From Rolling Quarters to Monthly Estimates: SIDRA Mensalization Guide"

In PNADCperiods: Identify Reference Periods in Brazil's PNADC Survey Data

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Overview

Brazil's Continuous National Household Sample Survey (PNADC) publishes labor market indicators as rolling (moving) quarters — 3-month moving averages where each published "quarter" shares 2 months with its neighbors. This smoothing hides short-term dynamics: turning points are delayed, seasonal patterns are distorted, and international comparison becomes difficult.

The PNADCperiods package includes a SIDRA mensalization module that recovers exact monthly estimates from rolling quarter data. This vignette explains how to use it.

Why Rolling Quarters Are Problematic

Each published "quarter" is actually a 3-month moving average:

• "2019-Q1" = average of Jan, Feb, Mar 2019
• "2019-Q2" = average of Feb, Mar, Apr 2019
• "2019-Q3" = average of Mar, Apr, May 2019

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When unemployment jumps sharply in a single month, the rolling quarter spreads that spike across multiple overlapping periods. The mensalization algorithm inverts this averaging process to recover the true monthly values.

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Quick Start

library(PNADCperiods)

# Step 1: Fetch rolling quarter data from SIDRA API
rolling_quarters <- fetch_sidra_rolling_quarters()

# Step 2: Convert to monthly estimates
monthly <- mensalize_sidra_series(rolling_quarters)

# Step 3: Use your monthly data!
head(monthly[, .(anomesexato, m_popocup, m_taxadesocup)])

That's it! You now have monthly estimates starting from January 2012.

1. fetch_sidra_rolling_quarters() downloaded 86+ economic indicators from IBGE's SIDRA API

2. mensalize_sidra_series() applied the mensalization formula using pre-computed starting points (bundled with the package)

3. The result is a data.table with one row per month and m_* columns for each mensalized series

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Understanding the Output

The mensalized output contains:

• anomesexato: Month identifier (YYYYMM format, e.g., 201903 = March 2019)
• m_* columns: Mensalized (monthly) estimates for each series
• Price indices: ipca100dez1993, inpc100dez1993 (passed through for deflation)

Key series include:

| Column | Description | Unit | |--------|-------------|------| | m_populacao | Total population | Thousands | | m_pop14mais | Population 14+ years | Thousands | | m_popocup | Employed population | Thousands | | m_popdesocup | Unemployed population | Thousands | | m_taxadesocup | Unemployment rate | Percent | | m_taxapartic | Labor force participation rate | Percent | | m_massahabnominaltodos | Total nominal wage bill | Millions R$ |

Rate series (like m_taxadesocup) are derived from mensalized level series when compute_derived = TRUE (the default). They are computed as ratios of the mensalized levels, not directly mensalized from the rolling quarter rates.

Discovering Available Series

Use get_sidra_series_metadata() to explore all 86+ available series:

meta <- get_sidra_series_metadata()

# View series organized by theme
meta[, .N, by = .(theme, theme_category)]

# Filter to specific theme categories
meta[theme_category == "employment_type", .(series_name, description)]

The metadata uses a hierarchical taxonomy: theme (top level, e.g., "labor_market"), theme_category (e.g., "employment_type"), and optionally subcategory (e.g., "levels", "rates").

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Data Flow

The mensalization process follows a three-step pipeline:

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Step 1: Fetching Rolling Quarter Data

fetch_sidra_rolling_quarters() downloads data from five SIDRA tables:

| Table | Content | |-------|---------| | 4093 | Population and labor force | | 6390 | Income (nominal and real) | | 6392 | Real income by occupation | | 6399 | Employment by sector | | 6906 | Underutilization indicators |

rq <- fetch_sidra_rolling_quarters(verbose = TRUE)

# Inspect structure
dim(rq)
names(rq)[1:20]

Key columns: anomesfinaltrimmovel (end month of rolling quarter, YYYYMM), mesnotrim (month position 1/2/3), plus one column per series.

Step 2: The Mensalization Transform

monthly <- mensalize_sidra_series(rq, verbose = TRUE)

# Compare dimensions
cat("Rolling quarters:", nrow(rq), "rows\n")
cat("Monthly data:", nrow(monthly), "rows\n")

The row count is approximately the same (one per month), but the meaning changes from "rolling quarter ending in month X" to "exact estimate for month X".

Step 3: Using Monthly Estimates

Show plotting code

# --- VIGNETTE CODE: plot-unemployment ---
library(ggplot2)

monthly[, date := as.Date(paste0(substr(anomesexato, 1, 4), "-",
                                  substr(anomesexato, 5, 6), "-01"))]

ggplot(monthly, aes(x = date, y = m_taxadesocup)) +
  geom_line(color = "#1976D2", linewidth = 0.8) +
  labs(title = "Monthly Unemployment Rate",
       x = NULL, y = "Unemployment Rate (%)")

Population Data for Weighting

For analyses requiring monthly population estimates separately:

pop <- fetch_monthly_population()
head(pop)

Returns a data.table with ref_month_yyyymm and m_populacao columns.

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Working with Series

Fetching by Theme

Instead of fetching all 86+ series, filter by theme or theme category:

# Only employment type series
employment <- fetch_sidra_rolling_quarters(theme_category = "employment_type")

# Only wage mass series
wages <- fetch_sidra_rolling_quarters(theme_category = "wage_mass")

# Only labor market theme (includes participation, unemployment, employment types, etc.)
labor <- fetch_sidra_rolling_quarters(theme = "labor_market")

Fetching Specific Series

For maximum efficiency, request only the series you need:

# Only unemployment-related series
unemp <- fetch_sidra_rolling_quarters(
  series = c("popdesocup", "taxadesocup", "popnaforca")
)

Excluding Derived Series

Some series are rates computed from other series. To fetch only "base" series:

# Exclude computed rates (only population and income levels)
base_only <- fetch_sidra_rolling_quarters(exclude_derived = TRUE)

Selecting Output Columns

After mensalization, select columns as needed:

monthly <- mensalize_sidra_series(rq)

# Select specific series
labor_market <- monthly[, .(
  anomesexato,
  employed = m_popocup,
  unemployed = m_popdesocup,
  unemp_rate = m_taxadesocup,
  participation = m_taxapartic
)]

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The Mensalization Methodology

This section can be skipped by users who just need results.

The Core Concept

Rolling quarters are 3-month moving averages. If we denote the true monthly value for month $t$ as $y_t$, then the rolling quarter value $x_t$ is:

$$x_t = \frac{y_{t-2} + y_{t-1} + y_t}{3}$$

The mensalization algorithm inverts this relationship to recover $y_t$ from the sequence of $x_t$ values.

The Mensalization Formula

Step 1: Compute first differences

$$d3_t = x_t - x_{t-1}$$

Step 2: Identify month position (mesnotrim)

Each month has a position within its quarter: - Position 1: Jan, Apr, Jul, Oct - Position 2: Feb, May, Aug, Nov - Position 3: Mar, Jun, Sep, Dec

Step 3: Cumulative sum by position

For each position separately, compute the cumulative sum of first differences, starting from a calibrated "starting point" $y_0$:

$$y_t = y_0 + \sum_{s \in \text{same position}, s \leq t} d3_s$$

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The Role of Starting Points ($y_0$)

The starting point $y_0$ is crucial. It determines the level of all subsequent monthly estimates. The package includes pre-computed starting points for 53 series, calibrated during the stable 2013-2019 period.

Starting points are computed by:

1. Processing PNADC microdata to get "true" monthly aggregates ($z$ values)
2. Comparing these to rolling quarters
3. Finding the $y_0$ that makes $y_0 + \text{cumsum}(d3)$ match the microdata

Assumptions and Limitations

• Monthly values within each position evolve smoothly
• The calibration period (2013-2019) reflects "normal" conditions
• Cannot recover intra-month variation
• Starting points are calibrated to national totals (not regional breakdowns)

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Practical Considerations

API Caching

The package caches SIDRA API responses in memory during your R session:

# First call: fetches from API (~10 seconds)
rq1 <- fetch_sidra_rolling_quarters()

# Second call with use_cache = TRUE: uses cached data (instant)
rq2 <- fetch_sidra_rolling_quarters(use_cache = TRUE)

# Clear all cached data (force fresh fetch on next call)
clear_sidra_cache()

The cache persists until you call clear_sidra_cache() or restart R.

Common Errors

| Error | Cause | Solution | |-------|-------|----------| | "Series not found" | Misspelled series name | Check get_sidra_series_metadata() | | "API timeout" | SIDRA server slow | Retry; use use_cache = TRUE | | "No starting points" | Custom series | See Custom Starting Points below |

# Check if series exists
meta <- get_sidra_series_metadata()
"taxadesocup" %in% meta$series_name  # TRUE

Data Quality Notes

COVID-19 disruptions (2020): IBGE suspended in-person interviews during the pandemic. Some indicators show unusual patterns in 2020-Q2.

CNPJ series availability: Series based on CNPJ registration (empregadorcomcnpj, contapropriacomcnpj, etc.) are only available from October 2015, when V4019 was introduced.

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Custom Starting Points

For users with calibrated PNADC microdata.

Use the bundled starting points (default) unless:

1. Your series isn't bundled — Custom variable definitions
2. Different calibration period — Non-standard reference period
3. Regional breakdown — State or metro-area mensalization

Option A: All-in-One Function

# Load your stacked PNADC microdata (with pnadc_apply_periods weights)
stacked <- readRDS("my_calibrated_pnadc.rds")

# Compute starting points
custom_y0 <- compute_starting_points_from_microdata(
  data = stacked,
  calibration_start = 201301L,
  calibration_end = 201912L,
  verbose = TRUE
)

# Use custom starting points
monthly <- mensalize_sidra_series(rq, starting_points = custom_y0)

Option B: Step-by-Step

# Step 1: Build crosswalk and calibrate
crosswalk <- pnadc_identify_periods(stacked)
calibrated <- pnadc_apply_periods(
  stacked, crosswalk,
  weight_var = "V1028",
  anchor = "quarter",
  calibration_unit = "month"
)

# Step 2: Compute z_ aggregates (monthly totals from microdata)
z_agg <- compute_z_aggregates(calibrated)

# Step 3: Fetch rolling quarters for comparison
rq <- fetch_sidra_rolling_quarters()

# Step 4: Compute starting points
y0 <- compute_series_starting_points(
  monthly_estimates = z_agg,
  rolling_quarters = rq,
  calibration_start = 201301L,
  calibration_end = 201912L
)

# Step 5: Use custom starting points
result <- mensalize_sidra_series(rq, starting_points = y0)

CNPJ-based series automatically use a later calibration period (2016-2019) when use_series_specific_periods = TRUE (the default in compute_series_starting_points()).

Validating Custom Starting Points

bundled <- pnadc_series_starting_points

# Merge and compare
comp <- merge(custom_y0, bundled,
              by = c("series_name", "mesnotrim"),
              suffixes = c("_custom", "_bundled"))

comp[, rel_diff := abs(y0_custom - y0_bundled) / abs(y0_bundled) * 100]
comp[rel_diff > 1]  # Flag series with >1% difference

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Case Study: COVID-19 Unemployment

How quickly did unemployment rise when COVID-19 hit Brazil? Rolling quarter data obscures these dynamics. Monthly estimates reveal the exact timing.

Show analysis code

# --- VIGNETTE CODE: covid-analysis ---
# Fetch all series and mensalize
rq <- fetch_sidra_rolling_quarters()
monthly <- mensalize_sidra_series(rq)

# Filter to COVID period
covid_period <- monthly[anomesexato >= 201901 & anomesexato <= 202212]

# Create date column
covid_period[, date := as.Date(paste0(
  substr(anomesexato, 1, 4), "-",
  substr(anomesexato, 5, 6), "-01"
))]

# Find peak
peak_month <- covid_period[which.max(m_taxadesocup)]
cat("Peak unemployment:", peak_month$m_taxadesocup, "% in",
    format(peak_month$date, "%B %Y"), "\n")

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Key findings from monthly estimates:

1. Exact peak timing: Monthly data pinpoints the peak month, while rolling quarters show only a gradual rise

2. Speed of impact: The monthly series reveals a sharp spike that rolling quarters smooth over 3+ months

3. Recovery dynamics: Monthly estimates show pauses and reversals in recovery that are hidden in quarterly averages

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Series Naming Conventions

| Pattern | Meaning | Example | |---------|---------|---------| | m_ | Mensalized monthly estimate | m_popocup | | pop* | Population count | populacao, pop14mais | | *comcart | With formal contract | empregprivcomcart | | *semcart | Without formal contract | empregprivsemcart | | *comcnpj | With CNPJ registration | empregadorcomcnpj | | taxa* | Rate (percent) | taxadesocup | | nivel* | Level/ratio (percent) | nivelocup | | rend* | Income (rendimento) | rendhabnominaltodos | | massa* | Wage bill (massa salarial) | massahabnominaltodos | | *hab* | Usually received (habitual) | rendhabnominaltodos | | *efet* | Actually received (efetivo) | rendefetnominaltodos |

For the complete catalog, use get_sidra_series_metadata():

meta <- get_sidra_series_metadata()

# Filter by theme category
meta[theme_category == "employment_type", .(series_name, description)]

# Filter by theme and pattern
meta[theme == "labor_market" & grepl("taxa|nivel", series_name),
     .(series_name, description)]

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Function Reference

| Function | Purpose | |----------|---------| | fetch_sidra_rolling_quarters() | Download rolling quarter data from SIDRA API | | fetch_monthly_population() | Get monthly population estimates | | mensalize_sidra_series() | Convert rolling quarters to monthly estimates | | get_sidra_series_metadata() | Explore available series and metadata | | clear_sidra_cache() | Clear cached API data | | compute_z_aggregates() | Compute monthly aggregates from calibrated microdata | | compute_series_starting_points() | Compute $y_0$ values from aggregates | | compute_starting_points_from_microdata() | All-in-one $y_0$ computation |

Bundled data: pnadc_series_starting_points — pre-computed $y_0$ for 53 series x 3 month positions (calibration period: 2013-2019).

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References

• HECKSHER, Marcos. "Valor Impreciso por Mes Exato: Microdados e Indicadores Mensais Baseados na Pnad Continua". IPEA - Nota Tecnica Disoc, n. 62. Brasilia, DF: IPEA, 2020. https://portalantigo.ipea.gov.br/portal/index.php?option=com_content&view=article&id=35453
• HECKSHER, M. "Cinco meses de perdas de empregos e simulacao de um incentivo a contratacoes". IPEA - Nota Tecnica Disoc, n. 87. Brasilia, DF: IPEA, 2020.
• HECKSHER, Marcos. "Mercado de trabalho: A queda da segunda quinzena de marco, aprofundada em abril". IPEA - Carta de Conjuntura, v. 47, p. 1-6, 2020.
• Barbosa, Rogerio J; Hecksher, Marcos. (2026). PNADCperiods: Identify Reference Periods in Brazil's PNADC Survey Data. R package version v0.1.0. https://github.com/antrologos/PNADCperiods

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Further Reading

• vignette("getting-started") — Setting up PNADC microdata analysis
• vignette("how-it-works") — The period identification algorithm
• vignette("applied-examples") — Applied research examples
• IBGE SIDRA API: https://sidra.ibge.gov.br/
• Package repository: https://github.com/antrologos/PNADCperiods

PNADCperiods documentation built on April 28, 2026, 9:07 a.m.