Tarefa paper_repro.mrw_1992.tab1_inter_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), Intermediate sample: in the 75 'intermediate' countries (no Summers-Heston grade of D and a 1960 population of at least 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 (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), Intermediate sample: in the 75 'intermediate' countries (no Summers-Heston grade of D and a 1960 population of at least 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 (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_1052aaf2gemini-3.8-flashFim: STOP9.509 ms14725 de entrada · 105 de saída · 541 de raciocínio · 0 em cache

   Texto visível

   I will estimate the regression of log GDP per working-age person in 1985 on the log of the investment share and the log of (n + g + δ) for the intermediate sample using ordinary least squares with classical standard errors as in the original study.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Replicating MRW (1992) Table I** Alright, so the primary objective here is to meticulously replicate a specific result from Mankiw, Romer, and Weil's seminal 1992 paper, specifically Table I. My focus needs to be on reproducing their "unrestricted textbook Solow regression" as applied to their "intermediate sample" of countries. Let's break down what this entails: 1. **The Core Regression:** The paper's core proposition in this context is that the logarithm of GDP per working-age person in 1985 should be explained by the logarithm of the investment share (I/GDP) and the logarithm of the sum of population growth, technological progress, and depreciation (n + g + delta). This is the standard Solow model prediction, without any restrictions imposed on the coefficients. 2. **The Specific Dataset and Sample:** I need to use the dataset provided, and crucially, I'm interested in the "intermediate sample." The dataset description indicates that the `inter` column (`'yes'` or `'no'`) flags countries belonging to this intermediate sample. So, I'll need to filter the data to include only those rows where `inter == 'yes'`. The paper states this sample consists of 75 countries. 3. **Outcome Variable:** The dependent variable is explicitly defined as the log of GDP per working-age person in 1985. Looking at the dataset description, this corresponds to the `ly` column. 4. **Predictor Variables:** * The first predictor is the logarithm of the investment share (I/GDP). The dataset description maps this to the `ls` column. * The second predictor is the logarithm of the sum of population growth, technological progress, and depreciation (n + g + delta). The dataset description refers to this as `lngd`. 5. **The Key Output:** The specific coefficient I need to report is the one associated with `log(n + g + delta)`, which is the coefficient on the `lngd` variable. 6. **Verification Strategy:** Before diving into the implementation, I need to establish a clear benchmark for success. I'll cross-reference the expected output with the actual numbers presented in Table I of the MRW (1992) paper for the intermediate sample. This means looking for: * The sample size (N=75). * The coefficients for the constant, ln(I/GDP), and ln(n+g+d). * The standard errors associated with these coefficients. * The R-squared value for the regression. The paper's Table I for the intermediate sample shows: * Constant: 5.36 (with standard error 1.59) * ln(I/GDP): 1.31 (with standard error 0.17) * ln(n+g+d): -2.01 (with standard error 0.53) * R-squared: 0.59 7. **Implementation Tool Considerations:** I'm planning to use a function called `infer__ols`. I need to confirm its capabilities relevant to this task: * **Subsetting:** Can `infer__ols` handle filtering the data? The documentation suggests it supports a `subset` argument, which is exactly what I need for `inter == 'yes'`. * **Standard Errors:** The MRW paper reports "OLS classical standard errors." I need to ensure `infer__ols` can produce these. The `se` parameter in `infer__ols` can take `"classical"` or `"HC1"`. Given the MRW report, I will aim for `"classical"` standard errors. I'll need to be mindful of this choice, as the default might be HC1. So, the plan is to call `infer__ols` with `ly` as the dependent variable, `ls` and `lngd` as regressors, specifying the `subset` to be `"inter == 'yes'"`, and crucially, setting `se="classical"` to ensure the standard errors align with the original publication. Then, I'll extract and report the coefficient and standard error for `lngd`.

   Chamadas pedidas

   • infer.ols

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

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
10. 9Ferramenta
    infer.olsv0.1.0call_c6890c71decidido pelo modeloreexecutável

    Motivo: I will estimate the regression of log GDP per working-age person in 1985 on the log of the investment share and the log of (n + g + δ) for the intermediate sample using ordinary least squares with classical standard errors as in the original study.

    Argumentos

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

    Figuras call_c6890c71

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	1,31755	1.3175526551860068	0,1709430.17094253097708434	0,976785 – 1,65832
    coef.lngd Coefficient on lngd in the regression of ly	-2,0172	-2.017199495235038	0,5338660.533865871049398	-3,08144 – -0,952957

    Diagnósticos

    • n_obs = 7575
    • k = 33
    • r2 = 0,5989080.5989084353517702
    • df_resid = 7272
    • se_type = "classical"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 8.42193032533697,
          "ci_low": 2.269800088693116,
          "coef": 5.345865207015043,
          "p": 0.0008989504601296264,
          "se": 1.5430756647701926,
          "t": 3.464421952251572,
          "term": "Intercept"
        },
        {
          "ci_high": 1.6583203626817928,
          "ci_low": 0.9767849476902208,
          "coef": 1.3175526551860068,
          "p": 5.383213566571891e-11,
          "se": 0.17094253097708434,
          "t": 7.707576620370919,
          "term": "ls"
        },
        {
          "ci_high": -0.9529573318138582,
          "ci_low": -3.081441658656218,
          "coef": -2.017199495235038,
          "p": 0.00032237256258626346,
          "se": 0.533865871049398,
          "t": -3.778476214015915,
          "term": "lngd"
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    17a2033d01aa90f0c25e0de16803ba430735fb389e23c3cfbffce4ae47f6e0d0

    Resultado mostrado ao modelo
11. 10Turno do modelo
    call_902d3d28gemini-3.8-flashFim: STOP16.514 ms15736 de entrada · 349 de saída · 1304 de raciocínio · 12636 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on the MRW (1992) Regression Results** I've been tasked with extracting specific information from the Mankiw, Romer, and Weil (1992) paper, focusing on the "unrestricted textbook Solow regression" using their "intermediate" sample. The core of the request is to report the coefficient on the log of `(n + g + δ)` and its associated uncertainty, along with the research design and potential limitations. First, I need to pinpoint the exact data and results. I see a reference to Table I in MRW (1992). The prompt specifies an "intermediate sample" of 75 countries, defined by certain criteria (no Summers-Heston grade D, 1960 population at least one million). The regression itself is an Ordinary Least Squares (OLS) estimation of log GDP per working-age person in 1985, regressed on the log of the investment share of GDP and the log of `(n + g + δ)`. I'm specifically asked for the coefficient on `log(n + g + δ)`. I've retrieved some promising figures from my tools: * **`call_c6890c71:coef.lngd`**: This looks like the coefficient for `log(n + g + δ)` (as `lngd` is often used as shorthand for `log(growth and depreciation)` or similar, aligning with `n+g+δ`). The reported coefficient is -2.0172, with a standard error of 0.533866 and a 95% confidence interval of [-3.08144, -0.952957]. This matches the magnitude and significance I'd expect for this variable in the Solow model's empirical application. * **`call_c6890c71:coef.ls`**: This is likely the coefficient for the log of the investment share of GDP, which is 1.31755. While not directly asked for, it's good to have context. * **`call_c6890c71:R_squared`**: The R-squared is reported as approximately 0.5989, indicating that about 60% of the variation in log GDP per working-age person is explained by these variables in this sample. * **Sample Size**: Confirmed as 75. Now, I need to pay close attention to Rule 7 regarding the output format. **Language of the Question and Decimal Comma:** The question is written in English. Rule 7 states: "Write the answer in the language of the question (Portuguese: decimal comma)". This is a bit ambiguous. Does it mean *always* use Portuguese if the parenthetical is present, or only use the Portuguese decimal comma *if* the language of the question happens to be Portuguese? Given the explicit instruction "Write the answer in the language of the question," and that the question is in English, I will proceed with English. The parenthetical "(Portuguese: decimal comma)" seems to be a specific instruction for handling decimal points *if* the output were to be in Portuguese. Since it's not, I will use the standard English decimal point. **Content of the Answer:** Rule 7 requires: 1. **The estimate with its uncertainty:** This means the coefficient and its standard error or confidence interval. 2. **The design that identifies it:** This refers to the empirical strategy, which is OLS regression in this case. 3. **What could undermine it:** This points to potential limitations or caveats. **Identifying the "Design":** The design is the OLS regression of log GDP per working-age person on the logs of the investment share and `(n + g + δ)`, using the specified intermediate sample of 75 countries from MRW (1992). **Identifying What Could Undermine It:** I've thought about the standard limitations of cross-sectional OLS in this context. Key issues include: * **Endogeneity:** The regressors (investment share, population growth) might be correlated with unobserved factors affecting GDP, such as technology or institutional quality. * **Omitted Variable Bias:** Important determinants of growth, like human capital or unobserved productivity differences, might be missing from the regression, leading to biased coefficients. MRW themselves addressed this by later including human capital. * **Assumptions of OLS:** The results rely on assumptions like homoskedasticity and orthogonality. * **Constant `g + δ`:** The assumption that `g + δ` is a constant 0.05 across all countries and time might be restrictive. **Cross-referencing and Formatting:** * **Figure References:** I need to list any figures quoted as `<call_id>:<key>`. The relevant figure is the output from `call_c6890c71`, specifically the coefficient on `lngd`. * **Caveats:** I will list the diagnostics that limit the conclusion as caveats. * **Numbers:** I must use the numbers as the tools stated them, without rounding or applying rule-of-thumb thresholds. Let's assemble the final answer according to Rule 7. I will use the coefficient estimate and its 95% confidence interval as the measure of uncertainty. **Final Check:** * Language: English. * Decimal: English standard (period). * Estimate: Coefficient and 95% CI. * Design: OLS regression, MRW (1992) intermediate sample. * Undermining factors: Endogeneity, omitted variables, OLS assumptions. * Figure refs: `call_c6890c71:coef.lngd`. * Caveats: Listed. * Numbers: Exact as per tool. The process seems complete. Now I will prepare the `submit_answer` call.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "In the unrestricted textbook Solow regression for the intermediate sample of 75 countries (Mankiw, Romer, and Weil, 1992, Table I), the estimated OLS coefficient on the log of (n + g + δ) is -2.0172, with a standard error of 0.533866 (95% CI: [-3.08144, -0.952957], p = 0.000322373).\n\nFor comparison, the coefficient on the log of the investment share (ln(I/GDP)) is 1.31755 (SE: 0.170943; 95% CI: [0.976785, 1.65832]), and the model R² is 0.59890843535177.",
        "caveats": [
          "The cross-sectional OLS specification assumes that the saving rate and population growth are uncorrelated with country-specific technology/efficiency levels (omitted productivity differences).",
          "The model imposes a constant value of 0.05 for (g + δ) across all countries.",
          "Omission of human capital accumulation may introduce omitted-variable bias, which motivated MRW's augmented Solow model."
        ],
        "figure_refs": [
          "call_c6890c71:coef.lngd",
          "call_c6890c71:coef.ls"
        ]
      }

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

    Números encontrados

    75 · 1992 · -2.0172 · 0.533866 · 95% · -3.08144 · -0.952957 · 0.000322373 · 1.31755 · 0.170943 · 95% · 0.976785 · 1.65832 · 0.59890843535177 · 0.05

    Sem lastro

    —

    Não citados

    —

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

    In the unrestricted textbook Solow regression for the intermediate sample of 75 countries (Mankiw, Romer, and Weil, 1992, Table I), the estimated OLS coefficient on the log of (n + g + δ) is -2.0172, with a standard error of 0.533866 (95% CI: [-3.08144, -0.952957], p = 0.000322373). For comparison, the coefficient on the log of the investment share (ln(I/GDP)) is 1.31755 (SE: 0.170943; 95% CI: [0.976785, 1.65832]), and the model R² is 0.59890843535177. Ressalvas: The cross-sectional OLS specification assumes that the saving rate and population growth are uncorrelated with country-specific technology/efficiency levels (omitted productivity differences). The model imposes a constant value of 0.05 for (g + δ) across all countries. Omission of human capital accumulation may introduce omitted-variable bias, which motivated MRW's augmented Solow model.

    • The cross-sectional OLS specification assumes that the saving rate and population growth are uncorrelated with country-specific technology/efficiency levels (omitted productivity differences).
    • The model imposes a constant value of 0.05 for (g + δ) across all countries.
    • Omission of human capital accumulation may introduce omitted-variable bias, which motivated MRW's augmented Solow model.

    Figuras citadas: call_c6890c71:coef.lngd, call_c6890c71:coef.ls · Parada: answered

    Figura da resposta: call_c6890c71:coef.ls = 1,317551.3175526551860068 (se 0,1709430.17094253097708434)
14. 13Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
15. 14Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_c6890c71:coef.ls (infer.ols)
16. 15Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.ols
17. 16Pontuação
    #3argumento igualpassouobrigatóriainfer.ols.y = 'ly'
18. 17Pontuação
    #4diagnósticopassouobrigatória75 vs 75
19. 18Pontuação
    #5figura da resposta próximafalhouobrigatória1.317552655 vs -2.0171994952350376
20. 19Pontuação
    #6figura da resposta próximafalhouregistrada0.170942531 vs 0.5338658710493988
21. 20Pontuação
    #7figura da resposta próximafalhouregistrada1.317552655 vs -2.01
22. 21Pontuação
    #8figura da resposta próximafalhouregistrada0.170942531 vs 0.53

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