The "macroeconomic forecast model" will cover a range of scenarios after a Yes vote, including the impact of "economic shocks".
It will analyse a complex web of interacting forces, including household income, government spending, taxes, labour markets, and North Sea oil and gas production.
The deadline for firms bidding for the job closes this week. However, the model is not expected to be fully operational until 2014, the same year as the independence referendum, and after publication of the government's white paper on independence. Opposition parties last night claimed the SNP, whose central case for independence is a healthier economy, had again been making assertions without the facts to back them up.
The First Minister Alex Salmond says an independent Scotland would have the sixth-highest per capita Gross Domestic Product in the developed world.
Finance Secretary John Swinney also said recently that a 3% corporation tax cut would support 27,000 jobs, that VAT changes could help tourism, that tax credits could see "a step change" in research and development, while "targeted interventions" could attract international investment.
But the current Government software is simply unable to predict how such changes would ripple through the wider, or macro, economy. The software even appears unable to model the impact of the changes to income tax arising from the 2012 Scotland Act.
In August, the First Minister's Fiscal Commission Working Group, which includes Nobel prize winning economist Joseph Stiglitz, raised the need for a better model and better input data as part of its work on a "fiscal framework" for independence.
Recent thinktank reports have suggested the Scottish economy could be less robust than previously thought after independence, due to declining income from North Sea oil.
A spokesman for the pro-Union Better Together campaign said the SNP seemed to have made its rosy economic predictions using "a ZX Spectrum gathering dust in St Andrew's House".
A Government spokesman said: "As we move to implement the taxation responsibilities in the Scotland Act, future Scottish budgets will depend to a much greater extent on tax revenues raised in Scotland."