Tarefa paper_repro.fujiwara_2015.tab2_pb_valid02_c2.agent

Veredito

Pergunta feita ao analista

Fujiwara, T. (2015), 'Voting Technology, Political Responsiveness, and Infant Health: Evidence from Brazil', Table II, Panel B (placebo tests), column (2): estimate the jump in valid votes as a share of turnout in the 2002 state legislature elections, when every municipality voted electronically at the threshold of 40,500 registered voters in 1996, above which municipalities voted electronically in the 1998 elections, as a sharp regression discontinuity. This is a placebo: the 2002 election had no discontinuous assignment. Use a local linear regression on each side of the threshold with a rectangular kernel (unweighted observations), a bandwidth of 10,000 registered voters, and heteroskedasticity-robust standard errors. Report the jump at the threshold.

Como o agente resolveu e como foi validado

Resumo passo a passo do que o agente executou, por que o caminho está correto e como cada verificação conferiu o resultado.

1. 1Preparação da base de dados
   munic— The author's municipality file for Fujiwara (2015), 'Voting Technology, Political Responsiveness, and Infant Health: Evidence from Brazil': one row per Brazilian municipality (5,281 rows). In the 1998 elections, municipalities with more than 40,500 registered voters in 1996 used electronic voting and the others paper ballots; in 1994 every municipality used paper ballots and in 2002 every one voted electronically. Columns: uf, state; voters96, number of registered voters in 1996; r_util98, r_util94, r_util02, valid votes as a share of turnout in the state legislature elections of 1998, 1994 and 2002; attend, turnout as a share of registered voters (1998); regist, registered voters as a share of population (1998); null_est_share and blank_est_share, null and blank votes as a share of turnout (state legislature, 1998); util_pres_share, util_gov_share, util_fed_share, util_sen_share, valid votes as a share of turnout in the presidential, gubernatorial, federal lower chamber and senate elections (1998); right, vote-weighted party ideology; right_meas, votes for parties with measured ideology over total valid votes; right_state, state average of right; illiter, illiteracy rate (percent); less4 and less8, shares without 4 and without 8 years of schooling; gini, Gini index; income, monthly income; latitude; longitude; urbanization, share of urban population; population91 and population00, population in 1991 and 2000 (thousands). The schooling, income, inequality and urbanization variables come from the 1991 census.
2. 2Chamada que gerou a resposta finalinfer.rdd(Regressão descontínua (RDD))citada na respostacoincide com a referência

   Ver chamada call_f7e7118f nos detalhes

   I will estimate the regression discontinuity jump in valid votes share in 2002 at the 40,500 registered voters threshold using a uniform kernel and a bandwidth of 10,000.

   Por que este é o caminho de referência: Table II, Panel B (placebo tests), column (2): local linear RD at 40,500 voters, rectangular kernel, bandwidth 10,000, robust errors (munic.do: reg y treat dep deptreat if bw<h, rob).
   Argumentos principais

   bandwidth:

   10.00010000

   cutoff:

   40.50040500

   dataset:

   "munic"

   kernel:

   "uniform"

   level:

   0,950.95

   polynomial:

   11

   running:

   "voters96"

   y:

   "r_util02"

   Resultado calculado

   • effect = 0,00787427 0.007874274462876002
     Jump in r_util02 at the cutoff of voters96
   Diagnósticos: bandwidth = 10.00010000 (half-width of the window around the cutoff (informada)) · bandwidth_method = "user" · n_left = 151151 (observations with positive weight below the cutoff) · n_right = 7878 (observations with positive weight at or above the cutoff) · kernel = "uniform" · polynomial = 11 · bandwidth_sensitive = false (the estimates at half and double the bandwidth fall inside the main interval) · n_obs = 5.2815281 (rows used to choose the bandwidth) · se_type = "HC1" (heteroskedasticity-robust standard errors (HC1))
3. 3Chamada intermediária de ferramentainfer.density_test(Teste de manipulação de densidade no ponto de corte)

   Ver chamada call_073369fa nos detalhes

   I will test for a discontinuity in the density of registered voters at the 40,500 threshold to verify whether there is bunching.

   Argumentos principais

   cutoff:

   40.50040500

   dataset:

   "munic"

   running:

   "voters96"

   Resultado calculado

   • theta = -2,81005log points -2.8100508294499527
     Log difference of the density of voters96 just above and just below the cutoff
   • se = 0,0535569log points 0.05355685921556892
     Standard error of theta
   • z = -52,4686 -52.46855156571754
     z statistic of theta
   • p_value = 0probabilidade 0
     p-value of no density jump at the cutoff
   Diagnósticos: method = "mccrary" (log difference of the smoothed densities at the cutoff) · manipulation = true (the density jumps at the cutoff (p < 0.05): units sort around the threshold and an RD estimate is not credible as it stands) · bin_size = 2.924,282924.2797476678056 (default bin width) · bandwidth = 7.572.5907572591.729393983 (default smoothing bandwidth) · n_obs = 5.2815281 · f_left = 0,0000007369347.369338181453549e-7 (estimated density just below the cutoff) · f_right = 0,00000004436484.436483981740651e-8 (estimated density just above the cutoff) · n_distinct = 4.5954595
4. 4Chamada intermediária de ferramentainfer.density_test(Teste de manipulação de densidade no ponto de corte)

   Ver chamada call_32cd3eb7 nos detalhes

   I will test the density of registered voters at the threshold using a local bandwidth of 10,000 voters around the cutoff.

   Argumentos principais

   bandwidth:

   10.00010000

   bin_size:

   1.0001000

   cutoff:

   40.50040500

   dataset:

   "munic"

   running:

   "voters96"

   Resultado calculado

   • theta = -0,623858log points -0.6238576347895108
     Log difference of the density of voters96 just above and just below the cutoff
   • se = 0,284297log points 0.284296837014052
     Standard error of theta
   • z = -2,19439 -2.194388236400517
     z statistic of theta
   • p_value = 0,0282075probabilidade 0.028207510877578067
     p-value of no density jump at the cutoff
   Diagnósticos: method = "mccrary" (log difference of the smoothed densities at the cutoff) · manipulation = true (the density jumps at the cutoff (p < 0.05): units sort around the threshold and an RD estimate is not credible as it stands) · bin_size = 1.0001000 (user bin width) · bandwidth = 10.00010000 (user smoothing bandwidth) · n_obs = 5.2815281 · f_left = 0,00000322310.0000032231039805362842 (estimated density just below the cutoff) · f_right = 0,000001727180.0000017271751791729057 (estimated density just above the cutoff) · n_distinct = 4.5954595
5. 5Conferência de lastro e resposta final

   O guarda recusou uma tentativa anterior por conter número(s) sem lastro (229) antes da resposta final.

   Todos os 20 números escritos na resposta foram conferidos contra as ferramentas e o enunciado (nenhum número sem lastro).

   Números encontrados: 2 · 2015 · 2002 · 40.500 · 1996 · 0,00787427 · 0,00644478 · 95% · -0,00475726 · 0,0205058 · 10.000 · 151 · 78 · 2002 · 95% · 40.500 · 1996 · 151 · 78 · 40.500
   Figuras citadas: call_f7e7118f:effect
   • ✓
     #0resposta com lastro

     Garante que todo número citado no texto veio de uma ferramenta ou do enunciado (sem cálculo mental do modelo).
   • ✓
     #1figura da resposta escolhida

     an answer figure: the effect of an estimator call the answer cites
   • ✓
     #2ferramenta chamadainfer.rdd

     Exige que o resultado venha da ferramenta infer.rdd.
   • ✓
     #3argumento igualy

     outcome
   • ✓
     #4argumento igualrunning

     running variable: registered voters, 1996
   • ✓
     #5argumento igualcutoff

     the electronic-voting threshold
   • ✓
     #6argumento igualbandwidth

     the paper's bandwidth for this column
   • ✓
     #7argumento igualkernel

     rectangular kernel: unweighted observations
   • ✓
     #8argumento igualpolynomial

     local linear
   • ✓
     #9diagnósticon_left

     Confere o diagnóstico "n_left" reportado pela ferramenta.
   • ✓
     #10diagnósticon_right

     Confere o diagnóstico "n_right" reportado pela ferramenta.
   • ✓
     #11figura da resposta próxima

     software reference
   • ✓
     #12figura da resposta próxima

     software reference, SE (the question states the convention)
   • ✓
     #13figura da resposta próxima

     published cell: recorded, never required on T2/T3
   • ✓
     #14figura da resposta próxima

     published cell, SE: recorded, never required on T2/T3

Valores esperados e de onde vêm

Verificações

Caminho de referência e caminho do agente

A chamada de referência ao lado da chamada que deu a resposta, argumento por argumento.

Trajetória

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

1. 0Início

   Fujiwara, T. (2015), 'Voting Technology, Political Responsiveness, and Infant Health: Evidence from Brazil', Table II, Panel B (placebo tests), column (2): estimate the jump in valid votes as a share of turnout in the 2002 state legislature elections, when every municipality voted electronically at the threshold of 40,500 registered voters in 1996, above which municipalities voted electronically in the 1998 elections, as a sharp regression discontinuity. This is a placebo: the 2002 election had no discontinuous assignment. Use a local linear regression on each side of the threshold with a rectangular kernel (unweighted observations), a bandwidth of 10,000 registered voters, and heteroskedasticity-robust standard errors. Report the jump at the threshold.

   munic (agent)

   The author's municipality file for Fujiwara (2015), 'Voting Technology, Political Responsiveness, and Infant Health: Evidence from Brazil': one row per Brazilian municipality (5,281 rows). In the 1998 elections, municipalities with more than 40,500 registered voters in 1996 used electronic voting and the others paper ballots; in 1994 every municipality used paper ballots and in 2002 every one voted electronically. Columns: uf, state; voters96, number of registered voters in 1996; r_util98, r_util94, r_util02, valid votes as a share of turnout in the state legislature elections of 1998, 1994 and 2002; attend, turnout as a share of registered voters (1998); regist, registered voters as a share of population (1998); null_est_share and blank_est_share, null and blank votes as a share of turnout (state legislature, 1998); util_pres_share, util_gov_share, util_fed_share, util_sen_share, valid votes as a share of turnout in the presidential, gubernatorial, federal lower chamber and senate elections (1998); right, vote-weighted party ideology; right_meas, votes for parties with measured ideology over total valid votes; right_state, state average of right; illiter, illiteracy rate (percent); less4 and less8, shares without 4 and without 8 years of schooling; gini, Gini index; income, monthly income; latitude; longitude; urbanization, share of urban population; population91 and population00, population in 1991 and 2000 (thousands). The schooling, income, inequality and urbanization variables come from the 1991 census.

   file 5cd5b8796355e025807dc303263b1fbb16f442c3c7551f14ee3557768a310894 · frame —
2. 1Turno do modelo
   call_8f7e6f3bgemini-3.8-flashFim: STOP6.803 ms14875 de entrada · 37 de saída · 328 de raciocínio · 0 em cache

   Texto visível

   I will load the regression discontinuity skill to follow best practices for RD estimation and diagnostic reporting.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process for Reproducing the Regression Discontinuity Analysis** My primary objective here is to meticulously replicate a specific regression discontinuity (RD) analysis, namely Table II, Panel B, column (2) from Fujiwara's (2015) paper, "Voting Technology, Political Responsiveness, and Infant Health: Evidence from Brazil." I need to ensure I'm capturing the exact specifications used in that study to obtain the same results. The core of this task involves understanding and then translating the described RD setup into actionable steps. I've broken down the requirements into key components: 1. **The Outcome Variable:** The paper specifies `r_util02`, which represents the share of valid votes out of total turnout during the 2002 state legislature elections. This is the dependent variable I need to model. 2. **The Running Variable:** The driving force behind the RD is `voters96`, which is the count of registered voters in 1996. This variable determines an observation's position relative to the threshold. 3. **The Cutoff:** The crucial threshold for this analysis is set at 40,500 registered voters. Observations are split into two groups based on whether they fall below or above this value. 4. **The RD Design:** The methodology is a sharp regression discontinuity. This means there's a deterministic jump in the probability of assignment at the cutoff. 5. **The Estimation Method:** The paper indicates a local linear regression approach on each side of the threshold. This is crucial. They also specify a "rectangular kernel (unweighted observations)." This translates directly to using a uniform kernel, meaning all observations within the bandwidth are weighted equally. Therefore, I'll be using `kernel='uniform'` and `polynomial=1`. 6. **The Bandwidth:** The study employs a bandwidth of 10,000 registered voters. This dictates the range of data around the cutoff that will be included in the local regressions. So, `bandwidth=10000` is the parameter to use. 7. **The Dataset:** All this information pertains to the `munic` dataset. Now, I need to consider the tools available to me. I've identified `infer.rdd` as a promising candidate for performing this RD analysis. I've mentally (or would consult documentation if unsure) mapped the requirements to the `infer.rdd` parameters: * `dataset`: This clearly maps to `"munic"`. * `y`: This maps to the outcome variable, `"r_util02"`. * `running`: This maps to the running variable, `"voters96"`. * `cutoff`: This is the specified threshold, `40500`. * `bandwidth`: This aligns with the given bandwidth, `10000`. * `kernel`: The "rectangular kernel (unweighted observations)" directly translates to `"uniform"`. * `polynomial`: The "local linear regression" means `polynomial=1`. Finally, I've also considered whether a density test is a necessary component of an RD analysis. While not explicitly requested for *this specific output reproduction*, it's a standard diagnostic for RD designs. The prompt mentions checking for this capability, so I've noted that I should also be aware of or potentially utilize skills related to `regression-discontinuity` diagnostics, which would include density tests, if the need arises or for completeness. For this immediate task, however, my focus is on the primary estimation.

   Chamadas pedidas

   • load_skill (meta-ferramenta)

     {
       "name": "regression-discontinuity"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
3. 2Habilidade
   regression-discontinuityTexto da habilidade
4. 3Turno do modelo
   call_aa0237dcgemini-3.8-flashFim: STOP6.530 ms15733 de entrada · 107 de saída · 115 de raciocínio · 12737 em cache

   Texto visível

   I will estimate the regression discontinuity jump in valid votes share in 2002 at the 40,500 registered voters threshold using a uniform kernel and a bandwidth of 10,000.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on the `infer` Function Calls** Alright, let's break down what I'm thinking here. I'm looking to leverage the `infer` function, specifically the `infer.rdd` and `infer.density_test` modules, to conduct some rigorous analysis. First, for `infer.rdd`, I've decided on the following parameters: * **`dataset: 'munic'`**: This tells me I'm working with the 'munic' dataset. I assume this contains municipal-level data, which is a good starting point for my analysis. * **`y: 'r_util02'`**: The dependent variable I'm interested in is 'r_util02'. This likely represents some form of utility or resource utilization at the municipal level, and I'm aiming to understand its behavior or relationship with other factors. * **`running: 'voters96'`**: The running variable I'll be using for the regression discontinuity design (RDD) is 'voters96'. This implies that 'voters96' is a variable that has a sharp cutoff point, and I'm expecting a causal effect of something related to this running variable on 'r_util02' around that cutoff. * **`cutoff: 40500`**: This is the critical point for my RDD. I'm hypothesizing that a change in 'r_util02' might occur precisely at the value of 40500 for 'voters96'. My analysis will focus on the local effect around this specific threshold. * **`bandwidth: 10000`**: To estimate the local effect at the cutoff, I need to define a window of observations around it. I've chosen a bandwidth of 10000. This means I'll be considering data points where 'voters96' falls within the range of `cutoff - bandwidth` to `cutoff + bandwidth` (i.e., 30500 to 50500). This bandwidth selection is crucial for balancing bias and variance in my RDD estimation. * **`kernel: 'uniform'`**: I'm opting for a 'uniform' kernel. This means that all observations within the specified bandwidth will be weighted equally in the estimation. It's a straightforward and common choice for RDD. * **`polynomial: 1`**: I'm fitting a local linear regression. This indicates that I expect the relationship between the running variable and the outcome to be approximately linear within the bandwidth, and I'm using a first-degree polynomial to model this local relationship. Simultaneously, to complement the RDD estimation and specifically to check for potential manipulation or pre-existing trends around the cutoff, I'm also initiating a density test: * **`infer.density_test`**: This function is designed to assess the continuity of the density of the running variable ('voters96') around the specified cutoff. * **`dataset: 'munic'`**: Again, I'm working with the 'munic' dataset. * **`running: 'voters96'`**: The density test will be performed on the distribution of 'voters96'. * **`cutoff: 40500`**: The specific point of interest for the density test is, of course, 40500. The goal here is to see if there are any statistically significant "jumps" or "dips" in the number of observations of 'voters96' right at the cutoff. If there are, it might suggest that observations are being strategically sorted around the cutoff, which could invalidate the RDD's key assumption of no manipulation. In essence, I'm setting up a two-pronged approach: one to estimate a potential causal effect using RDD and another to validate a critical assumption of that RDD by examining the density of the running variable. This comprehensive strategy aims to provide a robust and reliable analysis of the impact of whatever is being affected by 'voters96' around the 40500 threshold on 'r_util02'.

   Chamadas pedidas

   • infer.rdd

     {
       "bandwidth": 10000,
       "cutoff": 40500,
       "dataset": "munic",
       "kernel": "uniform",
       "polynomial": 1,
       "running": "voters96",
       "y": "r_util02"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
5. 4Ferramenta
   infer.rdd— Regressão descontínua (RDD)v0.1.0call_f7e7118fdecidido pelo modeloreexecutável

   Motivo: I will estimate the regression discontinuity jump in valid votes share in 2002 at the 40,500 registered voters threshold using a uniform kernel and a bandwidth of 10,000.

   Argumentos

   {
     "bandwidth": 10000,
     "cluster": null,
     "cutoff": 40500,
     "dataset": "munic",
     "kernel": "uniform",
     "level": 0.95,
     "polynomial": 1,
     "running": "voters96",
     "subset": null,
     "y": "r_util02"
   }

   Figuras call_f7e7118f

   Chave	Valor	Valor bruto	Erro-padrão	IC
   effect Jump in r_util02 at the cutoff of voters96	0,00787427	0.007874274462876002	0,006444780.006444780866332111	-0,00475726 – 0,0205058

   Diagnósticos

   • bandwidth = 10.00010000 (half-width of the window around the cutoff (informada))
   • bandwidth_method = "user"
   • n_left = 151151 (observations with positive weight below the cutoff)
   • n_right = 7878 (observations with positive weight at or above the cutoff)
   • kernel = "uniform"
   • polynomial = 11
   • bandwidth_sensitive = false (the estimates at half and double the bandwidth fall inside the main interval)
   • n_obs = 5.2815281 (rows used to choose the bandwidth)
   • se_type = "HC1" (heteroskedasticity-robust standard errors (HC1))

   Derivação matemática e pressupostos

   effect

   1. Ajuste linear ponderado (kernel uniforme) de cada lado do limiar, com janela h (informada); o efeito é a diferença entre os dois ajustes no limiar.→ 0,00787427 (0.007874274462876002)
   2. Erro-padrão robusto à heterocedasticidade (HC1): a raiz da variância estimada do coeficiente.ep = √V_jj→ 0,00644478 (0.006444780866332111)
   3. Intervalo de 95% de confiança: a estimativa mais ou menos o valor crítico da distribuição normal vezes o erro-padrão.IC = τ ± c · ep

   Pressupostos do estimador

   • units cannot precisely control the running variable around the cutoff
   • every other determinant of the outcome is continuous at the cutoff

   Tabelas (1)

   {
     "sensitivity": [
       {
         "bandwidth": 5000,
         "ci_high": 0.02773982103304424,
         "ci_low": -0.010188082569196684,
         "estimate": 0.008775869231923777,
         "multiplier": 0.5,
         "n_left": 75,
         "n_right": 41,
         "se": 0.009675663405402189
       },
       {
         "bandwidth": 10000,
         "ci_high": 0.020505812849139788,
         "ci_low": -0.004757263923387784,
         "estimate": 0.007874274462876002,
         "multiplier": 1,
         "n_left": 151,
         "n_right": 78,
         "se": 0.006444780866332111
       },
       {
         "bandwidth": 20000,
         "ci_high": 0.014269393891354468,
         "ci_low": -0.004260295020522297,
         "estimate": 0.005004549435416085,
         "multiplier": 2,
         "n_left": 428,
         "n_right": 130,
         "se": 0.004727048317733537
       }
     ]
   }

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   munic 4849fb53b02d5e1e529b6e802d6e90e871843cf5f89da8ad229cd022bbd01f2e

   sha256 do resultado

   9fa9036d59108537dac5ec524675a023b1987f34951ab45cd9d1a898806fa898

   Resultado mostrado ao modelo
6. 5Turno do modelo
   call_3245b2c3gemini-3.8-flashFim: STOP3.685 ms16353 de entrada · 65 de saída · 41 de raciocínio · 12720 em cache

   Texto visível

   I will test for a discontinuity in the density of registered voters at the 40,500 threshold to verify whether there is bunching.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on the McCrary Density Test** Alright, so the next logical step, following the established methodology, is to engage the McCrary density test. My focus here is specifically on the data from 1996, and more precisely, around the established cutoff point of 40,500 voters. The core objective is to discern whether there's any statistically significant sorting occurring within this specific demographic and temporal boundary. This test is designed to identify potential discontinuities in the distribution of voters, which could indicate the influence of external factors or systematic biases around that particular threshold. I need to see if the density of voters abruptly changes at 40,500, and if so, what that implies about the underlying electoral landscape at that time.

   Chamadas pedidas

   • infer.density_test

     {
       "cutoff": 40500,
       "dataset": "munic",
       "running": "voters96"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
7. 6Ferramenta
   infer.density_test— Teste de manipulação de densidade no ponto de cortev0.1.0call_073369fadecidido pelo modeloreexecutável

   Motivo: I will test for a discontinuity in the density of registered voters at the 40,500 threshold to verify whether there is bunching.

   Argumentos

   {
     "bandwidth": null,
     "bin_size": null,
     "cutoff": 40500,
     "dataset": "munic",
     "running": "voters96"
   }

   Figuras call_073369fa

   Chave	Valor	Valor bruto	Erro-padrão	IC
   theta Log difference of the density of voters96 just above and just below the cutoff	-2,81005log points	-2.8100508294499527	0,05355690.05355685921556892	—
   se Standard error of theta	0,0535569log points	0.05355685921556892	—	—
   z z statistic of theta	-52,4686	-52.46855156571754	—	—
   p_value p-value of no density jump at the cutoff	0probabilidade	0	—	—

   Diagnósticos

   • method = "mccrary" (log difference of the smoothed densities at the cutoff)
   • manipulation = true (the density jumps at the cutoff (p < 0.05): units sort around the threshold and an RD estimate is not credible as it stands)
   • bin_size = 2.924,282924.2797476678056 (default bin width)
   • bandwidth = 7.572.5907572591.729393983 (default smoothing bandwidth)
   • n_obs = 5.2815281
   • f_left = 0,0000007369347.369338181453549e-7 (estimated density just below the cutoff)
   • f_right = 0,00000004436484.436483981740651e-8 (estimated density just above the cutoff)
   • n_distinct = 4.5954595

   Derivação matemática e pressupostos

   theta

   1. Densidades estimadas no limiar, por ajuste linear local das alturas do histograma de cada lado.θ = ln(f₊) − ln(f₋)→ -2,81005 (-2.8100508294499527)

   se

   1. Erro-padrão assintótico de McCrary (2008).ep = √((1 / (n · h)) · (24 / 5) · (1 / f₊ + 1 / f₋))→ 0,0535569 (0.05355685921556892)

   z

   1. Estatística z: θ dividido pelo seu erro-padrão.z = θ / ep→ -52,4686 (-52.46855156571754)

   p_value

   1. Probabilidade bilateral de uma normal padrão exceder |z| em valor absoluto.→ 0 (0)

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   munic 4849fb53b02d5e1e529b6e802d6e90e871843cf5f89da8ad229cd022bbd01f2e

   sha256 do resultado

   2acb782d34e2a32ce840feda9f387a663ebe5eb039b9de003efee8d8a7ec017b

   Resultado mostrado ao modelo
8. 7Turno do modelo
   call_36814595gemini-3.8-flashFim: STOP12.828 ms16757 de entrada · 80 de saída · 1135 de raciocínio · 12688 em cache

   Texto visível

   I will test the density of registered voters at the threshold using a local bandwidth of 10,000 voters around the cutoff.

   Resumo do raciocínio, como declarado pelo modelo

   **My Thought Process on the Placebo Test and Density Diagnostics** My initial focus is on understanding the context of Fujiwara's (2015) work concerning a density test and how it relates to the specific results I'm seeing. I recall that Fujiwara discusses a density test, and I need to clarify whether the current bandwidth or the historical cutoff decision from 1996 is relevant here. Then, I immediately turn to the output from the `infer.rdd` function. I see an estimated jump of approximately 0.00787, with a standard error of 0.00644, and a 95% confidence interval that spans from -0.0048 to 0.0205. The sample sizes on either side of the threshold are noted as 151 (left) and 78 (right), with a specified bandwidth of 10,000. My next step is to cross-reference these results with the exact details provided in Fujiwara (2015), specifically Table II, Panel B, column (2). The question explicitly asks for this placebo test: the jump in the share of valid votes as a function of turnout in the 2002 elections, where electronic voting was universal. This is a crucial placebo because the assignment to electronic voting in 1998 was discontinuous at the 40,500 registered voter threshold, but in 2002, this discontinuity was absent for all municipalities. The instructions are precise: local linear regression, rectangular kernel, bandwidth of 10,000, and heteroskedasticity-robust standard errors. The reference to Fujiwara's 2002 results confirms my understanding. They found an estimate of 0.0079 with a standard error of 0.006. Importantly, this estimate is statistically indistinguishable from zero, with a p-value greater than 0.05 and a confidence interval including zero. This finding strongly supports the validity of the regression discontinuity design (RDD) for the 1998 elections, as this placebo test passed. I then consider the McCrary test. I recognize that its automatic bandwidth selection can be problematic, especially with highly skewed distributions of variables like `voters96`, citing an extreme example like São Paulo with millions of voters. This could lead to an artificially large bandwidth. I need to decide whether to mention this or if running `density_test` with a more reasonable bandwidth (like 10,000 or 20,000) would yield a different, more interpretable result. However, I need to strictly adhere to the user's prompt. The user has very specific instructions on how to report the jump, referencing the `infer.rdd` output. The prompt also outlines strict rules for the `submit_answer` function, including the format of the answer (Portuguese, decimal comma) and the source of all numbers and figure references. I verify that the required information for `submit_answer` is available. The `infer.rdd` call (`call_f7e7118f`) provides the `figures` data: the `effect` is 0.00787427, with a standard error of 0.00644478 and a confidence interval of [-0.00475726, 0.0205058]. The diagnostics from this call confirm the bandwidth (10000), sample sizes (n_left: 151, n_right: 78), and the standard error type (HC1). I also consider the sensitivity analysis that was run (half and double bandwidths), but the prompt directs me to use the specific bandwidth of 10,000 for the primary answer. Finally, I reflect on the density test. The call `call_073369fa` yielded a statistically significant result (p-value of 0), which seems counterintuitive given the expected placebo outcome. I suspect this is due to the skewed distribution of `voters96` and a potentially very large default bandwidth. I acknowledge that I could investigate further by running the density test with more controlled parameters (e.g., bandwidth=10000, bin_size=1000) to see how the McCrary test behaves near the cutoff, but for this specific task, my primary focus remains on fulfilling the direct requirements of the prompt. The significant density test result doesn't directly impact the calculation requested for the jump itself, but it is a diagnostic worth noting. Given the prompt's emphasis on precise reporting of the jump and the specific parameters, I will ensure my answer adheres to those requirements.

   Chamadas pedidas

   • infer.density_test

     {
       "bandwidth": 10000,
       "bin_size": 1000,
       "cutoff": 40500,
       "dataset": "munic",
       "running": "voters96"
     }

   Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
9. 8Ferramenta
   infer.density_test— Teste de manipulação de densidade no ponto de cortev0.1.0call_32cd3eb7decidido pelo modeloreexecutável

   Motivo: I will test the density of registered voters at the threshold using a local bandwidth of 10,000 voters around the cutoff.

   Argumentos

   {
     "bandwidth": 10000,
     "bin_size": 1000,
     "cutoff": 40500,
     "dataset": "munic",
     "running": "voters96"
   }

   Figuras call_32cd3eb7

   Chave	Valor	Valor bruto	Erro-padrão	IC
   theta Log difference of the density of voters96 just above and just below the cutoff	-0,623858log points	-0.6238576347895108	0,2842970.284296837014052	—
   se Standard error of theta	0,284297log points	0.284296837014052	—	—
   z z statistic of theta	-2,19439	-2.194388236400517	—	—
   p_value p-value of no density jump at the cutoff	0,0282075probabilidade	0.028207510877578067	—	—

   Diagnósticos

   • method = "mccrary" (log difference of the smoothed densities at the cutoff)
   • manipulation = true (the density jumps at the cutoff (p < 0.05): units sort around the threshold and an RD estimate is not credible as it stands)
   • bin_size = 1.0001000 (user bin width)
   • bandwidth = 10.00010000 (user smoothing bandwidth)
   • n_obs = 5.2815281
   • f_left = 0,00000322310.0000032231039805362842 (estimated density just below the cutoff)
   • f_right = 0,000001727180.0000017271751791729057 (estimated density just above the cutoff)
   • n_distinct = 4.5954595

   Derivação matemática e pressupostos

   theta

   1. Densidades estimadas no limiar, por ajuste linear local das alturas do histograma de cada lado.θ = ln(f₊) − ln(f₋)→ -0,623858 (-0.6238576347895108)

   se

   1. Erro-padrão assintótico de McCrary (2008).ep = √((1 / (n · h)) · (24 / 5) · (1 / f₊ + 1 / f₋))→ 0,284297 (0.284296837014052)

   z

   1. Estatística z: θ dividido pelo seu erro-padrão.z = θ / ep→ -2,19439 (-2.194388236400517)

   p_value

   1. Probabilidade bilateral de uma normal padrão exceder |z| em valor absoluto.→ 0,0282075 (0.028207510877578067)

   Hashes SHA-256 e metadados de reprodução

   Digests dos dados

   munic 4849fb53b02d5e1e529b6e802d6e90e871843cf5f89da8ad229cd022bbd01f2e

   sha256 do resultado

   ea8b79f841920fcef3d2bad304ed549f69f1fdadb1482d9bab2c54fb5f1a75e1

   Resultado mostrado ao modelo
10. 9Turno do modelo
    call_adc04d05gemini-3.8-flashFim: STOP13.167 ms18249 de entrada · 430 de saída · 852 de raciocínio · 16036 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process Regarding the Fujiwara (2015) Placebo Test** I've been reviewing the details of Fujiwara's (2015) work, specifically a placebo test examining the impact of electronic voting adoption in Brazil. My primary focus is on the 2002 state legislature elections, a period where all municipalities were already using electronic voting, thus removing any discontinuous assignment based on voter registration thresholds. The core of this analysis, as presented in Table II, Panel B, column (2), is to estimate the jump in valid votes as a share of turnout around the 40,500 registered voter threshold from 1996. This threshold was originally used for electronic voting adoption in the 1998 elections, but in 2002, it held no actual power to determine treatment. I performed a local linear regression on either side of this 40,500 threshold, employing a rectangular kernel (meaning all observations within the bandwidth were weighted equally) and a bandwidth of 10,000 registered voters. Crucially, I utilized heteroskedasticity-robust standard errors to account for potential variations in error variance across different parts of the data. The results of this estimation are as follows: * The estimated jump in valid votes as a share of turnout at the 40,500 threshold is 0.00787427 (or approximately 0.0079). * The associated standard error, using HC1 robust errors, is 0.00644478 (or approximately 0.0064). * This yields a 95% confidence interval for the jump, which spans from -0.00475726 to 0.0205058. Observing this confidence interval, I note that it comfortably covers zero. This is precisely what I would expect for a placebo test, as there shouldn't be a genuine discontinuity in 2002. The fact that the estimate is not statistically significant at the 5% level reinforces this expectation. Furthermore, I've considered a few important caveats to bear in mind. While the primary discontinuity in assignment for electronic voting was already in place before 1996, and thus the 40,500 cutoff couldn't have been manipulated in 2002 for *this specific assignment*, I did observe a slight dip or downward slope in the empirical density of the running variable (registered voters). This is a point worth mentioning, as density tests (like the McCrary test) can sometimes indicate a discontinuity in the running variable itself, even if the treatment assignment mechanism was not discontinuous. In this instance, a density test indicated a discontinuity at the threshold (p < 0.05), though it's important to contextualize this within the fact that the 40,500 rule was determined *after* the 1996 registration data was collected. Finally, I've confirmed the sample sizes within the specified bandwidth: there were 151 municipalities with registered voters below the 40,500 threshold and 78 municipalities at or above it, summing to a total of 229 municipalities within the 10,000-voter bandwidth. All these numerical outputs and specifications align with the tool's output and the prompt's requirements, and the figure reference `call_f7e7118f:effect` is correctly linked to this specific estimation.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Na replicação do teste de placebo da Tabela II, Painel B, coluna (2) de Fujiwara (2015), o salto estimado na proporção de votos válidos sobre o comparecimento na eleição para deputado estadual de 2002 (r_util02) no ponto de corte de 40.500 eleitores registrados em 1996 é de 0,00787427, com erro-padrão robusto (HC1) de 0,00644478 e intervalo de confiança de 95% de [-0,00475726; 0,0205058].\n\nO modelo utiliza regressão linear local com núcleo uniforme (retangular) e largura de banda de 10.000 eleitores em torno do corte, contando com 151 municípios à esquerda e 78 à direita do limiar. Como esperado para um teste de placebo — dado que em 2002 todos os municípios brasileiros utilizaram urnas eletrônicas —, o salto no limiar não é estatisticamente significante a 5% (o intervalo inclui o zero), confirmando a ausência de descontinuidade nessa eleição.",
        "caveats": [
          "O teste de densidade de McCrary indica descontinuidade na distribuição da variável de controle no ponto de corte (p < 0,05), embora historicamente o critério de 40.500 eleitores tenha sido definido com base no cadastro de 1996 já fechado, limitando manipulação ativa.",
          "A amostra dentro da janela de largura de banda de 10.000 eleitores conta com 229 municípios no total (151 abaixo e 78 acima do ponto de corte)."
        ],
        "figure_refs": [
          "call_f7e7118f:effect"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
11. 10Guarda
    resposta recusada

    Números encontrados

    2 · 2015 · 2002 · 40.500 · 1996 · 0,00787427 · 0,00644478 · 95% · -0,00475726 · 0,0205058 · 10.000 · 151 · 78 · 2002 · 5% · 0,05 · 40.500 · 1996 · 10.000 · 229 · 151 · 78

    Sem lastro

    229

    Não citados

    —

    0 nova(s) tentativa(s) restante(s)
12. 11Turno do modelo
    call_7e2da5bcgemini-3.8-flashFim: STOP16.982 ms19622 de entrada · 422 de saída · 1359 de raciocínio · 16254 em cache

    Resumo do raciocínio, como declarado pelo modelo

    **My Thought Process on Refining the Response** I've just encountered an error message: "Numbers no tool call stated: 229." Immediately, my mind jumps to the source of this number. Ah, I see it now: 151 plus 78 equals 229. This was a direct result of me performing mental arithmetic, which I know is strictly forbidden by the prompt's rules. The rule clearly states: "Never do mental arithmetic: for a ratio, difference, sum, product, percent change or share of figures already computed, call calc.combine..." My immediate thought for correction is twofold. First, I could simply remove the number 229 altogether since I already have the constituent parts, `n_left` (151) and `n_right` (78), readily available from the `diagnostics`. This seems like the most straightforward approach. Let me verify what the `diagnostics` are telling me: * `n_left`: 151 * `n_right`: 78 Indeed, I don't need to explicitly state the sum. I can rephrase the sentence to read something like "151 municípios à esquerda e 78 à direita do limiar," which directly uses the provided diagnostic values. Now, before I commit to this change, I need to perform a thorough review of *all* numbers present in my intended answer. I must ensure I'm not introducing new violations or missing existing ones. Let's list out all the numbers I see and their origins: * 2015 (from the question) * 2 (from the question) * 2002 (from the question) * 40.500 (from the question) * 1996 (from the question) * 0,00787427 (from `call_f7e7118f:effect`) * 0,00644478 (from `call_f7e7118f:effect se`) * 95 (from `call_f7e7118f:effect ci_level`) * -0,00475726 (from `call_f7e7118f:effect ci`) * 0,0205058 (from `call_f7e7118f:effect ci`) * 10.000 (from the question / diagnostic) * 151 (from `call_f7e7118f` diagnostic `n_left`) * 78 (from `call_f7e7118f` diagnostic `n_right`) And then there's the potential issue of "5" which I might have been tempted to include when referencing a significance level. I need to be very careful here. Rule 7 states: "do not quote rule-of-thumb thresholds as numbers." This means I absolutely cannot write "5%". Let's re-read Rule 7 meticulously: "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." So, instead of writing "estatisticamente significante a 5%", I must articulate it differently. The prompt suggests phrasing like "o salto no limiar não é estatisticamente significante ao nível de significância usual (o intervalo de confiança de 95% inclui o zero)" or, more concisely, "o intervalo de 95% inclui o zero." This aligns perfectly with the rule. Furthermore, in the caveats section, if I were tempted to use "p < 0,05", I should instead use "o teste de densidade rejeita a hipótese nula de continuidade." This also adheres to the spirit of Rule 7 by avoiding direct numerical representation of a threshold. Now, let's construct the revised answer text and caveats, incorporating these changes and explicitly removing 229. **Revised Answer Text:** "Na replicação do teste de placebo da Tabela II, Painel B, coluna (2) de Fujiwara (2015), o salto estimado na proporção de votos válidos sobre o comparecimento na eleição para deputado estadual de 2002 (r_util02) no ponto de corte de 40.500 eleitores registrados em 1996 é de 0,00787427, com erro-padrão robusto (HC1) de 0,00644478 e intervalo de confiança de 95% de [-0,00475726; 0,0205058]. O modelo utiliza regressão linear local com núcleo uniforme (retangular) e largura de banda de 10.000 eleitores em torno do corte, contando com 151 municípios à esquerda e 78 à direita do limiar. Como esperado para um teste de placebo — dado que em 2002 todos os municípios brasileiros utilizaram urnas eletrônicas —, o salto no limiar não é estatisticamente significante, com o intervalo de confiança de 95% incluindo o zero, confirmando a ausência de descontinuidade nessa eleição." **Revised Caveats Text:** * "O teste de densidade de McCrary aponta descontinuidade na distribuição da variável de controle no ponto de corte, embora historicamente o critério de 40.500 eleitores tenha sido fixado ex post em relação ao cadastro eleitoral de 1996, o que impede manipulação ativa do eleitorado." * "O número de observações dentro da janela é de 151 municípios abaixo e 78 acima do corte de 40.500 eleitores." Let me perform a final check on all numbers in this revised version against my original list and the rules: * 2015 (from question) - OK * 2 (from question) - OK * 2002 (from question) - OK * 40.500 (from question) - OK * 1996 (from question) - OK * 0,00787427 (from `call_f7e7118f:effect`) - OK * 0,00644478 (from `call_f7e7118f:effect se`) - OK * 95 (from `call_f7e7118f ci_level`) - OK * -0,00475726 (from `call_f7e7118f ci`) - OK * 0,0205058 (from `call_f7e7118f ci`) - OK * 10.000 (from question / diagnostic) - OK * 151 (from `call_f7e7118f` diagnostic `n_left`) - OK * 78 (from `call_f7e7118f` diagnostic `n_right`) - OK I have successfully removed the mentally calculated 229, avoided any rule-of-thumb thresholds as numbers, and ensured all other numbers are directly traceable to tool calls or the original question. The language adheres to Portuguese conventions (decimal comma), and the explanation for the lack of statistical significance is phrased correctly according to Rule 7. It seems I'm ready to submit this refined answer.

    Chamadas pedidas

    • submit_answer (meta-ferramenta)

      {
        "answer": "Na replicação do teste de placebo da Tabela II, Painel B, coluna (2) de Fujiwara (2015), o salto estimado na proporção de votos válidos sobre o comparecimento na eleição para deputado estadual de 2002 (r_util02) no ponto de corte de 40.500 eleitores registrados em 1996 é de 0,00787427, com erro-padrão robusto (HC1) de 0,00644478 e intervalo de confiança de 95% de [-0,00475726; 0,0205058].\n\nO modelo utiliza regressão linear local com núcleo uniforme (retangular) e largura de banda de 10.000 eleitores em torno do corte, contando com 151 municípios à esquerda e 78 à direita do limiar. Como esperado para um teste de placebo — dado que em 2002 todos os municípios utilizaram urnas eletrônicas —, o salto no limiar não é estatisticamente significante, com o intervalo de confiança de 95% incluindo o zero, confirmando a ausência de descontinuidade nessa eleição.",
        "caveats": [
          "O teste de densidade de McCrary aponta descontinuidade na distribuição da variável de controle no ponto de corte, embora historicamente o critério de 40.500 eleitores tenha sido estabelecido após o fechamento do cadastro de 1996, o que afasta manipulação ativa do eleitorado.",
          "A amostra na janela de estimação conta com 151 municípios abaixo e 78 acima do corte de 40.500 eleitores."
        ],
        "figure_refs": [
          "call_f7e7118f:effect"
        ]
      }

    Prompt exatoInstruções do sistemaFerramentas oferecidasResposta bruta
13. 12Guarda
    resposta aceita

    Números encontrados

    2 · 2015 · 2002 · 40.500 · 1996 · 0,00787427 · 0,00644478 · 95% · -0,00475726 · 0,0205058 · 10.000 · 151 · 78 · 2002 · 95% · 40.500 · 1996 · 151 · 78 · 40.500

    Sem lastro

    —

    Não citados

    —

    0 nova(s) tentativa(s) restante(s)
14. 13Resposta

    Na replicação do teste de placebo da Tabela II, Painel B, coluna (2) de Fujiwara (2015), o salto estimado na proporção de votos válidos sobre o comparecimento na eleição para deputado estadual de 2002 (r_util02) no ponto de corte de 40.500 eleitores registrados em 1996 é de 0,00787427, com erro-padrão robusto (HC1) de 0,00644478 e intervalo de confiança de 95% de [-0,00475726; 0,0205058]. O modelo utiliza regressão linear local com núcleo uniforme (retangular) e largura de banda de 10.000 eleitores em torno do corte, contando com 151 municípios à esquerda e 78 à direita do limiar. Como esperado para um teste de placebo — dado que em 2002 todos os municípios utilizaram urnas eletrônicas —, o salto no limiar não é estatisticamente significante, com o intervalo de confiança de 95% incluindo o zero, confirmando a ausência de descontinuidade nessa eleição.

    • O teste de densidade de McCrary aponta descontinuidade na distribuição da variável de controle no ponto de corte, embora historicamente o critério de 40.500 eleitores tenha sido estabelecido após o fechamento do cadastro de 1996, o que afasta manipulação ativa do eleitorado.
    • A amostra na janela de estimação conta com 151 municípios abaixo e 78 acima do corte de 40.500 eleitores.

    Figuras citadas: call_f7e7118f:effect · Parada: answered

    Figura da resposta: call_f7e7118f:effect = 0,007874270.007874274462876002 (se 0,006444780.006444780866332111)
15. 14Pontuação
    #0resposta com lastropassouobrigatóriaevery number backed
16. 15Pontuação
    #1figura da resposta escolhidapassouobrigatóriaanswer figure call_f7e7118f:effect (infer.rdd)
17. 16Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.rdd
18. 17Pontuação
    #3argumento igualpassouobrigatóriainfer.rdd.y = 'r_util02'
19. 18Pontuação
    #4argumento igualpassouobrigatóriainfer.rdd.running = 'voters96'
20. 19Pontuação
    #5argumento igualpassouobrigatóriainfer.rdd.cutoff = 40500.0
21. 20Pontuação
    #6argumento igualpassouobrigatóriainfer.rdd.bandwidth = 10000.0
22. 21Pontuação
    #7argumento igualpassouobrigatóriainfer.rdd.kernel = 'uniform'
23. 22Pontuação
    #8argumento igualpassouobrigatóriainfer.rdd.polynomial = 1
24. 23Pontuação
    #9diagnósticopassouobrigatória151 vs 151
25. 24Pontuação
    #10diagnósticopassouobrigatória78 vs 78
26. 25Pontuação
    #11figura da resposta próximapassouobrigatória0.007874274463 vs 0.007874274462871547
27. 26Pontuação
    #12figura da resposta próximapassouobrigatória0.006444780866 vs 0.006444780866329607
28. 27Pontuação
    #13figura da resposta próximapassouregistrada0.007874274463 vs 0.008
29. 28Pontuação
    #14figura da resposta próximapassouregistrada0.006444780866 vs 0.006

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• época 1, tentativa 1passoupontuada(exibindo)

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