This study aims to spot the inflation – generating expenses. The expenses items are represented by series of prices statistical indexes. We are going to determine the series of gaps on these prices indexes. We will afterwards study the data- generating process in the context of the ARCH model and the V-GARCH model. We will find out the following items (food, clothes and transports) as inflation- generating items

Hassen, Ben Naceur

Copyright © 2014 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT: This study aims to spot the inflation – generating expenses. The expenses items are represented by series of prices statistical indexes. We are going to determine the series of gaps on these prices indexes. We will afterwards study the data- generating process in the context of the ARCH model and the V-GARCH model. We will find out the following items (food, clothes and transports) as inflation- generating items

Hassen Ben Naceur

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Expense items: test on items generating inflation

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Munich Personal RePEc ArchiveExpense items: test on items generatinginflationHassen, Ben NaceurUniversité Tunis El Manar, Faculté des Sciences Economiques et deGestion de Tunis, TunisiaSeptember 2014Online at https://mpra.ub.uni-muenchen.de/78977/MPRA Paper No. 78977, posted 08 May 2017 02:53 UTCInternational Journal of Innovation and Scientific Research ISSN 2351-8014 Vol. 8 No. 2 Sep. 2014, pp. 291-298 © 2014 Innovative Space of Scientific Research Journals http://www.ijisr.issr-journals.org/  Corresponding Author: Hassen Ben Naceur 291   Expense items: test on items generating inflation Hassen Ben Naceur Université Tunis El Manar, Faculté des Sciences Economiques et de Gestion de Tunis, Tunisia    Copyright © 2014 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.   ABSTRACT: This study aims to spot the inflation – generating expenses. The expenses items are represented by series of prices statistical indexes. We are going to determine the series of gaps on these prices indexes. We will afterwards study the data- generating process in the context of the ARCH model and the V-GARCH model. We will find out the following items (food, clothes and transports) as inflation- generating items. KEYWORDS: White noise, ARCH model, V-GARCH process, generator, inflation, statistical index. 1 INTRODUCTION We will study the series of prices statistical indexes in the category of expenses items. The test, achieved on these series, enables us to spot inflation-generating items. 2 CHOICE OF THE MODEL We will study the series of prices statistical indexes within the expenses items. These series may bring out temporal or instantaneous dependencies. Therefore, we will study these series of observations in the context of a V-GARCH model. The expenses items studied are the following:  Expenses items  item i Food 1 Housing 2 Clothes 3 Health care 4 Transport 5 Leisure and education 6  In the category of expenses items, we will determine series of gaps of prices statistical indexes: .         ,, mtitt ppy −= m=o, i. - itp ,   indicates the price index in the expenses item i. - 0,tp   represents the consumption prices index. Expense items: test on items generating inflation   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 292   The variations of the new series, ty , enable us to compare the trajectories of both series,  and  ,itp   0,tp  The series  ty  is submitted, in terms of values and signs, to an instantaneous variability. In this context, the series studied, varies in risky way, at the proximity of fixed parameter: te+= it by  i=1, 2,…, 6. [ ] ib=tyE           The inflation-generating process is described by these gaps between  and  , jtp    ,mtp  In another way, the series  ty  is not following the normal distribution. The skewness and kurtosis coefficients do not indeed belong to the proximity of the reference values: ==   30  **ks If ( )==      30  :  ,   ~ **2ksmNX σ  Because     ( )[ ]     ii mXE −=µ  ( ) =−∏= =otherwise                0        2    si    1212 sijsjsσ   [ ] 5,0323*µµ=s  224*µµ=k Then:  The series represents: - Leptokurtic aspect, - A quite high asymmetry coefficient, which is a sign of non-linearity. As a matter of fact: Expenses items 1 2 3 4 5 6 ∗s  0.25 -1.08 0.58 1.05 0.94 -0.14    ∗k  2.32 4.52 3.64 9.32 3.52 2.16    Hassen Ben Naceur   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 293   We will take these series of gaps between  and  , jtp    ,mtp as patterns in the category of the six expenses items. Then, we will study in the context of ARCH pattern, the series of observations, ty   : [ ]=+=<+=∑=−. h          ,  /t120qiitisttitecctseeVeby The parameters    explain the weight of the past in the conditional variance of disturbances. The model enables us to spot the inflation-generating items. We will,  here,  realize the ARCH test:   caqHHcc010 0...:H====.  cH 0  indicates the complementary of  0H         . We will, afterwards, realize the following test: 0:0:H i0≠=iiaibHb i=1, 2,…, 6. This means to test: titiattebyHey+==::H i0     . Then, under 0:Hi0 =ib , the series  ty  is following a process of white noise. It is then the chocks symmetry hypothesis in the prices series. This hypothesis comes out to spot the series following a process of white noise in the category of expenses items. The alternative hypothesis enables us to spot the inflation-generating expenses if: - 0fib  - ib  is significantly different of zero. As a matter of fact, this model enables us to spot the inflation-generating items thanks to the sign and significance on the parameter,  ib . We will, afterwards, that study these series of gaps in the context of the V-GARCH model. 0,,*tjtt ppy −=  itjtt ppy ,,** −= The series available may bring out temporal or instantaneous dependencies. [ ]=<+=.        ,  /0tstttHtseeVeby .        ***t =ttyyy Expense items: test on items generating inflation   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 294   =20100 bbb =***ttt eee. The choice of the V-GARCH model is dictated by the two first conditional moments of the process studies:   [ ] 0,/ =〈tseeE st     [ ] [ ]tsttstHtseeeEtseeV=〈=〈 ,/,/ '   tH  is a square matrix of order  N. It is the matrix of the conditional covariances of the disturbances. We will here study the signs of the parameters 10b  and    20b  . The expenses item j is an inflation-generating item if : -  010 fb  - The parameter   10b  is significantly different from zero. In this context, we will spot the item j as an inflation-generating item: - 010 fb  : 0,, tjt pp ≥  -≥〉≤〈itjtitjtppbppb,,20,,20:0:0 As a matter of fact, the expenses item j can be a first or a second- class inflation generator. We will then realize the test of significance on the parameters  10b  and 20b   : 0:0:000≠=ssassbHbH s=1, 2. 3 ESTIMATIONS We will approach the data- generating process with a whole class of models:  3.1 ARCH(Q) MODEL  ++=+=∑=− .     c1202tqititititeceebyω We will here achieve the test:  caqHHcc010 0...:H====   Hassen Ben Naceur   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 295   The disturbances are here following a process ARCH(1).  Expenses items ib̂  1  2,11 (10,50) 2 -9,07 (-47,42) 3 1,84 (4,14) 4 -0,37 (-1,47) 5 0,92 (3,28) 6 -1,98 (-9,96)  The numbers in brackets are the t of Student.   The estimations are achieved on quarterly frequencies data corresponding to a period of observations between [1974 :1, 2011 :4].  :0ˆ fib  The expenses item i is an inflation-generating item.  Thus, the inflation – generating items are the following items: food, clothes and transport. The series available are then described in terms of increase rate.  The gap between the two rates is interpreted as the gap between the rate in the expenses items i ( *,itp ) and the inflation rate ( *0,tp ): ** ,, otitt ppy −=  i=1, 2,…,6 . =− mtmtmt ppLogp,1,, *  m=0, i. The data-generating process is a conditionally heteroskedastic white noise process: ++==∑=− .     c1202tqitititteceeyω 3.2 V-GARCH  MODEL  We will study, in the context of the V-GARCH model, the series of observations:   [ ]=<+=.        ,  /0tstttHtseeVeby  Expense items: test on items generating inflation   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 296   The vector of the dependent variables is then: .        t=∗∗∗ttyyy ∗∗∗∗∗∗+=+=ttttebyeby2010     . .     20100 =bbb -Test of significance:  We will here realize the test:  0:H 100 =b  cH 0aH =  The parameter 10b  is significantly different from zero. -Signs of parameter 10b    and   20b    The expenses item j is an inflation- generating item if the parameter 10b    has a positive sign. The price index in the expense items j, which is jtp , , is compared to  the price index of the expense item i ( itp , ) and to the consumption prices index  ( 0,tp ). a. Let us assume that: 020 ≤b  <>0ˆ0ˆ2010bb The signs of the two parameters studied lead us to a double liaison: ≤−≥−.   0  0,,0,,itjttjtpppp Then :  .      ,,0, itjtt ppp ≤≤  The expenses items j  is a second-class inflation-generating item.              b. 020 ≥b  If  020 ≥b  : .      ,,0, jtitt ppp ≤≤  The expenses item  j  is a first-class inflation-generating.  Hassen Ben Naceur   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 297   This model enables us to spot food, clothes and transport as inflation-generating. The choice of estimations is dictated by the signs of parameters 10b  and   20b .  The observations on the two interest variables, *ty  and   **ty  , are conditionally the values of these parameters:  0,,*tjtt ppy −=   itjtt ppy ,,** −= Expenses items j 3 5 i 1 ( )54.361.1ˆ10 =b( )28.255.1ˆ20−−=b ( )47.910.4ˆ10 =b( )00.145.0ˆ20 =b 3  ( )05.478.1ˆ10 =b( )05.478.1ˆ10 =b( )00.254.1ˆ20 =b  The numbers in the brackets are the t Student.  The results enable us to spot the first of the second-class inflation-generating expenses items.       (*)      .      ,,0, itjtt ppp ≤≤     ( )≤≤≤≤5,3,0,5,1,0,**ttttttpppppp The item 5 is a first-class inflation-generating item. 4 CONCLUSION We have hence realized series of gaps between series of prices statistical indexes in the category of expenses items. Then we have studied the data-generating process in the context of ARCH and V-GARCH models. The test on these series of observations enables us to spot food, clothes and transport as inflation-generating items. These items can be a first or a second-class inflation generating items.     Expense items: test on items generating inflation   ISSN : 2351-8014 Vol. 8 No. 2, Sep. 2014 298   REFERENCES  [1] Bakhshi  H. [2002] : “Inflation and relative price variability”. Economics letters, 76, p. 27-33. [2] Basrak B.,Davis R. A. et T. 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Expense items: test on items generating inflation

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