A simple index of innovation with complexity

•I study limitations of existing innovation indices.•I propose two indices of innovation with complexity weights.•I analyze empirically how size-dependent and size-independent innovation behave.•New rankings are similar to mainstream index, differences in highly innovative countries.•Size-dependent index is highly correlated with country size (GDP) and technology.

Patents are the main source of data on innovation. Since most of the innovative activity happens outside of the patenting system, and since patents −and innovations- have different quality, complexity, and impact on each market, unweighted sums of patents and proxies are an imperfect indicator of a country's innovative activity. I generate two very simple indices of innovation (one dependent on the size of a country, and another that normalizes country-size), based on weighting patents and exports by a complexity measure. Each index captures the technological complexity of innovations inside and outside the intellectual property rights system. I empirically analyze the rankings of these innovation indices, and contrast the results with technological development, GDP, and the existing mainstream innovation index.