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U N E M P L O Y M E N T A N D I N F L A T I O N I N S P A I N , 1 9 5 5 - 1 9 9 8


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Pedro A. Pérez Pascual (pperez@cee.uned.es) Departamento de Economía Aplicada Cuantitativa I


Basilio Sanz Carnero (bsanz@cee.uned.es) Departamento de Economía Aplicada Cuantitativa I


1. Introduction

Professor A.W. Phillips paper, The relation between unemployment and the rate of money wage rates in the United Kingdom, 1861-1957, published in 1958 raised the question of the relationship between unemployment and the rate of change in money wages. The purpose of Phillips was,

… to see whether statistical evidence support the hypothesis that the rate of change of money wage rates in the United Kingdom can be explained by the leves of unemployment and the rate of change of unemployment…” (Phillips, 1958, p. 284)

He supports this idea in the analysis of labour market, in particular in static demand and supply conditions,

When the demand for a commodity or service is high relatively to the supply of it we expect the price to rise, the rate of rise being greater the greater the excess demand. Conversely when the demand is low relatively to the supply we expect the price to fall, the rate of fall being greater the greater the deficiency of demand. It seems plausible that this principle should operate as one of the factors determining the rate of change of money wage rates, which are the price of labour services (Phillips, 1958, p. 283)

The original relationship was set out between unemployment and wages but later economic generalisation related unemployment with the rate of change in prices (inflation), due to the general assumption that these two series move in the same


direction. In figure 1 we can see the plausibility of this hypothesis for the Spanish figures in the period 1976:01-1998:04 (quarterly data from INE):

-2 -1 0 1 2

76 78 80 82 84 86 88 90 92 94 96 98


Figure 1. Wages and Prices in Spain. 1976:01-1998:04 (INE)

Behaviour is just the same in the two variables. In figure 2 we have depicted the same two variables in the historical period of 1501-1650, now in annual figures,

20 40 60 80 100 120 140 160 180

1520 1540 1560 1580 1600 1620 1640


Figure 2. Wages and Prices in Spain, 1501-1650 (Hamilton)


Again this historical evidence clearly support this assumption. Therefore we can´t expect important variations if we study the relationship between unemployment and inflation.

The argument of professor Phillips in terms of aggregate demand and supply curves, runs as follows,


p2 B

p1 A DA2 DA1

y1 y2 YP Y

Figure 3. Aggregate demand and supply curves

In A production (y1) is far from potential production or full employment (Yp), so economy shows high rates of unemployment. If aggregate demand shifts from DA1 to DA2 production, and employment, rises but prices also rises moving from p1 to p2. Thus by means of properly policy measures we can reduce unemployment but only if we are ready to accept higher price levels (more inflation). Unemployment reduction (rise in production) will be greater the closer the economy is from horizontal zone (Keynesian zone). On the contrary, if economy is in C that is to say, close to full employment or potential production (neoclassical zone), shifts in aggregate demand produce only inflation without more production and employment, due to in that economic conditions it is not possible to move production and employment beyond Yp where unemployment is in its natural level.

From this line of argument we can easily arrive to the so called Phillips curve that is depicted in figure 4. Point A in figure 3 represents a production level of y1 and, taking into account the production function, a given unemployment level, dA. This economic conditions correspond to point A in figure 4. Moving from A to B in figure 3 imply, as we have pointed out, more production and employment but a higher level of prices. Point B in figure 4 reflects this situation. Relationship is no lineal because as we


get closer to potential production (full employment) is more difficult to reduce unemployment and vice versa.


B iB

iA A

dB dA Rate of unemployment

Figure 4. Phillips curve

Economists accepted this relationship immediately and it has been maintained till the strong criticism of Friedman and Phelps has led to discredit it. It is not to mean that the Phillips trade off has disappeared from economic discussion. When Makiew (2001) tried to summarize the ten most important principles in economics, he decided to devote the tenth command to the trade off between inflation and unemployment. As he pointed out this statement turned to be controversial but he felt sure enough to maintain it.

But now the question is only about the plausibility (of this hypothesis) in the short run. This idea was already present in Friedman and is coherent with his proposition that a monetary injection, although in the long run only exert effects on prices, in the short run produces also an incremented production.


2. Friedman criticism

Phillips trade off was not completely new. Makiew quote to Hume (1752),

In my opinion, it is only in the interval or intermediate situation between the acquisition of money and the rise in prices, that the increasing quantity of gold or silver is favourable to industry…

that accept the relation only in the short run as early as 1752. On the other hand Friedman quote to Fisher (1926) who also postulated the same relation. But there is a difference between Fisher and Phillips view. Phillips causality runs from employment to wages (prices) while Fisher causal direction is just opposite. According to Friedman Fisher is right because,

What mattered for unemployment, we argued, was not wages in dollars or pounds or kronor, but real wages. (Friedman, 1976)

In other words, is wrong to relate a real variable (unemployment) with a nominal one (prices). What must be done is to relate unemployment and real wages.

Taking this criticism into account, argument in section 1 is no more right. A monetary expansion increments aggregate demand and business men demand more employment at current wage. At first workers are willing to work at that wage, but the effect of a monetary injection and more aggregate demand, is also a higher level of prices so nominal current wage is eroded. Thus unless we suppose monetary illusion in workers, unemployment can’t be reduced. This confusion between nominal and real wages was favoured by keynesian economic paradigm widely expanded in that days.

According to Keynes what workers demand is a given nominal wage rather than real wage,

“A fall in real wages due to a rise in prices, with money-wages unaltered, does not as a rule, cause the supply of available labour on offer at the current wage to fall below the amount actually employed prior to the rise of prices” (Keynes, 1936 p. 12)

or in the same vein,

“Thus it is fortunate that the workers, though unconsciously, are instinctively more reasonable economics than the classical school, inasmuch as they resist reductions of money wages, … even though the existing real equivalent of these wages exceeds the marginal disutility of the existing unemployment; whereas they do not resist reductions on real wages, which are associated with increases in aggregate employment …(Keynes, 1936, p. 14)

Phillips mistook real and nominal prices due to this Keynesian assumption of rigidity in prices and salaries, but it is not a reasonable assumption. Sooner or later workers realize that inflation is eroding their nominal wages and refuse to offer the required level of employ unless wages rise. Therefore employment will fall remaining inflation and so the postulated relationship will have disappeared.


In summary Friedman arguments against Phillips trade off was,

a) Criticism against Keynesian theoretical system being Phelps and himself outstanding figures of that reaction,

b) Empirical evidence in seventies showed high levels of unemployment and inflation, so it was difficult to accept the hypothesis,

c) Empirical evidence extracted from countries different of Phillips original paper, produce results that seriously questioned the existence of Phillips trade off.

Later on accelerationist hypothesis try to restore Phillips hypothesis but only in the short run.


π3 C3 π2 b c C2

π1 a N0 C1 N

Figure 5 Accelerationist hypothesis

This hypothesis pay especial attention to the role of expectations. Point a placed in C1 Phillips curve (figure 5) represents a situation in what expectation about inflation is π = 0. Economics agents support this expectative in recent experience. The expansion in aggregate demand (as a consequence of policy measures) reduce the unemployment from a to b. But this reduction is only possible because workers aren’t able to anticipate the rise in the level of prices (due to recent experience of cero inflation). As soon as they realize that the inflation reduces their real wages, they demand higher salaries to balance that reduction, but at this incremented salaries employment will fall. According with accelerationism economists, the unemployment will move from b to c in Phillips curve C2. As a result we are faced with just the same level of unemployment as in the previous situation and a new inflation π2 > 0. Any subsequent attempt to expand aggregate demand, shifts the Phillips curve from C2 to C3 and so on. Therefore reduction of unemployment is only possible in the short run but in the long run, unemployment returns to its natural level N0: Phillips curve is completely vertical in the long run at N0. Most part of economists recognize the difference between short and long run but they still think that long run curve has a negative slope although more steeply so than the short run.

Rational expectations hypothesis refuse the existence of any relation even in the short run: as soon as the economic agents heard about policy measures to expand aggregate demand, anticipate its consequences and higher salaries will be needed in order to reduce unemployment.


3. Spanish Phillips curve

In this section we analyse the situation in Spain by using the figures of both rate of unemployment and inflation in the period 1955-1999.

These series are depicted in figure 6,

0 5 10 15 20 25

55 60 65 70 75 80 85 90 95


Figure 6. Inflation and rate of unemployment. Source: FBBV

We can’t appreciate a clear relationship: there exist periods of a parallel relation with others in what that relation runs in opposite direction.

Scatter in figure 7 shows a line of regression close to horizontal, in other words an extremely low correlation.


0 5 10 15 20 25

0 5 10 15 20 25



Figure 7. Scatter and line of regression When we take shorter periods for the analysis what we obtain is:

2 4 6 8 10

1.0 1.2 1.4 1.6 1.8 2.0



5 10 15 20 25

0 5 10 15 20 25



0 2 4 6 8

14 16 18 20 22 24



Figure 8. Period 1955-71 Figure 9. Period 1972-85 Figure 10. Period 1986-99

Until we get the first petrol crisis, slope in Phillips curve is positive (figure 9) what is just contrary to Phillips hypothesis. Later the relation seems to be in the direction postulated by Phillips. It could be possible that from the mid ninety Phillips curve moves backward as a consequence of prices reduction in this years. In any case no linearity it is not evident.

Original Phillips relationships is one of no linearity,

y= bxc (1)

where y is the rate of change of wage rates and x is the percentage unemployment.

Taking logarithms,

log y = log b + c· log x (2)


In figure 11 we have depicted series in logarithms, where we have used prices instead of wages following an habitual practice in economic literature,

0 1 2 3 4

55 60 65 70 75 80 85 90 95

LParo LPrecios

Figure 11. Prices and unemployment. Logarithms.

There are no signs of Phillips relationship. Figure 12 and table 2 confirm the lack of correlation,

0 1 2 3 4

0 1 2 3 4



Figure 12. Scatter diagram

Dependent Variable: LPRE Method: Least Squares Date: 07/07/01 Time: 10:35 Sample(adjusted): 1956 1999

Included observations: 44 after adjusting endpoints


Variable Coefficient Std. Error t-Statistic Prob.

C 2.098732 0.158770 13.21869 0.0000

LP -0.038771 0.075799 -0.511497 0.6117

R-squared 0.006191 Mean dependent var 2.031237

Adjusted R-squared -0.017471 S.D. dependent var 0.580612 S.E. of regression 0.585662 Akaike info criterion 1.812242 Sum squared resid 14.40602 Schwarz criterion 1.893342

Log likelihood -37.86933 F-statistic 0.261629

Durbin-Watson stat 0.308479 Prob(F-statistic) 0.611682

Table 2. Regression

R-squared value is close to cero so percentage unemployment can’t explain inflation.

Thus it is difficult to accept the hypothesis for the Spanish period analysed.

Replacing prices by salaries remain the things equal (figure 13 and table 3),

1.5 2.0 2.5 3.0 3.5

0 1 2 3 4



Figure 13. Scatter diagram

Dependent Variable: LSAL Method: Least Squares Date: 07/14/01 Time: 10:26 Sample(adjusted): 1956 1995

Included observations: 40 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 2.841313 0.095586 29.72509 0.0000

LU -0.139414 0.047514 -2.934194 0.0056


R-squared 0.184716 Mean dependent var 2.613227 Adjusted R-squared 0.163261 S.D. dependent var 0.384601 S.E. of regression 0.351808 Akaike info criterion 0.797243 Sum squared resid 4.703213 Schwarz criterion 0.881687

Log likelihood -13.94487 F-statistic 8.609497

Durbin-Watson stat 0.351558 Prob(F-statistic) 0.005644

Table 3. Regression with quarterly series

In figure 14 we show scatter diagrams (relating rates of prices an percentage unemployment in log) for the 18 Spanish CCAA,

-1 0 1 2 3 4

1.0 1.5 2.0 2.5 3.0 3.5 4.0 LU


14.1 Andalucía

0 1 2 3 4

-2 -1 0 1 2 3



14.2 Aragón

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-2 -1 0 1 2 3 4



14.3 Asturias

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-2 -1 0 1 2 3



14.4 Baleares

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-1 0 1 2 3 4



14.5 Canarias

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-2 -1 0 1 2 3 4



14.6 Cantabria


0 1 2 3 4

-2 -1 0 1 2 3 4



14. 7 Castilla León

0 1 2 3 4

-2 -1 0 1 2 3 4



14.8 Castilla La Mancha

0 1 2 3 4

-1 0 1 2 3 4



14.9 Cataluña

0 1 2 3 4

-1 0 1 2 3 4



14.10 Extremadura

0 1 2 3 4

-2 -1 0 1 2 3



14.11 Galicia

0.5 1.0 1.5 2.0 2.5 3.0 3.5

0 1 2 3 4



14.12 Madrid

0 1 2 3 4

0 1 2 3 4



0 1 2 3 4

-6 -4 -2 0 2




14.13 Murcia 14.14 Navarra

0 1 2 3 4

-4 -2 0 2 4



14.15 País Vasco

0 1 2 3 4

-4 -2 0 2 4



14.16 La Rioja

0.5 1.0 1.5 2.0 2.5 3.0 3.5

0 1 2 3 4



14.17 Comunidad Valenciana

0.5 1.0 1.5 2.0 2.5 3.0

2.6 2.8 3.0 3.2 3.4 3.6



14.18 Ceuta y Melilla

Figure 14 Phillips relationship in Spanish CCAA

Any of them provide empirical evidence to support Phillips hypothesis. On the contrary line regression is close to horizontal (points highly scattered) and even with positive slope (Aragón, Canarias, Castilla la Mancha y Navarra).

Quarterly figures for the spanish period 1976:4-1998:2 are plotted in figure 15,

-4 -2 0 2 4

78 80 82 84 86 88 90 92 94 96 98


Figure, 15. Unemployment and inflation. Quarterly figures


This figures produce better evidence but not good enough to confirm the existence of Phillips trade off,

Dependent Variable: LP1 Method: Least Squares Date: 07/15/01 Time: 09:24 Sample: 1976:3 1999:2 Included observations: 92

Variable Coefficient Std. Error t-Statistic Prob.

C 3.873332 0.616663 6.281115 0.0000

LU1 -1.268837 0.220378 -5.757548 0.0000

R-squared 0.269180 Mean dependent var 0.365351

Adjusted R-squared 0.261060 S.D. dependent var 1.061287 S.E. of regression 0.912299 Akaike info criterion 2.675802 Sum squared resid 74.90608 Schwarz criterion 2.730623

Log likelihood -121.0869 F-statistic 33.14936

Durbin-Watson stat 1.760994 Prob(F-statistic) 0.000000

Table, 4. Regression with quarterly figures

Elasticity of – 1.27 is according with theoretical hypothesis and in comparison with table 2 its standard error allow us to reject the null hypothesis. On the other hand the Durbin Watson statistic indicate no residual correlation. But goodness of fit is very low so it casts serious doubts on the relationship,

-4 -2 0 2 4

1.0 1.5 2.0 2.5 3.0 3.5



Figure, 16


Elimination of seasonality (by using moving average) doesn’t improve the results substantially. From an stochastic point of view the situation is worse because of Durbin Watson value.

In summary, all the evidence analysed above, whether annual or quarterly, referred to Spain or its CCAA, lead us to reject the relationship proposed by professor A.W. Phillips between unemployment and the rate of change of prices (or wages). There is no evidence supporting the existence of postulated trade-off.

4. An alternative approach

If we want to get an explanation of employment behaviour we can employ a neoclassical model of the labour market. According to this, what determine the supply and demand of labour is its price: in fact the wages in real terms. Employers, given their aim of profit maximization, demand labour force till wages are equal to labour marginal productivity. On the other hand, workers are willing to supply their labour services until the wage is equal to marginal disutility. This is just an special case of Marshall demand law.

In order to measure the law we employ unobserved components approach.

Foundations of this approach can be seen, for instance, in Álvarez (1999). In short, scientific knowledge is basically concerned with regularities so we should try to check economic laws between cyclical movements the only components that are recurrent.

This view imply we need first separate trend and cycle from the original series. Once we have detrended the series we get empirical cycle. But this component consists of the sum of theoretical cycles of different periodicities. In order to find this unobserved cycles we use the Fourier Analysis. Peaks in the periodogram (basic instrument in Fourier Analysis) tell us the periodicities in what cycles are. If we find common peaks in unemployment and inflation, causal relation is checked by regression between that theoretical cycles, we need estimate previously.

Following this plan we will analyse employment and salaries, that are plotted in figures 18 and figure 19,

16.24 16.28 16.32 16.36 16.40 16.44

55 60 65 70 75 80 85 90 95


11 12 13 14 15 16 17 18

55 60 65 70 75 80 85 90 95


Figure 18. Employment Figure 19. Nominal salaries


Figure 20 shows empirical cycles (detrended series). To eliminate trend movement we have estimated and subtracted the line between the first and the last points in the two series,

-2 -1 0 1 2

55 60 65 70 75 80 85 90


Figure 20. Empirical cycles

Marshall demand law is stated ceteris paribus. Detrended the series is a way to fulfil this condition: other factors important apart from wages (in order to determine the employment movements) are included in trend movement. Once we have eliminated these movements those other factors can’t exert its influence in employment behaviour, so we can consider the relation ceteris paribus.

The regression between empirical cycles is not clear enough,

Sample: 1955 1994 Included observations: 40

Variable Coefficient Std. Error t-Statistic Prob.

C 0.038914 0.005375 7.240026 0.0000

LSA_C -0.055922 0.020945 -2.669987 0.0111

R-squared 0.157966 Mean dependent var 0.029909

Adjusted R-squared 0.135807 S.D. dependent var 0.028471 S.E. of regression 0.026468 Akaike info criterion -4.377089 Sum squared resid 0.026620 Schwarz criterion -4.292645

Log likelihood 89.54178 F-statistic 7.128829

Durbin-Watson stat 0.108505 Prob(F-statistic) 0.011099

Table 5. Regression between empirical cycles. Logarithms.

Elasticity is negative, according to what the law states, but it is very low. On the other hand R-squared tells us that empirical cycle of wages explains only a 16% of the employment empirical cycle. We are far from the ideal situation postulated by the law.

But, as we have already pointed out, empirical cycles are not the final stage. We need find theoretical cycles rather than empirical one. Table 6 shows the periodograms:


CICLOS LE_C LSA_C 40.00000 71.98984 89.89198 20.00000 12.88823 6.770014 13.33333 10.62987 2.209660 10.00000 2.714506 0.461139 8.000000 0.453338 0.232918 6.666667 0.352392 0.178087 5.714286 0.333509 0.048325 5.000000 0.065432 0.033930 4.444444 0.134244 0.037455 4.000000 0.064589 0.008141 3.636364 0.106734 0.000113 3.333333 0.013195 0.014416 3.076923 0.069286 0.001259 2.857143 0.045602 0.000546 2.666667 0.027907 0.001563 2.500000 0.049125 0.000798 2.352941 0.048888 0.033188 2.222222 0.002509 0.000221 2.105263 0.009269 0.038714 2.000000 0.001535 0.037535

Table 6. Periodograms

We have got a common peak in the periodicity of 40 years. The theoretical cycles in this periodicity have been estimated and depicted in figure 21,

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

55 60 65 70 75 80 85 90


Figure 21. Theoretical cycles of employment and salaries (40 years)

As we can see there is a lag (or lead) between these two cycles. In order to discover causal direction (the series what is lagged) we use the cross correlation function.

According to that, the higher correlation takes place when wages are lagged seven periods (years), so causal direction runs from salaries to employment just what the law postulates. The regression once we take this information into account, is:

Dependent Variable: LE_ES Method: Least Squares


Date: 07/16/01 Time: 10:48 Sample(adjusted): 1962 1994

Included observations: 33 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 0.050291 0.000109 463.0073 0.0000

LSA_ES(-7) -0.125593 0.000435 -288.8240 0.0000

R-squared 0.999629 Mean dependent var 0.031904

Adjusted R-squared 0.999617 S.D. dependent var 0.025817 S.E. of regression 0.000506 Akaike info criterion -12.28314 Sum squared resid 7.92E-06 Schwarz criterion -12.19244

Log likelihood 204.6718 F-statistic 83419.33

Durbin-Watson stat 0.037057 Prob(F-statistic) 0.000000

Table 7. Regression between employment and salaries.

Elasticity, -0.13, is again low but now we are closer to the theoretical hypothesis: R- squared is close to 1. Goodness of fit can be seen in figures 22 and 23 that represents static and dynamic aspects of the same law: points in figure 22 are all in the line regression with negative slope and this lack of scattering correspond with inversed movements in figure 23 that represents the law in dynamic terms.

-0.2 0.0 0.2 0.4 0.6

-0.02 0.00 0.02 0.04 0.06 0.08



R2 = 0.999

e = -0.13

Figure 22. Scatter diagram


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

55 60 65 70 75 80 85 90


Figure 23. Theoretical cycles of employment and salaries (lagged)

The low elasticity has some precedent. Álvarez (1998) reports an elasticity of – 0.16 between theoretical cycles of employment and wages in the periodicity of 38 years without any lag.

Following the same method we have studied the Spanish CCAA. Results are reported in table 8,

Cycle Causality Lag R2 Elasticity España 40 year SE 7 0.999 - 0.13 Andalucía 40 year ES 1 0.995 - 7.63 Aragón 40 year ES 1 0.992 - 6.92 Asturias 40 year SE 9 0.999 - 0.16

Baleares (*) - - - - -

Canarias 40 year E→S 7 0.999 + 11.17 Cantabria 40 year S→E 10 0.999 - 0.13 Castilla la Mancha 40 year E→S 5 0.999 - 6.95 Castilla León 40 year - 0 0.999 - 0.17 Cataluña 40 year SE 9 0.999 - 0.26

Com. Valencian (*) - - - - -

Extremadura 40 year ES 6 0.995 - 2.69 Galicia 40 year ES 8 0.994 + 4.17

Madrid 40 year S→E 11 0.999 - 0.34

Murcia(*) - - - - -

Navarra 40 year S→E 4 0.999 - 0.18

País Vasco 40 year SE 10 0.999 - 0.38 La Rioja 40 year SE 1 0.999 - 0.21

Table 9. Results in Spanish CCAA

(*) There is no common peak in this CCAA


5. Summary

We have tried to analyse the behaviour of (un)employment. First of all we have studied the relationship postulated by professor A.W. Phillips between percentage unemployment and inflation. By using this theoretical hypothesis we have analysed Spanish figures for the period 1955-1998. Whether the series are annual or quarterly, applied to Spain or CCAA, we have got empirical evidence just contrary to what stated by this hypothesis.

When we have considered a neoclassical model of the labour market that related (un)employment with wages (ceteris paribus) we obtain results close to the theoretical law and so, a satisfactory explanation of spanish unemployment. By means of Fourier Analysis we have found a common peak in the first harmonic (40 years). The relationship in this periodicity is in accordance with theoretical hypothesis: salaries explain the level of employment being the elasticity – 0.13 and the R-squared close to unity. This elasticity value is close to what obtained by Álvarez (1998) who has studied a similar period.

Results for the Spanish CCAA are reported in table 9.


6.- References

Álvarez Vázquez, N. (1998) La comprobación empírica de la teoría del empleo.

- (1999) Introducción a la econometría. Ed. UNED. Madrid.

Friedman, M. (1975) ¿Desempleo versus inflación? Evaluación de la curva de Phillips. IEA, Ocasional paper nº 44.

- (1976) Inflation and unemployment, in The essence of Friedman, Hoover Institutions Press, 1987.

Fisher, I. (1926) A statistical relation between unemployment and the price changes.

International Labour Review.

Keynes, J.M. (1936) La teoría general del interés la ocupación y el dinero. Fondo de Cultura Económica (XIV reimpresión, 1997)

Mankiw, N.G. (2001) The inexorable and mysterious tradeoff between inflation and unemployment. The Economic Journal, 111, nº de Mayo.

Mochón, Francisco (2000) Economía. Teoría y Política. Ed. MC Graw-Hill, 4ª edición. Madrid.

Phillips, A.W. (1958) The relation between unemployment and the rate of change of money wage rates in United Kingdom, 1861-1957. Economica, nº de noviembre.


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