A health economist wants to investigate if people who visit their doctor more often

have lower health expenditures in the long run. She thinks that regular doctor consultations and check-ups may have a preventive effect that lowers spending on prescription drugs and medical treatments. She wants to collect data on a random sample of people and run a simple regression of health expenses in the last three years (in $) on the number of doctor visits in the past 3 years:

HealthExpensesi = 0 + 1DoctorV isitsi + 2Agei + 3Incomei + i

However, she worries about a variable, which is not included in the model: the person's health.

Do you think the estimate 1 obtained from the regression above suffers from omitted variable bias caused by the omitted variable "health of a person"?