ECON 102: National Accounts Formulas
In this document, we present the most important formulas used in Module 5.
GDP Related Measures
GDP versus GNP
The link between the gross domestic product (GDP) and the gross national product (GNP) is: GDP + NFP = GNP ,
where NFP is the net factor payments from abroad: income paid to domestic factors of production by the rest of the world, minus income paid to foreign factors of production by the domestic economy.
GDP: Expenditure Approach
Y = C + I + G + X − M ≡ C + I + G + NX
where Y is the GDP, C is private expenditure in final goods and services, G is public expenditure in final goods and services, I is expenditure in capital goods (or investment), X is exports, M is imports and NX is net exports (X-M).
Net Domestic Product (NDP): Income Approach
NDP =labour income + corporate profits + interest income + self-employed income + indirect taxes − subsidies
Net Versus Gross
The difference between gross and net measures is depreciation. Net = Gross − Depreciation
Therefore:
GDP = Depreciation + NDP ,
where NDP is net domestic product. Similarly, gross investment (I) minus depreciation is equal to net
investment.
Private Disposable Income (PDI)
PDI = Y + NFP + TR + INT − T
where Y is the GDP, NFP is the net transfer payments from abroad, TR is the transfers received from
the government, INT is the interest payments on the government debt and T is taxes.
Econ 102 Module 5: Formulas Page 1 of 4
Net Government Income (NGI)
NGI = T − TR − INT ,
where TR the transfers received from the government, INT is the interest payments on the government
debt and T is taxes.
Current Account Balance (CA)
CA = NX + NFP ,
where NX is the net exports and NFP is the net factor payments from abroad.
Private Saving (Spvt)
Spvt =PDI−C=(Y+NFP+TR+INT−T)−C,
where PDI is the private disposable income, C is consumption expenditure, Y is the GDP, NFP is the net transfer payments from abroad, TR is the transfers received from the government, INT is the interest payments on the government debt and T is taxes.
Government Saving (Sgovt)
Sgovt =NGI−G=(T−TR−INT)−G,
where NGI is the net government income, G is government consumption expenditure, TR is the transfers received from the government, INT is the interest payments on the government debt and T is taxes.
National Saving (S)
S = Sgovt + Spvt ≡ I + CA ,
where Sgovt is the government saving, Spvt is the private saving, CA is the current account balance
and I is the investment expenditure.
Unchained Indexes
In the following, t is the current period and 0 is the base period. Therefore, Pit and Qit are the price and quantity of good i at time t, and Pi0 and Qi0 are the price and quantity of good i at the base period.
Paasche Quantity Index
Laspeyres Quantity Index
Ni=1 PitQit PQt/0=N PQ ×100
i=1 it i0
Ni=1 Pi0Qit LQt/0=N PQ ×100
i=1 i0 i0
Econ 102
Module 5: Formulas
Page 2 of 4
Fisher Quantity Index
formula:
Paasche Price Index
Laspeyres Price Index
Fisher Price Index
P Qt/0 LQt/0 FQt/0 =100× 100 × 100
Ni=1 PitQit PPt/0=N PQ×100
i=1 i0 it
Ni=1 PitQi0 LPt/0=N PQ ×100
i=1 i0 i0
F Qt/0 = P Qt/0 × LQt/0
Note that there is no need to multiply by 100 if PQ and LQ are not divided by 100. It is simply a geometric mean of PQ and LQ. Alternatively, if you prefer, you can use the following equivalent
F Pt/0 = P Pt/0 × LPt/0
Note that there is no need to multiply by 100 if PP and LP are not divided by 100. It is simply a
geometric mean of PP and LP. Alternatively, you can use the following equivalent formula:
P Pt/0 LPt/0 FPt/0 =100× 100 × 100
Chained Indexes
This formula is a little more complicated. To simplify, suppose that It/2000 is an index base 100 = 2000 for the year t. Then the chained indexes (CIt/0) for t greater than 2000 are:
C I2001/2000 C I2002/2000
= I2001/2000
= I2001/2000 × I2002/2001 × 100
100 100
= I2001/2000 × I2002/2001 × I2003/2002 × 100
C I2003/2000
and so on, where I could be PQ, PP, LQ, LP, FQ or FP. For t less than 2000, the indexes are
C I1999/2000 C I1998/2000
C I1997/2000
= I1999/2000
= I1999/2000 × I1998/1999 × 100
100 100
= I1999/2000 × I1998/1999 × I1997/1998 × 100
100 100 100
100 100 100
and so on.
Econ 102
Module 5: Formulas
Page 3 of 4
Nominal Versus Real
Nominal to Real
Let X be a nominal variable expressed in dollars and P be the price index base 100 = Y, where Y is a particular year. The real value of X expressed in dollars of the year Y is:
RealX= X . P /100
For example, if X is equal to 150 dollars and the index base 100 = 2012 is equal to 120, the value in
dollars of 2012 is
Real Interest Rate
150 = 125 dollars of 2012 . 120/100
Let i be the nominal interest rate and π be the inflation rate. Then, the real interest rate r expressed in percentage is:
(1 + i)
r= (1+π)−1 ×100%,
where i and π are not expressed in percentage. For example, if i = 5% and π = 3%, the real interest rate expressed in percentage is:
(1+0.05)
r= (1+0.03)−1 ×100%=1.94%.
Using the approximation for growth rates from module 2, the real interest rate is approximately equal to
r≈i−π,
where i and π can be expressed in percentage or not. For example, if i = 5% and π = 3%, the real
interest rate expressed in percentage is approximately equal to: r ≈ 5% − 3% = 2% .
Econ 102 Module 5: Formulas Page 4 of 4