If you are talking about Financial Performance, you may use ROE, ROA, Profit Margin, Tobin's Q, etc. As regards non-financial, you may use KPIs or similar indicators used in the insurance industry.
You should consider different types of insurance to find different multipliers of insurance premium to GDP. Please, look at insurance premium, not at insurers' net profits. In most cases you will find the negative multipliers -- the lower the insurance premium, the higher is the growth of GDP. This is applicable to social insurance premium, marine insurance etc. Thus, do not use DEA and other similar methods, look how insurance makes cheaper the inputs, not how profits increase outputs.
Various indicators to use as independent variables are those related to financial performance as in the banking industry plus insurance premium and payouts (or net insurance premium). I guess your dependent variable is real GDP growth rather than just GDP.
Insurance is a market for pricing risk; insurance provides participants the opportunity to offload risk in exchange for a fee. In an efficient risk market, the cost of risk is low to participants than in a inefficient insurance market.
Risk detracts from GDP growth. Businesses finding the price of risk to high will resist investment, as potential returns are inadequate. Some countries have higher sovereign risk than others, some countries offer higher returns on equity investments (shares market) than others. As there are no free lunches this comes down to an issue of risk and return.
Where a country has difficulty providing insurance such as say Iran where due to sanctions insurers cannot access international reinsurance, there are distortions present. This means the price of risk coverage is too high by global norm. Consequently, distortions concerning which sectors of the economy attract investment are distorted – like property investment becomes the favourite – with an end result of lower sustainable GDP growth.
I think your research question has great potential. Ask, is Insurance market efficiency related to GDP growth? You can test causality etc. as you proceed. This does seem to be a tractable question and one that should make a serious contribution to knowledge. Good luck!