Economics Letters 117 (2012) 91–95
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On the structure of US unemployment disaggregated by race, ethnicity, and gender Hervé Queneau a,b,∗ , Amit Sen c,1 a
Department of Finance and Business Management, 2900 Bedford Avenue, Brooklyn College of the City University of New York, Brooklyn, NY 11210-2889, United States
b
IDHE-Paris I Panthéon-Sorbonne/CNRS, France
c
Department of Economics, 3800 Victory Parkway, Xavier University, Cincinnati, OH, 45207-1212, United States
article
info
Article history: Received 8 December 2010 Received in revised form 19 April 2012 Accepted 23 April 2012 Available online 30 April 2012
abstract We present empirical evidence regarding the structure of unemployment in the US disaggregated by race, ethnicity, and gender. Popp’s (2008) unit-root test reveals that the dynamics of unemployment for all groups is characterized by the hysteresis hypothesis except for Hispanic Males. © 2012 Elsevier B.V. All rights reserved.
JEL classification: E24 Keywords: Unemployment rate Persistence Unit root Gender Race Ethnicity
1. Introduction As emphasized by Ewing et al. (2005), it is important to analyse the unemployment rates disaggregated by both race and gender so as to help policy makers evaluate and compare the effects of monetary and fiscal policies on the unemployment rates across men and women and across Whites and Blacks.2 That is, effective policy formulation requires an understanding of the varying effects that random and unexpected shocks have on the unemployment rates of the different demographic groups. Following Papell et al. (2000), we use unit-root tests to assess whether these unemployment rates follow the natural rate of unemployment
∗ Corresponding author at: Department of Finance and Business Management, 2900 Bedford Avenue, Brooklyn College of the City University of New York, Brooklyn, NY 11210-2889, United States. Tel.: +1 718 951 5000x2097; fax: +1 718 9514867. E-mail addresses:
[email protected] (H. Queneau),
[email protected] (A. Sen). 1 Tel.: +1 513 745 2931; fax: +1 513 745 3692. 2 Zavodny and Zha (2000), Rodgers (2008), and Ewing et al. (2005) discuss the varying effects of monetary and fiscal shocks on unemployment rates for Whites and for Blacks. 0165-1765/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2012.04.065
hypothesis, the structuralist view of unemployment, or the hysteresis hypothesis.3 While the presence of a unit-root in the unemployment series suggests hysteresis, the absence of a unitroot implies that the unemployment rate evolves according to either the natural rate hypothesis or the structuralist hypothesis. Ewing et al. (2005) find evidence that the unemployment rate series disaggregated by both gender and race in the US follow the hysteresis hypothesis based on the Augmented Dickey–Fuller unit-root test over the time period 1972:01–1999:08. We argue that the Augmented Dickey–Fuller test may mask the effect of structural breaks in the dynamics of unemployment of each group. There are several reasons to expect a structural break during the early 1980s that impacted the evolution of the unemployment rates disaggregated by race, ethnicity, and gender. First, the
3 According to the natural rate of unemployment, macroeconomic shocks have a temporary effect on the unemployment rate, which will therefore fluctuate around the natural rate. The theory of unemployment hysteresis posits that macroeconomic shocks have a permanent (or highly persistent) effect on the unemployment rate. The structuralist view, however, states that the unemployment rate fluctuates around a natural rate of unemployment with structural shifts in this natural rate owing to such changes as the real exchange rates or tax rates.
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Federal Reserve instituted contractionary monetary policy to fight inflation. There is evidence that the unemployment rate of less-skilled workers was more negatively impacted by this contractionary monetary policy than the unemployment rate of more-skilled workers, see Carpenter and Rodgers (2004). Second, as argued by Krusell et al. (2000) and Jefferson (2008), biased technological change that favoured more-skilled workers led to an increase in capital-skill complementarity, which in turn increased the relative demand for skilled workers and may have contributed to an increase in the unemployment of less-skilled workers. Since African Americans, Hispanics, and women had, on average, lower levels of human capital compared to White men during the 1980s, we would expect an adverse effect from both the contractionary monetary policy and the capital-skill complementarity on the unemployment rates of these groups. Finally, the pull back on Affirmative Action and the enforcement of equal employment opportunity laws may have adversely affected the unemployment rates of African Americans, Hispanics, and women, see Leonard (1990). Such a pull back in Affirmative Action and equal employment opportunity laws may have adversely impacted the hiring and dismissal behaviour of employers with regard to women and minorities. In order to capture a possible break in the unemployment rates, we use the new-Perron type unit-root test proposed by Popp (2008) to examine the structure of unemployment in the US across six demographic groups, namely, White Males, White Females, Black Males, Black Females, Hispanic Females, and Hispanic Males. The unit-root statistic of Popp (2008) allows for a one-time break under the trend-stationary alternative. In addition, it has the desirable property of estimating the break-date accurately, and, unlike Perron’s (1997) original tests, it does not suffer from spurious rejection of the null hypothesis in the presence of a break under the unit-root null hypothesis. Therefore, rejection of the null hypothesis based on the Popp’s (2008) unit-root statistic will imply that the unemployment rates across race, ethnicity, and gender follow the natural rate or the structuralist view of unemployment, and the break-date, if it exists, will be estimated very accurately. We find that the unemployment rates disaggregated by race, ethnicity, and gender follow the hysteresis hypothesis with the exception of the unemployment rate for Hispanic Males. Further, there is considerable variation in the level of persistence in the unemployment rates by race, ethnicity, and gender. In particular, we find that the level of persistence is: (a) higher for Males compared to Females within each racial group; and (b) highest for Whites and lowest for Hispanics. In the next section, we present the data, a discussion of Popp’s (2008) unit-root test, and empirical results regarding the dynamics of the unemployment rate series for White Males, White Females, Black Males, Black Females, Hispanic Males, and Hispanic Females. Some concluding comments are included in Section 3. 2. Unemployment rates by race, ethnicity, and gender The data for US unemployment rates by race, ethnicity, and gender were obtained from the Bureau of Labor Statistics website over the period 1972:01–2011:07.4 The unemployment rates for the White Male (WM), Black Male (BM), and Hispanic Male (HM) are shown in Fig. 1, and those for White Female (WF), Black Female (BF), and Hispanic Female (HF) are shown in Fig. 2. To facilitate comparison of the level of persistence
4 The series for the Hispanic Males and Hispanic Females are seasonally unadjusted. The result from using the seasonally unadjusted series and seasonally adjusted based on month dummies are very similar, and so we only report the results from the seasonally unadjusted series here.
Fig. 1. US unemployment rates for White Males, Black Males, and Hispanic Males, 1972:01–2011:07.
Fig. 2. US unemployment rates for White Females, Black Females, and Hispanic Females, 1972:01–2011:07.
across the different demographic groups to the national average, we include the results for the total unemployment rate (T) as well. Several features are worth noting when comparing the unemployment rates across the different demographic groups. The average Total Black unemployment rate is almost always more than twice the Total White unemployment rate. The Total Hispanic unemployment rate is lower than the Total Black unemployment rate, but higher than the Total White unemployment rate. There are only marginal differences between the White Female and the White Male unemployment rates, with periods when the White Female unemployment rate is in fact lower compared to the White Male unemployment rate. While the Black Female unemployment rate was, on average, higher than the Black Male unemployment rate before 1980, it has been consistently lower compared to the Black Male unemployment rate after 1980. The Hispanic Female unemployment rate remains higher compared to the Hispanic Male unemployment rate except for the most recent 2008–2011 period. Although the focus of our paper is on the persistence of unemployment by race, ethnicity, and gender, it may be insightful to also examine the persistence patterns of the employment–population ratio and labour force participation rate for the various demographic groups, see Clark and Summers (1981) and Carpenter and Rodgers (2004). Indeed, the employment–population ratio and labour force participation rate are important measures of labour
H. Queneau, A. Sen / Economics Letters 117 (2012) 91–95
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Table 1 ADF tests for US unemployment rate by race and gender, 1972:01–2011:07. Series
Without trend with trend
With trend
k∗
tµ
ρˆ
u(T) u(WM) u(WF) u(BM) u(BF) u(HM) u(HF)
24 24 24 24 24 21 23
−2.09 −1.89 −2.17 −2.36 −2.01 −2.23 −2.10
0.9860 0.9841 0.9821 0.9715 0.9787 0.9592 0.9543
lfpr(T) lfpr(WM) lfpr(WF) lfpr(BM) lfpr(BF) lfpr(HM) lfpr(HF)
24 24 24 24 23 24 23
−1.92 0.69 −3.48** −0.65 −1.90 −0.75 −2.33
0.9925 1.0035 0.9899 0.9913 0.9897 0.9682 0.9752
−2.59 −0.74 −2.65*** −2.64*** −1.48 −0.22 −1.48
0.9914 0.9956 0.9946 0.9653 0.9933 0.9934 0.9443
αˆ
k∗
tτ
ρˆ
0.0928 0.0940 0.1026 0.3769 0.2626 0.3586 0.4398
24 24 24 24 24 14 23
−2.08 −1.79 −2.50 −2.49 −2.90 −3.66** −2.01
0.9840 0.9845 0.9703 0.9676 0.9539 0.9335 0.9375
0.4947
24 24 24 24 36 24 23
1.01
−1.58 −0.64 −2.54 −0.50 −1.55 −1.50
1.0059 0.9535 0.9974 0.9080 0.9923 0.9254 0.9563
−0.2973 0.6045 0.5494 0.6204 2.5286 1.3985
αˆ
βˆ
HLρ
0.1128 0.0895 0.2022 0.4724 0.7062 0.6998 0.6767
0.0000 0.0000 −0.0002 −0.0002 −0.0007 −0.0006 −0.0004
42.97 44.37 22.99 21.04 14.69 10.07 10.74
−0.2985
−0.0003 −0.0007 −0.0005 −0.0013 −0.0002 −0.0006
117.83 14.56 266.25 7.18 89.67 8.94 15.51
3.6769 0.3139 6.6343 0.5256 6.0840 2.2710
0.0006
−0.34 0.9979 0.1651 −0.0001 329.72 −1.95 0.9810 1.4117 −0.0002 36.13 −0.10 0.9996 0.1278 −0.0003 1732.52 −2.93 0.9580 2.5891 −0.0003 16.15 −0.64 0.9921 0.3982 0.0001 87.39 −0.59 0.9825 1.4935 −0.0028 39.26 −1.66 0.9379 3.4662 −0.0029 10.81 Note: The finite sample (T = 100) critical values: (i) for the tµ statistics are: −2.58 at the 10% level, −2.89 at the 5% level, and −3.51 at the 1% level; and (ii) for the tτ statistic are: −3.15 at the 10% level, −3.45 at the 5% level, and −4.04 at the 1% level. In all cases, we used k max = 24 except for the Employment–Population Ratio series for all epr(T) epr(WM) epr(WF) epr(BM) epr(BF) epr(HM) epr(HF)
36 24 24 24 24 22 24
0.5323 0.2973 0.3020 2.0760 0.3464 0.4502 2.8517
36 24 36 24 24 22 23
individuals. * Denote significance at the 1% significance level. ** Denote significance at the 5% significance level. *** Denote significance at the 10% significance level.
market performance that are related to the unemployment rate.5 Unlike the unemployment rate, the employment–population ratio is not impacted by movements in and out of the labour force, including discouraged workers. Therefore, we assess the time series properties for the labour force participation rates and the employment–population ratios for each demographic group.6 We examine the underlying dynamics of US unemployment rates disaggregated by both race, ethnicity, and gender, that is, White Male (WM), White Female (WF), Black Male (BM), Black Female (BF), Hispanic Male (HM), and Hispanic Female (HF). To facilitate comparison, we report results for the total unemployment rate and the corresponding level of persistence.7 We first calculate the Augmented Dickey–Fuller (ADF) unit-root tests using the following regressions: yt = αˆ + ρˆ yt −1 +
k∗
denoted by ττ . The results, summarized in Table 1, show that only the Hispanic Male unemployment rate series is trend stationary. The estimated trend coefficient HM reveals that it is falling over time. For the WM, WF, BM, BF, and HF unemployment rates, we fail to reject the unit-root null hypothesis, and so these unemployment rates are characterized by the hysteresis hypothesis. Given that the Dickey–Fuller statistics fail to reject the unitroot null hypothesis in the presence of a structural break, we use the new Perron-type statistic proposed by Popp (2008) that allows for a simultaneous break in the intercept and slope at an unknown date. Following Sen (2003), we use the Mixed model characterization of Perron (1997). For each possible break-date TB = [τ T ] corresponding to all τ in [λ, 1 −λ], Popp (2008) suggests estimating the following regression: yt = α + β t + ξ D(TB )t + κ DU (TB )t −1 + ζ DT (TB )t −1
cˆj 1yt −j + eˆ t
(1)
j =1
cj 1yt −j + et
(3)
j=1
k∗
yt = αˆ + βˆ t + ρˆ yt −1 +
+ ρ yt −1 +
k∗
cˆj 1yt −j + eˆ t .
(2)
j =1
The ADF test from regression (1) without a time trend is denoted by τµ , and the ADF test from regression (2) with a time trend is
5 The unemployment rate (u) is equal to 1 minus the ratio of the employment–population ratio (epr) and the labour force participation rate (lfp). 6 In almost every instance, we reject the unit root null hypothesis. It is interesting to note that the level of persistence in the labour force participation rates and the employment–population ratio are higher for Females compared to Males within each racial and ethnic group except for the employment–population ratio of Hispanics. Further, the level of persistence is highest among Whites and lowest among Hispanics. 7 We also examined the unemployment rate by the level of education based on data between 1992:01–2011:07. Our results do not show any consistent relationship between the level of persistence and the level of education. We do not report the results in the paper owing to space constraints, but they are available from the authors upon request.
where D(TB )t = 1(t = TB + 1), DU (TB )t = 1(t > TB ), DT (TB )t = 1(t > TB ) (t − TB ), and 1(.) is the indicator function.8 Popp (2008) suggests using the following estimated break-date: TˆB = arg max |tξ (TB )|
(4)
TB
and the unit-root statistic is the t-statistic for H0 : ρ = 1 in regression (3) evaluated at the estimated break-date TˆB as defined in (4). The results for the full-sample based on the new Perrontype unit-root test are denoted by tρˆ (TˆB ). We set the trimming parameter, λ, equal to 0.1, and assess the significance of the
∗
8 The extra ‘k∗ ’ regressors {1y }k are included in the regression to account for t −j j=1 additional correlation in the time series {yt }. We use the k (t-sig) data-dependent method of Perron and Vogelsang (1992) to choose the appropriate lag truncation parameter ‘k∗ ’ which is typically unknown a priori. For all our calculations, we set k max = 24.
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Table 2 Popp’s (2008) unit-root test results for US unemployment rates by race and gender, 1972:01–2011:07. Series
TˆB
k∗
ρˆ
tρˆ
σˆ
HLρ
u(T) u(WM) u(WF) u(BM) u(BF) u(HM) u(HF)
1983:06 1981:01 1983:07 1977:05 1991:10 1983:04 1986:03
24 24 24 24 24 21 23
0.9861 0.9880 0.9671 0.9674 0.9448 0.9507 0.9184
−1.719 −1.315 −2.718 −2.227 −3.118 −2.194 −2.414
0.1633 0.1940 0.2027 0.6628 0.5675 0.7731 0.7903
49.52 57.41 20.72 20.91 12.21 13.71 8.14
lfpr(T) lfpr(WM) lfpr(WF) lfpr(BM) lfpr(BF) lfpr(HM) lfpr(HF)
1981:05 1981:05 1979:03 1999:05 1988:06 1981:08 1983:12
24 24 24 24 23 24 23
1.0034 0.9601 0.9983 0.8346 0.9755 0.9085 0.9284
0.1295 0.1773 0.1713 0.5129 0.4645 0.5907 0.6961
204.21 17.02 407.39 3.83 27.94 7.22 9.33
epr(T) epr(WM) epr(WF) epr(BM) epr(BF) epr(HM) epr(HF)
1981:05 1983:05 1984:07 2000:03 1995:10 1974:12 1977:10
24 24 24 24 24 22 23
0.9982 0.9850 0.9910 0.9315 0.9510 0.9787 0.8743
0.1480 0.2112 0.1789 0.5680 0.4640 0.6717 0.6046
384.74 45.86 76.67 9.77 13.80 32.19 5.16
0.3845
−1.3611 −0.2876 −3.9101** −1.2026 −1.8161 −1.8104 −0.3009 −1.4918 −1.2970 −4.2483* −2.7798 −0.6629 −1.5883
Note: The asymptotic critical value at the 10% significance level is −3.20, at the 5% significance level is −3.69, and at the 1% significance level is −4.24. The critical values are taken from Table 1 of Costantini and Sen (2012). In all cases, we used k max = 24. *** Denote significance at the 10% significance level. * Denote significance at the 1% significance level. ** Denote significance at the 5% significance level.
new Perron-type statistic using the finite-sample critical values reported in Table 1 of Costantini and Sen (2012) who derive the limiting distribution of the unit-root statistics based on the estimated break date. The results for the new Perron-type unit-root statistic are presented in Table 2. For each series, we report the test statistic, the estimated break-date, and the half-life of a unit shock (HLρ ) implied by the estimated regressions, see Andrews (1993). The unit-root statistics for all the unemployment rate series are insignificant and, therefore, consistent with the hysteresis hypothesis. That is, shocks to these unemployment rates will have a persistent effect. Our results are based on a longer sample period compared to Ewing et al. (2005), and a unit root test that guards against spurious rejection of the unit root null in the presence of a break under the null hypothesis. However, our empirical evidence re-affirms the results presented by Ewing et al. (2005) who treat all the unemployment rates as non-stationary series. In order to measure the degree of persistence in the series for which we fail to reject the unit-root null hypothesis, we calculate the half-life (denoted by HLρ ) of a unit shock. The halflife, calculated as | log(1/2)/ log(α)|, measures the time required for a shock to decay to half its initial value, see Andrews (1993) for a discussion of the half-lives measure for persistence. We find that the half-life range between 8.14 months for HF and 57.41 months for WM.9 While the level of persistence is relatively high across all groups, it should be noted that the level of persistence is highest for White Males and White Females, and lowest for Hispanic Males and Hispanic Females. In addition, the level of persistence is higher for Males compared to Females within each racial group. 3. Policy discussion Historically, the unemployment rates among Blacks and, to a lesser extent among Hispanics, have been substantially higher
9 We use the half-life measure based on regression (3) for all series except u(HM) for which use the half-life measure implied by regression (2).
compared to Whites. While the unemployment rate for women was higher compared to men prior to the mid 1980s, there has been a reversal in this trend among Blacks and Whites, but not among Hispanics. Our empirical results show that all unemployment rates disaggregated by race, ethnicity, and gender are characterized by the hysteresis hypothesis with the exception of Hispanic Males. Specifically, our results indicate that the level of persistence, as measured by the half-life, is higher for Males compared to Females within each racial group. Further, the level of persistence is highest among Whites, and lowest amongst Hispanics. There are significant policy implications of our empirical results. First, the persistence in the total unemployment rate masks the variation in the unemployment persistence across different demographic groups. Specifically, the level of persistence among White Males is higher compared to that of the total unemployment rate, but it is lower for all other demographic groups. Second, the effect of shocks on the dynamics of unemployment of a demographic group depends both on the level of unemployment persistence for that group and the nature of the change in the unemployment rate resulting from the shocks. The effect of a high level of persistence on the dynamics of unemployment, referred to as the ‘‘persistence effect’’ in what follows, is the most favourable when the unemployment rate decreases whereas it is the least favourable when the unemployment rate increases. Therefore, shocks that lower the unemployment rates will have the most favourable persistence effect on Whites and the least favourable persistence effect on Hispanics. Also, the effect of a shock that reduces the unemployment rates will have a more favourable persistence effect on men compared to women within each racial and ethnic group. Conversely, the impact of an adverse shock that increases the unemployment rates will have the most favourable persistence effect on Hispanics and the least favourable persistence effect on Whites. However, we should emphasize that the unemployment rates among Blacks and Hispanics are substantially higher compared to those of Whites, and so any adverse impact of shocks on the unemployment rate can be quite severe for Blacks and Hispanics. Our major empirical finding that the level of persistence is higher for Whites compared to Blacks can be explained as follows. Consider, for instance, a stimulatory macroeconomic policy that is intended to lower the unemployment rates for each demographic group. However, given that Whites have, on average, a higher level of human capital and face less discrimination, the decrease in the White unemployment rates will be more persistent (stay at lower levels for a longer period of time) compared to the Black unemployment rates as these would begin to increase more quickly once the effect of the stimulatory policy wears off. Therefore, policy makers should be aware of both the level of unemployment rates within each demographic group as well as the varying levels of persistence among these groups when assessing the effects of monetary and fiscal policies, affirmative action policies, and the impact of technological change on these unemployment rates. References Andrews, D.W., 1993. Exactly median-unbiased estimation of first order autoregressive unit root models. Econometrica 61, 139–165. Carpenter, S.B., Rodgers, W.M., 2004. The disparate labour market impacts of monetary policy. Journal of Policy Analysis and Management 23, 813–830. Clark, K.B., Summers, L.H., 1981. Demographic differences in cyclical employment variation. Journal of Human Resources XVI, 61–79. Costantini, M., Sen, A., 2012. On the distribution of a perron-type innovational outlier unit root test for trending and breaking series. Journal of Statistical Planning and Inference 142, 1690–1697. Ewing, B.T., Levernier, W., Malik, F., 2005. Modeling unemployment rates by race and gender: a nonlinear time series approach. Eastern Economic Journal 31, 333–347.
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