Abstract
This paper estimates the extent of spare capacity in the U.K. economy using a range of methodologies pointing to an output gap and the behavior of inflation during large output gaps. The usefulness of fiscal rules in supporting fiscal consolidation is generally positive, and a more permanent rules-based fiscal framework is required. The banking system has recovered fast; however, the sustainability of the sector’s recovery is still uncertain, and risks remain. An update on reforms to the financial sector’s regulatory and supervisory framework is also provided.
I. Estimating the UK’s Output Gap1
This chapter estimates the extent of spare capacity in the UK economy using a range of methodologies. Although results vary, all standard filter and model-based approaches point to a sizeable output gap. Survey-based evidence, however, suggests more limited slack.
A. Introduction
1. The financial crisis has made it more challenging to estimate the size of the output gap.2 Even when there is no major structural break in the economy, estimation of the output gap involves some margin of error due to measurement issues and difficulty in identifying temporary demand factors. However, the uncertainty today is particularly large because the lasting effect of the financial crisis on each component of potential output—labor, capital, and the total factor productivity (TFP) residual—is very difficult to quantify.
2. With this heightened uncertainty, reviewing a range of output gap estimates based on different approaches can help inform macroeconomic policy. Estimates based on different approaches might point to a similar view of the gap, at least qualitatively. In this case, macroeconomic policies could more confidently be based on this view. If instead different approaches point to divergent assessments, a risk management approach could be given greater emphasis, with attention paid not just to the central forecast, but also to the error band around it.
3. This annex examines three estimates of the UK’s output gap based on the following approaches:
a univariate Hodrick-Prescott (HP) filter;
a multivariate filter based on an unobserved component model; and
a production function approach.
Each of these approaches is prone to certain biases at times of large structural changes because they all rely on historical patterns of observable variables. The nature of such biases is discussed below.
4. Output gap estimates vary across the three approaches, but each methodology suggests significant spare capacity. Specifically, the estimated output gaps range from minus 1.8 percent to minus 3.9 percent as of the second quarter of 2010 (see text chart).
5. As a check on these estimates, the chapter also examines survey-based information on spare capacity. Although survey responses cannot be mapped straightforwardly into output gap estimates, the relevant time series are significantly correlated. As such, firms’ own assessment of spare capacity would have provided useful guidance to policymakers in the past. Results from the most recent business surveys, in turn, point to continued slack, albeit to a more limited extent than standard output gap estimation suggests.
Output Gap Estimates
(Percent of potential GDP)
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Sources: IMF staff estimates.B. HP Filter Approach
6. The HP filter has been widely used to derive approximations for potential output. This approach assumes that, because of self-equilibrating forces, actual output fluctuates around potential output over time. In particular, the filter fits a trend output line that minimizes a weighted average of (i) the difference between actual and trend output and (ii) the rate of change in trend output itself. More specifically, potential output,
where λ denotes a smoothing parameter.
7. The method is subject to several shortcomings. Lacking a close link to economic theory, the HP filter abstracts from any potentially relevant economic information other than the output series itself. As a purely statistical tool, which smoothes actual GDP to estimate potential, it may also be slow in “discovering” structural breaks. This entails the risk that the HP filter could overestimate potential GDP if the sample period ends with a sudden and large loss of output, as occurred during the recent financial crisis. More generally, estimates are prone to revision as new GDP data become available, with revisions for the most recent quarters tending to be particularly large (the “end-point problem”). These problems can be mitigated by including forecasts in the sample under study, though this potentially makes results sensitive to the forecast assumptions.3
8. The HP filter-based estimate points to a negative output gap of close to 2 percent. To avoid the end-point problem mentioned above, the sample, which starts at Q1-1970, includes staff projections up to the fourth quarter of 2015.4 The estimated gap, measured in percent of potential GDP, bottomed at minus 3.4 percent in Q3-2009 and stood at minus 1.8 percent as of Q2-2010. This is still considerable, but smaller (in absolute terms) than the output gap estimates obtained from the approaches discussed in the following two sections.
C. Multivariate Filter Model 5
9. A multivariate filter is a reduced-form approach based on an operational definition of potential output. It estimates the output gap based on estimated relationships between the unobservable output gap and other relevant macroeconomic variables, including unobservable equilibrium values of these variables. In particular, the model builds on an operational definition of potential output as the path of output that may be sustained without causing inflation to change. This definition is combined with other identifying constraints (based on relationships between the output gap and other economic variables) to form a small macroeconomic model. The model is in a reduced form in the sense that underlying structural (i.e., behavioral) relationships themselves are not identified. The model is estimated using a Kalman filter.
10. Output gap dynamics in the model are assumed to be influenced by monetary policy. One of the key channels through which monetary policy exerts its influence on inflation is via aggregate demand and hence the output gap. It is therefore natural to link the output gap to the deviation of actual inflation from the long-term inflation target:
where π4 denotes core inflation,
The term εt captures other factors driving the output gap, such as demand shocks. The output gap equation above is a reduced-form representation that could be derived from a range of different micro foundations, notably a combination of a standard IS curve and a Taylor rule.
11. The model also includes three empirical relationships that are key to identifying the output gap. The first key relationship is represented by an inflation equation (or Phillips Curve). A higher output gap leads to an increase in the inflation rate, as summarized by the following equation:
Note that in addition to the level of the output gap, the equation also includes the change in the output gap as a determinant of current inflation. The idea is to allow for certain rigidities in the adjustment process. Specifically, the term (yt—yt–1) is positive when the economy is coming out of a recession; at this point, the mere closing of the output gap might create some inflationary pressure if the available supply capacity cannot be brought on stream instantaneously, for example, due to labor market frictions. The second key relationship is between the output gap and unemployment (Okun’s Law):
where ut denotes the unemployment gap, defined as the difference between the NAIRU
The third key relationship is between the capacity utilization gap and the output gap, defined in a similar way as Okun’s law:
where ct denotes the capacity utilization gap, defined as the difference between the actual manufacturing capacity utilization rate (Ct) and its equilibrium level
12. These four equations are combined with laws of motion for equilibrium variables and estimated using a Kalman filter. To close the model, it is necessary to define laws of motion for the remaining equilibrium variables, i.e., the NAIRU, potential output, the equilibrium capacity utilization rate, and the perceived long-term inflation target. Appendix I discusses the relevant assumptions. Data sources are reported in Appendix II.
13. The estimated model points to a negative output gap that is larger than the HP filter-based estimate. The model is estimated for a sample period from Q2-1988 through Q2-2010.6 The gap is estimated to have bottomed at minus 4 percent in Q3-2009 and to have equaled minus 2.6 percent as of Q2-2010. A key driver of these results is the recent behavior of inflation. Unlike during the previous recession in the early 1990s, when inflation decelerated sharply, UK inflation has remained somewhat more elevated during the recent downturn (text chart). To the extent that this reflects one-off price level shocks such as the increase in the VAT rate in January 2010, current inflation rates overstate the strength of underlying price pressures. Correspondingly, the estimated output gap is likely to be underestimated (in absolute terms). However, adjusting for the estimated effect of the VAT change had no more than a negligible impact on the size of the estimated gaps.
United Kingdom: Core CPI inflation 1/
(y/y percent change)
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Souces: Haver, OECD, and IMF staff calculation.1/ CPI excluding food and energy.D. Growth Accounting Approach
14. The growth accounting approach estimates potential output (and thus the output gap) using an assumed aggregate production function and estimates for potential employment, potential capital, and total factor productivity (TFP).
15. The first step of this approach in its simplest form is to derive TFP. TFP is calculated as a residual determinant of output that is not explained by labor and capital. In particular, the following two-factor Cobb-Douglas production function is fitted to measures of the capital stock and the labor input:
where Y is output, P is the working age population, PR is the labor participation rate, u is the unemployment rate, H is the number of hours worked per worker, K is the capital stock, and α is the average labor share for the sample period. TFP, denoted by ε, is derived as the residual of this equation.
16. However, the estimated TFP series is polluted by changes in the intensity of capital utilization. It is well known that fluctuations in TFP, as measured by the method above, account for a considerable part of output fluctuation over the business cycle. The upper panel of Figure 1 confirms this result for the sample under study. Such a finding is not surprising because the estimation relies on the total capital stock, not the flow of services actually provided by the stock at any point in time. In reality, however, capacity utilization varies considerably over the business cycle (Figure 1, lower panel). Any changes in the flow of capital services due to changes in demand conditions are thus captured by the TFP residual.
United Kingdom: Growth Accounting and Capacity Utilization, 1985-2010
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Sources: Haver; and IMF staff calculation.17. The second step, therefore, involves deriving trend TFP by smoothing the TFP time series. While measured TFP tends to be volatile, in part reflecting fluctuations in the capacity utilization rate, it usually shows a clear trend behavior that can be readily extracted using a simple HP filter or a regression of measured TFP on a time trend. This estimated TFP trend smoothes away cyclical fluctuations in capacity utilization and can therefore be plugged into the production function to estimate a series for potential output (see below).
18. However, deriving trend TFP by simply smoothing residuals could be problematic under current circumstances because the UK’s productivity could have been adversely affected by the crisis. Estimated TFP for recent periods reflects both the effect of a sharp cyclical downturn and any permanent loss of productivity. It is therefore difficult to tell how much of the recent decline in TFP represents lasting damage from the financial crisis. Simply smoothing the estimated TFP by an HP filter could be misleading, for reasons already discussed in Section B above. To separate the permanent loss from purely cyclical factors, it is better to control directly for the effect of varying capacity utilization.
19. This chapter thus modifies the original production function equation to purge the influence of changes in the capacity utilization rate from TFP. In particular, the following equation is fitted to the data to derive capacity utilization rate-adjusted TFP (adjusted TFP):
where cu is the capacity utilization rate and
20. Adjusted TFP looks more stable than TFP but still shows a marked decline after peaking in the third quarter of 2007. The text chart shows TFP and adjusted TFP derived from fitting the two equations above. Since fluctuations of both labor inputs and capacity utilization rates have been controlled for in the adjusted TFP series, the decline likely reflects factors whose effects are lasting even when adjusted TFP resumes its trend growth. These factors could include, among others, a higher cost of capital due to elevated risk premia, and a permanent shift of demand away from sectors that enjoyed high productivity growth, such as financial services.
TFP: Unadjusted and Adjusted for Capital Utilization Rate
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
21. The final step of estimating potential output and the output gap involves taking cyclical factors out of adjusted TFP and factor inputs. For the equilibrium unemployment rate and capacity utilization rate, estimates from the reduced-form unobserved component model in the previous section are used, as this approach is less prone to the “end-point problem” than simpler filtering methods. Equilibrium values of the other variables are derived through filtering techniques, with a few modifications (Figure 2):
Before showing a characteristic decline during the recent recession, the labor participation rate had risen by 0.02 percentage point per quarter on average from Q4-1994 through Q1-2009. Accordingly, the equilibrium labor participation rate is derived by smoothing the raw series by an HP filter through Q1-2009 and assuming a 0.02 percentage point increase each quarter afterwards.
Hours worked per employee have steadily declined over the past two decades. A simple HP-filtered series is used to determine equilibrium hours.
By construction, adjusted TFP should not be affected by cyclical factors. A smoothed adjusted TFP series should be a good representation of trend TFP for potential output, and an HP-filtered series is used in this section.
United Kingdom: Equilibrium Aggregate Inputs and Output Gap, 1985-2010
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Sources: Haver; and IMF staff calculation.22. The resulting negative output gap estimate is larger than estimates based on the other approaches discussed above. The gap is estimated to have bottomed at minus 5 percent in Q3-Q4 2009. Since then, it has recovered to minus 3.9 percent in Q2-2010. Moreover, this estimate is still smaller in absolute terms than the OECD’s latest UK output gap estimate of minus 6.3 percent in Q2-2010, which uses a similar approach based on a production function but does not adjust for the capacity utilization rate.7
23. Still, some caution is needed when interpreting results based on adjusted TFP. For example, labor hoarding, which is suspected as one reason for the surprisingly modest increase in the unemployment rate despite the sharp economic downturn, would cause adjusted TFP to be underestimated. Correspondingly, potential output and the size of the (negative) output gap would also be underestimated. Another source of bias is the manufacturing sector capacity utilization rate. If the capacity utilization rate of the non-manufacturing sector is less volatile than that of the manufacturing sector—for example, the retail sector might find it more difficult to adjust store hours when demand declines—adjusted TFP would be overestimated. HP-filtered series would thus overestimate trend TFP, possibly resulting in overestimation of the size of the output gap.
E. Survey-based Measures of Spare Capacity
24. Additional evidence on the output gap comes from survey-based measures of spare capacity. Each of the methodologies discussed so far relies on a specific economic or statistical model of potential output and hence spare capacity. The results from these approaches can be usefully compared to another more direct source of evidence on spare capacity, namely from company surveys. For the UK, there exist a number of such surveys, conducted by the Bank of England’s regional agents, the British Chambers of Commerce, the Confederation of British Industry, and Eurostat, respectively. Despite some variation in scope and design, these surveys all contain specific questions on whether or not companies have free capacity to expand production of their goods or services. In addition, some surveys include questions on whether or not companies are facing difficulty recruiting staff.8
25. To facilitate a quantitative interpretation, we normalize the time series data for each relevant survey response. In a first step, the time series are transformed so as to have a zero mean and unit standard deviation over the period in which the respective survey has been available. However, these periods are sometimes relatively short. As a result, the survey data may not cover a full economic cycle, in which case the within-sample mean and standard deviation provide a distorted picture of their likely long-run values. To give a concrete example, the mean capacity utilization rate over the period 1998Q1–2006Q4 is likely to overstate the long-run mean, given that the period did not include a single UK recession. For this reason, we conduct a second transformation, by recalibrating the normalized responses so as to ensure a zero mean over a full cycle (defined as a period over which historical OECD output gap data average to zero) and a unit standard deviation over the longest available period up to the eve of the recent financial crisis, i.e., 1971Q4–2006Q4. The recalibrated responses are subsequently averaged first within, and then across, survey provider categories.
26. The resulting data point to a limited, and diminishing, margin of spare capacity. In line with economic intuition and the findings of previous sections, the recession of 2008–09 initially led companies to report resource slack, especially in the manufacturing sector. However, the extent of spare capacity at the cyclical trough in early 2009 appears more limited than might have been expected. Moreover, capacity utilization appears to have steadily increased since, leaving only a moderate margin of spare capacity as of 2010Q2.
27. To be sure, some caution is warranted in interpreting this finding, given the nature of the underlying data. First, the relevant surveys capture significant parts of the UK economy, but not all of it—the construction sector is a notable exception. Second, as with all surveys there is some uncertainty over how exactly participants understand a particular question. In the case of questions about spare capacity, for instance, it is unclear how companies take into account temporarily idle resources, such as a mothballed assembly line or staff on part-time work. Third, the relationship between survey responses and average spare capacity across firms could be nonlinear, as surveys typically reveal the share of companies reporting spare capacity, but not the extent of such capacity. Lastly, capacity-related survey questions capture only the scope for expanding production for a given set of production factors. Yet, idle resources are likely to exist outside of firms as well, for instance in the form of unused real estate. Similarly, questions about recruitment difficulties may only give a rough sense of spare capacity in the labor market.
Survey Measures of Capacity Utilization by Sector 1/
(normalized and aggregated, - = below average)
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Sources: Haver; and IMF staff calculations.1/ Based on a range of survey indicators (provided by Bank of England, British Chambers of Commerce, Confederation of British Industry, and Eurostat, respectively) for capacity constraints and recruitment difficulties; normalized to average zero over the cycle, with unit standard deviation. Vertical bars in chart mark structural breaks in series due to inclusion of new indicators.28. Despite these caveats, survey-based measures of spare capacity should not be discarded lightly, insofar as they exhibit a relatively close relationship with historical output gap data (as reported in the OECD’s Economic Outlook No. 87). Over the period 1989–2006, for example, our aggregate measure of survey-based spare capacity co-moves closely with ex-post data on the output gap: the contemporaneous correlation is 0.75; it rises to 0.80 at the first lag, 0.82 at the second, and 0.83 at the third lag, before declining again. This suggests that survey-based measures have some predictive power for the output gap. Such a finding should not be too surprising, given that some of the survey questions have a forward-looking component, notably by asking about capacity relative to production plans over the following months. In addition, it is conceivable that over the course of the cycle, spare capacity first emerges and diminishes within firms, and only then in the economy as a whole, for instance because of lags in hiring and firing.
Aggregate Survey Measure of Capacity Utilization vs. Historical Output Gap Estimates 1/
Citation: IMF Staff Country Reports 2010, 337; 10.5089/9781455208449.002.A001
Sources: Haver; OECD; and IM F staff calculations.1/ Survey measures for industry/manufacturing and services as shown in previous chart; aggregated using sector weights in total value added. Vertical bar marks structural break in survey data series due to inclusion of new indicators.29. If the historical relationship apparent from the above text chart is assumed to have persisted in recent years, the latest survey data suggest a rather small output gap, perhaps no greater than 1 percent of GDP in absolute terms by mid-2010. This implication is undoubtedly surprising, given the sharp earlier fall in GDP along with a considerable drop in average labor productivity, which could naturally be interpreted as a sign of widespread labor hoarding (and hence spare capacity within firms). Taken at face value, the survey data thus send a cautionary message that the crisis may have caused greater-than-expected damage to the economy’s supply, perhaps reinforced by the sharp curtailment of capital expenditure as firms strove to shore up cash flow.
F. Conclusion
30. The empirical approaches considered in this chapter consistently point to a negative output gap, although they differ on the extent of economic slack. The three standard methodologies at the center of our analysis unequivocally suggest that there continues to be significant slack in the UK economy. Specially, the output gap in Q2-2010 is estimated to have been within a range from minus 1.8 to minus 3.9 percent. The relative width of this range reflects the large uncertainty about the lasting effect of the financial crisis on potential output. Survey-based measures, in turn, also suggest continued economic slack, albeit to a more limited extent than the standard methodologies imply. Taken together, the available evidence supports the dominant view that economic activity currently falls short of potential. At the same time, the significant uncertainty around output gap estimates puts a premium on nimble monetary policy along with adequate contingency planning for scenarios in which inflation and growth outturns depart from baseline projections.
Prepared by Hajime Takizawa and André Meier (EUR).
In this chapter, the output gap is defined as the extent to which actual output exceeds potential output. If actual output is below the potential, the gap is negative; and the more spare capacity there is in the economy, the smaller is the numerical value of the output gap. However, because this chapter mainly discusses negative output gaps, it is convenient to refer to situations of more spare capacity as larger output gaps (in absolute terms).
HP filter-based estimates are also sensitive to the value of the smoothing parameter, λ. It is standard practice in the literature to set λ equal to 1,600 for quarterly data. The estimation in this chapter follows this practice.
Varying the forecasts within a reasonable range does not materially change the results. For example, using the OBR’s growth projections as reported in the June 2010 budget yields the same Q2-2010 output gap as the estimation based on staff projections.
The model is based on J. Benes et al. (2009), “The Global Financial Crisis and its Implications for Potential Output,” IMF, mimeo.
Data availability limits the sample length.
The OECD estimates the NAIRU by applying a Kalman filter to a Phillips curve that relates inflation to an unobserved unemployment gap.
See Figure 11 in United Kingdom–Staff Report for the 2010 Article IV Consultation for an overview of a few key surveys.
Appendix I. Details of the Multivariate Filter Model
As discussed in the text, laws of motion for unobservable equilibrium variables are needed to estimate the multivariate filter model using a Kalman filter. NAIRU, potential output, the equilibrium capacity utilization rate, and the perceived long-term inflation target are modeled as follows:
NAIRU
NAIRU is assumed to be subject to both transitory level shocks,
where Uss denotes the steady-state NAIRU.
Potential output
Potential output depends on the trend growth rate of potential,
The second term represents the immediate impact of a change in NAIRU on potential output, while the third term captures a lagged effect that persists for another 19 quarters. Thus, the impact of a permanent one-percentage-point increase in NAIRU is an immediate decline in potential output by θ percent, followed by a cumulative additional decline in potential output by (1–θ) percent over the following 19 quarters. The total effect on potential output five years later is one percent.
One interpretation of this specification is to envisage a gradual change in the capital stock in response to a change in NAIRU within a simple Cobb-Douglas aggregate production function. Since the production technology remains the same, there should be no change in the equilibrium capital-labor ratio and labor productivity. An adjustment to the new equilibrium would, however, proceed gradually as capital adjusts to the change in NAIRU. Therefore, parameter theta can be interpreted as the elasticity of output with respect to labor, which will be equal to the labor share. The underlying trend growth,
Equilibrium capacity utilization
Equilibrium capacity utilization,
where
Perceived long-term inflation target1
Appendix II. Data Sources
Data sources for the variables used in the multivariate filter model are as follows:
Real GDP, CPI, unemployment rate, labor participation rate, and labor force: Office for National Statistics.
Core CPI: For 1996 and subsequent years, CPI excluding food and energy from Office for National Statistics, seasonally adjusted by IMF staff. Prior to 1996, OECD estimates.
Capacity utilization rate: Harmonized capacity utilization for manufacturing from the European Commission.
Perceived long-term inflation target: Semiannual data on long-term inflation expectations by Consensus Forecast, spliced for a quarterly frequency by IMF staff.
Data sources for the growth accounting approach are as follows:
Capital stock: Annual data on production capital stock, defined as gross capital stock minus dwelling excluding land, spliced for a quarterly frequency by IMF staff.
Real GDP, labor force, number of unemployed and employed, population, and number of hours worked: Office for National Statistics.
Capacity utilization rate: Harmonized capacity utilization for manufacturing from the European Commission.
This simple random-walk assumption is chosen for analytical convenience. However, it is relatively straightforward to consider the special case of credible inflation targeting, in which long-term inflation expectations are well-anchored around the central bank’s inflation target. This case can be modeled by replacing the lagged term on the right hand side with the central bank’s explicit inflation target. In the present case, results were found to be little changed when we imposed a stable inflation target of 2 percent. Specifically, the estimated output gap in Q2-2010 would be 2.2 percent instead of 2.6 percent as reported in the text.
