The Relationship between Wages and Prices in Colombia

Munich Personal RePEc Archive

The Relationship between Wages and Prices in Colombia

Julio, Juan Manuel and Cobo, Adolfo

Banco de la Republica

1 July 2000

Online at https://mpra.ub.uni-muenchen.de/52676/

MPRA Paper No. 52676, posted 04 Jan 2014 18:31 UTC

The Relationship between Wages and Prices in Colombia

Juan Manuel Julio and Adolfo León Cobo July 2000

A bst r act

Due t o t he fact t hat many reliable indicat ors of furt her in‡at ionary pressures do not seem t o work any more, …nding whet her or not wages Granger cause prices is an import ant concern for policy making. However, int ernat ional evidence on t he relat ionship between wages and prices does not show st rong evidence in favor of causat ion in t he direct ion of prices. The result s present ed here for Colombian dat a point t o t he same direct ion. T his paper di¤ers from previous ones published in Colombia in two aspect s. First , we include t he Unit Labor Cost (product ivity adjust ed wages) as a more sensible measure of wages. Second, we base our analysis on a price markup expect at ions augment ed Phillips curve in which we include indicat ors of aggregat e demand and supply shocks, t hus avoiding omit t ed variables bias in our inferences. We worked under alt ernat ive st at ionary / non st at ionary VAR models. We found evidence in favor of Granger causality from prices t o wages but no evidence of Granger causality in t he direct ion of prices. T his result s hold only whe unit labor cost is used as t he wage indicat or and under alt ernat ive measures of aggregat e demand and under di¤erent assumpt ions on t he int egrat ion propert ies of t he series. The policy implicat ion of t hese result s point t he very careful use of wages as leading indicat or of in‡at ion.

1 Introduction.

Cent ral banks need t o pay close at t ent ion t o signals of in‡at ionary pressures.

In order t o do so, aut horities usually keep t rack of di¤erent variables t hat may cont ain informat ion about t he fut ure evolution of prices. One of such variables is t he nominal wage. Analyst and aut horit ies look at wages as an indicat or of cost pressures t hat may ant icipat e fut ure changes in t he rat e of in‡at ion.

However, from a t heoret ical point of view, it is not always clear why wages may be used as a leading indicat or of in‡at ion. Depending on the t heoret ical approach, causality may arise in any direct ion and not necessarily

from wages t o prices. Thus, t he wage - price relat ionship becomes an issue t hat have t o be confront ed on empirical grounds.

Since 1980, some research has been done using American data which focuses on the relat ionship between t his two variables and t ries t o est ab- lish weat her causality runs in one speci…c direct ion or t here is a feedback relat ionship. Working wit h di¤erent price and wage de…nit ions and using di¤erent stat ist ical t echniques, t he majority of works have found no enough empirical evidence t hat support s t he view t hat t he rat e of change in wages cont ains informat ion t o ant icipat e the fut ure pat h of in‡at ion. Alt hough many of t his works …nd a coint egrat ing relat ionship between t he series of prices and wages, t hey only …nd causality running from prices t o wages at most.

Working on similar basis, t his paper …nds mixed evidence t hat support s t he …ndings of t he int ernat ional lit erat ure on t his t opic. Using Colombian dat a, our main results show evidence of Granger-causality from prices t o wages but no evidence of causality from wages t o prices. This …ndings con- t radict s some previous result s obt ain for similar dat a, as we will point lat er.

The second sect ion of t his paper brings a short review of some of t he lit er- at ure on t his t opic using American and Colombian dat a, t he t hird sect ion clari…es some of t he t heoret ical basis t hat lies underneat h t he empirical rela- t ionship between prices and wages, t he fourt h present s t he empirical result s and …nally we report t he main conclusions.

2 Some International and Colombian Evidence

One of t he most in‡uent ial papers in t he last two decades has been t he one by Gordon (1988). In his paper, t he aut hor clearly est ablishes t he link between wages and prices from a t heoret ical point of view. T his link is derived from t radit ional price and wage equations and allow t he aut hor t o obt ain two new equat ions: an in‡at ion equat ion in which lagged changes in t he labor’s share determine t he rat e of in‡at ion, and one equat ion for t he wage variable. As t he price variable, t his paper considers a Fixed Weight De‡at or and employs t he Unit Labor Cost instead of t he nominal wages. Previous papers had employed t he nominal wages direct ly; however as Gordon correct ly points, t his decision did not t ake int o account the fact t hat a rise in t he rat e of change of t he nominal wage do not pass-t hrough t o a higher in‡at ion rat e if it is joined by an increasing labor product ivity. By de…nit ion, unit labor cost corresponds t o wages adjust ed by labor product ivity.

Using st andard regression t echniques, Gordon …nds t hat t he labor’s vari- able is st at istically insigni…cant , which can be int erpret ed as t he rat e of change of wages being irrelevant t o explain in‡ation. Result s also show t hat price changes do not help t o explain wage changes. However, at t his

point , t he aut hor recognizes t hat t his last conclusion is less support ed by t he empirical evidence.

Working on a similar line of research but explicit ly t est ing for Granger- causality, Mehra (1991) o¤ers new evidence on t he wage - price relat ionship.

The price variable is speci…ed as t he log of t he …xed-weight GNP de‡at or and t he wage variable as t he log of unit labor cost s of t he non-farm busi- ness sect or (i.e.: t he product ivity-adjust ed wage). The aut hor quest ions the implicit assumpt ion on det erminist ic t rend component of t he series used by Gordon and ot her works. A misspeci…cat ion of t he t rend like t he one men- t ioned before, may lead t o incorrect t est s of hypot hesis, which can drawn wrong conclusions about the direct ion of causality between prices and wages.

According t o Mehra, rat es of growt h of wages and prices for t he American case do not cont ain a det erminist ic t rend but t hey share a common st ochas- t ic t rend, which t echnically means that t he variables are coint egrat ed. T hus, long run movement s in t he rat e of change of prices and wages are correlated over t ime, and t his is due t o Granger- causality from t he growt h rat e of prices t o t he growt h rat e of wages and not the ot her way around. In ot her words, past in‡at ion det ermines t he growt h rat e of wages only.

A not very di¤erent result is obt ained by Huh and Trehan (1995), who est imat e a VEC model cont aining wages, prices and product ivity t o look at t he dynamic relat ionship among t hese variables. T his met hodology allows t hem t o examine t he long-run relat ionship between wages and prices and speci…cally t he nat ure of t he long-run adjust ment s between t hese variables.

Having found t hat wages and prices are coint egrat ed, t hey show t hat it is t he level of wages, and not t he level of prices, t hat adjust s t o maint ain the coint egrat ing relat ionship in t he model. T hus, as in Mehra (1991), Huh et al. also conclude t hat prices Granger cause wages but t hat wages do not Granger cause prices.

A more general and recent work by Emery and Chang (1996) support s most of t heresult s found by previous works and o¤ers someaddit ional insight into t he relat ionship between t he two series. In t heir paper, unit labor cost s are t aken as t he wage variable and CPI and core CPI as two alt ernat ive price indicat ors. Granger t est are applied for a longer period spanning from 1960 t o 1996 and for two sub-periods: from 1960 t o 1980 and from 1980 to 1996.

The breaking point (1980) is found using st andard st ability t est s developed by St ock and Wat son (1993). Along t he longer period, t he result s show again t hat in‡at ion always Granger causes t he wage growt h, regardless of t he choices of t he price series. Similarly, wage growt h Granger causes core CPI in‡at ion, however no enough evidence was found t hat wage growt h Granger causes CPI in‡at ion.

When analysis is performed on t he sub-periods, t he aut hors conclude t hat t he series behavior is di¤erent . In part icular, the Granger causality

from wage growt h t o core CPI in‡at ion found above, can only be assured for t he period before 1980. Aft er t his year, the dat a do not support t hese

…ndings. Anyway, the dat a consist ent ly shows no Granger causality from wage growt h t o CPI in‡at ion in any sub-period, but st ill shows Granger causality from CPI and core CPI in‡at ion t o wage growt h for bot h.

Finally, t aking a fart her step, Emery et al. perform out -of-sample fore- cast s of in‡at ion using wages in an error-correct ion model in order t o o¤er a more de…nit ive clue of t he roll labor cost s play on fut ure in‡at ion. This exercise show no evidence t hat wage growt h cont ribut es t o any reduct ion in forecast errors compared wit h univariat e aut orregresive models of in‡at ion.

This means again, t hat wages are of lit t le help t o predict in‡at ion.

As opposed t o t he American evidence, t he Colombian evidence is far less numerous, clear and conclusive. Mont enegro (1994) examines t he relation- ship between t he minimum wage and t he CPI, performing Granger causality t est for t hem. As for t he American dat a, he …nds causality running from prices to wages. This result s, however, are subject t o many crit icisms due, mainly, t o t he nat ure of the wage variable used. In fact , in Colombia, mini- mum wage is an indexed-st aggered variable which does not originat e from a free int eract ion between labor demand and supply. This set s serious doubt s about t he right connect ion between t his variable and prices from a t heoret- ical point of view.

In part as a response t o t his analyt ical weakness, Misas and Oliveros (1994) st udy t he relat ionship between di¤erent price and wage indicat ors. In t heir work, t heaut hors useindust rial wages in addit ion t o t heminimum wage as wage indicat ors and t he CPI and CPI wit hout food prices (CPIF) and CPI excluding food, t ransport at ion and ut ility prices (CPIB) as price indicat ors.

Working on a mont hly frequency and performing st andard Granger causality t est s on t he series for t he 1982-1994 period, t hey …nd a feedback Granger- causal relat ionship between indust rial wages and CPI, CPIF and CPIB.

Similarly, result s show a feedback relat ionship between minimum wage and CPI.

One of t he main problems wit h t he previous works for Colombian dat a has t o do wit h the ut ilizat ion of wages without adjust ing by product ivity gains. As it has been clear wit h most of t he lit erat ure on t his t opic, an increase in wages do not necessarily imply higher unit cost s of product ion if it happens t o be similar t o that in labor product ivity. Thus, in order t o check t he exist ence of in‡at ion generat ed by wage pressures a variable such as product ivity adjust ed wages or unit labor cost s has t o be used t o avoid misleading result s. By t he same t oken, not t aking into account demand variables may lead t o problems because of t he omit t ed variable bias, and t he few works on Colombian dat a fail t o consider t his fact t oo.

3 What Theory Has to Say?

Economic lit erat ure o¤er two basic approaches t o underst and t he wage - price relat ionship: t he demand-pull and t he cost -push models. T he demand- pull model derives from monet arist s arguments which see in‡at ion as de- mand det ermined. In a part icular economy, t he rat e of change of all prices depends on t he demand for real balances. More precisely, changes in prices and wages are bot h direct ly relat ed t o monet ary policy and are not exoge- nous. T he price t hat mat t ers t o t he labor market is t he real wage, t herefore nominal wages are the ones t hat respond t o price changes so as t o preserve it s init ial level. By increasing t he rat e of money growt h, t he monet ary au- t hority may induce a rise in production and employment in t he short run as long as people are expect ing price st ability in t he near fut ure. However, higher product ion requires t hat prices increase fast er t han cost s do, in par- t icular labor cost s. T his allows …rms t o temporarily pro…t more from their business. But if prices go up, wages will have t o go up t oo in order t o drive real wages back t o it s equilibrium level. This will occur since, according t o monet arist assumpt ions, wages are fully ‡exible; but it will happen at a slower pace t han price increases because init ial workers´ expect at ions are wrong. Thus, from t his point of view it is possible t o see a sequence of price increases followed by nominal wage increases which would mean t hat prices may o¤er informat ion t o ant icipat e fut ure changes in wages but not t he ot her way around.

On t he ot her side, t he so called cost -pushed model is rooted in a Key- nesian type of model. T hus, t his approach is based on t he assumpt ion t hat prices are set as a mark up on labor cost s (St ein 1979). In t his case, nom- inal wage is set in t he labor market as in t he demand-pull model. Once it s level has been est ablish by t he market , …rms add a …xed mark-up on wages t o de…ne prices, which guarant ies t hem a …xed pro…t margins. To keep t his margins const ant , a rise in wages relat ive t o product ivity (a rise in unit labor cost s) has t o be t ransfered t o prices. When monet ary aut horit ies increase the growt h rat e of money, …rms´ …rst response is t o increase product ion and not prices. More product ion, however, leads t o a higher labor demand pushing nominal wages up. Only t hen, prices will rise as a respond t o higher labor cost s. T hus, changes in wages over product ivity gains precede changes in prices implying t hat t he rat e of change of wages have informat ion to predict fut ure in‡at ion rat es.

As Gordon (1982) showed, a more formal view of t he wage-in‡ation re- lat ionship can be obt ain from an explicit model which considers a Phillips curve type of adjust ment . In t his case, t he nominal wage rat e adjust t o gradually close t he gap between t he labor supply and demand. Adding a mark-up price hypot hesis, it is possible t o derive equations (1) t o (4), which

are the basic relat ions underlying augment ed Phillips curve models .

p_t = a₀+ a₁ulc_t + a₂d_t + a₃Sp_t (1) ulc_t = b₀+ b₁p^e_t + b₂d_t + b₃Sw_t (2)

ul c_t = w_t ¡ ¹

µ_t (3)

p^e_t = ®(L )p_{t¡ 1} (4)

In t his set of equat ions all variables are in nat ural logarit hms and lower caselet t ers correspond t o rat es of change. pis t he price level;ulccorresponds t o t he unit labor cost s and it is de…ned as t he rat e of change of wages divided by t he gains in productivity ; p^e is t he expect ed price level; d represent s cyclical demand andSrepresent s di¤erent supply shocks. Equat ion 1 is the price mark-up equat ion while equat ion 2 corresponds t o what is known in t he lit erat ure as t he wage equat ion.

T he model present ed above shows how wages and prices are connect ed , and suggest s t hat a feedback causal relat ionship between bot h variables is t hinkable, at least from a t heoret ical point of view. In fact , from equations 2 and 4 it is clear t hat past prices a¤ect fut ure wages and, aft er a lit t le algebra, from equat ions 1, 2 and 4 it can be seen how past wages may a¤ect fut ure prices. Thus, t heory does not help much in clarifying t he direct ion of t he causal relat ionship between t his two variables, and t his issue has t o necessarily be solved on empirical grounds for t he Colombian dat a as it has been done for American dat a.

4 Empirical Evidence

4.1 The Data

Our dat a base cont ains quart erly measures of t he annual growt h rat e of t he geomet ric average of t he consumer price index, DCPI4, t he unit labor cost , DULC4, t he indust rial nominal wages, DW4, and a measure of supply shocks, S, de…ned as t he cent ered di¤erence between t he CPI in‡at ion wit h- out food, CPIF, and t he CPI in‡at ion. The out put gap, YG, is t he deviat ion of output wit h respect t o a linear t rend as concluded by Julio and Gomez (1999), and our measure of unemployment gap, UG, is t he deviat ion of the unemployment wit h respect t o a const ant as was concluded by Gomez and Julio (2000).

Figure 1 displays t he dat a used in t he analysis. T he upper left …gure shows t he in‡at ion rat e wit h and without food, and t he lower left panel

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 8.0

12.0 16.0 20.0 24.0 28.0 32.0

DCPI4 DCPIF4

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 -1.00

-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

-600 -400 -200 0 200 400 S

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 5

10 15 20 25 30 35

DW4 DULC4

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 -0.15

-0.10 -0.05 0.00 0.05 0.10

-5.0 -2.5 0.0 2.5 5.0 7.5 10.0 YG

UG

Figure 1: Original Dat a

shows our measure of supply shocks suggest ed by King and Wat son (1994, foot not e 18). T he upper right panel cont ains t he annual growt h of t he wages indicat ors, and t he lower right panel cont ains t he unemployment and out put gaps, which clearly sat isfy t he Okun’s law.

Figure 2 Displays the CPI in‡at ion rat e and the annual growt h of the wage indicat ors. Although t he …gures show t he expect ed form of relat ionship between wages and prices, it looks closer for t he case of nominal wages and CPI in‡at ion. Moreover, and from t he peaks and t hrougs of t he series it seems t hat prices ant icipat e nominal wages. However, for t he case of the ULC it is not clear from t his …gure t he direct ion of t he causality.

4.2 Results

Table 1 cont ains t he result s of t he augment ed Dickey - Fuller and KPSS t est s for unit root on t he original variables. A number wit hout st ars indicat es non

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 5

10 15 20 25 30 35

DCPI4 DULC4

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

8.0 12.0 16.0 20.0 24.0 28.0 32.0

DCPI4 DW4

Figure 2: Wages and Prices

reject ion of t he null, a st ar indicat es reject ion at 5% and two st ars indicat es reject ion at 1% or less. T he result s of t his t est s cont radict each other.

While Dickey - Fuller t est s t end t o indicat e t he exist ence of a unit root in all variables, t he KPSS t est s indicat e t hat all variables are st at ionary¹. In t he spirit of Kiwat owski, Phillips, Schmidt and Shin (1992, page 165), t his result help us conclude t hat the series are not very informative t he exist ence of unit root s. The only except ion t o this result is t hat of DULC4, in which bot h t est s (marginally t he Dickey - Fuller) agree on the non st at ionarity and S in which bot h t ests (marginally t he KPSS) agree on non st at ionarity.

T he result s of t he ADF t est is part icularly st riking for t he case of the unemployment and out put gaps and t he measure of supply shocks, which are expect ed t o have no unit root s alt houg t hey may be somewhat persist ent .

Since agreement between t hese result s are marginal at t he signicance level 10%, we conclude t hat t here is no st rong evidence about whet her or not t here is a unit root in all our series.

1T his is clearly a border case since t he t est st at ist ic is 0.347 and t he crit ical value 0.346 .

L EV EL S D I F FER EN CES

Var iable A D F K P SS A D F K P SS

CR I T ( 5%) ¡ 2:890 0:347 ¡ 1:950 0:347 D W 4 ¡ 0:451 1:480 ¡ 10:740^¤¤ 0:141 D CP I 4 ¡ 0:911 0:283 ¡ 5:853^¤¤ 0:124 D U L C4 ¡ 3:143^¤ 0:450 ¡ 6:117^¤¤ 0:047 U G ¡ 0:789 0:318 ¡ 1:392 0:300 Y P ¡ 2:386 0:093 ¡ 2:494^¤ 0:092 S ¡ 2:711 0:346^¤ ¡ 4:824^¤¤ 0:054

Table 1: Unit Root Test s 4.2.1 Choosing Between two Evils.

Whet her or not t he series used in t his analysis have a unit root is a mat t er of great pract ical import ance, part icularly for t he CPI in‡at ion, and the unemployment and out put gaps. If t hese series have unit root s, for inst ance, our current est imat es of t he Phillips curve should likely be speci…ed as coin- t egrat ion models inst ead of st andard regressions. However, if t hese series do not have unit root s convent ional linear regression would do t he job.

For t he case of t he two indicat ors of wages, DW4 and DULC4, and the CPI in‡at ion, DCPI4, we could make a case for st at ionarity reasoning as follows:

Let Y_t be t he any of t he wages and prices variables in levels. Let y_t = log(Y_t), be it s logarit hm, and assume t hat t he yearly growt h of t he series D₄Y_t = (Y_t=Y_{t¡ 4}¡ 1) di¤er from ¢⁴y_t = (y_t ¡ y_{t¡ 4}) by a negligible amount . Let us furt her assume t hat y_t » I (1), as has been shown ext ensively in the Colombian literat ure, t hat isz_t = ¢y_t » I (0).

Under t his assumpt ions

(y_t ¡ y_{t¡ 4}) = ¢y_t + ¢y_{t ¡ 1}+ ¢y_{t¡ 2}+ ¢y_{t¡ 3} (5)

= z_t + z_{t¡ 1}+ z_{t ¡ 2}+ z_{t¡ 3}

is clearly a st at ionary variable. Which means t hat t he yearly growt h of Y_t, z_t = D₄Y_t is a st at ionary variable.

In order for t he yearly growt h of t he variables t o have a unit root , it is required t hat t he logarit hm of Y_t has an addit ional seasonal root . For inst ance, if y_t » I (1; 4); which means t hat ¢ ¢⁴Y_t is a st ationary variable but z_t = ¢y_t and x_t = ¢⁴y_t are nonst at ionary.

Var iables FP E A I C H Q SW

DW4-DCPI4-UG 2 13 2 1

DULC4-DCPI4-UG 5 13 1 1

DW4-DCPI4-YG 6 13 2 1

DULC4-DCPI4-YG 6 6 6 1

Table 2: Est imat ed Lag Coe¢ cient s for Trivariat e VARs

T he exist ence of seasonal unit root s in our t ime series is unknown. The phenomenon of seasonal root s appears correspopnds t o slowly evolving sea- sonal e¤ect s, t he type of variat ions t hat can be ident i…ed only wit h a fair amount of sample information. Moreover, even if we had t he required sample size and t ime span t o perform t he t est for seasonal unit root s, it s result s are plaged wit h t he same power di¢ cult ies of any unit root t est , which leaves us wit h t he same level of uncert ainty we already have.

Since our only at t empt is t o …nd a good represent at ion of t he sample dat a at hand, and our sample span is short for ident ifying slowly evolving seasonal e¤ect s, we argue t hat a st at ionary represent at ion …ts more parsimoniously our dat a. However, since we are not sure about t he non exist ence of a seasonal unit root , we will present t he result s for Granger causality under bot h assumpt ions.

4.2.1.1 T he St at ionar y Case. Table 2 presents t he est imat ed lag co- e¢ cient s in t rivariat e VAR models of in‡at ion, wages and t he corresponding gap measure in which t he supply shocks indicat or is exogenous. As expected t he Akaike Informat ion Crit eria, AIC, present s an overest imat ed number of lags, followed by t he Final Predict ion Error, FPE, and t he more consist ent Hannan - Quinn and Schwart z Bayesian crit eria, which bot h present the smaller est imat e.

Table 3 present s t he result s of t he Granger causality t est s for t he same VAR models. T he result s are very clear. The null of no Granger causality form prices t o bot h indicat ors of wages is reject ed in all cases, but the null of non Granger causality from t he indicat ors of wages t o prices is not reject ed. This result s is robust t o t he choice of aggregat e demand and wages indicat ors.

However, t he signi…cance levels of t he Granger causality t est in t he di- rect ion of prices great ly di¤er depending on t he wage indicat or considered.

In t he case of nominal wages we can easily reject t he null of no causality

VA R A ut ocor r el D ir ect ion W I T H L A G S F ® =b p-value Si gn. level

D CP I 4 ! D W 4 UG 2 5:420 0:006 0:934

D W 4 ! D CP I 4 UG 2 2:284 0:087 0:307

D CPI 4 ! D U L C4 UG 5 3:909 0:004 0:848

D U L C4 ! D CP I 4 UG 5 1:045 0:407 0:450

D CP I 4 ! D W 4 YG 2 6:113 0:003 0:936

D W 4 ! D CP I 4 YG 2 2:222 0:094 0:298

D CPI 4 ! D U L C4 YG 6 2:972 0:015 0:687

D U L C4 ! D CP I 4 YG 6 1:203 0:319 0:375

Table 3: Granger Causality Test s

Var i ables N or m al it y ®b A ut oc D F ®b

DW4-DCPI4-UG 5.258 0.261 25.552 24 0.318

DULC4-DCPI4-UG 4.711 0.318 10.780 12 0.547

DW4-DCPI4-YG 5.783 0.215 28.283 24 0.248

DULC4-DCPI4-YG 1.918 0.750 14.100 8 00791

Table 4: Mult ivariat e Resudual Test s

at a 10% level as found in Misas and Oliveros(1991). T he higher p-value in t he case of t he Unit Labor Cost assures that at any reasonable signi…cance level t he null of non causality from wages t o prices is not reject ed as found in t he most signi…cant st udies on american dat a. Since nominal wages may be t he result of changes in labor product ivity, t he …rst variable may yield wrong conclussions on t he prices and labor cost s relat ionship. This problem is avoided by t he use of unit labor cost in t he analysis.

Table 4 cont ains the mult ivariat e residual test s for each of t he t rivari- at e syst ems. From t his t able we conclude t hat residual normality and no aut ocorrelation are support ed by t he dat a, which validates our result s.

4.2.1.2 T he N on-St at i onar y Case. Using t he same lag paramet er es- t imat es from Table 3 we conduct coint egration t est s for each of t he t rivariat e

EN D O EX OG W EA K N U L L T R A CE CR I T ( 10%)

VA R VA R EX OG H I P STAT

VA R ®^b

DW4 S UG 0.19 R= 0 25.17 21.38

DCPI4 R= 1 7.27 10.35

DULC4 S UG 0.33 R= 0 20.44 21.58

DCPI4 R= 1 1.75 10.35

DW4 S YG 0.59 R= 0 34.59 31.88

DCPI4 R= 1 13.71 17.79

DULC4 S DCPI4 0.25 R= 0 47.36 31.88

YG R= 1 16.68 17.79

Table 5: Coint egrat ion Test s

syst ems using Johansen’s (1991) maximum likelihood met hodology. Table 5 present s t he result s of t he Johansen t est for coint egrat ion in t he last t hree columns, and t he result of t he weak exogeneity t est s on t he fourt h column.

In general t he result s of t he t ests show coint egration, except for t he VAR t hat includes DULC4, DCPI4, UG and S in which t he null of no coint egra- t ion is not reject ed².

From t his t able we can observe t hat regardless of t he aggregat e demand and wages indicat ors t he in‡at ion rate is weakly exogenous. This means t hat in t he equat ion of t he accelerat ion of prices t he lagged coint egrat ing error does not appear, hence t he relevant equat ions of t he model become

¢w_t = ®_0;1+ ®₁Z_{t¡ 1}+ Xp i = 1

µ_{i ;1}¢¼_{t¡ i} + Xp i = 1

±_{i ;1}¢w_{t¡ i} + lags of ot her variables +(6)"^w_t

¢¼_t = ®_0;2+ Xp i = 1

µ_{i ;2}¢¼_{t¡ i} + Xp i = 1

±_{i ;2}¢w_{t¡ i} + lags of ot her variables + "^¼_t Z_t = ¯₀+ ¯₁¼_t + ¯₂w_t + ¯₃d_t + ¯₃s_t

wherew_t is t he annual growt h of t he wages indicator, d_t is t he aggregat e demand variable, s_t is t he supply shocks indicat or, t he¯_i’s are t he coint e- grat ing coe¢ cient s andZ_t is t he coint egrating error.

2However, since t he power of coint egrat ion t est s is low, t he probability of falling int o an error of type I I could be high. Moreover, since t he t race st at ist ic is close t o t he crit ical value, we can assume t hat t he coint egrat ing rank is 1.

D CPI 4 R ESI D U A L A N A LY SI S W I T H N OR M A L I T Y A U CT OC

T^¤ ®^b Q ®^b

DW4-UG 7.444 0.28 11.259 0.26

DULC4-UG 3.950 0.68 10.452 0.32

DW4-YG 4.106 0.66 8.086 0.53

DULC4-YG 1.911 0.93 8.359 0.50

Table 6: Residual Analysis

T he null of no Granger causality from ¼_t t o w_t corresponds to ®₁ = µ_{i ;1}= 0 for all i, and t he null of no coint egrat ion fromw_t t o¼_t corresponds t o±_{i ;2}= 0 for i = 1; 2; 3; 4:.

Table 6 displays t he result s of t he mult ivariat e normality and non aut o- correlat ion t est s for t he residuals of each of t he VAR models, and t he ap- pendix A shows t he result s of t he coint egrating space st ability t est s. From here we can conclude t hat t he assumpt ions on the residuals are supported by t he dat a, and t hat t he long run relat ionship between wages and prices is st able. T hese validat es our result s of coint egrat ion and weak exogeneity t est s.

As shown by Mehra (1996), since our coint egrat ing coe¢ cient s est imat ors are consist ent and asympt ot ically unbiased, we can readily est imat e the error correct ion represent at ion of t he model by linear regression. Under the assumpt ion of known coint egrat ion coe¤cient s the st andard errors and t est s are valid.

Table 7 cont ains t he Wald Test s for t he hypot hesis of non causality in the short run paramet ers in equat ion6³. Sincet helagged cointegrat ing error does not appearin t he equat ion of t he accelerat ion of prices, non reject ion of the null implies no Granger causality. However, since the lagged coint egrat ing error appear in t he equat ion of wages accelerat ion, non reject ion of t he null does not indicat e non Granger causality. In t his case causality could be t ransmit ted through t he lagged coint egrat ion error.

.

From t his t able we can conclude that t here is no causality from unit

3H0: ±i = 0 8i in t he equat ion of prices in 6, and H0: µi = 0 8i in t he equat ion of wages in 6.

VA R

D ir ect i on W I T H D F T^¤ ® =b p-value

D CP I 4 ! D W 4 UG 1 1.234 0.266

D W 4 ! D CP I 4 UG 1 3.518 0.060

D CP I 4 ! D U L C4 UG 4 0.736 0.946

D U L C4 ! D CP I 4 UG 4 0.897 0.924

D CP I 4 ! D W 4 YG 1 0.837 0.360

D W 4 ! D CP I 4 YG 1 3.492 0.061

D CP I 4 ! D U L C4 YG 5 0.403 0.525

D U L C4 ! D CP I 4 YG 5 1.243 0.264

Table 7: Granger Causality on Short Run Paramet ers

labor cost s t o prices eit her in t he long or t he short run. However, t here seems t o be Granger causality from wages t o prices running t hrough the short run adjust ment parament ers. Moreover, we can observe t hat the short run coe¢ cient s in t he equat ion of wages (eq. 6) do not seem di¤erent from zero. However, since prices are weakly exogenous, t he lagged coint egrat ing error appears in t he equat ion of wages implying Granger causality in the direct ion of wages. T his …nding also accords wit h some result s for american dat a. Once more, by using wages as indicat or of labor cost s we could be get t ing misleading result s on Granger causality t est s.

5 Conclusions.

In t his paper we studied t he relat ionship between wages and prices for Colombia using quart erly data from 1980:1 t o 1999:3. This st udy di¤ers from previous st udies in Colombia in two aspect s; First , we use t he unit la- bor cost as a measure of wages. And second, we avoid t he omit t ed variables bias by int roducing in t he speci…cat ion a measure of supply shocks and a measure of economic act ivity. T hat is, we base our analysis on equations derived from a Phillips curve as presented by Gordon(1982).

We show t hat t here is no evidence t o conclude on t he exist ence of a unit root in t he series used in our analysis. If we assume t hat t he series are st at ionary, causality runs exclusively from prices t o wages regardless of the indicat or of wages or economic act ivity. If we assume t hat t here are unit root s, we …nd a st able long run relat ionship between t he variables analyzed,

and prices become weakly exogenous. That is, t he error correct ion term does not appear on t he prices equat ion, which means t hat t he causality from wages t o prices should t ransmit t hrough t he short run coe¢ cient s. By t est ing t he null t hat t hese paramet ers are joint ly zero we can not reject the null of non causality from wages t o prices, but t he evidence is weak when we use t he nominal wage indicat or.

On t he ot her hand, alt hough t here is no evidence t hat t he short term paramet ers of prices are di¤erent from zero in t he equat ion of wages, t he fact t hat t he error correct ion t erm appears in t his equat ion allows us to conclude t hat t here is Granger causality running from wages t o prices t hrough the error correct ion term, no mat t er which indicat or is used.

As we have point ed out , when using nominal wages t he result s seem t o be less conclusive and could support some of t he …ndgs obt ained by previous work done on Colombian dat a. However, by int roducing unit labor costs, t he result s show causality running from wages t o prices and not t he ot her way around, as it has been found for American dat a. Since unit labor cost s t akes int o to account product ivity adjusment s, it is a more adequate variable t o st udy t he wages-pices relat ionship t han nominal wages. Hence t he result s present ed here are more reliable.

Bibliography.

References

[1]Emery, Kennet h. and Chih-Ping Chang (1996). ” Do Wages Help Predict In‡at ion?” Economic Review, Federal Reserve Bank of Dallas, First Quart er 1996, 2-9.

[2]Kiwat kowsky, Denis, P.C.B. Phillips, P. Schmidt , and Yongcheol Shin (1992). “ Test ing t he Null of St at ionarity Against the Alt ernat ive of a Unit Root : How Sure are we t hat Economic T ime Series Have a Unit Root ?” . Journal of Economet rics. Vol. 54. No 1-3. 159-178.

[3]Julio, Juan M. and Javier Gómez (1999). “ Out put Gap Est imat ion, Es- t imat ion Uncert ainty and it s E¤ect s on Policy Rules” . Borradores Sem- anales de Economía # 125. Banco de la Republica.

[4]Gomez, Javier and Juan M. Julio (2000). “ On t he Phillips Curve in Colombia” . Paper present ed t o t he Workshop on Applied Macro Models.

Sant iago de Chile, Chile. January 2000.

[5]Gordon, Robert (1982). ” Price inert ia and Policy Ine¤ect iveness in the U S 1890 1980” , Journal of Polit ical Economy, Dec, 90 , 1087-1117.

[6]Gordon, Robert (1988). ” T he Role of Wages in t he In‡at ion Process” , American Economic Review, May, 78, 276-283.

[7]Huh, and Trejan (1995) ”

[8]Mehra, Yash, P. (1991), ” Wage Growt h and t he In‡at ion Process: An Empirical Not e” American Economic Review, Sept ember, 81, 931-937.

[9]Mont enegro, Alvaro (1994), ” El salario Mínimo y la In‡ación” , Docu- ment o CEDE 095.

[10]Misas, Mart a and Oliveros, Hugo (1994). ” La Relación Ent re Salarios y Precios en Colombia: Un Análisis Economét rico” . Borradores Semanales de Economía, No 7. Oct ubre 1994.

[11]Johansen, Soren (1988). “ Stat ist ical Analysis of Coint egrat ion Vect ors” . Journal of Economic Dynamics and Cont rol, Vol. 12, # 2,3.

[12]St ock, James and Mark Wat son (1993), ” A Simple Est imat or of Coin- t egrat ing Vect ors in Higher Order Int egrat ed Syst ems” , Economet rica, July, 783-820.

Apendix A: Figures of Cointegration Space Stability Tests.

Figures A1 t o A4 show t he result s of t he cointegrat ing space st ability t est . Each graph cont ains two lines, bot h for t he same hypot hesis of st ability.

The dashed line is t he test s st atist ic for t he R represent at ion from Johansen (1991) and correspond t o t he test st at ist ic when t he short run paramet ers are kept const ant along t he sample. T he cont inuous line corresponds t o t he Z represent at ion in which t he const ancy of t he short run paramet ers is dropped. The horizont al line at height one corresponds t o t he 5% crit ical value for st ability. The …rst quarter of each …gure is not wort h analyzing since t he sample size is small.

From t his …gures we can observe t hat t he dashed line lies consist ently below t he crit ical value, which indicat es st ability of t he coint egrat ing space.

The continuous line is almost always below t he critical value for t hree of t he VAR models, but for t he VAR t hat includes DULC4 and UG it lies well above t he crit ical value. The cont radict ing result for t his lat er model implies t hat some of t he est imat ed short run paramet ers are highly correlat ed wit h some long run ones and t hat t he syst em as a whole is not st able. However, we can not conclude t hat t he long run relat ionship is not st able. All we can say on t his respect is t hat t he sample dat a is not informat ive on t he long run relationship st ability except if we st rongly believe t hat t he short run paramet ers are st able. In such a case we could conclude t hat the long run relat ionship is st able as indicat ed by t he dashed line.

Test of known beta eq. to beta(t)

1 is the 5% significance level

1986 1988 1990 1992 1994 1996 1998

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

BETA_Z BETA_R

Coint . Space St ability Tests for DW4, CPI and UG.

Test of known beta eq. to beta(t)

1 is the 5% significance level

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

BETA_Z BETA_R

Coint . Space Stability Test s for DULC4, CPI and UG.

Test of known beta eq. to beta(t)

1 is the 5% significance level

1986 1988 1990 1992 1994 1996 1998

0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6

BETA_Z BETA_R

Coint . Space St ability Tests for DW4, CPI and YG.

Test of known beta eq. to beta(t)

1 is the 5% significance level

1991 1992 1993 1994 1995 1996 1997 1998 1999

0 1 2 3 4 5 6 7 8

BETA_Z BETA_R

Coint . Space Stability Test s for DULC4, CPI and YG.