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DYNAMIC ECONOMETRIC MODELS 
Vol. 10 – Nicolaus Copernicus University – Toruń – 2010 

Anna Michałek 
Nicolaus Copernicus University in Toruń 

The Importance of Calculating the Potential Gross 
Domestic Product in the Context of the Taylor Rule 

A b s t r a c t. Taylor stated humorously that his rule was so easy that it could be written down on 
the back of a business card. The reality shows that the practical use of this type of rule implies 
accepting many assumptions about its final shape. The article mentions only the matter of influ-
ence of calculating the potential GDP and output gap on the empirical relevance of the Taylor 
rule. Two ways of calculating potential GDP were presented, i.e. the HP filter and linear trend of 
the current and the real GDP both seasonally adjusted (an additive model with seasonal dummies; 
TRAMO/SEATS procedure). 

K e y w o r d s: Taylor rule, output gap.  

1. Introduction 
 While the opinion that the central bank's actions can influence both inflation 
and the economy's real sphere is common, the economic reality shows, howev-
er, that precise specification of their effects is difficult for decision-makers. 
There is not one specific answer to the question how to run the monetary policy. 
The decision-makers should take into account the fact that good monetary poli-
cy must be more transparent, coherent and understandable for participants of the 
economic life. That is the reason why a possibility of basing the monetary poli-
cy on a certain rule has been recently often considered. It does not mean, how-
ever, that calculation of the interest rate should be carried out in the mechanical 
way. It is rather generally about outlining certain frames which could acquaint 
economic subjects with the essence of the interest rate policy. 
 Enhancing the monetary policy lies in taking into account the complementa-
ry elements of so called Taylor's triangle, consisting of the direct inflation tar-
geting strategy, the floating rate of exchange and the rule of the monetary policy 
understood as some plan of action (Wojtyna, 2004). 



Anna Michałek 132 

 The Taylor rule, which is most popular among researchers, belongs to the 
category of instrument rules1, which means that it determines the interest rate 
considering only current values of variables: the output gap and the difference 
between inflation and the inflationary target (Żyżyński, 2006). The rule of the 
monetary policy considered in this paper is a classic Taylor rule represented by 
the formula (Taylor, 1993)2: 

,5,0

,21
∗∗ −=

+++=

πα

εβπβα

r

yi tttt  (1) 

where: i  – interest rate, π  - the rate of inflation, ∗π  – the predetermined rate of 
inflation (inflation target), ∗r  – the real interest rate responding to the level of 
full employment, y  – the output gap as the percentage deviation of real GDP 
(Y) from potential GDP (Y*), hence: 

.100⋅⎟⎟
⎠

⎞
⎜⎜
⎝

⎛ −
= ∗

∗

Y
YYy  (2) 

Parameters β1 and β2 should be positive, what more the parameter β1 should be 
higher than one (β1>1) in order to treat the Taylor rule as a nominal anchor for 
inflation and expectations. In other words, the nominal interest rate should rise 
more than one-for-one with an increase in inflation above inflation target. Only 
in that case, real interest rate is positive, when inflation is above the target. 

2. Seeking the Optimal Taylor Rule 
 Generally, it is assumed that a good rule should characterize itself by its 
simplicity, be commonly comprehensible, durable and valid. It is also important 
to announce a rule in advance, in order to inform about it the highest possible 
number of economic subjects. According to J. B. Taylor (2000) a monetary 
policy rule is just “some emergency plan defining in the most coherent way the 
circumstances in which the central bank should make changes in the monetary 
policy instrument”. 
 The rule suggested by Taylor has a specific form which has been modified 
for years. At present, there is no agreement among researchers on applied 
measures of inflation and output gap, types of data, degree of rule complexity or 
even weights attributed to inflation and the gap. Thereby, the differences occur-
ring in empirical studies make impossible to compare the results. The types of 

                                                 
1 Basically, the rules of the monetary policy are divided into instrument rules and targeting 

rules which characterize decision makers’ aim in more general categories. 
2 Taylor has suggested a function of reaction which describes well the FED monetary policy 

in 1987-92, in which federal funds’ rate is lifted or lowered according to inflation’s deflection 
from the aim of inflation and the size of the output gap. The β1 and β2 parameters amounted to 1.5 
and 0.5, respectively. 



The Influence of Calculating the Potential Gross Domestic Product… 133

problems with empirical verification of the Taylor rule and some of its modifi-
cations are shown in Figure 1. 

 
Figure 1.  Types of the Taylor rule’s modification 

 It is important to mention that not all of the variants of the monetary policy 
rules were shown here. The chart was limited only to the most often estimated 
types of the Taylor rule. There are researches, who consider different interest 
rate measures. Economists use both the official interest rates of central banks 
and short-term market rates3. 
 Many different combinations regarding the performance of monetary policy 
rule exist. This paper is restricted only to the selected measure of output gap, 
taking the consumer price index, CPI, as a measure of inflation, and the central 
bank reference rate – as a measure of interest rate. 
 In practice, the measuring of the level and growth rate of potential GDP can 
be inaccurate. There is no one recommendation how to estimate the potential 
GDP because of its unobservability. Taking into account the unobservability of 
the potential GDP, there is no fixed and recommended measuring method. The 
evidence of that may be the numerous works on calculating the output gap for 
Poland, in which the results vary greatly (compare: Gradzewicz, Kolasa, 2004; 
Petru, Mrowiec, 2005; Białkowski, Rosiak-Lada, Zwiernik, Żochowski, 2007). 
The HP filter beside the trend function is one of the most used empirical tech-
niques by researches who deal with the calculation of potential GDP in the con-
text of the Taylor rule. The Hodrick-Prescott filter and the deterministic trend 
are easier in comparison with structural methods, but they do not take into ac-

                                                 
3 While the rate of open market’s short-term operations influences mostly market interest 

rates short term maturity. Long-term instruments are shaped under the market participants’ expec-
tations. 

Taylor rule’s mo-
dification

measures

inflation

CPI

core inflation

inflation expecta-
tions

output gap

structural approach

dynamic production 
function

permanent profit

analytical approach

determini-stic trend

HP filter

types of data

real-time data ex-post data

additional variables

interest rate lags

currency exchange 
rate

other features

value of parameters

reacting of the 
interest rate



Anna Michałek 134 

count structural changes occurring in the economy. However, the use of the 
Cobb-Douglas dynamic function requires availability of quarterly data on the 
real level of fixed assets which are not published by Central Statistical Office 
(CSO) and accepting many assumptions referring to data calculation, that may 
deform the final result (see: Gradzewicz, Kolasa, 2004). 
 The aim of this paper is to evaluate the influence of different methods of 
calculating the potential GDP on estimation of the parameters of Taylor rule. 
Methods of estimating the potential GDP resting on the smoothing of the real 
GDP using Hodrick-Prescott filter and the linear trend are presented. Author 
tests the hypothesis that Poland’s Monetary Policy Council sets the interest rate 
according to the Taylor rule. 

3. Empirical Analysis for Poland 
 In the study the following data were used: quarterly GDP data, CPI – the 
indicator of goods’ prices and consumer services (corresponding period of pre-
vious year=100) published by CSO and the level of the NBP reference rate 
(from the end of a quarter). Two not seasonally adjusted GDP series were 
based: current GDP (current prices in billions PLN) and real GDP – nominal 
GDP corrected by the change in prices, expressed in annual average fixed prices 
from the previous year. The GDP deflator is utilized as a measure of the propor-
tional change in prices of all goods and services and is published annually by 
CSO. Using this procedure presented in the paper CSO information on quarterly 
Gross Domestic Product estimate4 enabled to calculate the price deflators for 
the period I quarter of 1998 – IV quarter 2007, where: 

  GDP nominal dynamics ith quarter 1998 
(current prices) GDP delator 

ith quarter 1998 
= 

GDP real dynamics ith quarter 1998 
(annual average prices from the previous year) 
 

  

 Quarterly data consist of 40 observations. The sample covers the period 
from I quarter of 1998 to IV quarter 2007. Data are presented in Figure 2. 

                                                 
4 http://www.stat.gov.pl/gus/45_1437_PLK_HTML.htm (18. 01. 09). It is important to notice 

that CSO publishes the annual GDP deflator. The way of calculating the quarterly GDP price 
indicators presented in the work is correct because the geometric average from the quarterly GDP 
price indicators for following years is equal to the annual GDP price indicators published by 
CSO. 



The Influence of Calculating the Potential Gross Domestic Product… 135

 

 
Figure 2.  Reference rate SRt and CPIt, current GDPt, real GDPt in Poland over the 

period 1998–2007 

 Behavior of current and real GDP in Figure 2 indicates the occurrence of 
seasonal fluctuations. There is no one recommended method of eliminating 
seasonal fluctuations. For seasonal adjustment of time series, the CSO uses the 
TRAMO/SEATS method. In this paper the procedure recommended by CSO as 
well as the method including seasonal dummies (the additive model with sea-
sonal dummies, where Qit

*= Qit – Qmt) are used. Only for the real GDP process 
slightly difference between the methods of seasonal adjustment in IV quarter of 
1998 is observed (see Figure 3). It is assumed that this difference will influence 
substantially the GDP gap series obtained at a later stage. Seasonally adjusted 
real GDP time series are presented in Figure 3. 

SR t

0
5

10
15
20
25
30

98 99 OOO1 O2 O3 O4 O5 O6 O7

%

CPI t

0

5

10

15

98 99 OOO1 O2 O3 O4 O5 O6 O7

%

current GDP t

100

150

200

250

300

350

98 99 OOO1 O2 O3 O4 O5 O6 O7

bil
lio

ns
 P

LN

real GDP t 

100

150

200

250

300

350

98 99 OOO1 O2 O3 O4 O5 O6 O7

bil
lio

ns
 P

LN



Anna Michałek 136 

 
Figure 3. Real GDPt seasonally adjusted in Poland over the period 1998–2007 

 In order to apply the Taylor rule, the assumptions concerning the real inter-
est rate r*, the inflationary target and the method of estimating the output gap 
should be taken. 
The real interest rate is treated as fixed, i.e. during the period 1998–2007 it took 
the value from the interval (3%–6.6%) (Brzoza-Brzezina, 2003)5. The inflatio-
nary target in 1998 was equal to 9.5%. Since 1999 an obligatory long-term tar-
get at 4 percent level was applied which was supposed to be reached by the end 
of 2003. Since 2004 the inflationary target was equal to 2.5%. 
 For calculating potential GDP the Hodrick-Prescott filter was used as well 
as the linear trend model for current and real GDP (seasonally adjusted using 
TRAMO/SEATS procedure and seasonal dummies). In the case of the HP filter 
the standard value of parameter λ was taken at the basic level for quarterly data, 
i.e. (Hodrick, Prescott, 1980). After obtaining the potential GDP the output gap 
(GDP gap) can be calculated. It is the rate of deviation of real GDP from poten-
tial GDP, showed in a formula (2), i.e.: 

GDPhpt
GDPhptGDPgapGDP

−

−−
=   or  ,

GDPtrend
GDPtrendGDPgapGDP

−

−−
=  

where: GDPhpt _  – potential GDP estimated using the Hodrick-Prescott filter; 
GDPtrend _  – potential GDP estimated using the linear trend model. 

 The output gap informs about the inequality existing in the real economy 
and is treated as a factor influencing the inflationary processes. Inflation usually 
decreases when real GDP is below potential GDP (negative output gap) and 
increases when real GDP is above potential GDP – positive output gap (Solow, 

                                                 
5 According to the author there exists a way of determining the real rate which does not re-

quire using intricate econometric techniques when time series of a moderately long period of 
stable inflation is observed. It is assumed that the beginning of the stabilization period in Poland 
have begun in 2002. 

         Real GDPt seasonally adjusted 

130

180

230

280

330

98 99 OO O1 O2 O3 O4 O5 O6 O7

bil
lio

ns
 P

LN

Real GDP (0-1) Real GDP (TRAMO/SEATS)



The Influence of Calculating the Potential Gross Domestic Product… 137

Taylor, 2002)6. Behavior of the output gap is presented in Figure 4 and 5. 
The following notations are used: 

gap_n (method of seasonal adjustment; method of calculating potential 
GDP; the initial time series). 

 
Figure 4. The GDP gap in Poland over the period 1998–2007 (current GDP) 

 
Figure 5. The GDP gap in Poland over the period 1998–2007 (real GDP)  

  

                                                 
6 Taylor suggests that this relation is rather short-term, nonetheless, he stresses that there is 

a necessity of choice between the size of inflation’s fluctuations and the size of deviation of real 
GDP from potential GDP. 

output gap - current GDP

-10

-5

0

5

10

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

%

gap1 (0-1; hp; c) gap2 (0-1; t; c)
gap3 (T/S; hp; c) gap4 (T/S; t; c)

output gap - real GDP

-10

-5

0

5

10

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

%

gap5 (0-1; hp; r) gap6 (0-1; t; r)
gap7 (T/S; hp; r) gap8 (T/S; t; r)



Anna Michałek 138 

gap 1  the GDP gap as a percent deviation of nominal GDP seasonally adjusted (the 
model with dummy variables (0-1)) from potential GDP calculated by the HP filter 
(hp), used for series GDP in current prices (c); (0-1; hp; c) 

 
 the GDP gap which is based on the GDP in current prices series takes the same 

value as the gap based on the GDP in constant prices series (average 1998=100);  
gap 2  the GDP gap as a percent deviation of nominal GDP seasonally adjusted (the 

model with dummy variables (0-1)) from potential GDP calculated as a trend of 
GDP (t) in current prices (c) seasonally adjusted (the model with dummy variables 
(0-1)); 

(0-1; t; c) 

 
gap 3  the GDP gap as a percent deviation of nominal GDP seasonally adjusted (T/S 

analysis) from potential GDP calculated by the HP filter (hp), used for the GDP 
series in current prices (c); (T/S;hp; c) 

 
gap 4  the GDP gap as a percent deviation of nominal GDP seasonally adjusted (T/S 

analysis) from potential GDP calculated as a GDP trend (t) in current prices (c) 
seasonally adjusted (T/S analysis); (T/S; t; c) 

 
gap 5  the GDP gap as a percent deviation of real GDP seasonally adjusted (the model 

with dummy variables (0-1)) from potential GDP calculated by the HP filter (hp) 
used for the real GDP series (r); 

(0-1; hp; r) 

gap 6 the GDP gap as a percent deviation of real GDP seasonally adjusted (the model 
with dummy variables (0-1)) from potential GDP calculated as a trend (t) of real 
GDP (r) seasonally adjusted (the model with dummy variables); 

(0-1; t; r) 

gap 7 the GDP gap as a percent deviation of real GDP seasonally adjusted (T/S analysis) 
from potential GDP calculated by the HP filter (hp) used for the real GDP series 
(r); 

(T/S; hp; r) 

gap 8 the GDP gap as a percent deviation of GDP seasonally adjusted (T/S analysis) 
from potential GDP calculated as the trend (t) of real GDP (r) seasonally adjusted 
(T/S analysis). 

(T/S; t; r) 

 Figure 4 and 5 shows that in 2002 the GDP fell below the potential level. 
When real GDP is placed below potential GDP the inflationary pressure does 
not exist. Negative output gap was observed in 2003, 2004 and 2005, respec-
tively. The situation where GDP was above the potential GDP occurred at the 
beginning of 1998 year and is maintained more or less until the beginning of 
2002 with a certain exception at the turn of 1998 and 1999. The differences 
between the GDP gap based on the current GDP (gap 1, 2, 3 and 4) and the gap 
based on the real GDP are observed. The greatest distance between gap 7 
(T/S;hp;r), gap 8 (T/S,t;r), which take negative values is noticed in 1998. The 
output gap based on the real GDP was closed in 2006 (gap 5, 6, 7 and 8). In the 
case of GDP gap based on the current (gap 1, 2, 3 and 4) the closing output gap 
was observed year later, in the second half of 2006 (compare Figure 4 and 5)7. 
 Alternative methods of estimating the potential product lead to various cal-
culations of the GDP gap. A much bigger fluctuations are observed, when the 
gap is calculating using the linear trend than the HP filter. It is especially rele-
vant to observations of the end of year 2007. Also the choice of methods elimi-

                                                 
7 The closure of the output gap means not only balance between real and potential GDP, but 

also the situation where real GDP grows faster than potential one. 



The Influence of Calculating the Potential Gross Domestic Product… 139

nating the seasonal fluctuations from the original GDP series impacts on the 
final results. In the case of output gaps calculated for series seasonally adjusted 
using dummies variables 0-1 (gaps 1, 2, 5, 6) the outlier values were observed, 
which are not likely from the point of view of economic reality (IV quarter of 
1998). 
 Using the obtained series of the GDP gap, an estimation (OLS) of the origi-
nal Taylor rule was carried out. Its results were presented in Table 1. 

Table 1. The results of the original Taylor rule’s estimation – types of output gap 

va
ria

ble
 gap1t         

(0-1;hp;c) 
gap2t         

(0-1;t;c) 
gap3t         

(T/S;hp;c) 
gap4t         

(T/S;t;c) 
gap5t         

(0-1;hp;r) 
gap6t         

(0-1;t;r) 
gap7t         

(T/S;hp;r) 
gap8t         

(T/S;t;r) 
coeff. coeff. coeff. coeff. coeff. coeff. coeff. coeff. 

const 3.27*** 2.90*** 3.38*** 2.90*** 3.37*** 3.27*** 3.42*** 3.28*** 
CPI t 1.44*** 1.52*** 1.42*** 1.52*** 1.41*** 1.44*** 1.41*** 1.44*** 
gap t 0.08 -0.12 0.16 -0.13 0.37*** 0.19* 0.64*** 0.27* 
Summary 

R2 89.42 89.71 89.56 89.67 91.23 90.13 92.53 90.41 
S(u) 2.01 1.98 2.00 1.99 1.83 1.94 1.69 1.92 
DW 0.27 0.3 0.27 0.29 0.45 0.28 0.29 0.25 

11ρ  0.89 0.86 0.90 0.87 0.83 0.92 0.91 0.93 
Note: ***, **, * denotes significance at 1%, 5%, 10%. R2 is the determination coefficient, S(u) is standard 
error of residuals, DW is the Durbin-Watson statistic and 11ρ  the partial autocorrelation coefficient of first 
order. 

 The coefficients of inflation impact are significant in all variants, positive 
and higher than 1 ( )11 >β  and what is more, close to the value pointed by Tay-
lor – 1.5. The choice of type of series like real GDP is crucial for estimation 
results. The impact of the gap turned out irrelevant in the models where the 
initial series for estimating the gap was GDP in current prices. In the models 
where the gap was based on the real GDP series significant parameters were 
received, however, for gap 6 and 8 (potential GDP calculated as real GDP’s 
trend) significance was at the 10% level. The coefficients of gap 5, 6, 7 and 8 
have positive sign, as expected. However, these models do not meet the statistic 
requirements. Low values of the DW statistics for all models show first order 
autocorrelation for residual process. Coefficients of the first order autocorrela-
tion turned out to be significant ( 11ˆ 0.35ρ > autocorrelation coefficient is dis-
tinctly higher that the corresponding critical value of the Quenouille test  
( n/2 ). The high, positive autocorrelation of a residual process may give evi-
dence about the omission of important variables or the elements of internal 
structure for given process. Additionally, the relation between R2 and DW indi-
cates a spurious relationship. The correct statistical inference requires taking 
into account the information about the internal structure of the processes being 
modeled (trend, autoregression). 
  



Anna Michałek 140 

4. Detecting the Internal Structure of Processes 

 Assuming the nonstationarity in mean, the level of a trend, occurrence of 
seasonality and order of autoregression were detected. The results of detecting 
the internal structure of the analyzed processes are presented in Table 2. 

Table 2.  The results of the study of the internal structure of particular processes 

structure  SRt  CPIt gap1t        
(0-1;hp;cb) 

gap2t    
(0-1;t;cb) 

gap3t    
(T/S;hp;cb) 

gap4t  
(T/S;t;cb) 

gap5t     
(0-1;hp;r) 

gap6t     
(0-1;t;r) 

gap7t 
(T/S;hp;r) 

gap8t 
(T/S;t;r) 

r 1 1 - - - - - - - - 
S no no no no no no no no no no 

AR(q) 4 5 5 5 4 4 5 5 1 2 
Note: r – degree of polynomial trend, S – occurrence of seasonality, Ar(q) – order of autoregression for given 
processes. 

 The choice of trend degree was made using the F-test. This test is most of-
ten used when comparing linear trend models and testing significant differences 
in the variances. 
 In all estimated trend and seasonality models the seasonal coefficients 
turned out to be insignificant, hence the lack of seasonality in the analyzed time 
series was found. 
 The third stage of studying the internal structure of processes is the identifi-
cation of lag length of particular processes; therefore the Akaike information 
criterion (AIC) was used. Because of the small sample size, the corrected AIC 
was used, in the form: 

2 ( 1)AIC AIC ,
1C

K K
n K

+
= +

− −
 

where K stands for the number of estimated parameters, including the constant 
and variance (Burnham, Anderson, 2004)8. The models with the lowest value of 
AICC were chosen.  
 Accepting the assumption of nonstationarity in mean, linear models of ref-
erence rate were built, in which the specification of an equation describing the 
monetary policy rule was broadened by information of the internal structure of 
processes. The inclusion of internal structure of given processes is the basis of 
congruent modelling, formulated by professor Zieliński. The concept of congru-
ent modelling is understood as the congruence of the harmonic structure of an 
endogenous process with the joint harmonic structure of explanatory processes 
and residual process which is independent from explanatory processes (Talaga, 
Zieliński, 1986). Hence, the estimated equations have the form:  

                                                 
8 The authors point that there is too much usage of AIC in research, while the requirement that 

n/k>40 instead of AICC. Thus, AICC should be used regardless of the sample size because with 
the growth observations’ number, AICC converges to AIC. 



The Influence of Calculating the Potential Gross Domestic Product… 141

∑ ∑∑
= =

−−
=

− +++++=
5

0 0

4

1
10 ,

k

q

k
tktykktk

k
ktikt gapCPISRtSR εβββαα π  

where q denotes the lag length depending on the method of estimating the out-
put gap. 

Table 3.  The reduced dynamic congruent models for the reference rate depending on 
different GDP gap’s variants 

va
ria

ble
 gap1t         

(0-1;hp;c) 
gap2t         

(0-1;t;c) 
gap3t         

(T/S;hp;c) 
gap4t         

(T/S;t;c) 
gap5t         

(0-1;hp;r) 
gap6t         

(0-1;t;r) 
gap7t         

(T/S;hp;r) 
gap8t         

(T/S;t;r) 
coeff. coeff. coeff. coeff. coeff. coeff. coeff. coeff. 

const  0.15 4.09** 0.15 5.59*** 11.61`*** 7.70*** 9.45*** 7.71*** 
t   -0.08**   -0.12** -0.20*** -0.16*** -0.17*** -0.16*** 
CPI t 0.59*** 0.42*** 0.59*** 0.38***   0.35***   0.35*** 
CPI t-1         0.73***   0.60***   
CPI t-2 -0.41*** -0.48*** -0.41*** -0.50***         
CPI t-3 0.19* 0.30** 0.19* 0.32*** 0.37*** 0.40*** 0.49*** 0.44*** 
CPI t-4                 
CPI t-5           -0.15** -0.22*** -0.17** 
gap t         0.27*** 0.12**     
gap t-1         0.24***   0.79*** 0.32*** 
gapt-2   0.12**   0.18*** 0.34*** 0.21***     
SR t-1 0.80*** 0.83*** 0.80*** 0.81***   0.47*** 0.34* 0.65*** 
SR t-2             -0.36** -0.37*** 
SR t-3           -0.19*     
SR t-4   -0.18**   -0.22*** -0.23***       
Sumary 
R2 99.38 99.54 99.38 99.56 99.65 99.57 99.61 99.60 
S(u) 0.43 0.40 0.43 0.38 0.35 0.39 0.36 0.37 
DW 1.55 1.96 1.55 2.08 1.85 1.97 2.28 2.31 

11ρ  0.21 -0.01 0.21 -0.08 0.06 -0.04 -0.14 -0.23 
Note: ***, **, * denotes significance at 1%, 5%, 10% level. R2 is the determination coefficient, S(u) is stan-
dard error of residuals, DW is the Durbin-Watson statistic and 11ρ  the partial autocorrelation coefficient of 
first order. 

After estimation of the starting version of congruent models the insignificant 
variables were eliminated using a posteriori selection method. The estimation 
results are presented in Table 3. The reduced congruent models contain signifi-
cant parameters at 10% significance level (except the constant in models 1 and 
3) and have the desired properties of residual process. In all estimated equations 
the inflation’s influence is significant. In models 1 and 3 (gap1 (0-1;hp;c), gap3 
(T/S;hp;c)) the impact of gap was not significant, and what is more, the reduced 
model has the same form in both cases. The impact of current inflation and out-
put gap is observed only in model 6 (gap6 (0-1;t;r)), but the coefficient of the 
impact of inflation on the reference rate is smaller than one. Taking into consid-
eration the lagged influence of inflation (its accumulated impact is equal to 0.6 
percentage point) the model does not satisfy the stability condition called the 



Anna Michałek 142 

Taylor principle. In model 5 (gap5 (0-1;hp;r)), the accumulated impact of infla-
tion and output gap amounted to 1.1 and 0.85 percentage point, respectively. 
Moreover, in each variant of model the lagged reference rate is significant, what 
means that changes of reference rate are autoregressive distributed (the interest 
rates’ smoothing effect). It shows the partial reaction of Monetary Policy Coun-
cil on changes in the economy, which may result from the unobservability of 
output gap and hence problems with estimating it precisely. 
The estimated reaction’s functions of reference rate to changes in the output gap 
and inflation level, differ from the original Taylor rule because they include the 
internal structure of processes (compare Table 1 and Table 3).  
Parameter estimates of lagged output gap (gap 2 and 4) are statistically signifi-
cant with expected positive signs. In the case of the remaining models the influ-
ence of estimating the potential GDP on the relevance of the Taylor rule is not 
so clear. It can be noticed that regardless of the way of seasonal adjustment of 
real GDP the accumulated impact of inflation and the output gap is similar in 
models where potential GDP was estimated using linear trend.  

4. Conclusions 
 Based on the obtained results one cannot tell categorically which of the 
analyzed methods of estimating the potential GDP gives better results in the 
contest of estimation of the Taylor rule. The inclusion of the internal structure 
of processes eliminates the autocorrelations of residual process, however it 
changes the coefficient estimates in comparison with the original Taylor rule. 
In that case, the Taylor-type rules were considered. The Taylor condition (the 
impact of inflation on the reference rate is bigger than one) was satisfied only in 
model 5 (gap5 (0-1;hp;r)). However it should be noticed, that the recommended 
original time series for estimating the output gap is real GDP. In the presented 
analysis, the assumption of nonstationarity in mean was taken into considera-
tion, however processes can also be nonstationary in variance. In such a case, 
the recommended method of estimating the output gap is the HP filter. 

References 
Białkowski, P., Rosiak-Lada, K., Zwiernik, P., Żochowski, D. (2007), Zintegrowane modelowa-

nie PKB, stopy bezrobocia i inflacji w oparciu o wielokomponentowe wskaźniki koniunk-
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Znaczenie szacowania potencjalnego PKB w kontekście reguły Taylora  

Z a r y s  t r e ś c i. Taylor wypowiedział się żartobliwie o swojej regule, że jest tak prosta, 
iż można ją zapisać na odwrocie wizytówki. Rzeczywistość pokazuje, że praktyczne wykorzysta-
nie tego typu reguły implikuje przyjęcie wielu założeń, co do ostatecznego jej kształtu. Artykuł 
porusza jedynie kwestię wpływu zastosowanych metod szacowania potencjalnego PKB, luki PKB 
na estymację parametrów reguły Taylora. Przedstawiono dwa sposoby szacowania PKB poten-
cjalnego: filtr HP oraz trend liniowy, przy czym bazowano na wyrównanych sezonowo (model 
addytywny ze zm. 0-1; procedura TRAMO/SEATS) szeregach: PKB bieżący oraz PKB realny. 

S ł o w a  k l u c z o w e: reguła Taylora, luka popytowa.  



 




