A new study from the Fraser Institute argues that expanding the Canada Pension Plan or CPP and raising contribution rates to increase benefits would reduce private retirement savings on almost a dollar for dollar basis. Thus they say a bigger CPP would do little to improve retirement income security.The key problem with the study is that it looks at the amount of money set aside as savings each year by households, an annual flow, not at the total stock of retirement saving.Returns on savings are not included in the annual saving rate, but are clearly an important factor in determining the total amount of savings a person has at the time of retirement.The savings rate looks at the amount of money invested in RRSPs or the CPP in any given year, but not at the investment returns  in RRSPs and the CPP over time. This is critically important since most studies show that investment returns in the CPP investment fund and large employer pension plans far exceed those in RRSPs which often have annual management fees of 2% per and above.To summarize, adequate savings for retirement are best judged by the total stock of savings at retirement,, not by the annual savings rate. A key argument for CPP expansion is that it will leave individuals much better off than saving through RRSPs.It also has to be taken into account that CPP contributions, unlike most RRSP contributions, are shared between employers and employees. They thus cost individuals much less. And individuals know that they will get the CPP benefit for life, fully indexed to inflation. The returns from a RRSP after retirement are far less certain.It is also very doubtful that increased CPP a contributions have significantly reduced private savings in RRSPs and other vehicles as much as the Fraser Institute claims.The study assumes that individuals have perfect knowledge such that they will adjust annual savings before retirement based on projections of  future CPP benefits. But in fact increased CPP contributions in the period under study from 1986 to 2004 were introduced to shore up promised CPP benefits, not to increase them.Thus the Fraser Institute is improbably claiming that individuals were cutting RRSP contributions dollar for dollar of increased CPP contributions, just because they were more confident that they would get the promised plan benefit.Further, savings rates likely fell for other reasons from 1986 to 2004 not taken into full consideration. The most important factor was probably the stagnation of real wages for most families, leaving little after tax income to put into RRSPs. Also, the voluntary nature of RRSPs means that many people fail to save enough to secure a decent retirement.The study fails to rebut the argument that an expanded CPP would increase future retirement security for many middle class Canadians who do not belong to defined benefit pension plans and are forced to rely on high cost RRSPs.Economist Andrew Jackson is Senior Policy Advisor at the Broadbent Institute