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## 5. The Fixed Time Effect Model

The fixed time effect model investigates how time affects the intercept using time dummy variables. The logic and method are the same as those of the fixed group effect model.

5.1 Least Squares Dummy Variable Models

The least squares dummy variable (LSDV) model produces fifteen regression equations. This section does not present all outputs, but one or two for each LSDV approach.

Time01: cost = 20.496 + .868*output - .484*fuel -1.954*load
Time02: cost = 20.578 + .868*output - .484*fuel -1.954*load
Time03: cost = 20.656 + .868*output - .484*fuel -1.954*load
Time04: cost = 20.741 + .868*output - .484*fuel -1.954*load
Time05: cost = 21.200 + .868*output - .484*fuel -1.954*load
Time06: cost = 21.412 + .868*output - .484*fuel -1.954*load
Time07: cost = 21.503 + .868*output - .484*fuel -1.954*load
Time08: cost = 21.654 + .868*output - .484*fuel -1.954*load
Time09: cost = 21.830 + .868*output - .484*fuel -1.954*load
Time10: cost = 22.114 + .868*output - .484*fuel -1.954*load
Time11: cost = 22.465 + .868*output - .484*fuel -1.954*load
Time12: cost = 22.651 + .868*output - .484*fuel -1.954*load
Time13: cost = 22.617 + .868*output - .484*fuel -1.954*load
Time14: cost = 22.552 + .868*output - .484*fuel -1.954*load
Time15: cost = 22.537 + .868*output - .484*fuel -1.954*load

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5.1.1 LSDV1 without a Dummy

Let us begin with the SAS REG procedure. The test statement examines fixed time effects.

PROC REG DATA=masil.airline;
MODEL cost = t1-t14 output fuel load;
RUN;

The REG Procedure
Model: MODEL1
Dependent Variable: cost

Number of Observations Used          90

Analysis of Variance

Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F

Model                    17      112.95270        6.64428     439.62    <.0001
Error                    72        1.08819        0.01511
Corrected Total          89      114.04089

Root MSE              0.12294    R-Square     0.9905
Dependent Mean       13.36561    Adj R-Sq     0.9882
Coeff Var             0.91981

Parameter Estimates

Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|

Intercept     1       22.53677        4.94053       4.56      <.0001
t1            1       -2.04096        0.73469      -2.78      0.0070
t2            1       -1.95873        0.72275      -2.71      0.0084
t3            1       -1.88103        0.72036      -2.61      0.0110
t4            1       -1.79601        0.69882      -2.57      0.0122
t5            1       -1.33693        0.50604      -2.64      0.0101
t6            1       -1.12514        0.40862      -2.75      0.0075
t7            1       -1.03341        0.37642      -2.75      0.0076
t8            1       -0.88274        0.32601      -2.71      0.0085
t9            1       -0.70719        0.29470      -2.40      0.0190
t10           1       -0.42296        0.16679      -2.54      0.0134
t11           1       -0.07144        0.07176      -1.00      0.3228
t12           1        0.11457        0.09841       1.16      0.2482
t13           1        0.07979        0.08442       0.95      0.3477
t14           1        0.01546        0.07264       0.21      0.8320
output        1        0.86773        0.01541      56.32      <.0001
fuel          1       -0.48448        0.36411      -1.33      0.1875
load          1       -1.95440        0.44238      -4.42      <.0001

The following are the corresponding Stata and LIMDEP commands for LSDV1 (outputs are skipped).

. regress cost t1-t14 output fuel load

REGRESS;Lhs=COST;Rhs=ONE,T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,

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5.1.2 LSDV2 without the Intercept

Let us use LIMDEP to fit LSDV2 because it reports correct (although slightly different) F and R2 statistics.

--> REGRESS;Lhs=COST;Rhs=T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,

+-----------------------------------------------------------------------+
| Ordinary    least squares regression    Weighting variable = none     |
| Dep. var. = COST     Mean=   13.36560929    , S.D.=   1.131971002     |
| Model size: Observations =      90, Parameters =  18, Deg.Fr.=     72 |
| Residuals:  Sum of squares= 1.088190223    , Std.Dev.=         .12294 |
| Fit:        R-squared=  .990458, Adjusted R-squared =          .98820 |
| Model test: F[ 17,     72] =  439.62,    Prob value =          .00000 |
| Diagnostic: Log-L =     70.9837, Restricted(b=0) Log-L =    -138.3581 |
|             LogAmemiyaPrCrt.=   -4.010, Akaike Info. Crt.=     -1.177 |
| Model does not contain ONE. R-squared and F can be negative!          |
| Autocorrel: Durbin-Watson Statistic =   2.93900,   Rho =      -.46950 |
+-----------------------------------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient  | Standard Error |t-ratio |P[|T|>t] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
T1           20.49580478       4.2095283    4.869   .0000  .66666667E-01
T2           20.57803885       4.2215262    4.875   .0000  .66666667E-01
T3           20.65573100       4.2241771    4.890   .0000  .66666667E-01
T4           20.74075857       4.2457497    4.885   .0000  .66666667E-01
T5           21.19983202       4.4403312    4.774   .0000  .66666667E-01
T6           21.41162082       4.5386212    4.718   .0000  .66666667E-01
T7           21.50335085       4.5713968    4.704   .0000  .66666667E-01
T8           21.65402827       4.6228858    4.684   .0000  .66666667E-01
T9           21.82957108       4.6569062    4.688   .0000  .66666667E-01
T10          22.11380260       4.7926483    4.614   .0000  .66666667E-01
T11          22.46532734       4.9499089    4.539   .0000  .66666667E-01
T12          22.65133704       5.0085924    4.522   .0000  .66666667E-01
T13          22.61655508       4.9861391    4.536   .0000  .66666667E-01
T14          22.55222832       4.9559418    4.551   .0000  .66666667E-01
T15          22.53676562       4.9405321    4.562   .0000  .66666667E-01
OUTPUT       .8677267843   .15408184E-01   56.316   .0000    -1.1743092
FUEL        -.4844835367       .36410849   -1.331   .1875     12.770359
LOAD        -1.954404328       .44237771   -4.418   .0000     .56046015
(Note: E+nn or E-nn means multiply by 10 to + or -nn power.)

The following are the corresponding SAS REG procedure and Stata command for LSDV2 (outputs are skipped).

PROC REG DATA=masil.airline;
MODEL cost = t1-t15 output fuel load /NOINT;
RUN;

. regress cost t1-t15 output fuel load, noc

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5.1.3 LSDV3 with a Restriction

In SAS, you need to use the RESTRICT statement to impose a restriction.

PROC REG DATA=masil.airline;
MODEL cost = t1-t15 output fuel load;
RESTRICT t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15=0;
RUN;

The REG Procedure
Model: MODEL1
Dependent Variable: cost

NOTE: Restrictions have been applied to parameter estimates.

Number of Observations Used          90

Analysis of Variance

Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F

Model                    17      112.95270        6.64428     439.62    <.0001
Error                    72        1.08819        0.01511
Corrected Total          89      114.04089

Root MSE              0.12294    R-Square     0.9905
Dependent Mean       13.36561    Adj R-Sq     0.9882
Coeff Var             0.91981

Parameter Estimates

Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|

Intercept     1       21.66698        4.62405       4.69     <.0001
t1            1       -1.17118        0.41783      -2.80     0.0065
t2            1       -1.08894        0.40586      -2.68     0.0090
t3            1       -1.01125        0.40323      -2.51     0.0144
t4            1       -0.92622        0.38177      -2.43     0.0178
t5            1       -0.46715        0.19076      -2.45     0.0168
t6            1       -0.25536        0.09856      -2.59     0.0116
t7            1       -0.16363        0.07190      -2.28     0.0258
t8            1       -0.01296        0.04862      -0.27     0.7907
t9            1        0.16259        0.06271       2.59     0.0115
t10           1        0.44682        0.17599       2.54     0.0133
t11           1        0.79834        0.32940       2.42     0.0179
t12           1        0.98435        0.38756       2.54     0.0132
t13           1        0.94957        0.36537       2.60     0.0113
t14           1        0.88524        0.33549       2.64     0.0102
t15           1        0.86978        0.32029       2.72     0.0083
output        1        0.86773        0.01541      56.32     <.0001
fuel          1       -0.48448        0.36411      -1.33     0.1875
load          1       -1.95440        0.44238      -4.42     <.0001
RESTRICT     -1     -3.946E-15              .        .        .

* Probability computed using beta distribution.

In Stata, define the restriction with the .constraint command and specify the restriction using the constraint() option of the .cnsreg command.

. constraint define 3 t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15=0
. cnsreg cost t1-t15 output fuel load, constraint(3)

Constrained linear regression                          Number of obs =      90
F( 17,    72) =  439.62
Prob > F      =  0.0000
Root MSE      =  .12294
( 1)  t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11 + t12 + t13 + t14 + t15 = 0
------------------------------------------------------------------------------
cost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
t1 |  -1.171179   .4178338    -2.80   0.007    -2.004115   -.3382422
t2 |  -1.088945   .4058579    -2.68   0.009    -1.898008   -.2798816
t3 |  -1.011252   .4032308    -2.51   0.014    -1.815078   -.2074266
t4 |  -.9262249   .3817675    -2.43   0.018    -1.687265   -.1651852
t5 |  -.4671515   .1907596    -2.45   0.017    -.8474239   -.0868791
t6 |  -.2553627   .0985615    -2.59   0.012    -.4518415   -.0588839
t7 |  -.1636326   .0718969    -2.28   0.026    -.3069564   -.0203088
t8 |  -.0129552   .0486249    -0.27   0.791    -.1098872    .0839768
t9 |   .1625876   .0627099     2.59   0.012     .0375776    .2875976
t10 |   .4468191    .175994     2.54   0.013     .0959814    .7976568
t11 |   .7983439   .3294027     2.42   0.018     .1416916    1.454996
t12 |   .9843536   .3875583     2.54   0.013     .2117702    1.756937
t13 |   .9495716   .3653675     2.60   0.011     .2212248    1.677918
t14 |   .8852448   .3354912     2.64   0.010     .2164554    1.554034
t15 |   .8697821   .3202933     2.72   0.008     .2312891    1.508275
output |   .8677268   .0154082    56.32   0.000     .8370111    .8984424
fuel |  -.4844835   .3641085    -1.33   0.188    -1.210321    .2413535
load |  -1.954404   .4423777    -4.42   0.000    -2.836268    -1.07254
_cons |   21.66698   4.624053     4.69   0.000      12.4491    30.88486
------------------------------------------------------------------------------

The following are the corresponding LIMDEP command for LSDV3 (outputs are skipped).

REGRESS;Lhs=COST;Rhs=ONE,T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,
+b(13)+b(14)+b(15)=0\$

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5.2 Within Time Effect Model

The within effect mode for the fixed time effects needs to compute deviations from the time means. Keep in mind that the intercept should be suppressed.

5.2.1 Estimating the Time Effect Model

Let us manually estimate the fixed time effect model first.

. egen tm_cost = mean(cost), by(year) // compute time means
. egen tm_output = mean(output), by(year)
. egen tm_fuel = mean(fuel), by(year)

+---------------------------------------------------+
| year    tm_cost   tm_output    tm_fuel    tm_load |
|---------------------------------------------------|
|    1   12.36897   -1.790283   11.63606   .4788587 |
|    2   12.45963   -1.744389   11.66868   .4868322 |
|    3   12.60706   -1.577767   11.67494     .52358 |
|    4   12.77912   -1.443695   11.73193   .5244486 |
|    5   12.94143   -1.398122   12.26843   .5635266 |
|    6    13.0452   -1.393002   12.53826   .5541809 |
|    7   13.15965   -1.302416   12.62714   .5607425 |
|    8   13.29884   -1.222963   12.76768   .5670587 |
|    9    13.4651   -1.067003   12.86104   .6179098 |
|   10   13.70187   -.9023156   13.23183   .6233943 |
|   11   13.91324   -.9205539   13.66246   .5802577 |
|   12   14.05984   -.8641667   13.82315   .5856243 |
|   13   14.12841   -.7923916   13.75979   .5803183 |
|   14   14.23517   -.6428015   13.67403   .5804528 |
|   15   14.32062   -.5527684   13.62997   .5797168 |
+---------------------------------------------------+

. gen tw_cost = cost - tm_cost // transform variables
. gen tw_output = output - tm_output
. gen tw_fuel = fuel - tm_fuel

. regress tw_cost tw_output tw_fuel tw_load, noc // within time effect

Source |       SS       df       MS              Number of obs =      90
-------------+------------------------------           F(  3,    87) = 2015.95
Model |  75.6459391     3   25.215313           Prob > F      =  0.0000
Residual |  1.08819023    87  .012507934           R-squared     =  0.9858
Total |  76.7341294    90  .852601437           Root MSE      =  .11184

------------------------------------------------------------------------------
tw_cost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
tw_output |   .8677268   .0140171    61.90   0.000     .8398663    .8955873
tw_fuel |  -.4844836   .3312359    -1.46   0.147    -1.142851    .1738836
tw_load |  -1.954404   .4024388    -4.86   0.000    -2.754295   -1.154514
------------------------------------------------------------------------------

If you want to get intercepts of years, use . For example, the intercept of year 7 is 21.503=13.1597-{.8677*(-1.3024) + (-.4845)*12.6271 + (-1.9544)*.5607}. As discussed previously, the standard errors of the within effects model need to be adjusted. For instance, the correct standard error of fuel price is computed as .364 = .3312*sqrt(87/72).

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5.2.2 Using the TSCSREG and PANEL procedures

You need to sort the data set by variables (i.e., year and airline) to appear in the ID statement of the TSCSREG and PANEL procedures.

PROC SORT DATA=masil.airline;
BY year airline;

PROC PANEL DATA=masil.airline;
ID year airline;
MODEL cost = output fuel load /FIXONE;
RUN;

The PANEL Procedure
Fixed One Way Estimates

Dependent Variable: cost

Model Description

Estimation Method             FixOne
Number of Cross Sections          15
Time Series Length                 6

Fit Statistics

SSE              1.0882    DFE                  72
MSE              0.0151    Root MSE         0.1229
R-Square         0.9905

F Test for No Fixed Effects

Num DF      Den DF    F Value    Pr > F

14          72       1.17    0.3178

Parameter Estimates

Standard
Variable        DF    Estimate       Error    t Value    Pr > |t|    Label

CS1              1    -2.04096      0.7347      -2.78      0.0070    Cross Sectional
Effect    1
CS2              1    -1.95873      0.7228      -2.71      0.0084    Cross Sectional
Effect    2
CS3              1    -1.88103      0.7204      -2.61      0.0110    Cross Sectional
Effect    3
CS4              1    -1.79601      0.6988      -2.57      0.0122    Cross Sectional
Effect    4
CS5              1    -1.33693      0.5060      -2.64      0.0101    Cross Sectional
Effect    5
CS6              1    -1.12514      0.4086      -2.75      0.0075    Cross Sectional
Effect    6
CS7              1    -1.03341      0.3764      -2.75      0.0076    Cross Sectional
Effect    7
CS8              1    -0.88274      0.3260      -2.71      0.0085    Cross Sectional
Effect    8
CS9              1    -0.70719      0.2947      -2.40      0.0190    Cross Sectional
Effect    9
CS10             1    -0.42296      0.1668      -2.54      0.0134    Cross Sectional
Effect   10
CS11             1    -0.07144      0.0718      -1.00      0.3228    Cross Sectional

CS12             1    0.114571      0.0984       1.16      0.2482    Cross Sectional
Effect   12
CS13             1    0.079789      0.0844       0.95      0.3477    Cross Sectional
Effect   13
CS14             1    0.015463      0.0726       0.21      0.8320    Cross Sectional
Effect   14
Intercept        1    22.53677      4.9405       4.56      <.0001    Intercept
output           1    0.867727      0.0154      56.32      <.0001
fuel             1    -0.48448      0.3641      -1.33      0.1875
load             1     -1.9544      0.4424      -4.42      <.0001

The following TSCSREG procedure gives the same outputs.

PROC TSCSREG DATA=masil.airline;
ID year airline;
MODEL cost = output fuel load /FIXONE;
RUN;

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5.2.3 Using Stata

The Stata .xtreg command uses the fe option for the fixed effect model.

. xtreg cost output fuel load, fe i(year)

Fixed-effects (within) regression               Number of obs      =        90
Group variable (i): year                        Number of groups   =        15

R-sq:  within  = 0.9858                         Obs per group: min =         6
between = 0.4812                                        avg =       6.0
overall = 0.5265                                        max =         6

F(3,72)            =   1668.37
corr(u_i, Xb)  = -0.1503                        Prob > F           =    0.0000

------------------------------------------------------------------------------
cost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
output |   .8677268   .0154082    56.32   0.000     .8370111    .8984424
fuel |  -.4844835   .3641085    -1.33   0.188    -1.210321    .2413535
load |  -1.954404   .4423777    -4.42   0.000    -2.836268    -1.07254
_cons |   21.66698   4.624053     4.69   0.000      12.4491    30.88486
-------------+----------------------------------------------------------------
sigma_u |   .8027907
sigma_e |  .12293801
rho |  .97708602   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(14, 72) =     1.17              Prob > F = 0.3178

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5.2.4 Using LIMDEP

You need to pay attention to the Str=; subcommand for stratification.

+-----------------------------------------------------------------------+
| OLS Without Group Dummy Variables                                     |
| Ordinary    least squares regression    Weighting variable = none     |
| Dep. var. = COST     Mean=   13.36560933    , S.D.=   1.131971444     |
| Model size: Observations =      90, Parameters =   4, Deg.Fr.=     86 |
| Residuals:  Sum of squares= 1.335449522    , Std.Dev.=         .12461 |
| Fit:        R-squared=  .988290, Adjusted R-squared =          .98788 |
| Model test: F[  3,     86] = 2419.33,    Prob value =          .00000 |
| Diagnostic: Log-L =     61.7699, Restricted(b=0) Log-L =    -138.3581 |
|             LogAmemiyaPrCrt.=   -4.122, Akaike Info. Crt.=     -1.284 |
| Panel Data Analysis of COST       [ONE way]                           |
|           Unconditional ANOVA (No regressors)                         |
| Source      Variation        Deg. Free.     Mean Square               |
| Between       37.3068               14.         2.66477               |
| Residual      76.7341               75.         1.02312               |
| Total         114.041               89.         1.28136               |
+-----------------------------------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient  | Standard Error |t-ratio |P[|T|>t] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
OUTPUT       .8827386341   .13254552E-01   66.599   .0000    -1.1743092
FUEL         .4539777119   .20304240E-01   22.359   .0000     12.770359
LOAD        -1.627507797       .34530293   -4.713   .0000     .56046016
Constant     9.516912231       .22924522   41.514   .0000
(Note: E+nn or E-nn means multiply by 10 to + or -nn power.)

+-----------------------------------------------------------------------+
| Least Squares with Group Dummy Variables                              |
| Ordinary    least squares regression    Weighting variable = none     |
| Dep. var. = COST     Mean=   13.36560933    , S.D.=   1.131971444     |
| Model size: Observations =      90, Parameters =  18, Deg.Fr.=     72 |
| Residuals:  Sum of squares= 1.088193393    , Std.Dev.=         .12294 |
| Fit:        R-squared=  .990458, Adjusted R-squared =          .98820 |
| Model test: F[ 17,     72] =  439.62,    Prob value =          .00000 |
| Diagnostic: Log-L =     70.9836, Restricted(b=0) Log-L =    -138.3581 |
|             LogAmemiyaPrCrt.=   -4.010, Akaike Info. Crt.=     -1.177 |
| Estd. Autocorrelation of e(i,t)     .573531                           |
+-----------------------------------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient  | Standard Error |t-ratio |P[|T|>t] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
OUTPUT       .8677268093   .15408179E-01   56.316   .0000    -1.1743092
FUEL        -.4844946699       .36410984   -1.331   .1868     12.770359
LOAD        -1.954414378       .44237791   -4.418   .0000     .56046016
(Note: E+nn or E-nn means multiply by 10 to + or -nn power.)

+------------------------------------------------------------------------+
|                Test Statistics for the Classical Model                 |
|                                                                        |
|        Model            Log-Likelihood    Sum of Squares    R-squared  |
| (1)  Constant term only     -138.35814   .1140409821D+03     .0000000  |
| (2)  Group effects only     -120.52864   .7673414157D+02     .3271354  |
| (3)  X - variables only       61.76991   .1335449522D+01     .9882897  |
| (4)  X and group effects      70.98362   .1088193393D+01     .9904579  |
|                                                                        |
|                                Hypothesis Tests                        |
|               Likelihood Ratio Test                F Tests             |
|          Chi-squared   d.f.  Prob.         F    num. denom. Prob value |
| (2) vs (1)    35.659     14     .00117     2.605   14    75     .00404 |
| (3) vs (1)   400.256      3     .00000  2419.329    3    86     .00000 |
| (4) vs (1)   418.684     17     .00000   439.617   17    72     .00000 |
| (4) vs (2)   383.025      3     .00000  1668.364    3    72     .00000 |
| (4) vs (3)    18.427     14     .18800     1.169   14    72     .31776 |
+------------------------------------------------------------------------+

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5.3 Between Time Effect Model

The between effect model regresses time means of dependent variables on those of independent variables. See also 3.2 and 4.6.

. regress tm_cost tm_output tm_fuel tm_load // between time effect

Source |       SS       df       MS              Number of obs =      15
-------------+------------------------------           F(  3,    11) = 4074.33
Model |  6.21220479     3  2.07073493           Prob > F      =  0.0000
Residual |  .005590631    11  .000508239           R-squared     =  0.9991
Total |  6.21779542    14  .444128244           Root MSE      =  .02254

------------------------------------------------------------------------------
tm_cost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
tm_output |   1.133337   .0512898    22.10   0.000     1.020449    1.246225
tm_fuel |   .3342486   .0228284    14.64   0.000     .2840035    .3844937
tm_load |  -1.350727   .2478264    -5.45   0.000    -1.896189   -.8052644
_cons |   11.18505   .3660016    30.56   0.000     10.37949    11.99062
------------------------------------------------------------------------------

The SAS PANEL procedure has the /BTWNT option to estimate the between effect model.

PROC PANEL DATA=masil.airline;
ID airline year;
MODEL cost = output fuel load /BTWNT;
RUN;

The PANEL Procedure
Between Time Periods Estimates

Dependent Variable: cost

Model Description

Estimation Method            BtwTime
Number of Cross Sections           6
Time Series Length                15

Fit Statistics

SSE              0.0056    DFE                  11
MSE              0.0005    Root MSE         0.0225
R-Square         0.9991

Parameter Estimates

Standard
Variable        DF    Estimate       Error    t Value    Pr > |t|    Label

Intercept        1    11.18504      0.3660      30.56      <.0001    Intercept
output           1    1.133335      0.0513      22.10      <.0001
fuel             1    0.334249      0.0228      14.64      <.0001
load             1    -1.35073      0.2478      -5.45      0.0002

You may use the be option in the Stata .xtreg command and the Means; subcommand in LIMDEP (outputs are skipped).

. xtreg cost output fuel load, be i(year) // between time effect model

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5.4 Testing Fixed Time Effects.

The null hypothesis is that all time dummy parameters except one are zero. The F statistic is . The p-value of .3180 does not reject the null hypothesis.

The SAS TSCSREG and PANEL procedures and the Stata .xtreg command conduct the Wald test. You may get the same test using the TEST statement in LSDV1 and the Stata .test command (the output is skipped).

PROC REG DATA=masil.airline;
MODEL cost = t1-t14 output fuel load;
TEST t1=t2=t3=t4=t5=t6=t7=t8=t9=t10=t11=t12=t13=t14=0;
RUN;

. quietly regress cost t1-t14 output fuel load
. test t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14