Pol­gá­ri Szem­le, 13. évf., 4–6. szám, 2017, 380–388., DOI: 10.24307/psz.2017.1228

Sum­ma­ry

The sta­tis­tics made by the In­ter­na­ti­o­nal Mo­ne­tary Fund of a samp­le of 30 count­ri­es analy­sed to as­sess the deg­ree of synch­ro­ni­ci­ty of changes under the im­pact of the cris­is on mac­ro­e­co­no­mic in­di­ca­tors such as inc­re­a­se in: GDP, the exc­han­ge rate of the na­ti­o­nal cur­rency; a count­ry’s in­ter­na­ti­o­nal in­vestment po­sit­i­on (which cha­rac­te­ri­zes the ex­ter­nal lia­bi­li­ti­es of res­idents to non-res­idents); fo­rei­gn exc­han­ge re­ser­ves; the value of govern­ment bonds. In order to qu­an­ti­fy the changes ob­ser­ved, the va­lues of the Ken­dall con­cor­dance co­ef­fi­ci­ent were cal­cu­lated for equal pe­ri­ods of time – in the cris­is and post-cris­is pe­ri­ods.

Jour­nal of Eco­no­mic Li­te­ra­tu­re (JEL) codes: G01, C82, E44, C45
Key­words: fi­nan­cial cri­ses, mac­ro­e­co­no­mic in­di­ca­tor, clas­si­fi­ca­ti­on, rank, co­ef­fi­ci­ent con­cor­dance, ne­u­ral net­work, Ko­ho­nen map

Prob­lem sett­ing

Mo­dern eco­no­mic po­li­cy is re­qu­i­red to be able to de­ter­mi­ne the growth of im­ba­lan­ces in the struc­tu­re and level of fi­nan­cial mar­kets in a ti­mely man­ner. In view of the ex­po­nen­ti­ally ac­ce­le­rat­ing pace of eco­no­mic in­te­gra­ti­on, this task is be­com­ing inc­re­a­singly comp­li­ca­ted. The rea­son for this is the laye­ring of in­ter­na­ti­o­nal re­la­tions bet­ween goods and money, the inc­re­a­sing pyra­mid of se­con­dary fi­nan­cial inst­ru-ments, and the sh­rink­ing time of cash flow cir­cu­la­tions.

When the cha­rac­te­r­is­tic fea­tu­res of fi­nan­cial mar­ket cri­ses are stu­di­ed, count­ri­es need to be dif­fe­ren­tiated ac­cord­ing to their res­pon­ses to ex­ter­nal fi­nan­cial shocks. The re­le­vance of the topic is high­ligh­ted in the Re­port on Glo­bal Fi­nan­cial Sta­bi­lity by IMF.

In order to iden­ti­fy pe­ri­ods when there is si­mil­arity (or dis­si­mil­arity) in be­ha­vi­o­ur bet­ween the va­ri­o­us eco­no­mic sys­tems, this paper pro­pos­es to cons­ider a non-pa­ra­met­ric rank cor­re­la­ti­on test.

Re­cent re­se­arch and pub­li­ca­tions

The re­le­vance of the study of the be­ha­vi­o­ur of eco­no­mic sys­tems is un­quest­ion­ab­le. The main task of app­li­ed re­se­arch is to descri­be and then pre­dict the dy­na­mics of de­ve­lop­ment in eco­no­mic sys­tems. Among the main the­o­re­ti­cal con­cepts it is ne­ces­sary to dist­in­gu­ish sys­tem the­ory (Ber­ta­lan­ffy, 1968; Nic­o­lis–Pri­go­gi­ne, 1977) and non-li­near dy­na­mics (Nic­o­lis–Pri­go­gi­ne, 1977; Der­bent­sev et al., 2010). As a sig­ni­fi­cant re­sult, re­se­arch has iden­ti­fi­ed that the par­ti­cu­lar cases of the comp­lex sys­tems func­tion­ing under strictly de­fi­ned input pa­ra­me­ters and const­ra­ints on the ini­ti­al con­di­tions can be for­mally descri­bed.

In this paper, we exa­mi­ne the pos­si­bi­lity of studying gro­ups of eco­no­mic ob­jects in order to iden­ti­fy si­mil­ari­ti­es in their be­ha­vi­o­ur. To this end, we pro­po­se the app­li­ca­ti­on of the rank co­ef­fi­ci­ent of con­cor­dance (Ken­dall, 1955; Ken­dall–Bab­ing­ton Smith, 1939; Le­gend­re, 2005). This was spe­ci­fi­cally cal­cu­lated for a test group of thirty count­ri­es at dif­fe­rent le­vels of eco­no­mic de­ve­lop­ment. The cal­cu­la­tions were done for two pe­ri­ods: the glo­bal fi­nan­cial cris­is (01.01.2007-31.12.2009) and the post-cris­is pe­ri­od (01.01.2010-31.12.2012). The re­se­arch ob­jec­tive is to ve­ri­fy the hy­pot­he­sis that the non-pa­ra­met­ric co­ef­fi­ci­ent of rank con­cor­dance can be used to clas­si­fy count­ri­es into gro­ups ac­cord­ing to the si­mil­arity of their res­pon­se to ex­ter­nal fi­nan­cial shocks.

Key re­se­arch find­ings

To test the hy­pot­he­sis of mis­match, the exist­ing IMF clas­si­fi­ca­ti­on of count­ri­es by level of eco­no­mic de­ve­lop­ment, for exp­lor­ing gro­ups of count­ri­es by the si­mil­arity of res­pon­ses to ex­ter­nal fi­nan­cial shocks, we use the rank co­ef­fi­ci­ent of con­cor­dance.

The co­ef­fi­ci­ent of con­cor­dance was pro­po­s­ed by M. G. Ken­dall and B. B. Smith as a me­a­sure of the ag­ree­ment among se­ve­ral qu­an­ti­ta­tive or se­mi-qu­an­ti­ta­tive va­ri­a­b­les that are as­ses­sing a set of in­te­rest ob­jects (Ken­dall, 1955; Ken­dall–Bab­ing­ton Smith, 1939; Le­gend­re, 2005):

$$W=\frac{12S}{m^2(n^3-n)-mT}\qquad\qquad(1)$$

where n is the num­ber of ob­jects and m is the num­ber of va­ri­a­b­les;

S – is a sum-of-squ­a­res sta­tis­tics over the row sums of ranks R_i:

$$S=\sum_{i=1}^n(R_i-\bar{R})^2;\qquad\qquad(2)$$

R – is the mean of the R_i va­lues.

The value of the co­ef­fi­ci­ent of con­cor­dance ranges from 0 to 1. If W=0, the rank order in rows does not agree (dis­si­mil­ar). If W=1, the re­sult is in­terp­re­ted as a full conc­ur­ren­ce in the est­ima­tes of the stu­di­ed pa­ra­me­ters. Than hig­her the value of co­ef­fi­ci­ent app­ro­a­ches unity, the hig­her co­he­ren­ce is ob­ser­ved in the input data se­ri­es.

In cont­rast to the pro­ce­du­res of fac­tor or clus­ter analy­sis, using the co­ef­fi­ci­ent of con­cor­dance in the ini­ti­al phase of the study has a num­ber of ad­van­ta­ges:

In this re­se­arch the va­lues of the co­ef­fi­ci­ent of con­cor­dance eva­lu­a­te the level of si­mil­arity in the dy­na­mics of the se­lec­ted in­di­ca­tors in cris­is and post-cris­is pe­ri­ods for the eco­no­mi­es of dif­fe­rent count­ri­es.

The hy­pot­he­sis about the disc­re­pancy bet­ween the exist­ing clas­si­fi­ca­ti­on of IMF for the study of gro­ups of count­ri­es ac­cord­ing to the si­mil­arity of the dy­na­mics of res­pon­se to ex­ter­nal fi­nan­cial shocks checks a samp­le of thirty count­ri­es with the rep­re­sen­ted count­ri­es in each group, na­mely:

1. Ad­van­ced Eco­no­mi­es: Aust­ra­lia (1), Aust­ria (2), Gree­ce (3), Es­to­nia (4), Is­ra­el cted in­dia­tor in iis ad pisi piod fr the ecn­mie of dif­fer (5), Ice­land (6), Ca­na­da (7), Ger­many (8), New Ze­aland (9), Uni­ted King­dom (10) Spe­ci­al ad­mi­nistra­tive re­gi­on of China Hong Kong (11), South Korea (12), Por­tugal (13) Uni­ted Sta­tes (14), Fin­land (15) France (16), Czech Re­pub­lic (17).

2. Emer­ging and De­ve­lop­ing Eco­no­mi­es: Bra­zil (18), Geor­gia (19), Ka­zakhs­tan ac­co­ding to the si­mil­arity of the dy­na­mics of re­pon­se to ex­ter­nal fi­nanc (20), Co­lom­bia (21), Mol­do­va (22), Pa­ra­guay (23) Peru (24), Po­land (25), Ro­ma­nia (26th), Tur­key (27) Cro­a­tia (28), Hun­gary (29), Uk­raine (30).

The sta­tis­ti­cal data used for cal­cu­lat­ing the rank co­ef­fi­ci­ent of the Ken­dall con­cor­dance is the of­fi­ci­al sta­tis­ti­cal fi­nan­cial re­port and is pub­licly ava­i­lab­le on the of­fi­ci­al web­site of the In­ter­na­ti­o­nal Mo­ne­tary Fund.

The con­se­qu­en­ces of the cris­is for the eco­nomy of any count­ry can be est­ima­ted on the basis of changes in the agg­re­ga­te the fol­lo­wing in­di­ca­tors: GDP, the exc­han­ge rate of the na­ti­o­nal cur­rency, part of the count­ry’s in­ter­na­ti­o­nal in­vestment po­sit­i­on that cha­rac­te­ri­zes the ex­ter­nal lia­bi­li­ti­es of res­idents to non-res­idents, fo­rei­gn exc­han­ge re­ser­ves, and the value of govern­ment bonds (Mat­viy­chuk–Str­el­chen­ko, 2015). These mac­ro­e­co­no­mic in­di­ca­tors are sen­sit­ive to fi­nan­cial shocks and show sharp fluc­tu­a­tions in the shor­test pos­sib­le time after the cris­is. In order for the re­sults of the eva­lu­a­ti­on it was pos­sib­le to com­pa­re each in­di­ca­tor sho­uld be a re­la­tive value and is cal­cu­lated as the ratio bet­ween the cur­rent value and value in the pre­vi­o­us time:

$$x_i=\frac{X_i^t}{{X_i}^{t-1}}\cdot100\%,\qquad\qquad(3)$$

where x_i – is growth ratio of mac­ro­e­co­no­mic in­di­ca­tors;

X_i^t, X_i^t-1 – is a the ab­so­lu­te value of the mac­ro­e­co­no­mic in­di­ca­tor at time t and t - 1 respec­ti­vely;

і = 1,…,5 – is a num­ber of mac­ro­e­co­no­mic in­di­ca­tor.

A cal­cu­lat­ing se­qu­en­ce of the rank­ing co­ef­fi­ci­ent of con­cor­dance by the examp­le of a mac­ro­e­co­no­mic in­di­ca­tor – the qu­ar­terly data of the exc­han­ge rate in a cris­is pe­ri­od (01.01.2007-31.12.2009) (table 1-3) is given below.

In case of tied ranks (see. Table 2) for­mu­la to cal­cu­late the rank co­ef­fi­ci­ent of con­cor­dance is as fol­lows (Ken­dall, 1955; Ken­dall–Bab­ing­ton Smith, 1939; Le­gend­re, 2005; Sie­gel–Cas­tel­lan, 1988):

$$W=\frac{12S}{m^2(n^3-n)-mT}\qquad\qquad(4)$$

where T – is cor­rec­ti­on fac­tor for tied ranks:

$$T=\sum_{k=1}^g(t_k^3-t_k),\qquad\qquad(5)$$

where t_k – is the num­ber of tied ranks in each k of g gro­ups of ties. The sum is com­pu­ted over all m va­ri­a­b­les of the input data. (Table 3.)

Ac­cord­ing to the for­mu­la (1-2, 4-5), the co­ef­fi­ci­ent of con­cor­dance W is cal­cu­lated and its sig­ni­fi­cance is de­ter­mi­ned by Fried­man’s chi-squ­a­re sta­tis­tics with n-1 deg­rees of fre­e­dom (Le­gend­re, 2005):

$$\chi^2=m(n-1)W.\qquad\qquad(6)$$

The final re­sults of the as­sess­ment of si­mil­arity in the dy­na­mics of the se­lec­ted in­di­ca­tors for the two gro­ups of eco­no­mi­es du­ring the glo­bal fi­nan­cial cris­is of 2007-2009 are shown in Table 4.

The co­ef­fi­ci­ent of con­cor­dance is cal­cu­lated si­mil­arly for each in­di­ca­tor for the post-cris­is pe­ri­od bet­ween 01.01.2010 and 31.12.2012 (Table 5).

On the basis of the ob­ta­ined re­sults it is highly pro­ba­ble (>95%) that du­ring the glo­bal fi­nan­cial cris­is (2007-2009) the dy­na­mics of the in­vestiga­ted in­di­ca­tors wass cha­rac­te­ri­zed by a low level of si­mil­arity (W<0.5 in 80% of cases) for both gro­ups.

Spe­ci­al ment­ion sho­uld be made of the re­sults of Table 5, which cha­rac­te­ri­ze the post-cris­is pe­ri­od (2010-2012). For the group of ad­van­ced eco­no­mi­es, the value of the con­cor­dance co­ef­fi­ci­ent is less than that of the pe­ri­od of the glo­bal fi­nan­cial cris­is. This in­di­ca­tes a sig­ni­fi­cant dif­fe­ren­ce in the re­ac­ti­on of each eco­no­mic sys­tem to sharp struc­tu­ral changes in the fi­nan­cial sec­tor under the inf­lu­en­ce of ex­ter­nal shocks.

As for gro­ups of count­ri­es with emer­ging mar­kets, it is im­pos­sib­le to make une­qu­i­vo­cal conc­lu­sions about the more sig­ni­fi­cant dif­fe­ren­ces in the dy­na­mics of in­di­ca­tors in the post-cris­is pe­ri­od. In some cases (for examp­le, when cal­cu­lat­ing the co­ef­fi­ci­ent of con­cor­dance for govern­ment bonds) the lo­west value and a low pro­ba­bi­lity due to the lack of sta­tis­tics for 35% of the samp­le count­ri­es.

Conc­lu­sions

As a re­sult of the stu­di­es, the fol­lo­wing conc­lu­sions were made:

Given the spe­ci­fic pre­re­qui­si­tes for sol­ving such a prob­lem, for the clas­si­fi­ca­ti­on of ne­u­ral net­works it may be rea­son­ab­le to use inst­ru­ments like the Ko­ho­nen maps or a ra­di­al-bas­ed ar­chi­tec­tu­re.