Estimating potential output is a basic tool in macroeconomics. The growth of potential provides an indicator of the likely evolution of activity over the next few years, while the output gap is central to making policy recommendations on short-term demand management.^{1} The marked contrast between the sparkling performance of the United States economy in the 1990s and the mediocre growth of much of continental Europe and Japan has brought renewed attention to the issue of how best to estimate potential growth and output. In particular, the assessment of how much of Japan’s recent slowdown represents cycle factors versus a slowdown in the growth of potential output is clearly crucial to deciding on the appropriate policy response. If the slowdown is largely cyclical, the solution is to raise aggregate demand, while if more fundamental forces are at work, structural issues should be given greater prominence.

Broadly speaking, there are two methods of estimating the output gap and growth in potential. In the first, the output gap is based on some direct measure of spare capacity, and potential is derived residually—for example, using the Okun coefficient to calculate the gap as a function of the unemployment rate. Alternatively, the level of potential output can be calculated directly, either using trends or structural approaches, such as combining factor inputs through an assumed production function, with the gap being derived residually. In the remainder of this chapter, the former methodology will be referred to as the “demand-side” approach and the latter as the “supply-side” approach. Some researchers have combined these methods using simultaneous equation methods, thereby producing a joint estimate of the two concepts. Examples of such an integrated approach include the simultaneous equation system proposed by Adams and Coe (1990) or the structural vector autoregression method suggested by Blanchard and Quah (1989).^{2}

All of these calculations work best when structural change is relatively limited, as this minimizes the uncertainties associated with measuring the intensity of factor inputs (for example, the natural rate of unemployment). Unfortunately, the 1990s have been a period of particularly significant underlying changes in the Japanese economy, associated with a switch from growth based on capital accumulation and catch-up to greater attention to profitability and innovation. It is an unfortunate fact of life that at the very moment when an estimate of the output gap is most useful, its calculation is also at its most uncertain. To assess these underlying uncertainties, this chapter compares the results from a range of alternative approaches to estimating the output gap and rate of increase in potential output.

Another issue is the degree to which temporary constraints on the supply of output should be reflected in potential, such as the impact of weather on agricultural output or financial intermediation problems on output more generally. In particular, in the case of Japan, should supply constraints associated with financial intermediation problems caused by banking strains (see Chapter 2) be reflected in potential output?^{3} Recalling that potential output represents the level of output at which inflation remains stable (that is, the output equivalent of nonaccelerating inflation rate of unemployment, or the NAIRU), it can be argued that such constraints should be included when the purpose of the exercise is to assess the appropriate stance of demand-management policies—provided they are likely to continue for the period over which changes to aggregate demand are likely to operate. These rigidities affect macroeconomic conditions, and hence the appropriate stance of current policies, while the future relaxation of these constraints can be incorporated in the future growth rate of the potential output of the economy. Demand-side estimates may, in these circumstances, provide a more accurate measure of the short-term movements of potential output, with supply-side approaches being more relevant for assessing medium-term conditions.

## Demand-Side Estimates of the Output Gap

In this section, the output gap is estimated using a series of measures of slack in the economy, namely the unemployment rate, the ratio of job seekers to job offers, capacity utilization, a combination of all of these measures, and an inverted Phillips curve. In all cases, the underlying methodology is similar, involving regressing the logarithm of real GDP on the chosen measure(s) of the output gap, a time trend, a time trend to the power one-half, and a time trend to the power one-third:

where *y _{t}* is real output,

*X*represents the measure(s) of demand pressures,

_{t}*t*is a time trend, ε

_{t}is an error term, and other Greek letters are estimated coefficients.

^{4}Such a regression assumes that the indicators of slack are contemporaneous with the cycle. This is reasonable for many measures, although unemployment is often thought to be a lagging indicator of the cycle, implying that it will tend to measure past values of the output gap.

Equation (5.1) can be used to provide a direct estimate of the output gap, together with a residually estimated level of potential output:

where

As noted earlier, a Phillips curve can be inverted to provide a specification of this type. Starting from a standard linear Phillips curve:

where π_{t} is the four-quarter rate of core inflation and ^{5} To turn equation (5.4) into the form of equation (5.1) simply requires moving the term in the log of output to the right-hand side. In addition, nonlinearities in the Phillips curve can be incorporated by adding a term in the square of the output gap (i.e.,

Table 5.1 reports the results of the demand-side regressions, estimated from the first quarter of 1975 to end-1998 for the measures of economic slack and the beginning of 1982 to end-1998 for the Phillips curves.^{6,7} The coefficients on the first three estimates of economic slack (the unemployment rate, vacancy ratio, and capacity utilization rate) are all highly significant, although, when the three measures are combined into a single regression, the coefficient on capacity utilization (which has the lowest *t*-statistic in the individual regressions) is no longer significant. In the case of the linear Phillips curve, the coefficients are all correctly signed, but only that on the current core inflation rate is significant at conventional levels. When the nonlinear term in the output gap is included in the Phillips curve it is insignificant and has almost no impact on the regression results. All of the regressions show evidence of autocorrelation in the residuals, presumably reflecting correlated changes in the path of potential output.

**Demand-Side Regressions of the Output Gap**

*T*-statistics are reported in parentheses, with one and two asterisks reflecting significance at the 5 and 1 percent level, respectively.

**Demand-Side Regressions of the Output Gap**

Unemployment Rate | Vacancy Ratio | Capacity Utilization | Combined Estimate | Linear Phillips Curve | Nonlinear Phillips Curve | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Unemployment rate | -0.07 | -0.03 | ||||||||||

(11.9) | ** | (4.4) | ** | |||||||||

Ratio of job sectors to job offers | 0.10 | (0.09) | ||||||||||

(16.3) | ** | (7.3) | ** | |||||||||

Capacity utilization rate | 0.33 | 0.00 | ||||||||||

(6.5) | ** | (1.3) | ||||||||||

Core inflation | 1.70 | 1.70 | ||||||||||

(5.7) | ** | (5.6) | ** | |||||||||

Fourth lag of core inflation | -0.67 | -0.67 | ||||||||||

(1.9) | (1.8) | |||||||||||

Imported inflation differential | 0.01 | 0.01 | ||||||||||

(0.6) | (0.5) | |||||||||||

Square of output gap | -0.24 | |||||||||||

(0.0) | ||||||||||||

Time trend | -0.01 | -0.00 | -0.01 | 0.00 | -0.14 | -0.14 | ||||||

(4.2) | ** | (0.9) | (3.2) | ** | (0.1) | (4.6) | ** | (4.5) | ** | |||

Time trend to the power one-half | 0.65 | 0.18 | 0.76 | 0.23 | 8.27 | 8.26 | ||||||

(6.6) | ** | (2.0) | * | (5.8) | ** | (2.6) | ** | (4.2) | ** | (4.1) | ** | |

Time trend to the power one-third | -1.18 | -0.27 | -1.45 | 0.36 | -17.65 | -17.63 | ||||||

(6.0) | (1.6) | (5.6) | ** | (2.0) | * | (4.0) | ** | (3.9) | ** | |||

Adjusted R^{2} | 0.995 | 0.997 | 0.992 | 0.998 | 0.992 | 0.992 | ||||||

DW | 1.05 | 0.37 | 0.17 | 0.76 | 0.74 | 0.74 |

*T*-statistics are reported in parentheses, with one and two asterisks reflecting significance at the 5 and 1 percent level, respectively.

**Demand-Side Regressions of the Output Gap**

Unemployment Rate | Vacancy Ratio | Capacity Utilization | Combined Estimate | Linear Phillips Curve | Nonlinear Phillips Curve | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Unemployment rate | -0.07 | -0.03 | ||||||||||

(11.9) | ** | (4.4) | ** | |||||||||

Ratio of job sectors to job offers | 0.10 | (0.09) | ||||||||||

(16.3) | ** | (7.3) | ** | |||||||||

Capacity utilization rate | 0.33 | 0.00 | ||||||||||

(6.5) | ** | (1.3) | ||||||||||

Core inflation | 1.70 | 1.70 | ||||||||||

(5.7) | ** | (5.6) | ** | |||||||||

Fourth lag of core inflation | -0.67 | -0.67 | ||||||||||

(1.9) | (1.8) | |||||||||||

Imported inflation differential | 0.01 | 0.01 | ||||||||||

(0.6) | (0.5) | |||||||||||

Square of output gap | -0.24 | |||||||||||

(0.0) | ||||||||||||

Time trend | -0.01 | -0.00 | -0.01 | 0.00 | -0.14 | -0.14 | ||||||

(4.2) | ** | (0.9) | (3.2) | ** | (0.1) | (4.6) | ** | (4.5) | ** | |||

Time trend to the power one-half | 0.65 | 0.18 | 0.76 | 0.23 | 8.27 | 8.26 | ||||||

(6.6) | ** | (2.0) | * | (5.8) | ** | (2.6) | ** | (4.2) | ** | (4.1) | ** | |

Time trend to the power one-third | -1.18 | -0.27 | -1.45 | 0.36 | -17.65 | -17.63 | ||||||

(6.0) | (1.6) | (5.6) | ** | (2.0) | * | (4.0) | ** | (3.9) | ** | |||

Adjusted R^{2} | 0.995 | 0.997 | 0.992 | 0.998 | 0.992 | 0.992 | ||||||

DW | 1.05 | 0.37 | 0.17 | 0.76 | 0.74 | 0.74 |

*T*-statistics are reported in parentheses, with one and two asterisks reflecting significance at the 5 and 1 percent level, respectively.

Table 5.2 and Figure 5.1 report the resulting estimates of the output gap and the implied annualized rate of growth of potential output (calculated as a moving average over the previous four years). The results for the nonlinear Phillips curve are not reported as they were virtually identical to the linear version. The estimates of the 1998 output gap fall into a fairly narrow range, varying between -3.6 and -1.8 percentage points of GDP, while the output gap is estimated to have been substantially positive in 1991, at the height of the bubble. The estimates for the rate of growth of potential output in 1998 vary within the relatively limited range of 1.4–2.2 percent, well below values for earlier in the 1980s and early 1990s.^{8} In terms of the contributing factors to the slowdown in activity through the 1990s, the output gap is estimated to have fallen between 3.7 and 9.4 percentage points of GDP between 1991 and 1998, while the rate of growth of potential output is estimated to have been reduced by between 1.1 and 3.0 percent per annum, implying that the slowdown in growth during the 1990s reflects both a marked swing in the output gap and a significant slowing of the growth of potential output.

**Demand-Side Estimates of the Output Gap and Potential Output Growth**

(Percent)

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Demand-Side Estimates of the Output Gap and Potential Output Growth**

(Percent)

Unemployment Rate | Vacancy Ratio | Capacity Utilization | Combined Regression | Phillips Curve | Range | ||
---|---|---|---|---|---|---|---|

Estimated output gap | |||||||

1998 | -3.6 | -2.5 | -2.9 | -3.0 | -1.8 | -3.6 to -1.8 | |

1991 | 3.3 | 6.7 | 2.5 | 6.4 | 1.9 | 1.9 to 6.7 | |

Estimated potential output growth ^{1} | |||||||

1998 | 2.2 | 1.5 | 1.4 | 1.8 | 1.5 | 1.4 to 2.2 | |

1991 | 3.5 | 3.1 | 4.4 | 3.0 | 4.1 | 3.0 to 4.4 | |

Estimated change 1991–98 | |||||||

Output gap | -6.9 | -9.2 | -5.4 | -9.4 | -3.7 | -9.4 to -3.7 | |

Potential output ^{1} | -1.3 | -1.6 | -3.0 | -1.1 | -2.6 | -3.0 to -1.1 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Demand-Side Estimates of the Output Gap and Potential Output Growth**

(Percent)

Unemployment Rate | Vacancy Ratio | Capacity Utilization | Combined Regression | Phillips Curve | Range | ||
---|---|---|---|---|---|---|---|

Estimated output gap | |||||||

1998 | -3.6 | -2.5 | -2.9 | -3.0 | -1.8 | -3.6 to -1.8 | |

1991 | 3.3 | 6.7 | 2.5 | 6.4 | 1.9 | 1.9 to 6.7 | |

Estimated potential output growth ^{1} | |||||||

1998 | 2.2 | 1.5 | 1.4 | 1.8 | 1.5 | 1.4 to 2.2 | |

1991 | 3.5 | 3.1 | 4.4 | 3.0 | 4.1 | 3.0 to 4.4 | |

Estimated change 1991–98 | |||||||

Output gap | -6.9 | -9.2 | -5.4 | -9.4 | -3.7 | -9.4 to -3.7 | |

Potential output ^{1} | -1.3 | -1.6 | -3.0 | -1.1 | -2.6 | -3.0 to -1.1 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

## Time-Series Estimates of Potential Output

The main alternative approach to estimating the output gap involves directly estimating potential output, then calculating the output gap residually. The easiest way of doing this is to assume that potential output follows a univariate time series process associated with the path of real GDP. Estimating from the first quarter of 1975, three approaches of this type were considered, regressing output on a split time trend (with the split occurring in the first quarter of 1990), regressing the logarithm of output on the power sequence of time trends already discussed in the preceding section (that is, time, time to the power one-half, and time to the power one-third), and using a Hodrick-Prescott (HP) filter. As results from an HP filter depend upon the smoothing parameter chosen, the results from two possible values (14,400 and 40,000) are reported.^{9}

The results from the estimation, shown in Table 5.3 and Figure 5.2, again show that the estimates of the output gap in 1998 cluster in a relatively narrow range.^{10} What is striking about this range, however, is that it does not correspond to that found in the earlier demand-side estimates. Compared to the equivalent figures in Table 5.2, the estimates of the 1998 output gap are universally larger (3½-4¾ percentage points of GDP as opposed to 1¾-3½ percentage points) and the estimated rate of growth of potential also tends to be larger. In short, univariate techniques generate significantly higher estimates of the current growth of potential output, and hence the output gap, than do direct measures of economic slack.

**Supply-Side Estimates of the Output Gap and Potential Growth Using Univariate Trends**

(Percent)

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Supply-Side Estimates of the Output Gap and Potential Growth Using Univariate Trends**

(Percent)

Split Time Trend | Power Sequence | Hodrick-Prescott Filter | Range | |||
---|---|---|---|---|---|---|

40,000 | 14,400 | |||||

Estimated output gap | ||||||

1998 | -3.7 | -4.7 | -4.8 | -3.5 | -4.8 to -3.5 | |

1991 | 3.9 | 5.2 | 4.7 | 3.7 | 3.7 to 5.2 | |

Estimated potential output growth ^{1} | ||||||

1998 | 2.1 | 2.3 | 2.2 | 1.8 | 1.8 to 2.3 | |

1991 | 3.3 | 3.1 | 3.3 | 3.5 | 3.1 to 3.5 | |

Estimated change 1991–98 | ||||||

Output gap | -7.6 | -9.9 | -9.5 | -7.2 | -9.9 to -7.2 | |

Potential output ^{1} | -1.2 | -0.8 | -1.2 | -1.7 | -1.7 to -0.8 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Supply-Side Estimates of the Output Gap and Potential Growth Using Univariate Trends**

(Percent)

Split Time Trend | Power Sequence | Hodrick-Prescott Filter | Range | |||
---|---|---|---|---|---|---|

40,000 | 14,400 | |||||

Estimated output gap | ||||||

1998 | -3.7 | -4.7 | -4.8 | -3.5 | -4.8 to -3.5 | |

1991 | 3.9 | 5.2 | 4.7 | 3.7 | 3.7 to 5.2 | |

Estimated potential output growth ^{1} | ||||||

1998 | 2.1 | 2.3 | 2.2 | 1.8 | 1.8 to 2.3 | |

1991 | 3.3 | 3.1 | 3.3 | 3.5 | 3.1 to 3.5 | |

Estimated change 1991–98 | ||||||

Output gap | -7.6 | -9.9 | -9.5 | -7.2 | -9.9 to -7.2 | |

Potential output ^{1} | -1.2 | -0.8 | -1.2 | -1.7 | -1.7 to -0.8 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Trend Estimates of Potential Output**

**Trend Estimates of Potential Output**

**Trend Estimates of Potential Output**

Further, comparing Tables 5.2 and 5.3, we find that this pattern—that the demand-side estimates of the output gap are smaller (in absolute value) than the supply-side estimates—does not hold true for 1991. Hence, the divergence between the demand- and supply-side estimates of the output gap appears to be a recent phenomenon, consistent with it being associated with short-term supply constraints, plausibly associated with financial system difficulties.^{11} Comparing the midpoints of the ranges of estimated output gaps using the two techniques implies that temporary supply constraints may have reduced potential output by 1–2 percentage points of GDP in 1998, with corresponding potential gains from relieving such constraints, although this is clearly a very rough calculation.

## Production Function Approaches

A more sophisticated method of directly estimating the level of potential output is to use a production function. This approach, which is currently used by the Japan desk as well as most other Group of Seven desks in the IMF, postulates an underlying production function, and proceeds to estimate potential output based on suitably adjusted inputs of labor, capital, and an assumed level of technological progress.^{12} In addition to being highly flexible, a major advantage of a production function approach is that it links the evolution of potential output to inputs of labor and capital. Given the need for the IMF staff to integrate estimates of potential output into an overall assessment of past and future trends in the Japanese economy, this link is very useful, particularly in the context of assessing the likely future evolution of the economy, and argues powerfully for maintaining this framework even if it is unlikely to identify temporary supply constraints associated with banking weakness.

In the case of Japan, a Cobb-Douglas production function is assumed, so that potential output can be calculated as:

where *TFP _{t}* is the level of technological progress, β is the share of labor income in GDP, and α is a scaling factor. While conceptually straight-forward, implementing this approach requires a number of judgments, which are best illustrated by reference to the approach currently taken by the Japan desk:

*Hours worked*. This is the product of the trend labor force, average hours worked, and (one minus) the natural rate of unemployment. Each of the components needs to be adjusted for the cycle (as the discouraged worker effect is quite strong in Japan, the labor force is cyclical). This is accomplished using a Hodrick-Prescott filter with a relatively high smoothing parameter (40,000) to minimize the impact of cyclical fluctuations on the trend. Even so, until recently these estimates of the natural rate of unemployment and hours worked were adjusted judgmentally as they were still considered to be likely to be affected by the current cycle.*Capital stock*. As capital is a stock series with limited cyclical variation, the actual level is used rather than a cyclically adjusted estimate. The IMF staff calculate their own capital stock series based on the permanent inventory method with a fixed rate of depreciation. By contrast, the official series assumes that additional investment is fully productive for a fixed number of years and is then eliminated, the so-called “one-horse shay” approach. The disadvantage of the official series is that, because the capital stock does not depreciate steadily over time, the current estimate of capital continues to include large amounts of the investment generated during the bubble period of the late 1980s. Another issue is that there is a widespread perception that much of the investment during the bubble years was not productive, as shown by the large amounts of bad debt in the banking system, and hence that the measured capital stock may overstate the productive capital stock.^{13}*Trend productivity*. This is estimated from actual productivity using a Hodrick-Prescott filter, and again until recently was adjusted judgmentally.

To investigate the importance of alternative assumptions, Table 5.4 shows a number of calculations using the production function approach. Previous desk estimates of the output gap, using a range of judgmental adjustments, are shown first, followed by the results implied by removing all such adjustments. From this new baseline, the effect of reestimating the model using two alternative capital stock series are then reported, namely replacing the IMF staffs capital stock estimate with the official capital stock series and reducing the staff’s estimate of the business capital stock by ¥3 trillion per quarter since the first quarter of 1990 (for a cumulated total of ¥99 trillion, or 20 percent of GDP), the approximate value of the aggregate bad loans in the banking system, in order to approximate the impact of accelerated scrapping of misallocated investments made during the bubble period. The final calculation removes the judgmental adjustments to productivity and the natural rate of unemployment, but retains some adjustments to average hours worked—and represents the series currently used by the IMF Japan desk.^{14}

**Supply-Side Estimates of the Output Gap and Potential Growth Using a Production Function**

(Percent)

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Supply-Side Estimates of the Output Gap and Potential Growth Using a Production Function**

(Percent)

Previous Estimate | Eliminating All Judgmental Adjustments | Using Official Capital Stock | Adjusting Capital for Scrapping | Range | Current Estimate | ||
---|---|---|---|---|---|---|---|

Estimated output gap | |||||||

1998 | -5.7 | -3.6 | -4.0 | -3.5 | -5.7 to -3.5 | -4.1 | |

1991 | 3.0 | 3.6 | 4.1 | 3.3 | 3.0 to 4.1 | 3.5 | |

Estimated potential output growth ^{1} | |||||||

1998 | 2.1 | 1.7 | 1.9 | 1.7 | 1.7 to 2.1 | 1.9 | |

1991 | 3.9 | 3.9 | 3.7 | 3.9 | 3.7 to 3.9 | 3.8 | |

Estimated change 1991–98 | |||||||

Output gap | -8.7 | -7.2 | -8.1 | -6.8 | -8.7 to -6.8 | -7.6 | |

Potential output ^{1} | -1.9 | -2.1 | -1.8 | -2.1 | -2.1 to -1.8 | -1.9 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

**Supply-Side Estimates of the Output Gap and Potential Growth Using a Production Function**

(Percent)

Previous Estimate | Eliminating All Judgmental Adjustments | Using Official Capital Stock | Adjusting Capital for Scrapping | Range | Current Estimate | ||
---|---|---|---|---|---|---|---|

Estimated output gap | |||||||

1998 | -5.7 | -3.6 | -4.0 | -3.5 | -5.7 to -3.5 | -4.1 | |

1991 | 3.0 | 3.6 | 4.1 | 3.3 | 3.0 to 4.1 | 3.5 | |

Estimated potential output growth ^{1} | |||||||

1998 | 2.1 | 1.7 | 1.9 | 1.7 | 1.7 to 2.1 | 1.9 | |

1991 | 3.9 | 3.9 | 3.7 | 3.9 | 3.7 to 3.9 | 3.8 | |

Estimated change 1991–98 | |||||||

Output gap | -8.7 | -7.2 | -8.1 | -6.8 | -8.7 to -6.8 | -7.6 | |

Potential output ^{1} | -1.9 | -2.1 | -1.8 | -2.1 | -2.1 to -1.8 | -1.9 |

^{1}Potential output growth is defined as the annualized growth rate over the last four years.

The results from this exercise are reported in Table 5.4 and Figure 5.3. When the judgmental adjustments applied by the staff are excluded, the estimated output gap for 1998 falls by over one-third, from 5.7 percentage points of GDP to 3.6 percentage points, and the rate of growth of potential output is reduced from 2.1 percent to 1.7 percent. These results approximately span the range of values produced by univariate supply-side estimates, but are larger than their demand-side equivalents.^{15} Switching to the official capital stock series raises both the output gap and potential output growth, while assuming a higher rate of scrapping has little impact on the estimates despite the size of the adjustment. These differences largely reflect the fact that significant short-term changes in behavior, such as judgmental adjustments, tend to be incorporated into the output gap while gradual changes in trends, such as the gradual reduction in the capital stock assumed to be caused by scrapping, is largely offset by changes in estimated trend growth in total factor productivity.

**Production Function Estimates of Potential Output**

**Production Function Estimates of Potential Output**

**Production Function Estimates of Potential Output**

The IMF staff’s current estimate of potential output, which removes most of the judgmental adjustments to the inputs, produces a 1998 output gap of 4.1 percent, at the lower end of the “supply-side” estimates of the output gap but above the results using “demand-side” techniques, and a current rate of growth of potential output of 1.9 percent.

To further examine the evolution of the IMF staff’s estimate of potential output over time, Table 5.5 reports the growth of potential over successive four year periods starting in 1987, 1991, 1995 and 1999, and decomposes the growth into its component parts, for both the current estimate of potential output and the earlier estimate incorporating a wider range of judgmental adjustments. The current series shows the growth in potential falling by almost 1 percent every 4 years, from 3.7 percent in the late 1980s to a projected value of 1.1 percent between 1999 and 2002. The main contributor to this decline is a fall in the growth of capital inputs, followed by lower trend growth in the labor force (particularly over 1999-2002). Trend growth in total factor productivity is also estimated to have declined modestly (by about ⅓ percent over the full period), while a marked decline in trend hours largely associated with a legislated reduction in the work week also lowered potential growth over the period to 1998. The current estimate of the growth rate of potential is consistently between 0.1 and 0.2 percent per annum below the old estimates, reflecting lower estimated trend productivity and trend labor inputs.

**Decomposing the Growth of Potential Output Over Time**

(Annualized percentage change)

**Decomposing the Growth of Potential Output Over Time**

(Annualized percentage change)

1987–90 | 1991–94 | 1995–98 | 1999–2002 | |||
---|---|---|---|---|---|---|

Potential output | ||||||

Current | 3.74 | 2.74 | 1.87 | 1.09 | ||

Previous | 3.88 | 2.86 | 2.07 | 1.20 | ||

Difference | -0.14 | -0.12 | -0.20 | -0.11 | ||

Of which: | ||||||

Labor force | ||||||

Current | 0.76 | 0.62 | 0.46 | 0.08 | ||

Previous | 0.76 | 0.67 | 0.56 | 0.09 | ||

Difference | — | -0.05 | -0.10 | -0.01 | ||

Average hours | ||||||

Current | -0.40 | -0.56 | -0.52 | -0.35 | ||

Previous | -0.40 | -0.56 | -0.49 | -0.18 | ||

Difference | — | — | -0.03 | -0.17 | ||

Capital stock | ||||||

Current | 2.19 | 1.68 | 1.06 | 0.52 | ||

Previous | 2.19 | 1.68 | 1.06 | 0.32 | ||

Difference | — | — | — | -0.20 | ||

Total factor productivity | ||||||

Current | 1.15 | 1.01 | 0.90 | 0.81 | ||

Previous | 1.30 | 1.08 | 0.94 | 0.91 | ||

Difference | 0.15 | 0.07 | 0.04 | 0.10 |

**Decomposing the Growth of Potential Output Over Time**

(Annualized percentage change)

1987–90 | 1991–94 | 1995–98 | 1999–2002 | |||
---|---|---|---|---|---|---|

Potential output | ||||||

Current | 3.74 | 2.74 | 1.87 | 1.09 | ||

Previous | 3.88 | 2.86 | 2.07 | 1.20 | ||

Difference | -0.14 | -0.12 | -0.20 | -0.11 | ||

Of which: | ||||||

Labor force | ||||||

Current | 0.76 | 0.62 | 0.46 | 0.08 | ||

Previous | 0.76 | 0.67 | 0.56 | 0.09 | ||

Difference | — | -0.05 | -0.10 | -0.01 | ||

Average hours | ||||||

Current | -0.40 | -0.56 | -0.52 | -0.35 | ||

Previous | -0.40 | -0.56 | -0.49 | -0.18 | ||

Difference | — | — | -0.03 | -0.17 | ||

Capital stock | ||||||

Current | 2.19 | 1.68 | 1.06 | 0.52 | ||

Previous | 2.19 | 1.68 | 1.06 | 0.32 | ||

Difference | — | — | — | -0.20 | ||

Total factor productivity | ||||||

Current | 1.15 | 1.01 | 0.90 | 0.81 | ||

Previous | 1.30 | 1.08 | 0.94 | 0.91 | ||

Difference | 0.15 | 0.07 | 0.04 | 0.10 |

The calculations can also be used to assess the reasons for the decline in the growth of output over the 1990s. If the estimated rate of growth of potential seen over the late 1980s period had been maintained between 1991 and 1998, potential output would have been over 10 percent higher at the end of the period. By comparison, between 1991 and 1998 the output gap is estimated to have changed by 8½ percentage points of potential, implying that long-term supply trends have a slight preponderance in explaining the slowdown in output compared to demand factors or more temporary constraints on supply.

## Conclusions

This chapter has examined the output gap and potential output growth in Japan using a number of different techniques, focusing on the results from demand indicators and estimates of potential output based on smoothing techniques or a production function. The results within each type of estimate were relatively consistent. However, estimates using demand indicators generally give smaller estimates of the output gap and growth of potential than do supply indicators in 1998, although not in 1991, consistent with the view that demand-side indicators may reflect short-term constraints on potential output while supply-side estimates provide a better assessment of the medium-term situation. Highly stylized calculations imply that such constraints could currently be lowering potential output by a percentage point or two. As a result, demand-side indicators tend to put more weight on a slowdown in potential in explaining the mediocre performance in the 1990s than do direct estimates of potential, although all approaches found both effects to be important.

In many respects, however, the divergences in estimates across different techniques were relatively small given the uncertainties illustrated by the wide range of views on both the outlook and appropriate policies in Japan. Most estimates of the output gap fell within the 2½-4½ percentage point range, and most estimates of potential growth were within 1½-2¼ percent. The staffs current estimates of the growth of potential output (1.9 percent) and the output gap (4.1 percentage points) are within these ranges, although above the midpoints in both cases, reflecting the fact that the methodology is not designed to identify short-term supply constraints. Overall, while the flexibility and analytical transparency of the production function makes it a particularly attractive approach, it may be useful to augment production function estimates with the results from alternative approaches. This is particularly true at times such as the present, when the level of uncertainty about the underlying output gap is large, especially in the light of the possible impact of financial system strains, while the importance of the output gap in policy assessment is high.

Looking to the future, an obvious way of extending this analysis is to incorporate direct indicators of the supply-side, such as unionization, demographics, replacement ratios and employers contributions to social security into the estimation. Such an extension could provide a more nuanced explanation for recent movements in potential output and the natural rate of unemployment than the univariate techniques used here.

## References

Adams, Charles, and David T. Coe, 1990, “A Systems Approach to Estimating the Natural Rate of Unemployment and Potential Output for the United States,”

Vol. 37 pp. 232–93.*IMF Staff Papers*Adams, Charles, Paul R. Fenton, and Flemming Larsen, 1987,

*“Potential Output in Major Industrial Countries,” in*(Washington: International Monetary Fund).*Staff Studies for the World Economic Outlook*World Economic and Financial SurveysBlanchard, Olivier, and Danny Quah, 1989, “The Dynamic Effects of Aggregate Demand and Aggregate Supply Disturbances,”

Vol. 79 pp. 655–73.*American Economic Review*Citrin, Daniel, 1991, “Potential Output and the Natural Rate of Unemployment: Recent History and Medium Term Prospects,”

*unpublished manuscript*, International Monetary Fund.Coe, David T., and Thomas Krueger, 1990,

*“Wage Determination, the Natural Rate of Unemployment, and Potential Output,”*ed. by Leslie Lipschitz and Donogh McDonald,(Washington: International Monetary Fund).*German Unification: Economic Issues*IMF Occasional Paper No. 75De Masi, Paula R., 1997,

*“IMF Estimates of Potential Output: Theory and Practice,” in*(Washington: International Monetary Fund).*Staff Studies for the World Economic Outlook*World Economic and Financial SurveysHodrick, Robert J. and Edward C. Prescott, 1981, “Post-War U.S. Business Cycles: An Empirical Investigation,”

*Carnegie-Mellon University Discussion Paper, No. 451*.International Monetary Fund, 1998,

, (Washington: International Monetary Fund), May.*World Economic Outlook*Laxton, Douglas, Peter Isard, Hamid Faruqee, Eswar Prasad, and Bart Turtelboom, 1998,

(Washington: International Monetary Fund).*MULTIMOD Mark III: The Core Dynamic and Steady-State Models*IMF Occasional Paper No. 164Prasad, Eswar, 1995, “Trends and Cycles in the Japanese Economy”, (unpublished manuscript, International Monetary Fund).

^{}1

Both the IMF and the OECD provide estimates of the level of potential output for developed economies in their macroeconomic forecasting exercises across member countries. A discussion of the methodology used in the IMF is provided in De Masi (1997) (see also Adams, Fenton and Larsen, 1987). We follow the usual convention in defining potential output as the level of output that leaves inflation unchanged.

^{}2

This approach is not considered here, largely because I suggest a structural explanation for any divergence between the two approaches. For similar models to that used by Adams and Coe for the United States, see Coe and Krueger (1990) for the (then) Federal Republic of Germany and Citrin (1991) for Japan. The Blanchard and Quah approach has been applied to Japan by Prasad (1995).

^{}3

Clearly, such banking strains are also likely to reduce aggregate demand, thus causing a widening output gap as well as lower potential output. A survey of the overall output costs of banking crises is contained in IMF (1998), Chapter IV.

^{}4

The time trend terms are included so as to provide an initial way of detrending output. It is well known that any function can be approximated by a Taylor expansion of the higher powers of *t*. However, in this case, the terms in the expression become progressively more explosive. As visual inspection and economic intuition both point to a slowing of the rate of growth of output in Japan over time, the trend was modeled using successively lower powers of time. Such an expansion would appear to be capable of approximating any concave time series, although I do not know of any formal proof of this proposition.

^{}5

Future expectations of inflation were not included in the estimation by instrumenting future actuals, as they often are in Phillips curve analysis, as this would have truncated the sample period and hence reduced its value for current analysis.

^{}6

The year 1975 was chosen as the starting date for most regressions so as to provide a long sample period without allowing the extraordinary growth rates during the golden years of the 1960s and early 1970s to dominate the sample. The more recent starting date for the Phillips curve regressions reflects the fact that inflation stabilized in Japan in the early 1980s having been quite variable through the 1970s. Given that inflation expectations presumably also stabilized in the early 1980s, a later starting period is likely to give better estimates, particularly in the absence of a term representing inflation expectations.

^{}7

Vacancies, capital utilization, and inflation were included in levels, while the unemployment gap was calculated as the difference between actual unemployment and the natural rate. The natural rate in turn was estimated using a Hodrick-Prescott filter (with a smoothing coefficient of 40,000). The interpretation of smoothing coefficients is discussed further below.

^{}8

This is unlikely to simply reflect short-term cyclical factors, as the revival of output in 1995 and 1996 is included in the calculation for 1998 due to the four-year lag used to calculate the growth of potential output.

^{}9

See Hodrick and Prescott (1981) and Laxton and others (1998) Box 7 pages 30–31 for a description of the properties of the Hodrick Prescott filter. Briefly, the HP filter minimizes a weighted average of the square of deviations from the trend and the square of changes in the underlying trend, with the smoothing parameter providing the weight to be put on deviations from the trend. The higher the smoothing parameter, therefore, the less the trend will vary with movements in the underlying variable. A smoothing parameter of 40,000, for example, uses a relative weight on deviations of the trend of 200 (the square root of 40,000), loosely implying that a 0.05 percent movement in the trend from one quarter to another is given the same weight as a 10 percent deviation from the trend.

^{}10

The two Hodrick-Prescott filters provide the upper and lower estimates of the output gap, illustrating the sensitivity of this filter to the assumed smoothing parameter.

^{}11

Comparison of Figures 5.1 and 5.2 shows that this divergence is true for 1996, the peak of the cycle prior to the current recession. Demand-side estimates of the output gap show the economy barely reaching potential in 1996, while supply-side estimates have the economy clearly above potential.

^{}12

De Masi (1997) describes approaches used within the IMF to calculate potential output.

^{}13

Another way of looking at this is that the Cobb-Douglas production function assumes that capital has a marginal return that is fixed over time. To the extent that overinvestment has depressed the marginal rate of return below its long-term level, the production function overestimates the potential level of output.