B. Movement of the borrowing constraints in the phase of business cycles

In the previous sections it is found that the investment decision is much affected by the borrowing constraints in many industries. The extent to which the borrowing constraints prevail is measured by the magnitude of the Lagrangian multiplier, which is in turn specified as a function of the land value or the cash flow. The upshot is that we can trace the path of the Lagrangian multiplier or the degree of borrowing constraints over time. Especially we are interested in evaluating the impacts of soaring land prices and abundance of the cash flow on the borrowing constraints in the recent business upturns starting from the fourth quarter of 1986.

The Lagrangian multiplier or the risk premium added on to the nominal discount rate is computed from eqs.(15) and (16) on the basis of the estimates obtained in the previous section. The time paths of the Lagrangian multipliers are depicted in Figure 1-1 to 1-14. They are shown for nine industries where the coefficient of land asset or cash flow in the Lagrangian multiplier is negative: all industries, construction, manufacturing, food and beverages, chemicals, steel, fabricated metal products, wholesale and retail trade, and real estate. One of the common characteristics to many industries is that the Lagrangian multipliers are drastically reduced in size in the middle of 1980's to early 90's. This tendency is notable for construction, manufacturing, steel, wholesale and retail trade, and real estate. As is stressed at the outset, the land price rose at the rate of some 25 % per annum and the cash flow increased a lot in this period and they led to a mitigation of the borrowing constraints.

The sample average of the Lagrangian multiplier is tabulated in Table 3. In Table 3 the sample average is shown in the upper row not only for the whole sample period (the second quarter of 1970 to the third quarter of 1990) but also for the sub-sample periods: the second quarter of 1970 to the third quarter of 1986 and the fourth quarter of 1986 to the third quarter of 1990. For construction, manufacturing, steel, wholesale and retail trade, and real estate industries, the sample average of the latter-half is much smaller than that of the first-half.

For some industries, the Lagrangian multipliers take negative values, or exceed unity. However, to be strict, the range of the Lagrangian multiplier should be between zero and unity, as is clear from eq.(7). It should be noted that the non-negativity condition is guaranteed when the Lagrangian multiplier is specified as an exponential function of the land value or the cash flow instead of the linear specification. We reestimated the Euler equations under this specification. $ ^{[11]} $ The results do not change much qualitatively. In other words, the industries that are trapped into the borrowing constraints under the linear specification are also constrained under the exponential specification. However, there are some quantitative differences in terms of the magnitude of the adjustment cost function and the Lagrangian multipliers estimates. The estimated results under the exponential specification with the Lagrangian multiplier explicitly taken into account are shown in Table 4. The sample average of the Lagrangian multipliers under the exponential specification are given in the