6. The Stochastic Equations of the ROW Model 
This chapter discusses the specification, estimation, and testing of
the stochastic equations of the ROW model.
It is an update of Chapter 6 in the 1994 book.
It relies heavily on the Chapter 6 tables, which are at the end of this
document. If you are reading this online, it may be helpful to print
the Chapter 6 tables for ease of reference.
Two recent papers are relevant for the material in this chapter. See "Evaluating the Information Content and Money Making Ability of Forecasts from Exchange Rate Equations" for discussion of exchange rate equations like equation 9. See "Is There Empirical Support for the 'Modern' View of Macroeconomics" for further tests of nominal versus real interest rates in consumption and investment equations like equations 2 and 3.

6.1 Introduction 
The stochastic equations of the ROW model are specified,
estimated, and tested in this chapter. This chapter does for the ROW
model what Chapter 5
did for the US model. Stochastic equations are estimated for 37
countries, with up to 15
equations estimated per country. The equations are listed in Table B.3,
and they were
briefly discussed in Section 3.3.5. The empirical results are presented
in the
"Chapter 6 tables" following Appendix B. Table 6a presents the
estimates of the
"final" specification of each equation, and Table 6b presents
the results of the
tests.
The 2SLS technique was used for the quarterly countries and for equations 1, 2, and 3 for the annual countries. The OLS technique was used for the other equations for the annual countries. The 2SLS technique had to be used sparingly for the annual countries because of the limited number of observations. The selection criterion for the first stage regressors for each equation was the same as that used for the US model. Briefly, the main predetermined variables in each country's model were chosen to constitute a "basic" set, and other variables were added to this set for each individual equation. As noted in Chapter 5, the choice of first stage regressors for large scale models is discussed in Fair (1984), pp. 215216. The estimation periods were chosen based on data availability. With three exceptions, the periods were chosen to use all the available data. The three exceptions are the interest rate, exchange rate, and forward rate equations, where the estimation periods were chosen to begin after the advent of floating exchange rates. The earliest starting quarter (year) for these periods was 1972:2 (1972). For the EMU countries the estimation periods for the interest rate, exchange rate, and forward rate equations end in 1998:4. Since from 1999:1 on the EMU countries have had one common monetary policy, there are no longer individual country interest rate, exchange rate, and forward rate equations. The tests are similar to those done for the US equations. To repeat from Chapter 5, the basic tests are 1) adding lagged values, 2) estimating the equation under the assumption of a higher order autoregressive process for the error term, 3) adding a time trend, 4) adding values led one or more periods, 5) adding additional variables, and 6) testing for structural stability. For the quarterly countries the autoregressive process for the error term was taken to be second order rather than fourth order, which was used for the US model. For the annual countries the autoregressive process was taken to be first order. Because fourth order was not used, the notation "RHO+" instead of "RHO=4" is used in the tables in this chapter to denote the autoregressive test. The led values were one quarter ahead for the quarterly countries and one year ahead for the annual countries. This means that no moving average process of the error term has to be accounted for since the leads are only one period. The estimation periods used for the leads test were one period shorter than the regular periods because of the need to make room at the end of the sample for the led values. One of the additional variables added, where appropriate, was the expected rate of inflation. As discussed in Chapter 5, this is a test of the nominal versus real interest rate specification. For the quarterly countries the expected rate of inflation was taken to be the actual rate of inflation during the past four quarters, and for the annual countries it was taken to be the inflation rate (at an annual rate) during the past two years. This measure of the expected rate of inflation will be denoted p^{e}. This variable was only added to the equations in which an interest rate was included as an explanatory variable in the final specification. Specification
The extra theorizing that is discussed at the beginning of Chapter 5 is also relevant here. For example, the searching procedure was the same as that used for the US equations. Lagged dependent variables were used extensively to try to account for expectational and lagged adjustment effects, and explanatory variables were dropped from the equations if they had coefficient estimates of the wrong expected sign. Both current and one quarter lagged values were generally tried for the price and interest rate variables for the quarterly countries, and the values that gave the best results were used. The equations were initially estimated under the assumption of a first order autoregressive error term, and the autoregressive assumption was retained if the estimate of the autoregressive coefficient was significant. Data limitations prevented all 15 equations from being estimated for all 37 countries. Also, some equations for some countries were initially estimated and then rejected for giving what seemed to be poor results. One difference between the US and ROW models to be aware of is that the asset variable A for each country in the ROW model measures only the net asset position of the country visavis the rest of the world; it does not include the domestic wealth of the country. Also, the asset variable is divided by PY^{.}YS before it is entered as an explanatory variable in the equations. (PY is the GDP index and YS is potential GDP.) This was done even for equations that were otherwise in log form. As discussed in Section 3.3.3, the asset variable is off by a constant amount, and so taking logs of the variable is not appropriate. Entering the variable in ratio form in the equations allows the error to be approximately[Footnote 1: If the level error, say A^{*}, is in A and not in A/(PY^{.}YS), then including the latter variable in the equation means that it is not A^{*} but A^{*}/(PY^{.}YS) that is part of the equation, and A^{*}/(PY^{.}YS) is not constant. This is what is meant by the error being only approximately absorbed in the estimate of the constant term.] absorbed in the estimate of the constant term. This procedure is, of course, crude, but at least it somewhat responds to the problem caused by the level error in A. Because much of the specification of the ROW equations is close to that of the US equations, the specification discussion in this chapter is brief. Only the differences are emphasized, and the reader is referred to Chapter 5 for more detail regarding the basic specifications. The Tables
There are obviously a lot of estimates and test results in this chapter, and it is not feasible to discuss each estimate and test result in detail. The following discussion tries to give a general idea of the results, but the reader is left to pour over the tables in more detail if desired. 
6.2 Equation 1. IM: Total Imports 
Equation 1 explains the total real per capita imports of the
country. The explanatory variables include price of domestic goods
relative to the price
of imports, per capital expenditures on consumption plus investment plus
government spending, and the lagged dependent variable. The
variables are in logs.
Equation 1 is similar to equation 27
in the US model. The main difference is that the expenditure
variable includes government spending, which it does not in
equataion 27.
The results in Tables 6a and 6b for equation 1 show that reasonable import equations seem capable of being estimated for most countries. The coefficient estimate for the expenditure variable is of the expected sign for all countries, and many of the estimates of the coefficients of the relative price variable are significant. 3 of the 29 equations fail the lags test (at the one percent level), 18 of 29 fail the RHO+ test, and 14 of 29 fail the T test. 22 of 27 fail the stability test. For the countries in which the relative price variable was used, the log of the domestic price level was added to test the relative price constraint. The constraint was rejected (i.e., logPY was significant) in 8 of the 23 cases. The overall test results are thus not strong except for the lags test. 
6.3 Equation 2: C: Consumption 
Equation 2 explains real per capita
consumption.
The explanatory variables include the short term or long term interest
rate, per capita
income, the lagged value of real per capita assets, and the lagged
dependent variable. The
variables are in logs except for the interest rates and the asset
variable. Equation 2 is
similar to the consumption equations in the US model. The two main
differences are 1)
there is only one category of consumption in the ROW model compared to
three in the US
model and 2) the income variable is total GDP instead of disposable
personal income.
As was the case for equation 1, the results in Tables 6a and 6b for equation 2 show that reasonable consumption equations seem capable of being estimated for most countries. The interest rate and asset variables appear in many of the equations in Table 6.2a, and so interest rate and wealth effects on consumption have been picked up as well as the usual income effect. Regarding the tests in Table 6.2b for equation 2, 5 of 34 fail the lags test, 9 of 34 fail the RHO+ test, 10 of 34 fail the T test, and 16 of 32 fail the stability test. The led value of the income variable was used for the leads test, and it is significant in only 5 of the 32 cases. The expected inflation variable is relevant for 21 countries, and it is only significant for 2. This is thus evidence against the use of real versus nominal interest rates in the consumption equations. 
6.4 Equation 3: I: Fixed Investment 
Equation 3 explains real fixed investment. It includes as
explanatory variables the lagged value of investment, the current value
of output, and the
short term or long term interest rate. The variables are in logs except
for the interest
rates. Equation 3 differs from the investment equation 12 for the US, which
uses a capital stock series. Sufficient data are not available to
allow good capital stock series to be constructed for most of
the other countries, and so no capital stock series were constructed
for the ROW model. The simpler equation just mentioned was estimated
for each country.
The results for equation 3 in Table 6a show that most of the estimated output coefficients are significant and that many of the estimated interest rate coefficients are. The test results in Table 6b are mixed. The lags test is not passed in 15 of 32 cases; the RHO+ test is not passed in 15 of 32 cases; and the T test is not passed in 15 of 32 cases. The dynamic and trend properties are thus not well captured in a number of the cases. The led value of output was used for the leads test, and in only 4 of 32 cases is the led value significant. Equation 3 fails the stability test in 16 of 30 cases. In only 1 of the 20 relevant cases is the price expectations variable significant, which is evidence against the use of real over nominal interest rates. 
6.5 Equation 4: Y: Production 
Equation 4 explains the level of production. It is the
same as
equation 11 for the US model, which is equation 5.22 in Chapter 5. It
includes as
explanatory variables the lagged level of production, the current level
of sales, and the
lagged stock of inventories.
The value of q presented in Table 6a for equation 4 is one minus the coefficient estimate of lagged production. Also presented in the table are the implied values of a and b. The parameters q, a, and b are presented in equations 5.195.21. a and q are adjustment parameters. For the quarterly countries q ranges from .469 to .875 and a ranges from .009 to .422. For the annual countries q ranges from .559 to .952 and a ranges from .067 to .255. For the United States q was .6318 and a was .5511. Equation 4 does well in the tests in Table 6b except for the stability test. 3 of the 18 equations fail the lags test; 3 of 18 fail the RHO+ test; 2 of 18 fail the T test; and 7 of 18 fail the leads test. The led value of sales was used for the leads test. The equation fails the stability test in 7 of 17 cases. As was the case for equation 11 in the US model, the coefficient estimates of equation 4 are consistent with the view that firms smooth production relative to sales, and so these results add support to the production smoothing hypothesis. 
6.6 Equation 5: PY: Price Index 
Equation 5 explains the GDP price index. It is the same
as equation
10 for the US model except for the use of different demand pressure
variables.
It includes as explanatory variables the lagged
price level, the
price of imports, the wage rate, a demand pressure variable, and a time
trend.
Up to 6 demand pressure variables were tried per country in an attempt to estimate the nonlinearity between the level of the unemployment rate or output to the price level that seems likely to exist at low levels of the unemployment rate or high levels of output. Two functional forms were tried for the unemployment rate (when data on the unemployment rate existed for a country). In addition, two other activity variables, both measures of the output gap, were tried in place of the unemployment rate. Two functional forms were also tried for each gap variable. Let u_{t} denote the unemployment rate, and let u_{t}' = u_{t}u^{min}, where u^{min} is the minimum value of the unemployment rate in the sample period (t=1, ..., T). The first form tried was linear, namely D_{t} = u_{t}'. The other was D_{t} = 1/(u_{t}'+ .02). For the second form D_{t} is infinity when u_{t}' equals .02, and so this form says that as the unemployment rate approaches 2.0 percentage points below the smallest value it reached in the sample period, the price level approaches infinity. The smaller is a, the more nonlinearity there is near the smallest value of the unemployment rate reached in the sample period. For the first outputgap variable, the potential output series, YS, was used. Define the gap, denoted GAP_{t}, as (YS_{t}  Y_{t})/YS_{t}, where Y_{t} is the actual level of output, and let GAP_{t}' = GAP_{t}  GAP^{min}, where GAP^{min} is the minimum value of GAP_{t} in the sample period. For this variable the first form was linear, and the other was D_{t} = 1/(GAP_{t}' + .02). For the second outputgap variable, a potential output series was constructed by regressing, over the sample period, logY_{t} on a constant and t. The gap GAP_{t} is then defined to be logY_{t}^{^}  logY_{t}^{^}, where logY_{t}^{^} is the predicted value from the regression. The rest of the treatment is the same as for the first outputgap variable. Two functional forms for the unemployment rate and two each for the outputgap variables yields 6 different variables to try. In addition, each variable was tried both unlagged and lagged once separately, giving 12 different variables. This searching was done under the assumption of a first order autoregressive error term, and the autoregressive coefficient was estimated along with the other coefficients. In addition, three other variables were added to the equation during the searching: the price level lagged twice, the wage rate lagged once, and the price of imports lagged once. The demand pressure variable chosen for the "final" equation was the one with the coefficient estimate of the expected sign and the highest tstatistic. No variable was chosen if the coefficient estimates of all the demand pressure variables were of the wrong sign. Once the demand pressure variable was chosen, three further specification decisions were made based on the estimates using the chosen demand pressure variable. The first decision is whether the current wage rate or the lagged wage rate should be included in the final specification, the second is whether the current import price or the lagged import price should be included, and the third is whether the autoregressive assumption about the error term should be retained. For each of the first two decisions the variable with the higher tstatistic was chosen provided its coefficient estimate was of the expected sign, and for the third decision the autoregressive assumption was retained if the autoregressive coefficient estimate was significant at the 5 percent level. If when tried separately both the current wage rate and the lagged wage rate had coefficient estimates of the wrong sign, neither was used, and similarly for the current import price and the lagged import price. Once the final specification of equation 5 was chosen for each country, various tests were performed on it. The results in Table 6a for equation 5 show that the price of imports is significant in most of the cases. Import prices thus appear to have important effects on domestic prices for most countries. A demand pressure variable (denoted DP in Table 6a) appears in 27 of the 32 equations. When the functional form of the demand pressure variable is linear, the coefficient estimate is expected to be negative, and otherwise it is expected to be positive. Although not directly shown in the table, the linear form was chosen for all the countries except JA. There is thus little evidence that nonlinear relationships can be picked up. For the measure of demand pressure, the unemployment rate was used for the UK; the first gap variable was used for CA, GE, GR, SP, CO, PA, PH, and CE; and the second gap variable was used for the rest. The variable was unlagged (as opposed to lagged once) for IT, CO, MA, TH, CH, and ME. Equation 5 does fairly well in the tests in Table 6b except for the stability test. The first lags test is passed in 25 of 32 cases, and the second lags test is passed in 24 of 32 cases. Only 10 of 32 equations fail the RHO+ test. The led value of the wage rate was used for the leads test. The wage rate appears in 12 equations, and of these 12 equations, only 3 fail the leads test. On the other hand, 18 of 29 equations fail the stability test. 
6.7 Equation 6: M1: Money 
[Footnote 6: Money demand equations are estimated in
Fair (1987)
for 27 countries, and the results in this section are essentially an
update of these
earlier results.]
Equation 6 explains the per capita demand for money. It is the same as equation 9 for the US model. The same nominal versus real adjustment specifications were tested here as were tested for US equation 9 (and for the US equations 17 and 26). Equation 6 includes as explanatory variables one of the two lagged money variables, depending on which adjustment specification won, the short term interest rate, and income. The estimates of equation 6 in Table 6a show that the nominal adjustment specification won in 12 of the 17 cases, and so this hypothesis continues its winning ways. Table 6b shows that equation 6 does well in the tests. Only 1 of the 17 equations fails the lags test; 4 of 17 fail the RHO+ test; 3 of 17 fail the T test; and 6 of 16 fail the stability test. The nominal versus real (NvsR) test results in Table 6b simply show that adding the lagged money variable that was not chosen for the final specification does not produce a significant increase in explanatory power. 
6.8 Equation 7: RS: Short Term Interest Rate 
Equation 7 explains the short term (three month) interest
rate. It
is interpreted as the interest rate reaction function of each country's
monetary
authority, and it is similar to equation 30 in the US model. The
explanatory variables
that were tried (as possibly influencing the monetary authority's
interest rate decision)
are 1) the rate of inflation, 2) two demand pressure variables, ZZ and
JJS, 3) the German short
term interest rate (for the European countries only), and 4) the U.S.
short term interest
rate. The U.S. interest rate was included on the view that
some monetary
authorities' decisions may be influenced by the Fed's decisions.
Similarly, the German
interest rate was included in the (non German) European equations on the
view that the
(non German) European monetary authorities' decisions may be influenced
by the decisions
of the German central bank.
The results for equation 7 show that the inflation rate is included in 14 of the 24 cases, a demand pressure variable in 11 cases, the German rate in 7 cases, and the U.S. rate in 16 cases. There is thus evidence that monetary authorities are influenced by inflation and demand pressure. Equation 7 does very well in the tests in Table 6b. None of the 24 equations fails the lags test, only 5 fail the RHO+ test, only 3 fail the T test, and 9 fail the stability test. This is quite a strong showing. 
6.9 Equation 8: RB: Long Term Interest Rate 
Equation 8 explains the long term interest rate. It is
the same as
equations 23 and 24 in the US model. For the quarterly countries the
explanatory variables
include the lagged dependent variable and the current and two lagged
short rates. For the
annual countries the explanatory variables include the lagged dependent
variable and the
current and one lagged short rates. The same restriction was imposed on
equation 8 as was
imposed on equations 23 and 24, namely that the coefficients on the short
rate sum to one
in the long run.
The test results in Table 6b for equation 8 show that the restriction that the coefficients sum to one in the long run is supported in 18 of the 19 cases. The equation does very well in the other tests. Only 3 equations fail the lags test, only 2 fail the RHO+ test, only 3 fail the T test, and only 4 fail the stability test. The led value of the short term interest rate was used for the leads test, and it is not significant at the one percent level in any of the 19 cases. As noted in Chapter 5, my experience with term structure equations like equation 8 is that they are quite stable and reliable, which the results in Table 6b support. 
6.10 Equation 9 E: Exchange Rate 
Equation 9 explains the country's exchange rate: E for
the non
European countries plus Germany and H for the non German European
countries. E is a
country's exchange rate is relative to the U.S. dollar, and H is a
country's exchange rate
relative to the German mark. An increase in E is a depreciation
of the country's
currency relative to the dollar, and an increase in H is a
depreciation of the
country's currency relative to the mark. The theory behind the
specification of equation 9
is discussed in Chapter 2. See in particular the discussion of the
experiments in Section
2.2.6 and the discussion of reaction functions in Section 2.2.7. Equation
9 is interpreted
as an exchange rate reaction function.
The equations for E and H have the same general specification except that U.S. variables are the base variables for the E equations and German variables are the base variables for the H equations. The following discussion will focus on E.
It will first be useful to define two variables:
r is a relative interest rate measure. RS is the country's short term interest rate, and RS_{US} is the U.S. short term interest rate (denoted simply RS in the US model). RS and RS_{US} are divided by 100 in the definition of r because they are in percentage points rather than percents. Also, the interest rates are at annual rates, and so the term in brackets in the definition of r is raised to the .25 power to put r at a quarterly rate. For the annual countries .25 is not used. p is the relative price level, where PY is the country's GDP deflator and PY_{US} is the U.S. GDP deflator (denoted GDPD in the US model). [Footnote x: The relative interest rate is defined the way it is so that logs can be used in the specification below. This treatment relies on the fact that the log of 1 + x is approximately x for small values of x.]
The equation for E
is based on the following two equations. The use of the relative price level in equation 6.6 is consistent with the theoretical model in Chapter 2. In this model a positive price shock led to a depreciation of the exchange rate. (See experiments 3 and 4 in Section 2.2.6.) In other words, there are forces in the theoretical model that put downward pressure on a country's currency when there is a relative increase in the country's price level. Because equation 6.6 is interpreted as an exchange rate reaction function, the use of the relative price level in it is in effect based on the assumption that the monetary authority goes along with the forces on the exchange rate and allows it to change in the long run as the relative price level changes. Similarly, the use of the relative interest rate in equation 6.6 is consistent with the theoretical model, where a fall in the relative interest rate led to a depreciation. (See experiments 1 and 2 in Section 2.2.6.) Again, the assumption in equation 6.6 is that the monetary authority goes along with the forces on the exchange rate from the relative interest rate change. Equations 6.6 and 6.7 imply that The equations for the European countries (except Germany) are the same as above with H replacing E, RS_{GE} replacing RS_{US}, and PY_{GE} replacing PY_{US}. Exchange rate equations were estimated for 25 countries. For a number of countries the estimate of the coefficient of the relative interest rate variable was of the wrong expected sign, and in these cases the relative interest rate variable was dropped from the equation. Also, for eight countriesJA, AU, IT, NE, DE, IR, PO, and NZthe estimate of q in equation 6.8 was very small ("very small" defined to be less than .025), and for these eight countries the equation was reestimated with q constrained to be .050. The results for equation 9 in Table 6a show that for the quarterly countries the relative interest rate variable appears in 7 of the 13 equations. Two of these countries are Japan and Germany, which are important countries in the model, and so in this sense the relative interest rate variable is important. The unconstrained estimates of q in the equation vary from .033 to .242 for the quarterly countries and from .052 to .498 for the annual countries. A small value for q means that it takes considerable time for the exchange rate to adjust to a relative price level change. Equation 9 does fairly well in the tests in Table 6b. The restriction discussed above that is tested by adding logE_{1} to the equation is rejected in 9 of the 25 cases. Only 5 equations fail the lags test; 7 fail the RHO+ test; 8 fail the T test; and 11 of 24 fail the stability test. The key German exchange rate equation passes all the tests, as does the Japanese equation. Since equation 9 is in log form, the standard errors are roughly in percentage terms. The standard errors for a number of the European countries are quite low, but remember that these are standard errors for H, not E. The variance of H is much smaller than the variance of E for the European countries. Exchange rate equations are notoriously hard to estimate, and given this, the results in Tables 6a and 6b do not seem too bad. The test results suggest that most of the dynamics have been captured and that more than half the equations are stable. 
6.11 Equation 10 F: Forward Rate 
Equation 10 explains the country's forward exchange rate,
F. This
equation is the estimated arbitrage condition, and although it plays no
role in the model,
it is of interest to see how closely the quarterly data on EE, F, RS, and
RS_{US} match the
arbitrage condition. The arbitrage condition in this notation is F/EE = [(1 + RS/100)/(1 + _{US}/100)]^{.25} In equation 10, logF is regressed on logEE and .25log(1 + RS/100)/(1 + USRS/100). If the arbitrage condition were met exactly, the coefficient estimates for both explanatory variables would be one and the fit would be perfect. The results in Table 6a for equation 10 show that the data are generally consistent with the arbitrage condition, especially considering that some of the interest rate data are not exactly the right data to use. Note the tstatistic for Switzerland of 14,028.30! 
6.12 Equation 11 PX: Export Price Index 
Equation 11 explains the export price index, PX. It
provides a link
from the GDP index, PY, to the export price index. Export prices are
needed when the
countries are linked together (see Table B.4 in Appendix B). If a country
produced only
one good, then the export price would be the domestic price and only one
price equation
would be needed. In practice, of course, a country produces many goods,
only some of which
are exported. If a country is a price taker with respect to its exports,
then its export
prices would just be the world prices of the export goods. To try to
capture the in
between case where a country has some effect on its export prices but not
complete control
over every price, the following equation is postulated: (6.11) PX = PY^{q}(PW$(^{.}E/E95))^{1q} PW$ is the world price index in dollars, and so PW$(^{.}E/E95) is the world price index in local currency. Equation 6.11 thus takes PX to be a weighted average of PY and the world price index in local currency, where the weights sum to one. Equation 11 was not estimated for any of the major oil exporting countries, and so PW$ was constructed to be net of oil prices. (See equations L4 in Table B.4.) Equation 6.11 was
estimated in the following form: Equation 11 was estimated for 33 countries. For 2 of the countries (SY and MA) the estimate of q was greater than 1, and for these cases the equation was reestimated with q constrained to be 1. When q is 1, there is a one to one link between PX and PY. For 7 of the countries (GR, PO, CH, AR, CE, ME, and PE) the estimate of q was less than 0, and for these cases the equation was reestimated with only the constant term as an explanatory variable. When this is done, there is a one to one link between PX and PW$(^{.}E/E95). Equation 11 was estimated under the assumption of a second order autoregressive error term. The results in for equation 11 in Table 6a show that the estimates of the autoregressive parameters are generally large. Equation 11 does moderately well in the tests in Table 6b. The restriction discussed above is rejected in 15 of 33 cases. The equation fails the stability test in 7 of 29 cases. It should be kept in mind that equation 11 is meant only as a rough approximation. If more disaggregated data were available, one would want to estimate separate price equations for each good, where some goods' prices would be strongly influenced by world prices and some would not. This type of disaggregation is beyond the scope of model. 
6.13 Equation 12: W: Wage Rate 
Equation 12 explains the wage rate. It is similar to
equation 16
for the US model. It includes as explanatory variables the lagged wage
rate, the current
price level, the lagged price level, a demand pressure variable, and a
time trend.
The same restriction imposed on the
price and wage equations in the US model is also imposed here. Given the
coefficient
estimates of equation 5, the restriction is imposed on the coefficients
in equation 12 so
that the implied real wage equation does not have the real wage depend on
either the
nominal wage rate or the price level separately. (See the discussion of
equations 5.35,
5.36, and 5.37 in Section 5.4.)
The same searching for the best demand pressure variable was done for the wage equation as was done for the price equation. This searching was done without imposing the coefficient restriction in (11) and under the assumption of a first order autoregressive error term. The estimates of equation 12 in Table 6a show some support for the demand pressure variables having an effect on the wage rate. A demand pressure variable (denoted DW) appears in 9 of the 11 equations. Again, when the functional form of the demand pressure variable is linear, the coefficient estimate is expected to be negative, and otherwise it is expected to be positive. Although not directly shown in the table, the linear form was chosen for all the countries. For the measure of demand pressure, the first gap variable was used for FR and SW; the second gap variable was used for JA, UK, AS, KO, GR, and SP; and the unemployment rate was used for IT. The variable was lagged once (as opposed to unlagged) for JA, IT, GR, and SP. The test results in Table 6b show that the real wage restriction is rejected in only 1 of the 11 cases. 1 of 11 equations fails the lags test; 2 of 11 fail the RHO+ test; and 10 of 11 fail the stability test. The test results are thus good except for the stability results, which are poor. 
6.14 Equation 13: J: Employment 
Equation 13 explains the change in employment. It is in
log form,
and it is similar to equation 13 for the US model. It includes as
explanatory variables
the amount of excess labor on hand, the change in output, the lagged
change in output, and
a time trend. Equation 13 for the US model does not include the lagged
change in output
because it was not significant. On the other hand, US equation 13
includes terms designed
to pick up a break in the sample period, which equation 13 does not, and
it includes the
lagged change in employment, which equation 13 does not.
Most of the coefficient estimates for the excess labor variable are significant in Table 6a for equation 13, which is at least indirect support for the theory that firms at times hold excess labor and that the amount of excess labor on hand affects current employment decisions. Most of the change in output terms are also significant. Equation 13 fails the lags test in 6 of the 15 cases, and it fails the RHO+ test in 4 of 15 cases. The led value of the change in output was used for the leads tests, and it was not significant in any case. The equation fails the stability test in 7 of 14 cases. 
6.15 Equation 14: L1: Labor ForceMen; Equation 15: L2: Labor ForceWomen 
Equations 14 and 15 explain the labor force participation
rates of
men and women, respectively. They are in log form and are similar to
equations 5, 6, and 7
in the US model. The explanatory variables include the real wage, the
labor constraint
variable, a time trend, and the lagged dependent variable.
The labor constraint variable is significant in many cases for equations 14 and 15 in Table 6a, which provides support for the discouraged worker effect. There is no real support for the real wage. It appears in only 2 cases for equation 14 and in only 4 cases for equation 15. When the real wage appeared in the equation, the log of the price level was added to the equation for one of the tests to test the real wage restriction. Table 6b for equations 14 and 15 shows that the log of the price level is significant in 2 of the 6 cases. Table 6b shows that equation 14 fails the lags test in 2 of 13 cases and the RHO+ test in 2 of 13 cases. Equation 15 fails the lags test in 3 of 11 cases and the RHO+ test in 3 of 11 cases. Both equations do poorly in the stability test. Equation 14 fails 9 of 12 cases, and equation 15 fails 10 of 11 cases. 
6.16 The Trade Share Equations 
As discussed in Chapter 3, a_{ij} is the fraction
of
country i's exports imported by j, where i runs from 1 to 58 and j runs
from 1 to 59. The
data on a_{ij} are quarterly, with observations for most ij pairs
beginning in
1960:1.
One would expect a_{ij} to depend on country i's export
price relative to an index of export prices of all the other countries.
The empirical work
consisted of trying to estimate the effects of relative prices on
a_{ij}. A
separate equation was estimated for each ij pair. The equation is the
following: With i running from 1 to 58, j running from 1 to 59, and not counting i=j, there are 3364, (= 58 x 58) ij pairs. There are thus 3364 potential trade share equations to estimate. In fact, only 1382 trade share equations were estimated. Data did not exist for all pairs and all quarters, and if fewer than 26 observations were available for a given pair, the equation was not estimated for that pair. A few other pairs were excluded because at least some of the observations seemed extreme and likely suffering from measurement error. Almost all of these cases were for the smaller countries. Each of the 1382 equations was estimated by ordinary least squares. The main coefficient of interest is b_{ij3}, the coefficient of the relative price variable. Of the 1382 estimates of this coefficient, 74.5 percent (1030) were of the expected negative sign. 33.9 percent had the correct sign and a tstatistic greater than two in absolute value, and 56.2 percent had the correct sign and a tstatistic greater than one in absolute value. 5.9 percent had the wrong sign and a tstatistic greater than two, and 13.2 percent had the wrong sign and a tstatistic greater than one. The overall results are thus quite supportive of the view that relative prices affect trade shares. The average of the 1030 estimates of b_{ij3} that were of the right sign is .0148. b_{ij3} measures the short run effect of a relative price change on the trade share. The long run effect is b_{ij3}/(1b_{ij2}), and the average of the 1030 values of this is .0780. The trade share equations with the wrong sign for b_{ij3} were not used in the solution of the model. The trade shares for these ij pairs were taken to be exogenous. It should be noted regarding the solution of the model that the predicted values of a_{ijt}, say, ^{^}a_{ijt}, do not obey the property that SUM^{58}_{i=1}^{^}a_{ijt} = 1. Unless this property is obeyed, the sum of total world exports will not equal the sum of total world imports. For solution purposes each ^{^}a_{ijt} was divided by SUM^{58}_{i=1}^{^}a_{ijt} = 1, and this adjusted figure was used as the predicted trade share. In other words, the values predicted by the equations in 6.13 were adjusted to satisfy the requirement that the trade shares sum to one. 
6.17 Additional Comments 
The following are a few general remarks about the results
in this
chapter.
