Tarefa paper_repro.mroz_1987.ex15_5.agent

Veredito

Pergunta feita ao analista

Wooldridge, Introductory Econometrics (7th edition), Example 15.5, using Mroz's (1987) data on married women: among the women who worked in 1975 (those with an observed wage), estimate by two-stage least squares the log hourly wage on years of schooling, years of experience and experience squared, using both the mother's and the father's years of schooling as instruments for schooling. Report the coefficient on years of schooling.

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Verificações

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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 15.5, using Mroz's (1987) data on married women: among the women who worked in 1975 (those with an observed wage), estimate by two-stage least squares the log hourly wage on years of schooling, years of experience and experience squared, using both the mother's and the father's years of schooling as instruments for schooling. 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_4a3a1de0gemini-3.8-flashFim: STOP6.322 ms14531 de entrada · 19 de saída · 176 de raciocínio · 12527 em cache

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Replicating Wooldridge's Example 15.5** Alright, so the task at hand is to reproduce a specific example, 15.5, from Wooldridge's "Introductory Econometrics." This involves delving into Mroz's (1987) dataset, which focuses on married women and their labor force participation and wages in 1975. My primary objective is to estimate the impact of education on wages using Two-Stage Least Squares (2SLS). First, I need to isolate the relevant subset of the data. The example specifies that I should only consider women who were actually working in 1975. This translates to filtering for observations where `inlf` is equal to 1, or equivalently, where `lwage` is not missing, and importantly, where their wage is strictly positive. The prompt also suggests a specific subsetting condition `'inlf == 1'`, which I'll adhere to. The core of the estimation will be a 2SLS regression. The dependent variable is the log of the hourly wage, `lwage`. The key endogenous regressor I'm interested in is `educ`, representing years of schooling. The rationale behind treating `educ` as endogenous likely stems from the idea that unobserved factors influencing a woman's decision to pursue more education might also influence her earning potential, creating an endogeneity problem if we were to simply use OLS. To address this endogeneity, I need instrumental variables. The example points to `motheduc` (mother's education) and `fatheduc` (father's education) as the instruments for `educ`. These are chosen because they are presumed to influence a woman's educational attainment but are unlikely to directly affect her current wage, except through their effect on her schooling. In addition to the endogenous regressor, I'll also include some exogenous control variables. The prompt specifies `exper` (years of potential experience) and `expersq` (its squared term) as these controls. These are assumed to be exogenous, meaning they are not correlated with the error term in the wage equation. Including them helps to isolate the effect of education by accounting for other determinants of wages. Before I jump into the estimation, I should, as a good econometrician, perform some initial checks. This includes examining the "skill" for instrumental variables, which I interpret as verifying the relevance and exogeneity of my chosen instruments (`motheduc`, `fatheduc`). This would typically involve checking the correlation of the instruments with the endogenous regressor (`educ`) and ensuring they have no direct effect on the outcome (`lwage`) outside of their influence on `educ`. I should also review the data description to ensure I understand the variables and their potential limitations. This methodical approach ensures the robustness of the subsequent 2SLS estimation.

   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_c76a2561gemini-3.8-flashFim: STOP6.250 ms15194 de entrada · 111 de saída · 288 de raciocínio · 12637 em cache

   Texto visível

   I will run a two-stage least squares regression using parents' education as instruments for education, controlling for experience and its square, for women in the labor force.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Applying `infer__iv_2sls` to the MROZ dataset** My initial impulse is to dive into the practical application of the `infer__iv_2sls` function. I'm specifically interested in how it handles the MROZ dataset, with `lwage` as the dependent variable, `educ` as the endogenous regressor, and `exper` and `expersq` as exogenous controls. The key aspect I want to examine are the instruments: `motheduc` and `fatheduc`. A crucial detail I need to confirm is the implication of the `subset='inlf == 1'` argument. I know this restriction isolates the subsample of individuals who are in the labor force, and I need to be mindful of its size – approximately 428 observations. This leads me to a broader question: is this specific subsetting common practice for this type of analysis, or is it more standard to proceed with the entire dataset and rely on robust standard error options? This line of questioning naturally leads me to consider the default standard error calculation in `infer__iv_2sls`. I'm asking myself if it defaults to `HC1` or uses 'classical' standard errors. My recollection of Wooldridge's textbook, specifically Example 15.5, suggests that classical standard errors are often reported in his tables. Therefore, I need to verify what `infer__iv_2sls`'s default behavior is in this regard. To gain clarity, I intend to run the `infer__iv_2sls` command with both `se='classical'` and let it use its default setting to see if there's a difference. I also want to explicitly confirm whether Wooldridge himself reports homoskedastic standard errors for the particular regression I'm considering, which is the log-wage equation with `educ`, `exper`, and `expersq` as predictors, and `motheduc` and `fatheduc` as instruments. In essence, I'm meticulously working through the practical steps of estimation, ensuring I understand the data subsetting, the choice of instruments, and critically, the implications of the standard error estimation methodology in relation to established econometric practice as presented in Wooldridge's seminal work.

   Chamadas pedidas

   • infer.iv_2sls

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

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

   Motivo: I will run a two-stage least squares regression using parents' education as instruments for education, controlling for experience and its square, for women in the labor force.

   Argumentos

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

   Figuras call_adcbcafa

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.educ 2SLS effect of educ on lwage	0,0613966	0.06139662866015408	0,03143670.031436695644695214	-0,000394545 – 0,123188

   Diagnósticos

   • first_stage_F.educ = 55,400355.40030042777673
   • partial_r2.educ = 0,2075690.20756926964482014
   • weak_instrument = false
   • overid_p = 0,5386370.5386372330714904
   • sargan = 0,3780710.3780713419638187
   • sargan_df = 11
   • n_obs = 428428
   • se_type = "classical"
   • n_clusters = —

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 0.8349750469784886,
         "ci_low": -0.7387744331141283,
         "coef": 0.048100306932180106,
         "p": 0.9044194793612478,
         "se": 0.4003280776041123,
         "t": 0.12015221919994053,
         "term": "Intercept"
       },
       {
         "ci_high": 0.07057292697452149,
         "ci_low": 0.017767858923003838,
         "coef": 0.04417039294876266,
         "p": 0.0010918384252699615,
         "se": 0.013432475529443424,
         "t": 3.2883285625157486,
         "term": "exper"
       },
       {
         "ci_high": -0.00010942651309300572,
         "ci_low": -0.001688512663218038,
         "coef": -0.0008989695881555219,
         "p": 0.025740027334257214,
         "se": 0.0004016856118761863,
         "t": -2.2379930014337086,
         "term": "expersq"
       },
       {
         "ci_high": 0.12318780219307032,
         "ci_low": -0.00039454487276216477,
         "coef": 0.06139662866015408,
         "p": 0.05147417391505394,
         "se": 0.031436695644695214,
         "t": 1.9530242412902723,
         "term": "educ"
       }
     ],
     "first_stage": [
       {
         "ci_high": 0.22815007550124894,
         "ci_low": 0.08704398999594125,
         "coef": 0.1575970327485951,
         "endog": "educ",
         "instrument": "motheduc",
         "p": 0.000014298403672048712,
         "se": 0.03589411554668934,
         "t": 4.390609166664114
       },
       {
         "ci_high": 0.25589971614954615,
         "ci_low": 0.12319710416036223,
         "coef": 0.1895484101549542,
         "endog": "educ",
         "instrument": "fatheduc",
         "p": 3.561512366875694e-8,
         "se": 0.03375646678192402,
         "t": 5.615173275671551
       }
     ],
     "reduced_form": [
       {
         "ci_high": 0.02756810644924526,
         "ci_low": -0.021429317804883524,
         "coef": 0.0030693943221808697,
         "instrument": "motheduc",
         "p": 0.8055968958254257,
         "se": 0.012463808356456057,
         "t": 0.24626456331791813
       },
       {
         "ci_high": 0.04045959911766131,
         "ci_low": -0.0056198180526244,
         "coef": 0.017419890532518457,
         "instrument": "fatheduc",
         "p": 0.1379859225819088,
         "se": 0.01172153503026715,
         "t": 1.48614413449579
       }
     ]
   }

   Digests dos dados

   mroz 909e3d99ac8070dc661ce7915c99f27631797719369832e227d4005096cbd479

   sha256 do resultado

   2dbcf29ef179d39ad837a6ac0b3282f5f089de5d348aa8e7fd9b960503366498

   Resultado mostrado ao modelo
6. 5Turno do modelo
   call_ae8e2b18gemini-3.8-flashFim: STOP6.379 ms16405 de entrada · 18 de saída · 285 de raciocínio · 12666 em cache

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Estimating Log Hourly Wage with Instrumental Variables** Alright, looking at this task, the core objective is to estimate the log hourly wage using a set of predictors, but crucially, with instrumental variables (IV) for years of schooling. The prompt explicitly asks for the coefficient on "years of schooling" after implementing this two-stage least squares (2SLS) estimation. First, I'm going to consider running a standard OLS (Ordinary Least Squares) model, perhaps referred to internally as "HC1," just to have it as a point of reference or in case it reveals something useful. It's always good practice to have a baseline. I recall seeing a similar example in Wooldridge's text – specifically Example 15.5 – which provides a concrete OLS result for `log(wage)` as a function of `educ`, `exper`, and `expersq`. The reported equation is: `log(wage) = 0.048 + 0.061 educ + 0.044 exper - 0.00090 expersq` with standard errors in parentheses: `(0.400) (0.031) (0.013) (0.00040)` and `n = 428`. From that example, the precise coefficient for `educ` is approximately `0.0613966`, or `0.0614`, with a standard error of `0.0314`. This OLS result will serve as a useful benchmark against the IV estimate. Now, the prompt specifies using the mother's and father's years of schooling as instruments for the individual's `educ`. This is a critical step to address potential endogeneity in `educ`. I need to ensure the 2SLS procedure is correctly implemented. Furthermore, the prompt mentions reporting the coefficient on years of schooling. It's also wise to consider how this coefficient should be presented. If the context or a subsequent step requires a percentage interpretation of the effect of schooling on wages, I should be prepared to calculate that. I'll make a mental note to potentially use a function like `core.scale_effect` on the estimated coefficient of `educ`. Specifically, if I need to translate the coefficient from a log-point change in schooling to a percentage change in wage, I'd apply `core.scale_effect` with `transform='log_points_to_percent'`. It's a good foresight to check if the prompt subtly implies this or if it's a standard requirement in this domain. Finally, I’ll ensure that the reporting mechanism or skill (`reporting-numbers skill`) is loaded, as it will be necessary for presenting the final, requested coefficient in a clear and appropriate format. My focus remains on the IV estimate of the `educ` coefficient, but I'll keep these other considerations (OLS baseline, percentage interpretation, reporting tools) in mind as part of a comprehensive analysis.

   Chamadas pedidas

   • load_skill (meta-ferramenta)

     {
       "name": "reporting-numbers"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
7. 6Habilidade
   reporting-numbersTexto da habilidade
8. 7Turno do modelo
   call_301465a6gemini-3.8-flashFim: STOP3.263 ms17144 de entrada · 53 de saída · 23 de raciocínio · 12773 em cache

   Texto visível

   I will convert the log-wage coefficient on schooling to a percentage effect.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Implementing `core.scale_effect`** Okay, so I'm looking at this `call_adcbcafa:coef.educ` entity, and my immediate instinct is to apply the `core.scale_effect` function to it. This feels like the most direct and appropriate way to handle the scaling operation required here. I need to ensure that the scaling is performed correctly on this specific coefficient within the `educ` domain.

   Chamadas pedidas

   • core.scale_effect

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

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
9. 8Ferramenta
   core.scale_effectv0.1.0call_b7a8f32cdecidido pelo modeloreexecutável

   Motivo: I will convert the log-wage coefficient on schooling to a percentage effect.

   Argumentos

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

   Figuras call_b7a8f32c

   Chave	Valor	Valor bruto	Erro-padrão	IC
   effect Effect as a percent change (from log points): 2SLS effect of educ on lwage	6,33206 %	6.332057397505915	—	-0,0394467 – 13,1097

   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

   19fa7abd620fcfb86651a130a6516a02a1a7082869901fc53980a06d59ebc2dd

   Resultado mostrado ao modelo
10. 9Turno do modelo
    call_39b3d02fgemini-3.8-flashFim: STOP12.724 ms17341 de entrada · 376 de saída · 793 de raciocínio · 12764 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Estimating the Impact of Education on Wages** Okay, the core task here is to estimate the causal effect of years of schooling (`educ`) on the log hourly wage (`lwage`) for women who worked in 1975, using Two-Stage Least Squares (2SLS) as outlined in Wooldridge's *Introductory Econometrics*, Example 15.5, with Mroz's data. The specific instruction is to report the coefficient on `educ`. First, I need to confirm the language of the output. The question is in English. Rule 7 mentions "Write the answer in the language of the question (Portuguese: decimal comma)". This is a bit of a tricky phrasing. It means *if* the question were Portuguese, I'd use a decimal comma. But since the question is English, I must write in English, and standard English number formatting applies. So, no decimal comma for me here. Now, let's dive into the `infer__iv_2sls` tool's output. * **Sample:** I'm looking at the results for the 428 women who worked in 1975, as specified. * **Variables:** The dependent variable is `lwage`. The endogenous variable is `educ` (years of schooling), which is precisely what I need to estimate the effect of. The other regressors are `exper` (years of experience) and `expersq` (experience squared), which are treated as exogenous. A constant term is also included. * **Instruments:** The instruments for `educ` are `motheduc` (mother's years of schooling) and `fatheduc` (father's years of schooling). This is crucial for the 2SLS approach to address potential endogeneity of schooling. Now, for the main result: * **Coefficient on `educ`:** The estimated coefficient is 0.0613966. I should report this with reasonable precision, perhaps to three or four decimal places, so approximately 0.0614. * **Uncertainty:** The standard error for this coefficient is 0.0314367 (or 0.0314). This gives me a sense of the precision of the estimate. The 95% confidence interval is [-0.000394545, 0.123188]. This interval includes zero, suggesting the effect, while positive, might not be statistically significant at the 5% level. Next, I need to consider the identification strategy and potential weaknesses. * **Identification Design:** The identification comes from the use of 2SLS, specifically employing mother's and father's education as instruments for a woman's own schooling. This design relies on the assumption that parental education influences a woman's schooling *but* does not directly affect her wage, except through its effect on her schooling. * **First Stage:** The F-statistic for the first stage is 55.40, which is robustly above the common threshold of 10, indicating that the instruments are strong predictors of schooling. This is good. * **Overidentification Test (Sargan):** The Sargan test statistic is 0.378 with a p-value of 0.538. Since the p-value is much greater than 0.05, I *cannot reject* the null hypothesis that the instruments are valid (i.e., uncorrelated with the error term in the second stage, conditional on at least one instrument being valid). This is also a positive sign for the identification strategy. Finally, I need to think about what could undermine these conclusions. * **Caveats:** * **Exclusion Restriction Violation:** The primary concern is whether parental education truly satisfies the exclusion restriction. It's plausible that parents' education might correlate with other family background factors (like unobserved ability, access to resources, or a general emphasis on education) that *also* directly influence a woman's wages, independent of her own years of schooling. If so, the instruments would be endogenous, and the 2SLS estimates would be biased. While the Sargan test doesn't reject, it's not a definitive proof of validity, especially if one instrument is weak or if the errors are heteroskedastic. * **Sample Selection:** The analysis is restricted to women who worked in 1975 (n=428). This means I'm not accounting for potential sample selection bias. Women with lower potential wages might be less likely to work, and this selection process might be correlated with schooling or the instruments. If this is the case, my estimates would only reflect the effect of education for *working* women, not all married women. So, to summarize the findings for the requested output format: * **Estimate:** The estimated coefficient on `educ` is 0.0614. * **Uncertainty:** The standard error is 0.0314, and the 95% CI is [-0.0004, 0.1232]. * **Design:** The identification comes from 2SLS using `motheduc` and `fatheduc` as instruments for `educ`. * **Undermining Factors:** Potential violations of the exclusion restriction for the instruments (e.g., shared unobserved family background) and sample selection bias (only observed working women). I should also include the figure reference `call_adcbcafa:coef.educ` as instructed. Looks like I have all the pieces now. I'll format this according to the `submit_answer` requirements.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "For the 428 women who worked in 1975, estimating the wage equation by two-stage least squares (2SLS) using mother's and father's education as instruments for schooling yields a coefficient on years of schooling (educ) of 0.0613966 (standard error of 0.0314367; 95% CI [-0.000394545, 0.123188]).\n\nThe instruments are strong in the first stage, with an excluded F-statistic of 55.4003004277767. The Sargan test for overidentifying restrictions yields a test statistic of 0.378071341963819 (p-value = 0.53863723307149), failing to reject the joint exogeneity of the instruments. The estimates for experience and experience squared are 0.0441704 and -0.00089897, respectively, with an intercept of 0.0481003.",
        "caveats": [
          "Validity of the instruments relies on the exclusion restriction that parental education affects women's wages solely through their own education, which may be violated if parental education correlates with unobserved ability or family connections.",
          "The sample is restricted to married women who reported positive hours and wages in 1975 (inlf == 1, n = 428), leaving potential sample selection unaddressed."
        ],
        "figure_refs": [
          "call_adcbcafa:coef.educ"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
11. 10Guarda
    resposta aceita

    Números encontrados

    428 · 1975 · 0.0613966 · 0.0314367 · 95% · -0.000394545 · 0.123188 · 55.4003004277767 · 0.378071341963819 · 0.53863723307149 · 0.0441704 · -0.00089897 · 0.0481003 · 1975 · 1 · 428

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
12. 11Resposta

    For the 428 women who worked in 1975, estimating the wage equation by two-stage least squares (2SLS) using mother's and father's education as instruments for schooling yields a coefficient on years of schooling (educ) of 0.0613966 (standard error of 0.0314367; 95% CI [-0.000394545, 0.123188]). The instruments are strong in the first stage, with an excluded F-statistic of 55.4003004277767. The Sargan test for overidentifying restrictions yields a test statistic of 0.378071341963819 (p-value = 0.53863723307149), failing to reject the joint exogeneity of the instruments. The estimates for experience and experience squared are 0.0441704 and -0.00089897, respectively, with an intercept of 0.0481003. Ressalvas: Validity of the instruments relies on the exclusion restriction that parental education affects women's wages solely through their own education, which may be violated if parental education correlates with unobserved ability or family connections. The sample is restricted to married women who reported positive hours and wages in 1975 (inlf == 1, n = 428), leaving potential sample selection unaddressed.

    • Validity of the instruments relies on the exclusion restriction that parental education affects women's wages solely through their own education, which may be violated if parental education correlates with unobserved ability or family connections.
    • The sample is restricted to married women who reported positive hours and wages in 1975 (inlf == 1, n = 428), leaving potential sample selection unaddressed.

    Figuras citadas: call_adcbcafa:coef.educ · Parada: answered

    Figura da resposta: call_adcbcafa:coef.educ = 0,06139660.06139662866015408 (se 0,03143670.031436695644695214)
13. 12Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
14. 13Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_adcbcafa:coef.educ (infer.iv_2sls)
15. 14Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
16. 15Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwage'
17. 16Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['educ']
18. 17Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['motheduc', 'fatheduc']
19. 18Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = ['exper', 'expersq']
20. 19Pontuação
    #7diagnósticopassouobrigatória428 vs 428
21. 20Pontuação
    #8figura da resposta próximapassouobrigatória0.06139662866 vs 0.061396628660153496
22. 21Pontuação
    #9figura da resposta próximapassouregistrada0.03143669564 vs 0.0314366956446951
23. 22Pontuação
    #10figura da resposta próximapassouregistrada0.06139662866 vs 0.061
24. 23Pontuação
    #11figura da resposta próximapassouregistrada0.03143669564 vs 0.031

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• época 1, tentativa 1passoupontuada(exibindo)

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