The differential effects of output shocks on unemployment rates by race and gender.

Bradley T. Ewing (*)

William Levernier (+)

Farooq Malik (++)

This article employs a recently developed time-series econometric technique to examine the magnitude and persistence of unanticipated changes in real output on unemployment rates by race and gender. Through the use of generalized impulse response analysis, we measure the extent to which the behavior of unemployment rates of white males, black males, black females, and white females differ in response to real output shocks. The results suggest that, while real output growth reduces the unemployment rate of all demographic groups, the effect is larger and more persistent for blacks than whites and for males than for females. The findings are particularly important for understanding the demographic impacts of policy initiatives aimed at inducing changes in real output growth.

1. Introduction

The issues of unemployment and output are central to many macroeconomic policy debates. A major source of disagreement among policymakers deals with the maximum sustainable level of output growth that is consistent with the absence of inflation. When the economy's rate of output growth exceeds the maximum sustainable rate, there will be upward pressure on the economy's overall price level. Traditional macroeconomic theory emphasizes the role that tight labor markets play in this inflationary pressure. The commonly held belief is that, in a tight labor market, firms must bid workers away from other firms if they wish to expand the size of their workforce. Hence, labor costs in the economy will tend to rise. Since labor is a major input in the production of virtually all goods and services, an increase in labor costs without an accompanying increase in productivity will tend to increase the economy's overall price level. Conversely, when the economy contracts, labor costs in the economy will tend to fall, induc ing a downward movement in the economy's overall price level. The labor market is therefore linked to changes in economic activity and to changes in the economy's price level.

A common feature in many macroeconomic models is the connection between departures from the equilibrium rate of unemployment (i.e., the natural or normal rate) and the business cycle. These macroeconomic models suggest that unanticipated departures from a steady state in the output market should be related to departures of the actual unemployment rate from the normal rate. However, the economy's aggregate unemployment rate is actually a weighted average of the unemployment rates of various demographic groups. The rate of each demographic group is influenced by that group's flows into and out of unemployment. Since many of the factors that determine these flows have been found to differ by demographic group, it is expected that a given aggregate output shock may have differential effects on the unemployment rates of various groups.

This article focuses on how unanticipated changes in real output affect the unemployment rate of different demographic groups. We examine the time-series behavior of black male, white male, black female, and white female monthly unemployment rates over the January 1972-August 1999 period. Specifically, we estimate a vector autoregression (VAR) and then conduct simulations in the form of impulse responses to determine the extent to which each of these unemployment rates is affected by an aggregate output shock (i.e., an unanticipated change in aggregate output). We compare and contrast the magnitude and the persistence of these responses across the groups. Because the traditional impulse response function generated from a VAR is sensitive to how the researcher chooses to order the variables, with different orderings often giving vastly different results, we employ the recently developed generalized impulse response function (Koop, Pesaran, and Potter 1996; Pesaran and Shin 1998). This technique allows research ers to examine impulse responses that are robust to changes in ordering. In the following sections, we highlight the major literature that this article builds upon and then we discuss the basics behind the nature of the relationship between the unemployment rate and output. A discussion of the data, the methodology, and the results follows. The article closes with concluding remarks and policy implications.

2. Related Literature

A number of studies have examined racial differences in unemployment rates and in factors that may affect unemployment rates. Using data on displaced workers, Fairlie and Kletzer (1998) examine racial differences in job displacement over the years 1984-1992 and find that black males experienced greater rates of job displacement and lower rates of reemployment than white males. Petterson (1998) uses data from the National Longitudinal Survey of Youth for the 1979- 1986 period to examine the reservation wages of black males compared with those of white males and, contrary to earlier research, argues that these differences do not explain much (if any) of the racial employment gap. Keith and McWilliams (1995, 1999) document differences in job mobility between men and women as well as differences in the degree of on-the-job search.

While much research has focused on recent differences in the unemployment rates of blacks and whites, Sundstrom (1997) finds evidence that such a gap existed in urban areas of the United States before 1940. He finds that, as blacks entered urban labor markets during the Great Migration from the rural South to the urban North, their probability of being unemployed exceeded that of similarly qualified whites. He further finds that differences in human capital and other personal characteristics explain the racial unemployment gap in the South but explains less than half the gap in the North.

One possible reason that there exists a racial difference in unemployment rates is that there may be racial differences in employment opportunities or a racial difference in the quality of the job search by unemployed persons. Kaplan (2000) examines the distribution of employment opportunities in the Cleveland, Ohio, metropolitan area, focusing on how prevalent job opportunities are for persons residing in particular neighborhoods. He finds that residents in low- and moderate-income neighborhoods that are predominately black have substantially fewer job opportunities than residents in predominately white neighborhoods. He also finds that there are fewer opportunities in segregated neighborhoods than in integrated neighborhoods and that there is less access to blue-collar jobs in predominately black neighborhoods than in other types of neighborhoods. Stoll and Raphael (2000) examine racial differences in spatial job search patterns in the Los Angeles metropolitan area. They find that the spatial job search qua lity is lower for blacks than for whites and that blacks tend to search for jobs in areas with lower employment growth than whites.

Bisping and Fain (2000) examine the affect of affirmative action on the unemployment rates of white males, white females, nonwhite males, and nonwhite females. Using a vector autoregressive model (VAR) and estimating responses with a cumulative impulse response function (CIRF), they estimate the effect that an unemployment rate shock to one demographic group has on the unemployment rates of the other three demographic groups. From this, they draw inferences about the demographic order of the job queue. They find that, before affirmative action, the order of the job queue was white males, white females, nonwhite males, and nonwhite females (i.e., white males are the most likely to be hired, white females the next most likely, and so on). After affirmative action was implemented, the order was white males and white females being equal or nearly equal, nonwhite females, and nonwhite males.

Bartlett and Haas (1997) contend that the natural rate of unemployment varies by demographic group. They argue that an economic policy geared toward changing the aggregate natural rate could, therefore, have positive effects on the unemployment situations of some groups while having adverse effects on other groups. Schwartzman (1997) documents the effects of government policies on the unemployment rate of black males over the last half century. Fairlie and Sundstrom (1999) use Census Bureau microdata from 1880 to 1990 (exclusive of 1920 and 1930) to examine the racial unemployment rate gap and, through the use of decomposition analysis, they uncover three trends. First, black gains in human capital (e.g., education) have helped reduce the gap. Second, since World War II, regional shifts in the economy, mostly the migration of blacks from the rural South, have attributed to a widening of the gap. Third, relative decreases in demand for less skilled workers have added to the gap since 1970.

The time-series relationship between aggregate output and the aggregate unemployment rate is examined by Evans (1989) using VARs and employing innovation accounting techniques. Evans documents the relationship and provides some evidence to suggest a persistent effect of output shocks on aggregate unemployment consistent with what is to be expected by Okun's Law.

While a number of studies examine the aggregate output-unemployment rate relationship, few look specifically at the effects of output changes on the unemployment rates of various demographic groups. Hyclak and Stewart (1995) examine the effects of changes in aggregate demand on unemployment rates by demographic group using establishment-level data and longitudinal/panel data techniques. They find that unemployment rates of blacks are significantly more responsive to demand growth than unemployment rates of whites. A time-series analysis by Lynch and Hyclak (1984) finds that unemployment rates of blacks and males are more adversely affected by downturns in the economy than the rates of whites and females. The latter article is based on the relationship spelled out by Okun's Law. The present article fills a gap in the literature by using advanced time-series techniques to study the question posed by Lynch and Hyclak (1984) about differential effects of output shocks on unemployment rates of various demographic groups.

3. A Brief Digression on the Equilibrium Rate of Unemployment

In the absence of macroeconomic shocks, the unemployment rate that the economy tends to gravitate toward is the equilibrium rate of unemployment. This natural rate can be thought of as the normal rate of unemployment, or the baseline. When the economy is at its equilibrium unemployment rate, two conditions will exist:

1. The flow of employed workers into unemployment and not-in-the-labor-force status will equal the flow of unemployed workers into employment and not-in-the-labor-force status.

2. The flow of non-labor-force participants to the labor force equals the flow of workers from the labor force to not-in-the-labor-force status.

To mathematically derive the above equilibrium conditions, we develop a model that describes the stock-flow analysis of Barron, Lowenstein, and Lynch (1989). To derive the first condition for the equilibrium unemployment rate, define [alpha] to be the fraction of employed workers who become unemployed each month; define [beta] to be the fraction of unemployed workers who become employed each month; define U to be the number of workers employed at the beginning of each month; define U to be the number of workers unemployed at the beginning of each month; define [pi] to be the fraction of nonparticipants who enter the labor force each month but who don't become employed during the month; define K to be the number of individuals not participating in the labor force each month; and define [[eta].sub.u] to be the fraction of unemployed workers who drop out of the labor force each month. The first equilibrium condition, that the flow from unemployment to employment and not-in-the-labor-force status equals the flow from employment to unemployment and not-in-the-labor-force status, can be written as

[alpha]N + [pi]K = ([beta] + [[eta].sub.u])U. (1)

The second condition states that the number of nonparticipants entering the labor force (some who become employed and some who become unemployed) equals the number exiting the labor force (from the ranks of both the unemployed and employed). If we let denote the fraction of employed workers who leave the labor force each month and p denote the fraction of the nonparticipants who enter the labor force each month as employed, then in equilibrium,

[pi]K + [rho]K = [[eta].sub.u]U + [[eta].sub.e]N. (2)

The term [pi]K + [rho]K gives the total number of nonparticipants entering the labor force, while [[eta].sub.u]U + [[eta].sub.e]N gives the total flow of labor force participants out of the labor force. The overall equilibrium condition is obtained by solving for K in Equation 1, solving for K in Equation 2, and then equating. This process yields

Solving Equation 3 for the equilibrium unemployment rate, U/L, where L = N + U, yields

([alpha][rho] + [alpha][pi] + [pi][[eta].sub.e])N = U([rho][beta] + [rho][[eta].sub.u] + [pi][beta]). (3)

[u.sup.*] = ([pi][[eta].sub.e] + [alpha]([rho] + [pi]))/[[pi][[eta].sub.e] + [alpha]([rho] + [pi]) + [beta]([rho] + [pi]) + [rho][[eta].sub.u]].

The six parameters in the above equation all affect the equilibrium unemployment rate. The comparative static analysis (1) implies that whenever more nonparticipants enter the labor force with jobs (high [rho]), the equilibrium unemployment rate falls. Likewise, the equilibrium unemployment rate decreases as the fraction of unemployed workers who become employed each month increases (high [beta]) and as the fraction of unemployed workers who drop out of the labor force increases (high [[eta].sub.u]. Conversely, if a higher proportion of nonparticipants enter the labor force as unemployed (high [pi]), then [u.sup.*] increases. (2) Also, the equilibrium unemployment rate increases as the fraction of employed workers that leave the labor force each month increases (high [[eta].sub.e]) and as the fraction of employed workers that becomes unemployed each month increases (high [alpha]).

One point to note is that the labor force drop-out rate of employed workers, [[eta].sup.*], plays a role in determining [u.sup.*]. If this rate differs by demographic group, then the unemployment rate will also vary by demographic group. There is no a priori expectation about whether [[eta].sub.e] is likely to fall or rise during a recession. However, it is likely that the five other parameters ([rho], [pi], [alpha], [beta], [[eta].sub.u]) are sensitive to current macroeconomic conditions. Typically, the labor market is characterized by higher values of [rho] and [beta] during an economic expansion, while recessions are associated with higher values of [pi], [alpha], and [[eta].sub.u]. For example, during a recession, there are typically a number of layoffs, which causes a to rise and [beta] to fall relative to their normal values. Together, these parameter changes work to increase the unemployment rate during a recession. The opposite is true during a period of economic growth. Since the equilibrium unemploy ment rate for each demographic group is affected by the values of the above parameters for that particular group, any differences in these parameters among demographic groups can potentially lead to demographic differences in the response of the unemployment rate to changes in aggregate output. (3)

4. Unemployment Rates and Demographic Groups

As discussed above, a particular demographic group's unemployment rate may be high for any number of reasons. For example, Barron, Lowenstein, and Lynch (1989) suggest that, if unemployed workers in a group require an unusually long time to obtain employment after becoming unemployed (low [beta]) or if after becoming employed they have a high probability of becoming unemployed again (high a) or if they frequently quit their jobs to pursue non-labor-market activities (high [[eta].sub.e]), then the unemployment rate of the group will be high. (4)

Historically, blacks have been unemployed a larger percentage of the weeks during a typical year than whites, implying that the median duration of unemployment is higher for blacks than for whites. (5) This suggests that unemployed blacks face poorer job prospects than unemployed whites and that the unemployment rate of blacks is likely to be higher than that of whites (i.e., blacks have a low [beta]), ceteris paribus. Similarly, blacks could have higher unemployment rates because they have a higher probability of moving from employment to unemployment (i.e., a high [alpha] for blacks).

While the unemployment rate for females has been lower than that for males in some years, it has typically been higher for females. (6) One possible reason is that unemployed females face poorer job prospects than unemployed males (i.e., a low [beta] for females). On the other hand, since 1978, unemployed females have been unemployed a slightly smaller percentage of weeks than males, implying that the median duration of unemployment is somewhat less for females than males. This suggests that unemployed females may actually face better job prospects than unemployed males (i.e., a high [beta] for females). (7) A lower labor-force attachment (i.e., high [[eta].sub.e]) for females may also be part of the reason that females typically have higher unemployment rates than males. (8)

Several factors may cause the value for the [beta] parameter to vary across demographic groups and are noted by Barron, Lowenstein, and Lynch (1989). For example, the intensity of the job search by unemployed workers and their reservation wage influences [beta] and the average duration of unemployment. The expected duration of unemployment should depend negatively on search intensity and positively on reservation wage. Government policies, such as unemployment benefits (e.g., unemployment insurance), also affect search behavior by increasing or decreasing the marginal cost of an unsuccessful search (i.e., a search that doesn't yield a job offer that is accepted), which will affect reservation wages. Together, a low intensity search and a high reservation wage will decrease the probability of moving from unemployment to employment (lower [beta]). (9) If the reservation wage or the search intensity differs by demographic group, then the average unemployment duration and unemployment rate will also differ by gro up.

Kaplan (2000) and Stoll and Raphael (2000) also suggest reasons why the value of [beta] may be lower for some groups than for others. The spatial quality of an individual's job search and the availability of job opportunities within a certain distance of his home influence the duration of unemployment for the person. If the spatial quality of the job search is lower for some demographic groups than others (Kaplan 2000) or if the availability of job opportunities is less for some demographic groups than others because of residential segregation (Stoll and Raphael 2000), then the unemployment rate and the duration of unemployment will differ among demographic groups.

The success that people in a particular demographic group have in finding a job and their attachment to the labor force will also affect the equilibrium unemployment rate for the group. If blacks and females, for example, face more trouble in finding jobs when they first enter the labor force than whites and males (i.e., high [pi] and low [rho]) because of discrimination, residential segregation, or a lower investment in human capital, then the equilibrium unemployment rate for blacks and females will be higher than that for whites and males. If recessions lead to higher rates of exit from the labor force for some demographic groups than others (high [[eta].sub.u]), then the unemployment rates of different groups will likely vary during a recession, even if they're identical during nonrecessionary periods.

Historically, actual unemployment rates have differed across demographic groups, particularly by race and gender (see Table 1 and Figure 1). Taken together, differences in the underlying factors that comprise the model of unemployment discussed in the previous section can lead to vast differences in both the equilibrium and actual unemployment rate of each demographic group. Since the underlying factors [rho], [pi], [alpha], [beta], and [[eta].sub.u]), are expected to be sensitive to macroeconomic conditions, if an output shock affects these factors differently across demographic groups, we would not expect each group's unemployment rate to respond in precisely the same way to a given output shock. To examine this issue, we will determine how the magnitude and persistence of the unemployment rate for each demographic group is affected by an unanticipated change in real output. Before proceeding to the empirical analysis, however, we discuss the link between output and the labor market.

5. A Brief Digression on Okun's Law

A relationship between the output gap (i.e., departures from the full employment level of output) and the deviation of the actual unemployment rate from the natural rate (i.e., equilibrium rate) is summarized in Okun's Law as

[psi] = k(u - [u.sup.*]),

where u denotes the actual unemployment rate, [u.sup.*] denotes the equilibrium rate of unemployment, and [psi] denotes the output gap given by (Y - [Y.sup.*])/[Y.sup.*], where Y is real output and [Y.sup.*] is the full employment level of real output. According to Okun's Law, k < 0. Note that, when u = [u.sup.*] economy-wide output is equal to the full employment level of output.

Rearranging Okun's Law gives

u - [u.sup.*] = (1/k)[psi].

In equilibrium, u = [u.sup.*] and Y = [Y.sup.*]. If [u.sup.*] and [Y.sup.*] are assumed to be constant (10) and normalizing [Y.sup.*] = 1 (which implies that in [Y.sup.*] = y = 0), then we can examine departures from equilibrium by focusing on

[DELTA]u = [lambda][DELTA]y,

where [lambda] < 0 and y is the natural logarithm of Y. A convenient and appealing way to examine the dynamics of this equation is through the use of impulse response functions (IRF) generated from a VAR. The appeal of the impulse response functions is that they measure how one series (e.g., [DELTA]u) responds to (standardized) shocks to another series (e.g., [DELTA]y), based on the deviation of the former series from its baseline (i.e., equilibrium) value. The IRF then allows one to examine both the magnitude and persistence of the response. The VAR technique has the additional advantage of treating all the variables in the model as endogenous, consistent with the treatment of output and unemployment outlined above.

6. Data

The data for this study include monthly unemployment rates (seasonally adjusted) for persons age 20 and over for black males (UBM), white males (UWM), black females (UBF), and white females (UWF). These data are obtained from the U.S. Bureau of Labor Statistics' Employment and Earnings (various issues). The measure of output growth is the growth rate of the industrial production index, obtained from the Federal Reserve Economic Database (FRED). (11) The sample consists of 332 monthly observations over the period January 1972-August 1999.

The first-difference of each unemployment rate series is used as the measure of unemployment rate change, as these were found to be stationary while the levels were not. (12) Table 1 provides descriptive statistics for the unemployment rate for each of the four demographic groups examined in this study. Note that the mean unemployment rate for blacks is higher than that for whites for both males and females. Also note that the standard deviation of the unemployment rate is higher for blacks than for whites, regardless of gender, and it is lower for females than for males within race. (13) These patterns can also be clearly seen in Figure 1, which plots the unemployment rates for white males, black males, white females, and black females. These rather large differences in unemployment rates by race and gender motivate an examination regarding whether the unemployment rate for each demographic group responds differently to a shock to aggregate output.

7. Empirical Methodology

One way to examine the dynamic relationship among economic time series is to estimate a VAR model and then conduct impulse response analysis (Sims 1980). However, this traditional method has been criticized for what is called the orthogonality assumption because results from impulse response analysis may differ markedly d depending on the ordering of the variables in the VAR (Lutkenpohl 1991). An alternative to the orthogonalized impulse response function (OIRF) has recently been developed by Pesaran and Shin (1998) and Koop, Pesaran, and Potter (1996). This technique is called the generalized impulse response function, and it is invariant to the ordering of the variables in the underlying VAR. Unlike the orthogonalized version proposed by Sims (1980), the generalized method does not impose the constraint that the underlying shocks to the VAR model are orthogonalized before impulse responses are computed. (14) As a result, inferences based on generalized impulse responses are robust to changes in the ordering of the variables in the VAR while those from orthogonalized responses are not.

The ensuing discussion briefly outlines the methodology developed by Pesaran and Shin (1998) as it is described in Pesaran and Pesaran (1997) (15) and is meant to provide a brief summary of the generalized impulse response analysis as it applies to the VAR model we estimate. An impulse response function traces out the effect of shocks at time t on the expected future values of the variables in the system. Two types of impulse response functions can be computed from the VAR: the traditional orthogonalized impulse response function (Sims 1980) and the recently developed generalized impulse response function of Pesaran and Shin (1998) and Koop, Pesaran, and Potter (1996). To facilitate our discussion of the impulse response analysis, we rewrite the VAR in its infinite moving average representation,

[x.sub.t] = [summation over ([infinity]/j=0)] [A.sub.j][u.sub.i-j],

where [x.sub.i] is an m x 1 vector of the variables under investigation, [A.sub.j] = [[PHI].sub.1][A.sub.j-1] + [[PHI].sub.2][A.sub.j-2] + ... + [[PHI].sub.p][A.sub.j-p], j = 1, 2, ..., with [A.sub.0] = [I.sup.m] and [A.sub.j] = 0 for j < 0. (16)

Let us denote the generalized impulse response function (G) for a shock to the entire system, [u.sup.0.sub.t], as (17)

[G.sub.s](N, [u.sup.0.sub.t], [[OMEGA].sup.0.sub.r-1]) = E([s.sub.t+N]\[u.sub.t] = [u.sup.0.sub.t], [[OMEGA].sup.0.sub.t-1]) - E([S.sub.t+N]\[[OMEGA].sup.0.sub.t-1]),

where the history of the process up to period t - 1 is known and denoted by the information set [[OMEGA].sup.0.sub.t-1]. Assume [u.sub.t] ~ N(0, [SIGMA]) and E([u.sub.t] \ [u.sub.jt] = [[delta].sub.j]) = ([[sigma].sub.1j], [[sigma].sub.2j],... , [[sigma].sub.mj])' [[sigma].sup.-1.sub.jj][[delta].sub.j], where [[delta].sub.j] = [([[sigma].sub.jj]).sup.-1/2] denotes a one standard error shock. Further, [e.sub.t] is m x 1, with the ith element equal to one and all other elements equal to zero. The generalized impulse response function for a one standard deviation shock to the jth equation in the VAR model on the jth variable at horizon N is

[G.sub.ij,N] = ([e'.sub.j][A.sub.N] [SIGMA] [e.sub.i])/[([[sigma].sub.ii]).sup.1/2], i, j = 1,2, ... , m.

Pesaran and Shin (1998) note that "the generalized impulse responses are invariant to the reordering of the variables in the VAR, but this is not the case with the orthogonalized ones" (p. 20). They further caution the researcher about using orthogonalized impulse responses since there is typically no clear guidance as to which of many possible parameterizations to employ. "In contrast, the generalized impulse responses are unique and fully take account of the historical patterns of correlations observed amongst the different shocks" (p. 20). (18)

As mentioned above, we use the first-differences of UBM, UWM, UWF, and UBF and the growth rate in industrial production (GIP) in the VAR estimations to generate the generalized impulse responses in the empirical analysis. We denote the first-difference operator by D.

We begin by estimating a vector autoregression containing five equations corresponding to the five variables GIP, DUBM, DUWM, DUWF, and DUBF in addition to a constant term. The optimal order of the VAR was determined to be six lags based on Akaike's information criterion and likelihood ratio tests. As discussed above, one of the major concerns and potential drawbacks of using orthogonalized impulse responses is that results are likely to be sensitive to the ordering of the variables. Indeed, if the shocks to the respective equations in a VAR are contemporaneously correlated, then the orthogonalized and generalized impulse responses may be quite different. Moreover, a reordering of the variables may lead to a number of markedly different conclusions based on the orthogonalized responses. If, on the other hand, shocks are not contemporaneously correlated, then the two types of responses would probably not be substantially different and the orthogonalized responses would probably be relatively insensitive to a r eordering of the variables. The results of a log-likelihood test indicate that the individual equations that comprise the VAR are contemporaneously correlated; thus, we use generalized impulse response functions rather than orthogonalized impulse responses to examine the responses of unemployment rates to unanticipated changes in real output. (19)

It should be noted that the unemployment rate responses to an output shock could, in fact, change over time. Bisping and Fain (2000) find evidence that the relative unemployment rate responses of various demographic groups are different in the period before affirmative action laws were enacted than in the period after they were enacted. Since affirmative action laws were first enacted in May 1968, the entire period covered in our study was subject to affirmative action laws. Potentially, other factors, such as the decline in union power or the emergence of the "new" economy, could also cause the unemployment rate responses to be different in recent years than they were in the past. (20)

8. Discussion of Results

Figure 2 presents the generalized impulse response functions to a shock in real output growth for each of the unemployment rates in the five-equation VAR. The VAR contains six lags and a constant. Panels A, B, C, and D show how the unemployment rates for white females, white males, black males, and black females, respectively, respond to the output shock. These graphs trace out the response of changes in each of the unemployment rates to a positive one standard error shock to real output growth. Responses are plotted out to the 18th month. Note that, in all cases, the unemployment rate initially deviates from the baseline level following the output shock but eventually subsides, returning to its equilibrium value.

Although the initial impact is actually larger in absolute value for white females than for black females, the response of black females is larger in magnitude once lags are considered and it is also more variable and lasts longer than the response of white females. The response of black females ranges from -0.062 after the first month to 0.03 at a two-month horizon. The maximum response of white females is found to be -0.057, which occurs at a one-month horizon. The output shock effect dies out after about 6-7 months for white females but lingers on to around 10 months for black females. Thus, an unanticipated increase in the economy's real output tends to reduce the unemployment rate of black females more strongly than that of white females.

The initial impact of an output shock on black males and white males is about the same. However, as with females, the black unemployment rate is affected much more than the white unemployment rate in terms of magnitude, especially at periods several months removed from the shock. The variability of the black male response is also much greater than that of the white male response. The output shock has a much more persistent effect on black males than on white males, with the effect dying Out around 13 months for black males, as compared with around 9-10 months for white males. The response of black males is greatest after one month, at about -0.137. For white males, the maximum response is -0.078 at initial impact. Thus, an unanticipated increase in the economy's real output tends to reduce the unemployment rate of black males more strongly than that of white males. (21)

The generalized impulse responses presented here indicate that an unanticipated change in the growth of real output has a contemporaneous impact on the unemployment rates of each of the four demographic groups examined in this study. However, the overall magnitude of the shock is much larger and more persistent for blacks than for whites and for males than females. (22)

9. Concluding Remarks and Policy Implications

This article has examined the effect that unanticipated changes in real output growth have on the unemployment rate of various demographic groups. The article adds to the literature by documenting these findings and provides information to policymakers regarding how the unemployment rates of different demographic groups are likely to respond to policy actions and events that affect output growth.

Our results indicate that male unemployment rates experience a stronger and more persistent response to an unanticipated output shock than female unemployment rates. In addition, black unemployment rates experience a greater and more persistent response to an unanticipated output shock than white unemployment rates. As such, an unanticipated output shock affects different demographic groups differently, which supports the findings of Lynch and Hyclak (1984) and Hyclak and Stewart (1995).

Although the purpose of the study is not to determine the factors that cause the unemployment rate response to an output shock to be stronger for males than females and to be stronger for blacks than whites, we can offer some possible reasons why this is the case. (23) One possible reason is that male and black workers may be disproportionately employed in cyclically sensitive industries compared with female and white workers. As such, when the economy experiences a contraction, the unemployment rates of males and blacks would be more affected than the unemployment rates of females and whites. Conversely, if blacks are disproportionately employed in cyclical industries, when the economy expands, there will tend to be a relatively greater increase in the hire rate of blacks than whites, leading to a larger reduction in the unemployment rate for blacks than for whites.

A second possible reason is that nonworking blacks may require a longer search to obtain employment than whites. This could be due to a variety of reasons, such as job discrimination against blacks, lower human capital investment by blacks, blacks having less developed job networks than whites, or blacks facing more limited job opportunities or conducting a lower quality spatial job search than whites because of residential segregation. When the economy contracts, causing previously employed workers to become unemployed, it may take blacks longer to find a replacement job than whites.

A possible explanation for the weaker unemployment rate response by females is that they may have a higher propensity to exit the labor force than males when they become unemployed. This is most likely to be true for a married female whose husband is the family's primary wage earner. When such women exit the labor force, they are no longer counted as unemployed. If females have a higher propensity to exit the labor force than males during a recession, the unemployment rate of females will tend to be less affected by a recession than the unemployment rate of males.

While the reduced-from nature of the VARs does not indicate which of the factors that affect the unemployment rate are responsible for the differential responses to output changes, the results do have important and practical implications. In implementing macroeconomic policies, government and Federal Reserve policymakers should be aware of the demographically diverse effects on the unemployment rate that fiscal or monetary action is likely to have. As expected, our results indicate that an expansionary (contractionary) policy will reduce (increase) the unemployment rate for all four demographic groups. Fiscal and monetary policies will have a stronger and more persistent effect on the black unemployment rate than the white unemployment rate and on the male unemployment rate than on the female unemployment rate, however. Thus, a particular expansionary (contractionary) policy is likely to reduce (increase) the unemployment rate of blacks more than that of whites and is likely to reduce the unemployment rate of males more than females.

The findings regarding the unemployment rate response of different demographic groups to an output shock imply that an economic policy aimed at a particular group may have some secondary effects. An economic policy aimed at reducing the female unemployment rate, for example, might also reduce the unemployment rate gap between blacks and whites since the reduction in the unemployment rate of black females will be greater than that of white females. As such, the black unemployment rate will decrease by more than the white unemployment rate, even though the policy was aimed toward females. In order to insure that economic policies have the desired effects, our findings suggest that government policymakers must consider the different demographic responses of unemployment rates to changes in output when constructing these policies.

(*.) Department of Economics, Texas Tech University, Lubbock, TX 79409-1014, USA; E-mail [e-mail].

(+.) Department of Finance and Economics, Georgia Southern University, Statesboro, GA 30460-8151, USA; E-mail [e-mail]; corresponding author.

(++.) Department of Economics, Pennsylvania State University, Berks-Lehigh Valley College, Reading, PA 19610, USA.

An earlier version of this article was presented at the 2000 Southern Economic Association Annual Conference and at the Georgia Southern University Economics Seminar Series.

The authors would like to thank the participants for their helpful suggestions. The authors would also like to thank Jamie Kruse, Tom Steinmeier, Kristen Keith, and two anonymous referees for insightful comments that greatly improved the quality of the article. The standard disclaimer applies.

Received May 2000; accepted June 2001.

(1.) An appendix showing the comparative static analysis is available from the authors on request.

(2.) Bartlett and Haas (1997) found higher natural rates for females and blacks during the 1980s, when more nonparticipants entered the labor market without jobs.

(3.) While it is beyond the scope of this article, future research could address such things as how the various parameters (e.g., [pi]) behave and what the sign of [delta]u*/[delta][pi] is during periods when the equilibrium conditions don't hold. Such research would probably involve a dynamic structural model of the determinants of key parameters in the transition equations.

(4.) The seminal article on this subject is Hall (1982).

(5.) The percent of weeks individuals 18-34 years old were unemployed during 1978-1998 for whites was 4.5%, compared with 10.2% for blacks. The percentage of weeks unemployed was higher for blacks in all education classes. See U.S. Bureau of Labor Statistics, National longitudinal surveys, (http://stats.bls.gov/news.release/n1soy.t02.htm).

(6.) During the 1972-1999 period, the period covered in this study, the average annual unemployment rate of females that are 20 years of age or older has been lower than the unemployment rate of males that are 20 years of age or older only six times (1982, 1983, 1990, 1991, 1992, and 1993). The unemployment rates were equal in 1987 and 1994 (U.S. Bureau of Labor Statistics, Labor farce statistics from tire current population survey [http://www.bls.gov/webapps/legacy/cpsatab1.htm]).

(7.) The percent of weeks individuals 18-34 years old were unemployed during 1978-1998 for females was 4.7%, compared with 6.0% for males. The percentage of weeks unemployed was higher for males in all education classes. See U.S. Bureau of Labor Statistics, National longitudinal surveys, (http://stats.bls.gov/news.release/nlsoy.t02.htm).

(8.) For evidence on this, see Marston (1976) and Hall (1982).

(9.) See Barron and Mellow (1979, 1981).

(10.) What is required is that [u.sup.*] and [Y.sup.*] are intertemporally stable. It has been argued that the natural rate has changed or is changing over time. In empirical work, this problem is often dealt with by detrending the data. However, as reported later, the unemployment rates used in this study are found to have unit roots suggesting that changes in the unemployment rate series are stationary. An easy way to interpret this is to consider a particular steady-state condition in which the constant rates of change are zero (i.e., the baseline in the VAR is zero). Models similar to those in this section can be found in Romer (1996) and McCallum (1989).

(11.) The growth rate of the industrial production index is used instead of the growth of real GDP because the industrial production index is available on a monthly basis while GDP data are available on a quarterly, but not monthly, basis. However, Robertson and Tallman (1999) describe a technique that can be used when a researcher wishes to make forecasts on a monthly variable but some of the variables he has in his model are reported on a monthly basis (such as the unemployment rate) while others are reported on a quarterly basis (such as real GDP). In this technique, one can regress quarterly real GDP on a variety of explanatory variables. The coefficients from this regression can then "be used to construct estimates of monthly real GDP in a way that ensures that the quarterly average of the resulting monthly GDP estimates equals the corresponding quarterly observation of GDP" (p. 6). We have chosen not to estimate monthly GDP and to use industrial production instead because use of such an estimate in a ti me-series model may be subject to the generated regressor problem (Pagan 1984).

(12.) This is consistent with Payne, Ewing, and George (1999), who found the aggregate U.S. unemployment and state unemployment rates to have unit roots. The augmented Dickey--Fuller test statistics for the levels of the unemployment rates were -1.02 for black females, -1.87 for black males, -1.57 for white females, and -2.82 for white males, none of which were significant at the 5% level. The augmented Dickey--Fuller test statistics for the first-differences of the unemployment rates were -9.41 for black females, -7.88 for black males, -6.60 for white females, and -5.13 for white males, all of which were significant at the 1% level.

(13.) One characteristic of the standard deviation of a variable is that it tends to increase as the mean of the variable increases. A measure that controls for the size of the mean is the coefficient of variation. We find that the coefficient of variation for males is larger than that of females. Further, we find the coefficient of variation is approximately the same for white males as for black males. Also, the coefficient of variation for white females is only slightly higher than that for black females.

(14.) Pesaran and Shin (1998) present an empirical illustration that shows how results may differ between the orthogonalized and generalized impulse response functions.

(15.) For a more detailed discussion, including proofs, see Pesaran and Shin (1998). Additional background material on the development of generalized impulse response analysis can be found in Koop, Pesaran, and Potter (1996). The description of Pesaran and Shin (1998) in Pesaran and Pesaran (1997) was actually a description of Pesaran and Shin (1998) when it was still in the working paper stage.

(16.) The traditional orthogonalized impulse response employs a Cholesky decomposition of the positive definite m x m covariance matrix, [SIGMA] of the shocks ([u.sub.t]) For a description of the Cholesky decomposition, see Patelis (1997). The generalized version does not impose this restriction.

(17.) In the interest of brevity, we do not discuss the orthogonalized impulse response function, as its use is widespread and its derivation is well known.

(18.) The generalized and orthogonalized impulse responses coincide only for the case where the covariance matrix is diagonal.

(19.) "For comparison purposes, we computed orthogonalized impulse responses and they were, in fact, quite different from the generalized responses reported in this article. The OIRFs are available upon request.

(20.) The stability of the estimated parameters in each of the unemployment rate equations was examined using cumulative sum of squares (CUSUM) tests. No evidence of parameter instability was detected.

(21.) It should be noted that an othogonalized or generalized impulse response function of the unemployment rate to an output shock for a particular demographic group is necessarily symmetric. Thus, the magnitude (in absolute value) and persistence of the unemployment rate response will be the same for an increase in real output as it will be for an equivalent decrease in real output. The direction of the unemployment rate response will, of course, differ between an output increase and an output decrease. Consequently, we can make an inference about the influence on the different unemployment rates arising from contractions in the economy based on the results of the impulse responses generated from an expansionary shock.

(22.) Generalized impulse responses were also computed and compared to determine if significant relationships existed among the unemployment rates. The findings were roughly consistent with the theory of job queuing proposed by Bisping and Fain (2000), with the ordering of job queue being white male, white female or black male, and black females. Specifically, we found that shocks to white male unemployment were transmitted to each of the other groups, exhibiting some persistence and creating some volatility. Shocks to white female unemployment were only contemporaneously correlated with the unemployment rates of white males and black females but not that of black males. Shocks to black male unemployment had a negligible effect on white female unemployment, with a slight lag, while shocks to black female unemployment had no impact on either white male or black male unemployment but were contemporaneously correlated with white female unemployment. These impulse responses are available on request.

(23.) An additional analysis was conducted in order to determine if the racial differences in the response of the unemployment rate could be traced to differences in the effect of an output shock on the employment ratio, the duration of unemployment, and the labor force participation rate. Four separate VARs were estimated, corresponding to each demographic group, that included changes in the group's unemployment rate, employment ratio, participation rate, duration of unemployment, and industrial production. Generalized impulse responses were computed to examine the responses to output shocks. In all cases, the participation rate failed to exhibit significant responses. However, changes in the employment ratio responded positively and significantly, with the least persistence being for white males and the greatest persistence for black females. The response of unemployment duration occurred with a lag and was similar in each VAR. The responses of the unemployment rates to output shocks were virtually identica l to those reported in the text.

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[Figure 1 omitted]

[Figure 2 omitted]

Table 1

Descriptive Statistics of Unemployment Rates by Race and Gender
(January 1972-August 1999)

                          Black  White    Black    White
                          Males  Males  Females  Females

Mean                      10.95   4.83    10.99     5.15
Maximum                   20.70   9.00    18.20     8.30
Minimum                    5.20   2.70     6.40     3.20
Standard deviation         3.04   1.32     2.26     1.12
Coefficient of variation  27.76  27.32    20.56    21.75

All unemployment rates are for workers 20 years of age and older and are
seasonally adjusted. The coefficient of variation is expressed in
percentage terms. Data are obtained from the U.S. Bureau of Labor
Statistics.