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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>QAIDS Model Based on Russian Pseudo-Panel Data: Impact of 1998 and 2008 Crises 1,2</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Maria D. Ermolova</string-name>
          <email>mermolova@hse.ru</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Henry I. Penikas</string-name>
          <email>penikas@hse.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Applied Economics, National Research University Higher School of Economics</institution>
          ,
          <addr-line>Moscow</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>International Laboratory of Decision Choice and Analysis, National Research University Higher School of Economics</institution>
          ,
          <addr-line>Moscow</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>JEL codes: D12</institution>
          ,
          <addr-line>E21</addr-line>
        </aff>
      </contrib-group>
      <fpage>48</fpage>
      <lpage>60</lpage>
      <abstract>
        <p>The aim of this work is to compare shifts in the consumer behaviour of Russian households since the mid-nineties till nowadays. The research considers the consumer behaviour of the Russians over almost the maximum possible available data RLMS period, focusing on the crisis years. Special attention is paid to analysis of the effects of crises in 1998 and 2008. To reveal effects as shifts in consumer behaviour in the aftermath of two crises panel data analysis is used to estimate QAIDS model. Due to the complete sample attrition observed in RLMS dataset since 1994, pseudo-panel approach is used.</p>
      </abstract>
      <kwd-group>
        <kwd>QAIDS</kwd>
        <kwd>RLMS</kwd>
        <kwd>pseudo-panel</kwd>
        <kwd>consumer behaviour</kwd>
        <kwd>crisis</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Economic recessions change consumer behaviour through consumers’ expectations
that can be also formed by economic policy, economy structure or distribution of
households. Structural or temporal shifts determine the subsequent economic policy,
whose efficiency, in turn, also evaluated by the change in the welfare of different
households. Therefore, analysis of shifts in consumer behaviour needs to be
determined accurately. However, any research about life quality is highly dependent on the
data used. Data may not always be suitable for study for the following
reasons: selection bias (no poorest or richest people), distrust of statistical authorities
(respondents often refuse to answer questions or deliberately distort the data), the lack
1 The study was implemented in the framework of the Basic Research Program at the
National Research University Higher School of Economics.
2 The authors are grateful to Rustam Zakirov for conducting initial calculations and to Sergey
Vinjkov for research assistance.
of representativeness relative to the general population, and a depletion of the sample
over a long period of time.</p>
      <p>The aim of this work is to compare shifts in the consumer behaviour of Russian
households since the mid-nineties till 2011. In this paper, the data from the survey
"Russian Longitudinal Monitoring Survey HSE" (hereafter RLMS) is used.3 The
paper shows that descriptive statistics or model using panel data do not provide enough
information about whether 1998 or 2008 crises leads to structural or temporal effect
on consumer behaviour. Using pseudo-panels it was found that the effect of 1998
crisis was stronger in consumer behaviour than the crisis of 2008.</p>
      <p>The paper is organized in the following way. Section 1 is introduction. Section 2
discusses the works based on QAIDS model briefly. In Section 3 the theoretical
demand model is described. Section 4 explains data processing. Model estimation is
given in section 5. Section 6 provides the conclusion about the effects of economic
shocks and the evolution of consumer behaviour in Russia.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Literature review</title>
      <p>As far as the authors know, there are no works devoted to the study of consumer
behaviour of Russian households for such a long time interval (due to the problem of
sample depletion).4</p>
      <p>There are articles covering a relatively short period of time 2000 – 2005 [Penikas,
2008] or focusing on specific aspects of consumer behaviour (differentiation of real
incomes of the population on the basis of consumer choice) [Matytsin et al., 2012]. In
foreign literature the number of publications on consumer behaviour is much higher,
because it is closely associated with the doctrine of welfare of the population.</p>
      <p>The article [Deaton et al., 1980] firstly provides a theoretical description of the
Almost Ideal Demand Model (AIDS). AIDS has proven its viability and vitality using
the British data from 1954 to 1974. [Gardes et al., 2005] concludes using AIDS model
that the estimates obtained using the pseudo-panel approach is less biased compared
to the cross-section data the usage of cross-section data.</p>
      <p>[Tovar et al., 2012] pseudo-panel estimation takes into account the time
dependence of the different cohorts, because the same households may be in different
households over time.
3</p>
    </sec>
    <sec id="sec-3">
      <title>Quadratic almost ideal demand model (theoretical model)</title>
      <p>Dynamics of consumer behaviour by consumption group and by various
consumption directions is considered from the perspective of analysis of coefficients of income
3 Source: “Russia Longitudinal Monitoring survey, RLMS-HSE”, conducted by the National
Research University Higher School of Economics and ZAO “Demoscope” together with
Carolina Population Center, University of North Carolina at Chapel Hill and the Institute of
Sociology RAS. URL: http://www.cpc.unc.edu/projects/rlms-hse
4 A gradual decrease in the number of observations.
elasticity derived from QAIDS (Quadratic Almost Ideal Demand System) (Banks et
al., 1997):

 =1</p>
      <p>
        Where   ℎ – share of household’s expenses ℎ for sets of goods  = 1,2,3 in the
moment  ,   – Stone Price Index ( 
=
∑     ),  ℎ – household’s income
(the costs are usually used as an equivalent because respondents in surveys tend to
understate their own revenues),  ℎ – the matrix of socio-economic characteristics,
 ( ) = ∏ 
  price index, ensuring the integrability of the entire system,   ℎ

includes both individual effect and random error. To estimate the elasticities it is
necessary to take derivatives of the above equation   and    :
  =    ⁄ ln  =   + 2  [ln( ℎ ⁄  ) − ln( ( ))]
  =    ⁄ ln   =   −   (   + ∑   ln   )

 =1
−     (ln( ℎ ⁄  ))2⁄ ( )
(
        <xref ref-type="bibr" rid="ref2">2</xref>
        )
(
        <xref ref-type="bibr" rid="ref3">3</xref>
        )
The income elasticity for each household will be defined as   =

compensated price elasticity for good  as  
=  
 −   (
        <xref ref-type="bibr" rid="ref5">5</xref>
        ), where  

uncompensated elasticity (  is the Kronecker symbol, that is equal to 1 when  = 
 
  + 1 (
        <xref ref-type="bibr" rid="ref4">4</xref>
        ), and
=  
 
−   is
and 0 in all other cases).
4
      </p>
    </sec>
    <sec id="sec-4">
      <title>Data</title>
      <p>This work is based on the second phase RLMS data, covering the period of 1994–
2011. The RLMS surveys constitute an unbalanced panel, i.e. a household can vary
from year to year in the survey (sample attrition). Only 35 % of the household (1 366
/ 3 975 of observations) that took participation in the survey of 1994 remain in the
polls by 2011.5 77% of households in the survey of 2008 are presented in the sample
of 2011. The observations are placed in the same income group after data processing.
It is the prevalent challenge in studying the effects of crises on different groups of
households. In connection with these problems, the paper proposes to use
pseudopanels, namely to generate quasi-households on the basis of real data. Further, data
processing will be described.</p>
      <sec id="sec-4-1">
        <title>5 Only 7.5% of households remain after data processing.</title>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Outliers</title>
      <p>If the difference between a one-year distribution of costs and incomes is more than
45 percentiles for a household, then the observation is recognized as atypical and
removed. The threshold of 45 percentiles has been chosen in such a way to eliminate
the problem of underestimating revenues, but at the same time to keep most of the
sample. For example, 30 percentiles are not applicable because the sufficient sample
part (16.3% of outliers) is removed in comparison with 45 percentiles (6.1 % of
outliers).
4.2</p>
    </sec>
    <sec id="sec-6">
      <title>OECD equivalence scale</title>
      <p>The welfare of individuals of the household can be measured either "per capita" or
"per consumption unit". The first approach is not applicable due to economies of
scale. Two people do not consume two times more goods, because they have both
public (car, refrigerator) and private goods (food) within a family. Therefore, it is
necessary to implement the concept of "per consumption unit" that will depend on
public-to-private goods ratio in the household.</p>
      <p>The public-to-private goods ratio varies depending on time and country. Time is
introduced through the function that depends on the age of household members. The
function is a linear combination of the number of family members belonging to
different groups. In our research the Oxford modified equivalence scale [Lubrano, 2010]
will be used, as it is the most popular in research on consumer behaviour (see [Banks
et al., 1997] and [Penikas, 2008]).
1 adult
2 adults
2 adults, 1 child
2 adults, 2 children
2 adults, 3 children
Elasticity</p>
      <p>Different measurement scales can lead to different estimates of elasticities by
income.
4.3</p>
    </sec>
    <sec id="sec-7">
      <title>Welfare</title>
      <p>The effects of the crises do not appear explicitly if weights of expenditures by
good classes are examined. Fig. 2 shows that the share of expenditures on food
decreased over time, which is consistent with the growth in real incomes because the
proportion of expenditure on food is a common first approximation of living
standards. Over the beginning of the two thousandth's the share of durable goods was
actively growing. In recent years an increase in the relative costs of services exceeded
all other.</p>
      <p>1500
1000
500</p>
      <p>0
0,8
0,6
0,4
0,2
0</p>
    </sec>
    <sec id="sec-8">
      <title>Homogeneous groups of income using cohort identification</title>
      <p>
        Both multi-criteria index of poor-rich (IMPR) and cluster analysis (k-means) are
used to identify homogeneous groups by material welfare. The hypothesis of
statistical independence of the IMPR and k-means approach is rejected at 1 % significance
level, because sample correlation coefficient of quadratic conjugacy [Ayvazian et al.,
1983] is X2 = 29 841 (p − value = 0.0000). Further, it was decided to abandon the
use of k- means. Using k-means there were two cases: (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) insignificant coefficients or
(
        <xref ref-type="bibr" rid="ref2">2</xref>
        ) their sign does not coincide with the sign of model coefficients based on IMPR
and with the sign of the correlation.
      </p>
    </sec>
    <sec id="sec-9">
      <title>Multi-criteria index of poor-rich.</title>
      <p>This method was proposed in [Gardes et al., 1999]. It was used in [Penikas, 2008].
Unlike simpler methods, it includes three main factors, each of which is assigned a
score from 1 to 3 depending on the poverty group (1 – poor, 2 – average, 3 – rich):</p>
      <p>Scores for each factor were assigned within one year. Based on the obtained
ratings for each criterion, IMPR takes 5 different values: 3 if poor, 4 if quasi-poor, 5–8 if
middle class, 8 if quasi-rich, and 9 if rich. Using IMPR scoring the following
distribution of households by its types was obtained. Each class has a fairly constant weight
(12%, 19%, 47%, 8% and 14% respectively for poor, quasi-poor, average, quasi-rich
and rich). Also, clear differences in consumption are visible for the classes. The
expenditure on food exceeds all other expenses for the two poorest groups over whole
time period, while the main item of expenditure is durable goods for the richer
households. The highest share of expenditure on services is observed for the two poorest
groups. Probably, it is the cost of housing services. All households pay for the
housing services, but the impact of these services is stronger for the poor population.</p>
      <p>Splitting the sample by income groups allows to identify the impact of the crises
on income per consumption unit for the richest three groups (Fig. 3). The constant
sample (presented over whole period since 1994) is added to show that the constant
sample differs insignificantly from quasi-poor households, but absolutely not
identified two richest groups for which changes in consumer behavior are obvious
particularly. It suggests that the original observations cannot provide sufficient variability to
examine differences in consumption behavior deeply. It stresses the relevance of
using pseudo-panels.6
2000
1500
1000
500</p>
      <p>Where  ̅ is the average of dependent variable in cohort с in time t,  ̅′ is the
average of explanatory variables,   is fixed effect for each cohort, с is cohort’s
number, and t is time. For QAIDS model   means w (the average weight of
good i for cohort c at time t). Average revenue and descriptive statistics of the cohort
are included in the vector of explanatory variables.</p>
      <p>In the current paper the type of settlement and the average age of the household are
used to identify cohorts. The optimal number of groups is formed in such way that the
number of households in each group must be positive and the variation should not
exceed a reasonable limit.</p>
      <p>RLMS surveys indicate 4 main types of settlements: regional center, town,
urbantype settlement, and village (44%, 27.7%, 5.7%, and 22.5% of observations,
respectively). Two categories are combined into one to obtain approximately constant
weights over time for each quasi-households. Urban-type settlement (town) and
vil6 The budget coefficients also differ for the three groups of goods insignificantly.
lage were joined, because there is no fundamental difference to interpret consumer
behaviour (in both types there is a possibility of employment in agriculture). The
weights of each settlement type are relatively stable over time (in average 44%, 28%,
and 28% for the regional center, cities, and towns/villages, respectively). Expected
differences concerning consumer behaviour are:
 the average income level for each settlement type is different. The larger the
settlement, the greater the expected income that affects welfare. Then people who live
in cities are rich people, and they need to be differentiated;
 the food expenditures are less in the rural population due to agriculture. The
majority of expenditures are on services for the urban dwellers.</p>
      <p>Three age groups are formed (Table 4). One can observe relatively stable weight
for each group over time but still with a slight tendency to increase the percentage of
senior households.</p>
      <p>Two criteria (settlement type and age) create 45 quasi-households (45 = 5 income
groups * 3 settlement types * 3 age groups) in each wave. Totally, there are 720
observations for the entite period (720 = 45 quasi-households in a year *16 years). The
average composition of quasi-households is 87 real households.
5</p>
    </sec>
    <sec id="sec-10">
      <title>Model estimation</title>
      <p>Quadratic Almost Ideal Demand Model is estimated for quasi-households both
based on income groups (5 quasi-households) and joint groups taking into account
income, settlement type, and age of households (45 quasi-households). The model
presented in Section 3 also includes the number of consumption units for each
household and dummy variables for each year to account for time effect (1994 as a base).
5.1</p>
      <p>The model with the fixed effect is the most preferred model, since every
quasihousehold is unique and cannot be regarded as the result of a random selection from
the general population. Although, consumer behavior is influenced by psychological
factors, then the random effect model may be more preferred.</p>
      <p>According to the results of F-test the model with a fixed effect is more preferred
than pool model for all goods at 1% significance level. Lagrange multiplier test
confirms the model with a random effect is chosen for food and durable goods, while a
final choice for services is the model with the fixed effect. Hausman test identifies
that the model with a random effect is the most preferred specification for food and
durable goods consumption. The results are in Table 5.
goods
7 It should be noted that covariance matrix for every type of goods was not positive definite.</p>
      <p>It makes difficult to make a strong conclusion.
5.2</p>
    </sec>
    <sec id="sec-11">
      <title>Analysis of structural changes</title>
      <p>The homogeneity of three time periods (before the first crisis, between crises and
after the second crisis) was studied using correlation analysis and Chow test. The
dynamic of correlations of the basic model factors shows that correlation has changed
over time. There is the probability to identify a structural change. Chow test rejects
the null hypothesis, i.e. there is heterogeneity, and there are two structural breaks that
confirms the potential impact of crises of 1998 and 2008. The result is consistent for
both 5 and 45 quasi-households.
goods</p>
      <p>Model</p>
      <sec id="sec-11-1">
        <title>Durable</title>
      </sec>
      <sec id="sec-11-2">
        <title>Services</title>
        <p>value
case with 5 quasi-households for the respective income groups.</p>
        <p>All income groups perceive food as basic necessity goods. However, the richer the
group, the smaller the elasticity of food by income (that is, the less necessary the
goods become). For the income group "Rich" there is a negative elasticity for the
period up to 1998. However, the estimated coefficients are statistically insignificant.
Then we can argue of perfectly inelastic demand on food before 1998, i.e. a change in
income has no effect on the food bought (“sticky good“). However, after 2008 a
negative elasticity (calculated using the statistically significant coefficients) confirms the
conclusion made previously that food products are inferior goods for rich groups.</p>
        <p>The income elasticity of demand for durable goods has increased strongly in 1998
and then gradually decreased until 2011 mostly for poor and quasi-poor households.
Over the most period durable goods are luxury goods for all income groups. The
model estimates for durable goods after 2008 are statistically insignificant, then the
durable goods can be recognized as “sticky good“ after 2008 until 2011.</p>
        <p>Fig. 4. Elasticity for food (5
quasihouseholds)</p>
        <p>Fig. 5. Elasticity for durable goods (5
quasi-households)</p>
        <p>The calculation with structural shifts for services showed that up to 2000 the
demand for services was inelastic (statistically insignificant model estimates for the
period before 1998). The calculations taking into account the structural changes also
show that the services were luxury goods for the three poorest groups and normal
goods for the others. Changes of the elasticities become visible at the moment of the
1998 crisis, namely the increase of elasticities in a time of crisis. The households
spent their additional income on services less.
[Varian, 2014] draws attention to the need to explore new methods of data analysis
for economics. Such necessity is explained by the fact that many modern solutions,
including economic policies, require more complex data analysis tools than using
only ordinary linear regressions. Our article provides an example of real data analysis
problems motivated by the problem of the variability of consumption.</p>
        <p>The work is aimed to study the effects of the crises of 1998 and 2008 on the
consumer behaviour of Russian households. The research is based on pseudo-panels,
which allowed to get rid of the sample attrition effect (a gradual decrease in the
number of observations). Pseudo-panels have allowed us to examine the evolution of
consumer behaviour for different groups of households according to two
classifications: only by income group; and by income group, type of settlement and age of
household members.</p>
        <p>Descriptive statistics does not provide any evidence of significant impact of crises
1998 and 2008 on Russian consumption (costs weights have not changed
significantly), although there was a decline in real income. The elasticity analysis and structural
breaks identification shows that some effects are observed for the 1998 crisis, and
there were no significant influence by the crisis of 2008. The estimation of the
coefficients of dummy variables demonstrates that the effect of 1998 is the highest
compared with all other years: a negative value for food products suggests that these
goods became more and more necessary for the Russians while the remaining goods
become relatively more luxurious. 1998 was preceded by unfavourable years after the
collapse of the Soviet Union, when the population practically had no savings.
Therefore the crisis affected consumer behaviour. In 2008 and 2009, the Russians have
sufficient savings after favourable period for the economy during the period of 2000–
2008.</p>
      </sec>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          1.
          <string-name>
            <surname>Banks</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Blundell</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lewbel</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>1997</year>
          ).
          <article-title>Quadratic Engel curves and consumer demand</article-title>
          .
          <source>Review of Economics and statistics</source>
          ,
          <volume>79</volume>
          (
          <issue>4</issue>
          ),
          <fpage>527</fpage>
          -
          <lpage>539</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          2.
          <string-name>
            <surname>Deaton</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>1985</year>
          ).
          <article-title>Panel data from time series of cross-sections</article-title>
          .
          <source>Journal of econometrics</source>
          ,
          <volume>30</volume>
          (
          <issue>1</issue>
          ),
          <fpage>109</fpage>
          -
          <lpage>126</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          3.
          <string-name>
            <surname>Deaton</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Muellbauer</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          (
          <year>1980</year>
          ).
          <article-title>Economics and consumer behavior</article-title>
          . Cambridge university press.
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          4.
          <string-name>
            <surname>Deaton</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Muellbauer</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          (
          <year>1980</year>
          ).
          <article-title>An almost ideal demand system</article-title>
          .
          <source>The American economic review</source>
          ,
          <volume>70</volume>
          (
          <issue>3</issue>
          ),
          <fpage>312</fpage>
          -
          <lpage>326</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          5.
          <string-name>
            <surname>Gardes</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Duncan</surname>
            ,
            <given-names>G. J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Gaubert</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Gurgand</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Starzec</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          (
          <year>2005</year>
          ).
          <article-title>Panel and pseudo-panel estimation of cross-sectional and time series elasticities of food consumption: The case of us and polish data</article-title>
          .
          <source>Journal of Business &amp; Economic Statistics</source>
          ,
          <volume>23</volume>
          (
          <issue>2</issue>
          ),
          <fpage>242</fpage>
          -
          <lpage>253</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          6.
          <string-name>
            <surname>Gardes</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Gaubert</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Langlois</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          (
          <year>2000</year>
          ).
          <article-title>Pauvrete et convergence des consommations au Canada</article-title>
          .
          <source>CRSA/RCSA</source>
          ,
          <volume>36</volume>
          (
          <issue>3</issue>
          ),
          <fpage>1</fpage>
          -
          <lpage>27</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          7.
          <string-name>
            <surname>Lubrano</surname>
            <given-names>M.</given-names>
          </string-name>
          <article-title>The econometrics of inequality and poverty</article-title>
          .
          <source>Lecture</source>
          <volume>7</volume>
          : Equivalence scales.
          <year>2010</year>
          . Available online: http://citeseerx.ist.psu.edu/viewdoc/download?doi
          <source>=10.1.1.169.3739&amp;rep=rep1&amp;type=pdf</source>
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          8.
          <string-name>
            <surname>Tovar</surname>
            ,
            <given-names>A. O.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zulaica</surname>
            ,
            <given-names>I. G.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Núñez-Antón</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          (
          <year>2012</year>
          ).
          <article-title>Analysis of pseudo-panel data with dependent samples</article-title>
          .
          <source>Journal of Applied Statistics</source>
          ,
          <volume>39</volume>
          (
          <issue>9</issue>
          ),
          <fpage>1921</fpage>
          -
          <lpage>1937</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          9.
          <string-name>
            <surname>Aivazyan</surname>
            <given-names>S.A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mkhitaryan</surname>
            <given-names>V.S.</given-names>
          </string-name>
          (
          <year>1983</year>
          ). Practical Statistics. Finances and Statistics.
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          10.
          <string-name>
            <surname>Matytsin</surname>
            <given-names>M.S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Yershov</surname>
            <given-names>E.B.</given-names>
          </string-name>
          (
          <year>2012</year>
          ).
          <article-title>Research of Real Income Differentiations of Russians</article-title>
          .
          <source>Economics Journal of the Higher School of Economics</source>
          ,
          <volume>16</volume>
          (
          <issue>3</issue>
          ),
          <fpage>318</fpage>
          -
          <lpage>340</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          11.
          <string-name>
            <surname>Penikas</surname>
            <given-names>H.I.</given-names>
          </string-name>
          <article-title>Analysis of Consumer Behaviour Evolution in Russia throughout 2000-2005</article-title>
          . (
          <year>2008</year>
          ).
          <source>Economics Journal of the Higher School of Economics</source>
          ,
          <volume>12</volume>
          (
          <issue>4</issue>
          ),
          <fpage>512</fpage>
          -
          <lpage>542</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          12.
          <string-name>
            <surname>Varian H.R. Big</surname>
          </string-name>
          <article-title>Data: New Tricks for Econometrics. (</article-title>
          <year>2014</year>
          ).
          <source>Journal of Economic Perspectives</source>
          ,
          <volume>28</volume>
          (
          <issue>2</issue>
          ),
          <fpage>3</fpage>
          -
          <lpage>28</lpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>