Tarefa paper_repro.card_1995.ex15_4_iv.agent

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Pergunta feita ao analista

Wooldridge, Introductory Econometrics (7th edition), Example 15.4, Table 15.1, IV column, using Card's (1995) data on men in 1976: estimate by instrumental variables the return to education, the effect of years of schooling on the log hourly wage, using as the instrument whether the man grew up near a four-year college in 1966. Include as exogenous controls years of experience and its square, a race indicator, indicators for living in a standard metropolitan statistical area and in a southern state in 1976, an indicator for living in a metropolitan area in 1966, and the 1966 region-of-residence dummies with the first region omitted. Report the coefficient on years of schooling.

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1. 0Início

   Wooldridge, Introductory Econometrics (7th edition), Example 15.4, Table 15.1, IV column, using Card's (1995) data on men in 1976: estimate by instrumental variables the return to education, the effect of years of schooling on the log hourly wage, using as the instrument whether the man grew up near a four-year college in 1966. Include as exogenous controls years of experience and its square, a race indicator, indicators for living in a standard metropolitan statistical area and in a southern state in 1976, an indicator for living in a metropolitan area in 1966, and the 1966 region-of-residence dummies with the first region omitted. Report the coefficient on years of schooling.

   card (agent)

   Wooldridge's CARD data set (the R package wooldridge, served by Rdatasets): David Card's (1995) sample of men from the National Longitudinal Survey of Young Men, observed in 1976; one row per man (3,010 rows). Columns used here: lwage, log hourly wage in 1976; educ, years of schooling in 1976; nearc4, 1 if the man grew up near a four-year college in 1966; nearc2, 1 if near a two-year college in 1966; exper, years of experience (age - educ - 6); expersq, exper squared; black, 1 if black; smsa, 1 if living in an SMSA in 1976; south, 1 if living in the South in 1976; smsa66, 1 if living in an SMSA in 1966; reg661 to reg669, indicators of the region of residence in 1966; also age, fatheduc, motheduc, IQ, KWW, married, wage (cents per hour) and the family-background indicators momdad14, sinmom14, step14, south66, libcrd14, enroll, weight, id and rownames.

   file 326dad817467b20d51bdfd015033e3e3e313931f51f812c38c0776249e7fd711 · frame —
2. 1Turno do modelo
   call_f65d6b0cgemini-3.8-flashFim: STOP8.366 ms14858 de entrada · 216 de saída · 331 de raciocínio · 0 em cache

   Texto visível

   I will run a two-stage least squares (2SLS) regression of log hourly wage on years of education instrumented by growing up near a four-year college, controlling for experience, experience squared, race, SMSA status in 1976 and 1966, South residence in 1976, and regional dummies for 1966.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Replicating Wooldridge's Example 15.4** Right, so the core task here is to reproduce a specific instrumental variables (IV) estimation, precisely the result shown in the "IV column" of Table 15.1 from Wooldridge's *Introductory Econometrics*, 7th edition. I'm going to use Card's (1995) dataset, which I understand is available as the `card` dataset. I need to make sure I'm implementing a two-stage least squares (2SLS) approach, as that's the standard IV method for this type of problem. Let's break down the components of the model I'll be specifying: * **The dependent variable (the outcome):** This is the natural logarithm of hourly wage, which is `lwage`. * **The endogenous regressor:** The key variable causing potential endogeneity is years of schooling, `educ`. This is the variable I need an instrument for. * **The instrument:** The instrument I'll be using for `educ` is a binary indicator: whether the individual grew up near a four-year college in 1966. This is represented by `nearc4`. The assumption here, of course, is that `nearc4` affects `lwage` *only* through its effect on `educ`, and is otherwise uncorrelated with the error term in the wage equation. * **Exogenous control variables:** These are the variables that are assumed to be exogenous and should be included in both stages of the 2SLS estimation. They are: * Years of experience (`exper`) * The square of years of experience (`expersq`) – this is important for capturing potential non-linearities in the experience-wage relationship. * A race indicator, specifically for being Black (`black`). * An indicator for living in an SMSA in 1976 (`smsa`). * An indicator for living in a southern state in 1976 (`south`). * An indicator for living in a metropolitan area in 1966 (`smsa66`). * A set of region-of-residence dummies for 1966. The text specifies that `reg661` is omitted, so I'll need to include `reg662` through `reg669`. This creates a complete set of regional dummies, avoiding perfect multicollinearity. Now, I need to figure out how to actually execute this in the software. I'm thinking about whether to use a dedicated `instrumental-variables` module if one exists, or if I should directly call a specific function like `infer__iv_2sls`. Given the explicit mention of 2SLS, a function named something like `infer__iv_2sls` seems highly probable. I'll quickly check its documentation to confirm the required arguments and how to specify the endogenous variables, instruments, and exogenous covariates. This will ensure I set up the model correctly according to the specified structure.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "card",
       "endog": [
         "educ"
       ],
       "exog": [
         "exper",
         "expersq",
         "black",
         "smsa",
         "south",
         "smsa66",
         "reg662",
         "reg663",
         "reg664",
         "reg665",
         "reg666",
         "reg667",
         "reg668",
         "reg669"
       ],
       "instruments": [
         "nearc4"
       ],
       "se": "classical",
       "y": "lwage"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
3. 2Ferramenta
   infer.iv_2slsv0.1.0call_6e617d10decidido pelo modeloreexecutável

   Motivo: I will run a two-stage least squares (2SLS) regression of log hourly wage on years of education instrumented by growing up near a four-year college, controlling for experience, experience squared, race, SMSA status in 1976 and 1966, South residence in 1976, and regional dummies for 1966.

   Argumentos

   {
     "cluster": null,
     "dataset": "card",
     "endog": [
       "educ"
     ],
     "exog": [
       "exper",
       "expersq",
       "black",
       "smsa",
       "south",
       "smsa66",
       "reg662",
       "reg663",
       "reg664",
       "reg665",
       "reg666",
       "reg667",
       "reg668",
       "reg669"
     ],
     "instruments": [
       "nearc4"
     ],
     "level": 0.95,
     "se": "classical",
     "subset": null,
     "y": "lwage"
   }

   Figuras call_6e617d10

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.educ 2SLS effect of educ on lwage	0,131504	0.13150383624470474	0,05496370.054963672601175226	0,0237335 – 0,239274

   Diagnósticos

   • first_stage_F.educ = 13,255813.255785330576108
   • partial_r2.educ = 0,004407930.004407934102325983
   • weak_instrument = false
   • n_obs = 3.0103010
   • se_type = "classical"
   • n_clusters = —

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 5.479516553400695,
         "ci_low": 1.8527852634542328,
         "coef": 3.666150908427464,
         "p": 0.00007538415974785308,
         "se": 0.9248295310138733,
         "t": 3.9641369414407985,
         "term": "Intercept"
       },
       {
         "ci_high": 0.1546598064790368,
         "ci_low": 0.06188240572195053,
         "coef": 0.10827110610049366,
         "p": 0.000004922903208547169,
         "se": 0.023658571085405363,
         "t": 4.576400903911081,
         "term": "exper"
       },
       {
         "ci_high": -0.001681030950206941,
         "ci_low": -0.0029888444048044374,
         "coef": -0.002334937677505689,
         "p": 3.1161246944085553e-12,
         "se": 0.00033349713755244625,
         "t": -7.001372469466829,
         "term": "expersq"
       },
       {
         "ci_high": -0.04109124105905192,
         "ci_low": -0.25246025330930105,
         "coef": -0.1467757471841765,
         "p": 0.006504376545512747,
         "se": 0.05389985881009377,
         "t": -2.7231193258096242,
         "term": "black"
       },
       {
         "ci_high": 0.1738897625009303,
         "ci_low": 0.04972685470035713,
         "coef": 0.11180830860064371,
         "p": 0.0004197459454284399,
         "se": 0.03166198833336174,
         "t": 3.5313103972953286,
         "term": "smsa"
       },
       {
         "ci_high": -0.09117299500874089,
         "ci_low": -0.19817000636948712,
         "coef": -0.144671500689114,
         "p": 1.2266258857565786e-7,
         "se": 0.027284622963645526,
         "t": -5.302308955556272,
         "term": "south"
       },
       {
         "ci_high": 0.06090028882943441,
         "ci_low": -0.023838079835042367,
         "coef": 0.01853110449719602,
         "p": 0.39119278809555685,
         "se": 0.021608588970484666,
         "t": 0.8575804983151744,
         "term": "smsa66"
       },
       {
         "ci_high": 0.17466030000544155,
         "ci_low": 0.026875261834297726,
         "coef": 0.10076778091986964,
         "p": 0.007538241795889867,
         "se": 0.0376857165904629,
         "t": 2.6738984962109194,
         "term": "reg662"
       },
       {
         "ci_high": 0.2204423366673024,
         "ci_low": 0.07607522011011421,
         "coef": 0.1482587783887083,
         "p": 0.000057840797772050855,
         "se": 0.03681413427830229,
         "t": 4.027224360837132,
         "term": "reg663"
       },
       {
         "ci_high": 0.13566022759527543,
         "ci_low": -0.035866069886474596,
         "coef": 0.049897078854400416,
         "p": 0.25405688043284264,
         "se": 0.04373982315600082,
         "t": 1.1407700181237441,
         "term": "reg664"
       },
       {
         "ci_high": 0.23855286385627722,
         "ci_low": 0.05399096224877149,
         "coef": 0.14627191305252435,
         "p": 0.001901645058086012,
         "se": 0.04706394912130858,
         "t": 3.107939639223742,
         "term": "reg665"
       },
       {
         "ci_high": 0.2646849853540353,
         "ci_low": 0.06112089839772622,
         "coef": 0.16290294187588075,
         "p": 0.001716385181435308,
         "se": 0.05190957477135003,
         "t": 3.1382060553073585,
         "term": "reg666"
       },
       {
         "ci_high": 0.2314381083788585,
         "ci_low": 0.03770631068276323,
         "coef": 0.13457220953081087,
         "p": 0.006486970827583493,
         "se": 0.04940230562501896,
         "t": 2.72400665977539,
         "term": "reg667"
       },
       {
         "ci_high": 0.03325735213331668,
         "ci_low": -0.1994113382810437,
         "coef": -0.08307699307386351,
         "p": 0.161550835975611,
         "se": 0.05933135339638065,
         "t": -1.4002207655511092,
         "term": "reg668"
       },
       {
         "ci_high": 0.1898006809461838,
         "ci_low": 0.0258277843270978,
         "coef": 0.10781423263664079,
         "p": 0.009971984091442317,
         "se": 0.041813678752432255,
         "t": 2.578444084649437,
         "term": "reg669"
       },
       {
         "ci_high": 0.23927422232576134,
         "ci_low": 0.023733450163648154,
         "coef": 0.13150383624470474,
         "p": 0.016792621890736437,
         "se": 0.054963672601175226,
         "t": 2.392559121711473,
         "term": "educ"
       }
     ],
     "first_stage": [
       {
         "ci_high": 0.4921785043603216,
         "ci_low": 0.147619375822603,
         "coef": 0.3198989400914623,
         "endog": "educ",
         "instrument": "nearc4",
         "p": 0.00027634008572957033,
         "se": 0.08786381779522222,
         "t": 3.640849534185134
       }
     ],
     "reduced_form": [
       {
         "ci_high": 0.07751371396063084,
         "ci_low": 0.006622161704650145,
         "coef": 0.04206793783264049,
         "instrument": "nearc4",
         "p": 0.020027629759561513,
         "se": 0.01807760095364329,
         "t": 2.3270752540957202
       }
     ]
   }

   Digests dos dados

   card 4ec4da8d7939f11a46d67bd248416cc7330bd0dddaddcd6c49c9872c5a427413

   sha256 do resultado

   f806185fec3e55a57b0cb952a5bb5a6c74257419ab50cdfa16e415dc80e94d67

   Resultado mostrado ao modelo
4. 3Turno do modelo
   call_c603c440gemini-3.8-flashFim: STOP11.746 ms16492 de entrada · 386 de saída · 711 de raciocínio · 0 em cache

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Estimating the Return to Education** I've just meticulously reviewed the results from applying an instrumental variables (IV) approach, specifically referencing Wooldridge's Table 15.1 from *Introductory Econometrics* (7th edition), concerning Example 15.4 and Card's (1995) data on men in 1976. My primary objective was to estimate the return to education, meaning the impact of years of schooling on the logarithm of hourly wages, utilizing the instrumental variable strategy outlined. First, I focused on the output generated using classical standard errors, as presented in Wooldridge's Table 15.1. I noted the coefficient for `educ`, which came out to be approximately 0.131504. This aligns precisely with the 0.132 reported in Wooldridge's table. The associated standard error for this coefficient was 0.0549637, which rounds nicely to 0.055, also matching the reported value. Next, I examined the first-stage regression results. The F-statistic for the first stage was 13.255785. This is a crucial indicator of the instrument's strength. I also observed the coefficient on the instrument, `nearc4` (whether the man grew up near a four-year college in 1966), in this first stage. It was 0.319899 with a standard error of 0.0878638, yielding a t-statistic of 3.64. Then, I looked at the reduced form coefficient for `nearc4`. This coefficient was 0.0420679, with a standard error of 0.0180776. To verify the IV estimate, I performed a simple calculation: the ratio of the reduced form coefficient to the first-stage coefficient on `nearc4`. This ratio, 0.0420679 / 0.319899, indeed equals 0.131504, confirming the IV estimate's consistency. Everything, down to the last decimal, lines up with the IV column in Wooldridge's Table 15.1. The IV estimate for `educ` is clearly presented as .132 with a standard error of .055. I also took a moment to confirm the language requirements of the prompt. It was written in English, and Rule 7 states that the answer should be in the language of the question. Therefore, I am proceeding in English. Digging a bit deeper into the specifics: the prompt also required me to include several exogenous control variables: years of experience and its square, a race indicator, indicators for living in a standard metropolitan statistical area (SMSA) and in a southern state in 1976, an indicator for living in a metropolitan area in 1966, and region-of-residence dummies for 1966, with the first region excluded. The coefficient of interest, the one on years of schooling, is what I've been reporting. The analysis was conducted on a sample size of 3010 observations. Finally, I considered the inherent assumptions and potential limitations of this IV strategy. The critical assumption underlying the instrument `nearc4` is the exclusion restriction. This means that growing up near a college should influence adult log wages *solely* through its effect on educational attainment, *after* accounting for the included exogenous controls (region, urban status, race, and experience). I'm acutely aware that if proximity to college is systematically correlated with unobserved factors like family background, innate ability, or unmeasured local labor market conditions that also affect wages, then this exclusion restriction would be violated, potentially leading to biased estimates. This is a standard but crucial caveat to keep in mind when interpreting these results. Now, I'm ready to compile these thoughts into the final answer format.

   Chamadas pedidas

   • submit_answer (meta-ferramenta)

     {
       "answer": "Using Card's (1995) dataset to replicate Wooldridge (7th edition, Example 15.4, Table 15.1, IV column), the two-stage least squares (2SLS) estimated return to education is:\n\n- **Coefficient on `educ`:** 0.131504 (SE = 0.0549637; 95% CI: [0.0237335, 0.239274])\n- **Sample size:** 3,010 observations\n- **First-stage F-statistic for `nearc4`:** 13.255785 (first-stage coefficient on `nearc4` = 0.319899, SE = 0.0878638)\n\nThe 2SLS estimate indicates an approximate return to an additional year of schooling of 13.15% (0.131504 log points).",
       "caveats": [
         "Validity of the instrument relies on the exclusion restriction that growing up near a 4-year college in 1966 affects adult wages solely through schooling, conditional on controls (region, urban status, race, and experience). If proximity correlates with unobserved ability, family wealth, or local economic conditions, the estimate may be biased.",
         "The first-stage F-statistic of 13.26 exceeds the conventional rule-of-thumb threshold of 10, but instrument strength is modest (partial R² = 0.004408)."
       ],
       "figure_refs": [
         "call_6e617d10:coef.educ"
       ]
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
5. 4Guarda
   resposta aceita

   Números encontrados

   1995 · 15.4 · 15.1 · 0.131504 · 0.0549637 · 95% · 0.0237335 · 0.239274 · 3,010 · 13.255785 · 0.319899 · 0.0878638 · 13.15% · 0.131504 · 4 · 1966 · 13.26 · 10 · 0.004408

   Sem lastro

   —

   Não citados

   —

   1 nova(s) tentativa(s) restante(s)
6. 5Resposta

   Using Card's (1995) dataset to replicate Wooldridge (7th edition, Example 15.4, Table 15.1, IV column), the two-stage least squares (2SLS) estimated return to education is: - **Coefficient on `educ`:** 0.131504 (SE = 0.0549637; 95% CI: [0.0237335, 0.239274]) - **Sample size:** 3,010 observations - **First-stage F-statistic for `nearc4`:** 13.255785 (first-stage coefficient on `nearc4` = 0.319899, SE = 0.0878638) The 2SLS estimate indicates an approximate return to an additional year of schooling of 13.15% (0.131504 log points). Ressalvas: Validity of the instrument relies on the exclusion restriction that growing up near a 4-year college in 1966 affects adult wages solely through schooling, conditional on controls (region, urban status, race, and experience). If proximity correlates with unobserved ability, family wealth, or local economic conditions, the estimate may be biased. The first-stage F-statistic of 13.26 exceeds the conventional rule-of-thumb threshold of 10, but instrument strength is modest (partial R² = 0.004408).

   • Validity of the instrument relies on the exclusion restriction that growing up near a 4-year college in 1966 affects adult wages solely through schooling, conditional on controls (region, urban status, race, and experience). If proximity correlates with unobserved ability, family wealth, or local economic conditions, the estimate may be biased.
   • The first-stage F-statistic of 13.26 exceeds the conventional rule-of-thumb threshold of 10, but instrument strength is modest (partial R² = 0.004408).

   Figuras citadas: call_6e617d10:coef.educ · Parada: answered

   Figura da resposta: call_6e617d10:coef.educ = 0,1315040.13150383624470474 (se 0,05496370.054963672601175226)
7. 6Pontuação
   #0resposta com lastropassouobrigatóriaevery number backed
8. 7Pontuação
   #1figura da resposta escolhidapassouobrigatóriaanswer figure call_6e617d10:coef.educ (infer.iv_2sls)
9. 8Pontuação
   #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
10. 9Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwage'
11. 10Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['educ']
12. 11Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['nearc4']
13. 12Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = ['exper', 'expersq', 'black', 'smsa', 'south', 'smsa66', 'reg662', 'reg663', 'reg664', 'reg665', 'reg666', 'reg667', 'reg668', 'reg669']
14. 13Pontuação
    #7diagnósticopassouobrigatória3010 vs 3010
15. 14Pontuação
    #8figura da resposta próximapassouobrigatória0.1315038362 vs 0.13150383624451933
16. 15Pontuação
    #9figura da resposta próximapassouregistrada0.0549636726 vs 0.054963672601153514
17. 16Pontuação
    #10figura da resposta próximapassouregistrada0.1315038362 vs 0.132
18. 17Pontuação
    #11figura da resposta próximapassouregistrada0.0549636726 vs 0.055

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• época 1, tentativa 1passoupontuada(exibindo)

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