The mid-arch portion of a shoe is called a waist. In general, the waist of a shoe should hourglass only minimally. The following image shows a Puma shoe with a waist that is ridiculously narrow – even for an average width foot.
If you excessively pronate, or have any conditions associated with excessive pronation (plantar fasciitis, posterior tibial tendonitis, Achilles tendonitis), then wearing a shoe lacking support in the waist (midfoot) could prevent you from getting better.
Next time you find yourself shoe shopping, in addition to checking the price tag on the sole of the shoe, also check the width of the waist. Having a wide waist is good for shoes, bad for cardiovascular health.
Dr. Jenny Sanders Shoe Blog 
Jenny, why is a wide waisted shoe bad for cardio vascular health?
LOVE your blog!!!
Nancy
Oh, Nancy I was trying to be clever — According to the National Heart, Lung and Blood Association
Measuring waist circumference helps screen for possible health risks that come with overweight and obesity. If most of your fat is around your waist rather than at your hips, you’re at a higher risk for heart disease and type 2 diabetes. This risk goes up with a waist size that is greater than 35 inches for women or greater than 40 inches for men. To correctly measure your waist, stand and place a tape measure around your middle, just above your hipbones. Measure your waist just after you breathe out.
Thanks for reading my blog!
–Dr. Shoe
I never knew this! Good to know when looking at shoes online–you can often view the bottom of the shoe.