TODAY’S polarized debates about the role of government often boil down to a single issue: the size of government compared with the size of the overall economy, as measured in gross domestic product.

This is true on both sides of the debate. One recent proposal featured in The Wall Street Journal argues for a “golden fiscal rule” that the size of government as a percentage of G.D.P. should always be shrinking; liberals frequently cite the higher ratio of government spending to G.D.P. in many European countries.

But such comparisons are not very meaningful: The way we measure government’s role in the economy is limited, inaccurate and unrealistic. If we want to understand how government and the overall economy interact, knowing the size of government tells us little if we are not measuring how government activities contribute to our economy over time.

The problem is that most government goods and services are provided free, so they do not have market prices like, say, mouthwash or financial planning. Standard national accounting — in G.D.P. and related economic indicators — addresses this by assuming that the value of government is exactly equal to what government spends, without any consideration of what government actually produces or of the value of this public output.