Tarefa paper_repro.ajr_2001.tab4_pa_c1.agent

Veredito

Pergunta feita ao analista

Acemoglu, Johnson and Robinson (2001), 'The Colonial Origins of Comparative Development', Table 4, Panel A, column (1): in the paper's base sample of former colonies, estimate by two-stage least squares the effect of average protection against expropriation risk over 1985-1995 on log GDP per capita in 1995 (PPP basis), instrumenting protection against expropriation risk with log European settler mortality and with no other regressors. Report the coefficient on average protection against expropriation risk.

Como o agente resolveu e como foi validado

Resumo passo a passo do que o agente executou, por que o caminho está correto e como cada verificação conferiu o resultado.

1. 1Preparação da base de dados
   maketable4— The authors' replication file for Table 4 of Acemoglu, Johnson and Robinson (2001), 'The Colonial Origins of Comparative Development': one row per country (163 rows). Columns: shortnam, the 3-letter country code; africa, 1 for countries in Africa; asia, 1 for countries in Asia; rich4, 1 for the four 'neo-Europes' (United States, Canada, Australia, New Zealand); lat_abst, absolute latitude of the capital divided by 90; avexpr, average protection against expropriation risk over 1985-1995 (Political Risk Services, 0 to 10, higher means more protection); logpgp95, log GDP per capita in 1995, PPP basis (World Bank); logem4, log settler mortality (mortality of European settlers); loghjypl, log output per worker in 1988 (Hall and Jones); baseco, 1 for the former colonies in the paper's base sample and missing for every other country.
2. 2Chamada intermediária de ferramentadata.describe(Inspeção descritiva das colunas e estatísticas da base)

   Ver chamada call_8f0e8396 nos detalhes

   I will describe the variables in the Acemoglu, Johnson and Robinson (2001) dataset to verify the sample and variable definitions.

   Argumentos principais

   columns:

   ["shortnam","baseco","logpgp95","avexpr","logem4"]

   dataset:

   "maketable4"

   Resultado calculado

   • n_rows = 163rows 163
     Rows in the dataset
3. 3Chamada que gerou a resposta finalinfer.iv_2sls(Variáveis instrumentais por mínimos quadrados em dois estágios (MQ2E))citada na respostacoincide com a referência

   Ver chamada call_debb9458 nos detalhes

   I will estimate the 2SLS model of log GDP per capita on average protection against expropriation risk instrumented by log European settler mortality for the base sample of former colonies using classical standard errors.

   Por que este é o caminho de referência: Table 4, Panel A, column (1): 2SLS of log GDP per capita on expropriation risk, instrumented by log settler mortality, in the base sample (the authors' maketable4.do: ivreg, classical errors).
   Argumentos principais

   dataset:

   "maketable4"

   endog:

   ["avexpr"]

   instruments:

   ["logem4"]

   level:

   0,950.95

   se:

   "classical"

   subset:

   "baseco == 1"

   y:

   "logpgp95"

   Resultado calculado

   • coef.avexpr = 0,944279 0.9442793851547994
     2SLS effect of avexpr on logpgp95
   Diagnósticos: first_stage_F.avexpr = 22,946822.94679658705377 (Wald F of the excluded instruments in the first stage for avexpr (classical (homoskedastic) standard errors)) · partial_r2.avexpr = 0,2701310.2701313941078145 (share of the variation the instruments explain beyond the controls) · weak_instrument = false (every first-stage F is at least 10) · n_obs = 6464 · se_type = "classical" (classical (homoskedastic) standard errors)
4. 4Chamada intermediária de ferramentainfer.iv_2sls(Variáveis instrumentais por mínimos quadrados em dois estágios (MQ2E))

   Ver chamada call_98c9510d nos detalhes

   I will also run the same specification with HC1 robust standard errors to observe any differences in standard error estimates.

   Argumentos principais

   dataset:

   "maketable4"

   endog:

   ["avexpr"]

   instruments:

   ["logem4"]

   level:

   0,950.95

   se:

   "HC1"

   subset:

   "baseco == 1"

   y:

   "logpgp95"

   Resultado calculado

   • coef.avexpr = 0,944279 0.9442793851547994
     2SLS effect of avexpr on logpgp95
   Diagnósticos: first_stage_F.avexpr = 16,320616.32061844215525 (Wald F of the excluded instruments in the first stage for avexpr (heteroskedasticity-robust standard errors (HC1))) · partial_r2.avexpr = 0,2701310.2701313941078145 (share of the variation the instruments explain beyond the controls) · weak_instrument = false (every first-stage F is at least 10) · n_obs = 6464 · se_type = "HC1" (heteroskedasticity-robust standard errors (HC1))
5. 5Conferência de lastro e resposta final

   Todos os 19 números escritos na resposta foram conferidos contra as ferramentas e o enunciado (nenhum número sem lastro).

   Números encontrados: 64 · 4 · 1 · 2001 · 1995 · 0.944279 · 0.156525 · 95% · 0.631389 · 1.25717 · 0.178914 · 95% · 0.586636 · 1.30192 · -0.606778 · 22.946797 · 16.320618 · 64 · 1
   Figuras citadas: call_debb9458:coef.avexpr, call_98c9510d:coef.avexpr
   • ✓
     #0resposta com lastro

     Garante que todo número citado no texto veio de uma ferramenta ou do enunciado (sem cálculo mental do modelo).
   • ✓
     #1figura da resposta escolhida

     an answer figure: the effect of an estimator call the answer cites
   • ✓
     #2ferramenta chamadainfer.iv_2sls

     Exige que o resultado venha da ferramenta infer.iv_2sls.
   • ✓
     #3argumento igualy

     outcome: log GDP per capita, 1995
   • ✓
     #4argumento igualendog

     the endogenous regressor: protection against expropriation
   • ✓
     #5argumento igualinstruments

     the instrument: log settler mortality
   • ✓
     #6argumento igualexog

     column (1) has no other regressors
   • ✓
     #7diagnósticon_obs

     Confere o diagnóstico "n_obs" reportado pela ferramenta.
   • ✓
     #8figura da resposta próxima

     software reference
   • ✓
     #9figura da resposta próxima

     software reference, SE: recorded, not required (the question does not state the convention)
   • ✓
     #10figura da resposta próxima

     published cell: recorded, never required on T2/T3
   • ✓
     #11figura da resposta próxima

     published cell, SE: recorded, never required on T2/T3

Valores esperados e de onde vêm

Verificações

Caminho de referência e caminho do agente

A chamada de referência ao lado da chamada que deu a resposta, argumento por argumento.

Trajetória

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

1. 0Início

   Acemoglu, Johnson and Robinson (2001), 'The Colonial Origins of Comparative Development', Table 4, Panel A, column (1): in the paper's base sample of former colonies, estimate by two-stage least squares the effect of average protection against expropriation risk over 1985-1995 on log GDP per capita in 1995 (PPP basis), instrumenting protection against expropriation risk with log European settler mortality and with no other regressors. Report the coefficient on average protection against expropriation risk.

   maketable4 (agent)

   The authors' replication file for Table 4 of Acemoglu, Johnson and Robinson (2001), 'The Colonial Origins of Comparative Development': one row per country (163 rows). Columns: shortnam, the 3-letter country code; africa, 1 for countries in Africa; asia, 1 for countries in Asia; rich4, 1 for the four 'neo-Europes' (United States, Canada, Australia, New Zealand); lat_abst, absolute latitude of the capital divided by 90; avexpr, average protection against expropriation risk over 1985-1995 (Political Risk Services, 0 to 10, higher means more protection); logpgp95, log GDP per capita in 1995, PPP basis (World Bank); logem4, log settler mortality (mortality of European settlers); loghjypl, log output per worker in 1988 (Hall and Jones); baseco, 1 for the former colonies in the paper's base sample and missing for every other country.

   file cd3a1cb197e3065411fce6fabbe06161555468049e6810a28c608d6e361aed34 · frame —
2. 1Turno do modelo
   call_47e5c3a1gemini-3.8-flashFim: STOP8.325 ms14441 de entrada · 79 de saída · 424 de raciocínio · 0 em cache

   Texto visível

   I will describe the variables in the Acemoglu, Johnson and Robinson (2001) dataset to verify the sample and variable definitions.

   Resumo do raciocínio, como declarado pelo modelo

   **Replicating AJR (2001) Table 4, Panel A, Column (1): My Thought Process** Okay, my primary objective here is to meticulously reproduce a specific result from a seminal paper: Acemoglu, Johnson, and Robinson's (2001) "The Colonial Origins of Comparative Development," specifically Table 4, Panel A, column (1). I know this requires a particular dataset, the `maketable4` dataset. My starting point, the base sample, needs to be restricted to observations where `baseco` equals 1. The outcome variable I'm interested in is `logpgp95`, which represents the log of GDP per capita in 1995, adjusted for purchasing power parity. The key endogenous regressor I'll be using is `avexpr`, representing the average protection against expropriation risk from 1985 to 1995. Crucially, for my instrumental variable (IV) estimation, the instrument I'll employ is `logem4`, the log of European settler mortality. The instructions are clear: no other regressors or control variables are to be included in this specific estimation. This means the model should be a clean, direct test of the relationship between expropriation risk and development, using settler mortality as the instrument. Therefore, the appropriate method for this analysis is two-stage least squares (2SLS). I need to locate the function within the `infer` library that handles instrumental variables estimation. I'm thinking it will be something like `infer.iv_2sls` or perhaps a broader `instrumental-variables` skill. Now, let's look at the specific arguments for `infer__iv_2sls`. I'll need to pass the `dataset` name, which is 'maketable4'. For the dependent variable (`y`), I'll specify 'logpgp95'. The endogenous regressor (`endog`) will be a list containing 'avexpr'. The `instruments` will similarly be a list containing 'logem4'. For the exogenous regressors (`exog`), the prompt explicitly states "No other regressors / controls," so this argument should either be an empty list or omitted, assuming the default behavior handles this correctly. I'll need to confirm the schema for `exog` to be sure, but it's generally expected to be an optional parameter or accept an empty list. The `subset` condition is straightforward: 'baseco == 1'. Now, a critical point arises regarding standard errors. The prompt mentions checking `se`: 'classical' or 'HC1'? I need to consider what Acemoglu, Johnson, and Robinson (2001) used in their original table. Typically, econometricians in leading journals around that time would use classical standard errors, or sometimes robust errors, but the default in many statistical packages is often robust. I'll need to check the default `se` option for `infer__iv_2sls` (which seems to be 'HC1') and see if 'classical' is an available option. My goal is to match the original publication, so if they reported classical, I must use that. If the function only outputs HC1 by default, I'll need to investigate if classical is an alternative or if I need to adjust something downstream. Before I jump into executing the command, I should probably either load the `instrumental-variables` skill explicitly or call `data.describe` to get a feel for the data, or I can just directly call `iv_2sls` if I'm confident in the function signature and its availability. My immediate next step is to confirm the standard error option and then proceed with the function call.

   Chamadas pedidas

   • data.describe

     {
       "columns": [
         "shortnam",
         "baseco",
         "logpgp95",
         "avexpr",
         "logem4"
       ],
       "dataset": "maketable4"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
3. 2Ferramenta
   data.describe— Inspeção descritiva das colunas e estatísticas da basev0.1.0call_8f0e8396decidido pelo modeloreexecutável

   Motivo: I will describe the variables in the Acemoglu, Johnson and Robinson (2001) dataset to verify the sample and variable definitions.

   Argumentos

   {
     "columns": [
       "shortnam",
       "baseco",
       "logpgp95",
       "avexpr",
       "logem4"
     ],
     "dataset": "maketable4"
   }

   Figuras call_8f0e8396

   Chave	Valor	Valor bruto	Erro-padrão	IC
   n_rows Rows in the dataset	163rows	163	—	—

   Tabelas (1)

   {
     "columns": [
       {
         "column": "shortnam",
         "dtype": "str",
         "n_missing": 0,
         "n_unique": 163
       },
       {
         "column": "baseco",
         "dtype": "float32",
         "max": 1,
         "mean": 1,
         "min": 1,
         "n_missing": 99,
         "n_unique": 1,
         "sd": 0
       },
       {
         "column": "logpgp95",
         "dtype": "float32",
         "max": 10.288749694824219,
         "mean": 8.30250908233024,
         "min": 6.10924768447876,
         "n_missing": 15,
         "n_unique": 138,
         "sd": 1.1053422036053233
       },
       {
         "column": "avexpr",
         "dtype": "float32",
         "max": 10,
         "mean": 7.06649138021075,
         "min": 1.6363636255264282,
         "n_missing": 42,
         "n_unique": 80,
         "sd": 1.804286796987983
       },
       {
         "column": "logem4",
         "dtype": "float32",
         "max": 7.9861650466918945,
         "mean": 4.595983834102236,
         "min": 0.9360933303833008,
         "n_missing": 76,
         "n_unique": 44,
         "sd": 1.3033334764007718
       }
     ]
   }

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   maketable4 dc8a5df19428e33e3bb4109922ccbd092a69bde0d19a217451baa154782debfc

   sha256 do resultado

   b101e1db07480e36916c13a6a76d7d3f811a105a29cab4e94050f7b24a471a6a

   Resultado mostrado ao modelo
4. 3Turno do modelo
   call_7ae96ef6gemini-3.8-flashFim: STOP4.147 ms15154 de entrada · 34 de saída · 12 de raciocínio · 0 em cache

   Texto visível

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

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Investigating the `instrumental-variables` Skill** Alright, so my immediate task is to evaluate the `instrumental-variables` skill. My first instinct is to delve into its core functionality and understand precisely *what* it's designed to do. I need to ascertain its purpose within the broader analytical toolkit I'm working with. Is it intended for causal inference, for instance, or perhaps for addressing endogeneity in a specific modeling context? Following that, I'll be scrutinizing the underlying methodology. Given my expertise, I'll be looking for robustness in the statistical techniques employed. This means understanding the specific algorithms or estimation methods it utilizes for identifying and estimating instrumental variables. I'll be curious about the assumptions it makes – for example, about the validity and strength of the instruments, and how it handles potential violations of these assumptions. Are there checks for exogeneity and relevance of the proposed instruments built in? Furthermore, I'll be assessing its practical application and implementation. How does one actually *use* this skill? What are the typical inputs and outputs? What kind of data does it expect? Are there clear guidelines or examples for integrating it into a workflow? I'll be looking for a straightforward and intuitive interface, assuming that the developers have considered usability for someone like me who needs to move efficiently from conceptualization to execution. Finally, I'll be considering its limitations and potential pitfalls. No analytical tool is perfect, and I need to understand where this `instrumental-variables` skill might fall short or what common mistakes users might make. Are there specific scenarios where it's not recommended, or where its results might be misleading? Understanding these boundaries is crucial for maintaining the integrity of my analysis. In essence, I'm performing a comprehensive due diligence on this skill, ensuring it meets my rigorous standards before I fully integrate it into my analytical repertoire.

   Chamadas pedidas

   • load_skill (meta-ferramenta)

     {
       "name": "instrumental-variables"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
5. 4Habilidade
   instrumental-variablesTexto da habilidade
6. 5Turno do modelo
   call_cf92bebfgemini-3.8-flashFim: STOP6.009 ms15668 de entrada · 105 de saída · 219 de raciocínio · 12626 em cache

   Texto visível

   I will estimate the 2SLS model of log GDP per capita on average protection against expropriation risk instrumented by log European settler mortality for the base sample of former colonies using classical standard errors.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Replicating AJR (2001), Table 4** Alright, I'm diving into this replication task, focusing specifically on the `infer__iv_2sls` function and its application to `maketable4`. My immediate goal is to reproduce the results presented in Table 4 of the AJR (2001) paper. I've identified the key parameters for the `infer__iv_2sls` call: * `maketable4` as the dataset. * `y='logpgp95'` as my dependent variable, representing log GDP per capita in 1995. * `endog=['avexpr']`, the endogenous variable, which is average protection against expropriation risk. * `instruments=['logem4']`, the instrument for `avexpr`. * `subset='baseco == 1'`, indicating I should only consider observations where `baseco` equals 1. Now, a critical point arises: the standard errors. I need to determine whether the standard errors reported in AJR (2001), specifically in Table 4, are `classical` or `HC1` (heteroskedasticity-consistent). The paper itself might be slightly ambiguous, or I might have a hunch that robustness is usually preferred in such analyses. To be thorough, I'm considering the need to run the estimation with *both* `se='classical'` and `se='HC1'` (or relying on the default if it happens to be HC1) to see which aligns with the reported numbers. Looking at AJR (2001) Table 4, Panel A, Column (1) is my target. It uses `logpgp95` as the dependent variable. The coefficient on `avexpr` is reported as 0.94. The question is, what are the standard errors? I see a parenthetical value, which could be either 0.16 (if `classical`) or 0.22 (if `HC1`). To resolve this, I'll need to run the regression with both options and compare. My initial inclination is to try the `classical` or default `HC1` first, as these are common starting points for robust standard error estimation. The ultimate goal is to match those reported standard errors to ensure the replication is accurate.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "maketable4",
       "endog": [
         "avexpr"
       ],
       "instruments": [
         "logem4"
       ],
       "se": "classical",
       "subset": "baseco == 1",
       "y": "logpgp95"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
7. 6Ferramenta
   infer.iv_2sls— Variáveis instrumentais por mínimos quadrados em dois estágios (MQ2E)v0.1.0call_debb9458decidido pelo modeloreexecutável

   Motivo: I will estimate the 2SLS model of log GDP per capita on average protection against expropriation risk instrumented by log European settler mortality for the base sample of former colonies using classical standard errors.

   Argumentos

   {
     "cluster": null,
     "dataset": "maketable4",
     "endog": [
       "avexpr"
     ],
     "exog": [],
     "instruments": [
       "logem4"
     ],
     "level": 0.95,
     "se": "classical",
     "subset": "baseco == 1",
     "y": "logpgp95"
   }

   Figuras call_debb9458

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.avexpr 2SLS effect of avexpr on logpgp95	0,944279	0.9442793851547994	0,1565250.15652545732957907	0,631389 – 1,25717

   Diagnósticos

   • first_stage_F.avexpr = 22,946822.94679658705377 (Wald F of the excluded instruments in the first stage for avexpr (classical (homoskedastic) standard errors))
   • partial_r2.avexpr = 0,2701310.2701313941078145 (share of the variation the instruments explain beyond the controls)
   • weak_instrument = false (every first-stage F is at least 10)
   • n_obs = 6464
   • se_type = "classical" (classical (homoskedastic) standard errors)
   • n_clusters = — (errors not clustered)

   Derivação matemática e pressupostos

   coef.avexpr

   1. Com um instrumento e um regressor endógeno, o MQ2E é a razão entre o coeficiente de logem4 na forma reduzida (logpgp95 sobre logem4) e no primeiro estágio (avexpr sobre logem4).β = ρ / π→ 0,944279 (0.9442793851547994)
   2. Erro-padrão clássico (homocedástico): a raiz da variância estimada do coeficiente.ep = √V_jj→ 0,156525 (0.15652545732957907)
   3. Intervalo de 95% de confiança: a estimativa mais ou menos o valor crítico da distribuição t de Student com 62 graus de liberdade vezes o erro-padrão.IC = β ± c · ep

   Pressupostos do estimador

   • the instruments affect the outcome only through the endogenous regressors (exclusion restriction)
   • the instruments are as good as randomly assigned given the controls
   • errors are independent and have the same variance for every observation

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 3.9620651347598503,
         "ci_low": -0.1427320536663681,
         "coef": 1.909666540546741,
         "p": 0.0676371961257388,
         "se": 1.0267272828674519,
         "t": 1.8599549972154334,
         "term": "Intercept"
       },
       {
         "ci_high": 1.2571693160472515,
         "ci_low": 0.6313894542623473,
         "coef": 0.9442793851547994,
         "p": 9.798644711494112e-8,
         "se": 0.15652545732957907,
         "t": 6.032752762807972,
         "term": "avexpr"
       }
     ],
     "first_stage": [
       {
         "ci_high": -0.3535713248767556,
         "ci_low": -0.8599851727910319,
         "coef": -0.6067782488338938,
         "endog": "avexpr",
         "instrument": "logem4",
         "p": 0.000010765461520046432,
         "se": 0.12666860022743895,
         "t": -4.79028147263329
       }
     ],
     "reduced_form": [
       {
         "ci_high": -0.4207319879491951,
         "ci_low": -0.7252043955191552,
         "coef": -0.5729681917341751,
         "instrument": "logem4",
         "p": 2.6586798876505685e-10,
         "se": 0.07615726511746891,
         "t": -7.523486969370543
       }
     ]
   }

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   maketable4 dc8a5df19428e33e3bb4109922ccbd092a69bde0d19a217451baa154782debfc

   sha256 do resultado

   4e2ab856b85a916584c8c569ce7cabcf2ff7687f69f9c1dc2ec9132030ed0be4

   Resultado mostrado ao modelo
8. 7Turno do modelo
   call_969e43cdgemini-3.8-flashFim: STOP4.812 ms16467 de entrada · 88 de saída · 75 de raciocínio · 12646 em cache

   Texto visível

   I will also run the same specification with HC1 robust standard errors to observe any differences in standard error estimates.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process:** Well, this is interesting. I've just run a calculation and the resulting coefficient is 0.944279, with a standard error of 0.156525. Immediately, this strikes me as remarkably close to a specific figure I recall seeing elsewhere. My mind immediately goes to Table 4, Panel A, column (1) of the AJR (2001) paper. I'm seeing a coefficient of *exactly* 0.94 (with a standard error of 0.16) reported there. The alignment is so precise, it’s quite striking and definitely warrants further attention. Given this strong initial correspondence, I want to be thorough. While the current calculation might be using a standard error estimation method, I think it's prudent to also check what the results look like if I were to employ a different approach. Specifically, I want to see what the Heteroskedasticity Consistent (HC1) standard errors would yield. This is just a precautionary step, a sort of double-check, to ensure that the robustness of my findings isn't unduly influenced by the specific error estimation method I've chosen for the initial run. It’s about ensuring that my conclusions hold up even under slightly different assumptions about the data's variance.

   Chamadas pedidas

   • infer.iv_2sls

     {
       "dataset": "maketable4",
       "endog": [
         "avexpr"
       ],
       "instruments": [
         "logem4"
       ],
       "se": "HC1",
       "subset": "baseco == 1",
       "y": "logpgp95"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
9. 8Ferramenta
   infer.iv_2sls— Variáveis instrumentais por mínimos quadrados em dois estágios (MQ2E)v0.1.0call_98c9510ddecidido pelo modeloreexecutável

   Motivo: I will also run the same specification with HC1 robust standard errors to observe any differences in standard error estimates.

   Argumentos

   {
     "cluster": null,
     "dataset": "maketable4",
     "endog": [
       "avexpr"
     ],
     "exog": [],
     "instruments": [
       "logem4"
     ],
     "level": 0.95,
     "se": "HC1",
     "subset": "baseco == 1",
     "y": "logpgp95"
   }

   Figuras call_98c9510d

   Chave	Valor	Valor bruto	Erro-padrão	IC
   coef.avexpr 2SLS effect of avexpr on logpgp95	0,944279	0.9442793851547994	0,1789140.17891351798924446	0,586636 – 1,30192

   Diagnósticos

   • first_stage_F.avexpr = 16,320616.32061844215525 (Wald F of the excluded instruments in the first stage for avexpr (heteroskedasticity-robust standard errors (HC1)))
   • partial_r2.avexpr = 0,2701310.2701313941078145 (share of the variation the instruments explain beyond the controls)
   • weak_instrument = false (every first-stage F is at least 10)
   • n_obs = 6464
   • se_type = "HC1" (heteroskedasticity-robust standard errors (HC1))
   • n_clusters = — (errors not clustered)

   Derivação matemática e pressupostos

   coef.avexpr

   1. Com um instrumento e um regressor endógeno, o MQ2E é a razão entre o coeficiente de logem4 na forma reduzida (logpgp95 sobre logem4) e no primeiro estágio (avexpr sobre logem4).β = ρ / π→ 0,944279 (0.9442793851547994)
   2. Erro-padrão robusto à heterocedasticidade (HC1): a raiz da variância estimada do coeficiente.ep = √V_jj→ 0,178914 (0.17891351798924446)
   3. Intervalo de 95% de confiança: a estimativa mais ou menos o valor crítico da distribuição t de Student com 62 graus de liberdade vezes o erro-padrão.IC = β ± c · ep

   Pressupostos do estimador

   • the instruments affect the outcome only through the endogenous regressors (exclusion restriction)
   • the instruments are as good as randomly assigned given the controls
   • errors are independent across observations; their variance may differ

   Tabelas (3)

   {
     "coefficients": [
       {
         "ci_high": 4.293917992701939,
         "ci_low": -0.47458491160845706,
         "coef": 1.909666540546741,
         "p": 0.11444349079561447,
         "se": 1.1927390819923254,
         "t": 1.601076521578278,
         "term": "Intercept"
       },
       {
         "ci_high": 1.301922411627538,
         "ci_low": 0.5866363586820607,
         "coef": 0.9442793851547994,
         "p": 0.0000017722510641748919,
         "se": 0.17891351798924446,
         "t": 5.277853768498172,
         "term": "avexpr"
       }
     ],
     "first_stage": [
       {
         "ci_high": -0.3065384195674211,
         "ci_low": -0.9070180781003664,
         "coef": -0.6067782488338938,
         "endog": "avexpr",
         "instrument": "logem4",
         "p": 0.00014986892666534062,
         "se": 0.15019715223959304,
         "t": -4.039878518242256
       }
     ],
     "reduced_form": [
       {
         "ci_high": -0.42710584400315166,
         "ci_low": -0.7188305394651986,
         "coef": -0.5729681917341751,
         "instrument": "logem4",
         "p": 7.141770691068322e-11,
         "se": 0.07296869739669624,
         "t": -7.852246403950703
       }
     ]
   }

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   maketable4 dc8a5df19428e33e3bb4109922ccbd092a69bde0d19a217451baa154782debfc

   sha256 do resultado

   490e724f33ee579ebbca14d6051367b8b40cdbf680cee250a16d382b9bd6c906

   Resultado mostrado ao modelo
10. 9Turno do modelo
    call_792df44cgemini-3.8-flashFim: STOP13.565 ms17114 de entrada · 416 de saída · 868 de raciocínio · 12638 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process** Okay, let's break down what I'm thinking about here, step by step, as I process this request to summarize and report findings from Acemoglu, Johnson, and Robinson (2001). First, I need to locate the specific data point the user is asking about. The request clearly specifies "Table 4, Panel A, Column (1)" of the AJR (2001) paper. I see the published coefficient is 0.94 with a standard error of 0.16, and crucially, I've confirmed this matches the classical standard error of 0.156525. The number of observations is also noted as 64. Next, I'm evaluating the first-stage results. The F-statistic is reported as 22.95 (classical) or 16.32 (HC1). I know that a common rule of thumb for a "strong" instrument is an F-statistic above 10, so both of these values comfortably satisfy that condition, indicating no weak instrument issue here (`weak_instrument = false`). I also see the first-stage coefficient of `logem4` on `avexpr` is -0.61, which again matches my calculated value of -0.606778. Now, I'm pausing to make sure I understand *exactly* what the user wants reported. They asked to "Report the coefficient on average protection against expropriation risk." This is a direct request for the estimated effect. This leads me to a critical consideration: the output language. The prompt states, "Write the answer in the language of the question (Portuguese: decimal comma)...". My immediate thought is, "Wait, the question is in English!" So, I need to adhere to the rule: "Write the answer in the language of the question." Since the question is in English, my answer should be in English. Now, about the decimal separator: in English, the standard is a decimal point, not a comma, so I'll use a point. Let me double-check the specific requirements for the `submit_answer` tool. It needs `answer`, `caveats`, and `figure_refs`. For the `answer` itself, I need the estimate and its uncertainty. I have the estimate from `call_debb9458:coef.avexpr` as 0.944279. The standard error is 0.156525. The 95% confidence interval is [0.631389, 1.25717]. I should also include the key diagnostics: the number of observations (64) and the first-stage F-statistic (22.95, using the classical one as it's generally preferred when available and strong). The `caveats` section is crucial for any expert audience. What could undermine the conclusion here? 1. **Exclusion Restriction:** The core identification strategy hinges on the assumption that European settler mortality (the instrument) *only* affects contemporary income through its influence on institutional quality (protection against expropriation risk). There shouldn't be any other direct or indirect channels through which settler mortality impacts modern development. This is a strong, untestable assumption that forms the basis of the critique for many IV studies. 2. **Instrument Strength:** Although the F-statistic is well above 10, meaning the instrument isn't "weak" in the statistical sense that causes severe bias in OLS, I should still acknowledge the first-stage results. In this case, it's a strength, not a weakness, as the F-statistic is robustly high. For `figure_refs`, I've noted that `call_debb9458:coef.avexpr` is the relevant identifier for the coefficient on `avexpr`. So, to summarize my thinking for the `submit_answer` call: * **Answer:** The estimated effect of average protection against expropriation risk on log GDP per capita is approximately 0.94 (SE = 0.16). This is identified using two-stage least squares with European settler mortality as an instrument in a sample of 64 former colonies. The first-stage F-statistic is 22.95, indicating a strong instrument. * **Caveats:** * The identification relies critically on the exclusion restriction: European settler mortality influences modern income solely through its impact on persistent institutional quality. * While the instrument is statistically strong (F=22.95), the interpretation is sensitive to the validity of the exclusion restriction. * **Figure Refs:** `['call_debb9458:coef.avexpr']` This covers all the requirements of the prompt and adheres to the expected format for the tool. I've cross-referenced my calculations with the published figures, considered the statistical diagnostics, and thought about the interpretative challenges from an expert perspective.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "In the base sample of 64 former colonies from Table 4, Panel A, column (1) of Acemoglu, Johnson, and Robinson (2001), the two-stage least squares (2SLS) estimated coefficient of average protection against expropriation risk (avexpr) on log GDP per capita in 1995 (logpgp95), instrumented by log European settler mortality (logem4), is 0.944279 with a classical standard error of 0.156525 (95% CI: [0.631389, 1.25717]; with HC1 robust standard error 0.178914, 95% CI: [0.586636, 1.30192]). \n\nThe first-stage regression shows that log settler mortality is strongly and negatively associated with protection against expropriation (coefficient: -0.606778), yielding a first-stage F-statistic of 22.946797 (classical) and 16.320618 (HC1 robust), well above conventional weak-instrument thresholds.",
        "caveats": [
          "The 2SLS estimate relies fundamentally on the exclusion restriction that historical settler mortality affects modern economic development solely through its persistent effect on institutions, with no direct effect or unmodeled channel (such as early disease environment directly shaping current health and human capital).",
          "The sample is restricted to the 64 former colonies in the authors' base sample (baseco == 1) for which both settler mortality and expropriation risk data are available."
        ],
        "figure_refs": [
          "call_debb9458:coef.avexpr",
          "call_98c9510d:coef.avexpr"
        ]
      }

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

    Números encontrados

    64 · 4 · 1 · 2001 · 1995 · 0.944279 · 0.156525 · 95% · 0.631389 · 1.25717 · 0.178914 · 95% · 0.586636 · 1.30192 · -0.606778 · 22.946797 · 16.320618 · 64 · 1

    Sem lastro

    —

    Não citados

    —

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

    In the base sample of 64 former colonies from Table 4, Panel A, column (1) of Acemoglu, Johnson, and Robinson (2001), the two-stage least squares (2SLS) estimated coefficient of average protection against expropriation risk (avexpr) on log GDP per capita in 1995 (logpgp95), instrumented by log European settler mortality (logem4), is 0.944279 with a classical standard error of 0.156525 (95% CI: [0.631389, 1.25717]; with HC1 robust standard error 0.178914, 95% CI: [0.586636, 1.30192]). The first-stage regression shows that log settler mortality is strongly and negatively associated with protection against expropriation (coefficient: -0.606778), yielding a first-stage F-statistic of 22.946797 (classical) and 16.320618 (HC1 robust), well above conventional weak-instrument thresholds.

    • The 2SLS estimate relies fundamentally on the exclusion restriction that historical settler mortality affects modern economic development solely through its persistent effect on institutions, with no direct effect or unmodeled channel (such as early disease environment directly shaping current health and human capital).
    • The sample is restricted to the 64 former colonies in the authors' base sample (baseco == 1) for which both settler mortality and expropriation risk data are available.

    Figuras citadas: call_debb9458:coef.avexpr, call_98c9510d:coef.avexpr · Parada: answered

    Figura da resposta: call_debb9458:coef.avexpr = 0,9442790.9442793851547994 (se 0,1565250.15652545732957907)
13. 12Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
14. 13Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_debb9458:coef.avexpr (infer.iv_2sls)
15. 14Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
16. 15Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'logpgp95'
17. 16Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['avexpr']
18. 17Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['logem4']
19. 18Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = []
20. 19Pontuação
    #7diagnósticopassouobrigatória64 vs 64
21. 20Pontuação
    #8figura da resposta próximapassouobrigatória0.9442793852 vs 0.9442793851548288
22. 21Pontuação
    #9figura da resposta próximapassouregistrada0.1565254573 vs 0.15652545732958245
23. 22Pontuação
    #10figura da resposta próximapassouregistrada0.9442793852 vs 0.94
24. 23Pontuação
    #11figura da resposta próximapassouregistrada0.1565254573 vs 0.16

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• época 1, tentativa 1passoupontuada(exibindo)

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