An Interpretative Note on the Nature of the Wage Curve

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An Interpretative Note on the Nature of the Wage Curve

John G. Sessions Scandinavian Journal of Economics, 95(2), 239-244, 1993.

    An Interpretative Note on the Nature of the Wage Curve

    John G. Sessions

    Loughborough University of Technology, Leicestershire, LE11 3TU, England, and London School of Economics, Houghton Street, London WC1A 1AE, England.

    I. Introduction

    The relationship between unemployment and pay has recently been encapsulated in terms of a „wage curve‟ whereby increasing unemployment acts to curb the general level of pay [Blanchflower and Oswald (1990) - hereafter BO]. Results from BO, and elsewhere, allude to the possibility of an upturn in the curve with the level of pay tending to rise as unemployment passes some critical rate. BO attribute the upturn observed in their study to a data aberration,

    1claiming that such a finding “... appears to go against commonsense.” The shape of the wage

    curve has important policy implications and although the empirical evidence for an upturn is relatively weak, such a possibility should not be dismissed a priori. The aim of this note is to

    stimulate further research into the nature of the wage curve by deriving sufficient conditions for an upturn from a formal model.

    The idea is to supplement the standard neo-classical model of the wage curve with

    2behavioural assumptions drawn from the social-psychology literature. The note concentrates

    in particular on the concept of „status‟. Workers are assumed to be primarily, but not exclusively, concerned with the monetary rewards to an occupation. The status associated with a particular occupation plays a significant role in their decision making.

    In what follows occupations are categorised as either „good‟, „bad‟, or „neutral‟. The status of a good occupation is denoted „prestige‟ and is assumed to increase worker utility. The status of a „bad‟ occupation is denoted „stigma‟ and is assumed to reduce worker utility.

    A neutral occupation is one that offers neither prestige nor stigma.

    1 See BO (Figures 1 and 2 and the accompanying commentary in the second paragraph of page 230 of their paper) and Groot et al (1992). An inherent problem with the empirical evidence is that, as BO note, few unemployment observations occur over the range where an upturn might be observed.

    2 The incorporation of behavioural assumptions into economic models has been advocated extensively by economists in recent years, e.g., Akerlof (1980, 1984), and Becker (1991).


John G. Sessions Scandinavian Journal of Economics, 95(2), 239-244, 1993.

    It is assumed that both prestige and stigma vary with the composition of the labour market. As the proportion of the workforce employed within a particular occupation declines the status associated with that occupation increases. To be sure, as the proportion of the workforce employed in good occupations declines, the prestige associated with good occupations increases. Conversely, as the proportion in bad occupations declines, the stigma associated with bad occupations increases.

    This behavioural assumption accords with the social psychology theory of minority-majority groups and is attractive in that it enables status to be modelled as, essentially, a reduced form. Whatever the social-psychological „root cause‟ of status the underlying social

    3pressures must operate via the conduit of society.

    These ideas are developed formally in the following Section. Final remarks are collected in Section III.

    II. A Formal Exposition

    Following BO workers are restricted to only three occupations; unionised employment, non-unionised (i.e., temporary) employment, and unemployment, where these are assumed to be „good‟, „neutral‟, and „bad‟ respectively. The key assumption regarding worker utility is

     (1) uwc?uy?uzc11233

    where the subscripts refer to union employment, temporary employment, and unemployment

    u1respectively. is the utility of union employment and comprises a monetary wage, w, and

    cu12prestige, ; is the utility of temporary employment and comprises monetary remuneration u3y; is the utility of unemployment and comprises the income equivalent value of leisure, z,

    c3and unemployment „stigma‟, .

    To ease the exposition of what follows it is assumed that the prestige of union employment depends on the total proportion of the working population employed, rather than on the proportion employed within the union sector only. This permits prestige and stigma to

    3 See Crocker and Major (1989) and Davies (1984). General discussions of the status of the unemployed are set out in Kelvin and Jarret (1985), Furnham and Lewis, (1986) and Warr (1987).


John G. Sessions Scandinavian Journal of Economics, 95(2), 239-244, 1993.

    cc(U)cc(1U)31be defined symmetrically through and respectively, where U is the rate

    cx;?x?;,0,1of unemployment. The „social pressure‟ function, , , is assumed to be declining

    maxcx;?0cx;?c1x)0x)1and convex with limits as , and as . There is no social

    pressure associated with an occupation if the entire workforce is employed in that occupation. The social pressure associated with an occupation increases as the proportion of the workforce employed in that occupation falls, and approaches a unique maximum as this proportion approaches zero.

    In all other respects the model follows BO. Solving and differentiating the Nash bargain yields the following equation defining the relationship between union wages and unemployment

    dsUdc1UdcU;?;?;?uu1sU;?;?;,23wdUdUdU (2) *:;Uuu?;11,;2?;w?;

    22??(w,p),,w?,w;?,?,wwhere is the wage elasticity of labour demand, is ;?

    the maximised (i.e., „right to manage‟) profit function of the firm,is *usU;?u1sU;?u;,123

    s(U)the union fall-back, and is a function representing the probability that a striking

    s(U)4employee will be successful in obtaining temporary employment. It is assumed that is

    sU;?1sU;?0U (;U)0U)(;U 1declining and convex with limits as and as . is

    interpreted as the „critical search rate of unemployment‟, that is, the rate of unemployment at which the striking union worker has no chance of obtaining temporary employment utility from the labour market.

    It can be shown that the denominator of (2) is positive for all U given an elasticity of

    51labour demand . The shape of the wage curve is therefore determined by the numerator of (2), an inspection of which reveals the following proposition.

4 Equation (2) corresponds to BO‟s equation (9).

    usU;?u1sU;?u??;,2:;;?w1235 Writing the denominator of (2) as , where , and rearranging yields

    ;?w1c;?1Uw???w1~~??;,?sU;?y1sU;?zcU;?01;,;,w?y?z, where . Since , and given

    ~?;,0,1~?;,0,1w?;,0,101the form of the social pressure function, it follows that and and so . Sufficiency therefore ensured by


John G. Sessions Scandinavian Journal of Economics, 95(2), 239-244, 1993.

    U(0.5Proposition. A sufficient condition for a negatively sloped wage curve is . A

    U (;U0.5necessary and sufficient condition for an upturn in the wage curve is .

    The above proposition is illustrated graphically in Figures 1 and 2 below.

    Increases in unemployment impact in two ways upon the fall back position of union workers. First, there is a direct effect on the probability of obtaining preferred temporary employment. Increases in unemployment always reduce this probability and so, ceteris paribus,

    lower the fall-back position of such workers. Second, the relative social pressures associated with employment and unemployment are altered. Once the majority of the workforce are unemployed, further increases in unemployment raise the prestige of unionised employment more than they reduce the stigma of unemployment. Ceteris paribus, workers become

    marginally more fearful of layoff and so marginally less strident in their wage demands.


John G. Sessions Scandinavian Journal of Economics, 95(2), 239-244, 1993.

    Although U > 0.5 is sufficient for a negative slope, the converse does not hold for U <

    0.5. This latter condition is necessary but not sufficient. Dominance of the „social pressure effect‟ by the „temporary employment effect‟ must be ruled out, and, given the form of the social pressure function, this is ensured by the second part of the above proposition. Intuitively, an upturn is possible if the temporary unemployment option becomes unobtainable with minority unemployment. Further increases in unemployment act only on the relative

    social pressures associated with primary employment and unemployment. The form of the social pressure function implies that increases in unemployment up to U = 0.5 reduce the

    stigma of unemployment more than they increase the prestige of employment. Workers accordingly become marginally less fearful of lay off and marginally more strident in their

    6wage demands.

    III. Final Remarks

    The shape of the wage curve in this model depends crucially on the size of the critical search

    U (;rate of unemployment, , and as such is ultimately an empirical question. Introspection

    U (;would suggest that > 0.5 is unlikely, and the studies by BO and Groot et al (1992) imply a

    U (;figure for of 0.10 - 0.12 and 0.20 - 0.40 respectively, neither of which precludes the

    7possibility of an upturn under the assumptions of this model.

    This analysis has therefore shown that a local upturn in the wage curve is possible. Whether such an upturn is a robust empirical phenomenon, and if so, whether it is attributable to the forces of social status is another question. This note serves merely to emphasis that such questions should not be addressed lightly.


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    6 It would be impossible to predict empirically this second turning point given the rates of unemployment commonly observed (or rather not observed) in most western countries. As a result estimated wage curves would appear to be „U‟ shaped.

    7 That is, interpreting U' as the rate of unemployment at which the wage curve is seen to turn in these studies.


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