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Author(s):
International Monetary Fund
Published Date:
September 1985
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    ANSWERS TO EXERCISES

    Chapter 3: WORKSHOP 1—Monetary and Financial Survey

    page 49, Exercise A

    Kenya: Monetary Survey, 1977(In millions of Kenya shillings)
    Net foreign assets3,633
    Foreign assets4,616
    Use of Fund credit460
    Other foreign liabilities523
    Domestic credit9,255
    Government (net)1,800
    Other public sector259
    Private sector17,196
    Other items (net)475
    Money plus quasi-money12,413
    Money8,427
    Currency2,782
    Demand deposits6,269
    Uncleared effects−24
    Quasi-money3,986
    Source: Tables 7 and 8.

    Includes 683.5 million Kenya shillings corresponding to CSFC and AFC.

    page 49, Exercise B

    Kenya: Changes in Monetary Survey Items
    Item1977
    Millions of

    Kenya shillings
    Per cent
    1. Net foreign assets2,174149.0
    2. Domestic credit1,78023.8
    3. Credit to Government (net)−98−5.2
    4. Credit to other general government4420.5
    5. Credit to private sector1,83434.2
    6. Assets = liabilities3,95444.3
    7. Money2,75348.5
    8. Quasi-money1,20643.4
    9. Other items−5−1.0
    Source: Tables 9 and 10.

    page 49, Exercise C

    2.Kenya: Net Foreign Assets of the Monetary Authorities(In millions of Kenya shillings)
    Item19761977
    Assets2,3014,282
    Liabilities−844−570
    Net foreign assets1,4573,712
    Percentage change154.8
    Reserve money2,0013,233
    Percentage change61.6
    Source: Table 7.
    3.Accounts for the Kenyan Government in the Monetary Authorities and Commercial Banks In 1977 Net Credit to Government(In millions of Kenya shillings)
    Monetary AuthoritiesCommercial Banks
    Item1976197719761977
    Claims8511,2431,1921,963
    Deposits−73−1,278−72−128
    Net credit778−351,1201,835
    Percentage change−104.563.8
    Source: Tables 7 and 8.
    4.Kenya: Monetary Survey(In millions of Kenya shillings)
    Item19761977
    Money plus quasi-money8,45412,413
    Percentage change46.8
    Percentage change in real GDP (1972 prices)7.5
    Percentage change in aggregate demand (current prices)21.5
    Sources: Table 9 and Kenya, Economic Survey.

    Chapter 4: WORKSHOP 2—Government Finance Statistics

    page 84, Exercise A

    Kenya: Principal Aggregates, Fiscal Year 1977(In millions of Kenya shillings; year ending June 30)
    Revenue6,149.2
    Grants234.1
    Expenditure7,240.0
    Lending minus repayments470.3
    Overall deficit/surplus−1,327.0
    Financing1,327.0
    Abroad463.6
    Domestic863.4

    page 85, Exercise C

    Kenya: Domestic Financing by Type of Debt Instrument, Fiscal Year 1977(In millions of Kenya shillings; year ending June 30)
    Domestic financing863.4
    Long-term bonds385.5
    Short-term bonds and bills552.0
    Long-term loans n.e.c.-0.5
    Short-term loans and advances n.e.c.42.2
    Changes in cash, deposits, etc.-115.8
    Note: n.e.c. = not elsewhere classified.

    Chapter 5: WORKSHOP 3—Balance of Payments Statistics

    page 121, Exercise 1

    Kenya: Standard Presentation of the Balance of Payments, 1976(In millions of SDRs)
    Item1976
    A.Goods, Services, and Unrequited Transfers−72.3
    Goods and services−100.2
    Total credit1,007.0
    Total debit−1,107.2
    1. Merchandise: exports f.o.b.644.3
    2. Merchandise: imports f.o.b.−734.7
    3. Nonmonetary gold
    4. Freight and insurance on merchandise credit37.9
    5. Freight and insurance on merchandise debit−100.3
    6. Other transportation: credit156.9
    7. Other transportation: debit−57.8
    8. Travel: credit88.8
    9. Travel: debit−26.9
    10. Undistributed income from direct investment abroad0.6
    11. Undistributed income from direct investment in Kenya−24.0
    12. Other direct investment income: credit11.8
    13. Other direct investment income: debit−56.9
    14. Other investment income: credit19.7
    15. Other investment income: debit−49.7
    16. Other government: credit17.6
    17. Other government: debit−24.0
    18. Other private: credit29.4
    19. Other private: debit−32.9
    Unrequited transfers27.9
    Total credit66.2
    Total debit−38.3
    20. Private: credit27.1
    21. Private: debit−33.3
    22. Government: credit39.1
    23. Government: debit−5.0
    B.Capital (excluding reserves and related items)150.0
    Nonmonetary sectors159.7
    24. Direct investment in Kenya38.7
    25. Direct investment abroad−2.7
    26. Other private long-term liabilities24.9
    27. Other private long-term assets−2.5
    28. Other private short-term liabilities32.1
    29. Other private short-term assets−3.1
    30. General government long-term liabilities72.7
    31. General government long-term assets0.8
    32. General government short-term liabilities
    33. General government short-term assets−1.2
    Monetary sectors−9.7
    34. Deposit money banks: long-term
    35. Deposit money banks: short-term−10.5
    36. Central institutions: long-term
    37. Central institutions: short-term0.8
    C.Allocation of SDRs (item 38)
    D.Reserves and Related Items−74.0
    Liabilities16.5
    39. Use of Fund credit16.5
    40. Other liabilities
    Assets−90.5
    41. Monetary gold
    42. SDRs1.0
    43. Reserve position in the Fund
    44. Foreign exchange and other claims−91.5
    E.Net Errors and Omissions (item 45)−3.7
    Source: International Monetary Fund, Balance of Payments Yearbook, Vol. 28 (Washington, December 1977), p. 336.
    Kenya: Analytic Presentation off the Balance off Payments, 1976(In millions of SDRs)
    Code1976
    A. Goods, Services, and Unrequited Transfers1 . . C Z−73.9
    Merchandise: exports f.o.b.1 A . A Z644.3
    To Tanzania and Uganda1 A1 A Y137.9
    To other countries
    Coffee1 A 1 A Q193.2
    Tea1 A1 A P65.8
    Other (Including adjustments)1 A . A Y247.4
    Merchandise: imports f.o.b.1 A . B Z−734.7
    Trade balance1 A . C Z−90.4
    Services: credit1 S . A Z362.7
    Transportation and merchandise insurance1 C . A Y194.8
    Travel1 D . A Z88.8
    Government services1 I . A Z17.6
    Other services1 M . A Y61.5
    Services: debit1 S . B Z−372.5
    Transportation and merchandise insurance1 C . B Y−158.1
    Investment income1 N . B Z−130.6
    Government services1 I . B Z−24.0
    Other services1 M . B Y−59.8
    Total (goods and services)1 . 1 C Z−100.2
    Private unrequited transfers1 K . C Z−6.2
    Total (excluding government
    unrequited transfers)1 . 2 C Z−106.4
    Government unrequited transfers: credit1 H 8 A W37.5
    Grants and technical assistance from
    U.K. Government1 H 8 A Y13.1
    Others1 H 8 A X24.4
    Government unrequited transfers: debit1 H . B Z−5.0
    B. Long-Term Capital, excluding
    Groups D and F1 W 1 X Z131.9
    Direct investment3 Z . X Z36.0
    Other private8 Z 1 X Z22.4
    General government7 Z 1 X Z73.5
    Long-term loans received7 P . X Q62.1
    Other7 Z 1 X Y11.4
    Total, A plus B1 . B X Z58.0
    C. Short-Term Capital, excluding
    Groups D and F1 W 2 X Z14.4
    Deposit money banks5 Z 2 X Z−10.5
    Liabilities5 Y 2 X Z−3.6
    Assets5 L 2 X Z−6.9
    Other private8 Z 2 X Z29.0
    General government7 Z 2 X Z−1.2
    Central monetary institutions4 Z 2 X Z0.8
    Net errors and omissions9 A . X Z−3.7
    Total, A through C1 . C X Z72.4
    D. Exceptional Financing1 W Z X Z1.6
    Grants to finance general imports1 H 8 A Q0.9
    Grants from Subsidy Account1 H 8 A V0.7
    Total, A through D1 . D X Z74.0
    E. Counterpart Items9 B . X Z
    Monetization/demonetization of gold9 B 3 X Z
    Allocation of SDRs9 B 1 X Z
    Total, A through E1 . E X Z74.0
    F. Reserves and Related Items2 Z . X Z−74.0
    Use of Fund credit2 M . X Z16.5
    Other liabilities2 Q . X Z
    Monetary gold2 A . X Z
    SDRs2 B . X Z1.0
    Reserve position in the Fund2 C . X Z
    Foreign exchange and other claims2 F . X Z−91.5
    Source: International Monetary Fund, Balance of Payments Yearbook, Vol. 28 (Washington, 1977), p. 335.

    page 121, Exercise 2

    As indicated in the text, there are alternative definitions of the current balance and the overall balance.

    1976
    BalanceLines in Analytic Presentation(In millions of SDRs)
    TradeTrade balance−90.4
    CurrentA. Goods, Services, and Unrequited Transfers−73.9
    Total (goods and services)−100.2
    Total (excluding government unrequited transfers)−106.4
    BasicTotal, A plus B58.0
    OverallTotal, A through C72.4
    Total, A through D74.0
    Total, A through E74.0

    Chapter 6: WORKSHOP 4—Flow of Funds

    page 142, Exercises 1 and 2

    A Hypothetical Economic System
    ItemSector PShSector PScSector GSSector BSector FSTotal
    SourceUseSourceUseSourceUseSourceUseSourceUseSourceUse
    I. Incomes and Expenditures
    1. Receipts
    Income12,1001,8004,70018,600
    Transfers and taxes3,5003,500
    2. Current expenditure
    Consumption9,7001,90011,600
    Imports4,0004,000
    Transfers and taxes2,0001,5003,500
    Wages and salaries1,0001,000
    Current account balance4003006007002,000
    3. Saving (current account
    balance)4003006007002,000
    4. Investment expenditure1004501,2002502,000
    5. Overall position300150600450750750
    II. Changes in Financial Balance
    Sheet
    1. Liabilities or claims
    to or on B1002805304105104501,1401,140
    to or on FS450450
    to or on PSH7050280100400100
    to or on PSC7040410530450600
    to or on GS5040510600
    2. Net financing300150600450750750
    Kenya: Summary of Income and Flow-of-Funds Accounts, 1976(In millions of Kenya shillings)
    ItemSector PSSector GSSector BSector FSTotal
    SourceUseSourceUseSourceUseSourceUseSourceUse
    I. Incomes and Expenditures
    1. Receipts
    Exports9,5609,43618,996
    Transfers2,6092183703,197
    Taxes4,9344,934
    Other income9,3587021,44411,504
    2. Current expenditure
    Consumption1,2411,241
    Imports9,4369,56018,996
    Transfers3472,2106403,197
    Taxes4,9344,934
    Other2,1461,7923524,290
    Current account balance4,6646116985,973
    3. Saving (current account balance)4,6646116985,973
    4. Investment expenditure4,7491,2245,973
    5. Overall position85613698698698
    II. Changes in Financial Balance Sheet
    1. Liabilities or claims
    to or on B9301,93925412390527
    to or on FS1,02455227905
    to or on PS6006701,9399301,024
    to or on GS670600123254552
    2. Net financing85613698

    Chapter 7: WORKSHOP 5—The Polak Model: An Application

    page 163, Exercise 1

    Hence,

    Note that

    αβ= 0.53.0.88 = 0.47 < 1, hence

    M = 0.53A + 0.47Mt−1

    is a stable dynamic equation.

    (b) Mt = αAt + α2βAt−1 + α3β2At-2 + …

    At = Xt + CMt + ΔNDCt

    (i) First period multiplier

    (ii) Truncated multiplier at the end of second period

    (iii) At the end of third period

    (iv) Long-run multiplier (total effect) is the sum of the declining geometric progression:

    Thus, a unit increase in one of the exogenous variables will cause an increase in imports of 0.53 unit in the first period, a total increase of 0.78 unit in the first two periods, 0.90 unit in the first three periods, etc. Over infinitely many periods the total effect will be 1 unit. Convergence is rapid, as 90 per cent of the total effect is manifested in the first three periods. Multiplier is the same for any component of At.

    (ii) Long run

    Long run

    Elasticity compares percentage changes. As X is larger than CM, a given percentage change in X has a relatively larger effect on imports than a given percentage change in CM.

    page 164, Exercise 2

    (b)PredictedActualDifferences
    M12,72811,688+ 1,040
    ΔNFA1,1342,174−1,040

    M forecast was too high, and thus NFA forecast was too low.

    Given

    MO1977 = 12,413

    i.e., people held larger money balances than expected.

    Given

    even with actual income (Yt), there was over-prediction of M:

    page 164, Exercise 3

    (a) Insertion of equation

    into the identity

    yields

    ΔMOt = 0, hence ΔYt = 0 and hence, ΔMt = 0

    Chapter 8: WORKSHOP 6—Projection of Monetary Aggregates

    page 181, Exercise A

    Kenya: Monetary Survey, December 1977(In millions of Kenya shillings)
    ItemProjection
    December 1977
    Net foreign assets3,650
    Central Bank1
    3,665
    Government2
    Commercial banks−15
    Domestic credit11,012
    Government (net)2,496
    Claims
    Deposits
    Nongovernment8,516
    Official entities
    Private sector3
    Other items (net)479
    Money and quasi-money14,183
    Money9,588
    Currency outside banks
    Demanddeposits
    Quasi-money4,595
    SDR allocations

    Foreign liabilities include use of Fund credit.

    Foreign exchange holdings.

    Includes Cereals and Sugar Finance Corporation and Agricultural Finance Corporation.

    page 182, Exercise B

    Chapter 9: WORKSHOP 7—Revenue Forecasting

    page 207, Exercise 1

    Kenya: Tax Revenues Adjusted for the Effects of Discretionary Tax Measures, Fiscal Years 1968–771(In millions of Kenya shillings; year ending June 30)
    Tax Revenue Source1968196919701971197219731974197519761977
    1.Taxes on income, profits, and capital gains2493.1506.9626.9811.1966.81,084.21,240.51,595.11,797.62,149.3
    5.1Sales tax3853.81,027.01,215.91,308.4
    5.2Excises269.7290.7320.4372.8392.2404.8515.9546.7521.4574.1
    6.1Import duties618.0666.0741.1861.6933.0741.31,087.81,154.51,068.71,057.2

    Adjusted to the fiscal-year 1977 tax structure, using the proportional data adjustment method.

    Excluding the graduated personal tax. which was abolished December 31, 1973.

    The sales tax, which was introduced in April-May 1973, generated KSh 54.1 million of revenue in fiscal year 1973. No attempt was made here to adjust this amount to a full-year, fiscal-year 1977 tax structure.

    page 207, Exercise 2

    (a) In equation (2), the elasticity of taxes on income, profits, and capital gains with respect to GDP at factor cost at current prices is equal to:

    where

    ATI = adjusted revenue from taxes on income, profits, and capital gains

    Y = GDP at factor cost at current prices.

    Thus, the null hypothesis is:

    which will be tested against the alternative hypothesis:

    as income taxes on individuals are progressive (see Chapter 9, Appendix II).

    The following variable has a t distribution with n – k degrees of freedom:

    where

    b^ is the least squares estimator of b

    sb^ is the estimated standard error of b^

    n is the number of observations, here equal to 10

    k is the number of parameters, here equal to 3.

    Using equation (2a), one can calculate the value of t under the null hypothesis:

    Choosing a 5 per cent significance level for a one-tail test, one can find from a table of the t distribution that, with 7 degrees of freedom, the critical region is:

    where t* is the critical value of t.

    Since t0 < t*, the “unit elasticity” hypothesis cannot be rejected at the 5 per cent level of significance.

    (b) In equation (6a) the elasticities of import duties with respect to import volume and import price are, respectively:

    where

    ATM = adjusted revenue from import duties

    LM = lagged, calendar-year imports at constant prices

    LPM = lagged, calendar-year import price index.

    Note that Ln LM = Ln LM + Ln LPM

    where

    LM = lagged, calendar-year imports at current prices.

    page 207, Exercise 3

    Kenya: Tax Revenue Forecasts for Fiscal Year 1978(In millions of Kenya shillings; year ending June 30)
    TaxRegression EquationBase ValuesAT781BD782T783
    1.Taxes on income,(1a)
    LY78 = 32,404
    profits, and capital gainsDA78 = 12,840.8−90.02,750.8
    4.3Estate duty10.4410.44
    5.1Sales tax(4a)LCP78 = 21,3381.574.3205.01,779.3
    5.2Excises(8a)LCP78 = 16,670596.2−32.0564.2
    5.4Taxes on specific services(11a)LCP78 = 21,33860.710.070.7
    5.5Taxes on use of,

    or permission to

    use, goods or to

    perform activities
    (9a)LY78 = 16,536104.7104.7
    6.1Import duties(6a)
    LM78 = 10,630
    LM78 = 3,7831,292.0100.01,392.0
    6.2Export duties300.05300.05
    7.2Stamp duties(10a)LY78 = 16,53658.458.4
    IV.Tax revenue6,537.5493.07,030.5

    AT78 = Tax revenue forecast for fiscal year 1978 based on fiscal-year 1977 tax structure.

    BD78 = Budget estimate of the revenue effect of discretionary tax measures in fiscal year 1978.

    T78=AT78 + BD78.

    Average of the three preceding fiscal years.

    Export duties were introduced in the budget for fiscal year 1978.

    page 208, Exercise 4

    (a) The expected built-in elasticity of tax revenue for fiscal year 1978 with respect to lagged, calendar-year GDP at factor cost at current prices is equal to:

    where

    AT78 = tax revenue forecast for fiscal year 1978 based on fiscal-year 1977 tax structure

    LY78 = lagged, calendar-year 1977 GDP at factor cost at current prices.

    (b) The expected overall elasticity (buoyancy) of tax revenue for fiscal year 1978 with respect to lagged, calendar-year GDP at factor cost at current prices is equal to:

    where

    T78 = tax revenue forecast for fiscal year 1978 based on fiscal-year 1978 tax structure

    LY78 = lagged, calendar-year 1977 GDP at factor cost at current prices.

    page 209, Exercise 6

    The forecast of nontax revenue (in millions of Kenya shillings) for fiscal year 1978 is equal to:

    where

    NT78 = nontax revenue forecast for fiscal year 1978

    LY78 = lagged, calendar-year 1977 GDP at factor cost at current prices.

    Chapter 10: WORKSHOP 8—Balance of Payments Forecasting

    page 255, Exercise 3

    VariablePercentage ChangeIndex or Value
    19761977
    Import prices7.7261281
    GDP deflator19.5164196
    GDP (real)7.3415,405116,5361

    In millions of Kenya shillings.

    (a) From equation (9):

    Imports at constant prices are forecast to rise to 3,892—a rise of 24.8 per cent over 1976. The value of imports rises by the product of the price and volume increase, i.e., 34.4 per cent.

    (b) Assume a 5 per cent devaluation increases the index of import prices for 1977 to 295. Substituting the revised import price data in equation (9):

    Imports at constant prices are now forecast to rise to 3,757—an increase of 20.5 per cent over 1976. This calculation suggests that a 5 per cent devaluation would lead to a 4 per cent decline in import volume. Note, however, the important and almost certainly unrealistic assumption that domestic prices and output are not affected by the devaluation.

    (c) Let Ep represent the price elasticity and Ey the income elasticity.

    The marginal response of import volume to changes in relative prices or incomes for the forecast year can be taken from the coefficients in equation (9). Data for the base year 1976 can be found in the Appendix to Chapter 10.

    Equation (9’) uses a logarithmic specification, and the price and income elasticities can be taken directly from the estimated equation.

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