From the US National Accounts, you find that in 2006, the share of Personal consumption expenditure in real GDP was 69.9 per cent and by 2008 it had fallen to 69.8 per cent. Similarly, the share of Gross private domestic investment on real GDP was 17.2 per cent in 2006 and by 2008 had fallen to 14.9 per cent (and further to 11.8 per cent in 2009). The net export deficit over the same period (2006 to 2008) fell from -5.7 per cent of real GDP to -4.9 per cent in 2008. Finally, the share of Government consumption expenditures and gross investment in real GDP rose from 18.8 per cent in 2006 to 18.9 per cent in 2008 (and 19.7 per cent in 2009). These relative changes tell you that real GDP was lower in 2008 compared to 2006 because the increase in Government spending and the falling negative contribution of net exports were not sufficient to offset the declining contribution from consumption and investment.
Answer: False
The answer is False.
The detail in the question relates to expenditure shares in real GDP and clearly does not tell you anything about the growth in GDP. All that you are being told are that the shares are changing over the period 2006 to 2008 in favour of public spending.
The shares are given by the following equation:
where A(t) is the value of aggregate A in quarter under consideration (say Personal consumption expenditure) and GDP(t) is the value of GDP in the same quarter.
So a change in the public spending share from 18.8 per cent in 2006 to 18.9 per cent in 2008 just says that in 2008 the flow of public spending is a greater proportion of the flow of real output in 2008 than it was in 2006. The rising share could be associated with a declining, constant or growing real GDP.
The fact you know that over this time that real GDP growth in the US was falling is irrelevant - the question asks whether you can conclude from the information before you.
The other related measure is the contributions to GDP growth which tell you each quarter what the expenditure components contributed to the GDP growth in that quarter.
From the Australian National Accounts - December 2009 you can find the definition of the contributions to GDP growth which is represented by the following equation:
where A(t) is as before; A(t-1) - value of aggregate A in previous quarter; and GDP(t-1) - value of GDP in previous quarter.
The ABS indicate that "the contributions to growth of the components of GDP do not always add exactly to the growth in GDP. This can happen as a result of rounding and the lack of additivity of the chain volume estimates prior to the latest complete financial year.
From the US National Accounts data you see that real GDP grew in 2005-06 by 2.7 per cent; then slowed to 2.1 per cent in 2006-07, 0.4 per cent in 2007-08 and plunged to -2.4 per cent in 2008-09. Over the period 2006-2008, real GDP grew overall by 2.6 per cent. The following table breaks down the contributions to that growth by the individual spending components (computed as per the Equation above).
The point of the question (if any) is to warn you into being careful to clarify the concepts being used before drawing conclusions. Too many people think they know what these terms mean and either mis-use them themselves to reach erroneous conclusions or allow themselves to be fooled by others who are touting erroneous conclusions.
If you are interested in more detail on national accounts then the 5216.0 - Australian National Accounts: Concepts, Sources and Methods, 2000 - is the place to go. Recommended reading if you want to get all the concepts and stock-flow relationships really sorted out. The system is universal and used by all statistical agencies.