Abstract
In the previous chapter, beside some biographical sketches, we provided a synthetic illustration of the four cards of the Post Keynesian labour market model, as conceived by Tarantelli: the mark up principle, the Phillips curve, Okun’s law and Tella’s equation.
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Notes
- 1.
- 2.
- 3.
For an exhaustive investigation of the new microeconomics see Pissarides (2000 [1990]).
- 4.
Phelps (ed. by) (1970).
- 5.
Archibald (1970).
- 6.
Mortensen (1970).
- 7.
Holt (1970, p. 58).
- 8.
In particular, we can assume u = û ± ε where\( \varepsilon :\varepsilon \sim N(0;\sigma_{\varepsilon }^2) \) This assumption implies that at any given time there is a flow of workers, for example, from production units in a restructuring phase, who have to leave their jobs, and at the same time there is a flow of labour force which is trying to find a job in expanding businesses. The constancy of the unemployment rate, apart from stochastic variations, implies that the flow of separations (as the sum of dismissals and resignations) is approximately the same as the flow of employment, that is approximately constant. This constancy is assured by the negative correlation between dismissals and voluntary resignations in response to variations of demand. When there is a steady demand, there is an increase in workers enticed to better posts; at the same time firms reduce dismissals in order to tame the loss of their labour force. On the other hand, when the demand is less favourable, fewer resignations tend to correspond to a larger number of dismissals.
- 9.
Synthetically, the procedure through which (11) can be obtained is the following. J is the total labour demand, which is the number of job posts offered on the market. Some of these, which we indicate with E, will result filled by workers; others indicated with V will result vacant. So, generally we can write (J = E + V). At the same time FL, the total labour force which is offered on the market, can be divided into employed workers, E, and in workers looking for a job, U (FL = E + U). Relativizing the two previous expressions compared with FL, we can write (j = e + v) and (1 = e + u). Where “e” indicates the employment rate, which is the percentage of the employed workers in the total labour force, and j the rate of labour demand. Subtracting (1 = e + u) from (j = e + v), we obtain a linear relationship between available posts and unemployment for every value of j, i.e. (v = u + j − 1). Given the amount of the labour force, FL and the number of available posts J, every increase or decrease in employment, E, will determine a variation of the same amount in unemployment and vacant posts. Now, substituting in (3.9) the expression of v derived from the last equation, it can be derived (3.11).
- 10.
Tarantelli (1974 [2], p. 38).
- 11.
Hall (1970).
- 12.
Tarantelli (1974 [2], p. 46).
- 13.
It will be useful to remember, with regards to the methodological mutual aspects, that in Tarantelli’s opinion, the temporal horizon in which the hypothesis of non Walrasian equilibrium and disequilibrium assumes validity, must be considered the Robinsonian notion of logical time. Historical time should be considered, instead, as a dimension inside of which the structural analysis would find legitimization (Tarantelli 1970 [1], p. 16) and (Tarantelli 1974 [2], pp. 1–18). For the concept of logical and historical time compare (Robinson 1962, pp. 23–28).
- 14.
Tarantelli (1974 [2], p. 67).
- 15.
Tarantelli (1979 [2]).
- 16.
Tarantelli (1979 [2], p. 448).
- 17.
However, it should be noted, that Holt himself, contemplates the hypothesis that the flow of employment and separations can vary with variations of labour demand (Holt 1971). However, in Tarantelli’s opinion, Holt would not draw “theoretical consequences in spite of the existence of previous discussions regarding this” (Tarantelli 1979 [2], pp. 455–456). Tarantelli refers to the fact that there was not a lack of studies reenforced with econometric esteems from which emerged, with reference to the United States’ system, that in a phase of expansion, more marginal workers, characterized by lower wages, were gradually employed. This would help to keep average wages level. Behman (1964) is a significant example to which Tarantelli refers.
- 18.
It is interesting to observe how Tarantelli’s propositions are in line with the conclusions reached in Hall (1972). Hall had conducted an analysis about the structural changes of the labour market with respect to the level of activity of the system, showing how, in correspondence to higher levels of aggregate demand, in the production process, shares of marginal workers were introduced. Compared to the non marginal labour force, according to Hall, these were characterized by a higher turnover because of lower job career opportunities, of the missed achievement of seniority and mainly because the marginal labour force, according to that that Tarantelli himself defines “Ricardian principle” of selectivity of labour demand, could be considered the last one to be employed in an expansive phase and the first one to be dismissed when the cycle inverts. Regarding this compare: (Tarantelli 1970 [1]) and (Tarantelli 1974 [2], pp. 148–149). Tarantelli was not the only one, amongst the Italian economists, to welcome the above-mentioned “Ricardian principle”. The case of (De Cecco 1972) can be considered significant. De Cecco subjects to empirical verification the thesis according to which, in case of a demand contraction, the rate of activity of all the workers does not diminish proportionally, but it is primarily the rate of the marginal workers that diminishes, identified by him in women, youngsters up to 25–30 years old and the over 40. On the contrary, he asserts “workers in their prime of life are not interested in the decline of demand if not in situations of real economic depression, because they are to be assimilated to the more productive machines that remain in production even when, in conditions of insufficient demand, the less productive machines are progressively stopped” (De Cecco 1972, p. 76).
- 19.
Tarantelli elaborated the implications of the hypothesis of disequilibrium for the first time in 1974. Compare (Tarantelli 1974 [2], pp. 111–120) (involuntary unemployment) and pp. 120–129 (over-employment). Then he examined these themes again in two following contributions. In the study elaborated with Modigliani 5 years later, Tarantelli, besides a demonstration confirmed by econometric estimations of the invalidity of the stochastic equilibrium à la Holt in the Italian context, examines the case of over-employment, in particular analysing its implications in Phillips curve terms. Centred on the reinterpretation of Holt’s model in subjective probability terms, are (Tarantelli 1980[2]), speech presented at the XIX reunion of the Italian Society of economists and (Tarantelli 1983 [1]). In these essays, Tarantelli reformulates, in terms of expected variables, the analysis of disequilibrium of which here we intend to take into account. On that occasion, it was reported to who writes by Duccio Cavalieri, who participated in that meeting, that Tarantelli debuted affirming that he had finished writing his speech during the flight that had taken him from the United States to Italy in the hours immediately preceding the beginning of the reunion. For the treatment of the hypothesis of involuntary unemployment the original symbolism is used.
- 20.
When Phillips curve is identified as a function that interpolates the observed couples (u, ŵ), and it is possible to evaluate its adaptation to the values registered during the economic cycles in the interval 1861–1957, we can see that the ascending part of each value positions itself above the average relation represented by the interpolating curve, while the descending part positions itself beneath. It can be therefore inferred that the variation rate of the nominal wage increases more than average for the level of unemployment considered in the ascending phase of the cycle, that is when unemployment is decreasing. On the contrary, it is positioned below when the cycle inverts and unemployment starts to increase. With regards to this, Phillips asserts: “there is a clear tendency for the rate of change of money wage rates to be high when unemployment is low and to be low or negative when unemployment is high. There is also a clear tendency for the rate of change of money wage rates, at any given level of unemployment, to be above the average for that level of unemployment when unemployment is decreasing during the upswing of a trade cycle and to be below when unemployment is increasing during the down swing of a trade cycle” (Phillips 1958, p. 290). A more recent analysis, lead by the same theories of Tarantelli, mainly concerning the formation of loops around Phillips curve is Ferri (2007).
- 21.
Tarantelli (1974 [2], pp. 139–140).
- 22.
Tarantelli (1974 [2], p. 140).
- 23.
Tarantelli (1974 [2], p. 149).
- 24.
The application of the Ricardian setting to the structural analysis of the Italian labour market constitutes a qualifying element of Tarantelli’s analysis since his first works on the productivity of work at the research group of the study service of the Bank of Italy. Compare Tarantelli (1970 [1]).
- 25.
Tarantelli (1974 [2], p. 149).
- 26.
The econometric esteems through which Tarantelli corroborates his own conclusions about the validity of the Ricardian principle can be found in Tarantelli (1970 [1], pp. 49–83).
- 27.
Tarantelli (1970 [1], p. 119).
- 28.
Tella (1964).
- 29.
For the empirical verification, which Tarantelli carries out according to a plan already tested by Filosa in the sphere of studies service of the Bank of Italy, see Tarantelli (1974 [2], pp. 154–158). (Filosa 1971).
- 30.
(Tarantelli 1974 [2], p. 161).
- 31.
Compare Tarantelli (1972 [1]), Tarantelli (1972 [2]), Tarantelli (1972 [3]) and Tarantelli (1972 [4]).
- 32.
They express \( u\prime =\, (U - {\beta^{\prime}}{U_n})/(LF - {\beta^{\prime}}{U_n}) \) and \( {U_n} = LF - (1 + \gamma )(LF - {U_m}) \); with \( {b^{\prime}} = {\beta^{\prime}}(1 + \gamma ) \) and \( {\gamma^{\prime}} = \gamma /(1 + \gamma ) \). \( 0 \le\,{\beta^{\prime}}\, \le\,1 \)represents the part of non skilled unemployed; Un represents the absolute value of non skilled workers; γ represents the frictional level of unemployment and Um represents the lowest level of unemployment reached. Note that, substituting the latter expression in the former and arranging opportunely the terms, we obtain (3.18). The method of construction of the unemployment rate in terms of efficiency units leads Tarantelli and Modigliani to obtain negative values also and not, as it would be right to expect, positive ones. From these results Prosperetti suggests a reformulation of the previous expression. The origin of the problem, in his opinion, should be looked for in the fact that Modigliani and Tarantelli overestimated the part of non skilled workers in a systematic way, in periods when the rate of unemployment decreased. They assume as an approximate measure of non skilled unemployment the difference between the total of unemployed u, and um, which is the lowest level of unemployment reached in the previous period. This procedure, observes Prosperetti, can be considered legitimate when unemployment is increasing, i.e. when part of the present unemployed were previously employed. But when u shows a tendency to diminish, part of the labour force previously unemployed will now be employed, so that the difference between u and um could result negative. The solution proposed consists in employing the current rate of unemployment instead of um, in periods where u is positioned at a lower level than um (Prosperetti 1981). As regards an application of such a model, see Ghezzi (1986).
- 33.
Even in this case we follow an analogous procedure. Formulated \( {u^{{\prime\prime}}} = (U - {\beta^{{\prime\prime}}}{U_n})/(LF - {\beta^{{\prime\prime}}}{U_n}) \), with \( 1 \le{\beta^{{\prime\prime}}} \le0 \), remembering the expression of Un and suitably arranging the terms, (3.19) can be obtained.
- 34.
The expression of the estimating equation is: \( \hat{w} = A + B\left\{ {\left. {\frac{{\left[ {1 - \beta ({u_m} - {\gamma^{\prime}})} \right]}}{{\left[ {u - \gamma - \beta ({u_m} - {\gamma^{\prime}})} \right]}}} \right\}} \right. + Dp_c^{\prime} \)
A more detailed illustration of the method of empirical verify and of the achieved results can be found in Tarantelli (1972 [4], pp. 345–377).
- 35.
Tarantelli (1974 [4], p. 376).
- 36.
Spinelli and Zis (1979). Even though well known, it is useful to remember that the econometric analysis carried out in those years were essentially based on the method of ordinary least squares (OLS) and, in some cases, of generalized least squares (GLS). This, in the best of cases, permitted to keep into account the presence of autocorrelation of the residuals and of heteroscedasticity. More refined methods of analysis of time series, such as ARIMA models and the more recent ECM, allow us today to obtain qualitative better adaptations to data.
- 37.
Valcamonici (1973).
- 38.
The position taken by Salvatore Vinci is particularly critical about Tarantelli and Modigliani’s formulation. He points out that substantially they carry out a study on the formation of industrial wages to analyze the price trend with regard to the whole economic system. Tarantelli and Modigliani, points out Vinci, include amongst the regressors of the Phillips equation an index of the price level calculated, as we said, in the constant mark up hypothesis. Starting with these considerations, Vinci asks himself about the following subjects: the possibility to employ “a price based on the constant mark up of the entire economy” and about the legitimacy to estimate “the parameters of the equation of relative wages in a reduced form relative to all the economy using the estimates of single industrial wages” (Vinci 1974, pp. 52–53). Moreover, Vinci does not agree with the segmentation of the labour market which was adopted by Tarantelli and Modigliani. Using a distinction between skilled and un-skilled, can make sense, he explains, in sectors such as agriculture and craftsmanship, and for some non mass industrial production. “But [assumes significance] – he asks himself – in the case of mass production where the work of each worker is reduced to some simple acts for which is not requested any particular training but only a certain level of instruction […] and a certain physical and psychic resistance?” (Vinci 1974, pp. 54–55). Tarantelli and Modigliani reply strongly to what Vinci asserts, and he asserts that both of them would lean towards the “quantitativist” thesis, whose main proposition would consist in denying the stability of Phillips curve in the long term. (Vinci 1974, p. 51). Tarantelli e Modigliani answer affirming that “Vinci labels us as quantitativist based on the fact that in our scheme Phillips curve is not stable. This is wrong because: a. according to quantitativists – e.g. Friedman et al. – The shift of the curve is due only to the wage-price spiral, for a framework suitable and constant of the labour market; b. but in our scheme, the shift is due only to the variations in the framework of the labour market, regardless of the wage-price spiral (or the prevailing mark up). For this reason, Modigliani and Tarantelli’s work not only falls within the quantitativist idea, but also criticizes the base hypothesis of a constant structure of the labour market”. See Vinci (1974, p. 80).
- 39.
The reader interested in a strict treatment on a formal level of the problem linked to the formation of inflationary expectations can compare (Tarantelli 1974 [2], pp. 62–65). Chiarini (1995) proposes some interesting considerations regarding the role of expectations in Tarantelli’s economic analysis.
- 40.
Tarantelli (1974 [2], p. 53).
- 41.
Tarantelli (1974 [2], p. 162). It is also appropriate to underline that Tarantelli was not willing to accept the Friedmanian hypothesis of a mark up constancy in the short term. Although this consideration does not emerge from the analysis of Phillips curve, it can be found in Tarantelli (1970 [1], pp. 88–102). In this essay, though testing with a positive result, the hypothesis of a constant long term mark up for Italian industry as a whole, Tarantelli uses a price equation which included, among the regressors, the market conditions and the variations in the income distribution.
- 42.
Solow (1969).
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Michelagnoli, G. (2012). Analytical Refinements of the Post Keynesian Model. In: Ezio Tarantelli - Economic Theory and Industrial Relations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22312-9_3
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