Tarefa paper_repro.mrw_1992.tab1_oecd_ls.agent

Veredito

Pergunta feita ao analista

Mankiw, Romer and Weil (1992), 'A Contribution to the Empirics of Economic Growth', Table I (the unrestricted textbook Solow regression), OECD sample: in the 22 OECD countries with populations above one million, estimate by ordinary least squares the regression of log GDP per working-age person in 1985 on the log of the investment share of GDP and the log of (n + g + δ), where n is the 1960-1985 growth rate of the working-age population and g + δ is assumed to be 0.05. Report the coefficient on the log of the investment share of GDP.

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Verificações

Caminho de referência e caminho do agente

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Trajetória

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

1. 0Início

   Mankiw, Romer and Weil (1992), 'A Contribution to the Empirics of Economic Growth', Table I (the unrestricted textbook Solow regression), OECD sample: in the 22 OECD countries with populations above one million, estimate by ordinary least squares the regression of log GDP per working-age person in 1985 on the log of the investment share of GDP and the log of (n + g + δ), where n is the 1960-1985 growth rate of the working-age population and g + δ is assumed to be 0.05. Report the coefficient on the log of the investment share of GDP.

   growthdj (agent)

   The data of Mankiw, Romer and Weil (1992), 'A Contribution to the Empirics of Economic Growth', as transcribed by Durlauf and Johnson (R package AER, GrowthDJ): one row per country (121 rows). Columns: rownames, a row number; oil, 'yes' for the oil producers MRW exclude from the non-oil sample, else 'no'; inter, 'yes' for the 'intermediate' sample (no Summers-Heston grade of D, 1960 population of at least one million); oecd, 'yes' for the OECD sample; gdp60 and gdp85, real GDP per working-age person in 1960 and 1985 (dollars); gdpgrowth, average annual growth of GDP per working-age person 1960-1985 (percent); popgrowth, average annual growth of the working-age population 1960-1985 (percent); invest, average share of real investment in real GDP 1960-1985 (percent); school, percent of the working-age population in secondary school; literacy60, adult literacy rate in 1960 (percent). Columns built from the paper's definitions (g + δ = 0.05): ly, log of gdp85; s_share, invest divided by 100; ls, log of s_share (ln(I/GDP)); n_rate, popgrowth divided by 100; g_plus_delta, the constant 0.05; ngd, n_rate + g_plus_delta; lngd, log of ngd (ln(n + g + δ)). Some countries miss gdp85 or popgrowth.

   file 3d06303f1da9959175e990eb068bf242fac0e9bc1f9daad1f5fffe96d100e796 · frame —

   1. derive {"args":{"column":"gdp85"},"name":"ly","op":"log"}
   2. derive {"args":{"column":"invest","factor":0.01},"name":"s_share","op":"scale"}
   3. derive {"args":{"column":"s_share"},"name":"ls","op":"log"}
   4. derive {"args":{"column":"popgrowth","factor":0.01},"name":"n_rate","op":"scale"}
   5. derive {"args":{"value":0.05},"name":"g_plus_delta","op":"constant"}
   6. derive {"args":{"columns":["n_rate","g_plus_delta"]},"name":"ngd","op":"sum"}
   7. derive {"args":{"column":"ngd"},"name":"lngd","op":"log"}
2. 1Transformação
   growthdj · derive {"args":{"column":"gdp85"},"name":"ly","op":"log"}

   121 → 121 linhas

   Frame antes → depois: 6f822eca9c87 → 256189baba87
3. 2Transformação
   growthdj · derive {"args":{"column":"invest","factor":0.01},"name":"s_share","op":"scale"}

   121 → 121 linhas

   Frame antes → depois: 256189baba87 → ddc60cb0ca4e
4. 3Transformação
   growthdj · derive {"args":{"column":"s_share"},"name":"ls","op":"log"}

   121 → 121 linhas

   Frame antes → depois: ddc60cb0ca4e → 832bd9c4b876
5. 4Transformação
   growthdj · derive {"args":{"column":"popgrowth","factor":0.01},"name":"n_rate","op":"scale"}

   121 → 121 linhas

   Frame antes → depois: 832bd9c4b876 → ff997d0e044f
6. 5Transformação
   growthdj · derive {"args":{"value":0.05},"name":"g_plus_delta","op":"constant"}

   121 → 121 linhas

   Frame antes → depois: ff997d0e044f → b9e3acd5adf8
7. 6Transformação
   growthdj · derive {"args":{"columns":["n_rate","g_plus_delta"]},"name":"ngd","op":"sum"}

   121 → 121 linhas

   Frame antes → depois: b9e3acd5adf8 → 837704298f36
8. 7Transformação
   growthdj · derive {"args":{"column":"ngd"},"name":"lngd","op":"log"}

   121 → 121 linhas

   Frame antes → depois: 837704298f36 → e3f509733efe
9. 8Turno do modelo
   call_9c8a71d9gemini-3.8-flashFim: STOP11.314 ms14705 de entrada · 118 de saída · 569 de raciocínio · 0 em cache

   Texto visível

   I will run an ordinary least squares regression of the log of 1985 GDP per working-age person (`ly`) on the log of the investment share (`ls`) and the log of population growth plus 0.05 (`lngd`) for the OECD subsample (`oecd == 'yes'`).

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Replicating the MRW (1992) Table I Regression** My primary objective here is to meticulously reproduce the unrestricted textbook Solow regression results presented in Table I of Mankiw, Romer, and Weil's seminal 1992 paper, specifically for the OECD sample comprising 22 countries. To begin, I need to access and examine the dataset labeled `growthdj`. My attention is immediately drawn to the variables that will form the core of this regression. The outcome variable, as per the description, is the logarithm of GDP per working-age person in 1985, denoted as `ly`. The regressors are clearly defined: the logarithm of the investment share of GDP, represented by `ls` (which corresponds to ln(I/GDP)), and the logarithm of (n + g + δ), captured by `lngd`. I need to ensure I understand how the sample is defined. The dataset includes an `oecd` variable, and I will need to filter for observations where `oecd == 'yes'` to isolate the 22 OECD countries. It's crucial to verify that this condition precisely selects the intended sample size. A quick check of the column descriptions confirms my understanding: * `oecd`: This binary indicator ('yes'/'no') specifies membership in the OECD sample. * `ly`: This variable represents the log of GDP in 1985. * `ls`: This variable is the log of the investment share of GDP (ln(I/GDP)). * `lngd`: This variable is the log of (n + g + δ), where 'n' is the growth rate of the working-age population from 1960 to 1985, and 'g + δ' is assumed to be a constant 0.05. The specific question posed requires me to estimate this regression using ordinary least squares (OLS). The core task is to report the coefficient on the `ls` (log of investment share of GDP) variable. Before I formally execute the regression, I'm double-checking the details. The problem statement specifically asks for the "unrestricted textbook Solow regression." This implies a straightforward OLS estimation without any constraints on the coefficients, other than those inherent in the model specification itself. I also pause to consider the standard error estimation used in the original MRW paper. The prompt mentions that MRW used classical OLS standard errors, which are equivalent to homoskedastic standard errors. While the choice of standard error estimation (e.g., `se="classical"` versus `se="HC1"`) will not affect the estimated coefficients themselves, it is a critical detail if I were to report standard errors or confidence intervals. Since the prompt only asks for the coefficient on `ls`, this is less of an immediate concern for the primary output, but I'll keep it in mind for completeness and potential verification. My plan is to use the `infer.ols` function, which is suitable for this type of regression analysis. I will first confirm that `oecd == 'yes'` indeed isolates exactly 22 observations, as stated. Then, I will proceed with the `infer.ols` estimation, specifying `ly` as the dependent variable and `ls` and `lngd` as the independent variables, while filtering the data for the OECD sample. For verification purposes, I recall the approximate coefficients reported in MRW (1992) for the OECD sample (N=22): * Coefficient on ln(I/GDP) (`ls`): approximately 0.29 (s.e. 0.39) * Coefficient on ln(n+g+δ) (`lngd`): approximately -0.76 (s.e. 0.84) * Constant: approximately 8.03 * R-squared: approximately 0.01 My immediate task is to run `infer.ols` on the filtered data to obtain these coefficients and compare them against the established benchmark. The focus remains on accurately replicating the coefficient for the log of the investment share of GDP.

   Chamadas pedidas

   • infer.ols

     {
       "controls": [
         "lngd"
       ],
       "dataset": "growthdj",
       "se": "classical",
       "subset": "oecd == 'yes'",
       "x": [
         "ls"
       ],
       "y": "ly"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
10. 9Ferramenta
    infer.olsv0.1.0call_dbc771f8decidido pelo modeloreexecutável

    Motivo: I will run an ordinary least squares regression of the log of 1985 GDP per working-age person (`ly`) on the log of the investment share (`ls`) and the log of population growth plus 0.05 (`lngd`) for the OECD subsample (`oecd == 'yes'`).

    Argumentos

    {
      "cluster": null,
      "controls": [
        "lngd"
      ],
      "dataset": "growthdj",
      "fe": [],
      "intercept": true,
      "level": 0.95,
      "se": "classical",
      "subset": "oecd == 'yes'",
      "weights": null,
      "x": [
        "ls"
      ],
      "y": "ly"
    }

    Figuras call_dbc771f8

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	0,49989	0.49988953745307024	0,4338960.43389556468033497	-0,408264 – 1,40804

    Diagnósticos

    • n_obs = 2222
    • k = 33
    • r2 = 0,1059260.10592625072020889
    • df_resid = 1919
    • se_type = "classical"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 13.29060842943676,
          "ci_low": 2.7506050830633963,
          "coef": 8.020606756250078,
          "p": 0.004870434342367383,
          "se": 2.5178887275982573,
          "t": 3.185449248943065,
          "term": "Intercept"
        },
        {
          "ci_high": 1.4080433914300876,
          "ci_low": -0.40826431652394707,
          "coef": 0.49988953745307024,
          "p": 0.2635721579961767,
          "se": 0.43389556468033497,
          "t": 1.1520964447317068,
          "term": "ls"
        },
        {
          "ci_high": 1.0417423402301624,
          "ci_low": -2.525585258573276,
          "coef": -0.7419214591715567,
          "p": 0.39483898692899355,
          "se": 0.852194601225429,
          "t": -0.8706009849213983,
          "term": "lngd"
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    6fe455a09a8704b46a69c40ed2f7ab3698ed0f472db693ee0ac7ad7a39f71fcb

    Resultado mostrado ao modelo
11. 10Turno do modelo
    call_44b460e0gemini-3.8-flashFim: STOP5.078 ms15697 de entrada · 39 de saída · 213 de raciocínio · 0 em cache

    Texto visível

    I will describe the variables in the `growthdj` dataset to inspect summary statistics and verify the sample variables.

    Resumo do raciocínio, como declarado pelo modelo

    **A Deep Dive into Coefficient Discrepancies and Model Specification** My immediate reaction to seeing a coefficient of 0.49989 was one of surprise. This value felt off, and my instinct was to immediately cross-reference it with a foundational piece of literature in this field – Mankiw, Romer, and Weil's (1992) seminal paper. I specifically recalled their Table I, which presented key empirical results. My first step was to pull up Table I from MRW (1992). I meticulously reviewed the reported coefficients for different sample specifications. I noted the figures for "Non-oil" (ln(I/GDP) 1.42 (0.14), ln(n+g+δ) -1.97 (0.56), R² 0.59, N=98) and "Intermediate" (ln(I/GDP) 1.31 (0.17), ln(n+g+δ) -2.01 (0.53), R² 0.59, N=75). However, my attention was then drawn to the "OECD" sample within that same table. I needed to confirm the exact details for this specific subsample. I quickly scanned the table again and confirmed that for the OECD sample, the number of observations (N) was stated as 22. At this point, a fundamental question arose: what were the precise variables being regressed in Table I of MRW? While I had the coefficients, I needed to be absolutely certain about the dependent and independent variables to ensure a valid comparison. To solidify this, I decided to check the descriptive statistics for my own dataset, specifically using `data.describe` on what I've labeled `growthdj`. This would allow me to directly compare the characteristics of my data with the implied specifications of the MRW table. This systematic approach, moving from an initial anomaly to consulting established work and then verifying against my own data, is crucial for rigorous empirical analysis.

    Chamadas pedidas

    • data.describe

      {
        "dataset": "growthdj"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
12. 11Ferramenta
    data.describev0.1.0call_ac9177d2decidido pelo modeloreexecutável

    Motivo: I will describe the variables in the `growthdj` dataset to inspect summary statistics and verify the sample variables.

    Argumentos

    {
      "columns": null,
      "dataset": "growthdj"
    }

    Figuras call_ac9177d2

    Chave	Valor	Valor bruto	Erro-padrão	IC
    n_rows Rows in the dataset	121 rows	121	—	—

    Tabelas (1)

    {
      "columns": [
        {
          "column": "rownames",
          "dtype": "int64",
          "max": 121,
          "mean": 61,
          "min": 1,
          "n_missing": 0,
          "n_unique": 121,
          "sd": 35.073731861133155
        },
        {
          "column": "oil",
          "dtype": "str",
          "n_missing": 0,
          "n_unique": 2
        },
        {
          "column": "inter",
          "dtype": "str",
          "n_missing": 0,
          "n_unique": 2
        },
        {
          "column": "oecd",
          "dtype": "str",
          "n_missing": 0,
          "n_unique": 2
        },
        {
          "column": "gdp60",
          "dtype": "float64",
          "max": 77881,
          "mean": 3681.8189655172414,
          "min": 383,
          "n_missing": 5,
          "n_unique": 114,
          "sd": 7492.87763679516
        },
        {
          "column": "gdp85",
          "dtype": "float64",
          "max": 25635,
          "mean": 5683.259259259259,
          "min": 412,
          "n_missing": 13,
          "n_unique": 105,
          "sd": 5688.670819195448
        },
        {
          "column": "gdpgrowth",
          "dtype": "float64",
          "max": 9.2,
          "mean": 4.094017094017094,
          "min": -0.9,
          "n_missing": 4,
          "n_unique": 62,
          "sd": 1.891464065228336
        },
        {
          "column": "popgrowth",
          "dtype": "float64",
          "max": 6.8,
          "mean": 2.2794392523364486,
          "min": 0.3,
          "n_missing": 14,
          "n_unique": 36,
          "sd": 0.9987481142926926
        },
        {
          "column": "invest",
          "dtype": "float64",
          "max": 36.9,
          "mean": 18.15702479338843,
          "min": 4.1,
          "n_missing": 0,
          "n_unique": 98,
          "sd": 7.853309561858628
        },
        {
          "column": "school",
          "dtype": "float64",
          "max": 12.1,
          "mean": 5.526271186440678,
          "min": 0.4,
          "n_missing": 3,
          "n_unique": 74,
          "sd": 3.532037207025466
        },
        {
          "column": "literacy60",
          "dtype": "float64",
          "max": 100,
          "mean": 48.16504854368932,
          "min": 1,
          "n_missing": 18,
          "n_unique": 58,
          "sd": 35.35425677767165
        },
        {
          "column": "ly",
          "dtype": "float64",
          "max": 10.1517138842178,
          "mean": 8.105513308731956,
          "min": 6.021023349349527,
          "n_missing": 13,
          "n_unique": 105,
          "sd": 1.0947131180666534
        },
        {
          "column": "s_share",
          "dtype": "float64",
          "max": 0.369,
          "mean": 0.1815702479338843,
          "min": 0.040999999999999995,
          "n_missing": 0,
          "n_unique": 98,
          "sd": 0.07853309561858629
        },
        {
          "column": "ls",
          "dtype": "float64",
          "max": -0.9969586349416099,
          "mean": -1.8151255835402953,
          "min": -3.1941832122778293,
          "n_missing": 0,
          "n_unique": 98,
          "sd": 0.4954514202322953
        },
        {
          "column": "n_rate",
          "dtype": "float64",
          "max": 0.068,
          "mean": 0.022794392523364487,
          "min": 0.003,
          "n_missing": 14,
          "n_unique": 36,
          "sd": 0.009987481142926925
        },
        {
          "column": "g_plus_delta",
          "dtype": "float64",
          "max": 0.05,
          "mean": 0.05,
          "min": 0.05,
          "n_missing": 0,
          "n_unique": 1,
          "sd": 0
        },
        {
          "column": "ngd",
          "dtype": "float64",
          "max": 0.11800000000000001,
          "mean": 0.07279439252336449,
          "min": 0.053000000000000005,
          "n_missing": 14,
          "n_unique": 36,
          "sd": 0.009987481142926925
        },
        {
          "column": "lngd",
          "dtype": "float64",
          "max": -2.137070654516472,
          "mean": -2.629459766807535,
          "min": -2.9374633654300153,
          "n_missing": 14,
          "n_unique": 36,
          "sd": 0.13797790927825018
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    72c8ee8eedfa45f859a62f402531c9567a94287dd534779d2f6b303416ecbee5

    Resultado mostrado ao modelo
13. 12Turno do modelo
    call_2216f4dbgemini-3.8-flashFim: STOP9.131 ms16402 de entrada · 79 de saída · 675 de raciocínio · 12602 em cache

    Texto visível

    I will run the regression with heteroskedasticity-robust standard errors (HC1) to compare the standard errors.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process Regarding the Mankiw, Romer, and Weil (1992) Regression Output** Okay, I'm reviewing the output from `infer.ols` and specifically focusing on the coefficient for `ls`. I see `n_obs` is 22, which aligns with the OECD sample mentioned in the prompt. The coefficient on `ls` is reported as 0.49989, with a standard error of 0.433896, a t-statistic of 1.1521, a p-value of 0.263572, and a 95% confidence interval from -0.408264 to 1.40804. Now, I recall a figure of 0.29 that I had in mind from Table I of the Mankiw, Romer, and Weil (1992) paper. This discrepancy prompts me to go back and meticulously check Table I of their original publication, "A Contribution to the Empirics of Economic Growth." My goal is to confirm what that table actually presents. Upon re-examination of Table I, which details the "Estimation of the textbook Solow model," I see the dependent variable is `log GDP per working-age person in 1985`. The samples are specified as Non-oil (98 observations), Intermediate (75 observations), and OECD (22 observations). Focusing on the OECD sample, Table I presents unrestricted regression results. I'm seeing: * Constant: 7.99 (or 8.02) * `ln(I/GDP)`: 0.50 (or 0.50) with a standard error of 0.43. * `ln(n+g+δ)`: -0.74 with a standard error of 0.85. And concerning the R-squared value, I'm seeing an R2 of 0.01 for the OECD unrestricted regression in the original paper. There's a slight confusion here, as I'm questioning whether the 0.01 R2 was for a restricted model, but the paper explicitly states 0.01 for the unrestricted OECD regression. However, I'm also aware that the `GrowthDJ` R package, which contains data transcribed by Durlauf and Johnson, yields a coefficient of 0.49989 for this regression. Regardless of whether I'm looking at the original paper or this dataset transcription, the output I'm currently working with (`infer.ols`) shows `coef.ls` as 0.49989 with a standard error of 0.433896. The prompt specifically asks for the coefficient on the log of the investment share of GDP from the unrestricted textbook Solow regression using the OECD sample (22 countries), regressing `log GDP per working-age person in 1985` on `log of the investment share of GDP` and `log of (n + g + δ)`, assuming `g + δ` is 0.05. Finally, I need to consider the standard error calculation. The prompt doesn't explicitly request robust standard errors, so I assume classical (homoskedastic) standard errors are acceptable. The calculated classical standard error is 0.433896. However, to be thorough, I should also check if robust standard errors (like HC1, which is often the default in statistical software) are required or if they would significantly alter the result. I'll proceed with the classical standard error as it appears to be the default unless otherwise specified, but I'm noting the potential for HC1. I will confirm `infer.ols` uses HC1 as the default.

    Chamadas pedidas

    • infer.ols

      {
        "controls": [
          "lngd"
        ],
        "dataset": "growthdj",
        "se": "HC1",
        "subset": "oecd == 'yes'",
        "x": [
          "ls"
        ],
        "y": "ly"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
14. 13Ferramenta
    infer.olsv0.1.0call_d5007946decidido pelo modeloreexecutável

    Motivo: I will run the regression with heteroskedasticity-robust standard errors (HC1) to compare the standard errors.

    Argumentos

    {
      "cluster": null,
      "controls": [
        "lngd"
      ],
      "dataset": "growthdj",
      "fe": [],
      "intercept": true,
      "level": 0.95,
      "se": "HC1",
      "subset": "oecd == 'yes'",
      "weights": null,
      "x": [
        "ls"
      ],
      "y": "ly"
    }

    Figuras call_d5007946

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	0,49989	0.49988953745307024	0,3436850.3436850968288728	-0,219452 – 1,21923

    Diagnósticos

    • n_obs = 2222
    • k = 33
    • r2 = 0,1059260.10592625072020889
    • df_resid = 1919
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 14.053469577102204,
          "ci_low": 1.987743935397953,
          "coef": 8.020606756250078,
          "p": 0.011863425370801203,
          "se": 2.8823666924160585,
          "t": 2.7826462113073624,
          "term": "Intercept"
        },
        {
          "ci_high": 1.2192307122575499,
          "ci_low": -0.21945163735140932,
          "coef": 0.49988953745307024,
          "p": 0.16212968651913526,
          "se": 0.3436850968288728,
          "t": 1.4544987317328295,
          "term": "ls"
        },
        {
          "ci_high": 1.5614956080864588,
          "ci_low": -3.0453385264295725,
          "coef": -0.7419214591715567,
          "p": 0.508332818810567,
          "se": 1.1005210677854271,
          "t": -0.6741547080643548,
          "term": "lngd"
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    449ee89496feccd15a51a6b0b8cad4637ab44c721dd38d3d51299ba4d5b27463

    Resultado mostrado ao modelo
15. 14Turno do modelo
    call_ebb9f106gemini-3.8-flashFim: STOP5.906 ms17464 de entrada · 38 de saída · 422 de raciocínio · 15851 em cache

    Texto visível

    I will load the reporting-numbers skill to follow the guidelines for reporting results and citing figure references.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thoughts on the Mankiw, Romer, and Weil (1992) Results** It's striking that in both analyses I've examined, the coefficient on the log of the investment share of GDP (`ls`) is virtually identical, landing precisely at 0.49989, or essentially 0.50. This consistency is a strong signal. Looking at the statistical precision, the classical standard error is 0.433896, while the HC1 standard error is 0.343685. The difference between these two error measures is worth noting, hinting at potential heteroskedasticity concerns, though the HC1 standard error offers a more robust estimate. When I cross-reference these findings with Table I from Mankiw, Romer, and Weil (1992) for the OECD sample with 22 observations, I see a remarkable alignment. Their reported coefficient for `ln(I/GDP)` is 0.50, with a standard error of 0.43, which perfectly matches my classical standard error. Their constant is reported as 7.99 (or 8.02), and `ln(n+g+δ)` is -0.74 with a standard error of 0.85. The R-squared value is particularly noteworthy. In my current run, it's 0.01. When I re-calculate the adjusted R-squared based on the provided formula and values (1 - (1 - 0.1059)*(21/19)), I arrive at 0.0118, which is indeed 0.01. This extremely low R-squared suggests that the investment share of GDP alone, within this specific model and sample, explains very little of the variation in the dependent variable. This is a significant limitation. The constraint to use only numbers stated by tool calls or the question, and to avoid mental arithmetic, is critical for maintaining rigor. This means I must directly quote the figures as presented. For the final output, I need to present the estimate with its uncertainty, identify the design that yields it, and acknowledge any factors that might undermine the conclusion. I also need to ensure all quoted figures are referenced with their call ID and key, and that any limitations are clearly stated as caveats. I should load the `reporting-numbers` skill, just in case it's needed for formatting or further analysis. submit_answer.

    Chamadas pedidas

    • load_skill (meta-ferramenta)

      {
        "name": "reporting-numbers"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
16. 15Habilidade
    reporting-numbersTexto da habilidade
17. 16Turno do modelo
    call_24d3792agemini-3.8-flashFim: STOP10.333 ms18360 de entrada · 263 de saída · 686 de raciocínio · 16007 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Replicating the Mankiw, Romer, and Weil (1992) Solow Regression** Okay, I've just gone through the process of replicating a specific regression from the foundational Mankiw, Romer, and Weil (1992) paper, specifically aiming to reproduce the "unrestricted textbook Solow regression" from their Table I. My goal was to extract the coefficient on the log of the investment share of GDP for the OECD sample as described in the prompt. First, I focused on the required details from the `call_dbc771f8` output, which I understand to be the results of my own executed regression. I noted the key figures: * The coefficient on `coef.ls` (which I interpret as my primary variable of interest, the log investment share) is 0.49989. * The standard error for this coefficient is 0.433896. * The 95% confidence interval for this coefficient is [-0.408264, 1.40804]. * The constant or intercept is 8.02061 with a standard error of 2.51789. * The coefficient on `lngd` (which, given the context of the MRW paper, likely represents the log of initial GDP per capita or a similar measure, although it's not explicitly the focus of *this specific* prompt's output) is -0.741921 with a standard error of 0.852195. * The R-squared of the regression is 0.105926250720209, which is approximately 0.11. * The number of observations (`n_obs`) is 22. Then, I cross-referenced these with the instructions derived from the question itself: * The paper referenced is indeed Mankiw, Romer, and Weil (1992), "A Contribution to the Empirics of Economic Growth." * I'm replicating the "unrestricted textbook Solow regression" from Table I. * The sample is the 22 OECD countries with populations above one million. * The method used is ordinary least squares (OLS). * The dependent variable is the log of GDP per working-age person in 1985. * The independent variables are the log of the investment share of GDP and the log of (n + g + δ), where 'n' is the 1960-1985 growth rate of the working-age population and 'g + δ' is assumed to be 0.05. * The specific request is to report the coefficient on the log of the investment share of GDP. Having confirmed that my `call_dbc771f8` output aligns with these specifications, I began to formulate the final response in Portuguese, as requested. For the estimation part, I would state: "O coeficiente estimado para o logaritmo da taxa de investimento sobre o PIB ($\ln(I/Y)$) é 0,49989." I would then add the associated classical standard error and the 95% confidence interval: "(erro padrão clássico de 0,433896; IC 95%: [-0,408264, 1,40804])." Regarding the design of the regression, I'd specify: "Mínimos Quadrados Ordinários (MQO) multivariado com 22 países da OCDE, replicando a regressão irrestrita do modelo de Solow clássico da Tabela I de Mankiw, Romer e Weil (1992)." This clearly outlines the methodology, sample, and context. Finally, I considered the "diagnostics/caveats" which are crucial for interpreting these results, especially given the historical context of this regression. I'd highlight: * The sample size is quite small: "Amostra pequena ($N = 22$)." * The coefficient on the investment share is not statistically significant at conventional levels: "coeficiente não estatisticamente significante ao nível usual ($p = 0,263572$)." (I'd infer this p-value from the reported coefficient and standard error, or assume it was provided elsewhere in the full `call_dbc771f8` output, as it's not explicitly listed in the provided snippet, but is standard practice to derive). * And importantly, the potential limitations of this basic Solow model specification, particularly the issue of omitted variable bias or endogeneity, which the authors themselves addressed in later parts of their paper by including human capital: "e potencial endogeneidade/omissão de variáveis (como capital humano, posteriormente incluído por MRW)." I've also mentally checked all the numerical figures provided to ensure they are correctly transcribed and consistently used. The `figure_refs` `call_dbc771f8:coef.ls` confirms that the primary coefficient of interest is indeed tied to that specific source within my execution. All other numbers mentioned in the prompt – 0.49989, 0.433896, -0.408264, 1.40804, 22, 1985, 1960, 0.05, and 95% – have been considered and incorporated where relevant. The structure and content seem to align with what an expert in the field would expect and consider.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Para a amostra de 22 países da OCDE (Tabela I de Mankiw, Romer e Weil, 1992), a regressão irrestrita do modelo clássico de Solow por Mínimos Quadrados Ordinários estima o coeficiente do logaritmo da taxa de investimento sobre o PIB em 0,49989 (erro padrão clássico de 0,433896; intervalo de confiança de 95%: [-0,408264; 1,40804]). O coeficiente não é estatisticamente significante ao nível convencional (t = 1,1521; p = 0,263572).",
        "caveats": [
          "A amostra é reduzida (N = 22 países), limitando o poder estatístico da estimação.",
          "O coeficiente da taxa de investimento não é estatisticamente significante nos níveis usuais.",
          "A especificação clássica omite capital humano, fator que os próprios autores incorporam na extensão do modelo."
        ],
        "figure_refs": [
          "call_dbc771f8:coef.ls"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
18. 17Guarda
    resposta aceita

    Números encontrados

    22 · 1992 · 0,49989 · 0,433896 · 95% · -0,408264 · 1,40804 · 1,1521 · 0,263572 · 22

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
19. 18Resposta

    Para a amostra de 22 países da OCDE (Tabela I de Mankiw, Romer e Weil, 1992), a regressão irrestrita do modelo clássico de Solow por Mínimos Quadrados Ordinários estima o coeficiente do logaritmo da taxa de investimento sobre o PIB em 0,49989 (erro padrão clássico de 0,433896; intervalo de confiança de 95%: [-0,408264; 1,40804]). O coeficiente não é estatisticamente significante ao nível convencional (t = 1,1521; p = 0,263572). Ressalvas: A amostra é reduzida (N = 22 países), limitando o poder estatístico da estimação. O coeficiente da taxa de investimento não é estatisticamente significante nos níveis usuais. A especificação clássica omite capital humano, fator que os próprios autores incorporam na extensão do modelo.

    • A amostra é reduzida (N = 22 países), limitando o poder estatístico da estimação.
    • O coeficiente da taxa de investimento não é estatisticamente significante nos níveis usuais.
    • A especificação clássica omite capital humano, fator que os próprios autores incorporam na extensão do modelo.

    Figuras citadas: call_dbc771f8:coef.ls · Parada: answered

    Figura da resposta: call_dbc771f8:coef.ls = 0,499890.49988953745307024 (se 0,4338960.43389556468033497)
20. 19Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
21. 20Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_dbc771f8:coef.ls (infer.ols)
22. 21Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.ols
23. 22Pontuação
    #3argumento igualpassouobrigatóriainfer.ols.y = 'ly'
24. 23Pontuação
    #4diagnósticopassouobrigatória22 vs 22
25. 24Pontuação
    #5figura da resposta próximapassouobrigatória0.4998895375 vs 0.4998895374530683
26. 25Pontuação
    #6figura da resposta próximapassouregistrada0.4338955647 vs 0.4338955646803343
27. 26Pontuação
    #7figura da resposta próximapassouregistrada0.4998895375 vs 0.5
28. 27Pontuação
    #8figura da resposta próximapassouregistrada0.4338955647 vs 0.43

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• época 1, tentativa 1passoupontuada(exibindo)

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