Tarefa paper_repro.card_1995.ex15_4_iv.design

Veredito

Pergunta feita ao analista

What is the causal return to a year of schooling for young men in the United States? Using Card's sample of men from the National Longitudinal Survey of Young Men observed in 1976, estimate the effect of education on the log hourly wage, using a source of variation in schooling that is not driven by ability or family background.

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Trajetória

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

1. 0Início

   What is the causal return to a year of schooling for young men in the United States? Using Card's sample of men from the National Longitudinal Survey of Young Men observed in 1976, estimate the effect of education on the log hourly wage, using a source of variation in schooling that is not driven by ability or family background.

   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_49662c67gemini-3.8-flashFim: STOP5.866 ms14756 de entrada · 40 de saída · 98 de raciocínio · 12572 em cache

   Texto visível

   I will load the instrumental variables skill to follow the best practices for estimating returns to schooling using an instrument.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Estimating the Causal Return to Schooling** Alright, I've received a very specific and well-defined research question here, which is excellent. The core objective is to understand the *causal* impact of an additional year of schooling on the log hourly wage for young men in the United States. The prompt explicitly points me to a particular dataset – Card's sample from the National Longitudinal Survey of Young Men (NLSYM) observed in 1976 – and crucially, it directs me to find a source of variation in schooling that is *independent* of unobserved ability or family background. This immediately flags the need for an instrumental variables (IV) approach. My first step, as always when tackling a new methodology or a seminal dataset, is to ground myself in the established best practices. The prompt even gives me a helpful nudge: "Let's load the instrumental variables skill to see best practices for instrumental variables and Card (1995)." This tells me I need to refresh my understanding of the fundamental assumptions and implementation details of IV estimation. What are the critical conditions for a valid instrument? I need to recall the relevance condition (the instrument must be correlated with the endogenous regressor – in this case, schooling) and the exclusion restriction (the instrument must *only* affect the outcome variable – log wage – through its effect on schooling, and not through any other channel). I also need to consider potential issues like weak instruments and how to test for them. Simultaneously, I need to delve into the specifics of Card (1995). This isn't just about general IV; it's about understanding how Card *himself* applied IV to this exact problem or a very similar one. What was his chosen instrument? What were the characteristics of that instrument that made it defensible? What were his findings, and what were the limitations he acknowledged? Reviewing Card's paper is paramount to ensure I'm not reinventing the wheel and that I'm adopting a robust and credible approach consistent with foundational work in this area. I'll be looking for details on sample selection, the specific variables used, the functional form of the model, and the diagnostic tests he performed. So, in essence, my mental roadmap is: 1. **Deconstruct the Request:** Identify the causal question, the target population, the outcome variable, and the key constraint regarding the source of variation. 2. **Recognize the Methodology:** The need for a source of variation *exogenous* to ability/background immediately points to instrumental variables. 3. **Consult Best Practices:** Revisit the core assumptions and common pitfalls of IV estimation (relevance, exclusion, exogeneity, weak instruments). 4. **Study the Canonical Reference:** Dive deep into Card (1995) to understand his specific instrument, his empirical strategy, and his conclusions in the context of this NLSYM data. This systematic approach ensures I am building my analysis on a solid theoretical foundation and leveraging the specific insights provided by the prompt's reference to Card's seminal work.

   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_01d42bd0gemini-3.8-flashFim: STOP11.655 ms15362 de entrada · 80 de saída · 756 de raciocínio · 12669 em cache

   Texto visível

   I will inspect the variables in the Card dataset to check their distributions and missing values.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Understanding Card (1995) and its Application** My primary objective is to grasp how Card (1995) approaches the estimation of the return to schooling, specifically utilizing geographic variation in college proximity as an instrumental variable. I'm immediately drawn to Card's methodological innovation: `nearc4`, a binary indicator of proximity to a 4-year college, is employed as an instrument for `educ` (years of schooling). This is a crucial starting point for my analysis. To fully contextualize this, I need to understand the available data. I’m thinking about what information is present in the 'card' dataset. I'd expect to see variables related to wages, education, geographic indicators, experience, and demographic characteristics. I'm mentally listing or would be checking column descriptions like: `lwage` (log hourly wage), `educ` (years of schooling), `nearc4` (proximity to 4-year college), `nearc2` (proximity to 2-year college), `exper` (years of experience), `expersq` (squared experience), `black` (race indicator), `smsa` (urban indicator), `south` (regional indicator), and various other regional indicators (`smsa66`, `reg661` to `reg669`). Next, I need to pinpoint the specific empirical strategy employed in Card (1995), particularly focusing on what's presented in Tables 2 or 3, as these often detail the core model specifications. I recall that a "typical baseline specification" in the context of Wooldridge and Card (1995) often involves a two-stage least squares (2SLS) model. My mental model of this 2SLS setup is: the dependent variable (`y`) is `lwage`, the endogenous variable is `educ`, and the primary instrument is `nearc4`. However, I also recognize that a complete model will include exogenous control variables. I'm thinking about what those controls would typically be. I'm considering variables like `exper`, `expersq`, `black`, `smsa`, `south`, `smsa66`, and potentially a set of regional dummy variables (`reg661` through `reg668`, with one omitted to avoid multicollinearity). I need to be precise about which controls Card uses in his standard specification, or at least what is commonly presented in accompanying analyses like those in Wooldridge. My thought is to cross-reference with the original paper or established textbook examples. A critical point of reflection arises: if `educ` is endogenous, what about `exper`? Since `exper` is calculated as `age - educ - 6`, it's inherently correlated with `educ`. This means `exper` (and its square, `expersq`) could also be endogenous. I need to confirm whether Card treats `exper` and `expersq` as strictly exogenous, or if they are included as endogenous variables, potentially requiring further instruments or a different estimation approach. Alternatively, he might be using age and age-squared as instruments or controls if the experience calculation is directly tied to the education choice. To clarify these nuances, I’m making a mental note to specifically look at Wooldridge's examples, particularly Example 15.4 and Example 15.5, as these are likely to provide a very direct and pedagogical illustration of Card's method. I remember Example 15.4 as focusing on `lwage` regressed on `educ`, `exper`, `expersq`, `black`, `smsa`, and `south`, with `nearc4` as the instrument for `educ`. This seems like the foundational setup. Then, I'm considering Example 15.5. This is where the regional controls like `reg66` and `smsa66` are likely introduced, potentially to account for spatial correlation or unobserved regional factors that might influence both college proximity and wages. My thought process is that to accurately represent Card's work and its common interpretation, I must distinguish between the simpler specifications and those that incorporate a broader set of controls. Therefore, checking the specifics of the Card (1995) paper itself, alongside how Wooldridge presents it, is paramount. Ultimately, I need to either consult the dataset directly (e.g., using `data.describe`) or rely on the provided descriptions to confirm the exact variables and their role in the models I am analyzing.

   Chamadas pedidas

   • data.describe

     {
       "columns": [
         "lwage",
         "educ",
         "nearc4",
         "exper",
         "expersq",
         "black",
         "smsa",
         "south",
         "smsa66"
       ],
       "dataset": "card"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
5. 4Ferramenta
   data.describev0.1.0call_087cfd35decidido pelo modeloreexecutável

   Motivo: I will inspect the variables in the Card dataset to check their distributions and missing values.

   Argumentos

   {
     "columns": [
       "lwage",
       "educ",
       "nearc4",
       "exper",
       "expersq",
       "black",
       "smsa",
       "south",
       "smsa66"
     ],
     "dataset": "card"
   }

   Figuras call_087cfd35

   Chave	Valor	Valor bruto	Erro-padrão	IC
   n_rows Rows in the dataset	3.010 rows	3010	—	—

   Tabelas (1)

   {
     "columns": [
       {
         "column": "lwage",
         "dtype": "float64",
         "max": 7.784889221191406,
         "mean": 6.261831955260217,
         "min": 4.605170249938965,
         "n_missing": 0,
         "n_unique": 755,
         "sd": 0.44379764068492095
       },
       {
         "column": "educ",
         "dtype": "int64",
         "max": 18,
         "mean": 13.263455149501661,
         "min": 1,
         "n_missing": 0,
         "n_unique": 18,
         "sd": 2.6769128552950434
       },
       {
         "column": "nearc4",
         "dtype": "int64",
         "max": 1,
         "mean": 0.6820598006644518,
         "min": 0,
         "n_missing": 0,
         "n_unique": 2,
         "sd": 0.4657534729010638
       },
       {
         "column": "exper",
         "dtype": "int64",
         "max": 23,
         "mean": 8.856146179401993,
         "min": 0,
         "n_missing": 0,
         "n_unique": 24,
         "sd": 4.141671574970938
       },
       {
         "column": "expersq",
         "dtype": "int64",
         "max": 529,
         "mean": 95.57906976744187,
         "min": 0,
         "n_missing": 0,
         "n_unique": 24,
         "sd": 84.61831430871867
       },
       {
         "column": "black",
         "dtype": "int64",
         "max": 1,
         "mean": 0.2335548172757475,
         "min": 0,
         "n_missing": 0,
         "n_unique": 2,
         "sd": 0.4231624453087617
       },
       {
         "column": "smsa",
         "dtype": "int64",
         "max": 1,
         "mean": 0.7129568106312293,
         "min": 0,
         "n_missing": 0,
         "n_unique": 2,
         "sd": 0.4524570799911211
       },
       {
         "column": "south",
         "dtype": "int64",
         "max": 1,
         "mean": 0.40365448504983387,
         "min": 0,
         "n_missing": 0,
         "n_unique": 2,
         "sd": 0.4907112602458
       },
       {
         "column": "smsa66",
         "dtype": "int64",
         "max": 1,
         "mean": 0.6495016611295681,
         "min": 0,
         "n_missing": 0,
         "n_unique": 2,
         "sd": 0.4772053116171187
       }
     ]
   }

   Digests dos dados

   card 4ec4da8d7939f11a46d67bd248416cc7330bd0dddaddcd6c49c9872c5a427413

   sha256 do resultado

   9145a6119479afecf260b67228534b23161adb7cf9604c993b5ce5675b54418b

   Resultado mostrado ao modelo
6. 5Turno do modelo
   call_992ccca3gemini-3.8-flashFim: STOP7.350 ms16554 de entrada · 118 de saída · 355 de raciocínio · 0 em cache

   Texto visível

   I will estimate the causal return to schooling using Two-Stage Least Squares (2SLS) with proximity to a four-year college (nearc4) as an instrumental variable, controlling for experience, experience squared, race, and geographic location.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process Regarding IV Regressions and Card (1995)** My immediate inclination is to explore the implications of using Instrumental Variables (IV) regressions. To do this effectively, I need to establish a baseline, and for that, I'm turning to established literature. My primary point of reference is Card (1995), as it's a seminal work in this area. I need to recall or ascertain the specific specifications commonly employed in that paper to ensure my analysis is grounded and comparable. Diving into Card (1995), specifically looking at Table 3, I see the following regressors for the OLS estimation: `lwage` is the dependent variable, and the independent variables are `educ`, `exper`, `expersq`, `black`, `south`, `smsa`, `reg661` through `reg668` (regional dummies), and `smsa66`. This provides a clear picture of the control variables used in that context. However, I also recall a related example from Wooldridge. It’s important to cross-reference and clarify potential discrepancies. In Wooldridge's Example 15.4, the basic model is presented as: `log(wage) = beta0 + beta1 educ + beta2 exper + beta3 expersq + beta4 black + beta5 smsa + beta6 south + u`. The instrumental variable in this Wooldridge example is `nearc4`. Now, I need to reconcile these two. My next step is to run an IV 2SLS estimation using the `infer.iv_2sls` function, starting with what I perceive as standard controls. But I immediately pause to ask myself: does the Wooldridge Example 15.4 *actually* include `smsa66` and the regional dummies, or is it limited to `exper`, `expersq`, `black`, `smsa`, and `south`? This distinction is crucial for an accurate comparison. I decide that I should check both or, if possible, perform a test to see the impact of including these additional controls. Recalling the specific findings from Wooldridge Example 15.4: the OLS estimate for the return to education is approximately 0.0747 (or 7.5%). The IV estimate, using `nearc4` as the instrument, is a notably higher 0.1315 (or 13.2%), with a standard error of 0.055. This significant difference underscores the importance of addressing potential endogeneity. Given this, my plan is to proceed by running `infer.iv_2sls` again, but this time incorporating the full set of controls found in Card's Table 3. This means setting `exog=['exper', 'expersq', 'black', 'smsa', 'south']` and also including the regional dummies (`reg661` to `reg668`) and `smsa66` to replicate the more comprehensive specification from Card. I'm eager to see how this more complete model affects the IV estimates, particularly the return to education, and whether it aligns more closely with or diverges from the simpler Wooldridge specification.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "card",
       "endog": [
         "educ"
       ],
       "exog": [
         "exper",
         "expersq",
         "black",
         "smsa",
         "south"
       ],
       "instruments": [
         "nearc4"
       ],
       "y": "lwage"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
7. 6Ferramenta
   infer.iv_2slsv0.1.0call_07648d37decidido pelo modeloreexecutável

   Motivo: I will estimate the causal return to schooling using Two-Stage Least Squares (2SLS) with proximity to a four-year college (nearc4) as an instrumental variable, controlling for experience, experience squared, race, and geographic location.

   Argumentos

   {
     "cluster": null,
     "dataset": "card",
     "endog": [
       "educ"
     ],
     "exog": [
       "exper",
       "expersq",
       "black",
       "smsa",
       "south"
     ],
     "instruments": [
       "nearc4"
     ],
     "level": 0.95,
     "se": "HC1",
     "subset": null,
     "y": "lwage"
   }

   Figuras call_07648d37

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.educ 2SLS effect of educ on lwage	0,132289	0.13228884000030414	0,04857790.04857786029781447	0,0370396 – 0,227538

   Diagnósticos

   • first_stage_F.educ = 17,513317.513316096885806
   • partial_r2.educ = 0,005536140.0055361440036182374
   • weak_instrument = false
   • n_obs = 3.0103010
   • se_type = "HC1"
   • n_clusters = —

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 5.356092439420627,
         "ci_low": 2.1494702433329946,
         "coef": 3.752781341376811,
         "p": 0.000004626903394222754,
         "se": 0.8177011912635523,
         "t": 4.589428732001512,
         "term": "Intercept"
       },
       {
         "ci_high": 0.14894342587530163,
         "ci_low": 0.06605254548576793,
         "coef": 0.10749798568053479,
         "p": 3.888605826495917e-7,
         "se": 0.021137498431247684,
         "t": 5.085653159487402,
         "term": "exper"
       },
       {
         "ci_high": -0.0016041963471551453,
         "ci_low": -0.0029639475868676298,
         "coef": -0.0022840719670113876,
         "p": 5.2706437873438126e-11,
         "se": 0.00034674187994194404,
         "t": -6.587239958997212,
         "term": "expersq"
       },
       {
         "ci_high": -0.029801068821362506,
         "ci_low": -0.2318027194948034,
         "coef": -0.13080189415808297,
         "p": 0.011157812992998796,
         "se": 0.051511210330424134,
         "t": -2.539289861741557,
         "term": "black"
       },
       {
         "ci_high": 0.18976010503132812,
         "ci_low": 0.07288722070648719,
         "coef": 0.13132366286890765,
         "p": 0.0000108790515982168,
         "se": 0.029803042234108595,
         "t": 4.406384483749517,
         "term": "smsa"
       },
       {
         "ci_high": -0.05994754998589312,
         "ci_low": -0.1498535172524446,
         "coef": -0.10490053361916887,
         "p": 0.000004942465956349897,
         "se": 0.022926372999369088,
         "t": -4.575539865030358,
         "term": "south"
       },
       {
         "ci_high": 0.22753808675064285,
         "ci_low": 0.037039593249965405,
         "coef": 0.13228884000030414,
         "p": 0.006502028722795576,
         "se": 0.04857786029781447,
         "t": 2.723233159906301,
         "term": "educ"
       }
     ],
     "first_stage": [
       {
         "ci_high": 0.495366256937643,
         "ci_low": 0.17927530323987692,
         "coef": 0.33732078008876,
         "endog": "educ",
         "instrument": "nearc4",
         "p": 0.00002934877999898834,
         "se": 0.08060442845485503,
         "t": 4.18489140801596
       }
     ],
     "reduced_form": [
       {
         "ci_high": 0.07674060806061869,
         "ci_low": 0.012506941351255657,
         "coef": 0.044623774705937175,
         "instrument": "nearc4",
         "p": 0.006480889664049237,
         "se": 0.016379836031683456,
         "t": 2.7243114411903497
       }
     ]
   }

   Digests dos dados

   card 4ec4da8d7939f11a46d67bd248416cc7330bd0dddaddcd6c49c9872c5a427413

   sha256 do resultado

   0245c50b205be09769212a1fca5c289c9f8347d787ad0f2f9b6360327603b7d9

   Resultado mostrado ao modelo
8. 7Turno do modelo
   call_25e54a47gemini-3.8-flashFim: STOP5.182 ms17825 de entrada · 167 de saída · 171 de raciocínio · 15955 em cache

   Texto visível

   I will also test Card's fuller specification including region in 1966 and SMSA residence in 1966 to see the sensitivity of the IV estimate.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process** Okay, so I'm looking at this regression output, and the coefficient on `coef.educ` is 0.132. That's interesting. I've got the standard error for that, 0.0486, and a confidence interval from about 0.037 to 0.227. This suggests that education has a statistically significant positive effect, at least within this model. Then I'm checking the first-stage regression. The F-statistic is 17.5, which is well above the common threshold of 10, so I'm not worried about weak instruments here. The coefficient on `nearc4` in that first stage is 0.337, with a t-statistic of 4.18. That's a strong predictor. Now, my mind immediately goes to how this compares to existing literature, specifically Card's seminal work. He used a particular set of control variables. So, my next thought is, "What happens if I replicate Card's specification exactly?" I need to incorporate those regional dummies (`reg661` through `reg668`) and the 1966 SMSA indicator (`smsa66`) into my model. This is a crucial step to see if my findings are consistent with his, and to understand the impact of those specific controls on the education coefficient.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "card",
       "endog": [
         "educ"
       ],
       "exog": [
         "exper",
         "expersq",
         "black",
         "smsa",
         "south",
         "smsa66",
         "reg661",
         "reg662",
         "reg663",
         "reg664",
         "reg665",
         "reg666",
         "reg667",
         "reg668"
       ],
       "instruments": [
         "nearc4"
       ],
       "y": "lwage"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
9. 8Ferramenta
   infer.iv_2slsv0.1.0call_62e2c716decidido pelo modeloreexecutável

   Motivo: I will also test Card's fuller specification including region in 1966 and SMSA residence in 1966 to see the sensitivity of the IV estimate.

   Argumentos

   {
     "cluster": null,
     "dataset": "card",
     "endog": [
       "educ"
     ],
     "exog": [
       "exper",
       "expersq",
       "black",
       "smsa",
       "south",
       "smsa66",
       "reg661",
       "reg662",
       "reg663",
       "reg664",
       "reg665",
       "reg666",
       "reg667",
       "reg668"
     ],
     "instruments": [
       "nearc4"
     ],
     "level": 0.95,
     "se": "HC1",
     "subset": null,
     "y": "lwage"
   }

   Figuras call_62e2c716

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.educ 2SLS effect of educ on lwage	0,131504	0.1315038362447041	0,05414360.05414362358466126	0,0253414 – 0,237666

   Diagnósticos

   • first_stage_F.educ = 14,138714.138670079757025
   • partial_r2.educ = 0,004407930.004407934102326205
   • weak_instrument = false
   • n_obs = 3.0103010
   • se_type = "HC1"
   • n_clusters = —

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 5.57757370074928,
         "ci_low": 1.9703565813789508,
         "coef": 3.7739651410641155,
         "p": 0.0000419083402491384,
         "se": 0.9198533472883026,
         "t": 4.102790028638413,
         "term": "Intercept"
       },
       {
         "ci_high": 0.15417017511206102,
         "ci_low": 0.0623720370889258,
         "coef": 0.10827110610049341,
         "p": 0.000003900696274095777,
         "se": 0.023408855564023938,
         "t": 4.62521996448603,
         "term": "exper"
       },
       {
         "ci_high": -0.001651102453669978,
         "ci_low": -0.0030187729013414002,
         "coef": -0.002334937677505689,
         "p": 2.5660531275407993e-11,
         "se": 0.0003487608862028947,
         "t": -6.694952816891624,
         "term": "expersq"
       },
       {
         "ci_high": -0.043832218317044896,
         "ci_low": -0.24971927605130947,
         "coef": -0.14677574718417719,
         "p": 0.0052129727827677046,
         "se": 0.052501940679762084,
         "t": -2.7956251765899927,
         "term": "black"
       },
       {
         "ci_high": 0.17287574913173331,
         "ci_low": 0.05074086806955459,
         "coef": 0.11180830860064395,
         "p": 0.00033605473372198943,
         "se": 0.031144834216498392,
         "t": 3.5899471425478193,
         "term": "smsa"
       },
       {
         "ci_high": -0.08752935335031128,
         "ci_low": -0.2018136480279177,
         "coef": -0.1446715006891145,
         "p": 7.284289486305898e-7,
         "se": 0.02914290643531583,
         "t": -4.964209764397394,
         "term": "south"
       },
       {
         "ci_high": 0.05885421455403568,
         "ci_low": -0.021792005559643463,
         "coef": 0.018531104497196107,
         "p": 0.3676098482833189,
         "se": 0.02056507636298483,
         "t": 0.9010958272224227,
         "term": "smsa66"
       },
       {
         "ci_high": -0.02727394276513405,
         "ci_low": -0.18835452250814655,
         "coef": -0.10781423263664029,
         "p": 0.008715546602998126,
         "se": 0.04107612754000647,
         "t": -2.624741890082838,
         "term": "reg661"
       },
       {
         "ci_high": 0.05920628927156932,
         "ci_low": -0.07329919270511046,
         "coef": -0.007046451716770569,
         "p": 0.8348211809261159,
         "se": 0.03378937477197794,
         "t": -0.2085404587780151,
         "term": "reg662"
       },
       {
         "ci_high": 0.10438002625736383,
         "ci_low": -0.023490934753228568,
         "coef": 0.04044454575206763,
         "p": 0.21494582694657896,
         "se": 0.03260755524665992,
         "t": 1.2403427808716347,
         "term": "reg663"
       },
       {
         "ci_high": 0.019170363716945166,
         "ci_low": -0.13500467128142712,
         "coef": -0.05791715378224098,
         "p": 0.14081582618392022,
         "se": 0.039315188778073766,
         "t": -1.473149578631595,
         "term": "reg664"
       },
       {
         "ci_high": 0.1357102652425628,
         "ci_low": -0.0587949044107947,
         "coef": 0.03845768041588406,
         "p": 0.43818584185911835,
         "se": 0.04959951825737383,
         "t": 0.7753639907614759,
         "term": "reg665"
       },
       {
         "ci_high": 0.15757738300021318,
         "ci_low": -0.047399964521732535,
         "coef": 0.05508870923924032,
         "p": 0.2920015088331547,
         "se": 0.052269961301706254,
         "t": 1.0539267270787525,
         "term": "reg666"
       },
       {
         "ci_high": 0.12526699792110546,
         "ci_low": -0.07175104413276424,
         "coef": 0.026757976894170605,
         "p": 0.5943501926517236,
         "se": 0.0502403097629661,
         "t": 0.5325997594444541,
         "term": "reg667"
       },
       {
         "ci_high": -0.0912357962570994,
         "ci_low": -0.2905466551639089,
         "coef": -0.19089122571050413,
         "p": 0.0001760407213371538,
         "se": 0.05082498631197954,
         "t": -3.75585395220285,
         "term": "reg668"
       },
       {
         "ci_high": 0.2376663057704683,
         "ci_low": 0.02534136671893991,
         "coef": 0.1315038362447041,
         "p": 0.015207536506545785,
         "se": 0.05414362358466126,
         "t": 2.428796366742598,
         "term": "educ"
       }
     ],
     "first_stage": [
       {
         "ci_high": 0.4867128322485119,
         "ci_low": 0.1530850479344127,
         "coef": 0.3198989400914623,
         "endog": "educ",
         "instrument": "nearc4",
         "p": 0.00017306417234451147,
         "se": 0.08507628567788403,
         "t": 3.760142295147489
       }
     ],
     "reduced_form": [
       {
         "ci_high": 0.07642248223904397,
         "ci_low": 0.007713393426237024,
         "coef": 0.04206793783264049,
         "instrument": "nearc4",
         "p": 0.016411329263879147,
         "se": 0.017521064921266014,
         "t": 2.40099206421985
       }
     ]
   }

   Digests dos dados

   card 4ec4da8d7939f11a46d67bd248416cc7330bd0dddaddcd6c49c9872c5a427413

   sha256 do resultado

   2e27906a1042cdd2d90ccbb176020a0bf1453085f4d506321f4c4aefd99e333e

   Resultado mostrado ao modelo
10. 9Turno do modelo
    call_c76d3935gemini-3.8-flashFim: STOP6.373 ms19267 de entrada · 88 de saída · 242 de raciocínio · 15958 em cache

    Texto visível

    I will run an OLS regression with the same baseline controls to provide the benchmark comparison between OLS and 2SLS.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on the Instrumental Variables Analysis** Looking at the initial specifications, I see two sets of results from my instrumental variables (2SLS) regressions. In both cases, the estimated coefficient for the key variable of interest is remarkably consistent. The first specification, which uses a set of baseline controls (exper, expersq, black, smsa, south), yields a coefficient of 0.132289 with a standard error of 0.0485779. This gives me a 95% confidence interval ranging from 0.0370396 to 0.227538. I also note that the first-stage F-statistic is 17.5133, which suggests the instruments are reasonably strong in this baseline model. When I move to the second specification, which includes the more extensive set of controls from Card's (1995) full baseline (smsa66 and the regional dummy variables reg661 through reg668), the results are very similar. The 2SLS coefficient is 0.131504, with a slightly larger standard error of 0.0541436. This results in a confidence interval of [0.0253414, 0.237666]. The first-stage F-statistic here is 14.1387, still above the common threshold for weak instruments. The stability of the primary coefficient across these two specifications, despite the change in covariates, is a positive sign. My next logical step is to perform the classic comparison that Card himself made: OLS versus 2SLS. To do this effectively, I need to run ordinary least squares (OLS) regressions on the *exact same* sets of controls that I used for the 2SLS models. I'll employ the `infer.ols` function for this purpose, allowing me to directly contrast the OLS estimates with the IV estimates for both specifications. This comparison is crucial for understanding the extent of any potential endogeneity bias that the instrumental variables approach is designed to address.

    Chamadas pedidas

    • infer.ols

      {
        "controls": [
          "exper",
          "expersq",
          "black",
          "smsa",
          "south"
        ],
        "dataset": "card",
        "se": "HC1",
        "x": [
          "educ"
        ],
        "y": "lwage"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
11. 10Ferramenta
    infer.olsv0.1.0call_1daabae1decidido pelo modeloreexecutável

    Motivo: I will run an OLS regression with the same baseline controls to provide the benchmark comparison between OLS and 2SLS.

    Argumentos

    {
      "cluster": null,
      "controls": [
        "exper",
        "expersq",
        "black",
        "smsa",
        "south"
      ],
      "dataset": "card",
      "fe": [],
      "intercept": true,
      "level": 0.95,
      "se": "HC1",
      "subset": null,
      "weights": null,
      "x": [
        "educ"
      ],
      "y": "lwage"
    }

    Figuras call_1daabae1

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.educ Coefficient on educ in the regression of lwage	0,074009	0.07400899420057862	0,003642030.003642033530508981	0,0668679 – 0,0811501

    Diagnósticos

    • n_obs = 3.0103010
    • k = 77
    • r2 = 0,2905050.290505451320644
    • df_resid = 3.0033003
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 4.871226268104078,
          "ci_low": 4.596102395509966,
          "coef": 4.733664331807022,
          "p": 0,
          "se": 0.07015766267685977,
          "t": 67.47180779966797,
          "term": "Intercept"
        },
        {
          "ci_high": 0.08115012697780932,
          "ci_low": 0.06686786142334791,
          "coef": 0.07400899420057862,
          "p": 4.0333778145199286e-86,
          "se": 0.003642033530508981,
          "t": 20.32078880675097,
          "term": "educ"
        },
        {
          "ci_high": 0.09679685534242152,
          "ci_low": 0.0703948230437394,
          "coef": 0.08359583919308046,
          "p": 1.4769273898337407e-34,
          "se": 0.006732621413508472,
          "t": 12.416536451218247,
          "term": "exper"
        },
        {
          "ci_high": -0.0016171419758476105,
          "ci_low": -0.0028646269122937864,
          "coef": -0.0022408844440706985,
          "p": 2.3017012515628646e-12,
          "se": 0.00031811353387996625,
          "t": -7.044291441294828,
          "term": "expersq"
        },
        {
          "ci_high": -0.15545081639852074,
          "ci_low": -0.2238122559889618,
          "coef": -0.18963153619374126,
          "p": 4.654385445952072e-27,
          "se": 0.017432434247413708,
          "t": -10.87808699016749,
          "term": "black"
        },
        {
          "ci_high": 0.19117759003500764,
          "ci_low": 0.13166832274200482,
          "coef": 0.16142295638850623,
          "p": 5.754419779377933e-26,
          "se": 0.015175095717880357,
          "t": 10.63736001337418,
          "term": "smsa"
        },
        {
          "ci_high": -0.09476245606908777,
          "ci_low": -0.15496057330216076,
          "coef": -0.12486151468562427,
          "p": 6.017891046127548e-16,
          "se": 0.015350755144576919,
          "t": -8.133900483047903,
          "term": "south"
        }
      ]
    }

    Digests dos dados

    card 4ec4da8d7939f11a46d67bd248416cc7330bd0dddaddcd6c49c9872c5a427413

    sha256 do resultado

    75230885bd059832a6c9c89610fdcce95fce07eb185474b784087ab85a0d26cb

    Resultado mostrado ao modelo
12. 11Turno do modelo
    call_ddd8ef4bgemini-3.8-flashFim: STOP6.411 ms20180 de entrada · 69 de saída · 215 de raciocínio · 15964 em cache

    Texto visível

    I will convert the estimated 2SLS coefficient from log points to a percentage effect on wages using core.scale_effect.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process Regarding the Return to Schooling Estimates** My initial observation concerns the estimated returns to schooling from two different estimation methods. Using Ordinary Least Squares (OLS), I found the return to schooling to be approximately 7.4% (a coefficient of 0.074009). This is a solid baseline, but my understanding of causal inference, particularly in this domain, suggests that OLS estimates are likely to be biased. My attention then turned to the Instrumental Variables (IV) approach, specifically using `nearc4` as an instrument. This yielded a significantly higher estimate for the return to schooling, around 13.2% (coefficient of 0.132289). Even with the inclusion of region controls, which is a good practice for addressing spatial heterogeneity, the estimate remained robustly higher, around 13.15% (coefficient of 0.131504). This divergence between OLS and IV is precisely what I would expect if unobserved factors correlated with both schooling and earnings are biasing the OLS results. However, I need to be precise in my interpretation and presentation of these coefficients. The outcome variable (likely earnings or wages) is specified in logarithms. This means the coefficients represent the percentage change in the outcome for a one-unit change in schooling. The standard interpretation of the OLS coefficient is already a percentage, but the IV coefficient, being larger and derived from a model that aims to capture a more causal effect, also needs to be presented clearly as a percentage. I recall a specific utility function, `core.scale_effect`, designed for precisely this type of conversion from log-point coefficients to percentage effects. The documentation for `instrumental-variables` explicitly states, "If the outcome is in logs, restate the coefficient as a percent with `core.scale_effect`, never by hand." This is a critical reminder to ensure consistency and accuracy in my reporting. Therefore, my next step is to apply `core.scale_effect` to both the OLS estimate and, more importantly, the IV estimates. The function `core__scale_effect` is structured to take a `coefficient` identifier and a `transform` argument. I will specify `transform: 'log_points_to_percent'` to correctly translate these log-point coefficients into interpretable percentage returns. This will allow me to present a more rigorous and accurately scaled comparison of the estimated returns to schooling under both OLS and the more robust IV framework.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_07648d37:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
13. 12Ferramenta
    core.scale_effectv0.1.0call_9880db37decidido pelo modeloreexecutável

    Motivo: I will convert the estimated 2SLS coefficient from log points to a percentage effect on wages using core.scale_effect.

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_07648d37:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_9880db37

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): 2SLS effect of educ on lwage	14,1438 %	14.143796459960642	—	3,77341 – 25,5505

    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

    63770ea417c482d4523f87e264f94593597549c7899711ceea3e092c14e070b0

    Resultado mostrado ao modelo
14. 13Turno do modelo
    call_a2dd0719gemini-3.8-flashFim: STOP5.060 ms20582 de entrada · 59 de saída · 20 de raciocínio · 15990 em cache

    Texto visível

    I will convert the OLS benchmark coefficient to a percentage effect using core.scale_effect.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Coefficient Conversion** Alright, so the immediate task at hand is to translate this Ordinary Least Squares (OLS) coefficient into a more interpretable metric: a percentage change. I know that a raw coefficient tells me the absolute change in the dependent variable for a one-unit change in the independent variable, but in many real-world applications, especially when dealing with variables that span a wide range or are inherently measured on a different scale, that absolute change isn't the most intuitive. This is precisely where the `core.scale_effect` function comes into play. I'm thinking about how this function is designed to handle that conversion. It's not just a simple division or multiplication; it needs to account for the inherent variability or scale of the variables involved to accurately represent the *proportional* impact. So, my thought is to leverage `core.scale_effect`. I'll need to ensure I'm feeding it the correct arguments. This will likely involve passing the estimated OLS coefficient itself, and critically, the relevant scaling factors for both the independent and dependent variables. The specific implementation will depend on the context of the data – for instance, if I'm dealing with log-transformed variables, the interpretation of "percent change" might shift slightly, but the principle of using `scale_effect` to get a relative magnitude remains. Ultimately, the goal here is clarity. I want to move beyond the raw numerical impact of a coefficient and articulate its significance in terms of percentage shifts. This makes the findings much more accessible and actionable for anyone reviewing the results, especially those who might not be steeped in the minutiae of OLS interpretation. The `core.scale_effect` function is my go-to tool for achieving this crucial step in making the model's outputs truly meaningful.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_1daabae1:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
15. 14Ferramenta
    core.scale_effectv0.1.0call_3de573a0decidido pelo modeloreexecutável

    Motivo: I will convert the OLS benchmark coefficient to a percentage effect using core.scale_effect.

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_1daabae1:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_3de573a0

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): Coefficient on educ in the regression of lwage	7,68165 %	7.681649055616758	—	6,91542 – 8,45337

    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

    91bb1a3baff9a6f4c53931c5c21afb4b29e4a44720349c8d7ed581ca3c4aa7ae

    Resultado mostrado ao modelo
16. 15Turno do modelo
    call_e6b09763gemini-3.8-flashFim: STOP3.369 ms20778 de entrada · 64 de saída · 42 de raciocínio · 19176 em cache

    Texto visível

    I will also convert the 2SLS coefficient from the specification with regional controls to a percentage effect.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process** I need to ensure that I can represent the educational coefficient, `call_62e2c716:coef.educ`, not just in its raw form but also as a percentage change. This is important because it might be useful for reporting or discussion to offer both interpretations of the coefficient's impact. Having it readily available as a percent change will facilitate this flexibility.

    Chamadas pedidas

    • core.scale_effect

      {
        "coefficient": "call_62e2c716:coef.educ",
        "transform": "log_points_to_percent"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
17. 16Ferramenta
    core.scale_effectv0.1.0call_9a47353bdecidido pelo modeloreexecutável

    Motivo: I will also convert the 2SLS coefficient from the specification with regional controls to a percentage effect.

    Argumentos

    {
      "baseline": null,
      "coefficient": "call_62e2c716:coef.educ",
      "sd": null,
      "transform": "log_points_to_percent"
    }

    Figuras call_9a47353b

    Chave	Valor	Valor bruto	Erro-padrão	IC
    effect Effect as a percent change (from log points): 2SLS effect of educ on lwage	14,0542 %	14.054228311327213	—	2,56652 – 26,8286

    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

    632d68f8eade66d0ddab39c15d287f91397557588ae7d2e6e8dd579a7abef4c5

    Resultado mostrado ao modelo
18. 17Turno do modelo
    call_a51f2c40gemini-3.8-flashFim: STOP28.711 ms21003 de entrada · 939 de saída · 2531 de raciocínio · 19171 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on the Causal Return to Schooling** I've been tasked with estimating the causal effect of an additional year of schooling on the log hourly wage for young men in the United States, using Card's sample from the National Longitudinal Survey of Young Men observed in 1976. The key challenge is to isolate a source of variation in schooling that isn't contaminated by unobserved ability or family background, which is where instrumental variables (IV) come into play. My initial step was to confirm the language of the user's request. It's in English. This is important because Rule 7 specifies how to format the output, including language and decimal notation. Although it mentions "(Portuguese: decimal comma)," the clarification seems to indicate that the language of the answer should match the language of the question. So, English it is, with standard English decimal formatting. Now, let's break down the requirements for the final answer: 1. **Numbers**: All numerical values must originate from tool calls (figures, standard errors, confidence intervals, diagnostics) or the original question. No independent calculations. 2. **Figure References**: Any figure I quote needs to be listed in `figure_refs` as `'<call_id>:<key>'`. 3. **Caveats**: Any diagnostics that limit the conclusion must be placed in `caveats`. 4. **Key Results**: I need to present the core findings: the estimate, its uncertainty, the identification strategy, and potential limitations. **Thinking about the Identification Strategy:** The OLS (Ordinary Least Squares) approach would likely suffer from omitted variable bias. Individuals who choose to pursue more education might also possess higher innate ability, stronger motivation, or benefit from more supportive family backgrounds – factors that also directly influence earnings. Therefore, a simple OLS estimate of the education return could be inflated. The instrumental variable strategy uses `nearc4`, a measure of whether an individual grew up near a four-year college in 1966, as the instrument for `educ` (years of schooling). The logic is that geographic proximity to a college lowers the cost of attendance (e.g., by allowing students to live at home), potentially influencing the schooling decisions of those on the margin of attending college. **Examining the Tool Outputs:** I've reviewed the results from the various tool calls. * **Baseline 2SLS Estimate**: * The instrumental variable approach (2SLS) yields a coefficient of `0.132289` for `educ` (`call_07648d37:coef.educ`). This translates to a substantial causal return. * The standard error for this estimate is `0.0485779`. * The 95% confidence interval for the coefficient is `[0.0370396, 0.227538]`. * When converted to a percentage effect on hourly wages, the 2SLS estimate suggests an increase of `14.1438%` per year of schooling (`call_9880db37:effect`), with a 95% confidence interval of `[3.77341, 25.5505]%`. This is a significant and economically meaningful return. * The first-stage F-statistic for the instrument `nearc4` on `educ` is `17.5133` (`first_stage_F.educ`), which is well above the common threshold of 10, indicating that the instrument is relevant. The first-stage coefficient on `nearc4` is `0.337321` (SE: `0.0806044`). * The number of observations used in this baseline model is `3010`. * **Extended 2SLS Estimate (with controls)**: * When I include regional and 1966 residence controls, the 2SLS coefficient (`call_62e2c716:coef.educ`) is `0.131504`, with a standard error of `0.0541436`. * The percentage effect (`call_9a47353b:effect`) is `14.0542%`, with a 95% CI of `[2.56652, 26.8286]%`. This is very close to the baseline 2SLS estimate, suggesting the controls don't dramatically alter the core finding. * The first-stage F-statistic in this extended model is `14.1387`, still indicating relevance. * **OLS Benchmark**: * For comparison, the OLS estimate for `educ` is `0.074009` (`call_1daabae1:coef.educ`), with a standard error of `0.00364203`. * This translates to a percentage effect of `7.68165%` (`call_3de573a0:effect`), with a 95% CI of `[6.91542, 8.45337]%`. * The OLS estimate is considerably smaller than the 2SLS estimate. **Interpreting the Results and Potential Violations:** The stark difference between the 2SLS and OLS estimates suggests that omitted variables, likely related to ability or background, are indeed biasing the OLS estimate downwards. The higher 2SLS estimate points to a larger causal return. Card's interpretation, which I find compelling, is that the IV estimate captures the Local Average Treatment Effect (LATE). The instrument `nearc4` only affects those individuals on the margin of college attendance. These individuals, often from less privileged backgrounds or facing higher borrowing costs, might experience higher marginal returns to education compared to the average individual in the sample. Thus, the estimated return of ~14% might be specific to this group of "compliers." However, I must acknowledge the potential limitations and assumptions of this IV approach: 1. **Exclusion Restriction**: The core assumption is that growing up near a college affects adult wages *only* through its effect on schooling. If college proximity also correlates with other unobserved local labor market advantages (e.g., better job networks, higher prevailing wages) or unobserved family advantages (e.g., inherited ambition or wealth), then the instrument is not valid, and the 2SLS estimate could be biased. 2. **Endogeneity of Experience**: The variable for potential experience is constructed as `age - educ - 6`. This means that experience is *mechanically* correlated with schooling, which could introduce complications in models that don't fully account for this. 3. **LATE Specificity**: As mentioned, the estimated return of ~14% is a LATE for compliers. It's not necessarily the average causal effect for all young men in the United States. The return for individuals who would have attended college regardless of proximity might be different. With these points in mind, I am ready to formulate the final answer according to Rule 7. * The 2SLS estimate of the causal return to a year of schooling for young men in the United States is `0.132289` log hourly wage points, equivalent to `14.1438%` (`call_07648d37:coef.educ`, `call_9880db37:effect`). * The design identifies this effect using proximity to a four-year college in 1966 (`nearc4`) as an instrumental variable for years of schooling (`educ`), leveraging the National Longitudinal Survey of Young Men (Card's sample). The first-stage F-statistic of `17.5133` (`first_stage_F.educ`) supports the instrument's relevance. * Potential limitations that could undermine the conclusion include: * The exclusion restriction, which assumes college proximity affects wages solely through schooling; if it also correlates with local labor market advantages or family unobservables, the estimate may be biased. * The mechanical relationship between potential experience (`exper`) and schooling (`educ`) in the construction of `exper`. * The fact that the estimate represents a Local Average Treatment Effect (LATE) for individuals whose schooling decisions were influenced by the presence of a local college (compliers), not necessarily the average effect for the entire population. submit_answer

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "To address ability bias and unobserved family background in the returns to schooling, we use proximity to a four-year college in 1966 (`nearc4`) as an instrumental variable for completed education (`educ`), following Card (1995).\n\n### Identification Strategy and First Stage\nCollege proximity reduces the direct and indirect costs of higher education (such as room and board), inducing young men on the margin of attending college to accumulate more schooling. In the first-stage regression (controlling for potential experience, experience squared, race, and metropolitan and southern residence):\n- Living near a 4-year college increases completed schooling by 0.337321 years (standard error: 0.0806044, t = 4.18489).\n- The first-stage Wald F-statistic is 17.5133160968858, well above the conventional threshold of ten, indicating that the instrument is strong.\n\n### Causal Return to Schooling (2SLS vs. OLS)\n- **2SLS Estimate (Baseline)**: The estimated return to an additional year of schooling is 0.132289 log points (standard error: 0.0485779; 95% CI: [0.0370396, 0.227538]). Transformed from log points to a percentage change using `core.scale_effect`, this corresponds to an estimated wage increase of 14.1438% per year of education (95% CI: [3.77341, 25.5505]%).\n- **2SLS Estimate with Region Controls**: When additionally controlling for 1966 SMSA residence and region of residence in 1966 (`reg661`–`reg668`), the 2SLS return is 0.131504 log points (standard error: 0.0541436; 95% CI: [0.0253414, 0.237666]), equivalent to a 14.0542% wage increase (95% CI: [2.56652, 26.8286]%), with a first-stage F-statistic of 14.138670079757.\n- **OLS Benchmark**: An ordinary least squares regression yields a return of 0.074009 log points (standard error: 0.00364203; 95% CI: [0.0668679, 0.0811501]), or 7.68165% (95% CI: [6.91542, 8.45337]%).\n\n### Interpretation\nThe IV estimate (~14.1%) is substantially larger than the OLS estimate (~7.7%). Under the LATE framework, this occurs because college proximity identifies the return to schooling specifically for \"compliers\"—disadvantaged youth who face financial or credit constraints and whose educational choices are sensitive to the local presence of a college, and who often have higher marginal returns to schooling than the average student.",
        "caveats": [
          "Exclusion restriction: growing up near a college may correlate with local economic dynamism, urban labor market amenities, or unobserved family background, which could directly affect wages.",
          "Experience endogeneity: potential experience is calculated as age - educ - 6, creating a mechanical correlation with the endogenous schooling variable.",
          "LATE vs. ATE: the 2SLS estimate reflects a local average treatment effect for compliers rather than the average return across the entire population."
        ],
        "figure_refs": [
          "call_07648d37:coef.educ",
          "call_9880db37:effect",
          "call_1daabae1:coef.educ",
          "call_3de573a0:effect",
          "call_62e2c716:coef.educ",
          "call_9a47353b:effect"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
19. 18Guarda
    resposta aceita

    Números encontrados

    1966 · 1995 · 4 · 0.337321 · 0.0806044 · 4.18489 · 17.5133160968858 · 0.132289 · 0.0485779 · 95% · 0.0370396 · 0.227538 · 14.1438% · 95% · 3.77341 · 25.5505 · 1966 · 1966 · 0.131504 · 0.0541436 · 95% · 0.0253414 · 0.237666 · 14.0542% · 95% · 2.56652 · 26.8286 · 14.138670079757 · 0.074009 · 0.00364203 · 95% · 0.0668679 · 0.0811501 · 7.68165% · 95% · 6.91542 · 8.45337 · 14.1% · 7.7% · 6

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    1 nova(s) tentativa(s) restante(s)
20. 19Resposta

    To address ability bias and unobserved family background in the returns to schooling, we use proximity to a four-year college in 1966 (`nearc4`) as an instrumental variable for completed education (`educ`), following Card (1995). ### Identification Strategy and First Stage College proximity reduces the direct and indirect costs of higher education (such as room and board), inducing young men on the margin of attending college to accumulate more schooling. In the first-stage regression (controlling for potential experience, experience squared, race, and metropolitan and southern residence): - Living near a 4-year college increases completed schooling by 0.337321 years (standard error: 0.0806044, t = 4.18489). - The first-stage Wald F-statistic is 17.5133160968858, well above the conventional threshold of ten, indicating that the instrument is strong. ### Causal Return to Schooling (2SLS vs. OLS) - **2SLS Estimate (Baseline)**: The estimated return to an additional year of schooling is 0.132289 log points (standard error: 0.0485779; 95% CI: [0.0370396, 0.227538]). Transformed from log points to a percentage change using `core.scale_effect`, this corresponds to an estimated wage increase of 14.1438% per year of education (95% CI: [3.77341, 25.5505]%). - **2SLS Estimate with Region Controls**: When additionally controlling for 1966 SMSA residence and region of residence in 1966 (`reg661`–`reg668`), the 2SLS return is 0.131504 log points (standard error: 0.0541436; 95% CI: [0.0253414, 0.237666]), equivalent to a 14.0542% wage increase (95% CI: [2.56652, 26.8286]%), with a first-stage F-statistic of 14.138670079757. - **OLS Benchmark**: An ordinary least squares regression yields a return of 0.074009 log points (standard error: 0.00364203; 95% CI: [0.0668679, 0.0811501]), or 7.68165% (95% CI: [6.91542, 8.45337]%). ### Interpretation The IV estimate (~14.1%) is substantially larger than the OLS estimate (~7.7%). Under the LATE framework, this occurs because college proximity identifies the return to schooling specifically for "compliers"—disadvantaged youth who face financial or credit constraints and whose educational choices are sensitive to the local presence of a college, and who often have higher marginal returns to schooling than the average student. Ressalvas: Exclusion restriction: growing up near a college may correlate with local economic dynamism, urban labor market amenities, or unobserved family background, which could directly affect wages. Experience endogeneity: potential experience is calculated as age - educ - 6, creating a mechanical correlation with the endogenous schooling variable. LATE vs. ATE: the 2SLS estimate reflects a local average treatment effect for compliers rather than the average return across the entire population.

    • Exclusion restriction: growing up near a college may correlate with local economic dynamism, urban labor market amenities, or unobserved family background, which could directly affect wages.
    • Experience endogeneity: potential experience is calculated as age - educ - 6, creating a mechanical correlation with the endogenous schooling variable.
    • LATE vs. ATE: the 2SLS estimate reflects a local average treatment effect for compliers rather than the average return across the entire population.

    Figuras citadas: call_07648d37:coef.educ, call_9880db37:effect, call_1daabae1:coef.educ, call_3de573a0:effect, call_62e2c716:coef.educ, call_9a47353b:effect · Parada: answered

    Figura da resposta: call_07648d37:coef.educ = 0,1322890.13228884000030414 (se 0,04857790.04857786029781447)
21. 20Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
22. 21Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_07648d37:coef.educ (infer.iv_2sls)
23. 22Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
24. 23Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lwage'
25. 24Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog[0] = 'educ'
26. 25Pontuação
    #5argumento igualpassouregistradainfer.iv_2sls.y = 'lwage'
27. 26Pontuação
    #6argumento igualpassouregistradainfer.iv_2sls.endog = ['educ']
28. 27Pontuação
    #7argumento igualpassouregistradainfer.iv_2sls.instruments = ['nearc4']
29. 28Pontuação
    #8argumento igualfalhouregistradainfer.iv_2sls.exog = ['exper', 'expersq', 'black', 'smsa', 'south']
30. 29Pontuação
    #9diagnósticopassouregistrada3010 vs 3010
31. 30Pontuação
    #10figura da resposta próximafalhouregistrada0.13228884 vs 0.13150383624451933
32. 31Pontuação
    #11figura da resposta próximafalhouregistrada0.0485778603 vs 0.054963672601153514
33. 32Pontuação
    #12figura da resposta próximapassouregistrada0.13228884 vs 0.132
34. 33Pontuação
    #13figura da resposta próximafalhouregistrada0.0485778603 vs 0.055

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