1 Chapter 8 Aggregate Accounts, Budget Constraints, and Model Consistency © Pierre-Richard Agénor The World Bank

2 l Production, Income, and Expenditure l A Consistency Accounting Matrix l National Income Identities and Budget Constraints l A Three-Good Model with Banks l An Intertemporal Framework

3 Production, Income, and Expenditure

4 l Production: Goods, services carried out by domestic agents; firms, self-employed workers, financial institutions, and the government. l Income: Wages and salaries, firms' operating surpluses, property income, and imputed compensation. l Expenditure: Outlays on durable and nondurable final consumption goods and investment.

5 Linked by three macroeconomic relationships: l Production and income: total value of production must equal the value of income (excluding transfers) generated domestically. l Income, expenditure, and savings: for any economic agent, income earned plus transfers must be equal to expenditure plus savings. l Savings and asset accumulation: savings plus borrowing must equal asset acquisition for any economic agent.

6 A Consistency Accounting Matrix l Current account transactions l Capital account transactions

7 Five sets of accounts incorporated in the consistency framework: l The national accounts. l The accounts of the nonfinancial private sector. l The government accounts. l The balance sheets of the financial sector. l The balance of payments.

8 Current Account Transactions

9 l See Table 8.1 è Rows: sources of finance for each sector. è Columns: uses of finance for each sector. l Ex Post: each sector’s deficit must be financed,  sum of rows = sum of columns. l Ex Ante: sectoral balances are constraints.

10 National Accounts l Row 1 & Column A, National Accounts: consolidated current-period activities of all production units; è incorporated enterprises (financial and nonfinancial); è informal sector firms; è producers of government services; è production by households for own consumption.

11 National Accounts l Row 1, allocation of goods, services produced domestically, Y, or imported, J, between: è government consumption, C g ; è private consumption, C p ; è exports, X; è government and private sector investment, I g and I p, with I = I g + I p.

12 National Accounts l Column A, GDP at current market prices, Y, decomposed into types of income generated through sale (plus own consumption) of domestic output; è net indirect taxes: indirect taxes, T I, less subsidies, SUB; è operating surplus of government enterprises, OS g ; è wages and salaries, W, and profits,  ; è incomes of the self-employed and own-account producers, Y s.

13 National Accounts l GDP at factor costs, Y fc : sum of employee compensation (wages, salaries and incomes of own- account producers) and operating surpluses of all enterprises. l Value added at factor cost, V fc : by convention, accrues to households or government. l Value added at Market Price: V fc + net indirect taxes. l Total amount of goods and services available for final use: sum of value added at market prices and imports.

14 Current Government Transactions Row 2 & Column B: l Government savings, S g, given by, S g = T g - G, Tg = T I - SUB + OS g + T D + NT gf, G = C g + NT pg + INT pg + INT fg.

15 l Row 2: Sources of government revenues, T g, as, è net indirect taxes, T I - SUB; è operating surpluses of government-owned enterprises, OS g ; è direct taxes on the nonfinancial private sector, T D ; è net transfers to government from external sector, NT gf.

16 Current Government Transactions Row 2 & Column B: l Column B: government expenditures, G, as è government consumption of goods and services, C g ; è net transfers to the nonfinancial private sector, NT pg ; è interest paid to the private sector on domestic public debt, INT pg ; è interest payments on public foreign debt, INT fg.

17 Row 3 & Column C: l Financial system: pure intermediary. There is no independent revenues, expenditure accounts. Financial Sector

18 Row 4 & Column D: l Private saving, S p : total private sector income, Y p, minus total current expenditures of the private sector, CC p : S p = Y p - CC p with Y p = W +  +  s + NT p + INT pg + NT pf + NFP pf, CC p = C p + T D + INT fp + S p. Nonfinancial Private Sector

19 Row 4 & Column D: l Row 4: private sector revenues, Y p, as, è factor income, including wages and salaries, W, profits, , and incomes of the self-employed,  s ; è net transfers received from the government, NT p ; è interest payments received on government debt holdings, INT pg ; è net transfers, NT pf, plus net factor payments from abroad, NFP pf. Nonfinancial Private Sector

20 Nonfinancial private sector Row 4 & Column D: l Column D: private sector expenditures, CC p, as, è private consumption, C p ; è payment of direct taxes, T D ; è interest payments on private external debt, INT fp.

21 External Sector Row 5 & Column E: l Current Account Balance, CA: - (savings by foreign residents); CA = X + (NT gf + NT pf ) + NFP pf - J - INT fg - INT fp

22 External Sector Row 5 & Column E: l Row 5: sources of income to foreign residents; è value of imports of goods and services, J; è public and private sector interest payments on their respective external debts, INT fg and INT fp. l Column E: sources of income from foreign residents; è exports of goods and services, X; è net current transfers to the government and private sectors, NT gf and NT pf ; è net factor payments to the private sector, NFP pf.

23 Capital Account Transactions

24 Financing of asset acquisition by government, private nonfinancial sector, and external sector. Government Row 6 & Column F: l Row 6: sources of financing: è government savings, S g ; è net borrowing from the financial system,  L gb ; è net borrowing from the private sector,  B p ; è net foreign borrowing,  FB g. l Column F: gross fixed capital investment by the government, I g.

25 Financial Sector Row 7 & Column G: l Row 7: financial system liabilities,  M; è new domestic currency issues, è demand deposits, è time deposits. l Column G: financial system assets; è loans to the government,  L gb, è loans to the private sector,  L pb, è net foreign assets,  R *.

26 Nonfinancial Private Sector Row 8 & Column H: l Row 8: private sector asset acquisition financing; è private sector savings, S p, è net borrowing from the financial system,  L pb, è net borrowing from abroad,  FB p. l Column H: private sector asset acquisitions; è private investment, I p ; physical assets, inventories and working capital, plus intangible nonfinancial assets; è net lending to the government,  B p ; è increases in holdings of monetary assets,  M, that is, liabilities issued by the financial sector.

27 External Sector Row 9 & Column I: l Row 9: savings by foreign residents, CA (deficit), and acquisition of net foreign exchange reserves by the financial system,  R *. l Column I: net foreign borrowing of the government,  FB g, and the private sector,  FB p. l Rise (fall) in either the current account deficit or foreign exchange reserves must be accompanied by a rise (fall) in foreign savings (borrowing from abroad).

28 Savings-Investment Balance Row 10 & Column J: Total domestic savings finances total investment; l Row 10: total domestic savings; government saving, S g, private saving, S p, plus foreign saving (CA). l Column J: Total investment; government investment, I g, plus private investment, I p.

29 National Income Identities and Budget Constraints l Gross domestic product and absorption l The government budget constraint l The private sector budget constraint l The balance sheet of the financial system l The savings-investment balance

30 Gross Domestic Product and Absorption l Two approaches for estimating GDP: expenditure approach and value added approach

31 l Set row 1 = column A, C g + C p + X + I g + I p = W +  +  s + OS g + (T I - SUB) + J (1) è GDP at market prices, Y: Y = C + I + X - J, (2) with, C = C p + C g, and I = I p and I g. è GDP at factor cost, Y fc : Y fc = W +  +  s + OS g (3)

32 Y = Y fc + (TI - SUB), l Y: GDP at market price equals Y fc : GDP at factor prices, plus indirect taxes net of subsidies. J - X = A - Y = I - (Y - C) = I - S, l J - X: net imports, equals A-Y: domestic absorption over output, equals I-S: investment over savings. l Reduction in trade deficit requires decrease (increase) in absorption (domestic savings).

33 The Government Budget Constraint l Government Revenues/Expenditures, è Row 2 = Column B, T I - SUB + OS g + T D + NT gf = C g + NT pg + (INT pg + INT fg ) + S g (6) or, T g - G = S g (7). è Current public revenues equal current expenditures plus current savings.

34 l Government savings and borrowing, è Row 6 = Column F, S g +  L gb +  B p +  FB g = I g (8) è Government savings plus net domestic and foreign borrowing equals physical assets acquired. l Substitute (T g – G) for S g in (8): G + I g - T g =  L gb +  B p +  FB g (9) with, G + I g - T g : overall fiscal deficit,  L gb +  B p +  FB g : sources of deficit financing.

35 The Private Sector Budget Constraint l Private Sector Income/Expenditures è Row 4 = Column D, W +  +  s + NT pg + INT pg + NT pf + NFP pf = C p + T D + INT fp + S p or Y p = CC p + S p (10) with CC p = C p + T D + INT fp Y p = W +  +  s + NT pg + INT pg + NT pf + NFP pf

36 Private Sector Saving/Borrowing è Row 8 = Column H: S p +  L pb +  FB p = I p +  B p +  M (11) Substituting (Y p – CC p ) for S p in (11)  l Private sector budget constraint: Y p - CC p +  L pb +  FB p = I p +  B p +  M è Private sector income plus borrowing net of expenditures equals asset acquisitions; money, physical investment, and lending to the government.

37 The External Sector Budget Constraint External sector income/expenditures l Row 5 = Column E, J + INT fg + INT fp = X + NT gf + NT pf + NFP pf + CA.

38 External sector saving/borrowing l Row 9 = Column I, CAD =  FB g +  FB p -  R * l CA deficit financing via, è increasing net foreign borrowing; è drawing down reserves.

39 External sector budget constraint: J - X =  F -  R *, with, J: J + INT fg + INT fp ; X: X + NT gf + NT pf + NFP pf ; è gross payments by domestic economy, J; sum of imports and all interest payments on external debt; è gross receipts to the domestic economy, X; exports plus net transfers; è and net factor payments from abroad.

40 The Balance Sheet of the Financial System l Pure Intermediary: not budget constraint per se, but rather a balance sheet accounting identity. l Row 7 = Column G,  L +  R * =  M, with  L =  L gb +  L pb,  R* =  M -  L

41 l Increases (decreases) in domestic credit (  L), with money demand unchanged, result in decreases (increases) in foreign reserves.

42 The Savings-Investment Balance l Add budget constraints of the government and private sectors to yield: S +  L +  F = I +  M. l Given that  F = J - X +  R *, l Then S +  L + (J - X) +  R * = I +  M

43 Savings-investment balance : l With  L +  R * =  M, we have, I = S + (J - X) l Domestic investment, I, financed by domestic savings, S, and foreign saving, J - X, (e.g. the current account deficit, CA).

44 A Three-Good Model with Banks

45 Open-economy macroeconomic model l Accounting relationships integrated with behavioral equations to analyze transmission process of macroeconomic policy and exogenous shocks. l 5 agents: households, producers, commercial banks, the government, and the central bank. l All households, firms, banks are identical in endowments and behavior. l Exchange rate fixed. l Economy produces two goods: home good and exportable good. l Fixed capital stock and perfect labor mobility.

46 Households l Supply labor inelasticaly. l Consume both home and importable goods. l Four types of financial assets: domestic money, bank deposits, domestic bonds, and foreign bonds. l Financial assets are imperfect substitutes. l Consumption decisions: two stage process.

47 l Stage 1: Consumption determined by, C = (1 - s)(Y - T), 0 < s < 1, (20) Y: net factor income, T: lump-sum taxes, s: marginal propensity to save.

48 l Stage 2: consumption of imported goods (C I ) and home goods (C N ) by, C I = (1 -  )C, (21)  : share of home goods in private expenditures. P N C N =  EC (22) l Using (20), (22) rewritten as, C N =  zC =  z(1 - s)(Y - T) (23) z  E/P N : real exchange rate.

49 l Asset Demand Equations: Money Demand: M d = M d (i b,Y) (24) Demand for Bank Deposits: D p = D p (i d,i b,Y) (25) l Demand for Foreign Bonds :  B* =  (i* +  a - i b ),  > 0, (26) i * : interest rate spread of foreign minus domestic bonds,  a : expected nominal exchange rate devaluation,  : degree of substitutability, or capital mobility in fixed income markets.

50 l Uncovered Interest Parity Condition: i b = i * +  a holds, when   , e.g. perfect capital mobility. l Using (24), (25), and (26), demand function for domestic bonds, B given by, B = W - M d - D p - B *.

51 Firms and the Labor Market Working capital needs financed via commercial banks. Total Production Costs: l Labor costs (only) plus interest payments on bank loans.

52 l Maximization problem written as: max Y h -  h N h - i L L h, (27) h: as exportable (h = X) and non-tradable goods (h = N) Y h : output of good h, N h : quantity of labor employed in sector h,  h : product wage in sector h, L h : bank loans obtained by firm operating in sector h, i L : nominal bank lending rate. YhYh

53 l Output-employment relationship, N h = Y h ,  > 1, (28) decreasing returns to labor. l Firm’s financial constraint: L h   h N h, (29) bank loans must cover labor cost.

54 è Output supply inversely related to the effective product wage  h (1+i L ). l Labor demand [(30) into (28)]: N h d = N h d [  h (1+i L )], N h d < 0 (31) l Maximizing (27) subject to (28) and (29) yields,  h (1+i L ) 1/(  -1) {} Y h s = 1 (30)

55 l Firm’s demand for credit: L h d = w h N h d = L h d [w h,i L ]. (32) è Wage increase both raises labor costs and lowers demand for labor. - ?

56 Wage determination l Wages are perfectly flexible. l Zero unemployment: perfect labor mobility across sectors. l Exportable/nontradable sector wages related by, l  N = z  X (33) l Equilibrium real wage negatively related to the real exchange rate and the bank lending rate,  X = W X (z,i L ) (34) - -

57 l Output of exportables (home goods) is positively (negatively) related to the real exchange rate. l Demand for credit, L d, in terms of exportables, Sectoral supply equations: l Substituting (33) and (34) into (30) yields, Y X s = Y X s (z,i L ), Y N s = Y N s (z,i L ) (35) L d = L X d + z -1 L N d = L d (z,i L ) - -

58 Commercial Bank l Bank assets: credit extended to firms, L s, and reserves held at the central bank, RR. l Bank liabilities: deposits held by households, D p. D p = L s + RR RR =  D p,  : coefficient of reserve requirements.

59 l Supply of credit: L s = (1 -  )D p l Under zero-profit conditions, lending/deposit rates, i L = i d / (1 -  ) l Credit supply given by, L s = (1 -  )D p [(1-  )i L,i b,Y].

60 Government and the Central Bank l Government: è levies lump-sum taxes on households; è consumes home goods, in quantity G N. l Central Bank: è ensures the costless conversion of domestic currency holdings into foreign currency at the prevailing fixed exchange rate, E; è lends only to the government; è does not engage in sterilized intervention.

61 l Real money supply, M s, given by M s = L g +R *, R * : foreign currency reserves. L g : credit to the government (exogenously determined).  R * : determined by the balance of payments; capital and current accounts,  R * = Y X s - C I -  B *, substituting,  R * = Y X s - (1 -  )C +  (i b - i * -  a ).

62 Credit Market Equilibrium condition: L s = L d Equilibrium bank lending rate: Money Market: Equilibrium condition: M s = M d (i b,Y) Solving for i b yields, i L = i L (z,i b ). ?+ Equilibrium Conditions. ê  i b   i L ê  z, ambiguous, why? êreal depreciation causes increase in output and demand for bank deposits, lowering lending rate. êand raises demand for loans, causing an increase in lending rate to maintain credit market equilibrium. i b = i b (z,i L ;M s ) - --

63 l Can be solved for the equilibrium real exchange rate as, z =  (i L ;T,G N ). The market for home goods l Equilibrium condition of the market for home goods, C N + G N - Y N s = l Thus, an increase in bank lending, or government spending on home goods requires an appreciation of the real exchange rates, z falls.

64 Extensions : Model can be applied to variety of macroeconomic issues: l Effects of changes in government spending on the real exchange rate, domestic interest rates, and capital flows. l Study terms of trade shocks: Unlike a dependent- economy framework, the production structure adopted here allows a distinction between the terms of trade and the real exchange rate (Figure 8.4). l Credit market imperfections, introduced through mark-up pricing by banks (see Agénor and Aizenman, 1999).

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67 l Production of importables and imported intermediate inputs can also be integrated in the analysis. Two Limitations l Behavioral functions for consumption and asset demand functions are postulated rather than derived from microeconomic considerations. l The static nature of the model implies that the stock budget constraints that the various agents faced are not explicitly accounted for.

68 An Intertemporal Framework

69 l Intertemporal model: addresses limitations of three- good model presented earlier; è explicitly derives behavioral rules from an optimization framework; è accounts for agents’ flow and stock budget constraints in a dynamic setting, ensuring across periods. l Useful in understanding current account deficits.

70 Basic Structure: l Two-period model. l No financial assets. l Only one good. l Assumes perfect foresight, optimal behavior of individual agents, and perfect capital mobility. l Output is supply determined with full employment assumed.

71 l GNP, Y, given as, Y = Q + Z, Q: GDP; Z: net factor payments from abroad. Y + R = C + S p + T thus GNP, Y, plus net unilateral transfers from abroad, R, can be used for consumption, savings and taxes.

72 l Current Account Surplus, CA, defined in three equivalent ways: è exports minus imports of goods and services plus unilateral transfers and net factor payments from abroad (income transfers, for short), CA = X - J + Z + R, è national income minus domestic absorption, CA = Y - (C + I + G) + R,

73 è national saving minus domestic investment, CA = S - I, with S = S p + S g.

74 Model: l Two periods; present (t = 1) and future (t = 2). l Single household with utility function U(C 1,C 2 ), l Supply Side of Model: Y 1 0 and Y 2 0 initial endowments (income) for each agent in periods 1 and 2.

75 l Intertemporal investment decisions: output in the second period Y 2, is linked to the endowment Y 2 0 through the following relationship: Y 2 =Y I 1 , 0 <  < 1 with I 1  = Y C 1

76 Return on marginal project, 1+r: l Ratio of return to cost; -  C 2 /  C 1 = 1 + r. l Production possibility frontier (PPF): Figure 8.5, slope given by -(1+r). l In autarchy, household's PPF = consumption possibility frontier. l Equilibrium at tangency between PPF and consumer indifference curves.

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78 l Household (country) maximization problem: max U(C 1,C 2 ), subject to production constraint, F(C 1 -Y 1 0,C 2 - Y 2 0 ) = 0 C1, C2C1, C2 l Solution found at F 1 /F 2 = U C1 /U C2, è F 1 /F 2 = 1 + r, è U C1 /U C2 = 1 + .   = r.

79 l In autarchy, savings must necessarily equal investment. l  serves as the ex post discount rate and the autarchy interest rate, i. ~

80 Financial Openness: l If world interest rate, i *, is lower than the autarchy interest rate i, it is optimal to run a current account deficit (capital account surplus). l Maximize the present value of profits, PV, given by, PV = I 1  /(1 + i) * - I 1 l With financial openness, i domestic converges to i * foreign. l Firms will increase investment, I 1, until the rate of return on the marginal project, r, equals the world interest rate.

81 l Figure 8.5 shows the effect of financial openness on investment levels demonstrating with isovalue lines and the tranformation function. l Isovalue line: maximum level of wealth, W 1, H + Y 2 /(1 +i * ) = Y Y 2 0 /(1 + i * ) + PV m  W1  W1 l Household’s intertemporal budget constraint C 1 + C 2 /(1 +i * ) = Y Y 2 0 /(1 + i * ) + PV m  W1 W1

82 l First period budget constraint, l C 1 = Y L 1 - I 1 l Second-period budget constraint, C 2 = Y I 1  - (1 + i * )L 1 L 1 : first period borrowing -(1 + i * )L 1 : gross repayment in second period.

83 Current Account l Period 1, CA, (surplus) CA 1 = Y C 1 - I 1 e.g. domestic savings minus investment and also equal to the trade balance, TB 1. l Period 2, CA, CA 2 = Y 2 - C 2 - i * L 1

84 Intertemporal solvency: l Discounted sum of first period and second period trade accounts equal zero: TB 1 + TB 2 /(1 + i * ) = 0. l Current account CA 1 + (CA 2 - L 1 )/(1 + i * ) = 0. l Homothetic utility function: given i, ratio of consumption in two periods is independent of wealth level. l See Figure 8.5.