In many countries, solar panels are heavily subsidized because they replace fossil fuels that apparently cause global warming. A mirror of the same size would - through a completely different effect - also reduce some global warming by reducing the solar energy reaching the earth. Considering that mirrors are much cheaper than solar panels, wouldn't they be more cost-effective in mitigating global warming?
Reflective roofs do prevent and reverse global warming. By increase the albedo of an area, you reflect light into the air which keeps that area cooler. More importantly, however, it prevents absorbtion of light/heat into the house which keeps the house cooler. As cooling a house is worse for global warming than heating a house, it has a large benefit to prevent global warming and saves the consumer energy costs without subsidies. The most popular roofing produce has a reflectance of roughly 3% while the same visible color product is produced with a reflectance of 20% and products (of lighter colors) are being developed with reflectances 80-90%.
A mirror, however, is not nessesary to do this. The mining and processing of the raw materials would add to the global warming issue. Using reflective surfaces that are not directional (aka bright white granules or ones that preferentially reflect infrared light) causes the same benefits but are cheaper and more beneficial than a literal mirror would be.
Space based mirrors would be more effective but much more expensive. It does not have to do with dust.
Solar roofs are well known but are certainly not the only option to have a more environmentally friendly roof.
I think this is somewhat of an apples/oranges comparison.
The benefit from a ground-based mirror is a fixed benefit per year, and lasts as long as someone is willing to leave it on their land and keep it clean. If lots of people put up mirrors for 25 years, then dismantled them, the earth would immediately warm back up.
The environmental benefit from a solar panel is that during its fixed lifetime (nominally 25 years for rooftop photovoltaics) it prevents the emission of a fixed amount of greenhouse gas that would otherwise have been released by burning fossil fuels. These gases would have stayed in the atmosphere for a very long time that is not accurately known, probably centuries. When the panel goes out of service, the benefits it gave continue to accrue.
In terms of economics, photovoltaics are economically viable in many areas without subsidies, whereas mirrors would require ongoing subsidies, and people would remove them as soon as the subsidies ended.