J. Wayne Robbins was a Louisiana native who served as mayor of Kimball from 1978-1982. Previously, he was a member of the Kimball School Board and the Kimball City Council. Robbins was born in Haynesville in northern Claiborne Parish just south of the Arkansas state line. He was in oil drilling and later the construction business.
As of the census of 2000, there were 2,559 people, 1,110 households, and 700 families residing in the city. The population density was 1,665.8 people per square mile (641.6/km²). There were 1,210 housing units at an average density of 787.6/sq mi (303.4/km²). The racial makeup of the city was 96.25% White, 0.35% African American, 1.06% Native American, 0.16% Asian, 0.39% from other races, and 1.80% from two or more races. Hispanic or Latino of any race were 3.52% of the population.
There were 1,110 households out of which 25.4% had children under the age of 18 living with them, 51.8% were married couples living together, 8.0% had a female householder with no husband present, and 36.9% were non-families. 33.7% of all households were made up of individuals and 18.0% had someone living alone who was 65 years of age or older. The average household size was 2.25 and the average family size was 2.84.
In the city the population was spread out with 24.1% under the age of 18, 6.1% from 18 to 24, 23.1% from 25 to 44, 23.3% from 45 to 64, and 23.4% who were 65 years of age or older. The median age was 43 years. For every 100 females there were 90.0 males. For every 100 females age 18 and over, there were 86.4 males.
The median income for a household in the city was $29,984, and the median income for a family was $37,273. Males had a median income of $29,222 versus $18,198 for females. The per capita income for the city was $18,762. About 7.9% of families and 10.2% of the population were below the poverty line, including 12.6% of those under age 18 and 6.6% of those age 65 or over.