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Is there chronic excess supply of labor?
193
Economics Letters 19 (1985) 193-197 North-Holland
IS THERE CHRONIC EXCESS Designing a Statistical Test
Richard
E. QUANDT
Princeton
Llniuers~t):
Received
22 March
and Harvey
Princeton,
NJ 08544,
SUPPLY
OF LABOR?
S. ROSEN USA
1985
We devise and implement a statistical data re_ject this hypothesis.
test of the hypothesis
that the labor market
has chronic
excess supply.
We find that the
1. Introduction
Since the late 1970’s, a number of attempts have been made to estimate disequilibrium models of the aggregate labor market. [See, e.g., Rosen and Quandt (1978.1984). Romer (1981). Eaton and Quandt (1983), Sarantis (1981), Briguglio (1984) and Smyth (1984).] These models have generally been fairly successful in the sense of being able to replicate key labor market developments over a long period of time. A problem with disequilibrium models is that they are difficult to deal with computationally. As a consequence of the ‘min condition’ present in these models, difficult non-linear estimation problems emerge, and standard econometric software packages generally cannot be used. These facts give rise to the following thoughts, which have been expressed to us by a number of people: ‘Why go to all the trouble? Suppose you are right, and the labor market really can be characterized by a disequilibrium model. Then surely it must be the case that there is chronic excess supply. After all, even in World War II, the unemployment rate was positive. Hence, the min condition implies that all observations are on the demand curve, and that is all you need to estimate.’ One response to this assertion is that the official government unemployment statistics upon which we condition our intuitions about the labor market do not correspond to the notions of unemployment used in most theoretical models. This was pointed out a long time ago by Lucas and Rapping (1970). Still, the thought is troubling to those who estimate disequilibrium models, and is worth careful consideration. In this paper we present and implement a statistical test of the hypothesis that the labor market has chronic excess supply. We proceed by estimating a disequilibrium labor model, and constructing a test statistic based on the unconditional probability that there is excess supply each period. ’ The model is briefly summarized in section 2. The statistical procedure is presented in section 3. Section 4 contains the results and conclusions. ’ Necessarily. the validity of the test is conditioned problem in applied econometrics.
0165.1765/85/$3,30
on the validity
‘a 1985, Elsevier Science Publishers
of the model as a whole. This, of course,
B.V. (North-Holland)
is a standard
R. E. Quundt. H.S. Rosen / I.7 there chronrc C.YCCLT .supp!,~ of luhor;~
194
2. The model Here we sketch the disequilibrium model. Since our focus is on the test for chronic excess supply. we refer the reader to Quandt and Rosen (1984) for a detailed discussion of economic, statistical and data issues. The model consists of six equations. The first three are the notional demand for labor, the notional supply. and a condition which states that the observed quantity is the minimum of the quantity demanded and quantity supplied. The next two equations describe the dynamic adjustment patterns of nominal wages and prices, respectively. The sixth equation relates excess demand to observed unemployment rates. For purposes of subsequent statistical analysis. it is useful to group all of the ‘exogenous’ variables on the right-hand side of each equation together. This is the purpose of the ‘z-notation’ used below. Demund for luhor (2.1)
D,=Q,(WP,)+~,~+UI,.
where t indexes time periods, D, = log of the notional demand for hours of work, W, = log of the nominal wage rate, P, = log of the price level. z,, = CX?Q[+ a,t. Q, = log real GNP, and u,, is a random error. Supp(~3 of ldw & = 4, + PI 14 K/p,)
(2.2)
+ i2, + h,
where S, = log of notional supply, IV,,, = log of after potential number of hours of work available.
tax wage,
z2, = &H,,
and
H, = log of the
Observed quantity of k&or L,=min(S,, Wqe
0,).
(2.3)
adjustment (2.4)
w = uz(/, + Y3P, + zj, + Ui, ) where
U, = reported
unemployment
rate. and z3, = y. + yI W,_ , - y3P,_ I + y4( P,_ I _ Pr-2) + Ysw,-*.
Price adjustment P, = s,w, + Z& + U‘$,,
(2.5)
where z4{ =80+&P,_,
-&K,
Vacancyunemployment
rate relutionship
0,-$=X/U,-
+&(&
1 - W-2).
(2.6)
U,+u,,.
Eq. (2.6) is based on the approximation assuming VA, = X/U,.
D, - S, = VA, - U,, where VA, is the vacancy
rate, and then
R. E. Quandt, H.S.Rmen
/ Is there chronic excess supp!v
The tests below are based on estimates of the model U.S. economy for the years 1929 through 1979.
3. Testing
the null hypothesis
obtained
195
of luhor?
from annual
observations
on the
of ‘all-excess-supply’
Various tests can be devised for the ‘all-excess-supply’ hypothesis. They differ principally in terms of the meaning attributed to the statement that only excess supply occurs. One possibility is that the conditional probability Pr{ 0, > S, 1L, } IS small for all t. Another is that the unconditional probability Pr{ D, > S,} is small for all t. The former concept permits a quasi-likelihood ratio test of H,, but may be difficult to implement, because it requires estimation of the parameters under H, which may not be possible since some of them may not be identified under H,, [Quandt (1985). Portes, Quandt and Ye0 (1985)]. It is relatively straightforward to test H,, using the second interpretation by employing the Rogers (1984) test. The Rogers test. Rogers (1984) has analyzed the following problem with exogenous variables x, and latent endogenous function that can be written
f*(y*Ix;
problem. Consider a latent variable variables .v,*, with a joint density
e)h(x).
As a rule, the form of f* is stated but that of h(x) is not, and instead of I;*, some _r, is observed. The hypotheses investigated by Rogers pertain to the probability that y* belongs to some subset of the space containing all y*, i.e., to Pr{ y* E Y, Ix; 0} =p(x;
0).
where 8 is the parameter of the f* density. In the simple demand and supply functions and a min condition, one can quantity Q, f( Q 1x; 6) and the density of excess demand F denotes the exogenous variables. Then the probability that Pr{F>O]x;
s)=kxg(F]x:
B)dF=p(x;
X; e)h(x)dx In order to test the hypothesis
M,=n-‘q(p(x,;
=
Ep(X;
that Ep(x;
and
6).
a) 2 c, Rogers introduces
B)-c)/o,
where 4 is the maximum
likelihood
estimator
i?=n-‘C(p(x,;
e)-c)2+&P?%
p=
f(Q,Ix,;d)/aeaef.
-n+Cazln
8),
disequilibrium model consisting only of easily obtain the density of the transacted = D - S, denoted by g( F 1x; 8), where x excess demand is positive is
6=
of 8,
n-lCap(x,; Qjae,
the statistic
Rogers shows that on the hypothesis as N(0, 1).
that Ep( X; 0) = c. the quantity
M,, is asymptotically
distributed
Derication
Define F, = D, - S,. Solve eqs. (2.4) and (2.5) for & and P,, yielding of Pr{ 0, - S, > 0). W, = c,,U, + ~~2, + ~13~3, + c14u4, and f’, = c7,U, + cT2, + c23~3, + c13u4,. where c,, = y2/(l - &y,), - (=ir - Y3i4,)/(1 (‘22( = (82:3, + z4,)/(l (‘13 = l/(1 - 62Y3), C14 = &YJ(l - 62Y3). - 62Y3k r;:x; c 23 = ~,A1 &Y3). _ Substituting in eqs. (2.1) and (2.2) yields F, = A,D; + Al, + A3U3, +
(3.1)
A4U4,.
where A, =(a, -P,)(c,, -c2,). A4
=
(a,
-
P,
X(.,4
-
c,~).
u,
F,-h/D;+
A2,=(q
-P,)(~17,-~21,)+=l,-:2,1
= 1lsr
F; - A,U,
u)z
I’
where
,
I’
IA,+1
+VU21exp
Completing
(F,-h/L/+
-Cam).
.
=JXJO f(F,. 0 -2
r/;)‘+
2 UC.2
of the transformation.
0
l/Z(u,;
+ a,?)
(3.3)
I/? exp --i
-B,
X@
u,,,u,.,/( u,?, + u,‘,)“2
(3.2)
We require
U,)dF;dl/.
= IA,+l+X/C(‘I /
(F,-A&-A,)’
5,
the square on F; allows eq. (3.3) to be written
Pr{ F, < 0} =
0,: = ~2 and u,‘? = A$J: + Aiu,’ + OF + 02.
2
2mJ.,u,,,
1A, + 1 + X/U,’ 1 is the Jacobian
Pr{ 4 ~0)
-P,)(c,,
-AL,=A;u3,+A4u4,+u,,-u2,d;.
F,, and II?, are jointly normal with means zero and variance Hence. the joint pdf f( F,, r/,) is
f(F
~,=(a,
Eqs. (2.6) and (3.1) are
1 2
dQ,
(A,,+(1
as
+A,)(/-A/(/)’ u,?, + U,‘I
(3.4)
i
where B, = [o;t( A,U, + A,,) + u,?~(X/U, - U,)]/(u,: + u,!,) and @( ) is the cumulative standard normal integral. The integral in eq. (3.4) is univariate and may be obtained by numerical integration. The model was estimated by maximum likelihood, and also with the additional feature that eqs. (2.4) and (2.5) were assumed to have first-order serial correlation. The analogue of eq. (3.4) was then evaluated at the maximum likelihood estimates.
4. Results and conclusions Eq. (3.4) was calculated by Gaussian quadrature and the first and second derivatives required for the Rogers test (6 and p) were obtained by numerical differentiation. The comparison of the
197
R. E. Quandr, H.S. Rosen / Is there chronic excess suppi~ of luhor?
Table 1 Rogers statistics.
Without
autocorrelation
With autocorrelation
corrrection correction
(‘= 0.80
(’ = 0.90
c = 0.95
c’= 0.99
- 1.996
- 3.284
- 3.807
- 4.169
- 0.980
- 1.996
- 2.460
-2.X06
unconditional probabilities Pr{ F, < 0) with the conditional probabilities Pr{ F,< 0 1L,}shows qualitative similarity, but conditioning on the observed quantity appears to allow much sharper discrimination between regimes. The Rogers statistic is based on the unconditional probabilities and table 1 displays its values for alternative c’s with and without the correction for autocorrelation of residuals. Each value of c corresponds to a different null hypothesis and asks the question ‘are the unconditional probabilities of excess supply on the whole larger than c?’ If the answer were yes, we would expect the test statistic to be significantly positive. A value of c = 0.99 is quite stringent, whereas a value of c = 0.80 is the opposite. Since a one-tailed test is appropriate, H, is rejected at the 0.05 level for every c, except in the case of c = 0.80 when we estimate autocorrelation coefficients in eqs. (3.3) and (3.4). Hence. the data reject the hypothesis of chronic excess supply in the labor market. One cannot assume that all observations lie on the demand curve, and the estimation technique must take this into account.
References Briguglio. P.L., 1984, The specification and estimation of a disequilibrium labour market model, Applied Economics 16. 5399554. Eaton, J. and R.E. Quandt, 1983, A model of rationing and labor supply: Theory and estimation, Economica 50, 221-234. Lucas, R. and L. Rapping, 1970, Real wages, employment and inflation, in: E. Phelps, ed., Microeconomic foundations of employment and inflation theory (Norton, New York). Portes. R.. R.E. Quandt and S. Yea. 1985. Testing the all excess demand hypothesis. Mimeo. (Princeton University, Princeton, NJ). Quandt, R.E., 1985. On the identifiability of structural parameters in ‘all-excess-demand disequilibrium models, Mimeo. (Princeton University. Princ_eton, NJ). Quandt, R.E. and H.S. Rosen. 1984. Unemployment, disequilibrium. and the short run Phillips curve: An econometric approach, Mimeo. (Princeton University, Princeton, NJ). Rogers, A.J.. 1984, Tests of some hypotheses in latent variable models with stochastic exogenous variables, Financial Research Center. Research memo no. 49 (Princeton University, Princeton, NJ). Romer. D.. 1981. Rosen and Quandt’s disequilibrium model of the labor market: A revision, Review of Economics and Statistics 62, 145-146. Rosen, H.S. and R.E. Quandt. 1978. Estimation of a disequilibrium aggregate labor market, Review of Economics and Statistics 40. 371-379. Sarantis. N., 1981. Employment, labor supply and real wages in market disequilibrium, Journal of Macroeconomics 3, 3355354. Smyth. D., 1982, The British labor market in disequilibrium: Did the dole reduce employment in interwar Britain, Working paper no. 165 (Wayne State University, Detroit, MI). Smyth. D.. 1984, Unemployment insurance and labor supply and demand: A time series analysis for the United States (Wayne State University. Detroit, MI).
Economics Letters 19 (1985) 193-197 North-Holland
IS THERE CHRONIC EXCESS Designing a Statistical Test
Richard
E. QUANDT
Princeton
Llniuers~t):
Received
22 March
and Harvey
Princeton,
NJ 08544,
SUPPLY
OF LABOR?
S. ROSEN USA
1985
We devise and implement a statistical data re_ject this hypothesis.
test of the hypothesis
that the labor market
has chronic
excess supply.
We find that the
1. Introduction
Since the late 1970’s, a number of attempts have been made to estimate disequilibrium models of the aggregate labor market. [See, e.g., Rosen and Quandt (1978.1984). Romer (1981). Eaton and Quandt (1983), Sarantis (1981), Briguglio (1984) and Smyth (1984).] These models have generally been fairly successful in the sense of being able to replicate key labor market developments over a long period of time. A problem with disequilibrium models is that they are difficult to deal with computationally. As a consequence of the ‘min condition’ present in these models, difficult non-linear estimation problems emerge, and standard econometric software packages generally cannot be used. These facts give rise to the following thoughts, which have been expressed to us by a number of people: ‘Why go to all the trouble? Suppose you are right, and the labor market really can be characterized by a disequilibrium model. Then surely it must be the case that there is chronic excess supply. After all, even in World War II, the unemployment rate was positive. Hence, the min condition implies that all observations are on the demand curve, and that is all you need to estimate.’ One response to this assertion is that the official government unemployment statistics upon which we condition our intuitions about the labor market do not correspond to the notions of unemployment used in most theoretical models. This was pointed out a long time ago by Lucas and Rapping (1970). Still, the thought is troubling to those who estimate disequilibrium models, and is worth careful consideration. In this paper we present and implement a statistical test of the hypothesis that the labor market has chronic excess supply. We proceed by estimating a disequilibrium labor model, and constructing a test statistic based on the unconditional probability that there is excess supply each period. ’ The model is briefly summarized in section 2. The statistical procedure is presented in section 3. Section 4 contains the results and conclusions. ’ Necessarily. the validity of the test is conditioned problem in applied econometrics.
0165.1765/85/$3,30
on the validity
‘a 1985, Elsevier Science Publishers
of the model as a whole. This, of course,
B.V. (North-Holland)
is a standard
R. E. Quundt. H.S. Rosen / I.7 there chronrc C.YCCLT .supp!,~ of luhor;~
194
2. The model Here we sketch the disequilibrium model. Since our focus is on the test for chronic excess supply. we refer the reader to Quandt and Rosen (1984) for a detailed discussion of economic, statistical and data issues. The model consists of six equations. The first three are the notional demand for labor, the notional supply. and a condition which states that the observed quantity is the minimum of the quantity demanded and quantity supplied. The next two equations describe the dynamic adjustment patterns of nominal wages and prices, respectively. The sixth equation relates excess demand to observed unemployment rates. For purposes of subsequent statistical analysis. it is useful to group all of the ‘exogenous’ variables on the right-hand side of each equation together. This is the purpose of the ‘z-notation’ used below. Demund for luhor (2.1)
D,=Q,(WP,)+~,~+UI,.
where t indexes time periods, D, = log of the notional demand for hours of work, W, = log of the nominal wage rate, P, = log of the price level. z,, = CX?Q[+ a,t. Q, = log real GNP, and u,, is a random error. Supp(~3 of ldw & = 4, + PI 14 K/p,)
(2.2)
+ i2, + h,
where S, = log of notional supply, IV,,, = log of after potential number of hours of work available.
tax wage,
z2, = &H,,
and
H, = log of the
Observed quantity of k&or L,=min(S,, Wqe
0,).
(2.3)
adjustment (2.4)
w = uz(/, + Y3P, + zj, + Ui, ) where
U, = reported
unemployment
rate. and z3, = y. + yI W,_ , - y3P,_ I + y4( P,_ I _ Pr-2) + Ysw,-*.
Price adjustment P, = s,w, + Z& + U‘$,,
(2.5)
where z4{ =80+&P,_,
-&K,
Vacancyunemployment
rate relutionship
0,-$=X/U,-
+&(&
1 - W-2).
(2.6)
U,+u,,.
Eq. (2.6) is based on the approximation assuming VA, = X/U,.
D, - S, = VA, - U,, where VA, is the vacancy
rate, and then
R. E. Quandt, H.S.Rmen
/ Is there chronic excess supp!v
The tests below are based on estimates of the model U.S. economy for the years 1929 through 1979.
3. Testing
the null hypothesis
obtained
195
of luhor?
from annual
observations
on the
of ‘all-excess-supply’
Various tests can be devised for the ‘all-excess-supply’ hypothesis. They differ principally in terms of the meaning attributed to the statement that only excess supply occurs. One possibility is that the conditional probability Pr{ 0, > S, 1L, } IS small for all t. Another is that the unconditional probability Pr{ D, > S,} is small for all t. The former concept permits a quasi-likelihood ratio test of H,, but may be difficult to implement, because it requires estimation of the parameters under H, which may not be possible since some of them may not be identified under H,, [Quandt (1985). Portes, Quandt and Ye0 (1985)]. It is relatively straightforward to test H,, using the second interpretation by employing the Rogers (1984) test. The Rogers test. Rogers (1984) has analyzed the following problem with exogenous variables x, and latent endogenous function that can be written
f*(y*Ix;
problem. Consider a latent variable variables .v,*, with a joint density
e)h(x).
As a rule, the form of f* is stated but that of h(x) is not, and instead of I;*, some _r, is observed. The hypotheses investigated by Rogers pertain to the probability that y* belongs to some subset of the space containing all y*, i.e., to Pr{ y* E Y, Ix; 0} =p(x;
0).
where 8 is the parameter of the f* density. In the simple demand and supply functions and a min condition, one can quantity Q, f( Q 1x; 6) and the density of excess demand F denotes the exogenous variables. Then the probability that Pr{F>O]x;
s)=kxg(F]x:
B)dF=p(x;
X; e)h(x)dx In order to test the hypothesis
M,=n-‘q(p(x,;
=
Ep(X;
that Ep(x;
and
6).
a) 2 c, Rogers introduces
B)-c)/o,
where 4 is the maximum
likelihood
estimator
i?=n-‘C(p(x,;
e)-c)2+&P?%
p=
f(Q,Ix,;d)/aeaef.
-n+Cazln
8),
disequilibrium model consisting only of easily obtain the density of the transacted = D - S, denoted by g( F 1x; 8), where x excess demand is positive is
6=
of 8,
n-lCap(x,; Qjae,
the statistic
Rogers shows that on the hypothesis as N(0, 1).
that Ep( X; 0) = c. the quantity
M,, is asymptotically
distributed
Derication
Define F, = D, - S,. Solve eqs. (2.4) and (2.5) for & and P,, yielding of Pr{ 0, - S, > 0). W, = c,,U, + ~~2, + ~13~3, + c14u4, and f’, = c7,U, + cT2, + c23~3, + c13u4,. where c,, = y2/(l - &y,), - (=ir - Y3i4,)/(1 (‘22( = (82:3, + z4,)/(l (‘13 = l/(1 - 62Y3), C14 = &YJ(l - 62Y3). - 62Y3k r;:x; c 23 = ~,A1 &Y3). _ Substituting in eqs. (2.1) and (2.2) yields F, = A,D; + Al, + A3U3, +
(3.1)
A4U4,.
where A, =(a, -P,)(c,, -c2,). A4
=
(a,
-
P,
X(.,4
-
c,~).
u,
F,-h/D;+
A2,=(q
-P,)(~17,-~21,)+=l,-:2,1
= 1lsr
F; - A,U,
u)z
I’
where
,
I’
IA,+1
+VU21exp
Completing
(F,-h/L/+
-Cam).
.
=JXJO f(F,. 0 -2
r/;)‘+
2 UC.2
of the transformation.
0
l/Z(u,;
+ a,?)
(3.3)
I/? exp --i
-B,
X@
u,,,u,.,/( u,?, + u,‘,)“2
(3.2)
We require
U,)dF;dl/.
= IA,+l+X/C(‘I /
(F,-A&-A,)’
5,
the square on F; allows eq. (3.3) to be written
Pr{ F, < 0} =
0,: = ~2 and u,‘? = A$J: + Aiu,’ + OF + 02.
2
2mJ.,u,,,
1A, + 1 + X/U,’ 1 is the Jacobian
Pr{ 4 ~0)
-P,)(c,,
-AL,=A;u3,+A4u4,+u,,-u2,d;.
F,, and II?, are jointly normal with means zero and variance Hence. the joint pdf f( F,, r/,) is
f(F
~,=(a,
Eqs. (2.6) and (3.1) are
1 2
dQ,
(A,,+(1
as
+A,)(/-A/(/)’ u,?, + U,‘I
(3.4)
i
where B, = [o;t( A,U, + A,,) + u,?~(X/U, - U,)]/(u,: + u,!,) and @( ) is the cumulative standard normal integral. The integral in eq. (3.4) is univariate and may be obtained by numerical integration. The model was estimated by maximum likelihood, and also with the additional feature that eqs. (2.4) and (2.5) were assumed to have first-order serial correlation. The analogue of eq. (3.4) was then evaluated at the maximum likelihood estimates.
4. Results and conclusions Eq. (3.4) was calculated by Gaussian quadrature and the first and second derivatives required for the Rogers test (6 and p) were obtained by numerical differentiation. The comparison of the
197
R. E. Quandr, H.S. Rosen / Is there chronic excess suppi~ of luhor?
Table 1 Rogers statistics.
Without
autocorrelation
With autocorrelation
corrrection correction
(‘= 0.80
(’ = 0.90
c = 0.95
c’= 0.99
- 1.996
- 3.284
- 3.807
- 4.169
- 0.980
- 1.996
- 2.460
-2.X06
unconditional probabilities Pr{ F, < 0) with the conditional probabilities Pr{ F,< 0 1L,}shows qualitative similarity, but conditioning on the observed quantity appears to allow much sharper discrimination between regimes. The Rogers statistic is based on the unconditional probabilities and table 1 displays its values for alternative c’s with and without the correction for autocorrelation of residuals. Each value of c corresponds to a different null hypothesis and asks the question ‘are the unconditional probabilities of excess supply on the whole larger than c?’ If the answer were yes, we would expect the test statistic to be significantly positive. A value of c = 0.99 is quite stringent, whereas a value of c = 0.80 is the opposite. Since a one-tailed test is appropriate, H, is rejected at the 0.05 level for every c, except in the case of c = 0.80 when we estimate autocorrelation coefficients in eqs. (3.3) and (3.4). Hence. the data reject the hypothesis of chronic excess supply in the labor market. One cannot assume that all observations lie on the demand curve, and the estimation technique must take this into account.
References Briguglio. P.L., 1984, The specification and estimation of a disequilibrium labour market model, Applied Economics 16. 5399554. Eaton, J. and R.E. Quandt, 1983, A model of rationing and labor supply: Theory and estimation, Economica 50, 221-234. Lucas, R. and L. Rapping, 1970, Real wages, employment and inflation, in: E. Phelps, ed., Microeconomic foundations of employment and inflation theory (Norton, New York). Portes. R.. R.E. Quandt and S. Yea. 1985. Testing the all excess demand hypothesis. Mimeo. (Princeton University, Princeton, NJ). Quandt, R.E., 1985. On the identifiability of structural parameters in ‘all-excess-demand disequilibrium models, Mimeo. (Princeton University. Princ_eton, NJ). Quandt, R.E. and H.S. Rosen. 1984. Unemployment, disequilibrium. and the short run Phillips curve: An econometric approach, Mimeo. (Princeton University, Princeton, NJ). Rogers, A.J.. 1984, Tests of some hypotheses in latent variable models with stochastic exogenous variables, Financial Research Center. Research memo no. 49 (Princeton University, Princeton, NJ). Romer. D.. 1981. Rosen and Quandt’s disequilibrium model of the labor market: A revision, Review of Economics and Statistics 62, 145-146. Rosen, H.S. and R.E. Quandt. 1978. Estimation of a disequilibrium aggregate labor market, Review of Economics and Statistics 40. 371-379. Sarantis. N., 1981. Employment, labor supply and real wages in market disequilibrium, Journal of Macroeconomics 3, 3355354. Smyth. D., 1982, The British labor market in disequilibrium: Did the dole reduce employment in interwar Britain, Working paper no. 165 (Wayne State University, Detroit, MI). Smyth. D.. 1984, Unemployment insurance and labor supply and demand: A time series analysis for the United States (Wayne State University. Detroit, MI).