ON THE TEMPORAL STABILITY OF GRAVITY MODELS OF
INTERNAL MIGRATION
by
Michael J. Greenwood and Jesse Sexton*
1
Abstract--In this note, we employ 1960, 1970, 1980, 1990, and 2000 Census data on state-tostate migration in the United States to test the temporal stability of modified gravity models of
migration. The double-log estimates relate to 5-year flows. The data are pooled and then stacked
to allow estimation of a five-equation seemingly unrelated regression model. Little temporal
work has ever been conducted on internal migration so the numerous differences that are
uncovered are noteworthy. Period effects and regional effects clearly are present, and the
coefficients on many variables vary considerably over time.
2
I. Introduction
For many years, modified gravity models have been widely used to study both
international trade patterns (Anderson, 1979) and aggregate place-to-place migration
(Greenwood, 1975). With few exceptions, when applied to migration, the gravity-model
approach has focused on a single period.1 Consequently, we have little idea regarding how
representative the coefficients estimated in these studies are in a temporal context. Indeed, due to
the paucity of temporal studies of migration, we have little knowledge regarding many temporal
aspects of internal U.S. migration. The coefficients may trend, or behave cyclically, or vary from
period to period in some other fashion, but the researcher has little idea regarding exactly where
his estimates place in a temporal context. In this note, we develop a modified gravity model to
study place-to-place interstate migration in the United States with a set of equations reflecting
five periods: 1955-60, 1965-70, 1975-80, 1985-90, and 1995-2000. The estimates are double-log,
which is common in the estimation of such models, and successive years are both pooled and
then stacked in a seemingly unrelated regression context as we test for parameter homogeneity.
Numerous differences are evident. Period and regional effects are clearly present, and the
coefficients vary considerably over time, but rarely in a single direction.
Although such studies are not common, a few prior studies have examined temporal
changes in the determinants of migration. For example, Mueser (1989) studies five-year
interstate migration over three periods (1955-60, 1965-70, and 1975-80), and White and Mueser
(1994) do so over four periods (1935-40, 1955-60, 1965-70, and 1975-80). Greenwood, Hunt,
and McDowell (1986) and Davies, Greenwood, and Li (2001) analyze annual data. The former
paper finds some cyclicality in the migrant attractiveness of jobs and the latter finds evidence of
temporal stability in many parameter estimates and some instability in others, but the studies
3
cover only 17 and 11 years, respectively, and therefore do not allow much time for changes to
occur. Molloy and Wozniak (forthcoming) study several temporal aspects of U.S. internal
migration. However, with few exceptions, these studies do not seek to find structural differences
in their estimated models over time.
II. The Model
The model is a fairly standard double-log modified gravity model. The dependent
variable (or migration rate) is the number of migrants five years of age and older who lived in
state i five years earlier and in state j when the census was conducted divided by the at-risk
population of state i (the end-of-period population of i five and over plus the out-migrants less
the in-migrants). The model contains four vectors of independent variables: (1) differential
economic returns; (2) costs of migrating; (3) differential amenities; and (4) regional fixed effects.
The model with five equations (one for each period) is of the following form:
(1)
Mijt / Pit = ∑n( βint Xint) + ∑m( βjmt Xjmt) + ∑k(βijkt Xijkt) + eijt
,
where Mijt refers to the migration from state i to state j in period t, Pit is the at risk population of i
at the beginning of the migration interval, βt refers to estimated parameters for a specific period,
the X's are vectors of independent variables, ∑n refers to n variables that relate to the origin state,
∑m refers to m variables that relate to the destination state, ∑k refers to k variables that relate to
specific pairs of states, and et is the error terms for each period. Comparable variables are
employed for each period. Except for certain dummy variables and a distance variable, the data
differ in each regression. Errors are assumed to be correlated across periods (nonzero
covariances) but uncorrelated within periods.
The vector for differential economic returns contains four characteristics of both state i
and state j: median income (one year before the census was taken), employment growth during
4
the previous 4-year period expressed as the ratio of year t (e.g., 1994) to year t-4 (e.g., 1990),
percent employment in manufacturing (t-10 at the time of the prior census), and percent of
population with 16 years or more of schooling (t-10). The vector for costs of migrating contains
the basic variables of the gravity model plus migrant stock: distance from state i to state j,
population of i and j (both relating to at risk), and number of persons born in i and living in j at
the time of the prior census. The amenities vector contains six variables for both state i and state
j: percent foreign-born population (t-10), population density (t-10), January temperature, July
temperature, July humidity, and a dummy variable indicating a seacoast. The vector for regional
fixed effects contains dummy variables for i and j states within the following census divisions
with New England as the benchmark: Middle Atlantic, South Atlantic, East South Central, West
South Central, East North Central, West North Central, Mountain, and Pacific.
The construction of the amenity variables is different than in previous studies and
requires mention. With the exception of the percent of foreign population (t-10) and the seacoast
variables, the amenity variables are built up from county-level data that are population weighted.
This procedure yields a measure that is more reflective of the amenities that are experienced by
the population from which the migrants are drawn or that the migrants experience at their
destination.
III. The Data and Econometric Approach
State-to-state migration data for each year (for coterminous states) were obtained from
the published Census matrices of interstate migration. The migration rate is expressed as a
percentage. The total number of observations is 2,256 for each period. Means and standard
deviations are reported in Table 1, except for estimation purposes the data are transformed into
logarithms. The mean migration rate for each period is very similar (0.241, 0.235, 0.236, 0.232,
5
and 0.203 from earliest to latest), but drops slightly in the 1995-2000 period. Over the five
periods, on average, about 23 percent of the at-risk population made an interstate move.
We use lagged values or beginning-of-period values of the independent variables to
avoid potential simultaneity problems. However, since the dependent variable is a specific i-j
flow and the independent variable is a state characteristic, simultaneity should be less critical.
Presumably, this has been the assumption when end-of-period values of the independent
variables have been used in earlier studies.
The econometrics proceeds in stages. First, we pool the data for all years and include
dummy variables for 1970, 1980, 1990, and 2000 with 1960 as the benchmark year. To account
for regional fixed effects, we also include origin and destination dummies for Census divisions
with New England as the benchmark region. Next, we stack the data for consecutive years (e.g.,
1960 and 1970) and use seemingly unrelated regression both to improve the efficiency of the
estimates and to ascertain any differences in the values of the estimated coefficients over time.x
Given the large number of observations, to get the estimates to converge we were required to
stack the years two (consecutive) at a time. The climate variables seem to refer to different years.
How, exactly are these measured?
IV. Empirical Findings
Results presented in Table 2 reflect period effects, which are clearly present, as well as
regional effects, which also are clearly present. The R2 (0.91) is very high, which is common in
modified gravity models. Almost all coefficients are statistically significant and most have the
expected sign. The dummy variable for each year is negative, and with the exception of 1970 is
statistically significant. Moreover, again with the exception of 1970, each coefficient is
significantly lower than its predecessor. Other factors held constant, migration rates have fallen
6
over time, perhaps in part due to the end of the draft and also in part due later to the aging of the
baby boom generation out of the most mobile age classes.1 Almost all division dummies are
significant. Relative to New England, out-migration was significantly lower for Middle Atlantic,
West North Central, East South Central, and West South Central, but significantly higher for
East North Central, South Atlantic, Mountain, and Pacific. In-migration was lower for all
divisions except Mountain and Pacific.
For the most part, coefficients on other variables are highly significant and have signs
that either are as expected or are not unexpected. Distance discourages migration from i to j,
whereas past migrants from i to j encourages migration. Even when southern states and regional
amenities are controlled, migration does not appear to have been to high-income states, a finding
not uncommon in place-to-place migration studies (Greenwood, 1975). Employment growth in
the destination was very attractive to migrants. The elasticity on destination employment growth
(2.99) is the highest in the regression. Migration was strongly away from states with relatively
high concentrations of the foreign born, which is consistent with the earlier finding of Borjas
(2006), and migration rates were lower to states with high foreign-born concentrations. Higher
population density discouraged both in-migration and out-migration. Both out- and in-migration
rates were lower for more densely populated states. Education is a key determinant of the
migration. Out-migration rates are higher from states with well-educated populations. Inmigration rates also are higher to states with well-educated populations, which was a noteworthy
pattern during the last half of the 20th century.
The results associated with the seemingly unrelated regression as well as tests for
parameter homogeneity are reported in Table 3, where many differences are evident in the values
of the estimated coefficients, although the signs tend for the most part to be consistent and as
7
expected. Only a few coefficients trend in the same direction or display no tendency to trend at
all. The East North Central region regularly became less desirable as a destination. Greater
employment growth in an origin always encouraged out-migration but this tendency grew
somewhat over time and especially during 1995-2000. Greater percentages of college graduates
at potential origins always encouraged higher rates of out-migration, but this coefficient never
moved in one direction or the other. Out-migration from coastal states as origins became less
likely over time, but the trend was not regular.
Distance is consistently negative, and it does not trend downward in absolute value, as
might be expected in light of a significantly improved national transportation system. Migrant
stock is consistently positive and its coefficient varies little from period to period. States with
higher incomes were significantly less likely to lose migrants during the 1955-60 and 1985-90
periods, but for the other periods the origin-income variable is not significant. The destination
income variable is never significant. Destination employment growth was always strongly
attractive for migrants with one of the highest estimated elasticities in each regression, but the
attractiveness of jobs dipped between the 1960s and the 1970s and then rebounded during the
1980s and remained equally strong during subsequent years. Types of jobs also were important.
Out-migration was regularly discouraged from states with higher percentages of jobs in the
manufacturing sector, but during the first three periods studied, these same states experienced
less in-migration.
Reinforcement for Borjas’s finding is evident in the coefficients on the variable for
foreign concentration in the origin state. This variable is positive and statistically significant for
each year. Migrants in general moved out of states with high foreign-born concentrations.
However, the results on the destination concentration variable are less consistent—positive and
8
significant for 1960, negative and significant for 1980 and 2000, and positive but not significant
for 1970 and 1990. As a further test of the hypothesis that migrants are, on net, moving away
from the foreign born, we replaced the i and j variables with the ratio (j/i), which should take a
negative sign if the net effect of the foreign born is to cause migration away. The new variable is
negative and significant for each year.x Again, migration tends to be lower if the destination state
has a high concentration of foreign-born persons relative to the origin state.
Mueser and Graves (1995) note that location-specific amenities ought to become more
attractive over time as real incomes rise in all locations. However, their empirical results do not
provide any support for this position, and neither do the present findings. Although the
temperature variables sometimes have the expected sign, the signs on the variables are not
consistent, and they do not trend in the expected direction in accord with this hypothesis.
Many of the fixed regional effects are consistently significant with either a positive or
negative sign. However, the Mountain and Pacific divisions are different in this respect. The
Mountain division as an origin is always positive and significant until 1995-2000, when it loses
its significance. As a destination, the Mountain division is positive and significant for the first
two periods, insignificant for the third period, and negative and significant for the last two
periods. The Pacific division as an origin is always positive and as a destination is positive for
the first three periods, but not significant for the last two. Even when all of the specific variables
included in the model are accounted for, the West census region appears to have become less
attractive for interstate migrants.
V. Summary and Conclusions
The results of this study suggest that qualitatively, based on regularity of the signs on
coefficients estimated for different periods, the empirical results associated with modified gravity
9
models are quite consistent and raise little cause for concern. However, the magnitude of many
coefficients differ sufficiently over time for investigators to be cautious in the weight they place
on specific coefficients.
Footnotes
*University of Colorado.
1. Rosenbloom and Sundstrom (2004) study U.S. interstate migration over a long span of history
(1850-1990), but they analyze microdata and do not estimate modified gravity models. They
conclude that interstate migration propensities fell during the last half of the 19th century and
then rose until about 1970. They attribute the rise during the 20th century to increased
educational attainment.
2. Molloy and Wozniak (forthcoming) address the issue of declining U.S. internal migration rates
but come to no strong conclusions regarding the causes.
References
Anderson, James E., "A Theoretical Foundation for the Gravity Equation," American Economic
Review, 69 (March, 1979), 106-116.
Borjas, G. J., "Native Internal Migration and the Labor Market Impact of Immigration," Journal
of Human Resources, XLI (XXXX, 2006), 221-258.
Davies, Paul S., Michael J. Greenwood, and Haizheng Li, "A Conditional Logit Approach to
U.S. State-to-State Migration," Journal of Regional Science, 41 (May, 2001), 337-360.
Graves,
Greenwood, Michael. J., “An Analysis of the Determinants of Geographic Labor Mobility in the
United States,” The Review of Economics and Statistics, LI (May 1969), 189-194.
Greenwood, Michael. J., “Research on Internal Migration in the United States: A Survey,”
Journal of Economic Literature, 13 (June, 1975), 397-433
10
Greenwood Michael J., Gary L. Hunt, and John M. McDowell, "Migration and Employment
Change: Empirical Evidence on the Spatial and Temporal Dimensions of the Linkage," Journal
of Regional Science, 26 (May, 1986), 223-234.
Molloy, Raven, Christopher L. Smith, and Abigail Wozniak, "Internal Migration in the United
States," Journal of Economic Perspectives, 25(Spring, 2011), 1-42.
Molloy, Raven, and Abigail Wozniak, "Labor Reallocation over the Business Cycle: New
Evidence from Internal Migration," Journal of Labor Economics (forthcoming).
Mueser, Peter, "The Spatial Structure of Migration: An Analysis of Flows in the USA over Three
Decades," Regional Studies, 23(June, 1989), 185-200.
Mueser, Peter.R., and Philip E. Graves, "Examining the Role of Economic Opportunity and
Amenities in Explaining Population Redistribution," Journal of Urban Economics, 37(1995),
176-200.
Rosenbloom, Joshua, L., and William A. Sundstrom, "The Decline and Rise of Interstate
Migration in the United States: Evidence from the IPUMS, 1850-1990." In Research in
Economic History, v.22, ed. Alexander Field. Amsterdam: Elsevier, 2004, 289-325.
White, Michael J., and Peter R. Mueser, "Changes in the Demographic Determinants of U.S.
Population Mobility: 1940-80," Review of Regional Studies, 24(Winter, 1994), 245-264.
11
Table 1
Summary Statistics: Means & Standard Deviations
Variable
Migration Rate i → j
Distance i → j
Population (thousands)
Migrant Stock i → j
Median Family Income
Employment Growth
Pct. of Jobs in Manufact.
Pct. with College Degree
Pct. Foreign-Born
Population Density
January Average Temp.
July Average Temp.
July Average Humidity
Variable
Migration Rate i → j
Distance i → j
Population (thousands)
Migrant Stock i → j
Median Family Income
Employment Growth
Pct. of Jobs in Manufact.
Pct. with College Degree
Pct. Foreign-Born
Population Density
January Average Temp.
July Average Temp.
July Average Humidity
Pooled
Mean Std. Dev.
0.229
1036.6
4325.7
23170.1
43362.3
1.1
23.369
6.910
4.308
1048.4
31.9
75.1
55.4
0.447
584.1
4681.3
55513.2
9279.7
0.1
10.571
3.772
3.719
2285.1
11.3
4.9
15.6
1980
Mean Std. Dev.
0.236
1036.6
4338.2
22238.1
45615.1
1.153
24.101
5.539
3.298
974.7
31.9
75.1
55.4
0.399
584.2
4506.0
52538.6
5332.4
0.077
9.128
1.084
2.712
2003.9
11.3
4.9
15.6
1960
Mean Std. Dev.
0.241
1036.6
3280.3
15318.0
31291.3
1.1
29.205
3.303
5.442
1160.1
31.9
75.0
55.3
0.603
584.2
3306.8
38244.8
5735.7
0.1
12.898
0.814
4.373
2729.2
11.3
4.8
15.6
1990
Mean Std. Dev.
0.232
1036.6
4754.8
28167.5
47111.0
1.043
20.256
9.204
4.105
963.8
32.0
75.1
55.4
0.407
584.2
5060.0
63100.7
7922.4
0.054
7.404
1.716
3.322
1928.9
11.3
4.9
15.6
1970
Mean Std. Dev.
0.235
1036.6
3839.1
19276.3
42451.1
1.1
26.906
4.039
4.076
1099.3
31.9
75.1
55.4
0.447
584.2
3993.4
47735.1
6399.8
0.1
10.835
0.871
3.227
2435.7
11.3
4.9
15.6
2000
Mean Std. Dev.
0.203
1036.6
5416.0
30850.4
50343.0
1.069
16.377
12.463
4.619
1044.2
32.0
75.1
55.3
0.331
584.2
5841.1
69058.0
7153.2
0.061
5.597
2.527
4.329
2230.1
11.3
5.0
15.6
12
Table 2
Pooled Interstate Migration: Logarithmic Regression Coefficients & Absolute t-Values
Variable
β
Costs of Migration
Distance i → j
-0.4689
Population i
-0.5550
Population j
0.4487
Migrant Stock i → j
0.5775
t
(41.87)
(51.97)
(42.15)
(90.30)
Variable
2000
1990
1980
1970
β
Yearly Fixed Effects
-1.3207
-0.8557
-0.5460
-0.0195
t
(20.00)
(16.30)
(16.43)
(0.75)
Pct. Foreign-Born i
Pct. Foreign-Born j
Population Density i
Population Density j
January Average Temp. i
January Average Temp. j
July Average Temp. i
0.1427
-0.0407
-0.0464
-0.0343
-0.0953
-0.1759
2.2887
(15.46)
(4.37)
(7.75)
(5.72)
(2.92)
(5.38)
(10.70)
Census Division Fixed Effects & β0
Middle Atlantic i
-0.2419 (9.67)
Middle Atlantic j
-0.5054 (20.16)
East North Central i
0.1226 (4.67)
East North Central j
-0.4219 (16.02)
West North Central i
-0.1146 (3.90)
West North Central j
-0.3510 (11.90)
South Atlantic i
0.0938 (4.04)
South Atlantic j
-0.2354 (10.13)
East South Central i
-0.1611 (5.19)
East South Central j
-0.4313 (13.89)
West South Central i
-0.1510 (4.82)
West South Central j
-0.4304 (13.69)
Mountain i
0.4403 (10.55)
Mountain j
0.0343 (0.81)
Pacific i
0.6192 (14.57)
Pacific j
0.0721 (1.65)
β0
-18.5372 (11.28)
July Average Temp. j
July Average Humidity i
July Average Humidity j
Coastal i
Coastal j
1.8431
0.0051
0.1658
0.1493
0.0291
(8.63)
(0.14)
(4.41)
(10.51)
(2.05)
Observations:
r-squared:
Economic Differentials
Median Family Income i
-0.5407
Median Family Income j
-0.0733
Employment Growth i
1.2751
Employment Growth j
2.9862
Pct. of Jobs in Manufact. i
-0.1418
Pct. of Jobs in Manufact. j
-0.0591
Pct. with College Degree i
0.7503
Pct. with College Degree j
0.0922
(9.08)
(1.24)
(14.92)
(34.78)
(9.88)
(4.12)
(18.09)
(2.20)
Amenities
11280
0.9109
13
Table 3
Interstate Migration: Seemingly Unrelated Logarithmic Regression Coefficients, Absolute z-Values, and Sig. Differences
1960
Variable
β
1970
z
β
1980
z
Distance i → j
Population i
Population j
Migrant Stock i → j
-0.5579
-0.5123
0.4056
0.5175
(21.25) ≫
(22.21)
(17.60) ≪
(39.10)
-0.4866
-0.5530
0.4695
0.5335
(22.00)
(26.18)
(22.46)
(43.86)
Median Family Income i
Median Family Income j
Employment Growth i
Employment Growth j
Pct. of Jobs in Manufact. i
Pct. of Jobs in Manufact. j
Pct. with College Degree i
Pct. with College Degree j
-0.3379
-0.2508
0.9061
2.3453
-0.3226
-0.1565
0.4791
-0.1155
(2.28)
(1.70)
(4.24)
(10.92)
(8.85)
(4.28)
(4.90)
(1.18)
-0.2181
-0.2091
1.3497
1.0571
-0.1560
-0.0687
0.5343
0.1747
(1.40)
(1.35)
(6.87)
(5.34)
(5.16)
(2.27)
(6.31)
(2.05)
Pct. Foreign-Born i
Pct. Foreign-Born j
Population Density i
Population Density j
January Average Temp. i
January Average Temp. j
July Average Temp. i
July Average Temp. j
July Average Humidity i
July Average Humidity j
Coastal i
Coastal j
0.1446
0.1086
-0.0465
0.0038
0.4010
-0.1719
0.3236
4.2170
-0.0316
0.6944
0.1441
0.2099
(6.11)
(4.49)
(3.75)
(0.31)
(5.24)
(2.21)
(0.59)
(7.71)
(0.37)
(8.21)
(4.44)
(6.49)
0.2277
0.0209
-0.0505
-0.0088
-0.0942
-0.3897
2.8131
4.0619
0.3631
0.3224
0.1867
0.0344
(10.79)
(0.96)
(4.46)
(0.77)
(1.46)
(5.96)
(6.43)
(9.30)
(4.89)
(4.35)
(6.89)
(1.27)
<
⋙
⋙
≫
≪
⋘
⋙
⋙
⋘
⋘
⋘
⋙
⋙
β
⋘
⋙
⋘
⋙
⋘
≫
≪
≫
⋘
⋘
⋘
>
⋙
≫
⋙
≫
1990
z
β
2000
z
β
z
-0.6249
-0.4252
0.6394
0.4560
(29.48)
(18.78)
(28.85) ⋙
(39.76)
-0.6487
-0.3907
0.5622
0.4798
(31.73) ⋙
(19.43) <
(27.37)
(38.07) ≪
-0.5818
-0.4291
0.5745
0.5110
(28.05)
(21.18)
(26.91)
(39.63)
0.0428
0.0211
1.5611
2.8361
-0.0709
-0.1509
0.6666
0.2310
(0.31)
(0.15)
(6.63)
(11.97)
(2.04)
(4.35)
(6.94)
(2.40)
≪
-0.2884
-0.0360
1.2704
3.0337
-0.1710
-0.0421
0.7052
-0.1111
(2.63) ≫
(0.33)
(6.20) ⋘
(14.71)
(5.71)
(1.40)
(7.61)
(1.19) ⋘
0.0214
-0.1265
3.1135
2.7058
-0.1679
-0.0438
0.7081
0.2885
(0.18)
(1.08)
(11.02)
(9.56)
(5.47)
(1.43)
(7.88)
(3.20)
0.1675
-0.1148
-0.0367
-0.0684
-0.3474
-0.2456
3.4388
1.0140
0.1512
-0.1451
0.1150
0.0503
(6.59)
(4.49)
(2.51)
(4.68)
(4.73)
(3.34)
(7.34)
(2.15)
(1.83)
(1.76)
(3.64)
(1.59)
0.1341
-0.0819
-0.0934
-0.0453
-0.0915
-0.0960
2.2056
1.6708
-0.1106
-0.0861
0.0354
-0.0029
(5.20)
(3.16)
(6.80)
(3.24)
(1.55)
(1.62)
(5.84)
(4.44)
(1.37)
(1.06)
(1.28)
(0.11)
⋘
⋙
⋙
≫ 0.09226 (3.32)
⋙ 0.00480 (0.17)
⋘ -0.09819 (7.64)
-0.06713 (5.17)
⋙ -0.14076 (2.25)
⋙ -0.03013 (0.48)
⋙ 1.57516 (3.79)
1.28841 (3.09)
0.06226 (0.88)
≪ -0.32723 (4.59)
0.13415 (4.90)
⋘ -0.05037 (1.84)
⋘
≪
⋙
⋙
>
14
Table 3 (cont.)
Interstate Migration: Seemingly Unrelated Logarithmic Regression Coefficients, Absolute z-Values, and Sig. Differences
1960
Variable
Middle Atlantic i
Middle Atlantic j
East North Central i
East North Central j
West North Central i
West North Central j
South Atlantic i
South Atlantic j
East South Central i
East South Central j
West South Central i
West South Central j
Mountain i
Mountain j
Pacific i
Pacific j
β0
Observations:
Pseudo r-squared:
1970
β
z
-0.3183
-0.5847
0.1187
-0.1651
-0.0813
-0.2470
0.1327
-0.1929
-0.0980
-0.3539
-0.1471
-0.4264
0.2813
0.7684
0.4166
0.6359
-19.8358
(5.49)
(10.09)
(1.98)
(2.74)
(1.17)
(3.54)
(2.21)
(3.19)
(1.25)
(4.51)
(1.87)
(5.36)
(2.93)
(7.88)
(4.26)
(6.31)
(4.57)
2256
0.9159
≫
⋘
≫
>
⋘
⋙
⋘
>
≪
1980
β
z
β
-0.1719
-0.6549
0.2149
-0.3917
0.0783
-0.3713
0.2165
-0.1728
0.0396
-0.3667
-0.0276
-0.3645
0.8481
0.2115
0.8646
0.4446
-30.0888
(3.51)
(13.42)
(4.20)
(7.61)
(1.26)
(5.92)
(4.46)
(3.55)
(0.60)
(5.51)
(0.40)
(5.31)
(10.07)
(2.47)
(10.05)
(5.04)
(7.91)
-0.2280
-0.5080
-0.0076
-0.5253
-0.2443
-0.3209
0.0167
-0.2658
-0.2349
-0.4133
-0.3326
-0.1643
0.3448
0.0087
0.6028
0.2108
-24.8448
2256
0.9335
≫
⋙
≪
⋘
⋙
⋘
⋘
≫
⋙
>
≫
≫
1990
z
(4.02)
(8.95)
(0.12)
(8.37)
(3.43)
(4.51)
(0.29)
(4.58)
(3.03)
(5.32)
(4.32)
(2.13)
(3.47)
(0.09)
(6.28)
(2.11)
(6.78)
2256
0.9029
β
⋘
⋙
⋙
⋙
⋙
⋘
⋘
⋘
⋙
2000
z
-0.2310
-0.5894
0.1813
-0.4534
0.1392
-0.3948
0.0634
-0.1436
-0.0689
-0.4385
0.2980
-0.6631
0.7105
-0.3938
0.6439
0.0755
-12.9818
(4.67)
(11.9)
(3.47)
(8.62)
(2.17)
(6.11)
(1.27)
(2.87)
(1.02)
(6.48)
(4.28)
(9.49)
(8.33)
(4.60)
(8.19)
(0.94)
(4.37)
2256
0.9350
≪
⋘
<
⋘
⋘
⋘
⋘
⋙
≫
≫
<
⋘
β
z
-0.3454
-0.5235
-0.2784
-0.5484
-0.3761
-0.4361
-0.0807
-0.2224
-0.3782
-0.5436
-0.3990
-0.5705
0.0266
-0.1817
0.4886
-0.0771
-21.5410
(7.29)
(10.98)
(5.43)
(10.74)
(6.50)
(7.66)
(1.72)
(4.74)
(6.11)
(8.78)
(6.50)
(9.34)
(0.33)
(2.28)
(6.36)
(0.99)
(8.98)
2256
0.9324
15