Does health insurance decrease out-of-pocket health expenses?

Some researchers have found that health insurance increases out-of-pocket heath expenses while other researchers have found the opposite. I estimate the change in per capita out-of-pocket health expenses verses per capita health insurance (dOOPHE/dinsurance) for 44 countries using a statistical technique that uses the vertical position of observations to capture the effects of omitted variables. This technique produces a separate dOOPHE/dinsurance for every observation which makes it possible to see how dOOPHE/dinsurance varies between countries and over time due to omitted variables. Between 2005 and 2017, I find that dOOPHE/dinsurance varies from a low of 0.081 in France in 2005 to 0.950 in India in 2005; however, by 2015 India's dOOPHE/dinsurance had fallen to 0.752. These estimates are for what happens on average in each country in each year, and, thus, do not show the catastrophic effects on those hit by the highest OOPHE. These results are consistent with health insurance reducing the OOPHE associated with any given visit to a medical facility; however, health insurance increasing the number of visits to medical facilities can result in total OOPHE increasing.