Saving does nothing to increase GDP. It decreases the cost of capital, nothing more.
Expenditure approach to GDP:
Y = C + I + G + (X − M)
Y = Nominal GDP
C = Consumption
I = Investment
G = Government Spending
X = Exports
M = Imports
G can be perhaps more properly divided among C, I, and NX (NX being Net Exports, or X-M), as most, if not all, of G is either on consumption or investment.
Definition of investment by wikipedia (which is pretty undisputed):
I (investment) includes business investment in equipments for example and does not include exchanges of existing assets. Examples include construction of a new mine, purchase of software, or purchase of machinery and equipment for a factory. Spending by households (not government) on new houses is also included in Investment.
In contrast to its colloquial meaning, 'Investment' in GDP does not mean purchases of financial products. Buying financial products is classed as 'saving', as opposed to investment. This avoids double-counting: if one buys shares in a company, and the company uses the money received to buy plant, equipment, etc., the amount will be counted toward GDP when the company spends the money on those things; to also count it when one gives it to the company would be to count two times an amount that only corresponds to one group of products. Buying bonds or stocks is a swapping of deeds, a transfer of claims on future production, not directly an expenditure on products.
Emphasis mine.
You are correct that savings does not directly increase GDP like consumption does. However, the question is,
from what source does investment arise. The answer is a mixture of G, corporate profits, financing, and credit. Credit and financing are the largest. Read almost any company's financial statements and you will find that credit and financing are the largest source of their investment moneys. Not direct government purchasing or annual profits. Credit. Financing.
What defines the availability of credit? Crudely, the interest rate. A lower interest rate indicates, ceteris paribus, more access to credit. What defines the availability of financing? The existence of inactive moneys; that is, the existence of savings (either corporate, household, or government). What generates a low interest rate? Tons of things affect interest rates. ONE of those things is the supply of loanable funds. What defines the supply of loanable funds? The existence of comparatively inactive moneys, and also monetary expansion.
In sum, "saving" (which is effectively synonymous with "inactive moneys" in this case) can affect GDP through:
1. Lowering interest rates, thereby, ceteris paribus, encouraging investment through credit
2. Increasing the availability of private financing, ceteris paribus, encouraging investment through financing
Investment tends to be more generative of long-term growth than consumption, in most macroeconomic theory of any part of the political spectrum.
It is true that a short-run exogenous positive consumption shock will boost the economy. For many years, the dwindling of American savings and the increased availability of credit was treated by macroeconomists as just such a shock. This was dumb. Dwindling savings and ballooning credit is not an exogenous shock, but symptom of systemically increasing risk tolerance (or decreasing risk aversion, much the same). Risk tolerance in the last few years, post-2007, has declined. Savings rates have risen. Growth has slowed. Corporate cash reserves and bank capital reserves have risen. What is necessary for an effective recovery to begin is not properly for consumption to pick up (that would help, but that's not really where the slack is: decreasing savings rates now won't pull money already stockpiled in institutions into circulation), but for institutions to find profitable investment ventures. Such ventures, in many developed countries, seem few and far between, and there is significant debate over how to find/cultivate them.
Cue politics.
In sum, yes, savings can (and does) have a non-negative role in GDP. Savings is not a "withdrawal" from a GDP account. It is a (if not the only) major driving force for one of the essential components of GDP, and a component that is uniquely essential to long-term growth.
I don't think I even needed to make any politically controversial statements to get there.
