Annex I: Analytical Approach
1. One way of estimating potential output is the production function approach which links output to inputs of labor and capital and total factor productivity. Under this approach, the current level of potential output is thought to be that which would emerge from the production function, given the current levels of fixed inputs and sustainable levels of variable inputs. Several institutions and prominent economists have followed this route in estimating potential output and its determinants for Japan with marked differences in the sophistication of the production function or disaggregation of data used.
2. However, it has been found that, in practice, not much is added to the precision of the measures as the uncertainty in pinning down potential output is simply transferred into uncertainty about total factor productivity. In essence, this uncertainty arises from how the sustainable levels of the factor inputs are derived as well as data uncertainty, including the aggregation of data across industries. For example, while both the Cabinet office (CAO) and the Bank of Japan (BoJ) use the traditional production function approach to estimate potential output, the two institutions differ (until recently) in how they define the factor inputs that are necessary for producing one unit of potential output, resulting in markedly different potential output estimates. The CAO defines potential output as that which would emerge from the production function, given the current levels of fixed inputs and sustainable levels of variable inputs; while the BoJ defined (until recently) potential GDP as the level of output that would result from variable inputs at full capacity.
3. Another way of estimating potential output is to use some variant of a filtering technique. What this means is that time-series techniques are used to fit trend lines through the data, and these trends provide the measures of the underlying “equilibrium” values. The trend lines are used to define “gaps”—deviations of actual observed values from these trends—that are, in turn, used to describe the dynamics of, say, inflation or the process of any other variable of interest. The trend lines are determined, at least in part, by their ability to represent these processes.
4. The methodology we use combines the two approaches described above, the production function and a filtering technique. It uses information from both the supply side and the demand side to condition the estimates of potential output. The essential idea behind this approach is that we can profit from considering more than just the data on output. In particular, since we know that there is a link between labor input and output, it may be useful to exploit information about the degree of excess demand in the labor market. Similarly, the behavior of inflation informs us about the likely existence of excess demand/supply in the product market.
5. Our methodology treats the filtering problem as a small system, where the estimates of potential output, trend labor participation, hours worked, capacity utilization, the NAIRU, and some of the parameters of the dynamic model are determined simultaneously, allowing us to account for interactions among unemployment, output, variables inputs, and inflation. The resulting trend-estimates of output, variable inputs, and unemployment rate should be seen as the levels that can be employed without causing inflation to rise or fall.
6. The system consists of four structural equations (see Annex II)—including a production function, a Phillips curve, and a NAIRU, an Okun’s law—and several identities.
The production function, equation (4), links output to hours worked, capital, and total factor productivity, with the share of hours worked and capital fixed at their 1995–2002 average of about 2/3 and1/3, respectively. At potential, hours worked is the product of working age population, trend participation rate, trend average hours worked, and one minus the NAIRU. The trend participation and average hours worked as well as the NAIRU are determined simultaneously, consistent with stable inflation. At the same time, the potential capital stock series is the product of the capital stock and the trend capacity utilization rate. The capital stock series is from the Japan Industry Productivity database. Total factor productivity depends on research and development intensity, the degree of competition, the degree of openness, and past realizations of total factor productivity.
The Phillips curve, equation (2), relates inflation to expected inflation, terms of trade shocks (changes in import prices and oil prices), and the past values of the output gap. The influence of excess demand is captured through the output gap. This model is a backward-looking autoregressive model that has been employed extensively to estimate the parameters of reduced-form expectations-augmented Phillips Curves. Inflation expectations are modeled as a pure distributed lag of past inflation, with a restriction that the coefficients sum to one. The influence of import prices and oil prices pass-through are also added to the inflation process. It is important to stress that, because it is the inflation expectations series that matters in the Phillips Curve, an alternative specification for the inflation expectations process would alter our gap estimates.
The NAIRU equation, equation (7), relates the unemployment rate to the share of old in the labor force, the replacement ratio, and past unemployment rate. The first variable aims to capture the impact of demographic changes on structural unemployment, while the second variable aims to capture that of the generosity of the unemployment insurance system. In particular, this later variable captures how high replacement ratio can raise the structural unemployment rate by lowering the gap between the income from work and the income received on support. It does not, however, fully represent the generosity of the unemployment system as it does not account for conditions on benefits eligibility, such as the minimum amount of time spent in employment required and requirements of enrolling in various schemes for certain groups. The effects of hysteresis in the labor market are captured through the past unemployment rate that introduces some persistence in the dynamics of unemployment. Indeed, it appears that employment protection legislation that complicates hiring and firing decisions raises the average duration of unemployment and the proportion of long-term unemployment (Alain de Serres 2003).
The Okun equation, equation (8), links the movements in unemployment to those in output gap. Some degree of persistence in the dynamics of the unemployment gap is captured by the presence of the lagged values of unemployment gap. By the same token, the resource utilization equation (equation 11) links the capacity utilization rate to the output gap, with excess demand translating into tight capacity.
Annex II. Model’s Equation
(1) Output decomposition
(2) Phillips Curve Equation
(3) Unemployment rate
(4) Stochastic Process for Potential Output
(5)Potential Capital Stock
(6) Stochastic Process for the Output gap
(7) Stochastic Process for the NAIRU
(8) Stochastic Process for the unemployment gap
(9) Capacity Utilization
(10) Stochastic Process for Trend Capacity Utilization
(11) Stochastic Process for the Capacity Utilization Gap
(12) Potential Labor Input
(13) Hours Worked
(14) Stochastic Process for Trend Hours Worked
(15) Stochastic Process for the Hours Worked Gap
(16) Participation Rate
(17) Stochastic Process for Trend Participation Rate
(18) Stochastic Process for the Participation Rate Gap
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Prepared by Papa N’Diaye.
A recent government-sponsored report “Japan’s 21st Century Vision” sets out the importance of raising productivity and reaping the benefits of globalization to avoid deteriorating living standards.
The system of equations (1)-(18) in Annex II has been estimated with the constrained maximum likelihood procedure applying the methodology described in Laxton and N’Diaye (2002) and Benes and N’Diaye (2004) over the period 1964:Q1-2005:Q4.
Innovation is often perceived as the main channel through which competition and openness affect on productivity growth.
The data were provided by the Bank of Japan. The official capital stock series assumes that additional investment is fully productive for a fixed number of years and is then eliminated. See Hara and others (2006) for greater details.
Japan has the lowest level of import penetration amongst OECD countries notwithstanding growing trade linkage with China and other Asian economies. See OECD (2006).
The OECD average R&D intensity is 2.2 percent based on 2003 data.