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In this paper, the Brechling model is used to measure employment inertia in five sectors of the Congolese economy between 1983 and 1993. During that period, the Congolese economy found itself at a crossroad. On the one hand, the implementation of the 1982-1986 five-year economic development plans involved considerable infrastructure investment. On the other hand, given the market reversal observed since 1985, the infrastructure funding and the tempo became less. A structural adjustment program had to be undertaken with the World Bank in 1987-1989 with its measures entirely designed to restore the country’s macroeconomic balance and to enable it to resume regular and sustainable growth over time. Thus, the result from the short-run employment model taken over the period in question demonstrates that there is strong employment inertia in the sectors investigated.

Thanks to oil revenues which represented for more than 61% of national revenues and 36% of GDP in 1980, the Congo got into a major economic recovery program. One of these objectives was the re-establishment of the public enterprises which were to be the driving force of the economic and social development of the country. For this purpose, considerable financial efforts have been made so that these enterprises have made a significant contribution to job creation. In the mid-1980s, when oil prices collapsed, the Congolese government found itself short of revenues to meet its obligations. The country has borrowed, both from the Congolese banks and from foreign bilateral and commercial institutions. Given the magnitude of the problems it faced and the economic repercussions of these problems, the Congolese government was obliged to seek the assistance of the Bretton Woods institutions. The project for the institutional development of public enterprises was thus designed. This project was intended to help the Congo to implement the measures required by the structural adjustment program of 1987-1989 in the context of the recovery of these public enterprises.

In view of all these measures, the present study attempts to evaluate the different ways of the development of employment based on the estimation of a short-term employment model [

That said, this paper is organized as follows: the second section presents the short-run employment model. Initially, we describe the partial adjustment process which helps define the employment adjustment speed which lends itself to analysis based on the relative hiring and layoff costs. We also demonstrate that adaptation to desired employment may occur by way of a geometric lag distribution. Then, we present a model specification. We first recall the model application hypotheses in [

F. Brechling [

The model in [

This model highlights above all short-run mechanisms and primarily, the effect the market environment has on employment. It does not account for phenomena related to the labor/capital substitution. Its frequent use is explained by greater robustness for estimation, on the one hand, and also by it being more flexible, on the other.

Let L t represent employees and L t * the optimum level of employment (desired employment). The partial adjustment process highlights the fact that the adjustment of Quantity L t to the desired quantity L t * over a given time period can only be partial because of the cost of employment adjustment and the rigidity of the employment market. The two theoretical reasons set forth in [

L t − L t − 1 = λ ( L t * − L t − 1 ) ; 0 ≤ λ ≤ 1. (1)

Or equivalently: L t L t − 1 = [ L t * L t − 1 ] λ ; λ is a parameter that describes the speed of

adjustment (the opposite of employment inertia). In other words, it measures the speed with which actual headcount variations adjust to the level of “normal” headcount variations. This is based on a phenomenon that is well known to French economists and is referred to as the “productivity cycle” [

L t = ∑ i = 0 ∞ λ ( 1 − λ ) i L t − i * (2)

In fact, if we defined the lag operator by the relation £ L t = L t − 1 * , the expression would turn into (2); thus, L t = ψ ( £ ) L t − 1 * , with:

ψ ( £ ) = λ [ 1 + ( 1 − λ ) £ + ( 1 − λ ) 2 £ 2 + ⋯ + ( 1 − λ ) n £ n + ⋯ ] = λ / ( 1 − λ ) £

The partial adjustment process implies two types of costs specified in quadratic form to stay within the constraints for optimizing profit: (i) on the one hand, there clearly exists a cost for failing to adjust to the optimal quantity equal to: c 1 t = a ( L t − L t * ) 2 ; it points either to the existence of idle time related to overstaffing or the use of overtime and/or an increase in work intensity whenever effective staffing is below the optimal value; (ii) on the other hand, the adjustment cost which follows the associated costs with every headcount fluctuation during hiring or layoff phases (hiring includes a training cost while layoff includes indemnity): c 2 t = b ( L t − L t − 1 ) 2 . Then, the total cost is as follows:

c T t = a ( L t − L t * ) 2 + b ( L t − L t − 1 ) 2

Minimizing the cost determines staffing L t . We derive the equation [

d c T t d L t = 2 a ( L t − L t * ) + 2 b ( L t − L t − 1 ) = 0 ⇔ L t ( a + b ) − a L t * − b L t − 1 = 0 ⇔ L t ( a + b ) − a L t * − ( a + b ) L t − 1 + a L t − 1 = 0 ⇔ ( L t − L t − 1 ) = a a + b ( L t * − L t − 1 ) ; 0 ≤ a a + b ≤ 1 ⇔ ( L t − L t − 1 ) = λ ( L t * − L t − 1 )

We see again the expression in (1) with λ = a a + b . In the event of low de-

mand, if the layoff cost is high compared to that of maintaining an excessive labor force, for instance, λ will be near 0, and adjustment will be very slow. If, on the other hand, the cost of overstaffing is high along with a relatively low cost of laying off some of the labor force, adjustment will be quick with λ approaching 1. The parameter λ being equal to 0.25, for example, is an indication that a quarter of the difference with optimal staffing is taken away every year. This parameter λ also helps calculate the mean adjustment lag which is referred to as “productivity cycle length” that is equal to the relation of two costs, i.e.

Θ = ψ ′ ( 1 ) ψ ( 1 ) = 1 − λ λ = b a (3)

Finally, let us note that the process adopted here is similar to that used in investment theory, that of flexible accelerator.

There is extensive and controversial literature regarding the short-run relationship between staffing levels and production. The specification first introduced in [

The short-term employment model essentially rests on the following hypotheses: (i) technology is represented by a two-factor production function:

Q t = A e ρ t K t β L t α (4)

where Q t represents the annual output t ; L t and K t represent labor and capital services in t , respectively; α and β denote the output elasticity with regard to the labor and capital services, respectively; ρ is the autonomous technological change whose effect is assumed to represent the trend over time; A is a positive constant. (ii) We assume that company supply (Q) determined by the demand funneled towards such companies is exogenous to business people’s choices. This implies that, on the one hand, sales are exogenous over the short term. A company cannot act on demand. Moreover, if it is restricted in prospects, it is not restricted in the job market. This set of hypotheses corresponds to Keynesian unemployment. On the other hand, sales determine production levels over the short term in a completely exogenous manner. (iii) Over the short run, capital services are exogenous to business people’s decisions, and their evolution is represented by temporal trend K t = η 0 e η t with η 0 being a positive constant. However, the belief that K t evolves in an exogenous manner also requires some very restrictive hypotheses which need to be elaborated [

We prefer the way the model was presented in [

Q t = A e ρ t K t β ( L h ) t α (5)

where h t is the normal number of productive hours per worker per period. Since K t is exogenous, it can be included in the constant A making the expression (5) become:

Q t = A e ρ t ( L h ) t α (6)

A cost function in the form in [

c t = W h ( L h ) t + F t (7)

F t represents the fixed cost and W h is the wage of a single employee in a period. In addition, the quadratic form was selected for W h . That is to say:

W h = a − b h + c h 2 (8)

By substituting (8) into the cost function, we get:

c t = a ( L h ) t − b L t h t 2 + c L t h t 3 + F t (9)

For the sake of brevity and without loss of generality, we can derive h t from (6) and include it in (9), and minimizing this last expression, we get the desired level of staffing which, when combined with (1) produces the regression equation in [

log L t = a 0 − λ β α t + λ α log Q t + ( 1 − λ ) log L t − 1 (10)

where a 0 = λ log [ 2 c A 1 / α b ] .

We can re-write (10) more simply. That is to say:

log L t = a 0 + a 1 t + a 2 log Q t + a 3 log L t − 1 (11)

with a 1 = λ ρ / α ; a 2 = λ / α ; a 3 = 1 − λ . Most macroeconomic estimates made on the basis of the regression in (11) reveal an increase in yield based only on the labor factor: a value of α much greater than unity. This result considered to be paradoxical, on the one hand, puts into question the theoretical foundations of the basic model with profit maximization criteria and, on the other hand, has given rise to lively interest in the research and the interpretation of the above result. Regarding this last point, we can name a few attempts at explanation proposed in literature [

In [

Q t = A e ρ t [ a ( L h ) t − ω + ( 1 − a ) ( K u ) t − ω ] − υ / ω (12)

where K u is the capital used. Once again without going into detail, the process borrowed by the two authors led to the following definition of desired employment:

L t * = Q t 1 / υ e − ( ρ / υ ) t G (13)

where G is a constant. Combining (13) with (1), we obtain:

L t = G λ e − ρ λ t / υ Q t λ / υ L t − 1 1 − λ (14)

whence the regression equation:

log L t = G − λ ρ υ t + λ υ log Q t + ( 1 − λ ) log L t − 1 (15)

(15) can be written exactly as (11) with a 1 = − λ ρ / υ ; a 2 = λ / υ ; a 3 = 1 − λ ; however, the coefficients interpret differently: ( 1 − a 3 ) / a 2 = α is the work productivity in (11), whereas υ is return to scale in (15); − a 1 / a 2 represents in (11) the output growth rate from the combined effect of capital growth and technological change, and in (15) solely the effect of technological change. In the expression (15), the employment demand function shows that over the short term, production-related employment elasticity is equal to λ / υ . On the other hand, over the long term, employment adjustments have time to occur in their entirety: long-term employment/production elasticity is greater, equal to 1 / υ , that is to say, equal to the inverse of the scale parameter. If we were to exclude the parameter λ which characterizes the short-term imbalance, we could note that employment depends on two factors in the relation (15): (i) a positive factor measured by the long-term labor elasticity 1 / υ with respect to production; (ii) the effect of technological change − ρ / υ which plays negatively from the standpoint of required labor savings whatever happens to demand.

The data was provided by the Congolese National Institute of Statistics. These are estimations made from the results of annual and market investigations at public and private companies. They have to do with five sectors of the Congolese economy over a period from 1983 to 1993. There are five sectors: (i) syviculture and forestry; (ii) manufacturing; (iii) power generation and water; (iv) construction and public works; (v) transportation and telecommunications. For the five sectors investigated, we note a labor force that is reduced overall by 16% (15% for syviculture and forestry, water and power generation, 65% for construction and public works, and 18% for transportation and telecommunications).

The only growth observed (29%) was in the manufacturing sector. A visual summary can be found in

The data that we have at our disposal include two dimensions: an individual dimension and a temporal dimension (cross-section and time series data). In an econometric treatment of this type of data, the individual dimension is generally higher than the temporal one. But there is nothing that prevents us from being able to observe a small number of units over a long period: this is the type of data in our study. Similar examples of data abound throughout literature [

the model make us adopt certain simplified hypotheses regarding the structure of the covariance matrix of the residual terms of the model. To accomplish this, we use the method in [

Before giving the model estimation results, it is worth noting that, in order to understand certain economic realities and to be inspired by the work of [

When Equation (15) is estimated over the period from 1983 to 1993, it yields the following results:

log L t = − 1.92324 − 0.0113 t + 0.12696 log Q t + 0.87326 log L t − 1 ( − 2 . 99 ) ( 2 . 143 ) ( 16 . 936 ) ( 2 . 219 )

R 2 = 0.97646 ; F = 636.08

The values in parenthesis are t-statistics. It can be observed that all the coefficients are statistically significant at the 5% level. The model’s explanatory power, on the other hand, is excellent judging from the coefficient of determination which indicates that the variance in employment is explained at about 98%. The identification of regression coefficients for the structural parameters in the employment equation helps arrive at an estimate of the speed of adjustment λ of the scale factor υ and of the technological change ρ . We find that λ is equal to 0.127. Therefore, we conclude that the behavior of private and public Congolese companies in the five sectors of the economy of interest was dominated by strong employment inertia. The adjustment of effective employment to the desired staffing levels over the period investigated occurred at a rate of 12.7% a year.

The result obtained with respect to employment inertia is comparable to that obtained in a goodly number of papers already written on the subject, namely those written by [

On the other hand, we note an almost unitary return to scale: υ = 1.003 . This is a rather surprising result given that in a country’s economy, there are mono- polies with natural monopolies operating at increasing returns being the extreme case. This result could also be placed in doubt if we were to recall the fact that the Congo is classified as a middle-income economy. In fact, according to the line of reasoning developed by [

The identification of the parameter ρ results in a fairly high estimated value for the rate of technological change, on the order of 13% (12.9 to be more exact). Again, this result is comparable to that obtained for public companies in Senegal: ρ = 15 % . Same as when interpreting other parameters, here, we also have to settle for conjectured explanations. First, the hypothesis of an overstated rate of technological change cannot be discarded. Then, it could be noted that during a period of structural adjustment, given the tighter budgetary constraints, more has to be done with less; this individual behavior theory based on a methodological hypothesis of bounded rationality [

In the early 1980s, considerable financial resources were provided for the recovery of public enterprises in the Congo. As a result, these companies have made a significant contribution to job creation, opening up the hinterland and improving the living standards of the population. However, these positive aspects have had a very negative financial result. It was necessary to subscribe to the structural adjustment program in 1986. The objective of this article was therefore to evaluate the measures implemented by examining the employment-production relationship. Thus, the short-term employment equation was estimated for five sectors of the Congolese economy over the period 1983-1993. The result obtained shows that the speed of employment adjustment was low over the time period in question.

Although the explanatory power of the model in question is good, the present study has some limitations which can be the scope for future research: (i) the model places employment determination solely within the context of Keynesian unemployment. This hypothesis is not completely verified yet for the sectors investigated even though it is true that some public companies lay the foundations of the economic infrastructure by making heavy investments; (ii) classically, the added value is a labor function rather than the inverse as assumed by the short-term employment model. Tests of this variable for exogeneity within the models are not always conclusive; (iii) macroeconomic data from developing countries are frequently subject to uncertainty which is not without consequence for econometric estimations.

The author would like to thank editor and anonymous reviewers for their constructive comments. Nonetheless, he is solely responsible for any errors and omissions in this study.

Ambapour, S. (2017) Measuring Employment Inertia in a Period of Crisis: An Interpretation of Brechling Short-Run Model. Theoretical Econo- mics Letters, 7, 939-950. https://doi.org/10.4236/tel.2017.74064