This Paper utilizes 188 countries' world panel data (i.e. Penn World Table, see Heston, Summers and Aten, 2006) available from 1950 to 2003 to inquire the dual side relationships between government size and economic development. On the one hand, the expanse of government activities promotes economic growth from the Keynesian theory on functional financial and monetary policy, but over interventions of government may reduce economic efficiency and thus damage economic development, which together will generate an inverted U relationship from government size to economic development, i.e. Armey curve relationship (Armey, 1995). On the other hand, this paper proposes theoretical hypotheses based on the substitution between government and market during economic development, which predict that the government size will fall during economic progress because of the improvement of market system.Thus, the relationship described by Wagner's law will fail according to the above hypotheses. Additionally, as for transitional countries, or so called government-lead economic development pattern in China, there is also a kind of inverted U relationship from economic development to government size, because both institutional inertia and new economic demand for government service in transition will lead to the growth of government departments faster than the growth of economy. However, this kind of inverted U relationship does not violate the general negative relationship between economic development and government size, but just a special passage when reaching for this general relationship. The results of empirical analysis fulfil the above hypotheses well. Firstly, the whole panel data and sub data from OECD countries, growth countries and transitional countries support the hypothesis of Armey curve, i.e. inverted U relationship. Secondly, the whole panel data and sub data from OECD and growth countries show that the government size falls as the growth of real GDP per capita, which are consistent to the substitution hypothesis between government and market, that is to say, Wagner's law fails. At Last, the data of transitional countries as well as China's provincial panel data reflect that, in accordance with the above hypothesis made for transitional countries, there is also a kind of inverted U shape relationship
