father's years of schooling as the instrument. Report the coefficient on years of schooling.

   mroz (agent)

   Wooldridge's MROZ data set (the R package wooldridge, served by Rdatasets): Mroz's (1987) sample of married women from the Panel Study of Income Dynamics, for 1975; one row per woman (753 rows). Columns used here: inlf, 1 if the woman was in the labour force in 1975; lwage, log hourly wage (missing for women who did not work); wage, hourly wage; educ, years of schooling; exper, years of labour-market experience; expersq, exper squared; fatheduc, father's years of schooling; motheduc, mother's years of schooling; also hours, kidslt6, kidsge6, age, repwage, hushrs, husage, huseduc, huswage, faminc, mtr, unem, city, nwifeinc and rownames.

   file bcfc04b6a87746b185ed972f1149c459cc1af5a6ff44443ce5dd004eb8204a78 · frame —
2. 1Turno do modelo
   call_db560663gemini-3.8-flashFim: STOP9.014 ms14534 de entrada · 34 de saída · 548 de raciocínio · 0 em cache

   Texto visível

   I will load the instrumental variables skill to review best practices and diagnostic checks.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Replicating Wooldridge's Example 15.1** My primary objective here is to meticulously replicate Example 15.1 from Wooldridge's *Introductory Econometrics*, specifically focusing on equation (15.17). This means I need to estimate the return to education using instrumental variables (IV) for a particular subset of women from the `mroz` dataset. The core task is to: 1. **Model Specification:** Regress the log of the hourly wage (`lwage`) on years of schooling (`educ`) and an intercept. 2. **Endogenous Variable:** `educ` (years of schooling) is the variable I suspect is endogenous and requires an instrument. 3. **Instrument:** The problem explicitly states to use `fatheduc` (father's years of schooling) as the instrumental variable for `educ`. 4. **Sample Selection:** The estimation must be performed *only* on women who worked in 1975. This translates to filtering the data to include only those women for whom `lwage` is observed, or equivalently, where `inlf` (in labour force indicator) is equal to 1. 5. **Output:** I need to report the estimated coefficient on `educ`. To achieve this, I'll be leveraging the `instrumental-variables` skill, specifically the `iv_2sls` function. My current understanding of the `iv_2sls` function's parameters is as follows: * `dataset`: This will be set to `"mroz"`. * `y`: The dependent variable, which is `"lwage"`. * `endog`: The endogenous regressor, which is `"educ"`. * `instruments`: The instrumental variable(s), which is `"fatheduc"`. * `exog`: This parameter is for additional exogenous controls. The problem statement specifies a *simple* regression of log wage on education and an intercept. So, this parameter should ideally be empty or omitted, implying that the function will automatically include an intercept by default. I need to confirm this behavior. If it doesn't automatically include an intercept, I'll have to explicitly pass it or check the documentation for the correct way to handle it. * `subset`: This is crucial for selecting the correct sample. I need to ensure I'm only using women who worked in 1975. The condition `inlf == 1` is the most direct way to define this subset. Alternatively, I could rely on `lwage` having missing values for non-working women and see if `iv_2sls` handles missing values by dropping observations for the dependent variable, but specifying the subset explicitly using `inlf == 1` is safer and more transparent. Before proceeding, I'll also ensure that the `instrumental-variables` skill is properly loaded to guarantee I'm using the most appropriate and well-defined tools. I'll pay close attention to how the function handles missing values and the inclusion of an intercept to ensure my replication is exact.

   Chamadas pedidas

   • load_skill (meta-ferramenta)

     {
       "name": "instrumental-variables"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
3. 2Habilidade
   instrumental-variablesTexto da habilidade
4. 3Turno do modelo
   call_5ae11788gemini-3.8-flashFim: STOP6.739 ms15584 de entrada · 82 de saída · 177 de raciocínio · 12710 em cache

   Texto visível

   I will estimate the IV regression using two-stage least squares with classical standard errors to match the standard textbook specification.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process Regarding Standard Errors in `infer__iv_2sls`** My primary objective here is to ascertain the specific type of standard errors reported by the `infer__iv_2sls` function within the `infer` library. Specifically, I need to understand whether it defaults to classical (homoskedastic) standard errors or robust (heteroskedasticity-consistent) standard errors, and how this aligns with the presentation in Wooldridge's textbook, particularly in the context of equation (15.17). I recall that the `se` argument in `infer__iv_2sls` is an enum that includes 'classical' and 'HC1' (which is the default). This immediately raises a question: does Wooldridge's textbook, in its demonstration of equation (15.17), present the results using classical standard errors or robust ones? To investigate this, I've pulled up Example 15.1 from Wooldridge's 7th edition. The presented regression results are: log(wage) = -0.185 + 0.059 educ (0.185) (0.035) n = 428. The numbers in parentheses are the standard errors. My next step is to empirically verify what `infer__iv_2sls` is actually outputting. I plan to run the `infer__iv_2sls` function with `se='classical'` explicitly to see the corresponding output. Concurrently, I'll also run it with the default setting (which is 'HC1') to compare. Alternatively, I could run both options and then cross-reference the results against the textbook's reported standard errors to definitively determine which type of standard error is being reported in the example, and by extension, what the default behavior of `infer__iv_2sls` is mimicking. Before I proceed with the actual code execution, I need to be clear about the precise arguments `infer__iv_2sls` expects and what it returns, so I can accurately interpret the output.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "mroz",
       "endog": [
         "educ"
       ],
       "instruments": [
         "fatheduc"
       ],
       "se": "classical",
       "subset": "inlf == 1",
       "y": "lwage"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
5. 4Ferramenta
   infer.iv_2slsv0.1.0call_f56f98fddecidido pelo modeloreexecutável

   Motivo: I will estimate the IV regression using two-stage least squares with classical standard errors to match the standard textbook specification.

   Argumentos

   {
     "cluster": null,
     "dataset": "mroz",
     "endog": [
       "educ"
     ],
     "exog": [],
     "instruments": [
       "fatheduc"
     ],
     "level": 0.95,
     "se": "classical",
     "subset": "inlf == 1",
     "y": "lwage"
   }

   Figuras call_f56f98fd

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.educ 2SLS effect of educ on lwage	0,0591735	0.05917347999936612	0,03514180.035141773970085714	-0,00989937 – 0,128246

   Diagnósticos

   • first_stage_F.educ = 88,840888.84076437074765
   • partial_r2.educ = 0,172560.17255969324676745
   • weak_instrument = false
   • n_obs = 428428
   • se_type = "classical"
   • n_clusters = —

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 1.3179379680966103,
         "ci_low": -0.4357311520259835,
         "coef": 0.4411034080353134,
         "p": 0.3233244980335768,
         "se": 0.44610176604739354,
         "t": 0.9887954758476587,
         "term": "Intercept"
       },
       {
         "ci_high": 0.12824633346921774,
         "ci_low": -0.0098993734704855,
         "coef": 0.05917347999936612,
         "p": 0.09294318274439199,
         "se": 0.035141773970085714,
         "t": 1.6838501109744002,
         "term": "educ"
       }
     ],
     "first_stage": [
       {
         "ci_high": 0.32562947283589605,
         "ci_low": 0.21325380614425338,
         "coef": 0.2694416394900747,
         "endog": "educ",
         "instrument": "fatheduc",
         "p": 2.764935579128143e-19,
         "se": 0.028586340944630733,
         "t": 9.425537882303994
       }
     ],
     "reduced_form": [
       {
         "ci_high": 0.03543143951439208,
         "ci_low": -0.003543840583667461,
         "coef": 0.01594379946536231,
         "instrument": "fatheduc",
         "p": 0.10855148999538793,
         "se": 0.009914607655702304,
         "t": 1.6081119918237377
       }
     ]
   }

   Digests dos dados

   mroz 909e3d99ac8070dc661ce7915c99f27631797719369832e227d4005096cbd479

   sha256 do resultado

   5f59c9752d406dd5ff382ad7e788a94c05736ef03adf15effb6a7e0e8bd7bfca

   Resultado mostrado ao modelo
6. 5Turno do modelo
   call_8fccab4fgemini-3.8-flashFim: STOP9.552 ms16316 de entrada · 63 de saída · 589 de raciocínio · 12713 em cache

   Texto visível

   I will use core.scale_effect to obtain the percentage effect implied by the log-wage coefficient.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Addressing the Wooldridge 15.17 Request** Alright, let's break down how I arrived at the answer for this Wooldridge 15.17 problem. I'm essentially retracing my internal steps to provide you with a clear and comprehensive understanding. First off, I see a coefficient of "0.441103" associated with an "Intercept." My immediate thought is, "Which equation are we looking at here? Is this 15.15 or 15.17?" This is a critical disambiguation step because the models differ, especially in their interpretation and the estimation method. So, my next action is to consult the source – Wooldridge. I need to be precise. I'm looking for the specific equations mentioned. I scan through, comparing what I have against what's presented in the text. Ah, there it is. Equation 15.15 represents the basic OLS model: `log(wage) = beta0 + beta1 * educ + u`. I see the OLS estimate for that: `log(wage) = -0.185 + 0.109 educ` with `n = 428`. This is good context, but it's not the instrumental variables (IV) result we need. Then, I look at the first stage of the IV estimation. This is crucial for understanding the instrument's relationship with the endogenous regressor. The text shows something like: `educ = 10.24 + 0.269 fatheduc`. This confirms that `fatheduc` is being used as an instrument for `educ`. Now, for the main event: the 2SLS estimation, which is presented in equation 15.17. I find it: `log(wage) = 0.441 + 0.059 educ`. I also note the standard errors and sample size: `(0.446) (0.035)` for the standard errors (though the text notes them as part of the equation line itself, I recognize them as SEs for the coefficients below) and `n = 428, R2 = 0.093`. A moment of confirmation: "Yes! Equation (15.17) in Wooldridge 7th edition is exactly: `log(wage) = 0.441 + 0.059 educ` (with standard error 0.035)!" I'm double-checking the coefficient and standard error values to ensure they align precisely with what's stated in the problem and the textbook. I verify my internal values: `coef: 0.0591735, se: 0.0351418`. They match. Next, I revisit the exact question asked: "Wooldridge, Introductory Econometrics (7th edition), Example 15.1, equation (15.17), using Mroz's (1987) data on married women: among the women who worked in 1975 (those with an observed wage), estimate by instrumental variables the return to education in a simple regression of the log hourly wage on years of schooling and an intercept, using the father's years of schooling as the instrument. Report the coefficient on years of schooling." The question is very specific: report the coefficient on `years of schooling` from this IV estimation. Then, a crucial detail regarding standard errors pops into my mind: "Let's check if we also want to report HC1 or if classical is the exact match for equation (15.17)." My knowledge base tells me that standard textbook examples like Wooldridge's often present results using classical (homoskedasticity-consistent) standard errors unless otherwise specified. I confirm that "Classical matches Wooldridge Example 15.1 equation (15.17) exactly (coef 0.059, SE 0.035)." This confirms the default approach for this specific problem. Finally, I consider a potential transformation of the coefficient. I recall a rule: "Wait, does the prompt or skill say: 'If the outcome is in logs, restate the coefficient as a percent with `core.scale_effect`, never by hand.'" Since the outcome variable (`log(wage)`) is in logs, this rule applies. It's a best practice to report the effect in a more interpretable percentage change format. Therefore, my next step is to check if I should indeed apply `core.scale_effect` to `call_f56f98fd:coef.educ`. To be safe and prepared, I decide to "Wait, let's call `core.scale_effect` just in case, so we have it available if needed." This ensures I have the tool ready for potential follow-up analysis or reporting requirements.

   Chamadas pedidas

   • core.scale_effect

     {
       "coefficient": "call_f56f98fd:coef.educ",
       "transform": "log_points_to_percent"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
7. 6Ferramenta
   core.scale_effectv0.1.0call_ed40e616decidido pelo modeloreexecutável

   Motivo: I will use core.scale_effect to obtain the percentage effect implied by the log-wage coefficient.

   Argumentos

   {
     "baseline": null,
     "coefficient": "call_f56f98fd:coef.educ",
     "sd": null,
     "transform": "log_points_to_percent"
   }

   Figuras call_ed40e616

   Chave	Valor	Valor bruto	Erro-padrão	IC
   effect Effect as a percent change (from log points): 2SLS effect of educ on lwage	6,09593 %	6.095927999135324	—	-0,985054 – 13,6833

   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

   36e9a8d80158c9c34d8b37676109867a7c1ee9b58dee32ed28db5a524ae46412

   Resultado mostrado ao modelo
8. 7Turno do modelo
   call_cad09fa7gemini-3.8-flashFim: STOP18.151 ms17087 de entrada · 404 de saída · 1492 de raciocínio · 12801 em cache

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Estimating the Return to Education** I've been tasked with a specific instrumental variables (IV) estimation, referencing Wooldridge's *Introductory Econometrics* (7th edition), Example 15.1, equation (15.17), using Mroz's (1987) data. The core objective is to estimate the return to education for married women who worked in 1975, using their father's years of schooling as an instrument for their own years of schooling. First, I need to gather all the relevant details from the provided tool outputs. * **IV Call ID:** `call_f56f98fd` * **Key Figure:** `coef.educ` (this is what I need to report) * **Value:** 0.0591735 (this is the estimated coefficient for years of schooling) * **Standard Error (SE):** 0.0351418 * **Confidence Interval (CI):** [-0.00989937, 0.128246] * **Intercept:** 0.441103 (SE: 0.446102) – while not directly asked for, it's good context. * **First-Stage F-statistic:** 88.8407643707476 – This is crucial for assessing instrument strength. The prompt's guidance states that an F-statistic above 10 indicates a strong instrument, so this is well above that threshold. * **First-stage coefficient of `fatheduc`:** 0.269442 (SE: 0.0285863) – This tells me the direct relationship between the instrument and the endogenous variable, and it makes intuitive sense: more father's education is associated with more years of schooling for the woman. * **Sample Size:** 428 women. This is important for understanding the scope of the findings. * **Core Scale Effect:** * **Figure:** `call_ed40e616:effect` * **Value:** 6.09593% – The prompt specifically mentions to use `core.scale_effect` for outcomes in logs and restate the coefficient as a percentage, which I will do. * **CI:** [-0.985054%, 13.6833%] Now, I need to carefully consider the rules for interpreting and reporting IV results, particularly those highlighted in the "Let's read the skill `instrumental-variables`" section. * **Diagnostics:** * **First-stage F-statistic:** I've confirmed it's 88.84, which is robustly above the weak instrument threshold of 10. This means the estimate is reliable from an instrument relevance standpoint. * **Sign of the first stage:** The coefficient for `fatheduc` in the first stage is positive (0.269442), which is consistent with the expectation that a father's higher education level is positively correlated with his daughter's schooling. * **Overidentification (overid_p):** This isn't applicable here as there's only one instrument (`fatheduc`) for one endogenous regressor (years of schooling), so I don't have extra instruments to test for overidentification. * **Compliance difference (infer.wald_late):** This isn't directly relevant to the reported output, but it's noted that a near-zero compliance difference would imply a weak instrument, which is not the case here. * **Reporting:** * **Whose effect:** The prompt specifies an IV estimation using Mroz's data, focusing on women who worked in 1975 (observed wage). The IV estimate identifies the Local Average Treatment Effect (LATE) – the effect of an extra year of education for the "compliers" – those whose education decisions were influenced by their fathers' education. I need to make this clear. * **Log outcome:** The outcome variable is the log hourly wage. The prompt mandates using `core.scale_effect` to report the coefficient as a percentage, rather than calculating it manually. I also need to consider the potential caveats mentioned: * **Exclusion Restriction:** The main concern is that father's education might directly influence a woman's earnings beyond its effect on her schooling. This could happen through mechanisms like family connections, inherited wealth, or shared unobserved abilities. If this is true, the exclusion restriction is violated, and the IV estimate would be biased. * **Sample Selection:** The analysis is restricted to women who worked in 1975 (had an observed wage). This inherently introduces potential sample selection bias related to labor force participation. Finally, I must adhere to the specific formatting and content requirements for the final answer, particularly Rule 7. * **Language:** The question is in English, so my answer should be in English. The mention of "(Portuguese: decimal comma)" seems to be a general instruction that applies only if the question itself is in Portuguese. * **Content:** I need to provide the estimate with its uncertainty, the design that identifies it (IV, LATE for compliers), and what could undermine it (exclusion restriction violation, sample selection). * **Figure References:** I must list all quoted figures as `<call_id>:<key>`. * **Diagnostics/Caveats:** Limitations must be placed in `caveats`. * **Numbers:** Numbers should be presented exactly as stated by the tools, not rounded or using rule-of-thumb thresholds as numbers. Let's pull together the specific numbers and references for the final output. * **Coefficient on years of schooling:** `call_f56f98fd:coef.educ` = 0.0591735 * **SE of coefficient:** 0.0351418 * **95% CI:** [-0.00989937, 0.128246] * **Percentage effect:** `call_ed40e616:effect` = 6.09593% * **95% CI for percentage effect:** [-0.985054%, 13.6833%] * **First-stage F-statistic:** 88.8407643707476 I'll frame the answer to clearly state the IV estimate of the return to education, the fact that it represents the LATE for compliers among women with observed wages in 1975, and the potential issues with the exclusion restriction and sample selection. The strong first-stage F-statistic is a positive diagnostic, so I'll mention that it supports instrument relevance. The final output should be concise and direct, as per Rule 7. I will use the exact numbers from the tool outputs. The decimal point usage should follow standard English conventions since the question is in English. This detailed breakdown ensures I've considered all aspects of the prompt, the provided data, and the specific output requirements. I'm now ready to construct the final `submit_answer`.

   Chamadas pedidas

   • submit_answer (meta-ferramenta)

     {
       "answer": "In Wooldridge (7th edition), Example 15.1, equation (15.17), estimating the return to education for the sample of 428 married women who worked in 1975 via two-stage least squares (2SLS) using father's education (fatheduc) as the instrument yields:\n\n- Coefficient on years of schooling (educ): 0.0591735 (SE: 0.0351418; 95% CI: [-0.00989937, 0.128246])\n- Intercept: 0.441103 (SE: 0.446102)\n- Implied percentage return per year of schooling: 6.09593% (95% CI: [-0.985054, 13.6833]%)\n\nThe first-stage regression indicates a strong instrument with an F-statistic of 88.8407643707476 (coefficient on fatheduc: 0.269442, SE: 0.0285863).",
       "caveats": [
         "Instrument validity requires the exclusion restriction: father's education must affect a woman's wage only through her own educational attainment, which fails if parental education correlates with unobserved ability or provides direct labour-market advantages.",
         "The estimation is restricted to the 428 women with observed wages in 1975, not accounting for potential sample selection into labour force participation."
       ],
       "figure_refs": [
         "call_f56f98fd:coef.educ",
         "call_ed40e616:effect"
       ]
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
9. 8Guarda
   resposta aceita

   Números encontrados

   15.1 · 15.17 · 428 · 1975 · 0.0591735 · 0.0351418 · 95% · -0.00989937 · 0.128246 · 0.441103 · 0.446102 · 6.09593% · 95% · -0.985054 · 13.6833 · 88.8407643707476 · 0.269442 · 0.0285863 · 428 · 1975

   Sem lastro

   —

   Não citados

   —

   1 nova(s) tentativa(s) restante(s)
10. 9Resposta

    In Wooldridge (7th edition), Example 15.1, equation (15.17), estimating the return to education for the sample of 428 married women who worked in 1975 via two-stage least squares (2SLS) using father's education (fatheduc) as the instrument yields: - Coefficient on years of schooling (educ): 0.0591735 (SE: 0.0351418; 95% CI: [-0.00989937, 0.128246]) - Intercept: 0.441103 (SE: 0.446102) - Implied percentage return per year of schooling: 6.09593% (95% CI: [-0.985054, 13.6833]%) The first-stage regression indicates a strong instrument with an F-statistic of 88.8407643707476 (coefficient on fatheduc: 0.269442, SE: 0.0285863). Ressalvas: Instrument validity requires the exclusion restriction: father's education must affect a woman's wage only through her own educational attainment, which fails if parental education correlates with unobserved ability or provides direct labour-market advantages. The estimation is restricted to the 428 women with observed wages in 1975, not accounting for potential sample selection into labour force participation.

    • Instrument validity requires the exclusion restriction: father's education must affect a woman's wage only through her own educational attainment, which fails if parental education correlates with unobserved ability or provides direct labour-market advantages.
    • The estimation is restricted to the 428 women with observed wages in 1975, not accounting for potential sample selection into labour force participation.

    Figuras citadas: call_f56f98fd:coef.educ, call_ed40e616:effect · Parada: answered

    Figura da resposta: call_f56f98fd:coef.educ = 0,05917350.05917347999936612 (se 0,03514180.035141773970085714)
11. 10Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
12. 11Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_f56f98fd:coef.educ (infer.iv_2sls)
13. 12Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
14. 13Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwage'
15. 14Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['educ']
16. 15Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['fatheduc']
17. 16Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = []
18. 17Pontuação
    #7diagnósticopassouobrigatória428 vs 428
19. 18Pontuação
    #8figura da resposta próximapassouobrigatória0.05917348 vs 0.05917347999936595
20. 19Pontuação
    #9figura da resposta próximapassouregistrada0.03514177397 vs 0.03514177397008675
21. 20Pontuação
    #10figura da resposta próximapassouregistrada0.05917348 vs 0.059
22. 21Pontuação
    #11figura da resposta próximapassouregistrada0.03514177397 vs 0.035

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• época 1, tentativa 1passoupontuada(exibindo)

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