Tarefa paper_repro.mrw_1992.tab1_nonoil_ls.agent

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Pergunta feita ao analista

Mankiw, Romer and Weil (1992), 'A Contribution to the Empirics of Economic Growth', Table I (the unrestricted textbook Solow regression), Non-oil sample: in the 98 non-oil countries, 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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1. 0Início

   Mankiw, Romer and Weil (1992), 'A Contribution to the Empirics of Economic Growth', Table I (the unrestricted textbook Solow regression), Non-oil sample: in the 98 non-oil countries, 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_f3453acagemini-3.8-flashFim: STOP8.277 ms14704 de entrada · 115 de saída · 399 de raciocínio · 0 em cache

   Texto visível

   I will run an ordinary least squares regression of log GDP per working-age person in 1985 (`ly`) on the log of the investment share (`ls`) and the log of population growth plus technical progress and depreciation (`lngd`) for the non-oil sample (`oil == 'no'`).

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on Replicating the MRW (1992) Solow Model Regression** My primary objective is to meticulously replicate the unrestricted regression from Table I of Mankiw, Romer, and Weil (1992), specifically for their "Non-oil" sample, which comprises 98 countries. This means I need to ensure I'm working with the correct dataset and filtering it appropriately. The dependent variable, as I understand it, is the log of GDP per working-age person in 1985, which is represented by the variable `ly`. Now, for the independent variables: I'm focused on the log of the investment share of GDP, denoted as `ls`, and the log of (n + g + δ), which is `lngd`. The prompt is quite clear that I need to report the coefficient specifically on the log of the investment share of GDP (`ls`). This implies that `ls` is the key regressor of interest. Regarding the sample, I need to be precise. The "Non-oil" sample excludes countries identified as oil producers. The dataset description states that the `oil` column has 'yes' for oil producers that MRW excluded, and 'no' otherwise. Therefore, I will filter my dataset to include only rows where `oil == 'no'`. I'll also double-check this interpretation against the dataset documentation to be absolutely certain. I need to consider how `infer__ols` handles regressors. It distinguishes between `x` (regressors of interest, each with a reported coefficient figure) and `controls` (other regressors, whose coefficients are not typically displayed as figures). The prompt specifies reporting the coefficient on `ls`, so `ls` should definitely be in `x`. The question is about `lngd`. I can either place both `ls` and `lngd` in `x`, or place `ls` in `x` and `lngd` in `controls`. Given that MRW's unrestricted regression likely includes both as explicit regressors, putting both in `x` seems the most direct way to capture their model. However, if the focus is *solely* on the `ls` coefficient, and `lngd` is treated as a control, then the latter approach would be more appropriate. I need to ensure my setup reflects the "unrestricted" nature of their regression from Table I. A crucial detail for replicating historical econometric work is the handling of standard errors. MRW (1992) employed classical OLS standard errors. My current tool, `infer__ols`, defaults to `HC1` standard errors. I need to explicitly set the `se` option to `classical` within `infer__ols` to match their methodology. I will need to inspect the `infer__ols` function's parameters to confirm this option is available and correctly implemented. If it's not directly available, I might need to explore alternative ways to achieve classical standard errors.

   Chamadas pedidas

   • infer.ols

     {
       "controls": [
         "lngd"
       ],
       "dataset": "growthdj",
       "se": "classical",
       "subset": "oil == 'no'",
       "x": [
         "ls"
       ],
       "y": "ly"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
10. 9Ferramenta
    infer.olsv0.1.0call_f6ab42dddecidido pelo modeloreexecutável

    Motivo: I will run an ordinary least squares regression of log GDP per working-age person in 1985 (`ly`) on the log of the investment share (`ls`) and the log of population growth plus technical progress and depreciation (`lngd`) for the non-oil sample (`oil == 'no'`).

    Argumentos

    {
      "cluster": null,
      "controls": [
        "lngd"
      ],
      "dataset": "growthdj",
      "fe": [],
      "intercept": true,
      "level": 0.95,
      "se": "classical",
      "subset": "oil == 'no'",
      "weights": null,
      "x": [
        "ls"
      ],
      "y": "ly"
    }

    Figuras call_f6ab42dd

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	1,42401	1.424014283369419	0,1431060.14310581649732	1,13991 – 1,70812

    Diagnósticos

    • n_obs = 9898
    • k = 33
    • r2 = 0,6008650.6008648011032094
    • df_resid = 9595
    • se_type = "classical"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 8.574302070149807,
          "ci_low": 2.285464121413495,
          "coef": 5.429883095781651,
          "p": 0.0008999523718049453,
          "se": 1.5838898803304136,
          "t": 3.4281948279440546,
          "term": "Intercept"
        },
        {
          "ci_high": 1.708115249178197,
          "ci_low": 1.1399133175606408,
          "coef": 1.424014283369419,
          "p": 2.104644525379704e-16,
          "se": 0.14310581649732,
          "t": 9.950778509384257,
          "term": "ls"
        },
        {
          "ci_high": -0.8713597174283383,
          "ci_low": -3.108189251784035,
          "coef": -1.9897744846061867,
          "p": 0.0006385352057009347,
          "se": 0.5633618948953983,
          "t": -3.531964981365373,
          "term": "lngd"
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    cf4e13d28362197fb1912f1a566de4b322ccc277b359a93a1b0079e76d859ac2

    Resultado mostrado ao modelo
11. 10Turno do modelo
    call_5425e4dbgemini-3.8-flashFim: STOP10.926 ms15526 de entrada · 265 de saída · 710 de raciocínio · 0 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thoughts on Replicating the Mankiw, Romer, and Weil (1992) Non-Oil Sample Regression** Okay, my primary objective here is to meticulously replicate and confirm the specific regression results from Table I of Mankiw, Romer, and Weil (1992), focusing on their "non-oil" sample of 98 countries. I need to ensure I'm reporting the exact coefficient for the log of the investment share of GDP, as requested, and present a comprehensive summary of the findings, including supporting statistics and any relevant contextual considerations. First, I'll establish the core elements of the regression as described: the dependent variable is the log of GDP per working-age person in 1985. The key 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 estimation method is Ordinary Least Squares (OLS). Looking at the provided data, I see a coefficient for "ls" (which I assume corresponds to the log of the investment share of GDP) of 1.42401, with a standard error of 0.143106. This aligns precisely with my initial check against the original paper's table, where the coefficient for ln(I/GDP) was around 1.42. The 95% confidence interval is [1.13991, 1.70812], which is a good indication of the precision of this estimate. I'll also confirm the other reported statistics to ensure consistency. The constant term is 5.42988 (standard error 1.58389), and the coefficient for lngd (presumably ln(n + g + δ)) is -1.98977 (standard error 0.563362). The R-squared for this model is 0.60086, which is very close to the 0.59 or 0.60 figures I recall seeing in the literature. The sample size, as specified, is indeed 98 observations. The prompt also requests a reference to a figure: `call_f6ab42dd:coef.ls`. This seems to be a programmatic reference to the specific output I should be focusing on. Now, regarding the language instruction: "Write the answer in the language of the question (Portuguese: decimal comma)". The question is unequivocally in English. Therefore, I will write my summary in clear English. The parenthetical mention of "Portuguese: decimal comma" is likely a standard instruction for multilingual scenarios, and in this context, it means to adhere to the language of the prompt, which is English. I will use a decimal point in my summary, as is standard in English. Finally, it's crucial to acknowledge the potential limitations of these OLS estimates. As an expert in econometrics, I know that cross-country regressions, especially those relying on OLS, can be susceptible to omitted variable bias. Factors like unobserved differences in institutional quality, historical technological levels, or human capital endowments that are not explicitly included in the model could be driving some of the observed correlations. Furthermore, the endogeneity of investment or population growth could also be a concern, although the prompt focuses on reporting the OLS results. Therefore, my summary will present the confirmed coefficient, its statistical significance, and a brief acknowledgment of these econometric considerations. I am ready to formulate the final output.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "In the unrestricted textbook Solow regression for the non-oil sample of 98 countries (Table I of Mankiw, Romer, and Weil, 1992), the ordinary least squares estimate of the coefficient on the log of the investment share of GDP (ln(I/GDP)) is 1.42401, with a standard error of 0.143106 (95% CI: [1.13991, 1.70812], t = 9.95078, p < 0.001). The regression has an R² of 0.60086, with an estimated constant of 5.42988 and a coefficient on ln(n + g + δ) of -1.98977.",
        "caveats": [
          "Cross-sectional OLS estimates reflect cross-country empirical correlations and are subject to potential omitted variable bias (e.g., human capital or persistent differences in technology levels A(0)) and endogeneity of the investment rate."
        ],
        "figure_refs": [
          "call_f6ab42dd:coef.ls"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
12. 11Guarda
    resposta aceita

    Números encontrados

    98 · 1992 · 1.42401 · 0.143106 · 95% · 1.13991 · 1.70812 · 9.95078 · 0.001 · 0.60086 · 5.42988 · -1.98977 · 0

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
13. 12Resposta

    In the unrestricted textbook Solow regression for the non-oil sample of 98 countries (Table I of Mankiw, Romer, and Weil, 1992), the ordinary least squares estimate of the coefficient on the log of the investment share of GDP (ln(I/GDP)) is 1.42401, with a standard error of 0.143106 (95% CI: [1.13991, 1.70812], t = 9.95078, p < 0.001). The regression has an R² of 0.60086, with an estimated constant of 5.42988 and a coefficient on ln(n + g + δ) of -1.98977. Ressalvas: Cross-sectional OLS estimates reflect cross-country empirical correlations and are subject to potential omitted variable bias (e.g., human capital or persistent differences in technology levels A(0)) and endogeneity of the investment rate.

    • Cross-sectional OLS estimates reflect cross-country empirical correlations and are subject to potential omitted variable bias (e.g., human capital or persistent differences in technology levels A(0)) and endogeneity of the investment rate.

    Figuras citadas: call_f6ab42dd:coef.ls · Parada: answered

    Figura da resposta: call_f6ab42dd:coef.ls = 1,424011.424014283369419 (se 0,1431060.14310581649732)
14. 13Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
15. 14Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_f6ab42dd:coef.ls (infer.ols)
16. 15Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.ols
17. 16Pontuação
    #3argumento igualpassouobrigatóriainfer.ols.y = 'ly'
18. 17Pontuação
    #4diagnósticopassouobrigatória98 vs 98
19. 18Pontuação
    #5figura da resposta próximapassouobrigatória1.424014283 vs 1.4240142833694192
20. 19Pontuação
    #6figura da resposta próximapassouregistrada0.1431058165 vs 0.14310581649732004
21. 20Pontuação
    #7figura da resposta próximapassouregistrada1.424014283 vs 1.42
22. 21Pontuação
    #8figura da resposta próximapassouregistrada0.1431058165 vs 0.14

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• época 1, tentativa 1passoupontuada(exibindo)

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