The first term on the right-hand side of equation (2) shows how fluctuations in the capacity utilization rate affect the nominal wage level. Nevertheless, we accept the rate of capacity utilization as an explanatory variable for the nominal wage Phillips curve. The second term on the right-hand side of equation (2) shows that a change in the price of a good affects the rate of change in the level of the nominal wage through bargaining between workers and management.

We specify the demand regime that represents how a change in wage share affects the rate of capacity utilization. The second term on the right-hand side of equation (11) shows how wage share affects the rate of capacity utilization, and the sign of φ2 corresponds to demand regimes.

## 3 Estimation

### Data

However, if φ1Ω2 > Ω1φ2, even under these combinations, the steady-state equilibrium is stable because the state of. The source of value-added nominal output is the corporate statistics, and the GDP deflator is the National Accounts Report. Real capital stock is the average of real fixed capital stock at the beginning and end of the period.

The source of this is the preliminary quarterly estimates of the gross capital stock of private enterprises published by the Bureau of Statistics. Labor input is obtained by multiplying the number of employees by working hours per employee. The source of the number of employees is the Corporation Statistics, and that of working hours per capita is the Monthly Labor Survey published by the Ministry of Health, Labor and Welfare.

Since none of the data series mentioned above are seasonally adjusted, we use them after seasonal adjustment based on X-12-ARIMA programs. The rate of change in each variable is obtained by calculating the rate in each quarterly data series year-on-year. The expected inflation rate pe is obtained by taking a linearly decreasing moving average of the price inflation rates with linearly decreasing weights over the past twelve quarters.8.

### Estimation results

If there are nonsignificant explanatory variables in the estimated outcomes, we retain them as long as the adjusted R-squared value of the estimated equation that includes them is higher than the value of the estimated equation that does not include them. However, if the adjusted R-squared value of the estimated equation increases using lagged data, we accept lagged explanatory variables. In all estimated equations from the p-value of the J-statistic, the null hypothesis that the model specification is correct is not rejected, even at the 10% significance level.

Therefore, the real wage turns out to be procyclical with the capacity utilization rate. Since the sign of Ω1 is negative, the wage share is shown to be countercyclical with the capacity utilization rate. In other words, the Japanese distribution regime was defined as a countercyclical wage share during the study period due to the rigidity of the domestic labor market.

As a result, even though real wages were procyclical to the rate of capacity utilization, wage shares were countercyclical. Since all the stability conditions are satisfied, we can consider that the dynamic system of the rate of capacity utilization and wage share was stable in Japan during the study period. Therefore, wage share was seen to be regulated within a constant range and the dynamic system was stable.

We therefore conclude that the stability of the Japanese economy depended on cooperative relations between the worker and the management.

## 4 Structural changes

### Structural change in the nominal Phillips curve

First, the capacity utilization rate coefficient ut is not statistically significant before 1991, even at the 10% level, while it is statistically significant at the 1% level thereafter. However, for a similar period, Kurosaka and Goto (1987) argue that the Japanese nominal wage was rigid to a change in output because the unemployment rate was stable and the Okun coefficient very large. In other words, in Japan until the 1980s, because most workers were classified as regular, whose employment was strongly secured, the nominal wage did not reflect the change in output, explaining the lack of a correlation between wage change nominal and capacity utilization rate. in 1977Q3–1991Q1.

By contrast, after the 1990s, due to the proportional increase in non-regular workers, nominal wages became sensitive to the change in output. Therefore, there is clear correlation between the change in nominal wage and rate of capacity utilization in 1991Q1-2007Q3. Second, the coefficient of the rate of change in price Pˆt−2 is statistically significant at the 1% level before 1991, while after 1991 it is not statistically significant even at the 10%.

For most of the 1990s and 2000s, inflation was very low or even negative, and it was difficult for firms to allow nominal wages to reflect the change in commodity prices due to the downward rigidity of the former. Therefore, there was no correlation between the change in the nominal wage and the change in the commodity price in Japan after the 1990s.12. However, after the 1990s, the proportion of non-regular workers whose nominal wages were not affected by collective bargaining increased, weakening the impact of labor-management compromise on the nominal wage.

In summary, in Japan after 1991, the effect of the rate of capacity utilization on the nominal wage strengthened, while the effects of the rate of price change and the wage share weakened.

### Structural change in the rate of change in labour productivity

Third, the wage share coefficient ψt−3 is statistically significant at the 1% level before 1991, but not statistically significant even at the 10% level after that. As noted above, the nominal wage until the 1980s was heavily influenced by labor-management cooperation because workers were typically employed on a regular basis with long-term employment contracts. Furthermore, Nakata (2007) demonstrates that after 2000, many large Japanese firms adjusted their employment levels of regular workers, who were heavily insured until the late 1990s.

As before, we check whether this breakpoint is appropriate using Wald and the likelihood ratio tests and find it statistically significant at the 1% level. First, the coefficient of the rate of capacity utilization ut is statistically significant at the 1% level before 2000, while it is not statistically significant after, even at the 10%. Before 2000, labor productivity and output were correlated because firms could not flexibly adjust their labor input in line with a change in output.

However, after 2000 there was no longer a correlation because companies flexibly adjusted their labor input and the labor hoarding effect was lost. Second, the coefficient of the wage share ψt−4 is statistically significant at the 1% level before 2000, while afterward it is not statistically significant, even at the 10% level. This change means that the effect of the creation of the reserve army was lost in the wage share.

In summary, in Japan after 2000, the effects of the capacity utilization rate and the wage share on the rate of change of labor productivity disappeared.

### The stability of dynamics in each period

On the contrary, the wage share was still countercyclical during this period because the employment adjustment remained rigid and the capacity utilization rate had positive effects on labor productivity. During this period there was a combination of profit-led demand and countercyclical wage share and the absolute value of Ω2 fell below that seen in 1977Q3-1991Q1. As a result, the sign of it changed from positive to negative, and therefore the dynamics were unstable.

J The absolute value of Ω2 was small because the mechanism for regulating the wage share through collective bargaining was weakened by the proportional increase in non-regular workers excluded from unions. 1991Q1-2000Q3 corresponds to the 'lost decade' in Japan, the prolonged recession after the bursting of the bubble economy. During this period, Japanese companies suffered from a decline in capacity utilization and a profit squeeze with an increase in the wage share.

During this period, the necessary condition was that the sign of Ω2 was negative and the absolute value of Ω2 large enough due to the combination of a profit-driven demand regime and a countercyclical wage share. In other words, the distributional regime shifted from a countercyclical wage distribution regime to a procyclical wage distribution regime as firms accelerated employment adjustment and with the change. As a result, the combination of demand and distribution regimes resulted in a profit-led demand regime and a procyclical wage share.

Therefore, despite the combination of a profitable demand regime and a countercyclical wage share, the dynamics were stable. During the period 1991Q1–2000Q3, the Japanese economy switched to a labor market-led regime (ie, real wages became procyclical) as the nominal wage reflected the change in output due to the increase in the share of nonregular workers. This proportional increase in the number of non-regular employees also weakened the mechanism of wage share regulation, as collective bargaining had little effect on the wages of non-regular employees.

As a result, dynamics became unstable during this period, leading to the long recession in Japan in the 1990s. In the third quarter of 2000 and the third quarter of 2007, the distributive regime switched from a countercyclical wage share regime to a procyclical wage share regime, as Japanese firms accelerated their employment adjustment and the labor hoarding effect was lost. As a result, the dynamics recovered despite the lack of wage share regulation, as the combination of the profit-oriented demand regime and the procyclical wage share unambiguously stabilized the dynamics.

Some studies of these two types of Phillips curves focus on the effect of monetary policy on macroeconomic stability.13. Second, we did not focus on the employment rate to avoid the problem of overdetermination in our model. Finally, we analyzed structural changes only in terms of the nominal wage Phillips curve and the rate of change in labor productivity.

Notes

The Institutional Structure of the Modern Japanese Economy and the Protracted Recession.” Kyoto University, 2006 (Chapter 5 of the doctoral dissertation in Japanese). An Empirical Analysis of the Income Distribution and Demand Formation Pattern of the Japanese Economy.” Political Economy Quarterly 47, no. Endogenous Technological Change, Income Distribution, and Unemployment Through Class Conflict.” Structural Change and Economic Dynamics 21, no.

Estimated Nonlinearities and Multiple Equilibria in a Model of Distributive-Demand Cycles.” International Review of Applied Economics 25, iss.