| Appendix B: Tables for the ROW Model |
| Table B.1: The Countries and Variables in the MC Model Table B.2: The Variables for a Given Country in Alphabetical Order Table B.3: The Equations for a Given Country Table B.4: Equations the Pertain to the Trade and Price Links Among Countries Table B.5: Links Between the US and ROW Models Table B.6: The Procedure Used to Create Quarterly Data from Annual Data Table B.7: Construction of the Balance of Payments Data: Data for S and TT |
| Table B.1: The Countries and Variables in the MC Model |
Table B.1
The Countries and Variables in the MC Model
Quarterly Countries Local Currency Trade Share Equations Only 1. US United States U.S. Dollars (mil.) 34. NI Nigeria 2. CA Canada Can. Dollars (mil.) 35. AL Algeria 3. JA Japan Yen (bil.) 36. IA Indonesia 4. AU Austria Schillings (bil.) 37. IN Iran 5. FR France Fr. Francs (bil.) 38. IQ Iraq 6. GE Germany D. Mark (bil.) 39. KU Kuwait 7. IT Italy Lire (bil.) 40. LI Libya 8. NE Netherlands Guilders (bil.) 41. UA United Arab Emirates 9. ST Switzerland Swiss Francs (bil.) 42. IS Israel 10. UK United Kingdom U.K. Pounds (mil.) 43. BA Bangladesh 11. FI Finland Markkaa (mil.) 44. SI Singapore 12. AS Australia Aust. Dollars (mil.) 45. AO All Other 13. SO South Africa Rand (mil.) 14. KO Korea Won (bil.) Annual Countries 15. BE Belgium Bel. Francs (bil.) 16. DE Denmark Den. Kroner (bil.) 17. NO Norway Nor. Kroner (bil.) 18. SW Sweden Swe. Kroner (bil.) 19. GR Greece Drachmas (bil.) 20. IR Ireland Irish Pounds (mil.) 21. PO Portugal Escudos (bil.) 22. SP Spain Pesetas (bil.) 23. NZ New Zealand N.Z. Dollars (mil.) 24. SA Saudi Arabia Riyals (bil.) 25. VE Venezuela Bolivares (bil.) 26. CO Colombia Col. Pesos (bil.) 27. JO Jordan Jor. Dinars (mil.) 28. SY Syria Syr. Pounds (mil.) 29. ID India Ind. Rupees (bil.) 30. MA Malaysia Ringgit (mil.) 31. PA Pakistan Pak. Rupees (bil.) 32. PH Philippines Phil. Pesos (bil.) 33. TH Thailand Baht (bil.) A Brief Listing of the Variables per Country Variables Determined by Stochastic Equations:
1. M Merchandise Imports, 90 lc
2. C Consumption, constant lc
3. I Fixed Investment, constant lc
4. Y Real GDP, constant lc
5. PY GDP Deflator, base year = 1.0
6. M1 Money Supply, lc
7. RS Three Month Interest Rate, percentage points
8. RB Long Term Interest Rate, percentage points
9. E or H Exchange Rate, lc per $ or lc per DM
10. F Three Month Forward Rate, lc per $
11. PX Export Price Index, 1990 = 1.0
12. W Nominal Wage Rate, base year = 1.0
13. J Employment, thousands
14. L1 Labor Force---men, thousands
15. L2 Labor Force---women, thousands
Variables Determined by Identities:
I-1. IM Total Imports (NIPA), constant lc
I-2. EX Total Exports (NIPA), constant lc
I-3. X Final Sales, constant lc
I-4. V1 Inventory Investment, constant lc
I-5. V Inventory Stock, constant lc
I-6. S Balance of Payments, lc
I-7. A Net Stock of Foreign Security and Reserve Holdings, lc
I-8. M90$A Merchandise Imports from the Trade Share Calculations, 90 $
I-9. EE Exchange Rate, end of period, lc per $
I-12. UR Unemployment Rate
I-13. JMIN Minimum Required Employment, thousands
I-14. JJ Employment Population Ratio
I-15. JJS Peak to Peak Interpolation of JJ
I-16. Z Labor Constraint Variable
I-17. YS Potential Y
I-18. ZZ Demand Pressure Variable
I-19. PM Import Price Index, 1990 = 1.0
I-20. E Exchange Rate, lc per $ (used for European countries except GE)
Variables Determined by the Trade Share Calculations:
a Trade Share Coefficients from Trade Share Equations
L-1. PX$ Export Price Index, 1990 = 1.0
L-2. X90$ Merchandise Exports from the Trade Share Calculations, 90 $
L-3. PMP Import Price Index from the Trade Share Calculations, 1990 =1.0
L-4. PW$ World Price Index, 1990 = 1.0
Exogenous Variables:
AF Level of the Armed Forces, thousands
EXDS Export Discrepancy, 90 lc
E90 E in 1990, 90 lc per 90 $
G Government Expenditures, constant lc
IMDS Import Discrepancy, 90 lc
JJP Peak to Peak Interpolation of JJ
LAM Peak to Peak Interpolation of Y/J
MS Non Merchandise Imports, 90 lc
M90$B Merchandise Imports from Countries other than
the 44 in the Trade Share Matrix, 90 $
PM90 PM in Base Year divided by PM in 1990
POP Population, millions
POP1 Population of men, thousands
POP2 Population of women, thousands
PSI1 Ratio of (EE + EE-1)/2 to E
PSI2 Ratio of PM to PMP
PX90 PX in Base Year divided by PX in 1990
STAT NIPA Statistical Discrepancy
T Time Trend
TT Total Net Transfers, lc
XS Non Merchandise Exports, 90 lc
Notation: lc local currency 90 lc 1990 local currency constant lc local currency in the NIPA base year |
| Table B.2: The Variables for a Given Country in Alphabetical Order |
Table B.2
The Variables for a Given Country in Alphabetical Order
Variable Eq.No. Description A I-7 Net stock of foreign security and reserve holdings, end of
quarter, in lc. [A-1 + S. Base value of zero used for the
quarter prior to the beginning of the data.]
AF exog Level of the armed forces in thousands. [OECD data.]
C 2 Personal consumption in constant lc. [OECD data or IFS96F/CPI.]
CPI none Consumer price index, 1990 = 1.0. [(IFS64 or IFS64X)/100.]
E 9 Exchange rate, average for the period, lc per $ . [IFSRF.]
EE I-9 Exchange rate, end of period, lc per $ . [IFSAE.]
EX I-2 Total exports (NIPA) in constant lc. [OECD data or (IFS90C
or IFS90N)/ PX.]
EXDS exog Discrepancy between NIPA export data and other export data
in 90 lc. [ EX - PX90(E90*X90$ + XS).]
E90 exog E in 1990, 90 lc per 90 $. [IFSRF in 1990.]
F 10 Three month forward rate, lc per $. [IFSB.]
G exog Government purchases of goods and services in constant lc.
[OECD data or (IFS91F or IFS91FF)/PY.]
H 9 Exchange rate, end of period, lc per GE mark. [E/EGE]
I 3 Gross fixed investment in constant lc. [OECD data or IFS93/PY.]
IM I-1 Total imports (NIPA) in constant lc. [OECD data or IFS98C/PM.]
IMDS exog Discrepancy between NIPA import data and other import data
in 90 lc. [IM - PM90(M + MS).]
IP none Industrial production index, 1990 = 100. [IFS66 or
other 66 options.]
J 13 Total employment in thousands. [OECD data or IFS67.]
JJ I-14 Employment population ratio. [J/POP.]
JJP exog Peak to peak interpolation of JJ. [See Section 3.3.3.]
JJS I-15 Ratio of JJ to JJP. [JJ/JJP.]
JMIN I-13 Minimum amount of employment needed to produce Y in thousands.
[Y/LAM.]
LAM exog Peak to peak interpolation of Y/J . [See Section 3.3.3.]
L1 14 Labor force of men in thousands. [OECD data.]
L2 15 Labor force of women in thousands. [OECD data.]
M 1 Total merchandise imports (fob) in 90 lc. [IFS71V/PM.]
MS exog Other goods, services, and income (debit) in 90 lc, BOP data.
[(IFS77AED*E)/PM.]
M90$A I-8 Merchandise imports (fob) from the trade share matrix in 90 $ .
[See Table B.3.]
M90$B exog Difference between total merchandise imports and merchandise
imports from the trade share matrix in 90 $ (i.e., imports
from countries other than the 44 in the trade share matrix).
[M/E90 - M90$A.]
M1 6 Money supply in lc. [IFS34 or IFS34..B.]
PM I-19 Import price index, 1990 = 1.0. [IFS75/100.]
PMP L-3 Import price index from DOT data, 1990 = 1.0. [See Table B.3.]
PM90 exog PM in the NIPA base year divided by PM in 1990.
POP exog Population in millions. [IFS99Z.]
POP1 exog Population of men in thousands. [OECD data.]
POP2 exog Population of women in thousands. [OECD data.]
PSI1 exog [(EE + EE-1)/2]/E.]
PSI2 exog [PM/PMP.]
PW$ L-4 World price index, $/90$. [See Table B.4.]
PX 11 Export price index, 1990 = 1.0. [IFS74/100.]
PX$ L-1 Export price index, $/90$, 1990 = 1.0. [(E90*PX)/E.]
PX90 exog PX in the NIPA base year divided by PX in 1990.
PY 5 GDP or GNP deflator, equals 1.0 in the NIPA base year.
[OECD data or (IFS99B/IFS99B.P.]
RB 8 Long term interest rate, percentage points. [IFS61 or IFS61A.]
RS 7 Three month interest rate, percentage points. [IFS60 or
IFS60B or IFS60C or IFS60X.]
S I-6 Total net goods, services, and transfers in lc. Balance of
payments on current account. Saving of the country.
[See Table B.7.]
STAT exog Statistical discrepancy in constant lc. [Y-C-I-G-EX+IM-V1.]
T exog Time trend. [For quarterly data, 1 in 1952.1, 2 in 1952.2, etc.;
for annual data, 1 in 1952, 2 in 1953, etc.]
TT exog Total net transfers in lc. [See Table B.6.]
UR I-12 Unemployment rate. [(L1 + L2 - J)/(L1 + L2 - AF).]
V I-5 Stock of inventories, end of period, in constant lc. [V-1 + V1.
Base value of zero was used for the period (quarter or year)
prior to the beginning of the data.]
V1 I-4 Inventory investment in constant lc. [OECD data or IFS93I/PY.]
W 12 Nominal wage rate. [IFS65 or IFS65EY.]
X I-3 Final sales in constant lc. [Y - V1.]
XS exog Other goods, services, and income (credit) in 90 lc. BOP data.
[(IFS77ADD*E)/PX.]
X90$ L-2 Merchandise exports from the trade share matrix in 90 $.
[See Table B.4.]
Y 4 Real GDP or GNP in constant lc. [OECD data or IFS99A.P or
IFS99B.P or IFS99A.R or IFS99B.R.]
YS I-17 Potential value of Y. [LAM*JJP*POP.]
Z I-16 Labor constraint variable. [min(0, 1 - JJP/JJ).]
ZZ I-18 Demand pressure variable. [(YS-Y)/YS .]
lc = local currency. NIPA = national income and product accounts. IFS xx = variable number xx from the IFS data. |
| Table B.3 The Equations for a Given Country |
Table B.3
The Equations for a Given Country
Stochastic Equations LHS Var. Explanatory Variables 1. log(M/POP)
cnst, log(M/POP)-1, log(PY/PM), RS or RB, log(Y/POP),
[A/(PY*YS)]-1
2. log(C/POP)
cnst, log(C/POP)-1, RS or RB, log(Y/POP), [A/(PY*YS)]-1
3. logI
cnst, logI-1, logY, RS or RB
4. Y
cnst, Y-1, X, V-1
5. logPY
cnst, T, logPY-1, logPM, logW, DP
6. log[M1/(POP*PY)]
cnst, log[M1/(POP*PY)]-1 or log[M1-1/(POP-1*PY)],
RS, log(Y/POP)
7. RS
cnst, RS-1, PCPY, ZZ or JJS, [A/(PY*YS)]-1,
[A/(PY*YS)]-2, RSUS :
PCPY = 100[(PY/PY-1 )^4 - 1]
8. RB - RS-2
cnst, RB-1 - RS-2, RS - RS-2, RS-1 - RS-2
9. <>logE
cnst, log(PY/PYUS) - logE-1, logEGE - log(PY/PYUS),
.25*log[(1 + RS/100)/(1 + RSUS/100)]
10. logF
logEE, .25*log[(1 + RS/100)/(1 + RSUS/100)]
11. log[PX/(PW$*E)]
logPY - log(PW$*E)
12. logW
cnst, T, logW-1, logPY, DW, logPY-1,
13. <>logJ
cnst, T, log(J/JMIN)-1, <>logY, <>logY-1
14. log(L1/POP1)
cnst, T, log(L1/POP1)-1, log(W/PY), Z
15. log(L2/POP2)
cnst, T, log(L2/POP2)-1, log(W/PY), Z
Identities I-1. IM = PM90(M + MS) + IMDS I-2. EX = PX90(E90*X90$ + XS) + EXDS I-3. X = C + I + G + EX - IM + STAT I-4. V1 = Y - X I-5. V = V-1 + V1 I-6. S = PX(E90*X90$ + XS) - PM(M + MS) + TT I-7. A = A-1 + S I-8. M90$A = M/E90 - M90$B I-9. EE = 2*PSI1*E - EE-1 I-12. UR = (L1 + L2 - J)/(L1 + L2 - AF) I-13. JMIN = Y/LAM I-14. JJ = J/POP I-15. JJS = JJ/JJP I-16. Z = min(0, 1 - JJP/JJ) I-17. YS = LAM*JJP*POP I-18. ZZ = (YS - Y)/YS I-19. PM = PSI2*PMP I-20 E = H*EGE Variables Explained When the Countries are Linked Together (Table B.4) L-1 PX$ L-2. X90$ L-3. PMP L-4. PW$ |
| Table B.4 Equations that Pertain to the Trade and Price Links Among Countries |
Table B.4
Equations that Pertain to the Trade and Price Links Among Countries
L-1. PX$i = (E90i/Ei)PXi, i = 1 ,..., 44
L-2. X90$i = Sum45j=1aijM90$Aj, i = 1, ..., 33
L-3. PMPi = (Ei/E90i)Sum44j=1ajiPX$j, i = 1, ..., 33
An element in this summation is skipped if aji is
missing or PX$j is missing. PMPi is not
computed if Ei is missing or E90i is missing.
L-4. PW$i = (Sum33j=1PX$jX90$j)/(Sum33j=1X90$j), i = 1, ..., 33
An element in this summation is skipped if PX$j is missing
or X90$j is missing or j = i. This summation also excludes
SA and VE, which are the oil exporting countries among the 33.
Construction of aij:
The raw data are:
XX$ij Merchandise exports i to j in $, i,j = 1, ..., 44 [DOT data.]
X$i Total merchandise exports (fob) in $. i = 1, ..., 33 [IFS70/E.]
The constructed variables are:
XX$i45 = X$i - Sum44j=1XX$ij, i = 1, ..., 33
XX90$ij = XX$ij/PX$i, i = 1, ..., 44, j = 1, ..., 45
XX90$ij is missing if XX$ij is missing or PX$i is missing.
M90$Ai = Sum44j=1XX90$ji, i = 1, ..., 45
X90$i = Sum45j=1XX90$ij, i = 1, ..., 33
aij = XX90$ij/M90$Aj, i = 1, ..., 44, j = 1, ..., 45
Linking of the Annual and Quarterly Data
Quarterly data exist for all the trade share calculations, and all
these calculations are quarterly. Feeding into these calculations from
the annual models are predicted annual values of PX$i, M90$Ai,
and Ei. For each of these three variables the predicted value
for a given quarter was taken to be the predicted annual value multiplied
by the ratio of the actual quarterly value to the actual annual value.
This means in effect that the distribution of an annual value into its
quarterly values is taken to be exogenous.
Once the quarterly values have been computed from the trade share
calculations, the annual values of X90$ i that are needed for the
annual models are taken to be the sums of the quarterly values. Similarly,
the annual values of PMPi and PW$i are taken to be
the averages of the quarterly values.
|
| Table B.5 Links Between the US and ROW Models |
Table B.5
Links Between the US and ROW Models
The data on the variables for the United States that are needed when the US model is imbedded in the MC model were collected as described in Table B.2. These variables are (with the US subscript dropped): EXDS, IMDS, M, MS, M90$A, M90$B, PM, PMP, PSI2, PW$, PX (= PX$), S, TT, XS, and X90$. The PX variable here is not the same as the PX variable in Appendix A. Variable Determination X90$US Determined in Table B.4
PMPUS Determined in Table B.4
PW$US Determined in Table B.4
PXUS Determined by equation 132 in the US model. This
equation is equivalent to equation 11 for the other
countries. See the discussion in Section 9.2.
PEX = DEL3*PXUS. In the US model by itself, PEX
is determined as PSI1*PX, which is equation 32 in Table A.2.
This equation is dropped when the US model is linked to
the ROW model. DEL3 is constructed from the data as
PEX/PXUS and is taken to be exogenous.
PMUS = PSI2US*PMPUS. This is the same as equation I-19
for the other countries.
PIM = DEL4*PMUS. PIM is an exogenous variable in the
US model by itself. DEL4 is constructed from the data as
PIM/PMUS and is taken to be exogenous.
EX = (X90$US + XSUS + EXDSUS)/1000.
This is the same as equation I-2 for the other countries.
EX is an exogenous variable in the US model by itself. EXDSUS
is constructed from the data as 1000*EX-X90$US - XSUS
and is taken to be exogenous.
MUS = 1000*IM - MSUS - IMDSUS. This is the
same as equation I-1 for the other countries. IMDSUS is
constructed from the data as 1000*IM - MUS - MSUS
and is taken to be exogenous.
M90$AUS = MUS - M90$BUS. This is the same as
equation I-8 for the other countries.
SUS = PXUS(X90$US + XSUS) - PMUS(MUS + MSUS) + TTUS.
This is the same as equation I-6 for the other countries.
Note:
The new exogenous variables for the US model when it is linked to the
ROW model are DEL3, DEL4, EXDSUS, IMDSUS, M90$BUS, MSUS,
PSI2US, TTUS, and XSUS. EX and PIM are exogenous
in the US model by itself, but endogenous when the US model is linked to the ROW model.
|
| Table B.6 The Procedure Used to Create Quarterly Data from Annual Data |
Table B.6
The Procedure Used to Create Quarterly Data from Annual Data
Let yt be the (observed) average value of the variable for yeart,
and let yit be the (unobserved) average value of the variable for
quarter i of year t (i = 1, 2, 3, 4). Then:
(i) y1t + y2t + y3t + y4t = q.yt
where
1 for flow variables (at quarterly rates)
q =
4 for stock variables and price variables
Assume that the annual data begin in year 1, and let q.y1 = a1,
q.y2 = a2, q.y3 = a3, ... The key assumption is that the four quarterly
changes within the year are the same:
d2 for t = 1,2
(ii) y1t - y4t-1 = y2t - y1t = y3t - y2t = y4t - y3t =
dt for t = 3,...
Given i and ii for t = 1,2, one can solve for y40 and d2 in terms of a1 and a2:
y40 = (13/32)a1 - (5/32)a2
d2 = (a2 - a1)/16
Using y40 and d2, one can then construct quarterly data for
years 1 and 2 using ii. Given y42 from these calculations and given i
and ii for t=3, one can solve for d3 in terms of a3 and y42:
d3 = (a3 - 4y42)/10
Using y42 and d3, one can then construct quarterly data for year 3.
One can then solve for d4 in terms of y43 and a4, and so on.
Note:
The annual population data that were collected for the model are mid
year estimates. In order to apply the above procedure to these data, the
assumption was made that the average value for the year equals the mid
year value.
|
| Table B.7 Construction of the Balance of Payments Data: Data for S and TT |
Table B.7
Construction of the Balance of Payments Data: Data for S and TT
The relevant raw data variables are: M$' Goods imports (fob) in $, BOP data. [IFS78ABD.] M$ Goods imports (fob) in $. [IFS71V/E.] X$' Goods exports (fob) in $, BOP data. [IFS78AAD.] X$ Goods exports (fob) in $. [IFS70/E.] MS$ Services and income (debit) in $, BOP data. [IFS78AED + IFS78AHD.] XS$ Services and income (credit) in $, BOP data. [IFS78ADD + IFS78AGD.] XT$ Current transfers, n.i.e., (credit) in $ BOP data. [IFS78AJD.] MT$ Current transfers, n.i.e., (debit) in $ BOP data. [IFS78AKD.]
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