## Abstract

The aim of this paper is to analyze fiscal sustainability in Poland after joining EU between 2004-2017. Unlike previous studies, which analyzed weak measures of fiscal sustainability, we analyze fiscal sustainability measures in the strong sense. Contrary to previous studies we estimate individual, not panel, fiscal reaction functions which allows us to provide possibly a more accurate picture of fiscal policy outcomes in Poland. Moreover, our empirical analysis takes a closer look at the series of structural breaks that occurred after the global crisis. Based on our analysis we may tentatively conclude that despite cyclical fiscal deterioration during the crisis fiscal policy in Poland has been sustainable in the strong sense up until 2017.

## 1 Introduction

Fiscal policy sustainability has always been in the center of attention of policymaking in the European Union (EU), but after the recent global financial crisis and the sovereign debt crisis in the euro area, its role has increased even more. The global financial crisis of 2008 and the subsequent sovereign debt crisis in the euro area caused a drastic drop in budget revenues, which resulted in increased budget deficits in many countries, including Poland, which raised pertinent policy questions regarding long-term sustainability of public finances in these countries.

Several recent studies have shown that by and large, the group of Central and Eastern European member states, including Bulgaria, the Czech Republic, Estonia, Lithuania, Latvia, Poland, Slovakia, Romania, and Hungary, despite the initial fiscal problems in the period of the global financial crisis after 2008, managed to stabilize their fiscal policy [Bökemeier and Stoian 2016; Krajewski et al., 2016; Wysocki, 2017].

However, these studies only confirmed fiscal sustainability in a weak sense, as measured by obtaining suitable cointegrating vectors between budget revenues and expenditures in these countries. So far, there have been no studies that would attempt to verify the sustainability of fiscal policy by estimating individual fiscal reaction functions, which would also verify fiscal sustainability in a strong sense.

Our key research question is whether fiscal policy in Poland has been sustainable up until 2017 despite strong deterioration of public finances during the crisis.

The outline of the reminder of the paper is as follows. The next section presents literature on measuring fiscal sustainability. section 3 provides data description and estimation methods. section 4 presents the results of econometric tests.section 5 concludes the paper.

## 2 Measuring fiscal sustainability: literature review

Literature distinguishes in principle two main approaches to examining fiscal sustainability: in the weak sense and in the strong sense. The former approach is primarily based on the stationarity tests of the relations of public debt stock to gross domestic product (GDP) [Hamilton and Flavin, 1986; Wilcox, 1989; Trehan and Walsh, 1991], as well as on the testing of the presence of cointegrating vectors between budgetary revenues and expenditures [Hakkio and Rush, 1991]. Examining fiscal sustainability in a strong sense, in turn, involves estimation of the fiscal reaction function in which the primary balance of the budget in relation to GDP is a dependent variable, while the level of public debt in relation to GDP is an independent variable [Bohn, 1998, 2007]. An interesting attempt to synthesize these two approaches mentioned above is the proposal of a stepwise algorithm [Ozkaya, 2013], which uses the following procedure: a) sequentially testing the stationarity of the level of public debt stock in relation to GDP and the primary balance in relation to GDP; b) searching for a cointegrating vector between budgetary revenues in relation to GDP and expenditures in relation to GDP; c) testing of the existence of a cointegrating vector between the primary balance in relation to GDP and the level of public debt stock in relation to GDP. It is worth noting that the stepwise algorithm does not lead to the estimation of the individual fiscal response functions.

Several recent studies have used these different approaches to analyze the fiscal sustainability for a set of the new EU member states, including Poland. For example, Krajewski et al. [2016] have used panel stationarity and cointegration tests, as well as estimates of certain parameters of the fiscal reaction function, for Bulgaria, the Czech Republic, Estonia, Lithuania, Latvia, Poland, Slovakia, Romania, and Hungary. They find that despite financial turmoil, these countries demonstrated the existence of a longterm relationship between revenues and expenditures and they have statistically relevant parameters of the fiscal reaction function. The study indicates that public finances in these countries were sustainable only in the weak sense, whereas panel data analysis used in the paper somewhat limits the inferences on individual countries.

In another recent study, Wysocki [2017] uses the stepwise algorithm based on quarterly data for a number of countries from Central and Eastern Europe (CEE). He also finds evidence of sustainability of fiscal policy in CEE countries. In that study, the author proves the existence of a long-term relationship between government expenditure and revenues. However, such an approach allows the examination of fiscal sustainability only in a weak sense. Furthermore, in that article, there has been no attempt to estimate the individual fiscal reaction functions. A similar limitation is found in the study of Poland’s fiscal stability by Pączek-Jarmulska [2016], in which the author – based on a yearly data – affirms the fiscal sustainability in Poland only in a weak sense.

The European Commission evaluates the long-term fiscal sustainability of member states. It uses the proprietary debt sustainability analysis approach, which highlights two approaches: analysis of fiscal sustainability indicators and deterministic projections of the level of public debt in the 10-year horizon; and stochastic projections of the level of public debt stock in the 5-year horizon. Deterministic projections of the debt level are prepared on the basis of macro-fiscal forecasts over a longer horizon in relation to the following variables: real GDP growth, inflation, real interest rates, the primary government and local government balance, and other stock-flow adjustments. Due to the uncertainty of forecasts and assumptions, debt paths consistent with alternative scenarios are also subsequently developed. In an aim to capture the potential changes in macroeconomic conditions in the future, sensitivity analyses are carried out. Finally, fiscal reaction functions are estimated on the basis of data for individual countries, and if it is not possible, with the usage of panel models. [European Commission, 2016]. In turn, stochastic projections are developed over a shorter horizon. Distributions of debt levels are summarized and presented using fan charts, which illustrate debt paths corresponding to various macroeconomic conditions, obtained as a result of the shocks to the variables determining debt dynamics. The assessment of fiscal sustainability is based on two measures: the probability that at the end of the projection horizon, the public debt stock will not exceed the level of the initial year; and the difference between the 10th and 90th percentiles of the distribution in the final year of projection. The probability distribution of the level of debt in individual years is obtained using Monte Carlo simulations [European Commission, 2016]. An important added value

of the European Commission’s approach is including the demographic factors related to the problem of the ageing of societies in Europe in the methodology. In the most recent report, the European Commission finds that over the long run, Poland faces medium risks to fiscal sustainability [European Commission, 2018]. While the analysis of the European Commission is without doubt comprehensive, its limitation is derivation of the actual debt path projections from the assumed normal distribution with a nondynamic covariance matrix. It does not capture the actual historical data; it captures a different aspect of what we are doing, because the approach of the European Commission is a forward-looking one.

## 3 Data and estimation methods

We use quarterly data from Eurostat for the period from 2004 Q1 to 2017 Q2 for the following time series: government consolidated gross debt (D), budget deficit (BB), primary budget surplus (PS), and output gap (OG). The output gaps are calculated using the Hodrick–Prescott filter [1997]. The unit of all the variables is percentage of GDP. We use data beginning from the year 2004 as we intend to evaluate the period from Poland’s accession to EU up until 2017.

Our approach involves three stages. First, we verify data quality and examine the integration level of key variables using augmented Dickey-Fuller (ADF), Kwiatkowski– Phillips–Schmidt–Shin (KPSS), Phillips-Perron (PP), and Zivot-Andrews tests [1992]. Second, we run cointegration analysis using the Johansen test [1991] and the Lütkepohl-Saikkonen-Trenkler test [2004]. Third, we estimate the fiscal reaction functions using the methodology explained in more detail later. We run the tests for the whole period between 2004 Q1 and 2017 Q2, and then we split the sample into the precrisis period (from 2004 Q1 to 2008 Q3) and the postcrisis period (from 2008 Q4 to 2017 Q2) and thereafter run sensitivity and robustness tests.^{1}

As indicated earlier, we aim to analyze fiscal sustainability in a strong sense. To this end, we use the following methods: a) unit root tests for public debt stock, primary budget balance, and output gap in relation to GDP; b) cointegration analysis of the abovementioned aggregates (in particular, between the primary balance of the budget and the level of public debt in relation to GDP); c) estimation of the fiscal reaction functions in which the primary balance of the budget is our dependent variable, and the level of public debt stock and the output gap are the key independent variables [see Bohn, 1995].

Our approach adds value to the previous studies on three levels. First, in the case of the examination of the integration order of time series of the variables, we have included, in addition to the classic tests, tests such as ADF, KPSS, PP, and the Zivot-Andrews tests, which investigate the presence of structural breaks [Zivot and Andrews, 1992]. Second, application of the Lütkepohl-Saikkonen-Trenkler test in the cointegration analysis, which takes into account the effect of structural breaks [Saikkonen and Lütkepohl, 2000; Trenkler, 2003; Lütkepohl et al., 2004; Konopczak, 2012], alongside the standard Johansen test [1991]. Third, the usage of quarterly data, which provides for a greater number of degrees of freedom (DF) in the case of estimation of the individual fiscal reaction functions.

The idea behind the estimation algorithm in the Zivot-Andrews test is to choose the date of the structural break for the point in time that gives the least favorable result for the null hypothesis of a random walk with drift. Contrary to Perron, Zivot and Andrews [1992] proposed that this break point is set endogenously, because then the risk of data mining is minimized.

The test statistic in the Zivot-Andrews test is the Student’s *t*-test:

where Δ is a subset of (0;1).

In a model with breaks in both intercept and trend, the test statistic is inferred from the following test regression [Pfaff, 2008]:

where

Lütkepohl et al. [2004] proposed a procedure for estimating a vector error correction model (VECM) in which the structural break is a simple shift in the level of the process and the date of break is estimated first. Next, the deterministic part, including the size of the shift, is estimated, and the data are adjusted accordingly. Finally, a Johansen-type test for determining the cointegration rank can be applied to these adjusted series [Pfaff, 2008].

Lütkepohl et al. assumed that the (K × 1) vector process {*y _{t}*} is generated by a constant, a linear trend, and level shift terms:

where *d _{t}* is a dummy variable defined by

*d*= 0 for

_{tτ}*t*< τ,

*d*= 1 for t ≥ τ.

_{tτ}The shift assumes that the shift point τ is unknown and is expressed as a fixed fraction of the sample size. The estimation of the break point is based on the following regression:

where *A _{i}* with

*i =*1, ...,

*p*represents the (K × K) coefficient matrices; and

*ɛ*is the spherical K-dimensional error process.

_{t}The estimator for the break point

where

variable

Once the break point

Following Krajewski et al. [2016], we estimated the parameters of the following behavioral equation:

where

The key parameter is

## 4 Results of the econometric analysis

We first checked the level of integration of every budgetary variable for Poland. In doing so, we used four different unit root tests: ADF, PP, KPSS, and Zivot-Andrews. However, for us, the ultimate criterion was the result of the Zivot-Andrews test. For our calculations, we used GNU R and the package urca. In every test, we chose the level of significance as 5%. In line with our previous data exploration, in all cases, we accepted the hypothesis about the existence of a structural break. Our analysis reveals that the use of the Zivot-Andrews test was justified (Table 1).

Unit root test results of primary surplus (PS), public debt stock (D), and output gap (OG) for Poland

Variable | ADF | PP | KPSS | ZA (intercept and trend) | |||
---|---|---|---|---|---|---|---|

Order | Test statistic | Critical value at a=5% | Break | ||||

Primary surplus (PS) | I(2) | I(0) | I(0) | I(2) | –12.2056 | –4.8 | 2010 Q4 |

Public debt stock (D) | I(I) | I(I) | I(I) | I(2) | –5.8836 | –4.8 | 2014 Q1 |

Output gap (OG) | I(0) | I(I) | I(I) | I(0) | –6.7067 | –5.08 | 2008 Q4 |

Contrary to the findings of Pączek-Jarmulska [2016], our analysis based on the Zivot-Andrews reveals that both primary surplus and public debt stock were integrated at the same level, namely, I(2), so further co-integration analysis would be justified. The structural break in output gap occurred as expected in 2008 Q4, but a visible impact of the economic slowdown upon the primary surplus in Poland occurred a few quarters later, so the structural break in primary surplus appeared in 2010 Q4. Furthermore, the structural break of Polish public debt stock in 2014 Q1 was related with the redemption of some series of Treasury bonds (T-bonds)as a result of the reform of the Polish pension system [Wysocki, 2017].

Next, we tested the cointegration of the variables. The test shows that according to the maximal eigenvalue test of the Johansen procedure [1991] at the level of significance of 5% (Table 2), in Poland, there exists at least one cointegration vector primary surplus (PS), public debt stock (D), and output gap (OG).

Values of the test statistic and the critical values of the maximal eigenvalue statistic of the Johansen procedure

Number of vectors | Test | 10% | 5% | 1% |
---|---|---|---|---|

r <= 2 | 3.74 | 6.5 | 8.18 | 11.65 |

r <= 1 | 8.10 | 12.91 | 14.9 | 19.19 |

r = 0 | 27.07 | 18.9 | 21.07 | 25.75 |

However, because of the existence of structural breaks in all the aforementioned macroeconomic time series in Poland, which has been proved earlier with the Zivot-Andrews test, the Lütkepohl-Saikkonen-Trenkler trace test [2004] with the critical values from Trenkler [2003] was used (Table 3). This test takes into account the presence of endogenous structural shifts in the time series, because it includes shift correction in the linear trend. This test also confirmed that at the level of significance of 5%, in Poland, there exists at least one cointegration vector primary surplus (PS), public debt stock (D), and output gap (OG).

Values of test statistic and critical values of trace statistic of Lütkepohl-Saikkonen-Trenkler test

Number of vectors | Test | 10% | 5% | 1% |
---|---|---|---|---|

r <= 2 | 6.30 | 5.42 | 6.79 | 10.04 |

r <= 1 | 19.30 | 13.78 | 15.83 | 19.85 |

r = 0 | 35.1 | 25.93 | 28.45 | 33.76 |

Estimation results of fiscal reaction function for Poland from 2004 Q1 to 2017 Q2

Coefficients | Estimate | Standard error | F-statistic | p-Value | Adjusted R-squared |
---|---|---|---|---|---|

(Intercept) | –8.48962 | 2.99832 | 7.441 on 4 and 45 DF | 1.09E–04 | 0.3446 |

PS4 | 0.55059 | 0.12596 | |||

OG | 0.06635 | 0.04602 | |||

OG4 | –0.01698 | 0.04840 | |||

D4 | 0.15418 | 0.06012 |

After tests of integration order and cointegration analysis, we estimated the fiscal reaction function. The structure of the fiscal reaction function is in line with the former specifications by Bohn [2007] and Krajewski et al. [2016]. Because we used quarterly data, all variables were lagged by four instead of one:

where

*PS _{t}* – primary surplus,

*PS _{t}*

_{- 4}– primary surplus four quarters lagged,

*OG _{t}* – output gap,

*OG _{t}*

_{- 4}– output gap four quarters lagged, and

*D _{t}*

_{- 4}– public debt stock four quarters lagged.

Next, we estimated the fiscal reaction function for Poland in our sample of 2004 Q1–2017 Q2 (Table 4). The estimation of parameter γ_{1} of the lagged public debt stock (D4) is positive and statistically significant, which means that the fiscal policy in Poland within this period has been sustainable in the strong sense. Furthermore, the estimations of the majority of parameters are statistically significant, and the results of the *F*-statistic confirm the proper specification of the model.

In our robustness check analysis, we split the sample to investigate the fiscal outcomes prior to and after the crisis. The analysis shows that for the period 2004 Q1–2008 Q3, the ^{γ}_{1} parameter is positive but not statistically significant. For the period from 2008 Q4 to 2017Q2, the ^{γ}_{1} parameter is positive and statistically significant, which means that the fiscal policy in Poland has been sustainable in a strong sense also since 2008 Q4 (Appendix 1). Furthermore, redemption of some series of T-bonds in 2014 Q1 for an amount of 8.5% of GDP had no impact upon our conclusions (Appendix 2)

## 5 Conclusions

The aim of this paper was to analyze the fiscal sustainability in Poland after integration into the EU between 2004 and 2017. Unlike previous studies, which analyzed weak measures of fiscal sustainability, we analyzed fiscal sustainability measures in the strong sense.

Contrary to previous studies, we estimated individual, not panel, fiscal reaction functions, which allowed us to provide possibly a more accurate picture of fiscal policy outcomes in Poland.

Moreover, our empirical analysis took a closer look at the series of structural breaks that occurred after the global crisis. The analysis reveals a cycle of structural breaks of 2- and 4-year lags: for output gap in 2008 Q4, for primary deficit in 2010 Q4, and for public debt in 2014 Q1. Our key research question was the following: has fiscal policy in Poland been sustainable up until 2017 despite strong deterioration of public finances during the crisis? Based on our econometric analysis, we may tentatively conclude that despite cyclical fiscal deterioration during the crisis, fiscal policy in Poland has been sustainable in the strong sense up until 2017. What is important, these results seem to be robust with respect to the pension fund reform, which led to a one-off redemption of T-bonds in amount of 8.5% of GDP in 2014 Q1.

Robustness check analysis – additional estimations on the samples prior to and after the crisis

Estimation results of the fiscal reaction functions for Poland from 2004 Q1 to 2008 Q3

Coefficients | Estimate | Std. error | F-statistic | p-Value | Adjusted R-squared |
---|---|---|---|---|---|

(Intercept) | –26.82728 | 20.4400 | 2.547 on 4 and 10 DF | 0.1051 | 0.3065 |

PS4 | 0.62989 | 0.34854 | |||

OG | –0.08150 | 0.08279 | |||

OG4 | 0.18791 | 0.19003 | |||

D4 | 0.57735 | 0.42912 |

Estimation results of the fiscal reaction functions for Poland from 2008 Q4 to 2017 Q2

Coefficients | Estimate | Std. error | F-statistic | p-Value | Adjusted R-squared |
---|---|---|---|---|---|

(Intercept) | –12.14877 | 3.51475 | 11.23 on 4 and 30 DF | 1.093E–05 | 0.5461 |

PS4 | 0.46872 | 0.11830 | |||

OG | 0.19921 | 0.07687 | |||

OG4 | 0.08874 | 0.04901 | |||

D4 | 0.21766 | 0.06726 |

Robustness check analysis – additional estimations without the effect of the redemption of the government bond share of the open pension funds

Estimation results of fiscal reaction functions for Poland from 2004 Q1 to 2017 Q2 for gross consolidated debt without the effect of the redemption of the government bond share of the open pension funds

Coefficients | Estimate | Std. error | F-statistic | p-Value | Adjusted R-squared |
---|---|---|---|---|---|

(Intercept) | –7.37635 | 2.11326 | 8.601 on 4 and 45 DF | 3.034E–05 | 0.3829 |

PS4 | 0.49810 | 0.12235 | |||

OG | 0.07357 | 0.04482 | |||

OG4 | –0.01576 | 0.04644 | |||

D4 | 0.12523 | 0.04005 |

Estimation results of fiscal reaction functions for Poland from 2008 Q4 to 2017 Q2 for the gross consolidated debt without the effect of the redemption of the government bond share of the open pension funds

Coefficients | Estimate | Std. error | F-statistic | p-Value | Adjusted R-squared |
---|---|---|---|---|---|

(Intercept) | –17.26222 | 3.72530 | 17.76on 4 and 45 DF | 3.857E–07 | 0.6908 |

PS4 | 0.25440 | 0.13643 | |||

OG | 0.15516 | 0.08800 | |||

OG4 | 0.06402 | 0.05499 | |||

D4 | 0.28941 | 0.06353 |

## References

Bohn H. (1995) The sustainability of budget deficits in a stochastic economy Journal of Money Credit and Banking Vol. 27 pp. 257–271.

Bohn H. (1998) The behavior of U.S. public debt and deficits The Quarterly Journal of Economics Vol. 113 No. 3 pp. 949–963.

Bohn H. (2007) Are stationary and cointegration restrictions really necessary for the intertemporal budget constraint? Journal of Monetary Economics Vol. 57 No. 7 pp. 1837–1847.

Bökemeier B. Stoian A. (2016) Debt sustainability issues in the central and eastern European countries Working Papers in Economics and Management No.07-2016 Universität Bielefeld Bielefeld.

European Commission. (2016) Directorate-general for economic and financial affairs fiscal sustainability report 2015 Institutional Paper 018 Brussels.

European Commission. (2018) Debt sustainability monitor 2017 Institutional Paper 071 Brussels.

Hakkio G.S. Rush M. (1991) Is the budget deficit too large? Economic Inquiry Vol. 29 pp. 429–445.

Hamilton J.D. Flavin M.A. (1986) On the limitations of government borrowing: a framework for empirical testing American Economic Review Vol. 76 No. 4 pp. 808–819.

Hodrick R. Prescott E.C. (1997) Postwar U.S. business cycles: an empirical investigation Journal of Money Credit and Banking Vol. 29 No. 1 pp. 1–16.

Johansen S. (1991) Estimation and hypothesis testing of co-integration vectors in Gaussian vector autoregressive models Econometrica Vol. 59 pp. 1151–1181.

Konopczak M. (2012) Ocena ryzyka kredytowego Polski metodą roszczeń warunkowych “Materiały i Studia NBP” Zeszyt nr 267 Narodowy Bank Polski Warszawa.

Krajewski P. Mackiewicz M. Szymańska A. (2016) Fiscal sustainability in central and eastern European countries – a post-crisis assessment Prague Economic Papers Vol. 25 No. 2 pp. 175–188.

Lütkepohl H. Saikkonen P. and Trenkler C. (2004) Testing for the cointegrating rank of a VAR with level shift at unknown time Econometrica Vol. 72 No. 2 pp. 647–662.

Ozkaya A. (2013) Public debt stock sustainability in selected OECD countries Central Bank Review Vol. 13 pp. 31–49.

Pączek-Jarmulska B. (2016) Analiza stabilności fiskalnej w Polsce w latach 1995-2014 Studia i Prace Kolegium Zarządzania i Finansów Szkoła Główna Handlowa Vol. 151 pp. 47–70.

Pfaff B. (2008) Analysis of integrated and cointegrated time series with R Springer New York.

Saikkonen P. Lütkepohl H. (2000) Testing for the cointegrating rank of a VAR process with structural shifts Journal of Business & Economic Statistics Vol. 18 No. 4 pp. 451–464.

Szyszka A. (2009) Behawioralne aspekty kryzysu finansowego Bank i Kredyt No. 4 pp. 4–29.

Trehan B. Walsh C.E. (1991) Testing intertemporal budget constraints: theory and applications to U.S. federal budget and current account deficits Journal of Money Credit and Banking Vol. 23 pp. 206–223.

Trenkler C. (2003) A new set of critical values for systems cointegration tests with a prior adjustment for deterministic terms Economics Bulletin Vol. 3 No. 11 pp. 1–9.

Wilcox D.W. (1989) The sustainability of government deficits: implications of present-value borrowing constraint Journal of Money Credit and Banking Vol. 21 No. 3 pp. 291–306.

Wysocki M. (2017) Sustainability of public debt stock in transition economies in central and eastern Europe countries in terms of solvency Studia Ekonomiczne No. 1 pp. XCII.

Zivot E. Andrews D. (1992) Further evidence of the great crash the oil-price shock and the unit-root hypothesis Journal of Business and Economic Statistics Vol. 10 No. 3 pp. 251–270.

## Footnotes

^{1}There is some debate as to the date of the crisis. Given that the outbreak of the financial turmoil took place in 2008 Q3, we decided – similar to Szyszka [2009] – to choose the year 2008 as the beginning of the global financial crisis.