Tarefa paper_repro.stock_watson_2007.eq12_16.agent

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Pergunta feita ao analista

Stock and Watson, Introduction to Econometrics (2nd edition), Chapter 12, equation (12.16): using the 1995 cross-section of the 48 continental U.S. states, estimate by two-stage least squares the price elasticity of cigarette demand, the effect of the log of the real price per pack (taxes included) on the log of packs per capita, with the log of real per capita income as an included exogenous regressor, using as instruments the real general sales tax per pack and the real cigarette-specific tax per pack (two instruments). Use heteroskedasticity-robust standard errors. Report the coefficient on the log real price.

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Verificações

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Trajetória

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

1. 0Início

   Stock and Watson, Introduction to Econometrics (2nd edition), Chapter 12, equation (12.16): using the 1995 cross-section of the 48 continental U.S. states, estimate by two-stage least squares the price elasticity of cigarette demand, the effect of the log of the real price per pack (taxes included) on the log of packs per capita, with the log of real per capita income as an included exogenous regressor, using as instruments the real general sales tax per pack and the real cigarette-specific tax per pack (two instruments). Use heteroskedasticity-robust standard errors. Report the coefficient on the log real price.

   cigarettes (agent)

   Stock and Watson's cigarette consumption panel for the 48 continental U.S. states, 1985 and 1995, as distributed in the R package AER (data set CigarettesSW, served by Rdatasets); one row per state and year (96 rows). Columns: state; year; cpi, the consumer price index; population; packs, packs of cigarettes per capita; income, total state personal income (nominal); tax, the average state, federal and local excise taxes per pack (cents); price, the average price per pack including taxes (cents); taxs, the average excise taxes per pack including sales tax (cents). Added by the declared transforms: rprice = price / cpi, the real price; lrprice = log(rprice); lpacks = log(packs); rincome = income / population / cpi, real per capita income; lrincome = log(rincome); salestax = (taxs - tax) / cpi, the real general sales tax per pack; cigtax = tax / cpi, the real cigarette-specific tax per pack; and the intermediate columns income_pc and sales_tax_nominal.

   file 629e887a8104d483d450a9bbe487cb5613e62d116c4ecc84d6c8893b7393fcd2 · frame —

   1. derive {"args":{"left":"price","right":"cpi"},"name":"rprice","op":"ratio"}
   2. derive {"args":{"column":"rprice"},"name":"lrprice","op":"log"}
   3. derive {"args":{"column":"packs"},"name":"lpacks","op":"log"}
   4. derive {"args":{"left":"income","right":"population"},"name":"income_pc","op":"ratio"}
   5. derive {"args":{"left":"income_pc","right":"cpi"},"name":"rincome","op":"ratio"}
   6. derive {"args":{"column":"rincome"},"name":"lrincome","op":"log"}
   7. derive {"args":{"left":"taxs","right":"tax"},"name":"sales_tax_nominal","op":"diff"}
   8. derive {"args":{"left":"sales_tax_nominal","right":"cpi"},"name":"salestax","op":"ratio"}
   9. derive {"args":{"left":"tax","right":"cpi"},"name":"cigtax","op":"ratio"}
2. 1Transformação
   cigarettes · derive {"args":{"left":"price","right":"cpi"},"name":"rprice","op":"ratio"}

   96 → 96 linhas

   Frame antes → depois: edb46c0b5416 → ef8fa78f0390
3. 2Transformação
   cigarettes · derive {"args":{"column":"rprice"},"name":"lrprice","op":"log"}

   96 → 96 linhas

   Frame antes → depois: ef8fa78f0390 → e105ed6c1d84
4. 3Transformação
   cigarettes · derive {"args":{"column":"packs"},"name":"lpacks","op":"log"}

   96 → 96 linhas

   Frame antes → depois: e105ed6c1d84 → d62b932706e1
5. 4Transformação
   cigarettes · derive {"args":{"left":"income","right":"population"},"name":"income_pc","op":"ratio"}

   96 → 96 linhas

   Frame antes → depois: d62b932706e1 → e733a0b104f8
6. 5Transformação
   cigarettes · derive {"args":{"left":"income_pc","right":"cpi"},"name":"rincome","op":"ratio"}

   96 → 96 linhas

   Frame antes → depois: e733a0b104f8 → e3dc0e2e1b4a
7. 6Transformação
   cigarettes · derive {"args":{"column":"rincome"},"name":"lrincome","op":"log"}

   96 → 96 linhas

   Frame antes → depois: e3dc0e2e1b4a → e131ae1b8f79
8. 7Transformação
   cigarettes · derive {"args":{"left":"taxs","right":"tax"},"name":"sales_tax_nominal","op":"diff"}

   96 → 96 linhas

   Frame antes → depois: e131ae1b8f79 → ad36a62c9d85
9. 8Transformação
   cigarettes · derive {"args":{"left":"sales_tax_nominal","right":"cpi"},"name":"salestax","op":"ratio"}

   96 → 96 linhas

   Frame antes → depois: ad36a62c9d85 → 33ace4f530f2
10. 9Transformação
    cigarettes · derive {"args":{"left":"tax","right":"cpi"},"name":"cigtax","op":"ratio"}

    96 → 96 linhas

    Frame antes → depois: 33ace4f530f2 → be62d9713478
11. 10Turno do modelo
    call_742f7b41gemini-3.8-flashFim: STOP6.717 ms14574 de entrada · 19 de saída · 412 de raciocínio · 0 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process for Replicating the Stock and Watson Cigarette Demand Model** My primary objective here is to meticulously replicate a specific econometric model from Stock and Watson's *Introduction to Econometrics*, specifically equation (12.16) from the second edition. This involves using the `cigarettes` dataset, focusing on the cross-section for the year 1995, and employing a two-stage least squares (2SLS) estimation strategy. I need to identify the correct components for the 2SLS estimation: * **Outcome variable (`y`):** This is the log of packs of cigarettes sold per capita, represented by `lpacks`. * **Endogenous regressor (`endog`):** The variable I suspect is correlated with the error term, which is the log of the real price per pack (including taxes), `lrprice`. * **Exogenous regressor (`exog`):** A variable that is not correlated with the error term, which is the log of real per capita income, `lrincome`. * **Instruments:** These are variables that are correlated with the endogenous regressor (`lrprice`) but not directly with the outcome variable (`lpacks`), and are uncorrelated with the error term. In this case, the prompt specifies `salestax` (real general sales tax per pack) and `cigtax` (real cigarette-specific tax per pack) as the instruments. Furthermore, the request specifies the use of heteroskedasticity-robust standard errors, denoted as `"HC1"`. The final output should be the estimated coefficient for the log real price (`lrprice`). Now, I need to determine the most appropriate way to implement this. The prompt mentions `infer.iv_2sls` as the direct function to use. I'll need to consult its schema to ensure I'm passing the parameters correctly. Looking at the schema for `infer__iv_2sls`: * `dataset`: "cigarettes" * `y`: "lpacks" * `endog`: ["lrprice"] * `exog`: ["lrincome"] * `instruments`: ["salestax", "cigtax"] * `se`: "HC1" * `subset`: "year == 1995" * `level`: 0.95 (though this is for confidence intervals, which aren't explicitly requested for the report, it's good to have in mind). Alternatively, the prompt suggests considering the `instrumental-variables` skill and using `load_skill(name)` if the design isn't immediately obvious. While the specific equation and parameters are quite clear here, loading a higher-level skill like `instrumental-variables` is generally a good practice for modularity and potentially leveraging other functionalities within that skill. I should investigate the `instrumental-variables` skill first to see if it offers a more streamlined or robust approach before directly calling `infer__iv_2sls`, though I'm confident I can achieve the result with the latter if needed. My plan is to first explore `instrumental-variables` for this task.

    Chamadas pedidas

    • load_skill (meta-ferramenta)

      {
        "name": "instrumental-variables"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
12. 11Habilidade
    instrumental-variablesTexto da habilidade
13. 12Turno do modelo
    call_35bec49dgemini-3.8-flashFim: STOP5.255 ms15473 de entrada · 76 de saída · 133 de raciocínio · 12690 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Data Analysis and Model Selection** Alright, so the immediate next step in my analysis is to delve into the descriptive statistics of my dataset. I want to get a solid understanding of what I'm working with before I dive headfirst into estimation. My current thinking is to first check `data.describe`. This will give me a quick overview of the central tendency, dispersion, and shape of my variables, which is crucial for identifying any immediate outliers or anomalies. Following that, I'm leaning towards directly executing the `infer.iv_2sls` function. I feel confident in the setup at this point, and I want to move towards estimation efficiently. As I recall the variables available in the dataset, I have: * `year`: This is a categorical or temporal variable, with observations falling into either 1985 or 1995. This immediately suggests a potential for time-based analysis or sub-setting. * `lpacks`: This is the natural logarithm of packs, likely representing cigarette consumption. Log transformations are standard for economic data, helping to stabilize variance and interpret coefficients as elasticities. * `lrprice`: This is the natural logarithm of the real price of cigarettes. Again, a log transformation is expected for price variables in this context. * `lrincome`: This is the natural logarithm of real income. Similar to price, income is often logged in demand analysis. * `salestax`: This variable is defined as `(taxs - tax) / cpi`. This looks like a measure of sales tax, possibly adjusted for inflation by the consumer price index (CPI). I need to be mindful of what `taxs` and `tax` specifically represent, but the deflation by CPI is good. * `cigtax`: This is defined as `tax / cpi`. This appears to be a direct measure of cigarette excise tax, also deflated by CPI. Given the presence of distinct `year` values, a critical decision arises: should I run the model on the pooled data, or should I separate the years? My instinct is to perform the analysis separately for each year, especially if I suspect that the price elasticities or the impact of taxes might have changed between 1985 and 1995. This will allow for a more nuanced understanding of the economic landscape at those different points in time. Therefore, my immediate plan is to execute `infer__iv_2sls` with a specific subset condition. I want to focus on the 1995 data first, so I'll be calling the function with `subset="year == 1995"`. This will give me an initial estimate of the instrumental variable (IV) 2SLS model for that year. After reviewing these results, I'll then proceed to run the same model for the 1985 data.

    Chamadas pedidas

    • infer.iv_2sls

      {
        "dataset": "cigarettes",
        "endog": [
          "lrprice"
        ],
        "exog": [
          "lrincome"
        ],
        "instruments": [
          "salestax",
          "cigtax"
        ],
        "se": "HC1",
        "subset": "year == 1995",
        "y": "lpacks"
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
14. 13Ferramenta
    infer.iv_2slsv0.1.0call_3ebac80edecidido pelo modeloreexecutável

    Argumentos

    {
      "cluster": null,
      "dataset": "cigarettes",
      "endog": [
        "lrprice"
      ],
      "exog": [
        "lrincome"
      ],
      "instruments": [
        "salestax",
        "cigtax"
      ],
      "level": 0.95,
      "se": "HC1",
      "subset": "year == 1995",
      "y": "lpacks"
    }

    Figuras call_3ebac80e

    Chave	Valor	Valor bruto	Erro-padrão	IC
    coef.lrprice 2SLS effect of lrprice on lpacks	-1,27742	-1.2774241334272798	0,249610.24961000039814105	-1,78016 – -0,774684

    Diagnósticos

    • first_stage_F.lrprice = 209,676209.67626939658422
    • partial_r2.lrprice = 0,9175210.9175207497862164
    • weak_instrument = false
    • overid_p = 0,5641190.5641191400175725
    • sargan = 0,3326220.3326221419365281
    • sargan_df = 11
    • n_obs = 4848
    • se_type = "HC1"
    • n_clusters = —

    Tabelas (3)

    {
      "coefficients": [
        {
          "ci_high": 11.826917636464222,
          "ci_low": 7.962993445846207,
          "coef": 9.894955541155214,
          "p": 1.9467019162255485e-13,
          "se": 0.9592169428712987,
          "t": 10.31565967917109,
          "term": "Intercept"
        },
        {
          "ci_high": 0.7917648364356482,
          "ci_low": -0.230955186268808,
          "coef": 0.2804048250834201,
          "p": 0.27527475270032126,
          "se": 0.253889653418621,
          "t": 1.104435810233984,
          "term": "lrincome"
        },
        {
          "ci_high": -0.7746837857268345,
          "ci_low": -1.780164481127725,
          "coef": -1.2774241334272798,
          "p": 0.000006210718082934866,
          "se": 0.24961000039814105,
          "t": -5.117680106525064,
          "term": "lrprice"
        }
      ],
      "first_stage": [
        {
          "ci_high": 0.015195848681257965,
          "ci_low": 0.006583808496625783,
          "coef": 0.010889828588941873,
          "endog": "lrprice",
          "instrument": "salestax",
          "p": 0.000006998551744539232,
          "se": 0.002136592920775031,
          "t": 5.096819559334532
        },
        {
          "ci_high": 0.01110467130342385,
          "ci_low": 0.00759872486537743,
          "coef": 0.00935169808440064,
          "endog": "lrprice",
          "instrument": "cigtax",
          "p": 6.820207505550646e-14,
          "se": 0.000869803226593554,
          "t": 10.751509994996315
        }
      ],
      "reduced_form": [
        {
          "ci_high": 0.018864366404242393,
          "ci_low": -0.03402221946515445,
          "coef": -0.007578926530456026,
          "instrument": "salestax",
          "p": 0.5664612772562537,
          "se": 0.01312082881059387,
          "t": -0.5776255936162153
        },
        {
          "ci_high": -0.005510298460779281,
          "ci_low": -0.021395893113518166,
          "coef": -0.013453095787148723,
          "instrument": "cigtax",
          "p": 0.001387396539754572,
          "se": 0.003941115966679991,
          "t": -3.4135244689289506
        }
      ]
    }

    Digests dos dados

    cigarettes be62d9713478ba73b51e4f20f511318a57aa1535f2538e36c274004942f80a1f

    sha256 do resultado

    1b6fa1b9c90a926082db3c2a0c53848b93b1d0289738d6d2abc3cda0e9dc1eff

    Resultado mostrado ao modelo
15. 14Turno do modelo
    call_88d8c9cbgemini-3.8-flashFim: STOP21.335 ms16439 de entrada · 305 de saída · 2099 de raciocínio · 12684 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Estimating Cigarette Demand Elasticity** Okay, so I've just run an instrumental variables estimation, specifically a two-stage least squares (2SLS) for the price elasticity of cigarette demand, using the `infer.iv_2sls` tool. I need to summarize the findings based on the output and the specific requirements of the prompt, which seems to be part of a larger system expecting a structured output. First, I'll extract the core result: the coefficient on the log of the real price per pack (`lrprice`). The tool output gives this as -1.27742. This is the key estimate of elasticity. Next, I need to report its uncertainty. The standard error (`se`) is 0.24961, and the 95% confidence interval (`ci`) is provided as [-1.78016, -0.774684]. These are crucial for interpreting the statistical significance and precision of the estimate. The prompt is very specific about the context: it's based on Stock and Watson's *Introduction to Econometrics* (2nd edition), Chapter 12, equation (12.16), using the 1995 cross-section of 48 continental U.S. states. The included exogenous regressor is the log of real per capita income, and the instruments are real general sales tax per pack and real cigarette-specific tax per pack. I need to ensure my summary reflects this design. Now, I have to consider the diagnostics provided by the IV estimation, which are vital for assessing the validity of the instruments. 1. **First-stage F-statistic:** The output shows `first_stage_F` as 209.676269396584. This is exceptionally high. The prompt explicitly states "well above 10, weak_instrument = false". This confirms that the instruments are strong and not weak, which is a fundamental requirement for reliable IV estimation. I should mention this strength. 2. **Overidentification test (Sargan test):** The `overid_p` (p-value) is 0.564119140017572, with a statistic of 0.3326. This test is relevant because we have two instruments and only one endogenous regressor (price), meaning we have one overidentifying restriction. A high p-value (typically > 0.05) means we *fail to reject* the null hypothesis that the instruments are valid and uncorrelated with the error term. This is a good sign, as it suggests the instruments satisfy the exogeneity assumption. 3. **Number of observations:** The `n_obs` is 48, which matches the description of the 48 continental U.S. states. A critical part of the instructions is how to format the final answer, specifically regarding language and punctuation, and what to include in `answer`, `caveats`, and `figure_refs`. * **Language and Punctuation:** The instruction states: "Write the answer in the language of the question (Portuguese: decimal comma)". The question itself is in English. This means I should write my answer in English. The parenthetical "(Portuguese: decimal comma)" is a clarification for *when* Portuguese is the language of the question, indicating that a decimal comma should be used. Since the question is in English, I will use standard English punctuation, which means a decimal point. * **Content of `answer`:** It needs to be short and direct: the estimate with its uncertainty, the design that identifies it, and what could undermine it. It should also list figure references. * Estimate: -1.27742 * Uncertainty: SE 0.24961, CI [-1.78016, -0.774684] * Design: 2SLS, 1995, 48 states, instruments (sales tax, cigarette tax) affecting price. * What could undermine it: Potential violations of the exclusion restriction (e.g., smuggling) and unobserved confounders. * **Content of `caveats`:** Diagnostics that limit the conclusion. This is where I'll put the potential issues that the good diagnostics (strong instruments, valid overidentifying restrictions) don't completely eliminate. The main ones for cross-sectional IV are: * The exclusion restriction: Do the tax instruments *only* affect demand through price? What if people cross borders to buy cheaper cigarettes (smuggling/avoidance)? This would violate the assumption that taxes only affect demand via price. * Unobserved heterogeneity: Cross-sectional data can't control for state-specific unobserved factors that might influence demand and be correlated with taxes (e.g., varying levels of antismoking sentiment or enforcement). * **Content of `figure_refs`:** Every figure quoted. The output clearly labels the coefficient of interest with `Figure key: call_3ebac80e:coef.lrprice`. This is the only figure I need to reference. * **Rule-of-thumb thresholds:** "Do not quote rule-of-thumb thresholds as numbers." I've noted the F-statistic is "well above 10" and the p-value is high, but I will report the actual numbers from the tool, not the "10" threshold itself. Let's assemble the final output components. **Estimate:** -1.27742 **Standard Error:** 0.24961 **95% Confidence Interval:** [-1.78016, -0.774684] **Design:** 2SLS estimation using 1995 cross-sectional data for 48 U.S. states, with real cigarette excise and general sales taxes as instruments for the log of real price per pack. **First-stage F-statistic:** 209.676 (indicates strong instruments) **Sargan overidentification test p-value:** 0.5641 (does not reject instrument validity) **Figure Reference:** `call_3ebac80e:coef.lrprice` **Caveats:** * The validity of the instruments rests on the assumption that state taxes affect cigarette consumption *only* through their impact on price. Interstate tax avoidance or smuggling could compromise this exclusion restriction. * This cross-sectional design does not control for unobserved state-specific factors (e.g., prevailing antismoking attitudes) that could be correlated with both price and demand. I'm confident the prompt wants a single, combined output under `submit_answer`. The structure will be: 1. The main descriptive sentence with estimate and uncertainty. 2. Mention of the design and instruments. 3. The results of the diagnostic tests (F-stat, Sargan). 4. The caveats. 5. The figure references. Re-reading rule 7: "Finish with submit_answer. Write the answer in the language of the question (Portuguese: decimal comma), short and direct: the estimate with its uncertainty, the design that identifies it, and what could undermine it. List in figure_refs every figure you quote, as '<call_id>:<key>' (each tool result carries its call_id), and put diagnostics that limit the conclusion in caveats. Write numbers as the tools stated them; do not quote rule-of-thumb thresholds as numbers." It seems the `answer` field should be the descriptive text, and `caveats` and `figure_refs` are separate fields. My final plan is to construct the `answer` string first, then list the caveats, and finally the figure reference. The prompt does not explicitly state what to put in the `answer` field itself, other than it's "short and direct: the estimate with its uncertainty, the design that identifies it, and what could undermine it." This is precisely what I will construct. Let's put it all together. I'm reporting the coefficient on `lrprice`. **Estimated Price Elasticity of Cigarette Demand** I've estimated the price elasticity of cigarette demand using two-stage least squares (2SLS) for the 1995 cross-section of 48 U.S. states, employing heteroskedasticity-robust standard errors. The estimated coefficient on the log of real price per pack (`lrprice`) is -1.27742, with a standard error of 0.24961 and a 95% confidence interval of [-1.78016, -0.774684]. The instrumental variables design uses real general sales tax per pack and real cigarette-specific tax per pack as instruments for price, and includes the log of real per capita income as an exogenous regressor. The first-stage Wald F-statistic for the excluded instruments is 209.676, indicating strong instruments. The Sargan overidentification test statistic is 0.3326 with a p-value of 0.5641, failing to reject the exogeneity of the instruments. **Caveats:** * The exclusion restriction assumes that state taxes affect cigarette consumption solely through their impact on price. Potential cross-border purchases or smuggling could compromise this assumption. * The cross-sectional nature of the data means that unobserved state-specific factors (e.g., varying levels of antismoking sentiment) that could influence demand and be correlated with taxes cannot be controlled for. **Figure References:** `["call_3ebac80e:coef.lrprice"]`

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Using the 1995 cross-section of the 48 continental U.S. states, the two-stage least squares (2SLS) estimate of the price elasticity of cigarette demand—the coefficient on the log of real price per pack (`lrprice`)—is -1.27742, with a heteroskedasticity-robust standard error of 0.24961 and a 95% confidence interval of [-1.78016, -0.774684].\n\nThe instruments (real general sales tax and cigarette-specific tax) are strong, with a first-stage F-statistic of 209.676. The Sargan test for overidentifying restrictions yields a test statistic of 0.3326 (p-value of 0.5641), not rejecting instrument validity.",
        "caveats": [
          "The identification relies on the exclusion restriction that cigarette and general sales taxes affect consumption only through retail prices. Cross-border shopping or bootlegging across state lines could challenge this assumption.",
          "The cross-sectional specification for 1995 does not control for time-invariant state-specific unobservables, such as local anti-smoking sentiment or cultural differences."
        ],
        "figure_refs": [
          "call_3ebac80e:coef.lrprice"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
16. 15Guarda
    resposta aceita

    Números encontrados

    1995 · 48 · -1.27742 · 0.24961 · 95% · -1.78016 · -0.774684 · 209.676 · 0.3326 · 0.5641 · 1995

    Sem lastro

    —

    Não citados

    —

    1 nova(s) tentativa(s) restante(s)
17. 16Resposta

    Using the 1995 cross-section of the 48 continental U.S. states, the two-stage least squares (2SLS) estimate of the price elasticity of cigarette demand—the coefficient on the log of real price per pack (`lrprice`)—is -1.27742, with a heteroskedasticity-robust standard error of 0.24961 and a 95% confidence interval of [-1.78016, -0.774684]. The instruments (real general sales tax and cigarette-specific tax) are strong, with a first-stage F-statistic of 209.676. The Sargan test for overidentifying restrictions yields a test statistic of 0.3326 (p-value of 0.5641), not rejecting instrument validity. Ressalvas: The identification relies on the exclusion restriction that cigarette and general sales taxes affect consumption only through retail prices. Cross-border shopping or bootlegging across state lines could challenge this assumption. The cross-sectional specification for 1995 does not control for time-invariant state-specific unobservables, such as local anti-smoking sentiment or cultural differences.

    • The identification relies on the exclusion restriction that cigarette and general sales taxes affect consumption only through retail prices. Cross-border shopping or bootlegging across state lines could challenge this assumption.
    • The cross-sectional specification for 1995 does not control for time-invariant state-specific unobservables, such as local anti-smoking sentiment or cultural differences.

    Figuras citadas: call_3ebac80e:coef.lrprice · Parada: answered

    Figura da resposta: call_3ebac80e:coef.lrprice = -1,27742-1.2774241334272798 (se 0,249610.24961000039814105)
18. 17Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
19. 18Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_3ebac80e:coef.lrprice (infer.iv_2sls)
20. 19Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.iv_2sls
21. 20Pontuação
    #3argumento igualpassouobrigatóriainfer.iv_2sls.y = 'lpacks'
22. 21Pontuação
    #4argumento igualpassouobrigatóriainfer.iv_2sls.endog = ['lrprice']
23. 22Pontuação
    #5argumento igualpassouobrigatóriainfer.iv_2sls.instruments = ['salestax', 'cigtax']
24. 23Pontuação
    #6argumento igualpassouobrigatóriainfer.iv_2sls.exog = ['lrincome']
25. 24Pontuação
    #7diagnósticopassouobrigatória48 vs 48
26. 25Pontuação
    #8figura da resposta próximapassouobrigatória-1.277424133 vs -1.2774241334268481
27. 26Pontuação
    #9figura da resposta próximapassouobrigatória0.2496100004 vs 0.24961000039848988
28. 27Pontuação
    #10figura da resposta próximapassouregistrada-1.277424133 vs -1.28
29. 28Pontuação
    #11figura da resposta próximapassouregistrada0.2496100004 vs 0.25

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