Niterói has 2.9 times the expected number of franchise network units, in a model that explains 86% of the variation across municipalities

The number of franchise network units in a municipality depends largely on how many inhabitants it has, its output per inhabitant, the state it is in and its position relative to the metropolitan region. For each of the 682 municipalities with 50,000 inhabitants or more, the indicator estimates how many units would be expected based on these four elements and compares the result with the active CNPJs (Brazilian company registry) of the 503 measured networks. The result measures the presence of networks relative to the national pattern and does not indicate business opportunity, demand or saturation.

Out of sample, the model explains 86% of the variation on a logarithmic scale, with a median relative error of 28.2%. With population alone, the share explained is 66% and the error reaches 45.1%. In absolute numbers, the largest differences above the expected are in Rio de Janeiro (RJ), with 3,220 units against 2,638 expected; Brasília (DF), with 1,843 units against 1,293 expected; and Goiânia (GO), with 1,077 units against 655 expected, and the largest below the expected are in São Paulo (SP), with 4,712 units against 5,312 expected; Manaus (AM), with 571 units against 873 expected; and Porto Alegre (RS), with 555 units against 839 expected. Rio de Janeiro, Brasília, São Paulo, Manaus and Porto Alegre are within the 90% prediction interval, with no statistical distinction, and Goiânia is above the 90% prediction interval. Large cities concentrate the largest differences in units and have proportionally wide prediction intervals, so the reading is made within each population band.

In relative terms, among municipalities with 100,000 inhabitants or more and at least 20 expected units, Niterói (RJ) has the highest ratio, 2.93 times the expected number, and Sabará (MG) the lowest, 0.21. Holding population, GDP per capita and metropolitan position constant, the level of presence outside state capitals is higher in Mato Grosso (1.69), Santa Catarina (1.52) and Goiás (1.50) and lower in Sergipe (0.58), Pará (0.57) and Amazonas (0.16), relative to the national average, among the states with at least 10 municipalities of 20,000 inhabitants or more outside the capital. Acre, Amapá, Roraima and Tocantins have a smaller base and appear only in the table, with the number of municipalities alongside. The deviation is persistent, with a correlation of 0.85 between the deviations of 2023 and those of 2026, and does not depend on specific networks, with a correlation of 0.67 between two randomly drawn halves of the networks. In all, 43 municipalities are above and 25 below the 90% prediction interval, a proportion close to the 10% that would fall outside the interval even with the correct model, and for this reason the count of municipalities outside the interval is not, in itself, a finding.

How we calculate

The observed variable is the number of active establishments attributed to the 503 measured networks in each municipality, in the open CNPJ data of Receita Federal (the federal tax authority), reference month October 2026, treated as network units. The model is a negative binomial regression with a log link, fitted separately for the 1,752 municipalities with 20,000 inhabitants or more and for the smaller ones. The variables are the estimated population for 2025 (table 6579 of IBGE, the national statistics institute) and GDP per capita for 2023 (IBGE, table 5938, capped at percentiles 1 and 99), both on a logarithmic scale and with restricted cubic splines, the municipality's position (state capital, another municipality in the capital's metropolitan area, a municipality in another metropolitan area, or outside any metropolitan area, according to the IBGE composition of 2025), the major region and the state. Outside state capitals, the state effect has a ridge penalty. In state capitals, the state is replaced by a separate slope on population and a region effect with a ridge penalty, because the interior of a state does not describe its capital.

The expected value is always calculated out of sample, in 10 randomly drawn groups, so that no municipality influences its own prediction. The 90% interval comes from the 5% and 95% quantiles of the negative binomial, with dispersion estimated by population band. The choice of the negative binomial follows from the overdispersion of the Poisson, with a Pearson ratio of 3.72 versus 1.11. Out of sample, the observed sum is between 0.93 and 1.01 times the expected sum in each band of 50,000 inhabitants or more, and the 90% interval covers between 86.7% and 90.7% of the municipalities. Moran's index of the deviation, with the 5 nearest municipalities, is 0.10, which indicates weak spatial dependence.

By segment, the expected and observed values are calculated only when the expected value is at least 5 units and the probability that the interval distinguishes twice the expected value is at least 50%. The criterion keeps 790 combinations of municipality and segment and leaves gyms and sports, food, and tourism and hospitality without sufficient combinations, since in these segments dispersion across municipalities is high or counts are low. This breakdown is not shown on this page.

Calculated on November 8, 2026. Method version 1.0. Sample: 682 municipalities with 50,000 inhabitants or more, 503 networks, 51,091 active units.

Report an error on this page (in Portuguese)