Tarefa paper_repro.mrw_1992.tab1_nonoil_lngd.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 (n + g + δ).

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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 (n + g + δ).

   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_05b28f64gemini-3.8-flashFim: STOP9.813 ms14705 de entrada · 96 de saída · 668 de raciocínio · 0 em cache

   Texto visível

   I will run an ordinary least squares regression of the log GDP per working-age person in 1985 on the log investment share and the log of (n + g + δ) for the non-oil sample.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Reproducing the MRW (1992) Solow Regression** Here I am, needing to replicate a specific regression from a foundational paper: Table I of Mankiw, Romer, and Weil (1992), the unrestricted textbook Solow regression for their non-oil sample. This is a crucial exercise for understanding the empirical underpinnings of their model. My goal is to reproduce this by estimating an Ordinary Least Squares (OLS) regression. The outcome variable is clearly defined: the logarithm of GDP per working-age person in 1985, which I'll refer to as `ly` or `log(gdp85)`. The independent variables, or regressors, are also specified: the logarithm of the investment share of GDP (`ls`) and the logarithm of (n + g + δ), which I'll denote as `lngd`. The sample is equally precise: the "non-oil" subset of countries, identified in the dataset as where `oil == 'no'`. The dataset I have available for this is `growthdj`. I need to be careful about how I interpret the variables. * `oil`: This flag distinguishes between oil-producing countries (which MRW excluded from their non-oil sample) and others. I'll filter for `oil == 'no'`. * `ly`: This is simply the natural logarithm of GDP per working-age person in 1985. * `ls`: This corresponds to the natural logarithm of the investment share of GDP, `ln(I/GDP)`. * `lngd`: This represents the natural logarithm of the sum of population growth rate, technological progress rate, and depreciation rate, `ln(n + g + δ)`. The core task is to "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)... Report the coefficient on the log of (n + g + δ)." Now, I need to consider the tools I have at my disposal, specifically the `infer.ols` function. I need to make sure I'm using it correctly to achieve the desired regression. The `infer.ols` function takes the dataset (`'growthdj'`), the dependent variable (`y='ly'`), and the independent variables (`x`). A key question arises: how should I specify the independent variables? The request asks for the *coefficient on the log of (n + g + δ)*. I can achieve this in a couple of ways within `infer.ols`. I could include both `ls` and `lngd` directly in the `x` argument (i.e., `x=['ls', 'lngd']`). The documentation for `infer.ols` states that "x: Regressors of interest; one coefficient figure each," implying that this will return coefficients for *both* `ls` and `lngd`. Alternatively, I could specify `lngd` as the primary regressor of interest in `x` and `ls` as a control, or put them both in `x`. Given the phrasing, including both in `x=['ls', 'lngd']` seems the most direct way to get both coefficients and then extract the one for `lngd`. A critical detail is the standard errors. Table I of the MRW (1992) paper reports standard errors. I need to ascertain which type of standard errors they used and ensure my `infer.ols` call matches. The paper reports: * Dependent variable: log GDP per working-age person in 1985 * Sample: Non-oil (N = 98) * Constant: 5.48 (standard error in parentheses: 1.59) * ln(I/GDP): 1.42 (standard error: 0.14) * ln(n + g + δ): -1.97 (standard error: 0.56) * R² = 0.59 * s.e.e. = 0.69 The `infer.ols` function has a `se` parameter which defaults to `'HC1'`. The MRW paper likely uses classical OLS standard errors. Therefore, I should investigate the output when using `se='classical'` to see if it aligns with the reported standard errors in MRW. If not, I might need to consider other options or investigate further into the `infer.ols` capabilities. For now, my strategy is to run the regression with both `ls` and `lngd` in `x`, subsetting the data for `oil == 'no'`, and paying close attention to the standard errors, likely by trying `se='classical'` first. Let's proceed with running `infer.ols` with these specifications.

   Chamadas pedidas

   • infer.ols

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

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
10. 9Ferramenta
    infer.olsv0.1.0call_d87aaab8decidido pelo modeloreexecutável

    Motivo: I will run an ordinary least squares regression of the log GDP per working-age person in 1985 on the log investment share and the log of (n + g + δ) for the non-oil sample.

    Argumentos

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

    Figuras call_d87aaab8

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	1,42401	1.424014283369419	0,1431060.14310581649732002	1,13991 – 1,70812
    coef.lngd Coefficient on lngd in the regression of ly	-1,98977	-1.9897744846061867	0,5633620.5633618948953983	-3,10819 – -0,87136

    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": 2.2854641214134954,
          "coef": 5.429883095781651,
          "p": 0.0008999523718049453,
          "se": 1.5838898803304133,
          "t": 3.428194827944055,
          "term": "Intercept"
        },
        {
          "ci_high": 1.708115249178197,
          "ci_low": 1.1399133175606408,
          "coef": 1.424014283369419,
          "p": 2.1046445253797267e-16,
          "se": 0.14310581649732002,
          "t": 9.950778509384255,
          "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

    c97308c1e73af64837f78ba99692887f475219a6f46e3b8c06fea2ff46fa97d1

    Resultado mostrado ao modelo
11. 10Turno do modelo
    call_a3486b95gemini-3.8-flashFim: STOP13.168 ms15832 de entrada · 267 de saída · 978 de raciocínio · 0 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process in Replicating the MRW (1992) Regression Coefficient** Alright, let's break down this request and my internal monologue to arrive at the correct answer. My primary goal is to isolate and report the coefficient for the log of `(n + g + δ)` from the specified regression, adhering strictly to the prompt's constraints and the output of the provided tools. First, I see the instruction to "Wait, let's also check HC1 just in case, or default se: HC1". This is a preemptive check, a habit to ensure I'm not missing any underlying assumptions or alternative calculations. Similarly, "Wait, Table I in Mankiw Romer Weil (1992): Let's check what HC1 gives" indicates I'm cross-referencing with the original source material, a crucial step for empirical work. Then, the core of the task emerges: "The question is: 'Report the coefficient on the log of (n + g + δ).'" This immediately narrows my focus. I note, "Notice that the coefficient itself does not depend on `se`! The coefficient is -1.98977 (or ~ -1.99)." This highlights the specific value I need to extract. However, a good researcher always questions and verifies. "Wait, why does MRW 1992 report -1.97?" This is a critical point of divergence. It prompts me to investigate potential discrepancies. My next thought, "Let's check if MRW did something slightly different or if Durlauf and Johnson's dataset GrowthDJ has slight differences in rounding or data," is the natural investigative step. I'm hypothesizing that the difference might lie in the specific dataset used or minor methodological variations. The subsequent section, "In Durlauf and Johnson (1995), GrowthDJ: With `growthdj`, N = 98: Intercept: 5.42988 (se 1.58389) ls: 1.42401 (se 0.143106) lngd: -1.98977 (se 0.563362)," is me executing that check. I'm looking at the output from the `growthdj` dataset, and I find that my extracted coefficient (`lngd: -1.98977`) matches my earlier observation. This tells me the tool has replicated the result from Durlauf and Johnson (1995), which uses a dataset derived from MRW. The slight difference from the original MRW (-1.97) is likely due to dataset specifics or rounding as hypothesized. Next, I encounter a potential complexity related to language: "Let's check if the question was in Portuguese or English: Question is: 'Mankiw, Romer and Weil (1992), ... Report the coefficient on the log of (n + g + δ).'" The question itself is clearly in English. This leads to a careful re-reading of the instructions: "Rule 7 states: 'Write the answer in the language of the question (Portuguese: decimal comma)'. Wait, the question is in English!" This is where I analyze the instruction about language and decimal commas. The parenthetical "(Portuguese: decimal comma)" seems to be a specific instruction for when the question *is* in Portuguese. The general rule is "Write the answer in the language of the question." Since the question is in English, my answer should be in English. I consider a bilingual approach ("Wait, let's re-read carefully: ... If the prompt is in English, the language of the question is English. But to be safe, I can write clearly in English, or bilingual? No, 'Write the answer in the language of the question'") but ultimately conclude that adherence to the primary instruction is best. Then, I confirm that no further tools are required: "Let's check if any other tools are needed. No other tools are needed. We have: `call_d87aaab8:coef.lngd`: value: -1.98977, se: 0.563362, ci: [-3.10819, -0.87136]" and also note the coefficient for `ls`. I then review the potential limitations: "Let's check the caveats: Cross-sectional OLS regression assumes that the error term (technology level / unobserved country-specific productivity shocks) is uncorrelated with investment and population growth, which may be violated if technology levels or institutions are omitted and correlated with fertility or investment rates." This is a crucial component for a fulsome answer, as it addresses potential econometric issues. Finally, I run through a checklist of all requirements: "- submit_answer tool - answer - caveats - figure_refs: `["call_d87aaab8:coef.lngd"]` (and `call_d87aaab8:coef.ls` if quoted)." I also re-confirm the precise wording of the question to ensure my answer directly addresses it. This thorough review ensures I haven't missed any crucial instructions or missed any required outputs. My conclusion is to use the precise numerical value obtained from the tool, explicitly stating the coefficient and its standard error, and incorporating the provided caveat.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "For the non-oil sample of 98 countries, the ordinary least squares (OLS) estimate of the coefficient on the log of (n + g + δ), ln(n + g + δ), is -1.98977 (standard error: 0.563362; 95% confidence interval: [-3.10819, -0.87136]). The corresponding coefficient on the log of the investment share, ln(I/GDP), is 1.42401 (standard error: 0.143106; 95% confidence interval: [1.13991, 1.70812]), with an R² of 0.6008648.",
        "caveats": [
          "Cross-sectional OLS estimates assume that initial efficiency/technology levels and other omitted country-specific factors are uncorrelated with population growth and investment rates; endogeneity or omitted variable bias could undermine causal interpretation."
        ],
        "figure_refs": [
          "call_d87aaab8:coef.lngd",
          "call_d87aaab8:coef.ls"
        ]
      }

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

    Números encontrados

    98 · -1.98977 · 0.563362 · 95% · -3.10819 · -0.87136 · 1.42401 · 0.143106 · 95% · 1.13991 · 1.70812 · 0.6008648

    Sem lastro

    —

    Não citados

    —

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

    For the non-oil sample of 98 countries, the ordinary least squares (OLS) estimate of the coefficient on the log of (n + g + δ), ln(n + g + δ), is -1.98977 (standard error: 0.563362; 95% confidence interval: [-3.10819, -0.87136]). The corresponding coefficient on the log of the investment share, ln(I/GDP), is 1.42401 (standard error: 0.143106; 95% confidence interval: [1.13991, 1.70812]), with an R² of 0.6008648. Ressalvas: Cross-sectional OLS estimates assume that initial efficiency/technology levels and other omitted country-specific factors are uncorrelated with population growth and investment rates; endogeneity or omitted variable bias could undermine causal interpretation.

    • Cross-sectional OLS estimates assume that initial efficiency/technology levels and other omitted country-specific factors are uncorrelated with population growth and investment rates; endogeneity or omitted variable bias could undermine causal interpretation.

    Figuras citadas: call_d87aaab8:coef.lngd, call_d87aaab8:coef.ls · Parada: answered

    Figura da resposta: call_d87aaab8:coef.ls = 1,424011.424014283369419 (se 0,1431060.14310581649732002)
14. 13Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
15. 14Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_d87aaab8: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 próximafalhouobrigatória1.424014283 vs -1.9897744846061867
20. 19Pontuação
    #6figura da resposta próximafalhouregistrada0.1431058165 vs 0.5633618948953987
21. 20Pontuação
    #7figura da resposta próximafalhouregistrada1.424014283 vs -1.97
22. 21Pontuação
    #8figura da resposta próximafalhouregistrada0.1431058165 vs 0.56

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