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]]>Here is the contrast.

(A) E/Y part

In NIPA T-accounting:

each sector E(t) = Y(t), All sectors in total E(t)=Y(t)

In L_G Model:

Each sector E(t) may not be equal to Y(t), Thus, all sectors in total E(t)

may not be equal to Y(t) as well. Sector or Total E(t) = Y(t) only in

equilibrium.

Note that “E(t) = Y(t)” is used as behavior equation in L_G model.

Thus this equation may not be true for all time periods. You can

see Table 1 data. For periods -1 and -2, they are equal. For periods 0, 1, and 2, they are not equal

(B) S/I part:

In NIPA T-accounting:

Each sector S(t) may not be equal to I (t), All sectors in total S(t) = I(t)

Each sector S(t) is defined as sector Y(t) – sector consumed spending

In L_G Model

Each sector S(t) may not be equal to I (t), All sectors in total S(t) may not be equal to I(t) . Sector or Total S(t) = I(t) only in equilibrium.

Household and business Saving S(t) are defined differently.

NIPA accounting identities can explain S-I dynamic behaviors adequately without need of equilibrium and behaviors equations. Table 1 data would not happen in NIPA.

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]]>Your equations seem right and its not the trade balance which enters the sectoral balances identity but the current account balance and correct definitions are needed for what is meant by “G” such as government purchases of goods and services is counted in GDP by expenditure but the one in the sectoral balances is slightly different.

However, I don’t see how your points are related to the issues raised here. Any place where such technicalities make a difference in the discuession?

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]]>The financial balance equation “I = S + (T – G) + (M – E)” is mentioned in many places such as MR, MMT, …

But the precise accounting identity should be

I ≡ S + (GS – GI) + (M – E) + (IP – IR)

I = private investment

S = private saving

GS = government saving

GI = government investment

IP = income payments to foreign

IR = income receipts from foreign

NX = (E – M) (net export)

NR = (IR – IP) (net income receipts)

There are few discrepancies.

(a) government budget surplus(+)/deficit(-) = GS – GI

G does not cover all government expenditures and only covers the

spending counted as GDP calculation from government sector.

G = Government Consumption(GC) + Government Investment(GI)

Thus, T – G is not equal to budget surplus(+)/deficit(-). We need

to subtract government non-G spending such as transfer payment, interest payments, etc.

Government budget surplus(+)/deficit(-) = T – G – non-G = GS – GI which is consistent with private sector S – I

(b) Current account surplus (+)/deficit(-) = E – M + IR – IP = NX + NR

Foreign T-account (Receipts ≡ Payments)

Receipts = E + IR

Payments = M + IP + balance_of_current_account

Note that capital account outflow (+)/inflow(-) = current account surplus(+)/deficit(-). E and M do not covers earnings from FDI investment, wages receipts/payments from/to foreign. As G, E and M only cover import’s payments and export’s receipts counted as GDP calculation.

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]]>But if you want to complete a model like this to other/all sectors (and I don’t understand why you’re introducing the foreign sector asymmetrically to the exclusion of government) I think the cleanest way is through the following sector financial balances equation:

I = S + (T – G) + (M – E)

which says that domestic investment is funded by domestic private sector saving, the government budget surplus, and the capital account surplus

NIPA gets adapted however it’s adapted; it is just an institutional decomposition of a functional tautology

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]]>Textbook teaching on “S=I” makes an implicit assumption that balance of current account (= NX+NR) is used either as foreign sector investment added to I or as minus foreign sector saving subtracted from S.

These terms: foreign investment and savings, are not defined formally in NIPA. In NIPA domestic capital T-account:

S = public saving + household saving + business saving

I = public investment + household investment + business investment

balance item of capital account (S – I) = NX+NR

Textbook teaching on “capital account + current account = 0” really means

“balance of capital account = balance of current account” in NIPA.

Accounting identities are temporal logic assertions on time-series data, and are truth statements for all past/future time periods.

Equilibrium and behavior equations are assumptions like dogma or axioms in math systems without proof. The equations may be true for specific group behaviors at particular time period. They are not general and are often not true.

Equation “S=I” has different meanings depending on the view as an accounting identity or as an equilibrium/behavior equation. This view determines the more accurate equation form, and how the form is derived or assumed axiomatically. Similarly, equation “MV = PQ” has a different form and meaning if considered as an accounting identity.

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]]>The equation will not be a NIPA accounting identity if I is for one sector, and S = BS+HS

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