_{1}

In this paper we test on data from Congo, what is come to know as Todaro Paradox. That is, on the one hand, the idea is put forward by Lewis that, industrial expansion will allow developing countries to reduce unemployment caused by an oversized rural workforce. However, on the other hand, Harris and Todaro argue that expanding urban employment will attract the rural population into the cities thus increasing unemployment. Our result seems to confirm Lewis’ theory that urban job creation leads to lower unemployment.

In the mid-fifties, Lewis [

The remainder of this paper was therefore the following: in Section 2, we presented a brief literature review followed by the model. In Section 3, the two specifications adopted by C & C from their theoretical model are described. The first specification concerns the nature of the returns to scale and explores the relationship between the level of employment and the apparent productivity of work in the modern and traditional sectors. The second functional form allows estimating the relationship between the unemployment rate and the proportion of jobs in the modern sector within the total active population. In section 4, after presenting the data, empirical tests are made on data from Congo. The results obtained show that the impact of modern sector job creation on unemployment is inferably ambiguous. However, these econometric results combined with certain characteristics of the Congolese economy, seem to favor the thesis of Lewis whereby urban job creation leads to lower unemployment. Our concluding remarks follow in Section 5.

In a famous 1954 paper, the 1979 Economics Nobel Prize winner, Lewis, [

Several commentators have shown that the validity of Todaro’s model depends on how migration flows are taken into account and how the balance of these flows is influenced by unemployment. In fact:

・ Todaro [

・ Blomqvist [

・ Arellano [

・ According to Nakagome (see [

In a different direction, urban wage variations were introduced into the Todaro model [

This is how Stiglitz and Calvo (see [

・ The modern sector’s unionization could explain the wage gap between the modern sector and the traditional sector [

・ The origin of this discrepancy could be regarded as a problem of controlling workers’ efforts that require firms to pay relatively high wages. This wage incentive pushes workers to increase productivity in the modern sector. This hypothesis of a positive connection between wages and individual productivity is at the base of the efficient wage theory [

・ The existence of labor cost rotation could explain the downward rigidity of wages in the modern sector, and therefore unemployment [

Recently, in order to assess the scope of the antagonism between the conclusions of Lewis and those of Harris and Todaro concerning the relationship between the modern sector’s expansion and unemployment in a dual economy, C & C, using a theoretical two-sector model of general equilibrium with endogenous wages, showed that [

・ This antagonism could be explained by the structural specificities of the different economies.

・ This relationship would strongly depend on each sector’s returns to scale.

This model allows identifying areas of relevance within Lewis’ and Todaro’s conclusions. The latter provided very satisfactory results when applied to data from Latin American countries.

According to Malinvaud [

The model used to examine the antagonism between the conclusions of Lewis and those of Todaro concerning the relationship between the modern sector’s expansion and unemployment in a dual economy based on theoretical framework of C & C. According to C & C, the negotiated wage character and technological dualism of underdeveloped economies is represented, not as an opposition between an urban and a rural sector, but between a modern industrial, private service and administrative sector and a traditional sector made up of agriculture and informal activities [

・ On the one hand by assessing the nature of each sectors’ returns to scale.

・ And on the other by estimating the influence of industrial employment variations on unemployment.

It is therefore a two-step approach:

・ First, the nature of returns to scale is estimated by studying the equation linking the employment level and the apparent labor productivity in both sectors.

・ Secondly, the unemployment rate is precisely modeled by the proportion of modern sector jobs in the total active labor force.

This second step intends to check if the elasticity of the modern sector’s unemployment rate relative to the employment rate agrees with the theoretical model.

Before specifying the two steps, let us first define the notations used to characterize the selected variables. These variables are as follows:

agriculture and other traditional activity cost factors;

The two equations estimated in the first stage are as follows:

and

By deriving Equations (1) and (2) from the time, we obtain the following relationships between growth rates:

and

If

If

The only equation estimated in the second step is:

Or by differentiation:

According to the authors, “this specification does not take into account the flexibility induced by modern sector job creation on the labor force; however it does correspond to the theoretical model that defines the relationship between the number of modern sector jobs and the number of unemployed in labor force, without describing the mechanism used for determining the volume of the working population”. Note that in Equations (5) and (6), in order to obtain robust estimates, a temporal trend was sometimes added. Sometimes, as with equations (1) and (2), we also completed tests by integrating temporal offsets. This was to take into account the various delays in propagating external effects on:

・ Returns induced by employment changes in the case of Equations (1) and (2);

・ Unemployment induced by changes in the share of modern sector employment in the case of Equations (5) and (6).

It should be noted that the growth rate specifications are only retained if the series level estimates are not significant. This is often due to the explanatory variable collinearity as a consequence of smoothing the logarithm series. C & C applied the above specifications to a sample of seventeen developing countries in Latin America and the Caribbean over the 1960-1988 period. The results comprehensively confirmed the relevance of their theoretical model. Returns in the modern sector are increasing or decreasing. However, only the assumption of decreasing returns in the traditional sector was confirmed. These results helped to reconcile the situations imagined by Lewis or Todaro. Indeed, we find:

・ On the one hand, countries whose returns to scale in both sectors are decreasing and have negative unemployment elasticity compared with the proportion of jobs in the modern sector. In fact, these are countries characterized by a very strong rural population, an important traditional sector of over 60% of the active population that represents more than three quarters of the total value of exports and consumption habits related to local production. These are the characteristics of the countries studied by Lewis. In the sample of countries studied by C & C, two countries match this description, El Salvador and Guatemala.

・ On the other hand, countries whose returns to scale in the traditional sector are decreasing and increasing or decreasing in the modern sector and have a positive unemployment rate elasticity. These countries are characterized by a relatively important modern sector that is industrial or public sector, and attractive based on salary levels and development prospects. These countries include: Brazil, Mexico, and Argentina.

Derived from the following two sources:

・ The “World Table” of the World Bank. These are official World Bank Statistics on production estimated according to the cost of factors (labor and capital) in the two sectors studied. That is the modern industrial, private service and administrative sector and a traditional sector made up of agriculture and informal activities.

・ Study report on the creation of the United Nations Development Program (UNDP) database [

It should, however, be mentioned that when dealing with developing country data where the statistical system is still faulty, one should always bear in mind the risk of “statistical illusion” enunciated by Morgenstern (1950): “Without acknowledging the errors, introducing economic data into high speed computers is devoid of meaning [

The results of the estimates of Equations (1) and (2) by ordinary least squares (OLS) on Limdep software [

―Modern sector;

―Traditional sector;

It was noted that the returns in the modern and traditional sectors appear significantly different from zero according to the Student’s test at a 5% confidence level and even by 1% (t-statistic are in the brackets). It was also noted that the explanatory power of the model is good; however it is better in the traditional sector and thus confirms the assumption of diminishing returns in this sector. The assumption of the independence of errors is rejected at the 5% threshold by the Durbin Watson test. Cochrane-Orcutt [

―For the modern sector;

―For the traditional sector;

The unemployment rate elasticity compared to the proportion of jobs in the modern sector within the active population is negative. Indeed, the best specification obtained by OLS using limdep software is as follows:

It can be seen that the unemployment rate elasticity compared with modern sector employment is significantly different from zero at the 5% and 1% threshold.

As the nature of returns to scale of each sector has an influence on the unemployment rate elasticity, generally we are reminded that the two conclusions drawn from the theoretical model are as follows:

・ Firstly, if returns to scale are strongly decreasing in both sectors, modern sector job creation induces a decrease in unemployment.

・ Secondly, if returns are slightly decreasing or increasing in both sectors, modern sector expansion causes a sharp increase in unemployment.

As already indicated, these two conclusions thus allow finding the situations imagined either by Lewis or by Todaro.

In the case of Congo, there are increasing returns in the modern sector and diminishing returns in the traditional sector. The unemployment rate elasticity compared to the proportion of jobs in the modern sector within the active population is negative. This last result, associated with those of returns to scale, represents a somewhat ambiguous scenario; a case not observed in the sample analyzed by C & C concerning the Latin America countries. A closer analysis was made by dividing the time into two periods: 1973-1984 and 1985-1993. The first sub-period is characterized by the creation of a public, industrial and agro-industrial modern sector and the process actually started around 1965. During this sub-period, the share of modern sector employment increased by 4%. The second sub-period corresponds to the Congolese Government’s adoption of structural adjustment measures. We can see a destruction of jobs through the scaling down of certain public enterprises. The share of employment in the modern sector fell by 3%. Thus, the application of the model on these two sub-periods only confirms the results of the analysis:

・ Increasing returns in the modern sector;

・ Decreasing returns in the traditional sector;

・ Negative unemployment rate elasticity compared to the proportion of jobs in the modern sector within the active population.

A general conclusion to these results can be made by examining the breakdown of the active working population based on certain economic considerations [

The purpose of this text was to verify, through empirical tests using data from the Congo, the conclusions of Lewis and Todaro concerning the relationship between the unemployment rate and modern sector employment. To do so, we relied on the theoretical framework developed by C & C. The results of econometric tests, taking into account certain characteristics of the Congolese economy, showed that urban jobs in the Congo lowered unemployment, thus confirming the thesis of Lewis.

SamuelAmbapour, (2015) The Todaro Paradox: An Econometric Test Using Data from Congo. Modern Economy,06,881-887. doi: 10.4236/me.2015.68083