3. The Data, Variables, and Equations 
This chapter presents the data, variables, and equations of the MC3 model.
It is an update of Chapter 3 in the 1994 book.
It relies heavily on Appendices A and B, which are at the end of this
document. If you are reading this online, it may be helpful to print
Appendices A and B for ease of reference.
Some of the US variables that are discussed in this chapter are not used in the current version of the US model (i.e., the US model that is part of the overall MC3 model). In the current version of the US model the unemployment rate (UR) is used as the demand pressure variable (in the price equation and the interest rate reaction function) and as the labor constraint variable (in the labor supply equations). This means that potential output (YS), the labor constraint variable (Z), and JJS are no longer used. This also means that the variables JJ and JJP are no longer used since they were only used in the determination of YS and JJS. Also, excess capital is no longer used in the US investment equation, which means that variables MUH and KKMIN are no longer used. Nevertheless, these variables may be of interest in their own right, and so they are discussed in this chapter and have been retained as variables in the model. Also, Z is used for some of the tests in Chapter 5.

3.1 Transition from Theory to Empirical Specifications 
The transition from theory to empirical work in macroeconomics is not
always
straightforward. The quality of the data are never as good as one might
like, so
compromises have to be made in moving from theory to empirical
specifications. Also, extra
assumptions usually have to be made, in particular about unobserved
variables like
expectations and about dynamics. There usually is, in other words,
considerable
"theorizing" involved in this transition process. [Footnote 1:
This transition
is discussed in detail in
Fair (1984),
Section 2.2] The first step in the transition, which is taken in this chapter, is to choose the data and variables. All the data and variables in the US and ROW models are presented in this chapter. The second step, also taken in this chapter, is to choose which variables are to be treated as exogenous, which are to be determined by stochastic (estimated) equations, and which are to be determined by identities. All the equations in the two models are listed in this chapter. The third step, which is where most of the theory is used, is to choose the explanatory variables in the stochastic equations and the functional forms of the equations. This is the task of Chapters 5 and 6. The discussion in the present chapter relies heavily on the tables in Appendices A and B. As noted in Section 1.1, the overall MC model consists of estimated structural equations for 38 countries. There are 30 stochastic equations for the United States and up to 15 each for each of the other countries. There are 101 identities for the United States and up to 20 each for each of the others. There are 58 countries in the trade share matrix plus an all other category called "all other" (AO). The trade share matrix is thus 59 x 59. The countries are listed in Table B.1. The data for the United States begin in 1952:1, and the data for the other countries begin in 1960:1. As will be discussed, some of the country models are annual rather than quarterly. The data referred to in this chapter are data available as of April 27, 2001. 
3.2 The US Model 
The data, variables, and equations for the US model are discussed in this section. The relevant tables are Tables A.1A.9 in Appendix A, and these will be briefly outlined first. 
3.2.1 The Tables (Tables A.1A.9) 
Table A.1 presents the six sectors in the US model: household (h),
firm (f),
financial (b), foreign (r), federal government (g), and state and local
government (s). In
order to account for the flow of funds among these sectors and for their
balancesheet
constraints, the U.S. Flow of Funds Accounts (FFA) and the U.S. National
Income and
Product Accounts (NIPA) must be linked. Many of the 101 identities in the
US model are
concerned with this linkage. Table A.1 shows how the six sectors in the
US model are
related to the sectors in the FFA. The notation on the right side of this
table (H1, FA,
etc.) is used in Table A.4 in the description of the FFA data. Table A.2 lists all the variables in the US model in alphabetical order, and Table A.3 lists all the stochastic equations and identities. The functional forms of the stochastic equations are given, but not the coefficient estimates. The coefficient estimates are discussed in Chapter 5 and are presented in the "Chapter 5 tables" following Appendix A. Tables A.2 and A.3 are the main reference tables for the US model. Of the remaining tables, Tables A.4A.6 show how the variables were constructed from the raw data, Table A.7 lists the first stage regressors that were used for the 2SLS and 3SLS estimates, and Table A.8 shows how the model is solved under various assumptions about monetary policy. Finally, Table A.9 shows which variables appear in which equations. It will be useful to begin with Tables A.4A.6 before turning to Tables A.2 and A.3. 
3.2.2 The Raw Data 
The NIPA Data Table A.4 lists all the raw data variables. The variables from the NIPA are presented first, in the order in which they appear in the Survey of Current Business. The Bureau of Economic Analysis (BEA) is now emphasizing "chaintype weights" in the construction of real magnitudes, and the data based on these weights have been used here. [Footnote 2: See Young (1992) and Triplett (1992) for a good discussion of the chaintype weights.] Because of the use of the chaintype weights, real GDP is not the sum of its real components. To handle this, a discrepancy variable, denoted STATP, was created, which is the difference between real GDP and the sum of its real components. (STATP is constructed using equation 83 in Table A.3.) STATP is taken to be exogenous in the model. It is small in magnitude. The Other Data
Some adjustments that were made to the raw data are presented next in Table A.4. These are explained beginning in the next paragraph. Finally, all the raw data variables are presented at the end of Table A.4 in alphabetical order along with their numbers. This allows one to find a raw data variable quickly. Otherwise, one has to search through the entire table looking for the particular variable. All the raw data variables are numbered with an "R" in front of the number to distinguish them from the variables in the model. The adjustments that were made to the raw data are as follows. The quarterly social insurance variables R195R200 were constructed from the annual variables R78R83 and the quarterly variables R38, R60, and R71. Only annual data are available on the breakdown of social insurance contributions between the federal and the state and local governments with respect to the categories "personal," "government employer," and "other employer." It is thus necessary to construct the quarterly variables using the annual data. It is implicitly assumed in this construction that as employers, state and local governments do not contribute to the federal government and vice versa. The constructed tax variables R201 and R202 pertain to the breakdown of corporate profit taxes of the financial sector between federal and state and local. Data on this breakdown do not exist. It is implicitly assumed in this construction that the breakdown is the same as it is for the total corporate sector. The quarterly variable R202a, INTPRI, which is the level of net interest payments of sole proprietorships and partnerships, is constructed from the annual variable R96a, INTPRIA, and the quarterly and annual data on PII, personal interest income, R53. Quarterly data on net interest payments of sole proprietorships and partnerships do not exist. It is implicitly assumed in the construction of the quarterly data that the quarterly pattern of the level of interest payments of sole proprietorships and partnerships is the same as the quarterly pattern of personal interest income. The quarterly variable R203, INTROW, which is the level of net interest payments of the rest of the world, is constructed from the annual variable R96, INTROWA, and the quarterly and annual data on PII, personal interest income, R53. Quarterly data on net interest payments of the rest of the world do not exist. It is implicitly assumed in the construction of the quarterly data that the quarterly pattern of the level of interest payments of the rest of the world is the same as the quarterly pattern of personal interest income. The tax variables R57 and R62 were adjusted to account for the tax surcharge of 1968:31970:3 and the tax rebate of 1975:2. The tax surcharge and the tax rebate were taken out of personal income taxes (TPG) and put into personal transfer payments (TRGH). The tax surcharge numbers were taken from Okun (1971), Table 1, p. 171. The tax rebate was 7.8 billion dollars at a quarterly rate. The multiplication factors in Table A.4 pertain to the population, labor force, and employment variables. Official adjustments to the data on POP, POP1, POP2, CE+U, CL1, CL2, and CE were made a few times, and these must be accounted for. The multiplication factors are designed to make the old data consistent with the new data. For further discussion, see Fair (1984), pp. 414415. Table A.5 presents the balancesheet constraints that the data satisfy. The variables in this table are raw data variables. The equations in the table provide the main checks on the collection of the data. If any of the checks are not met, one or more errors have been made in the collection process. Although the checks in Table A.5 may look easy, considerable work is involved in having them met. All the receipts from sector i to sector j must be determined for all i and j (i and j run from 1 through 6). 
3.2.3 Variable Construction 
Table A.6 explains the construction of the variables in the model
(i.e., the
variables in Table A.2) from the raw data variables (i.e., the variables
in Table A.4).
With a few exceptions, the variables in the model are either constructed
in terms of the
raw data variables in Table A.4 or are constructed by identities. If the
variable is
constructed by an identity, the notation "Def., Eq." appears,
where the equation
number is the identity in Table A.2 that constructs the variable. In a
few cases the
identity that constructs an endogenous variable is not the equation that
determines it in
the model. For example, equation 85 constructs LM, whereas stochastic
equation 8
determines LM in the model. Equation 85 instead determines E, E being
constructed directly
from raw data variables. Also, some of the identities construct exogenous
variables. For
example, the exogenous variables D2G is constructed by equation 49. In
the model equation
49 determines TFG, TFG being constructed directly from raw data
variables. If a variable
in the model is the same as a raw data variable, the same notation is
used for both. For
example, CD, consumption expenditures on durable goods, is both a
variable in the model
and a raw data variable. The financial stock variables in the model that are constructed from flow identities need a base quarter and a base quarter starting value. The base quarter values are indicated in Table A.6. The base quarter was taken to be 1971:4, and the stock values for this quarter were taken from the FFA stock values. There are also a few internal checks on the data in Table A.6 (aside from the balancesheet checks in Table A.5). The variables for which there are both raw data and an identity available are GDP, MB, PIEF, PUG, and PUS. In addition, the saving variables in Table A.5 (SH, SF, and so on) must match the saving variables of the same name in Table A.6. There is also one redundant equation in the model, equation 80, which the variables must satisfy. There are a few variables in Table A.6 whose construction needs some explanation. HFS: Peak to Peak Interpolation of HF
HO: Overtime Hours
TAUS: Progressivity Tax Parameters
Given TAUS, D1S is defined to be THS/YT  (TAUS^{.}YT)/POP (see Table A.6). In the model D1S is taken to be exogenous, and THS is explained by equation 48 as [D1S + (TAUS^{.}YT)/POP]YT. This treatment allows a state and local marginal tax rate to be defined in equation 91: D1SM = D1S + (2^{.}TAUS^{.}YT)/POP. TAUG: Progressivity Tax Parameterg
Given TAUG, D1G is defined to be THG/YT  (TAUG^{.}YT)/POP (see Table A.6). In the model D1G is taken to be exogenous, and THG is explained by equation 47 as [D1G + (TAUG^{.}YT)/POP]YT. This treatment allows a federal marginal tax rate to be defined in equation 90: D1GM = D1G + (2^{.}TAUG^{.}YT)/POP. KD: Stock of Durable Goods
KH: Stock of Housing
KK: Stock of Capital
V: Stock of Inventories
Excess Labor and Excess Capital
The measurement of the capital stock KK is discussed above. The
production
function of the firm sector for empirical purposes is postulated to be
Equation 92 for KK and the production function 3.1 are not consistent with the puttyclay technology of the theoretical model. To be precise with this technology one has to keep track of the purchase date of each machine and its technological coefficients. This kind of detail is not possible with aggregate data, and one must resort to simpler specifications. Given the production function 3.1, excess labor was measured as follows. [Footnote 3: The estimation of excess labor in the following way was first done in Fair (1969) using three digit industry data.] Output per paid for worker hour, Y/(JF^{.}HF), was plotted for the 1952:12001:1 period. The peaks of this series were assumed to correspond to cases in which the number of hours worked equals the number of hours paid for, which implies that the values of LAM in equation 3.1 are observed at the peaks. The values of LAM other than those at the peaks were assumed to lie on straight lines between the peaks. This gives an estimate of LAM for each quarter. Given an estimate of LAM for a particular quarter and given equation 3.1, the estimate of the number of worker hours required to produce the output of the quarter, denoted JHMIN in the model, is simply Y/LAM. In the model, LAM is denoted LAM, and the equation determining JHMIN is equation 94 in Table A.3. The actual number of workers hours paid for ( JF^{.}HF) can be compared to JHMIN to measure the amount of excess labor on hand. The peaks that were used for the interpolations are listed in Table A.6 in the description of LAM. [Footnote 4: The values of LAM before the first peak were assumed to lie on the backward extension of the line connecting the first and second peaks. Similarly, the values of LAM after the last peak were assumed to lie on the forward extension of the line connecting the second to last and last peak. Contrary to the case for LAM, for some of the peak to peak interpolations in this study the values before the first peak were taken to be the value at the first peak. This is denoted "flat beginning" in Table A.6. Also, for some of the interpolations the values after the last peak were taken to be the value at the last peak. This is denoted "flat end" in Table A.6.] For the measurement of excess capital there are no data on hours paid for or worked per unit of KK, and thus one must be content with plotting Y/KK. This is, from the production function 3.1, a plot of MU^{.}HK^{a}, where HK^{a} is the average number of hours that each machine is utilized. If it is assumed that at each peak of this series HK^{a} is equal to the same constant, say H', then one observes at the peaks MU^{.}H'. Interpolation between peaks can then produce a complete series on MU^{.}H'. If, finally, H' is assumed to be the maximum number of hours per quarter that each unit of KK can be utilized, then Y/(MU^{.}H') is the minimum amount of capital required to produce Y (denoted KKMIN). In the model, MU^{.}H' is denoted MUH, and the equation determining KKMIN is equation 93 in Table A.3. The actual capital stock (KK) can be compared to KKMIN to measure the amount of excess capital on hand. The peaks that were used for the interpolations are listed in Table A.6 in the description of MUH. The estimated percentages of excess labor and capital by quarter are presented in Table 3.1. (These are numbers based on data through 1993:2; they have not been updated through the latest data.) For labor each figure in the table is 100 times [(JF^{.}HF)/ JHMIN  1.0], and for capital each figure is 100 times (KK/KKMIN 1.0). The table shows that in the most recent recession both excess labor and capital peaked at 3.6 percent in 1991:1. The largest value for excess labor during the entire 1952:11993:2 period was 4.9 percent in 1960:4. The largest value for excess capital was 10.5 percent in 1982:4. [Footnote 5: A few values in Table 3.1 are negative. A negative value occurs when the actual value of output per paid for worker hour or output per capital is above the interpolation line. The peak to peak interpolation lines were not always drawn so that every point between the peaks lay on or below the line.] Table 3.1 Estimated Percentages of Excess Labor and Capital Quar. ExL ExK Quar. ExL ExK Quar. ExL ExK Quar. ExL ExK 1952:1 1.0 1.9 1962:3 .1 .0 1973:1 .8 1.1 1983:3 1.7 4.7 1952:2 1.1 3.3 1962:4 .4 1.2 1973:2 .0 .7 1983:4 1.5 3.1 1952:3 1.2 2.8 1963:1 .7 .7 1973:3 1.1 .3 1984:1 1.2 1.1 1952:4 1.4 1.2 1963:2 .7 .5 1973:4 .9 .2 1984:2 1.0 .0 1953:1 .6 .2 1963:3 .4 .3 1974:1 2.3 2.2 1984:3 .8 .1 1953:2 .1 .0 1963:4 .1 .2 1974:2 2.5 3.2 1984:4 1.0 .6 1953:3 .5 1.3 1964:1 1.5 1.1 1974:3 3.3 4.9 1985:1 1.4 1.0 1953:4 .0 2.9 1964:2 .7 .8 1974:4 2.9 6.4 1985:2 1.2 1.6 1954:1 1.4 4.9 1964:3 .4 .4 1975:1 3.2 9.8 1985:3 .5 1.1 1954:2 1.2 5.8 1964:4 .8 .7 1975:2 1.1 8.6 1985:4 .8 1.5 1954:3 .2 4.9 1965:1 .5 .0 1975:3 .4 6.9 1986:1 .3 1.1 1954:4 .0 3.6 1965:2 1.5 .6 1975:4 .6 6.0 1986:2 .0 2.1 1955:1 .3 1.4 1965:3 .1 .3 1976:1 .0 4.2 1986:3 .2 2.0 1955:2 .2 .7 1965:4 .0 .0 1976:2 .3 4.3 1986:4 .7 2.4 1955:3 1.2 .0 1966:1 .7 1.3 1976:3 .4 4.7 1987:1 1.0 2.0 1955:4 2.3 .2 1966:2 .2 .2 1976:4 .0 4.0 1987:2 .9 1.4 1956:1 2.6 .7 1966:3 .6 .2 1977:1 .1 3.2 1987:3 1.1 1.1 1956:2 3.0 1.1 1966:4 .5 .8 1977:2 .5 2.1 1987:4 .7 .2 1956:3 3.5 1.9 1967:1 1.0 1.2 1977:3 .0 1.2 1988:1 .5 .0 1956:4 2.3 1.3 1967:2 .1 1.5 1977:4 1.4 2.3 1988:2 1.2 .1 1957:1 1.9 1.2 1967:3 .3 1.2 1978:1 1.7 2.6 1988:3 1.1 .1 1957:2 2.1 2.0 1967:4 .9 1.5 1978:2 1.0 .0 1988:4 1.4 .2 1957:3 2.1 2.2 1968:1 .0 1.0 1978:3 1.0 .1 1989:1 2.1 .2 1957:4 2.5 4.5 1968:2 .1 .3 1978:4 1.0 .1 1989:2 2.0 .0 1958:1 2.2 7.0 1968:3 .3 .3 1979:1 2.1 1.0 1989:3 2.5 .3 1958:2 1.5 6.6 1968:4 1.1 1.0 1979:2 2.4 1.8 1989:4 2.4 .3 1958:3 .1 3.9 1969:1 1.6 .0 1979:3 2.4 2.0 1990:1 2.6 .0 1958:4 .5 1.4 1969:2 2.3 1.3 1979:4 2.6 2.7 1990:2 2.4 .2 1959:1 1.0 1.6 1969:3 2.4 2.0 1980:1 2.2 3.4 1990:3 2.5 .9 1959:2 2.2 .0 1969:4 3.1 3.7 1980:2 3.4 6.9 1990:4 3.5 2.2 1959:3 3.0 1.9 1970:1 3.5 5.2 1980:3 3.1 7.4 1991:1 3.6 3.6 1959:4 2.8 2.1 1970:2 3.8 6.6 1980:4 2.2 5.8 1991:2 3.1 3.5 1960:1 1.8 1.3 1970:3 2.0 6.3 1981:1 1.8 4.9 1991:3 2.9 3.3 1960:2 3.9 2.9 1970:4 2.8 8.3 1981:2 1.7 5.4 1991:4 2.7 3.3 1960:3 4.2 3.3 1971:1 1.0 5.7 1981:3 1.4 5.3 1992:1 2.0 2.8 1960:4 4.9 5.2 1971:2 1.6 6.0 1981:4 2.6 7.2 1992:2 1.5 2.0 1961:1 4.0 5.1 1971:3 1.0 5.8 1982:1 3.3 9.1 1992:3 .0 .5 1961:2 1.3 3.9 1971:4 1.8 5.4 1982:2 2.6 9.1 1992:4 .0 .0 1961:3 .6 2.9 1972:1 1.5 3.9 1982:3 3.3 10.4 1993:1 .6 .6 1961:4 .0 1.4 1972:2 .9 2.6 1982:4 3.0 10.5 1993:2 1.2 .8 1962:1 .6 .7 1972:3 .3 1.8 1983:1 2.6 9.5 1962:2 .7 .4 1972:4 .1 1.0 1983:2 1.2 6.4 Comparisons to the FayMedoff Estimates
It is of interest to compare the estimates of excess labor in Table 3.1 with the survey results of Fay and Medoff (1985). Fay and Medoff surveyed 168 U.S. manufacturing plants to examine the magnitude of labor hoarding during economic contractions. They found that during its most recent trough quarter, the typical plant paid for about 8 percent more blue collar hours than were needed for regular production work. Some of these hours were used for other worthwhile work, usually maintenance work, and after taking account of this, 4 percent of the blue collar hours were estimated to be hoarded for the typical plant. The estimates of excess labor in Table 3.1 probably correspond more to the concept behind the 8 percent number of Fay and Medoff than to the concept behind the 4 percent number. If, for example, maintenance work is shifted from high to low output periods, then JHMIN is a misleading estimate of worker hour requirements. In a long run sense, JHMIN is too low because it has been based on the incorrect assumption that the peak productivity values could be sustained over the entire business cycle. This error is not a serious one from the point of estimating the labor demand equations in Chapter 5. If the same percentage error has been made at each peak, which is likely to be approximately the case, the error will merely be absorbed in the estimates of the constant terms in the equations. The error is also not serious for the FayMedoff comparisons as long as the FayMedoff concept behind the 8 percent number is used. This concept, like the concept behind the peak to peak interpolation work, does not account for maintenance that is shifted from high to low output periods. There are two possible troughs that are relevant for the FayMedoff study, the one in mid 1980 and the one in early 1982. The first survey upon which the FayMedoff results are based was done in August 1981, and the second (larger) survey was done in April 1982. A follow up occurred in October 1982. The plant managers were asked to answer the questionnaire for the plant's most recent trough. For the last responses the trough might be in 1982, whereas for the earlier ones the trough is likely to be in 1980. Table 3.1 shows that the percentage of excess labor reached 3.4 percent in 1980:2 and 3.3 percent in 1982:1. [Footnote 7: The estimates in Fair (1985) using earlier data were 4.5 percent in 1980:4 and 5.5 percent in 1982:1. The use of more recent data has thus lowered the excess labor estimates by a little over a percentage point. Also, the FayMedoff estimate of 4 percent hoarded labor cited above was 5 percent in an earlier version of the paper cited in Fair (1985).] The FayMedoff estimate of 8 percent is thus compared to the 3.4 and 3.3 percent values in Table 3.1. These two sets of results seem consistent in that there are at least two reasons for expecting the FayMedoff estimate to be somewhat higher. First, the trough in output for a given plant is on average likely to be deeper than the trough in aggregate output, since not all troughs are likely to occur in the same quarter across plants. Second, the manufacturing sector may on average face deeper troughs than do other sectors, and the aggregate estimates in Table 3.1 are for the total private sector, not just manufacturing. One would thus expect the FayMedoff estimate to be somewhat higher than the aggregate estimates, and 8 percent versus a number around 3 to 3.5 percent seems consistent with this. The FayMedoff results appear to provide strong support for the excess labor hypothesis. At a micro level Fay and Medoff found labor hoarding and of a magnitude that seems in line with aggregate estimates. This is one of the few examples in macroeconomics where a hypothesis has been so strongly confirmed using detailed micro data. Labor Market Tightness: The Z Variable
YS: Potential Output of the Firm Sector

3.2.4 The Identities 
The identities in Table A.3 are of two types. One type simply defines
one
variable in terms of others. These identities are equations 31, 33, 34,
43, 55, 56, 5887,
and 89131. The other type defines one variable as a rate or ratio times
another variable
or set of variables, where the rate or ratio has been constructed to have
the identity
hold. These identities are equations 32, 3542, 4454, and 57. Consider,
for example,
equation 50: (50) TFS = D2S^{.}PIEF where TFS is the amount of corporate profit taxes paid from firms (sector f) to the state and local government sector (sector s), PIEF is the level of corporate profits of the firm sector, and D2S is the "tax rate." Data exist for TFS and PIEF, and D2S was constructed as TFS/PIEF. The variable D2S is then interpreted as a tax rate and is taken to be exogenous. This rate, of course, varies over time as tax laws and other things that affect the relationship between TFS and PIEF change, but no attempt has been made to explain these changes. This general procedure was followed for the other identities involving tax rates. A similar procedure was followed to handle
relative
price changes. Consider equation 38: Another identity of the second type is equation 57: Many of the identities of the first type are concerned with linking
the FFA data
to the NIPA data. An identity like equation 66 
3.2.5 The Stochastic Equations 
A brief listing of the stochastic equations is presented in Table A.3. The left hand side and right hand side variables are listed for each equation. Chapter 5 discusses the specification, estimation, and testing of these equations. Of the thirty equations, the first nine pertain to the household sector, the next twelve to the firm sector, the next five to the financial sector, the next to the foreign sector, the next to the state and local government sector, and the final two to the federal government sector. 
3.3 The ROW Model 
The data, variables, and equations for the ROW model are discussed in this section. Remember that the ROW model includes structural models for 37 countries. The relevant tables for the model are Tables B.1B.6 in Appendix B, and these will be outlined first. 
3.3.1 The Tables (Tables B.1B.6) 
Table B.1 lists the countries in the model and provides a brief
listing of the
variables per country. The 37 countries for which structural equations
are estimated are
Canada (CA) through Peru (PE) excluding Brazil (BR).
Data were
collected for Brazil, but there was not enough data to allow
structural equations to be estimated. Countries 40 through
59 are countries for which only trade share equations are estimated. A
detailed
description of the variables per country is presented in Table B.2, where
the variables
are listed in alphabetical order. Data permitting, each of the countries
has the same
set of variables. Quarterly data were collected for countries 2 through
14, and annual
data were collected for the others. Countries 2 through 14 will be
referred to as
"quarterly" countries, and the others will be referred to as
"annual"
countries. The way in which each variable was constructed is explained in
brackets in
Table B.2. All of the data with potential seasonal fluctuations have been
seasonally
adjusted. In some cases, quarterly data for a particular variable, such
as a population
variable, did not exist.
Table B.3 lists the stochastic equations and the identities. The functional forms of the stochastic equations are given, but not the coefficient estimates. The coefficient estimates for all the countries are presented in Chapter 6. Table B.4 lists the equations that pertain to the trade and price links among the countries. It also explains how the quarterly and annual data were linked for the trade share calculations. Table B.5 lists the links between the US and ROW models. Finally, Table B.6 explains the construction of the balance of payments datadata for variables S and TT. It will be useful to begin with a discussion of the construction of some of the variables in Table B.2. 
3.3.2. The Raw Data 
The data sets for the countries other than the United States (i.e., the countries in the ROW model) begin in 1960. The sources of the data are the IMF and OECD. Data from the IMF are international financial statistics (IFS) data and direction of trade (DOT) data. Data from the OECD are quarterly national accounts data, annual national accounts data, quarterly labor force data, and annual labor force data. These are the "raw" data. As noted above, the way in which each variable was constructed is explained in brackets in Table B.2. When "IFS" precedes a number or letter in the table, this refers to the IFS variable number or letter. Some variables were constructed directly from IFS and OECD data (i.e., directly from the raw data), and some were constructed from other (already constructed) variables. 
3.3.3 Variable Construction 
S, TT, and A: Balance of Payments Variables One important feature of the data collection is the linking of the balance of payments data to the other export and import data. The two key variables involved in this process are S, the balance of payments on current account, and TT, the value of net transfers. The construction of these variables and the linking of the two types of data are explained in Table B.6. Quarterly balance of payments data do not generally begin as early as the other data, and the procedure in Table B.6 allows quarterly data on S to be constructed as far back as the beginning of the quarterly data for merchandise imports and exports (M$ and X$). The variable A is the net stock of foreign security and reserve holdings. It was constructed by summing past values of S from a base period value of zero. The summation begins in the first quarter for which data on S exist. This means that the A series is off by a constant amount each period (the difference between the true value of A in the base period and zero). In the estimation work the functional forms were chosen in such a way that this error was always absorbed in the estimate of the constant term. It is important to note that A measures only the net asset position of the country visavis the rest of the world. Domestic wealth, such as the domestically owned housing stock and plant and equipment stock, is not included. V: Stock of Inventories
Excess Labor
Given the production function 3.2, excess labor was measured as follows for each country. Y/J was plotted over the sample period, and peaks of this series were chosen. This is from 3.2 a plot of LAM^{.}HJ^{a}. If it is assumed that at each peak HJ^{a} is equal to the same constant, say HJ', then one observes at the peaks LAM^{.}HJ'. Straight lines were drawn between the peaks (peak to peak interpolation), and LAM^{.}HJ' was assumed to lie on the lines. If, finally, HJ' is assumed to be the maximum number of hours that each worker can work, then Y/(LAM^{.}HJ') is the minimum number of workers required to produce Y, which is denoted JMIN in the ROW model. LAM^{.}HJ' is simply denoted LAM, and the equation determining JMIN is equation I13 in Table B.3. The actual number of workers on hand (J) can be compared to JMIN to measure the amount of excess labor on hand. Labor Market Tightness: The Z variable
YS: Potential Output

3.3.4 The Identities 
The identities for each country are listed in Table B.3. There are
up to 20
identities per country. (The identities are numbered I1 through I22,
with no identities
I10 and I11.) Equation I1 links the non NIPA data on imports (i.e.,
data on M and MS)
to the NIPA data (i.e., data on IM). The variable IMDS in the equation
picks up the
discrepancy between the two data sets. It is exogenous in the model.
Equation I2 is a
similar equation for exports. Equation I3 is the income identity;
equation I4 defines
inventory investment as the difference between production and sales; and
equation I5
defines the stock of inventories as the previous stock plus inventory
investment. The
income identity I3 is the empirical version of equation 2.4 in Section
2.2.3 except that
the level of imports (IM) has to be subtracted in I3 because C, I, and G
include imports.
Equation I6 defines S, the current account balance. This is the empirical version of equation ii in Section 2.2.3. Equation I7 defines A, the net stock of foreign security and reserve holdings, as equal to last period's value plus S. (Remember that A is constructed by summing past values of S.) This is the empirical version of equation i' in Section 2.2.8. Equation I8 links M, total merchandise imports in 95 lc, to M95$A, merchandise imports from the countries in the trade share matrix in 95$. The variable M95$B is the difference between total merchandise imports (in 95$) and merchandise imports (in 95$) from the countries in the trade share matrix. It is exogenous in the model. Equation I9 links E, the average exchange rate for the period, to EE, the end of period exchange rate. If the exchange rate changes fairly smoothly within the period, then E is approximately equal to (EE + EE_{1})/2. A variable PSI1 was defined to make the equation E = PSI1[(EE + EE_{1})/2] exact, which is equation I9. One would expect PSI1 to be approximately one and not to fluctuate much over time, which is generally the case in the data. Equation I12 defines the civilian unemployment rate, UR. L1 is the labor force of men, and L2 is the labor force of women. J is total employment, including the armed forces, and AF is the level of the armed forces. UR is equal to the number of people unemployed divided by the civilian labor force. Equations I13 through I18 pertain to the measurement of excess labor, the labor constraint variable, and potential output. These have all been discussed above. Equation I19 links PM, the import price index obtained from the IFS data, to PMP, the import price index computed from the trade share calculations. The variable that links the two, PSI2, is taken to be exogenous. Equation I20 links the exchange rate relative to the U.S. dollar (E) to the exchange rate relative to the German mark (H). This equation is used to determine H when equation 9 determines E, and it is used to determine E when equation 9 determines H. Equation I21 determines NW, an estimate of the net worth of the country. Net worth is equal to last period's net worth plus investment plus net exports. Finally, equation I22 defines the country's export price index in terms of U.S. dollars. 
3.3.5 The Stochastic Equations 
The stochastic equations for a given country are listed in Table B.3.
There are
up to 15 estimated equations per country. It will be useful to relate
some of the
equations in the table to those in the theoretical model in Chapter 2,
Section 2.2.3.
Chapter 6 discusses the specification, estimation, and testing of these
equations. As will
be discussed in Chapter 6, many of these equations are similar to the
corresponding
equations in the US model.
Equation 1 in Table B.3 explains the demand for imports. It is matched to equation 2.2 of the theoretical model. Equation 2 explains consumption. It is matched to equation 2.1 except that consumption for equation 2 includes consumption of imported goods. In the theoretical model X_{h} is only the value of domestically produced goods consumed. Equation 3 explains fixed investment, and equation 4 explains production with sales as an explanatory variable, which is in effect an inventory investment equation. Neither of these equations was included in the theoretical model. The price equation 5 is matched to equation 2.3. Equation 6 explains the demand for money, and it is matched to equation 2.6. Equation 7 is an interest rate reaction function, explaining the short term interest rate RS. RS is equivalent to R in the theoretical model. (Interest rate reaction functions are discussed in Section 2.2.7.) Equation 8 is a term structure of interest rates equation, explaining the long term interest rate RB. The theoretical model does not contain a long term rate. Equation 9 is an exchange rate reaction function, explaining the exchange rate E or H. E or H is equivalent to e in the theoretical model. (Exchange rate reaction functions are also discussed in Section 2.2.7.) Equation 10 is an estimated arbitrage condition and explains the forward exchange rate. In the theoretical model this equation would be F = e((1+R)/(1+r)), where F is the forward rate. Equation 11 explains the price of exports. In the theoretical model the price of exports is simply the price of domestic output, but this is not true in practice and an additional equation has to be introduced, which is equation 11. Equation 12 explains the wage rate; equation 13 explains the demand for employment; and equations 14 and 15 explain the labor force participation rates of men and women, respectively. These equations are not part of the theoretical model because it has no labor sector. 
3.3.6 The Linking Equations 
The equations that pertain to the trade and price links among
countries are
presented in Table B.4. (All imports and exports in what follows are
merchandise imports
and exports only.)
The equations L1 determine the trade share coefficients, a_{ij}.
The trade share equations are discussed in Section 6.16 of Chapter 6,
and the use of these equations
in the solution of the model is discussed in Section 9.2 of Chapter 9.
a_{ij} is the share of i's merchandise exports to j out of total
merchandise imports of j.
Given a_{ij} and M95$A_{j}, the total merchandise imports
of j, the equations L2 determine the level of exports from i to j,
XX95$_{ij}. The equations L3 then determine the total exports
of country i by summing XX95$_{ij} over j.
The equations L4 link export prices to import prices. The price of imports of country i, PMP_{i}, is a weighted average of the export prices of other countries (except for country 59, the "all other" category, where no data on export prices were collected). The weight for country j in calculating the price index for country i is the share of country j's exports imported by i. The equations L5 define a world price index for each country, which is a weighted average of the 58 countries' export prices except the prices of the oil exporting countries. (As discussed in Section 6.12, the aim is to have the world price index not include oil prices.) The world price index differs slightly by country because the own country's price is not included in the calculations. The weight for each country is its share of total exports of the relevant countries. Table B.5 explains how the US and ROW models are linked. When the two models are combined (into the MC3 model), the price of imports PIM in the US model is endogenous and the level of exports EX is endogenous. 