Dynamic factor demand in the Japanese manufacturing industry Dynamic structure of Japanese manufacturing

Purpose – This study investigates the dynamic productionstructureof the Japanese manufacturing industry by usingthe adjustmentcost approach. The studyistoshed some lighton the uniquedynamicstructureof the Japanese manufacturing industry. The study attempts to help design and predict industrial policies that are implemented to enhance domestic investments by the Japanese government. Design/methodology/approach – This study obtains a system of dynamic factor demand and output supply equations by applying the dual approach to the intertemporal value function as represented by the Hamilton – Jacobi equation. By using industrial panel data for 1973 – 2012 of the Japanese manufacturing industry, the study estimates the systemof the behavioralequationsand corresponding elasticities. The study uses hypothesis tests and dynamic elasticities to investigate the dynamic structure of the Japanese manufacturing industry. Findings – Estimation results show that labor and capital are quasi-fixed variables that adjust about 0.2 percent annually to the long-run optimum levels. Estimated adjustment rates are very slow as often presumed about the Japanese manufacturing industry, which uses lifetime employment practice and slow decision- making process in investment decisions. The results also show that output supply and factor demand elasticities vary greatly depending on time horizon. Factor demand increases when its own price increases in the short run, suggesting that factor adjustment is mostly determined factor prices in the past due to sluggish factor adjustment. However, factor demand becomes a normal downward-sloping curve in the long run as factor adjustment gets completed. Originality/value – Japanese manufacturing firms hire employees through lifetime contract to exploit the benefits of dynamic learning-by-doing and execute investments carefully considering all the possible impacts. Under the strategy, adjustment costs for changing workers and capital stock are minimized. Dynamic adjustment model is expected to shed some light on the unique dynamic structure of the Japanese manufacturing industry. However, researches regarding the dynamic factor adjustment of the Japanese manufacturing industry are hard to find. This study is expected to fill the research vacuum.


Introduction
The Japanese manufacturing industry has endured intense transformation since the 1970s. The manufacturing industry restructured itself successfully toward an energy-saving industry after oil shocks in the 1970s, and it introduced automatic production process to cope with eroding price competitiveness after the Plaza Accord in 1985. It tried to eliminate Dynamic structure of Japanese manufacturing overcapacity after the burst of the bubble in the early 1990s, and it undertook strong investments to utilize information technology (IT) since the 2000s. It plunged into depression after the world economic crisis in 2007, and it has been the focus of government industrial policy to boost its competitiveness.
Considering its active transformation, the problem of resource adjustment in the Japanese manufacturing industry can be adequately investigated within a dynamic adjustment cost framework. In this regard, this paper can shed some light on the production structure of the Japanese manufacturing industry.
Continuity of the Japanese manufacturing industry is well known to the world as Japanese firms continue their businesses over generations through booms and busts. The firms endeavor to make perfect their products over the long haul by improving their practices and processes step by step. They hire employees through lifetime contract to exploit the benefits of dynamic learning-by-doing and execute investments carefully considering all the possible impacts. Under the strategy, adjustment costs for changing workers and capital stock are minimized. On the downside, however, factor adjustments are likely to be lumpy due to the lack of frequent adjustments. Dynamic adjustment model is expected to shed some light on the unique dynamic structure of the Japanese manufacturing industry.
The dynamic model provides a consistent theoretical basis for explaining manufacturing investment patterns based on the dynamic optimization of economic agents. Despite their significant implication, researches regarding the dynamic factor adjustment of the Japanese manufacturing industry are hard to find. This study is expected to fill the research vacuum.
In dynamic factor demand models, behavioral equations can be obtained either primarily from the first-order optimization conditions of the Hamilton-Jacobi equation (Berndt et al., 1981;Mortensen, 1973;Nadiri and Prucha, 1989;Treadway, 1970) or dually by applying the envelop theorem to the equation (Epstein, 1981;Epstein and Denny, 1983;McLaren and Cooper, 1980). This study obtains a system of dynamic factor demand and output supply equations by applying the dual approach to the intertemporal value function as represented by the Hamilton-Jacobi equation. By using industrial panel data for 1973-2012 of the Japanese manufacturing industry, the study estimates the system of the behavioral equations and corresponding elasticities. Previous studies applied dynamic factor demand model to empirically investigate the production structure of various industries. For example, Berndt et al. (1981), Epstein and Denny (1983) and Nadiri and Prucha (1996) investigated the US manufacturing industry, and Taylor and Monson (1985), Howard and Chunway (1988) and Vasavada and Chambers (1986) applied the model to the US agricultural industry. These studies used a dynamic factor demand system to test the existence of adjustment costs and dynamic interaction between factor demands. These studies showed that the dynamic factor demand model can deliver factor adjustments responding to changing economic environments. This is very important in accurately analyzing the impacts of industrial policy of the government on factor investment.
Following previous empirical studies, this study will test the hypothesis whether there exists adjustment costs in the Japanese manufacturing industry and whether factor adjustments interact dynamically or not. The study will also investigate what characterizes the structure of the Japanese manufacturing industry, which has not yet been pursued. Currently, the Japanese government applies a set of structural reform and industrial policies to enhance domestic investments. Even though these industrial policies are less heralded than expansionary monetary and fiscal policies, these are a vital part of Abenomics that prepared three arrows to attack economic depression [1]. In particular, the government reduced corporate tax rate from 38 percent to about 30 percent since Prime Minister Abe took office in 2012. The government further reduced it by 5-10 percent for the firms that raised wages by more than 3 percent or invested in selected new technologies in 2018.
In analyzing impacts of industrial policies on investments, the dynamic factor adjustment model can provide an empirical basis for policy analysis in predicting input and output adjustments brought by changing relative prices through industrial policies.
Empirical results of this study show that adjustment coefficients for labor and capital are very low, suggesting the existence of great adjustment costs inherent in the Japanese manufacturing industry. The results also show that elasticities of output supply and factor demand vary greatly depending on time horizon and that there exists disembodied technical change in labor even after the input is adjusted for quality.
The study suggests that policy makers should consider time dimension to assess policy impacts accurately when implementing industrial policies that affect output supply and factor demand. Furthermore, the Japanese government should apply policy measures large enough to overcome sluggish factor adjustment to successfully affect factor investments. In this respect, this study confirms a great corporate tax reduction of 8-18 percent executed by the current government to boost corporate investments.
This study is organized as follows. Section 2 provides a theoretical background for dynamic dual model and gives the functional form of the estimation model. Section 3 discusses the data and estimation results. Section 4 presents the conclusions.

The dynamic factor demand
A perfectly competitive firm maximizes the current stream of future profits over the infinite time horizon at a base period t, yielding the intertemporal value function as follows: (1) where P is the price of output Fð$Þ, V is the price of variable input M, C is the rental price vector of the quasi-fixed input K, r is the real discount rate, I is the gross investment in K, δ is the constant depreciation rate, k is the initial endowment of K, _ K is the net change in K and t is the time trend denoting technical change. Time subscript t is dropped for brevity even though all variables are implicit functions of time.
The value function J ð$Þ represents the optimal value of problem (1) when an interior solution exists. The value function is the long-run profit function for a competitive firm, representing the maximized sum of discounted profit flow over the entire planning horizon. Besides the regularity assumptions that production function Fð$Þ is twice continuously differentiable and concave, it should be further assumed that F _ K <0, lim t→∞ _ KðtÞ ¼ 0 and that J ð$Þ is twice continuously differentiable, convex in prices and concave in quasi-fixed inputs.
A sequence of static optimization problems linked over time can replace the dynamic optimization problem (1), assuming that the firm expects the prices denoting actual market at time t to persist indefinitely. Therefore, decisions made in period t are based on information available in that period containing all relevant information about future prices. Now the static optimization problem can be defined by the Hamilton-Jacobi equation: The Hamilton-Jacobi equation enables us to convert the dynamic problem in (1) into a more manageable form. Especially, the value function is identified as the discounted present value of the current profit plus the marginal value of optimal change in net investment. According to Epstein (1981), the properties of Fð$Þ are fully expressed in the value function J ð$Þ if the Dynamic structure of Japanese manufacturing regularity conditions on Fð$Þ are satisfied, establishing a dynamic duality between Fð$Þ, J ð$Þ and rJð$Þ. The dynamic factor demand and supply functions can be derived by applying the envelope theorem to the Hamilton-Jacobi Eqn (2) as follows: In addition to the regularity properties of the value function, the value function should be affine in capital for consistent aggregation across firms, satisfying J kk ¼ 0 (Blackorby and Schworm, 1982). Furthermore, the value function must have a form such that J kc is not a function of prices, which allows us to express the net demand for quasi-fixed inputs in the flexible accelerator form. The restriction on J kc also facilitates determination of the curvature properties on the production technology. However, convexity of J in prices is sufficient for the existence of the curvature properties if J k is linear in price (Epstein, 1981).
In estimation, a modified general Leontief function is used to specify the value function because the Leontief function satisfies the above requirements and maintains linear homogeneity in prices and concavity in quasi-fixed inputs. The modified generalized Leontief function can be defined as follows: where P is the output price, V is the material price, K is the (2 3 1) vector of quasi-fixed factors where k 1 is the number of employees and k 2 is the fixed capital asset, C is the (2 3 1) vector of corresponding rental prices including the wage rate and the capital rental rate and t represents year. Parameters A, B À1 , E, G and F are each a (2 3 2) matrix, and H is a (1 3 4) vector denoting disembodied technical change.
The dynamic factor demand for the quasi-fixed inputs (5) can be rewritten as follows: where M is an adjustment matrix and K * is the vector of steady-state stocks [2]. In this case, Thus, the optimal net investment demand vector is consistent with the multivariate flexible accelerator model with constant adjustment coefficient (Nadiri and Rosen, 1969).

Data and variables
The data used in this paper represent a balanced panel of Japanese manufacturing industries taken from the Japan Industrial Productivity (JIP) database 2015. Based on the database, a panel of 52 manufacturing industries for 1973-2012 is compiled, from which all the variables required for estimation can be constructed. The sample period starts from the early 1970s in which the Japanese manufacturing dominated the world with successful structural reforms JABES after the oil shocks in the 1970s. Thus, the sample encompasses the dynamic adjustment of manufacturing sector of the Japanese economy through booms in 1980s, structural transformation in 1990s after the burst of bubble in the early 1990s, IT innovation in the 2000s and two quantitative easing monetary policies before and after the world economic crisis in 2007. For the estimations, labor input (k 1 ) is proxied by the number of employees, capital stock (k 2 ) is given by the real amount of tangible fixed assets, intermediate material goods (M) are measured by total value of intermediate input and total value of output (Y) is used for output. Both labor and capital are augmented by respective quality indices provided by the database to account for embodied technical change [3]. The quality of employment is estimated as the weighted average composition of employees in gender, education, age and employment status (full time vs part time) with a weight derived from the ratio of compensation paid to each category of employees. Likewise, the quality of capital stock is estimated by the valueaugmented capital stock with a value defined by the average share of compensation paid for specified capital stock components [4].
Wage rate (c 1 ) is constructed to denote labor price by dividing the total labor cost by the number of working hours [5]. The rental price of capital (c 2 ) is used for capital price, and material price (v) and the output price (p) are represented by an intermediate input deflator and an output deflator, respectively. All nominal variables are converted into 2000 constant prices using deflators obtained from the JIP database 2015. Then, all prices are changed into price indices with their 2000 prices equaling to ones. Table I presents the parameter estimates of the value function (6) obtained by applying the feasible generalized nonlinear least square (FGNLS) method to the system of Eqs (3), (4) and (5), assuming constant real discount rate of 4 percent. In the full model, the symmetry of the value function is imposed with F 12 ¼ F 21 and G 12 ¼ G 21 [6]. Also reported are two additional models that assume independent adjustment of quasi factors ðB 12 ¼ B 21 ¼ 0Þ and no dynamic adjustment of the factors (B 12 ¼ B 21 ¼ 0 and B 11 ¼ B 22 ¼ −1). For all the models, four-fifths of coefficient estimates are statistically significant at the 1 percent significance level, and all the significant estimates are mostly significant at the 1 percent.

Parameter estimation and hypothesis test
The adjustment rates for labor ðM 11 ¼ B 11 þ rÞ and capital ðM 22 ¼ B 22 þ rÞ are estimated as À0.0023 and À0.0020, respectively. The rates are significantly different from À1.0, indicating that both labor and capital are very slow in changing their stocks toward steady-state levels. The estimates suggest that the number of employees and capital stock adjust 0.23 percent and 0.20 percent annually, respectively, to their long-run optimal levels[7]. This implies not only that both factors are quasi-fixed in their nature but changing them requires large adjustment costs.
The estimations suggest that the Japanese manufacturing industry is very slow in moving the number of employees and capital stock toward the long-run optimal levels. The estimations are consistent with business practices of Japanese manufacturing firms that prefer gradual improvement (Kaizen) to rapid innovation. The firms endeavor to make perfect their products over the long haul by improving their practices and processes step by step. They take time to fully utilize technology embodied in machinery and equipment, and they try to modify or fine-tune them to fit their jobs. Because adapting to new capital is slow and thorough, the firms execute investments carefully considering all the possible impacts. On the other hand, craftsmanship is highly valued; so the firms hire employees through lifetime contract to exploit the benefits of dynamic learning-by-doing. After recruiting new employees, the firms try to train and educate them extensively. Therefore, adjustment costs for changing workers and capital stock are great for Japanese manufacturers, which can Dynamic structure of Japanese manufacturing be minimized through gradual adjustment [8]. In this respect, the estimations confirm the sluggish investment behavior of the Japanese manufacturing industry.  Table I. FGNLS estimates for parameters of the value function for dynamic factor demand for Japanese manufacturing JABES Independent adjustment occurs when each quasi-fixed input adjusts to its optimum level independently with B 12 ¼ B 21 ¼ 0. The null hypothesis of independent adjustment is rejected at the 1 percent significance level. Instantaneous adjustment of labor and capital is tested to see if quasi-fixed factors move to their desirable level instantaneously. Instantaneous adjustment of labor (capital) arises when not only B 11 ¼ −1ðB 22 ¼ −1Þ but B 12 ¼ B 21 ¼ 0. The null hypothesis of instantaneous adjustment is rejected for both factors, suggesting the existence of dynamic adjustment of the factors. The tests confirm that the factors are not variable inputs.
The null hypothesis of no technical change, H i ¼ 0 for i 5 1, 2, 3 and 4, is rejected for the sampling period. Also, the null hypothesis of no disembodied technical change in labor, H 3 ¼ 0 is rejected significantly, but the null hypothesis in capital, H 4 ¼ 0 is accepted. The test results suggest that there exists disembodied technical change in labor even after labor input is adjusted for its quality over time. The disembodied technical change occurs in the form of labor usage for the Japanese manufacturing industry during the sampling period. For capital, however, no disembodied technical change suggests that the quality change of capital stock represents well the technical change occurred in capital for the Japanese manufacturing industry during the sampling period.

Short-run and long-run elasticities
Base on the coefficient estimates of the full model, short-run and long-run elasticities are estimated to summarize the dynamic behavior of output supply and input demands. Table III reports estimated elasticities of output supply and input demands for the Japanese manufacturing industry for selected periods.
Own-price output supply elasticity is about 0.0216 in the short run and 0.1578 in the long run. Own-price elasticity of demand for material input is 0.0039 in the short run and À0.0635 in the long run, whereas the elasticities for labor and capital are 0.0000 and 0.0001, respectively in the short run and À0.0024 and À0.0429 in the long run, respectively.
All the elasticities become much larger in the long run, compared to those in the short run. Especially, the demand for both labor and capital does not respond to own-price changes with almost zero elasticity in the short run. The demand for labor and capital is still inelastic in the long run even though its size is much larger in the long run than in the short run. Noticeably, factor input demand responds positively to its own-price changes for every factor in the short run, but the demand becomes negative in the long run. For dynamic models, profitmaximizing behavior does not require input demand to be negative theoretically (Treadway, 1970;Caputo, 1990)[9].
Factor-price output elasticity is the most responsive to capital and the least responsive to labor both in the short run and long run. All the factor inputs are very weak substitutes in production in the short run, except material input and capital, but all of them become complements in the long run. Relation between any pair of factors becomes much stronger in the long run than in the short run, as any cross-price long-run elasticities are much greater than their short-run counterparts. Table IV reports estimated short-and long-run elasticities of output supply and input demands for the Japanese manufacturing industry by four technology sectors following OECD (2011) to consider difference in investment owing to technology disparity.
Noticeably, the demand for labor is the least elastic for the high-technology sector in the long run whereas the demand for capital is the most elastic, compared with the other sectors, in the long run. The estimations suggest that a large and growing number of firms in the hightechnology sector are venture or IT firms consisting mostly of manpower of technicians, programmers, engineers and researchers. These firms concentrate on research activity in designing new products, outsourcing a large portion of manufacturing process. Because high Dynamic structure of Japanese manufacturing technology firms become more specialized in R&D than manufacturing, the firms require less capital as technology level increases. Thus, the demand for labor is relatively less inelastic for the high-technology sector than the other sectors because quality labor is necessity for the high-technology sector. However, firms in the high-technology sector are most flexible in investing in capital.
On the other hand, for firms for traditional manufacturing in the medium-technology sectors, their production is capital intensive. The sectors utilize machinery and equipment greatly with large plants and assembly lines, and the demand for capital is more elastic than the other sectors.

Conclusions
By applying a dynamic factor demand model to the Japanese manufacturing industry, estimation results show that labor and capital are quasi-fixed variables that adjust about 0.2 percent annually to the long-run optimum levels. Estimated adjustment rates are very slow as  Table III. Elasticity of short-and long-run output supply and input demand for the Japanese manufacturing industry for selected periods JABES often presumed about the Japanese manufacturing industry, which uses lifetime employment practice and slow decision-making process in investment decisions. Labor and capital factors are augmented with quality indexes to allow for embodied technical progress in estimation, but disembodied technical change still remains to be observed for labor. This suggests that a portion of technical change is disembodied or quality indexes do not fully represent technical change itself.
The results also show that elasticities of output supply and factor demand vary greatly depending on time horizon. Factor demand increases when its own price increases in the short run, suggesting that factor adjustment is mostly determined by factor prices in the past due to sluggish factor adjustment. However, factor demand becomes a normal downward-sloping curve in the long run as factor adjustment is completed. Labor and capital are substitutes in the short run but become complements in the long run.
Policy makers should consider time dimension in implementing policy measures that affect output supply and factor demand to assess their impacts accurately. The Japanese government should apply policy measures large enough to boost factor investments when implementing an industrial policy because manufacturers respond to policy shocks very  Table IV. Elasticity of short-and long-run output supply and input demand for the Japanese manufacturing industry by technology sectors Dynamic structure of Japanese manufacturing reluctantly to reduce factor adjustment cost. In this respect, this study positively confirms a great corporate tax reduction of 8-18 percent adopted by the current government to boost corporate investment since 2012.
Finally, output loss that firms should bear during the adjustment process provides another concern for policy makers when trying to boost the economy through investment expansion. For this, an industrial policy should be announced well in advance to provide manufacturing firms with sufficient time to prepare for their future adjustments to policy shocks. This can enhance the speed of factor adjustment and reduce the adjustment costs borne by manufacturers during the transition period.