Forecasting Japanese GDP:
How Will U.S. Imports and Exports Be Affected?
College of Business
Western Carolina University
Japan's phenomenal economic growth during the post war period is a testament to the country's industry and trade. Maintenance of large positive net exports has been key to their success maintaining such an abundant surplus in their current account. The U.S., by far the largest consumer of Japanese exports, is inextricably linked to the Japanese economy. Exchange rates play a large role in determining the amount of Japanese goods Americans consume. As the yen depreciates against the dollar, Japanese goods become less expensive and U.S. consumption of those goods rises. The increased demand for Japanese goods increases the demand for yen with which to pay for them, and the robust demand for Japanese goods helps prevent the yen from depreciating. In this manner, exports and imports are influenced by exchange rates and, in turn, influence exchange rates. The magnitude and volume of trade between the U.S. and Japan creates a dependency on one another which is subject to fluctuations based on domestic economic conditions and exchange rates between the two currencies. This paper provides an explanation of how these variables affect each country and forecasts GDP, imports, exports, and exchange rates for Japan and the U.S. for 1998 and 1999. (JEL: C53, F17)
Part 1. Introduction

This paper forecasts U.S. and Japanese GDP, imports, exports and dollar-to-yen exchange rates for the years 1998 and 1999. Some data was not available from 1998, such as Japanese exports and imports, so this paper forecasts two years ahead of the latest year all necessary information is available, 1997. The variables used are: U.S. GDP, explained by U.S. exports, GDP and Japanese GDP; Japanese GDP, explained by Japanese exports, GDP and U.S. GDP; and the Yen/Dollar exchange rate explained by U.S. GDP and Japanese exports.

Real GDP is the most comprehensive measure of national income and output. Growth in both countries' real GDP is necessary to sustain both economies. A forecast downturn of one country's GDP would signal a recession. The recession would affect the imports/exports of the affected country which carries consequences for the other's GDP, since each country's net exports is a function of the other nation's GDP.

The forecast horizon of two years minimizes the possibility of external factors, such as exports and imports with other trading partners, impacting either economy in an unforeseen way. The chances for inaccuracy in a forecast model increase the further out a forecast is made, so the two-year estimate should provide the best blend of accuracy and time. This amount of time is short enough to avoid seriously overstating or understating future GDP.

The rest of this paper is organized as follows: Part 2. presents the data used to forecast GDP, exports, imports and exchange rates; Part 3. presents the theoretical basis for the approach adopted in forecasting GDP, exports, imports and exchange rates; Part 4. presents forecasts for the variables in years 1998 and 1999; Part 5. evaluates the importance of the forecasts for the economy; and Part 6. discusses conclusions for economic policy.

Part 2. Data

Variables were taken from a number of sources, including the St. Louis Federal Reserve Economic Data (FRED), Statistical Abstract of the United States (SAUS), Direction of Trade Statistics Yearbook (DTSY), Japanís Ministry of International Trade and Industry (MITI), the Federal Reserve Board of Governors (FRBG), and the Bank of Japanís Management and Coordination Agency (MCA). U.S. GDP is FRED variable GDPC92, Japanese GDP is SAUS variable GDPC90, U.S. and Japanese imports and exports are reported by the DTSY in nominal dollars and supplemented by MITI in base-year 1990 chained yen, and the exchange rates are FRBG variable EXJPUS.

Most data was in chained 1990 currency so the most convenient way to establish a common base year was to convert all data to real 1990 dollars. Converting U.S. chained 1992 data was accomplished by using the implicit price deflator (IPD) from the U.S. Department of Commerce, Bureau of Economic Analysis. Since the IPD had 1992 for the base year, it became necessary to first convert that data with 1990 as the base year. This was accomplished by changing the quarterly data into yearly averages. Each annual datum was multiplied by 100, and divided by the base-year 1990 IPD. This converted the real data from base-year 1992 to base-year 1990. By multiplying each yearly U.S. GDP figure by the new IPD, U.S. GDP was converted to 1990 dollars.

Since Japanese exports and imports were reported by DTSY in nominal dollars, the dollars had to be converted to real yen. Using the exchange rates reported by the Department of Commerce, the dollars were converted to nominal yen amounts. After that conversion, the yearly nominal yen figures were converted to chained 1990 yen by using the MCAís consumer price index (CPI). The CPI measures the percentage change in consumer prices from the preceding year, making it a proxy for the IPD since the Japanese IPD was not available. After converting Japanese imports and exports to chained 1990 yen, the exchange rates were again used to change these figures to dollars.

Real data, as opposed to nominal data, is a better gauge of performance over a period of time since it removes the effects of inflation. To better evaluate Japanese figures initially reported in dollars, it was necessary to consider the inflationary effects on the yen during each year. For this reason Japanese exports and imports were converted to yen, multiplied by the CPI, then converted back to dollars.

Part 3. Economic Theory: GDP as a Function of Imports and Exports
This forecast assumes all other factors outside the variables being measured are held constant for 1998 and 1999. The annual growth rates for each variable will be calculated over the sample period of the data. The explanatory variables will be lagged 2 years and used to calculate the dependent, or Y, variable. The expenditures approach model is used to explain the effects of imports and exports on GDP:
GDP = C + Ig + G + (X-M)
where C is personal consumption expenditures of households, Ig is gross private domestic investment, G is government purchases, X (exports) minus M (imports) equals net exports. Consumption, investment, and government purchases are held constant.

Establishing the fact that Japanese and U.S. GDP are closely related and both countries domestic aggregate expenditures are affected by domestic exports and the other counties aggregate expenditures, we derive the following explanatory models:

where domestic GDP is a function of domestic exports and foreign GDP.
To test the viability of the preceding functions as forecasting equations, the right-hand-side explanatory data were lagged and lagged domestic GDP was added as an additional explanatory variable:
GDPUS = f(XUS t-2, GDPJPN t-2, GDPUS t-2)
GDPJPN = f(XJPN t-2, GDPUS t-2 ,GDPJPN t-2)
Interestingly, regressions estimated with lagged data had higher explanatory power than regressions with unlagged data.

The foreign exchange model was estimated with the exchange rate being a function of both Japanese exports and U.S. GDP and U.S. Exports and Japanese GDP so that:

er = f(XJPN, GDPUS)
Estimates of these regressions are presented in part 4.
Part 4. Forecast of GDP, Imports, Exports and Exchange Rates
All regressions were estimated with yearly data from 1991 through 1997. The regression estimate for U.S. GDP (with t-statistics in parentheses) is:
GDPUS = -9444.22(-2.92) + .8467(6.45) GDPUS t-2 +
3.477(2.94) GDPJPN t-2 -0.0041(-1.13) XUS t-2
The regression equation indicates that a $1 billion increase in Japanese GDP increases U.S. GDP by $3.477 billion and a $1 billion increase in U.S. exports decreases U.S. GDP by $4.1 million. The result that GDP decreases with an increase in exports runs counter to how GDP is computed. As exports increase, net exports increase and are added to GDP, so this result is necessarily flawed. It may be an artifact of the U.S. experience that U.S. GDP has risen as U.S. exports have fallen (as a percentage of GDP) over the past twenty years. On a positive note, the error is relatively small at .004.

T-statistics for the intercept and U.S. exports, -2.92 and -1.13, are less than 1, which indicate failure to reject the null hypotheses that the coefficients equal zero. The t-statistics for lagged U.S. GDP and Japanese GDP, 6.45 and 2.94, indicate strong rejection of the null hypotheses that the coefficients equal zero. A high adjusted R-square of 0.9934 for this regression indicates the independent variables data points lie very close to the regression line. This means their predicted values will be very close to actual values for the sample period.

While t-statistics test whether individual coefficients are statistically significant, the F-statistic is used to see if all the coefficients taken together are statistically significant. This computed number, 202.55, greatly exceeds the critical value of 7.71, which leads to rejection of the null hypothesis. The critical value is based on the degrees of freedom assigned to the numerator, 1, and denominator, 4, and interpolated on the critical value of the F-distribution chart at the .05 significance level (Oyen, pp. 439).

The regression estimate for Japanese GDP is:

GDPJPN  = 5908.1(0.6080) + -2.236(-0.383) GDPJPN t-2 +
0.828(0.407) GDPUS t-2 - 0.005(-0.154) X JPN t-2

The regression equation indicates that a $1 billion increase in U.S. GDP increases Japanese GDP by $828 million and a $1 billion increase in Japanese exports decreases Japanese GDP by $5 million. As with the previous regression, GDP decreases with an increase in exports. The sum is small, again, only numbering 0.005. All t-statistics for the equation are less than 1, which means the null hypotheses of the coefficients equaling zero cannot be rejected. While these results are independently disappointing, the adjusted R-square is .903 which indicates 90% of variations in Japanese GDP is explained by variation in the right-hand-side (RHS) variables. Also encouraging is the significance of the computed value for the F-statistic, 13.35, exceeding the critical value of 7.71.

The exchange rate regression uses monthly foreign exchange rates of yen per dollar from 1991.1 through 1997.12, taking the mean average of each yearís exchange rates to estimate the forecasting regression with annual data. The regression estimate is:

er = -126.96(-0.301) + 0.055(0.472)XJPN t-2 Ė 0.0008(-0.33) GDPUS t-2
This regression equation indicates a one billion dollar increase in Japanese exports increases the exchange rate by 0.055 yen per dollar and a one billion dollar increase in U.S. GDP decreases the exchange rate by 0.0008 yen per dollar.

This is interesting in that the regression predicts opposite the theoretical approach to how supply and demand influence exchange rates. As Japan exports more of their goods to the U.S., the U.S. demands more yen to pay for the Japanese goods. The increase in demand raises the exchange rates between the two and the yen appreciates. This theoretical approach serves to decrease the amount of yen a dollar buys whereas the regression says the dollar will buy more yen, or that the yen depreciates.

Also worth notice is how an increase in the U.S. GDP causes the yen/dollar exchange rate to fall. By U.S. aggregate expenditures rising, the U.S. is spending more on goods and services. The increase in spending signifies an increase in demand. If this demand is met with Japanese exports, then the model accurately predicts the theory of a dollar purchasing fewer yen as the demand curve for yen shifts right, signifying the yenís appreciation relative to the dollar.

The t-statistics are all less than 1, which signifies failure to reject the null hypotheses that the regression coefficients equalzero. The adjusted R-square is negative, -0.48, which is a clear sign that even after adjusting for the size of the sample and the number of coefficients being estimated, hardly any of the variation in Y is explained by the RHS variables. The F-statistic fails to reject the null hypothesis equaling zero. The computed value of .343 does not exceed the critical value of 9.55. Statistically speaking, this regression bears little similarity to the factors that influence the actual yen/dollar exchange rate.

Upon estimating the future mean yearly yen/dollar exchange rate with the given regression equation, the predicted number of yen per dollar was 138.94. Actual data for the 1998 exchange rates were available and, taking the actual mean yen/dollar exchange rate for 1998, it is very encouraging to see it totaled 130.818, not even a 10 yen difference between actual and predicted values for that year.

Forecasts are summarized in Table 1.

Table 1
Forecast Real Japanese and U.S. GDP (billions of chained 1990 dollars) and Exchange Rates (yen per dollar) for 1998 and 1999
% Chng.
% Chng.
Exchg Rt.
% Chng.
This forecast projects real U.S. GDP to increase 8.45% throughout 1998 and 3.67% throughout 1999. Real Japanese GDP is forecast to grow at negative 3.48% throughout 1998 and positive 4.17% throughout 1999. The yen/dollar exchange rates increase by 7.93% in 1998 and by 6.31% in 1999 which signify a sharply depreciating yen relative to the dollar.
Part 5. Forecast Implications: Surging U.S. GDP,
Troubled Japanese GDP, and a Depreciating Yen
This paper relates the international economics of trade between the U.S. and Japan in the form of domestic exports. Foreign currency exchange, which constitutes the largest amount of transactions of the three markets, is also considered. By comparing trade statistics and aggregate expenditures of these two countries it is hoped that a relative movement of the yen to dollar exchange rate can be accurately predicted. This forecast suggests the U.S. GDP will move along to record growth while the Japanese GDP becomes troubled in 1998 and pulling through in 1999.

It is promising to see a recovery predicted for Japan in 1999. The yen will depreciate against the dollar, possibly linked to a decrease in Japanese domestic exports, which reduces demand for the yen. The rising U.S. economy will bring strength to the dollar which, managed floats held constant, will cause it to appreciate. The opposite pressures on the yen and dollar help to explain the widening predicted gap between the two currencies in 1998 and 1999.

Part 6. Policy Conclusions
Based on predicted growth of U.S. GDP, American aggregate expenditures will be rising. This robust economy will mean a further increase in employment in order to meet the increase in consumption that rising aggregate expenditures signifies. The additional employment will increase the supply of money to laborers while decreasing the government's need for unilateral transfers in the form of unemployment compensation and welfare benefits. The increase in the supply of money will lead to a greater demand for goods, which will further strengthen the U.S. economy. This promises to be a good market for securing a job out of school and selling homes, as increased demand will support price premia for workers and high-end goods.
The weakening Japanese GDP will cause their economy to be more dependent on U.S. consumption of their goods and services to make up for tapering domestic Japanese expenditures. This weakness in their economy should be a good time for the U.S. to push for further trade concessions and additional attempts at opening the relatively closed Japanese economy.
The depreciating yen, if left to float freely, will eventually be a key factor in Japanís recovery. The weakened yen causes Japanese products to be cheaper than the domestic products of the countries Japan exports to. As the price in dollars of Japanese goods falls, our demand for those products will increase and U.S. consumption of Japanese goods will rise. To meet the increasing demand for Japanese goods, more Japanese labor will be hired and production will again increase thus aiding in their recovery. This process will continue and cause the yen to appreciate against the dollar.

U.S. producers should be cautious of the potential for having their prices eventually undercut by cheap imports, and U.S. exporters will certainly face decreasing demand for their products. To protect U.S. producers, the U.S. should consider raising tariffs on some Japanese products in order to offset the effects of the weakened yen, in as far as that would be permitted under WTO regulations. The downside to raising tariffs is the Japanese recovery will be hampered by this restriction on demand for their productivity and U.S. consumers will miss out on price cuts, while U.S. producers will not be subject to economic pressure to cut costs in order to meet the lower prices.