Tarefa paper_repro.mrw_1992.tab1_inter_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), 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 the investment share of GDP.

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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), 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 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_b0be278bgemini-3.8-flashFim: STOP7.931 ms14724 de entrada · 93 de saída · 374 de raciocínio · 0 em cache

   Texto visível

   I will run the unrestricted Solow regression using ordinary least squares on the intermediate sample (inter == 'yes') with classical standard errors as reported in Mankiw, Romer, and Weil (1992).

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Replicating MRW (1992) Table I** My objective is quite specific: I need to reproduce Table I from the seminal 1992 paper by Mankiw, Romer, and Weil (MRW). To be precise, I'm focusing on their "unrestricted textbook Solow regression" as applied to the "Intermediate" sample of countries. To achieve this, I've identified the core components of the regression I need to run: * **Dependent Variable:** The outcome I'm interested in is the logarithm of GDP per working-age person in 1985, which the dataset labels as `ly`. * **Independent Variables:** The key regressors, based on the Solow model and the MRW specification, are the logarithm of the investment share of GDP (`ls`) and the logarithm of the sum of population growth rate, technological progress, and depreciation rate (`lngd`). * **Sample Selection:** I need to filter the dataset to include only those countries designated as part of the "Intermediate" sample. The dataset uses a column named `inter` for this, where `'yes'` signifies inclusion in this sample. The tool I intend to use for this regression is `infer__ols`. Now, before diving into execution, I'm taking a moment to thoroughly understand the dataset and the tool's capabilities. First, I've consulted the dataset description for `growthdj`. I've confirmed that the columns I need are present and correctly defined: `ly` for log GDP, `ls` for log investment share, `lngd` for log (n + g + δ), and `inter` for the sample indicator. This is crucial for ensuring I'm feeding the correct data into the model. Next, and this is a critical step, I need to consider the standard error estimation. MRW (1992) is a foundational paper, and understanding their methodological choices is paramount. My initial recollection and a quick check confirm that Table I in their paper reports results using **classical OLS standard errors**. This is a key detail. Now, I turn my attention to the `infer__ols` function's parameters. I need to ensure it’s configured to produce the correct standard errors. The documentation for `infer__ols` indicates a `se` parameter. Its default is `HC1`, which is a heteroskedasticity-consistent standard error. However, given MRW's use of classical standard errors, I need to override this. The `se` parameter accepts an enum that includes `'classical'`. Therefore, I should either explicitly set `se='classical'` or, to be thorough, I might even consider running the regression with both `se='classical'` and `se='HC1'` (the default) to compare and ensure I'm precisely matching MRW's approach. Finally, the sample selection needs to be implemented. The `infer__ols` function has a `subset` parameter. I will use this parameter with the condition `"inter == 'yes'"` to correctly filter the data to my target "Intermediate" sample. So, to recap my plan: I will use `infer__ols` on the `growthdj` dataset, specifying `ly` as the outcome, `ls` and `lngd` as regressors, and importantly, setting `se='classical'` for the standard errors. I will also apply the `subset="inter == 'yes'"` argument to ensure I'm working with the correct country group. This systematic approach should allow me to faithfully reproduce the results presented in MRW's Table I.

   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_d449d3acdecidido pelo modeloreexecutável

    Motivo: I will run the unrestricted Solow regression using ordinary least squares on the intermediate sample (inter == 'yes') with classical standard errors as reported in Mankiw, Romer, and Weil (1992).

    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_d449d3ac

    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

    41f22bb56371266ee0bb9ecb025b9e6a6f70a5236c3df41b14cdb8306d722855

    Resultado mostrado ao modelo
11. 10Turno do modelo
    call_d61129e7gemini-3.8-flashFim: STOP6.158 ms15555 de entrada · 72 de saída · 268 de raciocínio · 12602 em cache

    Texto visível

    I will also estimate the same specification using robust (HC1) standard errors to verify standard error sensitivity.

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process in Replicating the Mankiw, Romer, and Weil (1992) Results** My primary objective here is to rigorously verify the findings presented in Table I of Mankiw, Romer, and Weil's (1992) seminal paper, specifically focusing on their "Intermediate sample" results. I'm not just looking for approximate agreement; I want to ensure that my own estimations align precisely with theirs. My initial step involves reconstructing the regression of `log GDP per working-age person in 1985` on the standard Solow model determinants: `ln(I/GDP)` and `ln(n + g + δ)`. I need to confirm the estimated coefficients and, crucially, their associated standard errors and overall model fit. Looking at the MRW paper, their Table I for the intermediate sample reports an R-squared of 0.59. This is a key benchmark for my own calculation. They also provide standard errors in parentheses next to the coefficients. I need to make sure my own output reflects these figures as closely as possible. Specifically, I've noted their reported coefficient for `ln(I/GDP)` as 1.32 with a standard error of 0.17. For `ln(n + g + δ)`, it's -2.01 with a standard error of 0.53. The constant is around 5.36. My own calculation yielded a coefficient of 1.31755 for `ln(I/GDP)` with a standard error of 0.170943, and the R-squared came in at 0.598908. These are remarkably close, giving me confidence that my replication is on the right track. The number of observations (75) also matches perfectly. Now, a point of careful consideration: the paper reports standard errors in parentheses. While this is a common practice, it's vital to understand *which* standard errors are being presented. My current results are likely based on classical standard errors. The question explicitly asks to check if HC1 standard errors were also used or if classical errors are sufficient. Since my current output closely matches the reported figures when interpreted as classical errors, I will proceed with that understanding, but I have also made a note to explicitly check HC1 standard errors as a safeguard, just in case there's any ambiguity or if the intended comparison necessitates it. The goal is absolute precision, and understanding the robustness of the standard errors is part of that.

    Chamadas pedidas

    • infer.ols

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

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
12. 11Ferramenta
    infer.olsv0.1.0call_40edbdd8decidido pelo modeloreexecutável

    Motivo: I will also estimate the same specification using robust (HC1) standard errors to verify standard error sensitivity.

    Argumentos

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

    Figuras call_40edbdd8

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.ls Coefficient on ls in the regression of ly	1,31755	1.3175526551860068	0,1645930.16459294610476607	0,989443 – 1,64566
    coef.lngd Coefficient on lngd in the regression of ly	-2,0172	-2.017199495235038	0,4843740.4843739068281363	-2,98278 – -1,05162

    Diagnósticos

    • n_obs = 7575
    • k = 33
    • r2 = 0,5989080.5989084353517702
    • df_resid = 7272
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (1)

    {
      "coefficients": [
        {
          "ci_high": 8.28068846962579,
          "ci_low": 2.4110419444042965,
          "coef": 5.345865207015043,
          "p": 0.0005248955697730653,
          "se": 1.4722231756285449,
          "t": 3.6311513739978327,
          "term": "Intercept"
        },
        {
          "ci_high": 1.645662696575399,
          "ci_low": 0.9894426137966146,
          "coef": 1.3175526551860068,
          "p": 1.501287654741228e-11,
          "se": 0.16459294610476607,
          "t": 8.00491568057457,
          "term": "ls"
        },
        {
          "ci_high": -1.0516177593314762,
          "ci_low": -2.9827812311386,
          "coef": -2.017199495235038,
          "p": 0.0000854553047702699,
          "se": 0.4843739068281363,
          "t": -4.1645502922410165,
          "term": "lngd"
        }
      ]
    }

    Digests dos dados

    growthdj e3f509733efe06358f9503c526bd45111b6a64feb75b292419aae56055b598f2

    sha256 do resultado

    af85b3428a2ea24c1098825f3b5c65a80e41b57eb9c0ddcd78dca74b49c8bd1e

    Resultado mostrado ao modelo
13. 12Turno do modelo
    call_fedc3b82gemini-3.8-flashFim: STOP10.973 ms16262 de entrada · 318 de saída · 782 de raciocínio · 12613 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on the Mankiw, Romer, and Weil (1992) Solow Regression** Okay, I need to carefully dissect this request. I'm being asked to perform a specific regression as described in Mankiw, Romer, and Weil (1992), specifically using their "Intermediate sample" of 75 countries. The goal is to estimate the coefficient on the log of the investment share of GDP. First, I'll confirm the core components of the regression: * **Dependent Variable:** The log of GDP per working-age person in 1985. * **Independent Variables:** The log of the investment share of GDP, and the log of (n + g + δ). * **Sample:** The "intermediate" sample, which means I'm working with 75 countries, excluding those with a grade of 'D' in the Summers-Heston data and a 1960 population less than one million. * **Assumptions:** The growth rate of the working-age population (n) is based on the 1960-1985 period, and the combined rate of technological progress and depreciation (g + δ) is assumed to be a constant 0.05. Now, I need to be very precise about the output required. The request specifically asks for "the coefficient on the log of the investment share of GDP." I have access to a tool that provides this information, and I see a relevant output: `call_d449d3ac:coef.ls`. This value is 1.31755. I also need to consider the language rule. The prompt is in English, and the rule states, "Write the answer in the language of the question (Portuguese: decimal comma)." This is a bit tricky, but my interpretation is that if the question *is* Portuguese, then I should use Portuguese and a decimal comma. Since the question is in English, I should respond in English, and I'll use a standard decimal point. Let's check the details associated with `call_d449d3ac:coef.ls`: * **Coefficient on `ls` (log investment share):** 1.31755 * **Standard Error (classical OLS):** 0.170943. This is important because the prompt mentions "unrestricted textbook Solow regression," which typically implies classical OLS. I also see a robust SE of 0.164593, but the classical one seems more aligned with the "textbook" description. * **95% Confidence Interval (classical OLS):** [0.976785, 1.65832]. This is good for context. * **R²:** 0.598908. This tells me about the explanatory power of the model. * **Sample Size:** 75 countries, which matches the "intermediate sample" description. I need to ensure all numbers I report come from tool calls or the question itself, as per Rule 1. I have identified all the necessary numbers. Finally, I should briefly acknowledge the potential limitations of this OLS estimation, as it's good practice for an expert audience. These include the assumption of constant parameters (g + δ) across countries, the potential for omitted variable bias due to unobserved country-specific productivity differences, and the assumption of homoskedasticity underlying the classical standard errors. So, to summarize, I am performing a specific OLS regression on a defined sample, extracting the coefficient for the log of the investment share. The result is 1.31755, with a classical OLS standard error of 0.170943.

    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 ordinary least squares coefficient on the log of the investment share of GDP (ls) is 1.31755, with a classical standard error of 0.170943 (95% CI [0.976785, 1.65832]; with HC1 robust standard errors, the standard error is 0.164593 and 95% CI [0.989443, 1.64566]). The regression R² is 0.598908.",
        "caveats": [
          "Identification via cross-country OLS relies on the assumption that investment rates and population growth are uncorrelated with unobserved country-specific efficiency levels (A_0).",
          "The model assumes a common rate of technological progress and depreciation (g + delta = 0.05) across all countries.",
          "Classical standard errors assume homoskedasticity across countries, though robust (HC1) standard errors yield a very similar standard error (0.164593)."
        ],
        "figure_refs": [
          "call_d449d3ac:coef.ls",
          "call_40edbdd8:coef.ls"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
14. 13Guarda
    resposta aceita

    Números encontrados

    75 · 1992 · 1.31755 · 0.170943 · 95% · 0.976785 · 1.65832 · 0.164593 · 95% · 0.989443 · 1.64566 · 0.598908 · 0.05 · 0.164593

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
15. 14Resposta

    In the unrestricted textbook Solow regression for the Intermediate sample of 75 countries (Mankiw, Romer, and Weil, 1992, Table I), the estimated ordinary least squares coefficient on the log of the investment share of GDP (ls) is 1.31755, with a classical standard error of 0.170943 (95% CI [0.976785, 1.65832]; with HC1 robust standard errors, the standard error is 0.164593 and 95% CI [0.989443, 1.64566]). The regression R² is 0.598908. Ressalvas: Identification via cross-country OLS relies on the assumption that investment rates and population growth are uncorrelated with unobserved country-specific efficiency levels (A_0). The model assumes a common rate of technological progress and depreciation (g + delta = 0.05) across all countries. Classical standard errors assume homoskedasticity across countries, though robust (HC1) standard errors yield a very similar standard error (0.164593).

    • Identification via cross-country OLS relies on the assumption that investment rates and population growth are uncorrelated with unobserved country-specific efficiency levels (A_0).
    • The model assumes a common rate of technological progress and depreciation (g + delta = 0.05) across all countries.
    • Classical standard errors assume homoskedasticity across countries, though robust (HC1) standard errors yield a very similar standard error (0.164593).

    Figuras citadas: call_d449d3ac:coef.ls, call_40edbdd8:coef.ls · Parada: answered

    Figura da resposta: call_d449d3ac:coef.ls = 1,317551.3175526551860068 (se 0,1709430.17094253097708434)
16. 15Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
17. 16Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_d449d3ac:coef.ls (infer.ols)
18. 17Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.ols
19. 18Pontuação
    #3argumento igualpassouobrigatóriainfer.ols.y = 'ly'
20. 19Pontuação
    #4diagnósticopassouobrigatória75 vs 75
21. 20Pontuação
    #5figura da resposta próximapassouobrigatória1.317552655 vs 1.3175526551860062
22. 21Pontuação
    #6figura da resposta próximapassouregistrada0.170942531 vs 0.17094253097708437
23. 22Pontuação
    #7figura da resposta próximafalhouregistrada1.317552655 vs 1.31
24. 23Pontuação
    #8figura da resposta próximapassouregistrada0.170942531 vs 0.17

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