Federal Reserve policy and inflation dynamics in the U.S.: Racial inequalities in unemployment outcomes

Transcription

1 Federal Reserve policy and inflation dynamics in the U.S.: Racial inequalities in unemployment outcomes James Heintz (University of Massachusetts, Amherst) and Stephanie Seguino (University of Vermont) October 2011 Abstract This paper explores the relationships behind previous findings that Federal Reserve interest rate policies have a larger impact on black unemployment compared to white unemployment. Most earlier studies employ a VAR methodology, which does not, however, permit a structural analysis of key relationships. This paper accounts for the endogeneity of unemployment, inflation, and the federal funds rate by estimating a system of structural equations with quarterly data from 1973 to We find that the higher the black/white unemployment rate ratio, the less responsive interest rate policy is to unemployment. Further, our evidence indicates that a higher relative black unemployment rate reduces the economy-wide sacrifice ratio. 1

2 I. Introduction This study examines the distributional effects of interest rate policy in the U.S. by race, focusing on black-white unemployment rates. We evaluate the determinants and effects of changes in the federal funds rate over the period 1973 to 2008 with an emphasis on race-based differences in unemployment rates. Given persistent racial inequalities in the U.S. and the findings of earlier studies, we hypothesize that monetary policies, which are potentially costly in terms of reducing employment opportunities, have differential impacts on employment of the black population relative to the white population. To explore this possibility in detail, we estimate a four-equation empirical model to investigate whether racial dynamics play a role with regard to inflation, unemployment, and policy interest rates. Central banks across the globe have steadily shifted their focus in recent decades away from attempting to influence real economic activity to an almost exclusive concern with longer run price stability, based on the argument that low inflation creates the necessary conditions for sustainable economic growth. Concerns have been expressed over the distributional consequences of this approach, with workers bearing a heavy cost due to increased unemployment as policy interest rates rise (Ball 1993). These distributional effects are complicated by the dynamics of race and gender stratification in labor markets. Several studies have explored the racial impact of monetary policy in the U.S. Results obtained in studies using a VAR methodology consistently find evidence that the ratio of black to white unemployment rates rises in response to a monetary contraction (Abell, 1991; Thorbecke, 2001; Carpenter and Rodgers, 2004). Seguino and Heintz (forthcoming) adopt a single-equation panel data 2

3 approach, exploring the effect of monetary policy on black/white unemployment rate ratios at the state level, incorporating the effect of state-level differences in black population shares. These studies illuminate the importance of moving beyond macroeconomic aggregates, including aggregate unemployment rates, in order to understand determinants of intergroup inequality. In theory, monetary policy effects should not differ by race. However, there are many reasons why we might observe differences in employment outcomes in response to monetary policy. These include: differences in educational attainment which are correlated with the risk of job loss (Blanchard and Katz, 1997; Thorbecke, 2001), concentration of black employment in interest-rate sensitive industries, and prevailing social norms and behavior which protect job opportunities among the dominant racial group. In general, when job opportunities either become scarcer or more abundant in response to macroeconomic policies, we would expect distributive dynamics to influence the relative impact of macroeconomic policies on different racial and ethnic groups. Racial job segregation and persistent evidence of employer discrimination can lead to unequal outcomes, as a number of studies demonstrate (Stratton 1993, Lindley 2005). A limitation of previous research on racial effects of monetary policy, however, is that earlier studies are unable to disentangle the dynamic relationships among the endogenous variables in the models. The institutional role of the Federal Reserve in contributing to unequal racial unemployment rates in these studies emerges as incidental rather than intentional. This is because the Federal Reserve's monetary policies, although 3

4 shown to affect the overall level of unemployment, do not directly determine the racial distribution of jobs at the micro level. Critical race theory has illuminated the complex ways in which racial inequality is linked to institutional structures that embed biases in a variety of settings. These biases are often implicit, and need not represent a conscious discriminatory intent. Is there any evidence the institutions that govern the setting of interest rate policy in the U.S. exhibit such biases? One way to explore the institutional role of the Federal Reserve in contributing to racial differences in unemployment rates, adopted in this paper, is to estimate a system of equations for all endogenous variables, assessing the Federal Reserve's reaction function in response to changes in the black/white unemployment rate ratio. 1 That is, the nature of Phillips curve-type dynamics or the reaction function of the Federal Reserve (modeled, for example, as a Taylor rule) can be estimated directly. In this paper, we estimate a four-equation structural model, which allows us to identify these specific relationships while addressing the endogeneity of the key macroeconomic variables. II. Model Specification Our empirical model consists of four equations: a Phillips curve, a Taylor Rule-type reaction function for the Federal Reserve, an unemployment function, and an equation which captures the relationship between our macroeconomic variables and the ratio of black to white unemployment rates. We present the specification of each of these equations below. Note that the lag structure of each of these specifications represents the 1 Galbraith, Giovannoni, and Russo (2007) pursue a different but related path, exploring the asymmetric responsiveness of the Federal Reserve to increases vs. decreases in the aggregate unemployment rate, and the impact of the Federal Reserve's policies on pay inequality. 4

5 lag structure that yielded statistically significant estimates in the actual estimations. Of course, there is no reason to place restrictions on the lag structure in the basic model. We do so here only for clarity of our exposition. The Phillips Curve (1) π t = β o + β 1 π t 1 + β 2 π t 2 + β 3 π t 3 + β 4 π Oil t + β 5 U t + β 6 R BW BW t + β 7 ( U t * R t )+ε 1 t. In the above, π t is the annualized inflation rate in period t, π Oil is the quarterly percent change in the cost of crude oil to capture important supply-side shocks over the period, U is the unemployment rate across the entire labor force, R BW is the black/white unemployment rate ratio, and ε 1 is the random error term. 2 With the exception of the inclusion of the black-white unemployment rate ratio, the above Phillips curve represents a common specification found in the literature, one that Robert Gordon (1997) calls the triangle model in which inflation is a function of inertial factors, aggregate demand, and supply-side shocks. We can think of the coefficient on the unemployment variable as an indicator of the sacrifice ratio, the loss in terms of output or employment of lowering inflation. Our innovation is to include as explanatory variables (1) the black-white unemployment rate ratio and (2) an interaction term with the overall level of unemployment which allows the black/white unemployment rate ratio to affect the slope of the Phillips curve. The inclusion of the black/white unemployment rate ratio with the overall unemployment rate 2 In the specifications described here, the lag lengths correspond to the estimates presented in the results section of the paper. Models with alternative lag structures were estimated and these variations did not substantively change the results presented here. The coefficients on variables with longer lags than those presented here were not statistically significant. 5

6 allows us to examine whether the distribution of the unemployment between subordinate and dominant groups affects the observed shape of the Phillips curve and, therefore, any trade-off between inflation and unemployment. For example, a positive significant sign on the interaction term implies that increases in black unemployment relative to white unemployment reduce the tradeoff between inflation and changes in the economy-wide unemployment. Changes in the black/white unemployment rate ratio may affect the location of the Phillips curve in addition to its slope. For instance, a negative sign on the black-white unemployment ratio variable would indicate that inflation would be lower for a given level of unemployment when the unemployment ratio increases. Why might the black-to-white unemployment rate ratio affect the shape of a traditional Phillips curve? African Americans have been described as the 'last hired, first fired' in the U.S. labor market. This suggests that working age blacks constitute a residual pool of labor that employers can draw on when labor market conditions tighten. In this sense, surplus black labor may serve as a safety valve, which can mitigate inflationary pressures during periods of aggregate demand growth. The availability of this pool of labor depends, in part, on the relative unemployment rate. As the black-white unemployment rate ratio declines, so does the availability of this pool of labor relative to the economy as whole, and could potentially alter the trade-off between inflation and the general level of unemployment. The Federal Reserve's reaction function (Taylor Rule) (2) FFR t = α o + α 1 FFR t 1 + α 2 π t + α 3 U t + α 4 R t BW + α 5 U t * R t BW ( )+ε t 2. 6

7 In Equation (2), FFR represents the nominal federal funds rate and ε 2 is a random disturbance term. The other variables are defined as in Equation (1). The specification is based on John Taylor s (1991) original formulation. However, we assume that the Federal Reserve targets unemployment instead of responding to the GDP gap as an indicator of excess capacity, and we include a lagged federal funds rate variable to account for the possibility of interest-rate smoothing. Again, our principal innovation to the standard specification is to include the ratio of the black to white unemployment rates in an interaction term. This allows us to determine whether there is any evidence that central bank policy is sensitive to changes in the relative burden of unemployment between blacks and whites. We expect a negative sign on the economy-wide unemployment rate coefficient, but, given stratification dynamics in the US, potentially a positive coefficient on the interaction term, reflecting that the relative weight the central bank gives to inflation and unemployment when setting interest rate policy depends on the relative magnitude of black and white unemployment rates. Determinants of unemployment (3) U t = δ o +δ 1 U t 1 +δ 2 U t 2 +δ 3 ( FFR t π t )+ε 3 t. In Equation (3), L represents the population aged 16 to 24 as a share of the total working age population (aged 16+) and ε 3 is a random disturbance term. This exogenous explanatory variable is included to capture the impact of unemployment rates that vary across age groups, with youths having the highest rates of unemployment. In the above specification, the unemployment rate is also a function of the previous period s unemployment rate and the real federal funds rate. We expect a positive coefficient on 7

8 the real interest rate - a higher real federal funds rate will tend to raise the unemployment rate and therefore have a dampening effect on inflationary pressures. Determinants of the black-white unemployment rate ratio BW BW B W 4 (4) R γ + γ R + γ L + γ L + γ ( FFR π ) + ε. t = o 1 t 1 2 t 3 t 4 t t t The variables in Equation (4) are defined as in the other equations. In addition, L B is youth (16 to 24) share of the black working age population, L W is the youth share of the white working age population, and ε 4 is a stochastic error term. In our system of equations, the black/white unemployment rate ratio is a function of its own value in the previous period, the relevant youth population shares, and the real federal funds rate. Based on the findings of earlier studies, we expect a positive coefficient on the real federal funds rate with higher interest rates having a disproportionate impact on black unemployment rates relative to that of whites. III. Data and Estimation We use quarterly data from 1973Q1 to 2008Q4 to estimate the model. 3 Data are taken from the Federal Reserve Board of Governors (federal funds rate) and the Bureau of Labor Statistics (seasonally-adjusted unemployment rates, population shares, and consumer price index for all urban consumers). Quarterly inflation rates are calculated from the seasonally-adjusted consumer price index and expressed in terms of their annualized values. The refiner s acquisition cost (RAC) of crude oil from the U.S. Energy 3 Because of missing values for the refiners acquisition costs of crude oil, the econometric estimates were restricted to the period 1974Q1 through 2008Q4. 8

9 Information Administration is used to model inflationary shocks from global oil markets (π oil in Equation 1). Specifically, quarterly differences in the natural logarithm of the refiners acquisition costs are used for π oil. Unit root tests were performed on all of the variables over the full period using Augmented Dickey-Fuller and Phillips-Perron techniques (Appendix A). We are able to reject the null hypothesis of unit root process for all variables over the time period in question. We employed three estimation techniques: simple OLS, single-equation GMM estimates, and a multiple-equation GMM estimation. We include OLS estimates for comparison purposes in order to provide a sense of the extent to which instrumental variable estimation alters the estimated coefficients (for example, by potentially correcting for bias introduced by simultaneity). We include both single-equation and system GMM estimates to determine whether the system-wide specification yields distinct results for the coefficient estimates. On the one hand, systems estimation should be more efficient than single equation estimation. On the other, a misspecification problem in a single equation can affect all estimates in the multiple equation system. By comparing the two sets of estimates, we can determine whether significant differences exist. For the single- and multiple-equation GMM estimates, the unemployment rate, the inflation rate, the black-white unemployment rate ratio, and the federal funds rate are all assumed to be endogenous. Lagged values of endogenous variables are treated as predetermined for the purposes of estimation. The remaining variables are considered exogenous: the change in the log of the refiner s acquisition cost and the various youth population shares. We use the full set of exogenous instruments in the single- and 9

10 multiple-equation GMM estimates. In addition, because the unit root tests (see appendix) indicate some of the variables are trend stationary, we include a deterministic trend variable to help ensure the correct specification. Table 1 summarizes regression results. J-statistics to test for overidentifying restrictions in the single- and multiple-equation GMM estimations indicate we cannot reject the null hypothesis that the instruments can be treated as exogenous for the purposes of estimation. 4 The sets of estimates presented in the first three columns of Table 1 represent the OLS (Column 1), the single-equation GMM (Column 2), and the system GMM (Column 3) estimates. In the following discussion of the results, we focus on the system GMM estimator, pointing out differences with the single-equation GMM and OLS results where appropriate. Turning first to the Phillips curve equation, coefficients have the expected signs in all sets of estimates the OLS, GMM single equation, and GMM systems estimator. Specifically, changes in the price of crude oil have significant and positive impacts on inflation. There is evidence of inertial inflation dynamics, with statistically significant coefficient estimates on the lagged inflation variables. These results are consistent with the triangle model specification discussed above. The trend variable is negative and significant, suggesting the existence of a secular decline in inflation. This is not surprising since the unit root tests found that the inflation rate and the unemployment rate are trend stationary. 4 The J-statistic follows a χ 2 distribution with degrees of freedom equal to the number of instruments minus the number of parameters to be estimated. Critical values of the J-statistic at the 95% level are for the system GMM model. In the single equation GMM estimations, critical values are 9.49 for Phillips curve; for the Taylor rule and unemployment rate; and for the ratio of black to white unemployment rates. 10

11 The coefficient on the black/white unemployment rate ratio interacted with the unemployment rate is positive and significant, indicating that a higher black/white ratio of unemployment rates reduces the negative slope of the Phillips curve. This suggests that an unequal distribution of the costs of unemployment along racial lines, with the burden of black unemployment rising relative to white unemployment, is associated with a weaker trade-off between unemployment and inflation. In addition, the coefficient on the black/white unemployment rate ratio, distinct from the interaction term, is negative and statistically significant, suggesting that inflation will be lower for a given level of unemployment, the higher black unemployment is relative to white unemployment. Overall unemployment, therefore, will be associated with weaker inflationary pressures when the burden of that unemployment falls disproportionately on the black population. [Table 1 about here]. The coefficient estimates on the Taylor rule/federal Reserve reaction function also have the expected signs in all three sets of estimates. The nominal federal funds rate is raised in response to higher inflation and lowered in response to higher rates of unemployment. The coefficient on the ratio of black to white unemployment, interacted with the unemployment rate, is positive and significant. These results indicate that the Federal Reserve's responsiveness to unemployment is influenced by the ratio of black to white unemployment: the Federal Reserve is less responsive to higher unemployment (in terms of lowering the federal funds rate) when the burden of rising unemployment falls disproportionately on the black population. 11

12 In the equation modeling the determinants of unemployment, the estimated coefficients have the expected signs in all three sets of estimations. 5 The real federal funds rate has a statistically significant positive impact on the unemployment rate in the two sets of instrumental variable estimates - the system GMM and single equation GMM, but not in the OLS estimates. This suggests that instrumental variable estimation is necessary to identify the relationship between the real interest rate and unemployment when the federal funds rate and inflation are endogenous. A higher youth share of the population is associated with higher overall unemployment rates. Finally, the unemployment rate ratio equation results yield an estimated coefficient on the real federal funds rate, which is negative and not statistically significant in any of the model specifications. This runs counter to the findings of earlier studies, which have found a direct relationship between the policy interest rate and black-white unemployment rate differentials. This result also does not support the simplest interpretation of the hypothesis with which we began this study - that monetary policy should have an unequal impact on employment opportunities for blacks and whites. Our results do suggest that the relationship between the federal funds rate and the black/white unemployment rate ratio operates indirectly in ways that are captured by the Phillips curve and central bank reaction function estimates. We examine a variation on the model specification concerning the measurement of the interest rate variable. Some of the earlier studies which use a VAR methodology allow the nominal federal funds rate and the inflation rate to enter the empirical model 5 It might be argued the unemployment regression should include a measure of aggregate demand, which is, however, endogenous. The challenge is to find an instrument correlated with aggregate demand but uncorrelated with the error term. We ran these regressions with the University of Michigan s Consumer Sentiment Index, lagged one period, as a proxy for demand. Results were broadly similar and are available on request. 12

13 separately - rather than defining a real interest rate variable (see, for example, Carpenter and Rodgers, 2004). In the specification used in the first three sets of equations in Table 1, we estimate the effect of the real interest rate on the overall unemployment rate and on the black-white unemployment rate ratio. In these two equations, this effectively imposes a restriction on the coefficients for the nominal federal funds rate and the inflation rate to be of the same magnitude but opposite signs. We relax this restriction and introduce the nominal federal funds rate and the inflation rate as separate variables in the equations with the overall unemployment rate and the black-white unemployment rate ratio as dependent variables. We estimate this model using the system GMM approach and present the results in Table 1 in column 4 as a set of estimates of the multiple-equation system. In the unemployment equation, the coefficient on the nominal federal funds rate is positive and significant, while the coefficient on the inflation rate is not statistically significant from zero, confirming that the nominal federal funds rate bears the heaviest responsibility for raising unemployment. In the unemployment rate ratio equation, neither the federal funds rate nor the inflation rate is statistically significant. Moreover, the coefficients on both variables are approximately of the same magnitude and of opposite signs. Therefore, separating the nominal interest rate and the inflation rate does not fundamentally alter the results. IV. Discussion How can we reconcile the estimates presented in this paper, using a structural model, with those of earlier studies? Our estimates are consistent with the argument that black/white unemployment ratios may be correlated with policy interest rates, but this 13

14 relationship is mediated by the institutional relationships suggested by the estimates of the structural model. Moreover, our results suggest that black/white unemployment rate ratios are causal rather than merely an outcome of monetary policy. To see this, imagine a positive shock, external to the empirical model, to black/white unemployment ratio. Our results indicate this change will reduce the responsiveness of the Federal Reserve to unemployment, thereby raising the relative importance of inflation in its reaction function. Considering only this one relationship, the end result would be a higher policy interest rate and this rate would be correlated with a higher black-white unemployment rate differential. There are, however, countervailing tendencies at work as well. Our estimates also suggest that inflationary pressures are reduced when the last hired, first fired can serve as a shock-absorber, curbing inflationary pressures. Consider the exogenous shock that increases the black/white unemployment ratio. Our Phillips Curve estimates suggest that this will reduce inflationary pressures for a given inflation rate. In terms of the Federal Reserve's reaction function, weaker inflationary pressures would reduce the tendency to raise the policy interest rate. To explore these relationships in greater detail, we conduct a simplified simulation based on the coefficients from the estimated equation system. To make the exercise more tractable, we make a number of assumptions. First, we assume that we begin from a steady state, in which X t-1 = X t-2 where X represents lagged variables in the empirical specification. Second, we assume that the exogenous variables do not change. Finally, we approximate the impact of the interaction terms using the means of the unemployment rate and the black-white unemployment rate ratios. 14

15 Taking the total differential of the first three equations of our four-equation system and applying these assumptions yields: (5) dπ = β 5 du + β 7 ( du * R BW +U dr BW ) (6) BW BW ( du * R U dr ) dffr = α α * 2 dπ t + α 3dU (7) du = 3 ( dffr ) δ dπ To conduct the simulation, we introduce an exogenous shock to the black/white unemployment rate ratio, dr BW in Equation (4) and trace the effects through the remainder of the system. This is plausible since the coefficients on the real interest rate variable are not statistically significant from zero and the black-white labor ratio is only a function of exogenous variables. Given this, the simulation results depend on the effect of a change in R BW on the above system of three equations [Equations (5) - (7)] with three unknowns - dπ, dffr, and du - which can be solved simultaneously. For the purposes of this exercise, we consider a transient short-term shock to R BW (a non-permanent change). The lagged structure of the empirical model would allow us to calculate long-run coefficients based on the coefficients on the lagged endogenous variables. We do not do so here, however, restricting our attention to the effect of a shortrun temporary change in R BW. We evaluate the effect of a one-standard deviation shock to the unemployment rate ratio for the entire time period, , and for the two most recent peak-to-peak 15

16 business cycles. Results of this exercise as well as the mean and standard deviation of the black-to-white unemployment rate ratio for each time period are reported in Table 2. [Table 2 about here]. Taking the results for the entire time period, an increase in the black-white unemployment rate ratio will have a positive impact on the federal funds rate. A onestandard deviation increase is associated with a 0.40 percentage point increase in the policy interest rate (that is, inflation becomes a relatively more important target than overall unemployment). Therefore, our estimates suggest that there is a net positive correlation between the federal funds rate and the relative unemployment rate of the black population. The higher policy interest rate modestly raises overall unemployment by 0.05 percentage points. However, the higher black-white unemployment ratio is also associated with a slight decrease in inflation, related to the fact that it acts to alter the slope (flattens) the Phillips curve. This reduces pressure on the Federal Reserve to maintain higher interest rates. A comparison of the results for the entire period with the two business cycle estimates reveals that the dampening effect on inflation of a one-standard deviation shock of the black/white unemployment rate ratio becomes more pronounced over time. That is, the black-white unemployment ratio has increasingly served as a shock absorber in the US economy, keeping inflation low and thus attenuating pressure on the Federal Reserve to raise interest rates, although the net effect on the federal funds rate is positive. VI. Conclusion 16

17 Previous research posits a Federal Reserve whose interest rate policies are exogenous and not affected by the distribution of the costs of unemployment. Several studies provide evidence that black unemployment is disproportionately affected by changes in the policy interest rate. One drawback of a number of those studies is that they rely on VAR techniques, which are not able to disentangle the complex dynamics between the model s endogenous variables. Using a simultaneous equations approach, our estimates suggest that the black/white unemployment rate ratio is not merely passively affected by monetary policy but is itself causal. Results of estimating the central banks s reaction function suggest that the Federal Reserve will respond to increasing rates of unemployment by lowering the federal funds rate. However, the responsiveness of monetary policy to changes in unemployment will be weaker, the higher the black/white unemployment rate ratio. In addition, our estimates of the Phillips curve suggest that if the black-to-white unemployment rate ratio remains high, the inflationary pressures associated with reducing the average rate of unemployment will be attenuated. However, we do not find that the policy interest rate (the federal funds rate) has a direct effect on the ratio of black to white unemployment rates. This result differs from other studies that use non-structural VAR models and find that increases in the federal funds rate have a disproportionately negative impact on black employment. Our estimates are consistent with the argument that black/white unemployment ratios may be correlated with policy interest rates, but this relationship is mediated by the institutional relationships suggested by the estimates of the structural model. Given these estimated relationships, our research indicates that Federal Reserve policy has been more 17

18 likely to try to control inflation by raising the federal funds rate when the burden of unemployment falls disproportionately on the black population. Moreover, this inequality in terms of labor market outcomes will facilitate the objectives of maintaining low inflation and keeping average unemployment rates at a reasonably low level. 18

19 References Abell, J. (1991). Distributional effects of monetary and fiscal policy, American Journal of Economics and Sociology, 50(3): Ball, L. (1993). What determines the sacrifice ratio?, NBER Working Paper No Blanchard, O. and Katz, L. (1997). What we know and do not know about the natural rate of unemployment, Journal of Economic Perspectives, 11(1): Carpenter, S. and Rodgers, W. (2004). The disparate labor market impacts of monetary policy, Journal of Policy Analysis and Management, 23(4): Galbraith, J., Giovannoni, O., and Russo, A. (2007). The Federal Reserve's real reaction function: Monetary policy, inflation, unemployment, inequality and presidential politics, The Levy Economics Institute Working Paper No Gordon, R. (1997). The time-varying NAIRU and its implications for economic policy, Journal of Economic Perspectives, 11(1): Lindley, J. (2005). Explaining ethnic unemployment and activity rates: evidence from the QLFS in the 1990s and 2000s, Bulletin of Economic Research, 57(2). Seguino, S. and Heintz, J. (2011, forthcoming). Monetary tightening and the dynamics of US race and gender stratification, American Journal of Economics and Sociology. Stratton, L. (1993). Racial differences in men s unemployment, Industrial Relations and Labor Relations Review, 46(3): Taylor, J. B. (1993). Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy 39: Thorbecke, W. (2001). Estimating the effects of disinflationary monetary policy on minorities, Journal of Policy Modeling, 23:

20 TABLE 1. Inflation and Unemployment Dynamics: Regression Results Phillips Curve Independent Variable (1) OLS (2) Single- Equation GMM (3) System GMM (4) System GMM Dep. Var.: π t π t ** 0.331** 0.333** 0.335** Taylor Rule (0.07) (0.07) (0.05) (0.05) π t (0.07) (0.08) (0.06) (0.06) π t ** 0.408** 0.389** 0.387** (0.07) (0.07) (0.05) (0.05) π Oil t 0.093** 0.094** 0.091** 0.090** (0.01) (0.02) (0.07) (0.01) U t ** ** ** ** (1.30) (0.31) (1.40) (1.44) BW U t *R t 1.836** 3.154** 2.593** 2.541** (0.58) (0.88) (0.61) (0.62) BW R t ** ** ** ** (3.80) (5.85) (3.96) (4.07) Trend ** ** ** ** (0.006) (0.01) (0.004) (0.005) Constant ** ** ** ** (8.83) (14.06) (9.36) (9.64) N Adj. R (2) Single- Independent Equation (4) System Variable (1) OLS GMM (3)System GMM GMM Dep. Var.: FFR t FFR t ** 0.835** 0.826** 0.829** (0.03) (0.03) (0.02) (0.02) π t 0.107** 0.113** 0.157** 0.152** (0.03) (0.03) (0.02) (0.02) U t ** ** ** ** (0.16) (0.16) (0.12) (0.12) BW U t *R t 0.336** 0.347** 0.366** 0.355** (0.08) (0.08) (0.05) (0.06) Trend (0.003) (0.003) (0.002) (0.002) Constant 1.705* (0.73) (0.79) (0.60) (0.64) N Adj. R Note: * Significant at the 5% level, ** Significant at the 1% level. 20

21 Unemployment TABLE 1. Inflation and Unemployment Dynamics: Regression Results, cont. Independent Variable (1)System GMM (2) Single- Equation GMM (3) OLS (5) System GMM Dep. Var.: U t U t ** 1.549** 1.598** 1.581** (0.06) (0.07) (0.07) (0.06) U t ** ** ** ** (0.05) (0.06) (0.06) (0.05) L t 4.163** (1.48) (2.11) (2.27) (1.72) (FFR t π t ) 0.021** 0.017* (0.005) (0.007) (0.008) FFR t 0.025** (0.005) π t (0.008) Trend (0.001) (0.001) (0.001) (0.0009) Constant (0.32) (0.48) (0.53) (0.34) N Black/White Unemployment Rate Ratio Adj. R Single- Independent System Equation System Variable GMM GMM OLS GMM Dep. Var.: R BW R t-1 BW 0.810** 0.797** 0.795** 0.802** (0.03) (0.04) (0.05) (0.03) L t B 9.878** ** (2.39) (4.07) (4.98) (2.51) ** ** (2.47) (4.18) (5.121) (2.64) (FFR t π t ) (0.0025) (0.004) (0.003) FFR t (0.003) π t (0.003) Trend (0.0004) (0.0007) (0.0008) (0.0005) Constant (0.22) (0.328) (0.37) (0.24) N L t W Adj. R Note: * Significant at the 5% level, ** Significant at the 1% level. 21

22 Table 2. Estimated Effects of Temporary One-Standard Deviation Increases in the Blackto-White Unemployment Rate Ratio Entire Period 1990(4)- 2001(1) 2001(1)- 2007(4) d FFR d U d π Additional information Standard deviation R BW Mean R BW Mean U Note: The shorter time periods represent the most two recent peak-to-peak business cycles. 22

23 Appendix A Unit Root Tests Unit root tests were performed on all variables, based on the standard autoregressive formulation in which X is the variable of interest with lag length m for the differenced variable: ΔX t m t 1 + iδx t i + i= 1 = α 0 X α v i (1) Two unit root tests were conducted: the standard Augmented Dickey-Fuller test and the Phillips-Perron test. In the latter case, GLS detrended variables were used to increase the power of the test. In most instances, the results from the two tests agreed (Table A1). Lag lengths were determined by the Akaike information criterion. Variable Π π oil U R BW FFR L L B L W TABLE A1 Unit root tests (no deterministic drift or trend terms included) Description Augmented Dickey- Phillips-Perron (PP) Fuller (ADF) GLS detrended Quarterly inflation rate (CPI, annualized) * Quarterly change, refiner s acquisition cost (log) *** *** Unemployment rate, total labor force Ratio of black to white unemployment rates Federal funds rate, quarterly average Youth (16-24) share of working age population ** *** Youth (16-24) share of working age population, black ** *** Youth (16-24) share of working *** *** age population, white Note: * indicates significance at the 10% level, ** significance at the 5% level, and *** significance at the 1% level. 23

24 For four variables (π, U, R BW, and FFR), we cannot decisively reject the null hypothesis of no unit root. Therefore, we modify the specification to include deterministic drift (intercept) and linear trend terms. Results are presented in Table A2. TABLE A2 Unit root tests with drift (intercept) and linear trend terms Drift only Drift and trend Variable ADF PP ADF PP Π ** *** U ** *** ** *** R BW * * * ** FFR ** ** Note: * indicates significance at the 10% level, ** significance at the 5% level, and *** significance at the 1% level. Based on the results of the unit root tests, we conclude that this set of variables can be considered to be stationary, stationary with drift, or trend stationary (that is, there is no evidence of unit roots once we account for deterministic factors that can produce trends in the data). 24