II. Underlying Trends and Cyclical Fluctuations: Pieces of the Same Puzzle1
Core Questions, Issues, and Findings
- What are the main stylized facts regarding trends in Italy’s growth performance? Potential growth has slowed since the early 1970s, in line—until the mid-1990s—with an enduring deceleration in total factor productivity (TFP) and a secular thinness of the labor contribution. Over the last decade, however, trend growth in both employment and labor participation have been drifting up, more than offsetting the sharp decline in underlying factor efficiency. As a result, potential output growth has progressively recovered from the downfall of the early 1990s, while productivity growth has tumbled since then.
- Does the exceptionally low productivity growth over the current protracted downturn point to a reversal in potential growth? Not necessarily. Even in the absence of market distorsions (such as imperfect competition or increasing returns), productivity—whether measured as labor productivity or TFP—is likely to rise in booms and fall in recessions, because of variable utilization of resources. Indeed, we find evidence that part of the disappointing productivity performance observed since 2002 reflects idling capacity.
- Are the estimated shifts in growth trends consistent with measures of demand pressures in labor and product markets? Yes. Temporary (demand) shifts are disentangled from permanent (supply) shifts to growth by exploiting additional information about the short-run output-unemployment and output-inflation trade-offs. To the extent that these processes are well-identified, a multivariate filter ensures consistency among estimates of potential output, the NAIRU, and underlying inflation. As a by-product, a congruent measure of trend labor productivity is also derived.
- What are the main sources of growth variation over the long- and over the short-run? The major source of trend growth variation is likely to be associated with changes in labor participation, confirming the permanent (i.e. structural) nature of the latter. Shifts in productivity, instead, are found to account for the bulk of business cycle fluctuations.
- Which are the policy implications of this chapter’s findings? From a normative viewpoint, it is important to address not only factors preventing further employment growth, but also those constraining factor efficiency. Stagnant productivity growth might in fact disguise the need to reduce distorsions in product markets, including inadequate competition in key sectors and overhead costs.
6. This chapter attempts to disentangle cyclical fluctuations from permanent shifts in Italy’s potential output, using both statistical- and model-based detrending techniques. Potential output can be defined as the equilibrium level of economic activity where no inflationary pressures emerge from the utilization of resourses and the resulting price setting behavior. The output gap identifies business cycle fluctuations as deviations of actual output from its potential. Intended to serve as summary indicators of (structural) supply conditions and (transitory) demand pressures, potential output and the output gap are used as diagnostic devices for a variety of purposes—such as inflation forecasting, monetary policy setup, and evaluation of cyclical sensitivity of budget policies. Unfortunately, such basic variables for economic analysis and policy are unobservable and need, therefore, to be “extracted” from observable aggregates, such as real GDP. To this end, different procedures have been developed by the literature.
7. Among statistical agencies, a popular method for measuring potential output is the production function approach (PFA).2 Its rationale is to obtain potential output from the trend levels of its structural determinants, such as productivity and factor inputs, given an existing technology that is used to appropriately weight the components. Estimates of factor inputs’ trend levels are commonly based on an extended version of the Hodrick-Prescott (HP) filter, to overcome the “end-point” problem intrinsic to the two-sided moving average smoothing procedure. Measures of potential output based on extended HP trends may prove, however, unreliable if a prolonged recession—or boom—occurs at the end of the sample (Box 1).
8. Based on the traditional PFA—and using annual data up to 2001—previous staff forecasts pointed to a decline in Italy’s potential growth.3 Trend growth was revised down to around 1.9 percent in 2001, though it was expected to rise steadily to 2.1 percent by 2007. In light of Italy’s disappointing growth performance since 2001, however, existing growth projections had implied a sizeable degree of slackness in the economy. With the aim of closing the output gap by 2009, updates of staff estimates relying on the same approach (and on quarterly data up to 2004Q2) would call for further deceleration in potential growth (Figure 1)—unless growth is expected to rebound sharply and steadily over the whole forecast horizon. The implied trend growth decline would be associated with a sharp dip in both total factor productivity (TFP) growth—as measured by the Solow residual—and in labor productivity growth, in the face of an enduring upturn in labor utilization, following wage moderation policies and structural reforms in the Italian labor market.
Figure 1.Looking at Potential and Labor Productivity Growth Using HP Trends
Source: OECD and staff calculation.
Box 1:Features and Pitfalls of the HP Filter
The Hodrick-Prescott filter (HP, henceforth) is derived by minimizing the sum of squared deviations of the log variable (e.g. y, in the case of GDP) from the estimated trend τ, subject to a smoothness constraint that penalizes squared variations in the growth of the estimated trend series. Thus, HP trend values are those that minimize:
The estimated trend variable τ is a function of λ and both past and future values of y. Higher values of λ imply a large weight on smoothness in the estimated trend series (for very large values the estimated trend series will converge to a linear time trend; as λ tends to zero, the trend is coincident with the series). Apart from the arbitrary choice of the λ parameter (set to the standard value 100*s2, where s denotes the number of observations per year in the series), the decomposition of cycle and trend estimated by an HP filter turns out to be inaccurate under two circumstances:1
- At the end of the sample—when the HP filter suffers from an in-sample phase shift problem—as it needs to rely on future information about the series. The end-period problem can be tackled by extending actual data out of the sample using the information carried by the average historical growth rate or autoregressive forecast models. However, if past growth rates are not reasonable proxies for future growth patterns, this extension may lead to a bias at the end of the filtered series. An alternative method of extending the data so as to better anchor the smoothed series is to use ad-hoc out-of-sample growth projections.2
- When cyclical fluctuations are highly persistent or when underlying trends are subject to temporary stochastic shocks with greater variance than that of the business cycle. Implicit in the choice of λ is, in fact, a strict assumption about the relative importance of supply and demand shocks: e.g., trend fluctuations account for 2 ½ percent of cyclical fluctuations in quarterly data (or 1 percent in annual data). Although, on average, such an estimate fits output data for industrial countries reasonably well, over relatively short periods this may not be the case.
For both reasons, analyzing macroeconomic fluctuations regarding Italy’s on-going prolonged slowdown using HP trends could prove misleading.1 See, e.g., Harvey and Jaeger (1993); and Conway and Hunt (1997).2 In the context of its bi-annual World Economic Outlook exercise, the IMF produces a set of annual projections, looking out five years. These projections assume that at the end of the forecast horizon output will be at its potential and unemployment will reach its equilibrium level. Existing staff estimates of Italy’s potential output use most recent WEO growth projections to extend output data beyond 2001.
9. Against this background, this chapter derives estimates of Italy’s key unobservable variables in the context of a modified production function framework, using stochastic components. This innovative approach has the advantage of allowing joint tests of hypotheses about the sources of long-run growth and business cycle fluctuations within models grounded in economic theory and based upon available information. The accuracy and suitability of resulting potential output and output gap measures are assessed against (i) univariate statistical filters for real GDP and (ii) multivariate unobserved component models exploiting additional information about the short-run unemployment-inflation trade-off. As by-products, mutually consistent estimates of trend labor productivity, the equilibrium unemployment rate, and underlying inflation are also obtained.
10. Results indicate that, even after correcting for cyclical factors, productivity growth—already on a downward slope for decades—has declined sharply since the mid-1990s, and it remains a drag on growth going forward. Potential growth slowed from the 1970s until the mid-1990s, in line with a secular weakness in labor utilization and an enduring deceleration in TFP growth. Over the last decade, however, trend growth in both employment and labor participation has been drifting up, more than offsetting the weakening in underlying factor efficiency. As a result, potential output growth has progressively recovered from the downfall of the early 1990s, even as productivity growth has tumbled.
11. Part of the disappointing productivity performance over the current downturn reflects cyclical factors. The fall in productivity partly mirrors a contraction in capacity utilization, notwithstanding a rising number of employees in the economy and a moderate acceleration in capital accumulation. Shifts in productivity are, indeed, found to account for the bulk of business cycle fluctuations and to be highly procyclical. Conversely, the major source of trend growth variation is likely to be associated with changes in labor participation, confirming the permanent (i.e. structural) nature of the latter. Results are robust across model specifications and essentially in line with recent findings for the euro area.4
12. The chapter is organized as follows. The next section outlines the main stylized facts regarding trends in Italy’s growth performance and investigates the factors behind them. Section C presents alternative model-based frameworks to estimate the relative importance of transitory and permanent shifts in Italy’s real GDP. The robustness of the output decomposition results is assessed by exploiting additional information about comovements of output, employment and inflation over the business cycle. Section D concludes the chapter by discussing the findings’ implications for policy.
B. The Puzzle: What’s Behind the 1990s Productivity Slowdown?
13. Annual GDP growth averaged almost 6 percent in the 1960s, but fell below 2 percent in the 1990s. Breaking down GDP growth into labor, capital, and TFP contributions shows that the significant slowdown in real growth observed in Italy over the period 1960-2001 is explained almost completely by the decline in TFP growth—as measured by the Solow residual within a standard production function framework based on period averages of aggregate OECD data (Table 1A). 5 In particular, over the 1990s, factor productivity growth has fallen by half with respect to the 1980s—from an annual average of 1.2 percent to 0.6 percent—to further decelerate to a mere 0.2 percent after 1995.
|Looking at contributions to growth…||Looking at capital deepening…|
|Labor||Avg. hours worked in business sector||Share of Labor in Business Sector||Employment||Labor force||Population||Capital||TFP||GDP||Capital Deepening||TFP||Labor|
14. Employment and average hours per employee have historically been a drag on growth. However, over the last decade, reforms to liberalize part-time and fixed-term labor contracts, tax incentives for permanent contracts, the creation of private employment agencies, pension reforms to discourage early retirement, and significant wage moderation have led to sizable increases in the employment ratio and in labor participation. As a result, the unemployment rate fell to 8.1 percent in 2004Q2 (seasonally adjusted)—below the euro area average—and labor factor services accounted to one fourth of GDP growth over the second half of the 1990s. Nonetheless, hours per employee have continued to decline and the employment ratio remains—at 56 percent—the lowest in the euro area.6
15. Capital accumulation has reliably contributed to growth over time. In particular, since the 1980s, its contribution to GDP growth has fluctuated just above 1 percent, without losing pace in the second half of the 1990s. Recent labor market developments have resulted into a slight moderation in capital deepening after 1995, as measured by the rate of increase in the capital-labor ratio. However, the deceleration in capital deepening was modest and accounted for only one third of the substantial fall in labor productivity growth.
16. The opposite movements of employment rates and labor productivity during the second half of the 1990s suggest that some of the recent decline in Italy’s factor productivity growth may be related to the reinsertion into jobs of lower-productivity workers. As firms responded to labor market reforms by shifting to less capital-intensive production methods, a somewhat reduced rate of capital deepening had hence to be expected. Nevertheless, it is striking that the drop in the growth of TFP observed since the mid-1990s has been so sharp as to neutralize most of the positive contribution to growth from the increase in labor supply that has accompanied structural reforms.
17. The exceptional sluggishness observed in TFP growth raises a number of relevant questions. What is the Solow residual accounting for? Does it strictly measure Hicks-neutral technological changes? Otherwise, what has been driving an equal deceleration in the marginal productivity of all factor inputs over the last decade?
18. Many studies have looked into the factors accounting for Italy’s productivity slowdown over the 1990s. Among the explanations offered are the following:
- Mismeasurement of factor quality changes. Estimates of TFP growth are often used to proxy technological progress. They are obtained as the residual output growth once the weighted contributions of changes in capital and labor inputs are accounted for. Therefore, TFP growth estimates involve a number of assumptions concerning the measurement of output and inputs.
- In the case of capital, quantities and prices should be adjusted for changes in quality. Table 1B shows growth decomposition results using available annual data from the Italy-specific total economy Groningen Growth and Development Center (GGDC) database, which takes into account price and quality changes in different categories of capital (for convenience grouped here into ICT and non-ICT). Compared with results obtained using unadjusted OECD data (Table 1A), it appears that quality improvements in capital are indeed absorbed by the Solow residual, roughly accounting for some 0.1 percent of TFP growth throughout the sample (Figure 2A). However, changes in the quality of capital do not seem to be able to explain the fall in productivity growth characterizing the second half of the 1990s.
- In the case of labor, changes in skills and educational attainment need to be explicitly taken into account. Brandolini and Cipollone (2001) adjust the labor contribution to value added growth in Italy’s industrial sector by correcting for changes in the composition of the employed labor force using wage differentials, as well as effective hours worked and capacity utilization. Overall, they find that a sizeable part of the growth in the Solow residual vanishes after the adjustment, although the latter is not sufficient to overturn the evidence of a productivity slowdown in the second half of the 1990s (Figure 2B).
- Measures of growth rates of TFP can also be sensitive to aggregation methods. This may be the case particularly when quantities and user costs of some disaggregated inputs evolve along different patterns than those of the aggregate. This is the case, for example, when quality improvements in some particular capital inputs (such as ICT) are faster than those in others. A measure of TFP growth that fully accounts for changes in the composition and quality of both labor and capital inputs captures “disembodied” technological and organizational improvements that increase output for a given amount of inputs. Table 1C reports results from a very recent study looking at this issue using Italian data:7 once compositional and quality changes are properly measured, TFP is left to explain less than ¼ of output growth. However, on average, compositional changes in capital accumulation seem to play a limited role—another 0.1 percent—in explaining the recent productivity deceleration in the Italian economy.
- It may also be interesting to assess the extent to which improvements in the quality of capital and labor have boosted productivity in industries and countries that have invested in them. For example, the shift towards ICT assets, whose relative prices have been falling, implies that with the same amount of resources it is possible to acquire a greater amount of productive capital services. This suggests that there is also an “embodied” element of technological change due to the expansion of the productive capacity from the shift toward ICT assets.8Bassanetti and others (2004) estimate that the major contribution to Italy’s TFP growth over 1981-2001 has come from the service sector—in particular transport, communication, and financial intermediation—where the ICT capital accumulation has been the largest. Net of “embodied” technological change—the authors conclude—the productivity slowdown in the second half of the 1990s would have been even larger.
- Variable factor utilization. Solow’s (1957) original contribution presumed that variations in capacity were a major reason for the procyclicality of measured productivity, a presumption widely held thereafter.9 In essence, the problem is one of cyclical mismeasurement: true inputs services are more cyclical than measured inputs services. As a result, productivity—as measured by the Solow residual—is spuriously cyclical. Within a cost-minimizing framework, variable factor use can be due to swings in marginal factor costs. According to this hypothesis, the decline in labor productivity over the second half of the 1990s may reflect a fall in the marginal cost of labor. If labor has become particularly cheap, firms will work existing employees for shorter periods (decreasing observed hours per worker) and less strenuously (thereby decreasing unobserved productivity).
- Distorsions and markets imperfections. Productivity and technology may also differ because of distorsions, such as imperfect competition, the presence of increasing returns, etc. In general, if firms are not all perfectly competitive, then it is not appropriate to use a standard production function framework and, consequently, to use the Solow residual as measure of exogenous technology shifts, since the Solow residual becomes endogenous.10 Following are few examples of distorsions and imperfections characterizing the Italian market structure, whose effects on factor efficiency might have been incorrectly captured by measures of the Solow residual.
- Relatively high tax ratios, deemed to have undercut Italy’s growth performance by discouraging labor supply and investment;11
- A heavy regulatory burden in labor and product markets and bureaucratic red tape, likely to have hampered competition and stifled incentives to invest;12
- The resilience of the intra-sectoral structure of the Italian economy, echoing an inability of reallocating resources towards sectors with higher-than-average factor productivity;13
- A large share of small and medium enterprises, which might have hobbled productivity growth by limiting the scope for economies of scale and technology transfers.14
Figure 2A.Looking at TFP Adjusting for Compositional and Quality Changes in Capital
Source: OECD; Marcel P. Timmer, Gerard Ypma and Bart van Ark, IT in the European Union: Driving Productivity Divergence?, 2003, Groningen Growth and Development Centre; and staff calculation.
Figure 2B.Looking at TFP Adjusting for Compositional and Quality Changes in Labor
Source: A. Brandolini and P. Cipollone, “Multifactor Productivity and Labour Quality in Italy, 1981-2000”, 2001, Banca d’Italia; and staff calculation.
|Looking at contributions to growth…||Looking at capital deepening…|
|Looking at contributions to growth…||Looking at capital deepening…|
|Labor||Capital||IT||Non-IT||TFP||Value Added||Capital Deepening||Capital Quality Changes||Labor Quality Changes||Output Composition||TFP||Labor|
19. A rigorous analysis of the mechanisms triggering suboptimal productivity performances in Italy over the last decade is clearly beyond the focus of this paper. We limit the analysis to arguing that any reasonable explanation of the productivity puzzle should account for key stylized facts across four dimensions. Namely: (i) the cross-country dimension, e.g. changes in comparative performance with respect to other industrial countries; (ii) the cross-sector dimension, e.g. changes in comparative performance across inputs and product markets; (iii) the structural dimension, e.g. changes in macroeconomic responses to structural shifts; and (iv) the cyclical dimension, e.g. changes in business cycle comovements among relevant aggregates.
20. Considering the vastness of the problems raised in this section, the focus of the rest of this chapter is modest. The next section is a first attempt to explore dimensions (iii) and (iv) of Italy’s productivity puzzle. The approach is agnostic. To measure the relative importance of structural and cyclical components in explaining growth variations, (the log of) real GDP is decomposed into a stochastic trend component characterized by a time-varying growth rate (i.e., potential output) and a stationary component exhibiting cyclical fluctuations (i.e., the output gap), using univariate and multivariate detrending techniques. Inter alia, we will look at model-based implementations of the production function growth accounting framework, to analyze structural shifts in factor input trends and business cycle comovements among macroeconomic aggregates of interest—such as output and productivity, output and unemployment, and productivity and hours.
C. The Pieces: Unobserved Components for Growth Accounting
The Business Cycle Revisited
21. Real Business Cycle macroeconomics traditionally identifies aggregate business cycle fluctuations with “those movements in the series associated with periodicity within a certain range of business cycle duration”.15 In conformity with the classical NBER definition of business cycle, this range of business cycle periodicities is assumed to be between 6 quarters and 8 years. Drawing on the theory of spectral analysis, Baxter and King (1999) proposed a univariate two-sided moving average filter able to “extract” from the data only fluctuations within this range of frequency—the Baxter-King filter (BK, henceforth). In this way, both high frequency fluctuations (lasting less than 6 quarters and mainly associated with measurement errors and seasonality) and low frequency fluctuations (lasting more than 8 years and possibly associated with variations in trend growth) are removed from the data.16 On this ground, macroeconomic series are decomposed into irregular, cycle, and trend components, respectively corresponding to the high, business cycle, and low frequency parts of the spectrum. Juxtaposing detrending outcomes obtained using the BK filter with those previously derived using the HP filter highlights that differences between these two approaches are, by and large, negligible (Figure 3). The robustness of the results holds with respect to both business cycle (top panel) and potential growth (bottom panel) estimates.
Figure 3.Two-sided moving average filters of output gap and potential growth
Source: OECD and staff calculation.
22. Spectral density analysis reveals that the Italian business cycle is characterized—on average—by 4½ years duration, just slightly shorter than the 5-year business cycle typifying the euro area.17 The standard deviation of output is estimated at 1.35 percent, suggesting that the Italian business cycle is somewhat more volatile than the euro area’s (0.84 percent), but comparable to that of the US (1.34 percent).18 Over the sample period, trough-to-peak expansions have an estimated average duration of 13 quarters and are longer than recessions, with 9-quarter average duration. This asymmetry is quite common in post-war data for industrial countries and it is generally associated to positively sloped output trends. Dating the business cycle indicates that the most severe recession occurred over the period 1974Q1-1975Q3 followed, in terms of amplitude, by those in 1963Q4-1965Q1, 1980Q2-1983Q1, and 1969Q1-1972Q4. The recessions of 1990Q1-1993Q3 and 1976Q4-1977Q4 had, instead, somewhat smaller amplitude.
23. Although its cycle was highly synchronized with that of the euro area cycle throughout the sample period, Italy experienced much larger fluctuations in the 1970s. This is likely due to the heavy Italian reliance on imported oil. The Italian fluctuations subsequently decreased, as the share of energy related imports declined (by around 40 percent) during the 1980s. However, as it is the case for other industrial countries, the fall in volatility of fluctuations experienced in Italy since the mid-eighties may also be the result of a combination of other factors, such as better policies and shifts in output composition.19
24. Comovements—as expressed by correlations—between the overall business cycle and corresponding fluctuations in labor market indicators show that aggregate employment, average hours worked, capacity utilization, and labor productivity are strongly procyclical.20 Interestingly, this is also true for participation in the labor market, a component that is hardly assumed to be subject to short-run shifts. Employment, labor force and labor participation lag the business cycle, whereas capacity utilization and labor productivity are coincident with it. There is also evidence that movements in the number of hours worked per employee in the business sector are a genuine predictor of the Italian business cycle, leading the cycle by approximately one quarter. In contrast, fluctuations in unemployment rate are only weakly countercyclical and lag the cycle by one year. Preliminary data analysis hence provides some evidence in favor of the existence of short-term frictions in the labor market—a hypothesis that justifies swings in labor efficiency to echo the business cycle, as firms would hire a more-than-optimal number of working hours for a given decline in production.
25. However, productivity responses in the current (i.e. post-2001) downturn seem to signal a greater degree of idling capacity with respect to productivity responses observed over the 1992-93 recession. Over the first half of the 1990s, the drop in total hours worked (and the reduced contribution from capital) more than offset the contraction in growth, while average hours work had remained roughly unchanged. Labor efficiency actually rose, as adjustments in the labor market occurred via downward shifts in the supply of labor. Over the recent slowdown, however, labor productivity has dropped sharply, with declines in average hours and spare capacity carrying the burden of the adjustment in the labor market. Such a correction, however, has not been sufficient (so far) to offset the exceptional upturn in labor supply resulting from structural factors such as the effects of pension and labor market reforms, wage moderation, and the emergence of underground economy.21 However, given that two-sided moving average filters are inapt to characterize economic developments after 2001 (Box 1), evidence of cyclical fluctuations over the recent slowdown has remained—so far—anecdotical.
Decomposing Real GDP
26. Attention is, hence, turned to real-time estimates of the output gap and potential output using unoberved components (UC) models. The attractiveness of the UC approach lies in the fact that it combines positive aspects of purely statistical and purely structural estimation methodologies. Moreover, it does not suffer from the end-point problem, as the filters implicitly defined by the model automatically adapt to the end of the sample. To this end, a quite flexible univariate UC model is specified in order to evaluate the relative importance of short-run variations in the degree of capacity utilization and permanent changes in the potential capacity of the economy in real time.22 The general form of the system can be written as follows:
where y is the log of real output, y* is potential output—with time-varying growth rate gt— and yc is the output gap following a stationary autoregressive process of second order, φ(L). Here,
27. In this model, potential output follows a random walk with drift, and the growth rate can take different shape, depending on the value of ρy. For instance, if ρy=1 real output is an integrated series of second order, i.e. I(2), while if 0<ρy<1 its growth rate varies over time but converges back to a steady-state rate, g0. The dynamics of potential output and the output gap depend on the nature of the shocks, that is, on the relative importance of supply and demand shocks. This relative importance, which determines the smootheness of the trend component, is the ratio of the variance of the cycle to the variance of the trend fluctuations. A small ratio—denoted as λ in Box 1—implies that shocks to the economy are mainly supply shocks, where potential output moves nearly with the data, and hence a small output gap is expected. On the contrary, a larger weight on the smoothness of the trend means that shocks to the economy are primarily shocks to aggregate demand. Such a parameter λ can either be selected a priori—as it is with the HP filter—or jointly estimated with other parameters of the model—as it is the case with UC models. In this sense, UC models somewhat encompass the HP filter.
28. Once model (1) is cast in the state space form, the Kalman filter and the associated smoothing algorithm enable maximum likelihood estimation of the model parameters and signal extraction of the unobserved components, conditional upon a discretionary set of starting values.23Table 2 reports estimates and standard errors of the model parameters, equation diagnostics, and the predicted final state for potential growth and the output gap. Estimates of the unrestricted univariate model (not reported) provide a poor representation of the Italian business cycle, featuring a very short cycle first-order autoregressive cycle with small disturbance variance coupled with non-stationary and highly volatile underlying output growth. Restricting the variance of the drift to zero reduces potential output to a random walk process with constant drift (also not reported)—a specification consistent with the stationarity of the GDP growth rate. However, ρy appears to be insignificantly different from unity, so that the model is actually forcing convergence towards the rate of trend growth at the end of the sample. Compared to unrestricted estimates, cyclical variability is slightly increased at the expenses of the trend.
|AR(5)||0.59 [0.71]||71.5 [0.00]*||0.57 [0.72]||0.87 [0.50]||1.02 [0.41]|
Standard errors are in parentheses. (--) indicates restricted estimates.
P-values are provided in square brackets. Starred probabilities indicate significance at 1 percent level.
Standard errors are in parentheses. (--) indicates restricted estimates.
P-values are provided in square brackets. Starred probabilities indicate significance at 1 percent level.
29. When the variance of the trend is restricted to zero, potential output becomes a local linear trend, with changes in the trend fully captured by changes in the slope, which evolves smoothly over time (model “UNI_s” in Table 2). Under the current specification, changes in potential output become overly “cyclical”, with swings in potential reflecting an interaction of the trend and the cycle component. The output gap follows a stationary second-order autoregressive process, with roots equal to 1.11 and -0.26 respectively, yielding a cycle with a period of 4½ years. The fit is satisfactory and there is no evidence of significant misspecification. At the end of the sample, potential growth is estimated to be around 1 ¼ percent, with output being below potential by some 1 percent. Uncertainty around the estimates is high, with predictive standard errors of 0.9 percent. Out of total uncertainty, about two thirds is due to uncertainty about disturbances, whereas only one third is associated with parameter uncertainty.
30. Finally, we restrict model (1) to yield HP estimates of the trend (model “UNI_hp” in Table 2). This amounts to setting the level shock to zero, a smoothing parameter to 1600, a random walk trend growth rate with nonzero variance, and a serially uncorrelated output gap. Under these conditions, only one parameter is to be estimated, namely the variance of the drift. Both the relatively low value of the likelihood and the diagnostics strongly reject these restrictions.
Conditioning on Okun’s Law…
31. In general, univariate methods lack important economic content. Accordingly, in this section, the detrending methodology presented above is extended to ensure theoretical consistency among fluctuations of relevant macroeconomic aggregates—such as output, unemployment, and inflation—over the business cycle.
32. Estimates of the output gap (and related potential growth) should ideally be consistent with estimates of deviations of unemployment from their corresponding equilibrium paths. To this aim, specification (1) is first augmented with a version of Okun’s law, thereby extending the original univariate model with smooth trend into a bivariate unobserved component model of real GDP and unemployment rate, where the unemployment rate is decomposed into a trend and cyclical component as well.24
33. Specifically, bivariate estimates of the output gap employ the additional information contained in the comovement of output and unemployment over the business cycle. By imposing a general version of Okun’s law linking the transitory components of unemployment to the output gap, unemployment can be defined as follows:
where u is the unemployment rate, u* is the non-accelerating inflation rate of unemployment (NAIRU), and uc is the transitory component of the unemployment rate that is assumed to be a function of the current and lagged output gaps with loading factors θi. Remaining notation is analogous to the univariate output model. The corresponding bivariate UC model can be obtained by combining the ouput equations (1) with the unemployment rate definition given by (2), under the assumption that disturbances are mutually independent and independent of any other disturbance in the output equation.
34. Estimates of the preferred UC bivariate model yield local linear trends for both unemployment and output, with changes in their respective slopes evolving smoothly over time (model “BIV_s” in Table 2). The transitory component of unemployment loads negatively and significantly on the common cycle, though with a small and lagged response. It indicates that a 1 percentage point increase of output over potential, decreases short-run unemployment by less than 0.05 percent in the next quarter. Both parameter estimates and the final states of unobserved components are in line with the output decomposition implied by the univariate specification (Figure 4A and 4B), yielding a NAIRU of about 8 ½ percent at the end of the sample.
Figure 4A.Real-time Estimates of the Output Gap
Source: OECD and staff calculation.
1/ Percentage deviations from sample average.
Figure 4B.Real-time Estimates of Potential Growth
Source: OECD and staff calculation.
35. Results are also remarkably consistent with observed business cycle stylized facts, confirming that dynamics in the unemployment rate are essentially permanent. The fit is satisfactory with no significant evidence of misspecification. With respect to the univariate UC model, the uncertainty surrounding output gap and potential output estimates is reduced, a consequence of imposing a common cycle. Overall, accounting for labor dynamics affects only marginally our univariate estimates of the output gap, which remain largely dependent on the nature of idiosyncratic shocks. In other words, the unemployment rate has little informational content for the evaluation of the relative importance of cyclical components of economic activity (e.g. demand pressures).
… and a Phillips Curve
36. In line with the notion that potential output is the level of output ensuring stable inflation, we hence attempt to condition the decomposition of output on the information contained in models (1)-(2) and on the ability of the output gap to explain inflation within a short-run Phillips curve relationship:
where π is 4 times the quarterly difference in the log of consumer prices; π* is the underlying (expected) annualized level of inflation—which is defined as a stationary autocorrelated process converging to a steady-state level πº; γ(L)yc are demand pressures—expressed as a function of the output gap previously defined. Finally, z captures exogenous factors affecting headline inflation (e.g., changes in the nominal effective exchange rate of the euro and in oil prices), whereas vut represents shocks to inflation. Note that the effect of changes in oil prices is immediate, but inertia in the inflation process is taken into account via the autoregressive processes characterizing both the output gap and underlying inflation. In this respect, ρπ can be viewed as the degree of backward-lookingness intrinsic in agents’ expectations formation process, so that πº would be the authorities’ long-term inflation objective. Parameter estimates of the preferred trivariate (labeled “TRI”) model (1)-(2)-(3) are reported in Table 2 for comparison with previous models.
37. The ouput gap enters the Phillips curve positively, significantly, and with a large coefficient, implying that a 1 percent increase of output over potential raises actual inflation by about 0.4 percent. In line with previous estimates, transitory unemployment is likely to fall by more than 0.04 percent in response to a 1 percent increase in the output gap. The response of inflation to changes in oil prices is expected to be very low (around 0.02), but subject to high uncertainty. The degree of inflation persistence is quite high, with a coefficient on backward-looking inflation likely to be above 0.5, with full pass-through taking longer than 3 years. However, the large confidence interval around this estimate suggests that a model with time-invariant inflation persistence may be inappropriate.
38. Potential growth is estimated around 1.3 percent by the end of the sample, whereas the size of the output gap is expected to be just below 1 percent. Corresponding final state estimates for the NAIRU are above 8½ percent. The long-term inflation objective is forecasted around 2 percent, although the estimate is also surrounded by high uncertainty. In spite of the similarity of parameter estimates provided by previous model specifications, the trivariate model implies greater variability of the output gap, especially over the 1970s (Figure 4A). Conditioning output decomposition on the ability of the output gap to predict inflation implies upward revisions of the measure of inflationary pressures over periods in which supply-side shocks have been predominant.
The Production Function Approach Revisited
39. In order to compare real-time estimates of potential output derived from UC models with corresponding measures based on traditional PFA, the output decomposition is then carried out within a revised production function framework. The rationale is to obtain estimates of potential output from the trend levels of its structural determinants, such as productivity and factor inputs. If technology has the usual Cobb-Douglas representation with constant returns to scale, the aggregate production function takes the general form:
where β is the labor share, L denotes total hours worked in the economy, K is the capital stock adjusted for the degree of capacity utilization C, taking values over the interval (0,1]. Taking logs of both side of equation (4)—here denoted by small caps—yields:
40. All factor inputs in equation (5) can be additively decomposed into their potential and transitory components, with the exception of the capital stock, which is assumed to be fully permanent and, hence, to contribute only to potential. Under the assumption of full capacity utilization, e.g. if c is fixed at 0, the cyclical component of the Solow residual is likely to absorb transitory swings in the intensity of capital use, hence displaying more business cycle variability than strictly defined TFP. Algebrically:
41. The log of total hours (l), in turn, can be additively decomposed into its determinants, e.g. working-age population (wpop), participation ratio (pr), the unemployment rate (u) and the average number of hours per employee (h).25 These determinants can be also disentangled into their own permanent and cyclical components, so that the permanent and cyclical labor contributions can be written as:
The intuition is that population dynamics are fully permanent, whereas labor force participation, employment, and average hours contain also cyclical information.
42. Combining identities (5)-(6)-(7) yields the required model-based output decomposition, where the reference cycle—ψt, an autoregressive process of second order that is here constrained to be common across factor inputs—is driven by fluctuations in the industrial production index, ip. As such, the four transitory components, e.g. the Solow residual, ac, the participation ratio, prc, the unemployment rate, uc, and the average hours, hc, can be expressed as linear combinations of current and lagged values of the reference cycle. Corresponding factor inputs trends—denoted by vector μt—are assumed to follow random walk processes with stochastic drifts—denoted by vector Kt. The growth rate of each factor trend can thus take a different shape, depending on the value of the corresponding element in the vector P. For instance, if the first element in P is estimated to be insignificantly different from 1, then TFP is an integrated series of second order; else, if 0<P1<1 the time-varying TFP growth rate converges back to a steady-state rate, K1*. The resulting multivariate UC model (8) -labeled “PFA” in Table 2—can be represented as follows:26
43. Overall, cyclical fluctuations in productivity and factor inputs load significantly on the common cycle and with expected signs. In particular, the cyclical behavior of TFP is found to be remarkably in line with the business cycle. Both have dramatically plunged below trend since 2002 and displayed a substantial increase in the degree of cyclical volatility since 1999. The unemployment rate is found to be significantly countercyclical and—consistently with previous model estimates—to fall by about 0.04 as ouput rises 1 percent above potential. Interestingly, labor participation variations are found to be broadly acyclical, whereas there is evidence of positive comovements between average hours worked per employee, output, and productivity, once structural shifts in factor trends have been identified. Implied output gap estimates tend to exhibit higher volatily than corresponding estimates from the univariate UC model specification (Figure 4A). Nonetheless, there is no evidence of significant residual misspecification.
44. At the end of the sample, potential growth is estimated to be lower than in previous models, reflecting a sharp drop in the permanent contribution of total factor efficiency. Interestingly, the structural behavior of real output and TFP is found to be markedly different, while comoving over the cycle. A structural break in cyclically-adjusted TFP trend growth is identified in the mid-1990s. The drift component of TFP has shifted down significantly since then, reducing the average rate of TFP growth from one percent to zero (Figure 5A). On the contrary, potential growth is found to have progressively recovered from the end of 1993 to the end of 2001, rising from an annual rate of 0.7 percent at the end of the 1992-93 recession to over 2 percent just before the current slowdown—a growth rate analogous to that of the early 1990s (Figure 5B). Finally, there exists a constant wedge between trend growth in labor and in factor productivity, confirming the idea that the rate of capital deepening has remained stable over time, at around 1 percent.
Figure 5A.Looking at Cyclically-Adjusted TFP
Source: OECD and staff calculation.
Figure 5B.Looking at Potential and TFP Productivity Growth Using UC Models
Source: OECD and staff calculation.
45. Interesting information can be extracted by decomposing the covariance matrices of trend slope and cyclical disturbances. The bulk of the permanent variation in output is found to be driven by shifts in labor trends, namely labor participation and employment. Conversely, the Solow residual appears to absorb almost 90 percent of the cyclical variation in real GDP. In other words, changes in employment are likely to respond very little to business cycle fluctuations, which have been largely associated with shifts to productivity and, to a much smaller extent, variations in per capita hours worked.
46. Overall, the robustness of the results is encouraging. In line with previous studies for Italy and the euro area, the chapter finds that a sizeable part of the growth in the Solow residual vanishes after adjusting for cyclical factors, although the adjustment actually reinforces the evidence of a slowdown in trend TFP growth over the second half of the 1990s. The chapter also provides evidence that the major source of potential growth variation is likely to be associated with changes in labor participation, confirming the permanent (i.e. structural) nature of labor market dynamics. Shifts in productivity, instead, are able to explain the bulk of business cycle fluctuations and are positively correlated with transitory movements in average working hours and capacity utilization. Because of the high volatility of the Solow residual, conditioning real-time output decomposition upon indicators of demand pressures in product and labor markets provides smoother estimates of potential growth than unobserved component models relying on a production function approach (Figure 4B).
D. Concluding Remarks
47. This chapter presents updated estimates of potential growth and the output gap, using new techniques that draw on comovements of output, employment and inflation over the business cycle to distinguish trends from cycles. One puzzling aspect of Italy’s growth performance over the last several years has been the limited response of output growth to the steady increase in labor supply that has accompanied structural reforms. The chapter’s results indicate that even after correcting for cyclical factors, trend productivity growth—already on a downward slope for decades—has declined sharply since the mid-1990s, and it remains a drag on growth going forward.
48. There is nonetheless evidence that a significant portion of the sharp decline in labor productivity over the current downturn is cyclical rather than structural, with capacity utilization falling despite the rise in the labor input. For this reason, the exceptionally low productivity growth over the current protracted downturn does not necessarily point to a deceleration in potential growth. It rather provides empirical basis to hope for some recovery in growth in the near future, as cyclical conditions improve and firms seek to maximize labor efficiency.
49. From a normative viewpoint, this chapter’s analysis carries noteworthy policy implications. It stresses the importance to address not only factors preventing further employment growth, but also those constraining factor efficiency. Evidence of stagnant and procyclical productivity growth may support the hypothesis of a (negative and persistent) demand shock within an economy featuring a (structural) increase in wage flexibility.27 At the same time, however, the enduring sluggishness in factor efficiency may conceal the need to reduce distorsions in product markets, including inadequate competition in key sectors and overhead costs. The negative link between long-term TFP performance and the degree of frictions and imperfections in the economy—such as imperfect competition or costs of reallocating inputs—has been widely recognized by the literature both on theoretical and empirical grounds.28 Further research is, however, warranted to assess whether this channel could explain the significant slowdown in Italy’s productivity growth over the second half of the 1990s.
In general, for Kalman filter estimation, a linear dynamic model involving unobserved state variables needs to be expressed in its state-space representation. The latter consists of two sets of equations: the measurement and the transition system. In this appendix an example of such systems is provided, with reference to the bivariate model defined by equations (1)-(2) in the main text. The Kalman filter estimation of its parameters is also discussed.29
Model (1)-(2) can be represented by two measurement equations linking real GDP and the current unemployment rate to six unobserved state variables, where the subscripts t reflect the fact that these unobserved components are assumed to vary over time. The notation is the same as in the main text:
The first measurement equation is an identity, stating that observed real GDP is given by the sum of two independent unobserved components, potential output and the output gap. Similarly, the second measurement equation defines the unemployment rate as the sum of a stationary (unobserved) component—the unemployment gap—and a non-stationary (unobserved) component—the NAIRU. Specifically, the unemployment gap is assumed to be a function of current and lagged output gaps, with loading parameters θ0 and θ1, respectively. The dynamics of the time-varying unobserved stochastic processes are described in the transition system below:
Note that and
Once a dynamic linear model is written in state-space form, a recursive procedure—e.g. the Kalman filter—allows the optimal estimate of the vector of unobserved components—e.g. potential output, the output gap, the NAIRU, and the two trend slopes—conditional upon an initial set of initial parameters and the appropriate information set. Hence, the Kalman filter provides the minimum mean squared error estimate of the unobserved state vector, given the appropriate information set. More specifically, the basic filter provides an estimate of the unobserved state vector conditional upon the information available up to time t. The smoothing provides a more accurate estimate on the vector, by using all the available information in the sample through time T.
Under the assumptions of model linearity and Gaussian disturbances, the conditional distribution of the observed variables—e.g. real GDP and unemployment—is also Gaussian. As such, the sample log-likelihood function can be maximized with respect to the unknown parameters of the model and the set of parameters can be estimated using a maximum-likelihood estimator. Iterating the basic filter starting from t=1 to T, while evaluating the log likelihood function from observation τ+1 (where τ is large enough) to T, minimizes the effects of some arbitrarily chosen initial values on the log-likelihood value. On the other hand, the last iteration of the basic filter provides the initial values for the smoothing.
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