Estimating Poland's Potential Output
A Production Function Approach
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

Author’s E-Mail Address: nepstein@imf.org; corrado.macchiarelli@unito.it.

The paper develops a methodology based on the production-function approach to estimate potential output of the Polish economy. The paper concentrates on obtaining a robust estimate of the labor input by deriving Poland's natural rate of unemployment. The estimated unemployment gap is found to track well pressures on resource constraints. Moreover, the overall results show that, prior to the recent global financial crisis, Poland's output and employment were both growing above potential. The production function is also used to derive medium-term projections of the output gap. According to our methodology, in the aftermath of the global crisis, Poland is not expected to experience a sizable and persistent negative output gap.

Abstract

The paper develops a methodology based on the production-function approach to estimate potential output of the Polish economy. The paper concentrates on obtaining a robust estimate of the labor input by deriving Poland's natural rate of unemployment. The estimated unemployment gap is found to track well pressures on resource constraints. Moreover, the overall results show that, prior to the recent global financial crisis, Poland's output and employment were both growing above potential. The production function is also used to derive medium-term projections of the output gap. According to our methodology, in the aftermath of the global crisis, Poland is not expected to experience a sizable and persistent negative output gap.

I. Introduction

1. It is well known that estimates of potential productivity levels are useful in evaluating the non-inflationary growth paths of both output and employment. In this regard, purely statistical methods applied to historical levels of output directly, such as the Hodrick-Prescott (HP) filter, tend to misidentify boom and bust periods and the extent to which wide fluctuations in growth are fully driven by economic fundamentals.2 The use of an HP filter can be particularly problematic in estimating potential growth in emerging market economies like Poland where output fluctuations can be relatively large, due to their vulnerability to global shocks and to structural changes (such as transition to the market economy, or EU accession). Consequently, a growing consensus has emerged toward ‘production function’-based methodologies, which have strong theoretical foundations (see e.g., Cotis et al., 2005, Dupasquier et al, 1997), although new non-parametric methods are also emerging.

2. In this paper, we adopt a standard Cobb-Douglas production function methodology to derive the output gap for Poland over the 1995-2008 period.3 To estimate Poland’s potential growth, we mainly require that potential output be consistent with the notion of ‘full employment.’ The estimation entails obtaining Poland’s natural rate of unemployment, for which we augment a Kalman decomposition of the unemployment rate with a Philips curve application.

3. We find that, during the boom years preceding the recent financial crisis, Poland was growing above its potential. This is consistent with the observed behavior of inflation and our estimated unemployment gap, and with the view that part of that growth could be characterized as “bubbly.” Finally, we employ the new methodology to project potential growth in the medium term. We find that, in the aftermath of the current downturn, Poland is not expected to experience a sizable and persistent negative output gap. Indeed, the crisis spillovers appear to not have been as severe relative to other countries in the region.4

4. The structure of the paper is as follows. Section II briefly discusses the production function and presents the parameter estimates for Poland. In section III, we derive the potential levels of the production function inputs, paying particular attention to the equilibrium employment estimates. Section IV discusses the potential output estimates. Section V concludes.

II. The Production Function and Parameter Estimates

5. Following a standard application in the literature, the Polish economy is assumed to be characterized by a Cobb-Douglas production function with constant returns to scale (CRS) technology:

Yt=AtLtKtβ(1)

where Yt is output, Lt and Kt are labor and capital, and At denotes total factor productivity; and where the output elasticities sum up to one, i.e., α + β =1.5

6. The labor input is defined as the number of employees in the economy based on the Polish Labor Force Survey (LFS). The capital stock series is constructed from total investment assuming perpetual inventories, hence:

Kt=(1δ)Kt1+It(2)

where capital stock in each period is measured by the previous-period stock (net of depreciation) augmented with new investment flows. Consistent with previous studies, the depreciation rate δ is assigned the value 0.05, while an initial benchmark is computed as K1995Q1=I1995Q1/(δ+i) with i being the average logarithmic growth rate of investment in the sample period 1995-2008. Unit root tests for GDP, capital and labor suggest that all variables are non stationary (Table 1), while standard Johansen’s (1991) cointegration tests suggest the existence of one long-run relationship among the variables (Table 2).6 Since a small sample bias remains, dynamic OLS estimates (Stock and Watson, 1993) are also obtained (Table 3).7 In contrast with the OLS estimates, the sum of the unrestricted DOLS is statistically close to one, hence the CRS assumption.8 Indeed, CRS is not rejected at a standard significance level. Moreover, the resulting restricted coefficients are broadly consistent with earlier studies adopting a production-function methodology for the Polish economy (see Gradzewicz and Kolasa, 2005).

Table 1

ADF test statistics for variables’ stationarity

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1\ (p-values) in parenthesis.
Table 2

Johansen’s cointegration test

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1\ Cointegration analysis based on an unrestricted VAR model with 1 lag and no constant term.

(*) denotes rejection at 5% critical level.

Table 3

Static and dynamic least squares estimation

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1\ In the regression it is used the robust standard errors option (Newey West).2\ (p-values) and [standard errors] in parenthesis. All coefficients are significant at 1% critical level.3\ The number of leads and lags in the DOLS regression is equal to four.

III. Estimating Potential Inputs

7. We begin by deriving standard measures for the trend total factor productivity and for the potential utilization of the existing capital stock. The total factor productivity term is obtained as a Solow residual from (1):9

At=(YtLtKt1)(3)

As for the potential utilization of the capital stock, a capacity utilization series is not available. In this regard, and consistent with the literature, we assume the full utilization of the existing stock of capital. Such a simplification mostly relies on the assumption that, given the perpetual inventories rule, the capital stock can be regarded as an indicator for the overall capacity of the economy (Denis et al., 2000)10.

8. In order to obtain potential employment, we first derive the non-accelerating inflation rate of unemployment (NAIRU). We estimate the NAIRU in two steps.11 First, the unemployment rate is modeled as the sum of a trend and a cyclical component, where the trend component is regarded as a benchmark for the equilibrium unemployment rate and the cyclical component as a reference for the unemployment gap. In the second step, a standard Philips curve relationship is applied to help model the cyclical component.

A. First step: Kalman Decomposition of Unemployment

9. The unemployment rate is assumed to be described by the sum of a stochastic trend component (U¯t) and a cyclical component (Gt), as:

Ut=U¯t+Gt(4)

where the trend component follows a local linear trend model; specifically:

U¯t=μt+U¯t1+ηt(5)

where the trend unemployment is described by a random walk plus drift process, and where the drift is allowed to be stochastic, i.e. μt=μt–1+ξt.12 The error term in (5) is assumed to be ηt ~ i.i.d. and N(0,ση2). When the standard deviation ση=0 the NAIRU is time-invariant (Box 1), otherwise the NAIRU varies by the amount ηt in each period. In this regard, we assume a “smoothness prior” (ση= 0.1) consistent with Gordon (1996), which allows the long-run unemployment rate to display the desirable property of shifting smoothly.13 Following Denis et al. (2002) and Fabiani and Mestre (2004), the cyclical component is modeled as a stationary (Ф1+Ф2<1) second-order autoregressive process,

Gt=ϕ1Gt1+ϕ2Gt2+Ψt(6)

In this paper we treat both the cyclical and the trend as unobserved components. A Kalman filter is employed to extract these components subject to equations 5 and 6 (Table 4, first column).14

Table 4.

Cyclical Component and Phillips Curve Estimates

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1\ For column I and III results are obtained using a Kalman smother (Broyden, Fletcher, Goldfarb and Shanno algorithm).2\ (*) denotes significant at 5%, (**) significant at 10%,(***) not significant. Otherwise significance is at 1%.3\ [standard errors] in parenthesis.

B. Second Step: Economic Identification—Philips Curve

10. We identify the cyclical component (Gt) according to a Philips curve relationship, i.e.

Δπt+1=γ+α(L)Δπt+ρ(L)Gt+β(L)Zt+ɛt(7)

where α(L), ρ(L) and β(L) are polynomials in the lag operator of order 2, 0 and 1, respectively. Δπt+1 is the change in the inflation rate at time t+1, while the exogenous regressor Zt proxies for supply side shocks by including changes in import price inflation.

11. Estimating equation (7) entails a non-linear estimation. For increased precision, the estimation is initialized with an OLS regression where the unemployment gap is first approximated by the cyclical component obtained in the first step.15 The cyclical component (Gt) is consequently treated as unobservedand hence re-estimated within equation (7) under the specification in (6). See Table 4 (third column).16

C. NAIRU Estimates

12. Figure 2 displays the actual unemployment rate together with the results obtained in step one and step two. The equilibrium unemployment derived in the second step is approximated by the predicted unemployment rate consistent with the NAIRU.17 Henceforth, the paper concentrates on the second step results. Figure 3 reports the unemployment gap (or cyclical component) derived from equation (6) instep two. By definition, the gap is assumed to be the difference between the actual unemployment rate and its equilibrium level. The estimated gap appears to follow the post-reform business cycle in Poland:18 it hits a trough at the outset of the 1998 Russia crisis, then rises steadily through the 2001–02 global recession, before declining following EU membership. The gap appears to hit a bottom again during the current downturn, driven by the global financial crisis. In Table 5, the observed unemployment rate series is reported together with the results obtained above. A standard HP filter of the unemployment rate is also reported as an additional reference.

Figure 1.
Figure 1.

Poland: Recursive Estimates of Cobb-Douglas Coefficients

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

1/ All series for the coefficients are plotted together with upper and lower (± 2) confidence bands.Source: Authors’ computations.
Figure 2.
Figure 2.

Poland: Actual, Equilibrium, and Trend Component of Unemployment

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

Figure 3.
Figure 3.

Poland: Unemployment Gap (Phillips Curve Estimation) 1/

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

Source: WEO and authors’ computations.1/ The unemployment gap is plotted together with upper and lower (± 2) confidence bands.
Table 5

Trend and Cyclical Components of Unemployment

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1\ Reported values based on annual averages.2\ The smoothing parameter for the HP filter is λ= 1600.

13. The empirical relationship between the estimated equilibrium unemployment rate and the rate of inflation is well documented. For example, Ball (1996; 2009) finds a strong empirical relationship between the natural rate of unemployment and disinflation, i.e., countries having experienced large disinflation have encountered a corresponding increase in their natural rate of unemployment.19 Poland is no exception to this rule (Figure 4).

Figure 4.
Figure 4.

Poland: Year-on-Year Inflation versus NAIRU Estimates

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

D. Potential Employment

14. Given the long-run unemployment rate estimates, Polish potential employment level can now be computed as:

Lt*=activetPRt*(1NAIRUt)(8)

where activet is the working age population and PRt* is the trend (or equilibrium) participation rate. The main advantage of using equation (8) is that it results in a potential employment series that is relatively smooth and takes account of changes in the working age population, the trend participation rate, and the structural unemployment rate (NAIRU). A proxy for the equilibrium participation rate is obtained by regressing the actual activity rate on a constant, the unemployment rate and a time trend. The resulting fitted values have been used as a measure for the potential participation rate (Figure 5)20. Indeed, the overall increase in unemployment during the period 1998–2004 is consistent with a downward trend in the participation rate21. Poland’s actual and estimated potential employment are depicted in Figure 6.

Figure 5.
Figure 5.

Poland: Observed and Potential Labor Market Participation Rate

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

Figure 6.
Figure 6.

Poland: Actual and Equilibrium Employment Level

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

Source: IMF World Economic Outlook and authors’ computations.

Time-Invariant NAIRU

The standard NAIRU model is based on an expectational augmented Phillips Curve relation (Greene, 2003):

  1. πt+1πt+1e=ρ(UU¯)t+βZt+vt

    where πt+1e is the expected inflation rate for period t+1. As in Staiger, Stock and Watson (1991), a random walk model for inflationary expectations is applied, i.e. πt+1e=πt so that πt+1 − πt = Δπt+1.

    Since equation (a) does not accommodate serial correlation, it is conventionally estimated in an autoregressive specification, as:

  2. Δπt+1=α(L)Δπt+ρ(L)(UU¯)t+β(L)Zt+ɛt,

    where α(L), ρ(L) and β(L) are lag polynomials and εt is a non-serially correlated error term.

    If U¯t is unobserved, the estimation of equation (b) is non linear. Alternatively, by assuming the equilibrium rate of unemployment to be time invariant (the so called “textbook” NAIRU), equation (b) can be reformulated in such a way to be conveniently estimated by OLS. Assuming U¯tto be constant, equation (b) can be reformulated as:

  3. Δπt+1=γ+α(L)Δπt+ρ(L)Ut+β(L)Zt+ɛt,

    with γ=ρ(L)U¯=U¯Σi=1ρi. It is straightforward to derive U¯=γ/Σi=1ρi. 22

UF2
Source: IMF World Economic Outlook and authors’ computations.

IV. Potential Output Estimates

15. Given the aforementioned trend TFP and potential labor, potential output can be estimated asYt=At*Lt*αKt1α. The key results are depicted in Figure 7. During the boom years preceding the recent financial crisis, Poland was growing above its potential, with an output gap of 2 percent by early 2008. This is also confirmed with an HP filter series. However, while the HP-based output gap peaked earlier and turned negative by end-2008, our new production-function output-gap series exhibits a more gradual reversal, indicating the Polish economy was at a level above potential even as late as the fourth quarter of 2008. This latter observation is also consistent with the behavior of employment relative to its potential. While the annual growth rate of potential employment was slowing down from about 3 percent in early-2008 to 2 percent by the fourth quarter, the growth rate of actual employment remained above 3 percent throughout the year. Thus, to some degree, these results provide evidence that Poland’s rapid output and employment growth pre-crisis was unsustainable.

Figure 7.
Figure 7.

Poland: Production Function Estimates 1/

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

1/ Output gap is computed as (YtYt*)/Yt*, where * denotes potential. GDP growth rates are in q/q annualized, while employment and TFP growth rates are in percent y/y.Source: WEO and authors’ computations.

16. Further evidence of the unsustainability of the growth pattern before the crisis can be uncovered by examining the changes in the contributions of underlying components to Poland’s potential growth in recent years (Box 2). We find that following the 2001–02 recession, the contribution of factor productivity growth was rising steadily through 2004. It remained positive until 2007, but then turned negative through late-2008—largely coinciding with the trend-reversal in potential output growth. At the same time, the contribution of capital was steadily increasing, but it was insufficient to prevent the growth in potential output from declining throughout 2008. Indeed, this suggests that the rapid investment-led output growth in 2006-07 was unsustainable and driven less by fundamentals than one might have considered at the time.

Contribution to Potential Growth

The production function framework allows us to estimate the contribution of each factor of production to potential GDP growth. Changes in these contributions can be assessed as a signal for structural changes in the Polish economy. Below, labor and capital contributions are plotted, accounting for their respective factor shares. Labor contribution has risen in recent years (largely reflecting a decrease in the NAIRU from 2004), while the contribution of capital has steadily increased, and the contribution of factor productivity decreased. Further insight can be obtained from a similar decomposition of the potential labor series. It shows that most of the increase in the potential labor force can be attributed to a corresponding decline in the NAIRU, with the rate of growth in Poland’s active population holding roughly constant since 2004. Concurrently, the participation rate has been decreasing at a constant rate with a negligible effect on the growth of the equilibrium employment rate.

UF3

Poland: Contributions to Potential Growth 1/

Citation: IMF Working Papers 2010, 015; 10.5089/9781451962093.001.A001

1/ Contributions are computed as year-on-year percentage changes. Labor, capital and TFP contributions sum up to potential GDP growth rates. Any discrepancy is due to rounding. The same applies for the decomposition of potential labor growth.Source: Author’s computations.

17. Finally, for the purpose of forecasting Poland’s potential growth, we extend the estimation through the fourth quarter of 2010.23 We find that our measure of the output gap turned negative in the first quarter of 2009 and is expected to remain negative throughout 2010. However, the output gap is projected to bottom out at just around minus 1 percent, during the second quarter of 2010, vs. minus 2 percent in the 2001–02 downturn. The output gap is expected to close in 2011. This contrasts somewhat with the experience of other European countries, many of whom currently have negative output gaps that are larger and expected to persist for a number of years.

V. Conclusion

18. In this paper, we adopt a standard Cobb-Douglas production function to estimate Poland’s potential growth. Given data limitations on the capital stock, the paper focuses on attaining a robust estimate of the labor input. In order to obtain the measure for potential employment, we derive a NAIRU in two steps. The unemployment rate is first assumed to be described by the sum of a trend and a cyclical component. The trend component is regarded as a benchmark for the equilibrium unemployment rate, while the cyclical component as a reference for the unemployment gap. In the second step, a standard Philips curve relationship is applied to help model the cyclical component.

19. We find that, compared with the HP filter approach, the production-function methodology helps to identify better the most recent boom-bust turning points. The results show that during the pre-crisis period, Poland’s output was growing above its potential. This is also confirmed by the behavior of employment relative to its equilibrium measure. Moreover, by disaggregating the contributions to potential growth, we find that the pre-crisis decline in TFP coincided with the deceleration in the growth of potential output. At the same time, the contribution of capital was steadily rising, suggesting that the rapid investment-led output expansion during that period was unsustainable. Finally, we find that in the aftermath of the global crisis, Poland is not expected to experience a sizable and persistent negative output gap.

Estimating Poland's Potential Output: A Production Function Approach
Author: Mr. Natan P. Epstein and Corrado Macchiarelli