A NEW MEASURE OF THE UNEMPLOYMENT RATE: WITH APPLICATION TO BRAZIL

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1 Plenary Session Paper A NEW MEASURE OF THE UNEMPLOYMENT RATE: WITH APPLICATION TO BRAZIL Hyun H. Son Nanak Kakwani A paper presented during the 5th PEP Research Network General Meeting, June 18-22, 2006, Addis Ababa, Ethiopia.

2 A NEW MEASURE OF THE UNEMPLOYMENT RATE: WITH APPLICATION TO BRAZIL Hyun H. Son and Nanak Kakwani UNDP-International Poverty Centre Brasilia, Brazil Abstract: This paper proposes a new measure of the unemployment rate. This measure takes into account not only people who are unemployed, but also those earning below the subsistence level of income in the labor market. In defining the new measure, people are classified as underemployed if their earnings are less than the predetermined subsistence level of income. The proposed new measure of the unemployment rate is a single index that takes both unemployment and underemployment into consideration. More importantly, the new measure is derived in such a way as to give the largest weight to the earnings of the poorest underemployed person in society, where the weight declines monotonically with earnings until earnings reach the minimum (subsistence) level. This property is of particular relevance if our focus is on poverty reduction. The proposed methodology is applied to Brazil s unit record household surveys covering the period between 1995 and Keywords: Open unemployment rate, Underemployment, Productive employment, Poverty address for correspondence: hyun.son@undp-povertycentre.org; Tel: ; Fax:

3 1. Introduction The standard measure of the unemployment rate relates the number of those counted as unemployed during a reference period (say a week) to the total labor force during the same period. This provides an overall unemployment figure for the reference period. Separate rates can be calculated in the same way for individual groups defined by age, sex, race or other common characteristics. Employment provides people with income and generates output. It facilitates access to essential goods and services. A high level of unemployment can lead to greater poverty, resulting in high levels of malnutrition, illiteracy and poor health because people are unable to meet minimum basic needs. Thus, the unemployment rate is a crucial variable in the analysis of poverty. An important feature of developing countries is that a large proportion of labor force is employed in the informal sector, which is characterized by providing low incomes for its workers. Incomes in the informal sector can be so low that workers are unable to provide the basic necessities of life for their families. Since the workers do not get any monetary support from the government when unemployed, they cannot afford to stay idle. Instead they do some work to survive but often report themselves as employed and so the standard unemployment rate as estimated from labor force surveys underestimates the true extent of their unemployment. Thus, many developing countries have low open unemployment rates but still suffer from acute poverty because of the low earnings of a large segment of their employed work force. 1 In this paper we suggest a modification of the standard unemployment rate so that it includes not only people who are unemployed, but also those earning below a subsistence income from the work they actually do. In the development of a new measure of the unemployment rate people whose earnings are less than the minimum (subsistence) wage 1 The International Labor Organization puts a special emphasis on productive employment. See Productive Employment for the Poor (ILO, 1992). 1

4 are regarded as underemployed. Thus, the new measure combines both the unemployment and underemployment profiles of people into a single index of the unemployment rate. An attractive feature of the proposed measure is that it is sensitive to the distribution of earnings of the underemployed persons. To put it differently, it gives the greatest weight to the earnings of the poorest underemployed person, and that weight declines monotonically as earnings rise until they reach the minimum (subsistence) income, where the weight becomes zero. This property is obviously very attractive if our concern is, in particular, with poverty reduction. This paper is organized in the following manner. While section 2 is devoted to the derivation of a new measure of unemployment rate, section 3 develops a number of properties for the new measure. Section 4 discusses the empirical results of the new measure as applied to Brazil s unit record household surveys covering the period from 1995 to A New Measure of the Unemployment Rate Suppose there are n persons in the labor force. The unemployment status of the ith person can be described by r i, which is defined as: r i = 1 if the ith person is unemployed = 0 if the ith person is employed Then the standard measure of unemployment rate is given by 1 U = n n r i i= 1 which is the proportion of persons in the labor force who are unemployed (i.e. those seeking a job but unable to find one). The standard measure of the employment rate is given by (1-U), which is the proportion of persons in the labor force who are employed (i.e. those having a job). Among those who are employed, some have earnings below the minimum wage, while others have earnings above it. (1) 2

5 It is reasonable to assume that those employed who have earnings below the minimum wage are not able to meet their minimum basic needs. In this respect, we may classify these persons as underemployed (or partially unemployed). The standard unemployment measure completely ignores partially unemployed persons, who are treated as if they were employed, and thus underestimates the true unemployment rate. Suppose that the ith person earns x i from working in the labor market and that the government has set a minimum wage of w. From this, we define a variable δ i as: δ i = 1 if x i > w = ( w x i / ) if x i w We define the ith person as fully employed if δ i = 1 and he/she earns more than the minimum wage. Similarly, he/she is defined as underemployed when δ i < 1. In this circumstance, his/her earnings are less that the minimum wage. The degree of his/her employment is thus measured by ( w x i / ), which will be less than 1 if > 0. In this paper, we propose a new measure of unemployment rate, which takes the form: n 1 i (1 r i i= 1 * U = δ ) (2) where which varies from 0 to. This measure takes into account the predicament of both the unemployed (who have no jobs) and the underemployed (who have jobs with inadequate earnings to meet their basic needs). 3. Properties of the New Unemployment Rate The basic properties for the proposed new unemployment rate are as follows: 3

6 Property I: If r i = 1 for all i, then * U = 1 When all persons in the labor force are unemployed, then there is a 100 percent unemployment rate in society. Property II: * If r i = 0 and δ i = 1 for all i, then U =0 When all persons in the labor force are employed with earnings greater than the minimum wage, then the unemployment rate takes the minimum value of zero. Property III: If =0, then * U = 1 n r i n i= 1 When =0, then the proposed measure of the unemployment rate is equal to the standard measure of the unemployment rate. In this case, all underemployed persons are regarded as fully employed. * U Property IV: > 0 The proposed unemployment rate increases monotonically with and, therefore, takes a minimum value when = 0. Thus, the standard unemployment rate is the lower boundary of the proposed unemployment measure. Property V: If =, * U is equal to the proportion of unemployed plus underemployed persons in the labor force. In this case, all underemployed persons are regarded as the unemployed. This is the upper boundary of the proposed unemployment rate. 4

7 Property VI: U x * j = ( x n j / w) 1 if x j < w which is negative when >0. This property implies that if the earnings of any underemployed person (say jth person) increase (or decrease), then the proposed unemployment measure decreases (or increases). This property is valid when >0. The standard measure of the unemployment rate for which, =0 is completely insensitive to any increase in the earnings of an underemployed person. Property VII: U 2 * 2 x j = n ( 1 ) 2 ( x j / w) (3) which is strictly positive when lies between 0 and 1. Property VI implied that if we increased the productivity of any underemployed person, the proposed unemployment measure would decrease. Property VII implies that the magnitude of reduction in unemployment rate would be larger if we increased the productivity of poorer persons, provided that lies between 0 and 1. When =1, the magnitude of unemployment reduction will be the same when we increase the productivity of any underemployed person. In this case, the unemployment measure gives equal weight to all incomes. If our concern is with the reduction of severity of poverty, then obviously the unemployment measure should give the largest weight to the poorest underemployed person and this weight should decline monotonically as income increases. To satisfy this requirement, we should choose the unemployment rate for which lies between 0 and 1. We have narrowed down the value of to lie in the range between 0 and 1. Can we further narrow down its value to a single number? The distribution of weight given to different individuals depends on the value of we choose. If we have a strong preference for poverty reduction, then we should choose where the weight given to the poorest person among the underemployed is maximum. The weight given to the jth person is given by the second derivation of the proposed unemployment rate, as shown in 5

8 (3). Thus, we choose so that the weight given in (3) is maximized. As can be seen from Figure 1 the weight increases until it reaches maximum value, and then, it declines. Assuming that the jth person is poor if his/her labor income is less than 50 percent of the minimum wage, then the weight given to the jth person attains the maximum value when = 0.4. This is the value we will choose in order to analyze the unemployment situation in Brazil. Figure 1: Weight given to the underemployed for different values of Values of 4. Empirical Illustration The proposed methodology for computing a new measure of the unemployment rate has been applied to Brazil and the results are presented in Table 1. The data source used for this study comes from the Pesquisa Nacional por Amostra de Domicilios (PNAD, the Brazilian Annual National Household Survey) covering the period from 1995 to The PNAD data are unit record household surveys that are conducted nationwide every year in Brazil. On average, each PNAD contains information on more than 30,000 households and 300,000 individuals. To calculate the new measure of the unemployment 6

9 rate, the study uses Neri s poverty line, which may be deemed as a good proxy for the minimum subsistence level of income in Brazil (Rocha 1993, Ferreira et al. 2003). 2 Table 1 compares the open unemployment rate with the proposed new measure of the unemployment rate over the period As shown, the new measure has a much lower value compared to the open unemployment rate. This suggests that if unemployment is defined in such a way as to take into account the minimum earnings in the labor market, the rate of unemployment becomes markedly higher than that measured in the conventional way. Moreover, the large gap between the open unemployment rate and the new measure of the unemployment rate points to the problem of underemployment that is prevalent in the Brazilian labor market. Underemployment is of particular concern in an economy with a large informal sector, such as that of Brazil. Further, the declining gap between the two measures of unemployment indicates a fall in underemployment as the economy has been increasingly formalized over the years. Table 1: The open unemployment rate and the new measure of unemployment Period Open unemployment rate New measure of unemployment rate Trend Trend Trend Source: Authors calculations based on PNAD Turning to the trend values, both measures display a different pattern. Over the decade , both measures of the unemployment rate show a positive trend, suggesting an 2 Although Brazil has an official minimum wage, we have not utilized it because it is far higher than the minimum subsistence level of income. 7

10 increase in unemployment. Yet, in comparison to the new measure, the increase in the open unemployment rate is much sharper: during , the open unemployment rate increased at an annual rate of 3.90 percent whilst the new unemployment rate has been more or less static at 0.02 percent per annum. On the whole, the open unemployment rate gradually increased over the period but the new measure of unemployment remained more or less unchanged. Thus, the gap between the two measures has narrowed over the years. As was pointed out earlier, this signifies that the economy undergoing a transformation to become increasingly more formalized. In a similar manner, we have compared the new measure of the unemployment rate with the open unemployment rate in three areas in Brazil, which include metropolitan, nonmetropolitan, and rural areas. Figure 2 presents the results over : while the left panel shows the open unemployment rates, the right panel displays the new measure of unemployment rates. Figure 2: Open unemployment rate and the new measure, by areas Open unemployment rate New measure of unemployment rate Metropolitan non-metropolitan Rural Metropolitan non-metropolitan Rural Source: Authors calculations based on PNAD Two points are worth noting. To begin with, the new measure of unemployment is the highest in rural areas but the open unemployment rate is the highest in metropolitan 8

11 areas. Indeed, the open unemployment rate in rural areas was merely 2.1 percent in 2004, whereas the rural unemployment rate was almost 43 percent in the same period, according to our proposed measure. The difference between the two measures explains the large underemployment that exists in the rural sector. What is more, the labor forces in the rural sector are mainly engaged in unpaid family work or agricultural primary sectors, where their rewards are likely to be below the minimum wage. Second, while the gap in the open unemployment rate between metropolitan and non-metropolitan areas widens over the period, the gap in the new measure between the two areas tends to converge. This finding suggests that productivity in the non-metropolitan areas has increased over the years and has, in fact, surpassed that in the metropolitan areas since We now turn to unemployment by gender. The results are depicted in Figure 3. As shown for the open unemployment rate, the new measure of unemployment is much higher among females compared to males. Compared to the open unemployment rate, the gap in the new measure between males and females is enormous. This suggests that underemployment among females is particularly high in the Brazilian labor market. Figure 3: Open unemployment rate and new measure by gender 14.0 Open unemployment rate 35.0 New measure of unemployment rate Male Female Male Female Source: Authors calculations based on PNAD 9

12 The proposed methodology is also extended to state level in Brazil. Due to limited space, we have only presented the estimates of both unemployment indicators for The result is presented in Figure 4. The 27 states included in the figure are arranged in ascending order of their headcount ratio in What emerges from the results is that the gap between the two measures of unemployment is smaller for richer states but greater for poorer states. This indicates the prevalence of higher underemployment in the poorest states such as Piauí, Maranhão, and Alagoas. 50 Figure 4: Open unemployment rate and new measure by 27 states in Santa Catarina São Paulo Rio de Janeiro Paraná Rio Grande do Sul Goiás Distrito Federal Mato Grosso Mato Grosso do Sul Espírito Santo Rondônia Minas Gerais Amazonas Pará Tocantins Acre Amapá Sergipe Rio Grande do Norte Roraima Bahia Pernambuco Paraíba Ceará Piauí Maranhão Alagoas Open unemployment rate New measure of unemployment rate Note: States are ranked by ascending order of their poverty incidence. Source: Authors calculations based on PNAD Finally, we have asked a question as to whether unemployment has a positive (or negative) relation with poverty. This can be answered through examining the correlation between a poverty measure and the rate of unemployment. To do so, we have carried out a simple regression of the headcount ratio on the open unemployment rate and also on the 10

13 new measure of the unemployment rate across 27 states over the period Table 2 displays the estimated coefficients along with t-statistics. According to Table 2, there has been overall a negative correlation between poverty and the open unemployment rate: as poverty declines (or increases), unemployment rises (or falls). Yet, this relationship appears to be insignificant in the sense that most of the estimated coefficients are statistically insignificant at the 5 percent level except for two periods, 1995 and On the contrary, different results emerge when we look at the correlation between poverty and the new measure of the unemployment rate. The results suggest that poverty has a significant and positive correlation with unemployment: as poverty decreases (or increases), unemployment also falls (or rises). This finding is found to be statistically robust: the estimated coefficients are highly statistically significant at the 5 percent level for the entire period. All in all, while the open unemployment rate is a poor and insignificant determinant of poverty, the new measure is significantly and positive correlated with poverty. Table 2: Correlation between poverty and the unemployment rate across 27 states Poverty & open unemployment rate Poverty & new measure of unemployment rate Period Estimated coefficient Estimated coefficient * (-2.21) 1.92 * (7.63) * (-2.31) 1.88 * (6.34) (-0.97) 1.83 * (7.60) (-1.16) 1.73 * (5.72) (-0.97) 1.91 * (6.66) (-0.87) 1.89 * (6.26) (-0.54) 1.51 * (4.68) (-0.73) 1.83 * (6.08) (0.50) 1.75 * (6.89) Note: Figures in brackets are values for t-ratio. * indicates a statistical significance at 5% level. Source: Authors calculations based on PNAD 11

14 References International Labor Organization. (1992). Productive Employment for the Poor, International Labor Review, Vol. 132, No. 1. Ferreira, F., Lanjouw, P. and Neri, M. (2003). A robust poverty profile for Brazil using multiple data sources, Revista Brasileira de Economica 57 (1), pp Rocha, S. (1993). Poverty lines for Brazil: New estimates from empirical evidence, mimeo IPEA working paper, Rio de Janeiro, Brazil. 12