Energy Policy 46 (2012) 594–600

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Energy Policy

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journal homepage: www.elsevier.com/locate/enpol

Communication

Persistence in natural gas consumption in the US: An unobservedcomponent model

Antonio A. Golpe a,n, Monica Carmona b, Emilio Congregado a

a Department of Economics, University of Huelva, Plaza de la Merced, 11, 21002 E-Huelva, Spainb Department of Business Administration and Marketing, University of Huelva, Spain

a r t i c l e i n f o

Article history:

Received 7 March 2011

Accepted 11 April 2012Available online 27 April 2012

Keywords:

Natural gas consumption

Hysteresis

Unobserved components model

15/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.enpol.2012.04.021

esponding author. Tel.: þ34 692841133; fax

ail addresses: Antonio.golpe@dehie.uhu.es (A.

@uhu.es (M. Carmona), congregado@uhu.es (

e authors are grateful to Silvestro Di Sanzo

available the Gauss computer codes.

apter 8. MIT Energy initiative, 2010. The Fut

rdisciplinary MIT Study./http://web.mit.edu/

as.htmlS.

a b s t r a c t

This article re-examines the persistence in natural gas consumption using an alternative methodology.

In particular we report estimates of an unobserved components model, in which hysteresis exists

if cyclical and natural gas consumptions do not evolve independently. In addition, this framework is

also extended by using the nonlinear approach, in which nonlinearities are introduced by allowing past

cyclical component to have a different impact on the natural component depending on the regime.

In a linear framework our results seem to indicate that hysteresis does not exist. However, when non-

linearity is taken into account, we provide evidence in favor of hysteresis in natural gas consumption

when the variations in natural gas consumption are above the threshold value. We also selectively

survey the empirical literature that examines the long-term properties of energy series in order to put

our contribution in perspective.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction1

Natural gas is now at the heart of the debate about the presentand future of energy in the US. There are several reasons behindthis growing interest in natural gas. Firstly, US authorities haveregarded natural gas as a means of reducing the dependence onother fuels fossils. Moreover, natural gas is considered as apromising candidate for meeting future demand under carbondioxide (CO2) emissions constraints (Apergis and Payne, 2010a).As a recent report from the MIT states natural gas may become abridge to a low carbon future.2

Secondly, over the past few years, the US has new disposals oflow cost gas that provide an enormous potential benefit to thenation—remember that the US has particularly large reserves ofshale gas.

Finally, the US natural gas industry has been subject to severalregulatory reforms with the aim of converting the natural gasmarket into a more competitive and efficient one (see Apergiset al., 2010b, p. 4735). As a result, not only efficiency gains appearbut also increases volatility and the economy’s susceptibility to

ll rights reserved.

: þ34 959217828.

A. Golpe),

E. Congregado).

and Alicia Perez for kindly

ure of Natural Gas.

mitei/research/studies/

external shocks (see, Mohammadi, 2011).3 In this way, thedramatic increase in energy prices associated with the wave ofpopular uprisings that have swept over the Middle East and NorthAfrica is a ‘‘hot’’ political issue at the time of writing. If tensionsspread, the global economic recovery will be affected dramati-cally.4 Some countries have reacted quickly, devising new con-servative energy policies and promoting energy efficiency; othersare rethinking the role currently played by alternative energysources. In the US, the Obama administration regards the promo-tion of natural gas consumption as a promising candidate in thisrespect.5 In fact, the existence of national large reserves of shalegas may be considered as a means of reducing the dependence onother fossil fuels and natural gas price volatility.

In this context, to know the long term properties of natural gasconsumption should be a key question (Aslan, 2011; Apergis et al.,2010b) for several reasons.

If natural gas consumption is trend-stationary, policy shockscan be regarded as transitory: natural gas consumption even-tually reverts to its underlying, long-run level. Then, policymakers should not adopt unnecessary targets (Hasanov and

3 This fact advises taking into account the potential existence of regime shifts.4 Apergis and Payne (2010a) provide evidence of bidirectional causality

between natural gas consumption and economic growth.5 In the last State of Union address (2011), the President Obama recognized

the role of natural gas in clean energy future. Although natural gas is the cleanest

of the fossil fuels, much of the enthusiasm in the United States and Europe for

natural gas comes from its relative abundance and its location in places friendly to

the West. The United States in particular has plentiful supplies.

A.A. Golpe et al. / Energy Policy 46 (2012) 594–600 595

Telatar, 2011, p. 7726). If natural gas consumption is stationary,the shock dies away once the policy has been implemented, andenergy consumption settles up at its new level. By contrast if thenatural gas consumption is non-stationary, such shocks can havepermanent effects.

On the other hand if natural gas consumption is non-station-ary, then the past behavior of this variable cannot be used informulating forecasts (Apergis et al., 2010b; Aslan, 2011; Barroset al., 2011,2012).

Finally, if natural gas consumption is non-stationary, then theunit root is transferred to other macroeconomic variables (Hsuet al., 2008, p. 2318; Narayan and Smyth, 2007, p. 338).

In our opinion, the lack of robust evidence associating energypolicies with long term effects on the consumption is particularlystriking and to provide robust evidence on how energy consump-tion evolves should be a key question in order to enhance theeffectiveness and consistency of energy policies.

By using the definition of hysteresis of Blanchard andSummers (1986) we can initially describe hysteresis in energyconsumption as a high degree of dependence of the currentconsumption level on the past. Using this definition, it is sufficientthat the sum of the autoregressive coefficients in a linear model isclose to – but not necessarily equal to – one. That is, hysteresisarises when energy consumption series has a unit root. Thepresence of a unit root in the process means it is path dependent.That is, any shock is entirely incorporated into the series level.Therefore, the easiest way to determine whether a hysteresiseffect exists focuses on testing for the existence of a unit root (seeRøed (1997) for a survey). In order to test the hypothesis of non-stationarity in this way, scholars have applied a wide range oftests: from the most widely used unit root tests, to the mostrecent tests which take into account possible structural breaksand non-linearities (Sollis, 2004).

However, in a time-series context, hysteresis can be definedand measured in various ways. An alternative approach proposedby Jaeger and Parkinson (1990, 1994) posits a more demandingcriterion: hysteresis exists if shocks affect the natural rate of avariable, which itself follows a unit root process. In this case,temporary shocks have permanent effects while the cycle doesnot evolve independently of the natural component; it thenfollows that a unit root is a necessary but not a sufficientcondition for hysteresis. In this article, we adopt Jaeger andParkinson’s (1990, 1994) definition of hysteresis in order toconduct a searching test and to explore whether energy policieson natural gas consumption have long-term effects.

To test for hysteresis in this way, we decompose natural gasconsumption into two unobservable components: a non-stationary‘‘natural’’ component, and a stationary ‘‘cyclical’’ component. Thesecomponents can be estimated by maximum likelihood.6 To thebest of our knowledge its application to energy economics is novel.

On the other hand, and since the failure in detecting persis-tence may be attributed to non-linearity (see Maslyuk and Smyth,2009; Aslan, 2011; Aslan and Kum, 2011; Hasanov and Telatar,2011), once hysteresis is tested in the linear model, the new testfor hysteresis based on a nonlinear unobserved componentsmodel, proposed by Perez-Alonso and Di Sanzo (2011), whichintroduces threshold type nonlinearities is applied. This is thesecond contribution of this paper.

This article has the following structure. The next section offersa selective review of key research to date on the topic ofpersistence in energy economics. It examines the existing evi-dence with respect to the ways in which the long-run properties

6 Applications of this approach can be found in Assarson and Janson (1998);

Salemi (1999); Congregado et al. (2011) or Perez-Alonso and Di Sanzo (2011).

of energy consumption/production time series have been ana-lyzed until now. The next section describes the estimationmethodology and the data. The fourth section presents anddiscusses the results. The final section concludes with a discus-sion of policy implications and some promising avenues for futureresearch.

2. Selective survey of previous research

The study of long memory properties of energy consumptionand production variables is an important and active research fieldin energy economics. Since the seminal article of Narayan andSmyth (2007), the empirical analysis on the persistence in energyconsumption and production variables has generated a sizableliterature that examines its long-run properties by using a widerange of recent econometric approaches, which are summarizedin Table 1.

At this point, it should be noted that there is also a vastliterature on the relationship between energy consumption andgrowth in which the presence of unit root is tested in order tostudy the Granger causality. Strictly speaking this literature is notoriented to the study of the persistence, and we have excluded,intentionally, this body of literature in this selective review.In any case this literature has been recently surveyed by Ozturk(2010) and Payne (2010a, 2010b).

In summary, this section selectively reviews this literature onpersistence in energy consumption and production, in terms ofthe lack of robustness in the findings, which seem to be highlysensitive to the assumption about the data generating process andwhether structural breaks are or not taken into account.

All in all, the evidence is mixed. The most part of earlierstudies on the stationarity properties of energy consumption/production have been carried out by using different kinds ofunivariate unit root tests by using time series or panel data(Narayan and Smyth, 2007; Hsu et al., 2008; Narayan et al., 2008).

Another group of studies reports evidence of structural breaksin energy variables. Allowing for such breaks reduces the persis-tence of deviations from the regime specific means, so breaksreduce local persistence. The structural breaks themselves, how-ever, still produce substantial global persistence in energy series ifnot a unit root (see, Narayan et al., 2010; Aslan and Kum, 2011;Apergis and Payne, 2010b; or by using panel data unit root testswith structural breaks Chen and Lee, 2007; Mishra et al., 2009;Apergis et al., 2010a, 2010b).

A number of studies, including Gil-Alana et al. (2010), Barroset al. (2011, 2012) and Apergis and Tsoumas (2011a, 2011b), testfor fractional integration7 following the alternative way to testthe property of long memory by means of the analysis of thespectral density function allowing the existence of a singlestructural break, proposed by Gil-Alana (2008).

All these previous studies have a common point: they supposethat energy variables follow a linear path. However, if energyvariables follow a nonlinear path, linear unit root tests tend tooveraccept the null hypothesis (Aslan, 2011, p. 4466). Only fourworks looking for nonlinear behavior in energy consumption andproduction variables identify regimes in which the energy vari-ables behave like a unit root process (Maslyuk and Smyth, 2009;Aslan, 2011; Aslan and Kum, 2011; Hasanov and Telatar, 2011).

In conclusion, to date literature offers contradictory findingswhether shocks to energy variables are transitory or permanent.This question is important for the design and effectiveness of energy

7 Lean and Smyth (2009) also use a LM test of fractional integration without

structural change.

Table 1Empirical approaches on long memory properties of energy variables.

DGP

assumption

Type

of test

Structural

breaks

Econometric approach Applications in energy economics

Authors Data Persistence

Linear unit

root tests

Univariate Without Augmented Dickey–Fuller unit root test Narayan and

Smyth (2007)

Annual per capita energy

consumption of 182 countries

Stationarity only in 56

countries

With LM univariate test of Lee and Strazicich (2003) Narayan,

Narayan and

Popp (2010)

Disaggregate Australian

energy consumption

Stationarity

Aslan and

Kum(2011)

Disaggregate Turkish energy

consumption

Stationarity with break in three

sectors

Narayan and Popp (2010) unit root test with

two structural breaks

Apergis and

Payne

(2010b)

Petroleum consumption in

the US

Stationary in most of the cases

Multivariate Without LM tests for fractional integration Nielsen

(2005)

Lean and

Smyth (2009)

24 series of US petroleum

consumption

Mixed evidence of fractional

integration

With Gil-Alana’s (2008) method of estimating

fractional differencing parameters with a

single structural break Gil-Alana (2008)

Gil-Alana,

Loomis and

Payne (2010)

Energy consumption by the

US electric power sector

Persistence

Barroset al.

(2011)

Oil production in OPEC

countries

Mixed evidence when

structural breaks are allowed

Apergis and

Tsoumas

(2011a)

Solar, geotermal and biomass

energy consumption (US)

Mixed evidence

Apergis and

Tsoumas

(2011b)

Disaggregated data on energy

consumption (US)

Mixed evidence

Barros et al.

(2012)

Renewable energy

consumption (US)

Persistence

Panel data Without t-bar test (Im et al., 2003) Narayan and

Smyth (2007)

Annual per capita energy

consumption of 182 countries

Stationarity

Panel SURADF test (Breuer et al., 2001) Hsu et al.

(2008)

Energy consumption per

capita of 84 countries

grouped in 5 regions

Mixed evidence of stationarity

properties affected by region

LM panel unit root test without structural

breaks (Im et al., 2005)

Narayan

et al. (2008)

Crude oil and NGL production

in 60 countries

Mixed evidence of stationarity

With Carrion-i-Silvestre et al. (2005) panel unit root

test

Chen and Lee

(2007)

Energy consumption per

capita of 7 geographical

groups made up of 104

countries

Stationarity

Mishra et al.

(2009)

Energy consumption per

capita of 13 Pacific Island

Countries

Stationarity

Apergis et al.

(2010a)

Coal consumption of 50 US

states

Stationarity

Apergis et al.

(2010b)

Natural gas consumption of

50 US states

Stationarity

LM panel unit root test with one structural

break (Im et al., 2005)

Narayan

et al. (2008)

Crude oil and NGL production

in 60 countries

Stationarity

Non-linear

unit root

tests

Univariate Without TAR unit root methodology proposed by Caner

and Hansen (2001)

Maslyuk and

Smyth (2009)

Oil production of 17 countries Unit roots in both regimes of

11 countries Unit roots at least

in one regime for the others

Harvey et al. (2008) test of non-linearity and

Kruse non-linear unit root test (2011)

Aslan (2011) Natural gas consumption for

50 US states

Mixed 27 Non-stationary 23

Stationary

Aslan and

Kum (2011)

Disaggregate Turkish energy

consumption

Mixed in 4 sectors non-

stationary

With Sollis (2004) test procedure Hasanov and

Telatar

(2011)

Total primary energy

consumption of 178 countries

Stationary in most of the

countries

A.A. Golpe et al. / Energy Policy 46 (2012) 594–600596

policies. However until there is a wider consensus, policy makerscannot have confidence in these results for practice purposes.

In this concern, our approach may further the boundariesof econometric methodologies for the analysis of stationarityproperties of energy series, since, for the first time in energyeconomics, we applied the Jaeger and Parkinson’ approach allow-ing nonlinear adjustments.

3. Methodology and data

The estimation strategy consists of decomposing our timeseries of natural gas consumption, Gt into the sum of its two

(unobservable) components: the non-stationary natural compo-nent, GN

t , and the stationary cyclical component, GCt :

Gt ¼ GNt þGC

t ð1Þ

The natural component is defined as a random walk plus aterm capturing a possible hysteresis effect:

GNt ¼ GN

t�1þbGCt�1þe

Nt ð2Þ

where the b coefficient measures, in percentage points, howmuch the natural component increases if the consumptionexperiences a cyclical increase of 1%. Evidently a unit root inthe consumption Gt is a necessary but not sufficient condition forthe existence of hysteresis since a unit root could be generated by

A.A. Golpe et al. / Energy Policy 46 (2012) 594–600 597

an accumulation of shocks to the natural component GNt , while at

the same time b¼0 (Røed, 1997). In contrast, there is hysteresis ifb40.

The specification of this model is completed by writing thecyclical component as a stationary second-order autoregressiveprocess8 :

GCt ¼j1GC

t�1þj2GCt�2þe

Ct ð3Þ

where j1 and j2 provide a measure of the periodicity of thecyclical component.

To identify the model, the system is completed by augmentingit with an equation, which relates natural gas consumption andoutput growth:

Dt ¼ aDt�1þdGCt þe

Dt ð4Þ

where Dt stands for the output growth rate at date t.The random shocks eN

t , eCt and eD

t are assumed to be mean-zerodraws from the normal distribution with variance–covariancematrix O; the state-space form of the model can be written as

Gt ¼1 1 0

0 d 0

! GNt

GCt

GCt�1

0BB@

1CCAþ 0

a

� �Dt�1þ

0

eDt

!ð5Þ

GNt

GCt

GCt�1

0BB@

1CCA¼

1 b 0

0 j1 j2

0 1 0

0B@

1CA

GNt�1

GCt�1

GCt�2

0BB@

1CCAþ

eNt

eCt

0

0B@

1CA ð6Þ

O¼s2

N 0 0

0 s2C 0

0 0 0

0B@

1CA ð7Þ

To summarize, hysteresis is inferred if the coefficient b issignificantly different from zero. The coefficients of the model(4)–(7) are estimated by maximum likelihood using a Kalmanfilter.

Furthermore, we should take account of the possibility thatnatural gas consumption displays asymmetries in adjustmentdynamics in response to positive and negative shocks. To explorewhether asymmetries exist, we estimate a non-linear version ofthe unobserved components model by allowing past cyclicalconsumption to have a different impact on the natural compo-nent, which depends on the regime of the economy (Perez-Alonsoand Di Sanzo, 2011, p. 5). Specifically, we replace the state-spaceequation (6) with a Threshold Autoregressive specification

GNt

GCt

GCt�1

0BB@

1CCA¼

1 0 0

0 j1 j2

0 1 0

0B@

1CA

GNt�1

GCt�1

GCt�2

0BB@

1CCAþ

bþ

0

0

0B@

1CAIþt GC

t�1

þ

b�

0

0

0B@

1CAI�t GC

t�1þ

eNt

eCt

0

0B@

1CA ð8Þ

where Iþt and I�t are the Heaviside indicator functions such that

Iþt ¼1 if GC

t�1Zt0 if GC

t�1otI�t ¼

1 if GCt�1ot

0 if GCt�1Zt

((

8 The assumption of a purely autoregressive process for the cyclical equation

can be relaxed in favor of more general (and possibly more parsimonious)

autoregressive moving-average specifications. In the present application, an

AR(2) fits the data best according to AIC comparisons. Full results are available

from the authors on request.

This model is also estimated via maximum likelihood using theKalman filter, where t is unknown and so it is estimated alongwith the other parameters of the model bþ and b�. In thiscontext a test for asymmetry becomes a test for linearity, i.e. atest for a single regime against the alternative of two regimes.The null hypothesis we are interested in isH0 : b

þ¼ b� vs.

H1 : bþab�

If we reject the null of linearity, there is evidence for thepresence of a type of nonlinear hysteresis in gas consumption.Therefore, cyclical shocks will propagate asymmetrically to thenatural component. Given our model, the asymptotic distributionof conventional test statistics is not w2.9 To circumvent thisproblem we follow Perez-Alonso and Di Sanzo (2011), whosuggest using bootstrap methods to approximate the samplingdistribution of the test statistic.

The data used are quarterly observations from 1973:1 to2010:3. The natural gas consumption (measured in billions ofcubic feet) and GDP data (measured in billions of chained 2005dollars) are extracted from the US Energy Information Adminis-tration (EIA) and the US Bureau of Economic Analysis (BEA),respectively. Before conducting the empirical analysis data wereseasonally adjusted and converted to natural logarithms.

4. Results

This section presents the results in three stages. First, we testthe existence of a unit root in the natural gas consumption timeseries. Second, we estimate the linear unobserved componentsmodel outlined in the previous section. The third subsectionexplores the possibility of asymmetric behavior in adjustmentdynamics, by estimating the nonlinear unobserved componentsmodel, using the estimation strategy proposed by Perez-Alonsoand Di Sanzo (2011).

4.1. Unit root tests

In order to test the hypothesis of non-stationarity, we apply thetraditional Augmented Dickey–Fuller (ADF) test and a modifiedversion of the Dickey–Fuller and Phillips–Perron tests proposed byNg and Perron (2001). This comprises a class of modified tests,M,with GLS de-trending of the data and use of the modified Akaikeinformation criteria to select the autoregressive truncation lag.Table 2 reports the results of Ng–Perron tests, MZGLS

a and MZGLSt ,

originally developed in Stock (1999) with GLS de-trending of thedata as proposed by Elliot et al. (1996). In addition, Ng–Perronproposed a similar procedure that corrects the problem associatedwith the standard Augmented Dickey–Fuller test, MSBGLS andMPTGLS. All test statistics formally examine the unit root nullhypothesis against the alternative of stationarity.

The results in Table 2 show that the null hypothesis of non-stationarity cannot be rejected, regardless of the test. However, itis well known that structural breaks Table 3 in time series canlead to spurious inferences of a unit root. To deal with thispossibility, we employ the Zivot and Andrews (1992) minimumADF-t(min-t) procedure. The min-t statistics reported in Table 2show that the null hypothesis of a unit root in the time series stillcannot be rejected. This buttresses our conclusion that a unit rootexists in natural gas consumption. As noted above, a unit root is amaintained assumption needed to test for Jaeger and Parkinson’snotion of hysteresis.

9 See e.g. Hansen (1999) and Lo and Zivot (2001).

Table 2Unit root tests.

Test

MZGLSa

�1.431

MZGLSt

�0.727

MSBGLS 0.508

MPTGLS 14.453

Lag length 4

ADF �0.638

Lag length 4

Range 1973:1–2010:3

Critical values MZGLSa MZGLS

t M SBGLS M PTGLS

1% �13.800 �2.580 0.174 1.780

5% �8.100 �1.980 0.233 3.170

10% �5.700 �1.620 0.275 4.450

Critical values ADF

1% �3.476

5% �2.881

10% �2.577

Notes: Test statistics defined in the text. ‘‘Lag length’’ refers to the lag length used

in the Ng–Perron and ADF tests. The critical values are tabulated in Ng and Perron

(2001).

***Rejects null hypothesis at 1% significance level.

** Rejects null hypothesis at 5% significance level.

* Rejects null hypothesis at 10% significance level.

Table 3Unit root tests allowing for structural breaks.

Model Test value

A Min-t �3.184 (1982:1)

Lag length 4

B Min-t �2.523 (1982:3)

Lag length 4

C Min-t �3.387 (1987:4)

Lag length 4

Range 1973:1–2010:3

Notes: Periods corresponding to min-t statistics are indicated in parentheses.

Critical values for the min-t are given by Zivot and Andrews (1992). Asterisks

are as in Table 1. Min t-statistics are computed using sequential regressions

over 1otrend breakoT based on the following equations: ðAÞDxt ¼ dA0þd

A1tþ

dA2 DUþaAxt�1þ

Pkj ¼ 1

fAj Dxt�jþetðBÞDxt ¼ dB

0þdB1tþdB

2 DTþaBxt�1þPk

j ¼ 1

fBj Dxt�jþet-

ðCÞDxt ¼ dC0þd

C1tþdC

2 DUþdC3 DTþaCxt�1þ

Pkj ¼ 1

fCj Dxt�jþet

where the dummy variables DUt¼1 and DTt¼t�TB for t4TB and 0 otherwise, and

TB denotes the period at which a possible trend break occurs. Critical values for

the min-t are given by Zivot and Andrews (1992). In model (A) 1% (�5.34) 5%

(�4.80) 10% (�4.58); model (B) 1% (�4.93) 5% (�4.42) 10% (�4.11) and; model

(C) 1% (�5.57) 5% (�5.08) 10% (�4.82).

Table 4Estimates of the linear unobserved component model.

Natural rate equation

b 0.000 (0.055)

sN 0.018nnn (0.003)

Cyclical rate equation

f1 0.357n (0.204)

f2 �0.032 (0.036)

sC 0.028nnn (0.003)

Identification equation

a 0.640nnn (0.080)

d �6.201nn (2.841)

sD 0.776nnn(0.075)

Range 1973:1–2010:3

Notes: Standard errors are in parentheses. Asterisks are as

in Table 1.

A.A. Golpe et al. / Energy Policy 46 (2012) 594–600598

4.2. Linear unobserved component model

Table 4 presents the results of estimating (5)–(7) for naturalgas consumption. The parameter b is not statistically significant.However, should the existence of hysteresis in natural gas con-sumption be rejected? A likely reason of this rejection could bethe presence of nonlinearity, and we should check it.

4.3. Asymmetries

We check now a nonlinear specification of the unobserved com-ponent model10. This involves jointly estimating the structure (4),

10 In this case, the assumption of stationarity should be tested by using an

alternative method. We employed the Caner and Hansen (2001) methodology to

(6) and (7) to determine whether there is a threshold for cyclicalconsumption which is associated with asymmetric hysteresisresponses. The null hypothesis H0 : b

þ¼ b� is rejected since the p-

value calculated following the bootstrap technique described indetail in Perez-Alonso and Di Sanzo (2011) is 0.000. Therefore, wereject the null of linearity (Aslan, 2011).

In Table 5, we report the ML estimates of the hysteresisparameters. The threshold parameter is t¼�0.0009 (i.e., a variationof �1.775 in terms of billions cubic feet). Hence, the threshold modelsplits the regression into two regimes depending on whether or notthe threshold variable is higher than this threshold parameter. Thatis, we consider we are in regime 1 (54.05% observations) whenGt�1�Gt�3Z�0.0009—which corresponds to all positive variationsin gas consumption and to the smallest negative ones—and inregime 2 when Gt�1�Gt�3o�0.0009 (4595% observations). Theestimated hysteresis parameter is statistically significant only in thefirst regime, i.e. when the gap is above the threshold value. Hence,only when the gap is above the estimated threshold parametertemporary shocks in gas consumption have permanent effects. Sincethis regime includes all positive variation we can conclude that thepromotion of natural gas consumption in the US will have perma-nent effects. By contrast, policy shocks oriented to reduce the naturalgas consumption will have permanent effects only if they are ofsmall scale. In other words, conservative policies only have, ingeneral, temporary effects. Therefore energy conservation policiesmight be less powerful than has been thought before. By contrast,any increase in natural gas consumption brought about by thesepolicies will be incorporated into all future levels of consumption.

4.4. Policy implications

Previous results should be carefully considered by policymakers. Our results indicate that after allowing for nonlinearitythe effects of policies on natural gas consumption may beasymmetric. That is, energy policy may not have the same effect,suggesting that the effects of shocks may be different dependingon the sign and size of shocks.

In the context of the new role assigned to natural gas by theObama’s administration, as a key driver of a long-term energy policyfor the United States, our results imply that the new incentivesoriented to encourage the use of natural gas—positive policyshocks—have permanent effects on natural gas consumption, sinceany increases brought about by these positive incentives areincorporated into all future levels of natural gas consumption.

(footnote continued)

test for a unit root in a TAR model. The null hypothesis is that there is not a unit

root. The p-value is 0.02. This methodology is also applied by Maslyuk and Smyth

(2009).

Table 5Non-linear model estimation results.

Natural rate equation

b 0.398nn (0.163) 0.414 (0.453)

sN 0.024n (0.013)

Cyclical rate equation

f1 0.115 (0.148)

f2 0.042nnn (0.012)

sC 0.031nnn (0.013)

Identification equation

a 0.661nnn (0.077)

d �4.208 (5.192)

sD 0.786nnn (0.076)

Threshold �0.0009

Delay lag 3

% obs. 54.05 45.95

Range 1973:1–2010:3

Notes: Standard errors are in parentheses. Asterisks are as in Table 2.

A.A. Golpe et al. / Energy Policy 46 (2012) 594–600 599

Furthermore, a second important lesson emerges on theduration of policy stimulus. In particular, one could argue infavor of a differentiated treatment, in terms of the duration ofpolicy measures. In view of evidence, promoting for just a shortperiod could be enough to trigger lasting change while conserva-tion could need long term support.

In any case, to date literature offers contradictory findings onwhether shocks to energy variables are transitory or permanent.Until there is a wider consensus, policy makers cannot haveconfidence in these results for practice purposes. Advances innew methods which contribute to increase a higher degree ofrobustness may be a key element in this respect.

5. Conclusions

This paper estimated a linear and nonlinear unobservedcomponents model for natural gas consumption in the UnitedStates. Unlike some previous works that just studied the statio-narity properties of energy variables assuming a nonlinear datageneration process our approach defines hysteresis in terms ofthe interdependent evolution of a non-stationary natural compo-nent and a stationary cyclical component.

The results provide evidence of hysteresis only when thevariation in the natural gas consumption is above the estimatedthreshold value, which corresponds with positive variations andthe less negative ones.

Our findings have two important implications. Firstly, ourestimates suggest that hysteresis arises when cyclical shocks arepropagated asymmetrically to the natural component. Sincelinear models are not able to describe the dynamic asymmetriesnonlinear models are needed to correctly test hysteresis phenom-ena. Secondly, given that natural gas consumption follows a non-stationary process in the regime characterized by positive varia-tions in consumption, policy actions oriented to promote thenatural gas consumption will have not only temporary but alsopermanent effects.

From this result a lesson for policy makers emerges: energypolicy may not have the same effect depending on the size andsign of shocks. However, and given that the incipient field of longmemory properties of energy consumption and production vari-ables offers still contradictory findings whether shocks to energyvariables are transitory or permanent, policy should be verycareful here.

The approach adopted in this paper further the boundaries ofeconometric methodologies for the analysis of stationarity prop-erties of energy series by using an alternative definition ofhysteresis and allowing non-linearities.

Future work might fruitfully apply the methodology used inthis article to a broader range of countries and energy sources inorder to revisit the robustness of previous studies on persistencein energy variables taking into account asymmetries, and employadequate econometric approaches to deal with structural breaks.

Acknowledgments

Comments of the editor and two anonymous referees aregratefully acknowledged.

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