Here's a very interesting study on the effects of direct democracy rules on the size of government. The paper: "Does Direct Democracy Reduce the Size of Government? New Evidence from Historical Data, 1890-2000", published in the Economic Journal, vol 121, issue 557, pages 1252-1280, 2011, but available free as an earlier draft working paper here, sets out to estimate the effect of direct democracy institutions on the size of government expenditure. The study uses Swiss cantons asa the 'test-bed' for direct democracy.
The study shows that once fixed effects are deployed to control for unobserved heterogeneity, and once instrumental variables are used to control for potential endogeneity, direct democracy can be linked to imposing constraints on cantonal spending. However, the overall impact of direct democracy on curtailing public spending is much more modest than previously suggested.
Thus: "a mandatory budget referendum reduces canton expenditures by 12%. Lowering signature requirements for the voter initiative by 1% reduces canton spending by 0.4-1.4%. We find little evidence that direct democracy at the canton level results in higher local spending or decentralization.
And another very interesting case study on effects of direct democracy, in this case - the study of Icelandic Constitutional change in the wake and in response to the crisis: