Hi, I'm currently studying the relation between construction tender price index and some economic variables (real GDP, building approvals, price index of private housing). I have searched relevant topics on this forum and resources on the internet and tried to estimate a VAR model on the data. But I am now facing the problem of interpretation of the coefficients estimated so I would like to ask for help here. First I would like to see if my works are correctly done:

The data are collected quarterly and covers the periods from year 1997 to 2010. I found that all variables are integrated at order 1so I decided to run VAR on them.

At first I ran VAR on the first order differenced data and see the lag-length criteria:

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Lag LogL LR FPE AIC SC HQ

0 -1305.396 NA 6.56e+17 52.37584 52.52880 52.43409

1 -1262.789 76.69339 2.27e+17 51.31154 52.07635 51.60279

2 -1227.069 58.57934 1.04e+17 50.52278 51.89944* 51.04702

3 -1204.974 32.70173 8.46e+16 50.27895 52.26745 51.03618

4 -1171.179 44.60934* 4.42e+16* 49.56715 52.16750 50.55738*

5 -1161.688 11.00912 6.40e+16 49.82753 53.03973 51.05075

6 -1147.021 14.66676 8.02e+16 49.88086 53.70490 51.33707

7 -1117.144 25.09694 6.01e+16 49.32576 53.76166 51.01498

8 -1093.219 16.26918 6.54e+16 49.00875* 54.05649 50.93096

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According to the third column, I decided to use lag length of four.

Then I ran Johansen Cointegration test on the variables at level with lag interval (1 4) and Eviews reports:

Unrestricted Cointegration Rank Test (Trace)

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Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.373539 60.00961 47.85613 0.0024

At most 1 * 0.300718 34.75552 29.79707 0.0124

At most 2 0.246171 15.43969 15.49471 0.0510

At most 3 0.003325 0.179835 3.841466 0.6715

Trace test indicates 2 cointegrating eqn(s) at the 0.05 level

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Since then I applied VECM on the variables at level, with lag interval (1 4) and 2 cointegrating equations, and the result is:

Cointegrating Eq: CointEq1 CointEq2

DLS(-1) 1.000000 0.000000

GDP(-1) 0.000000 1.000000

CONSENT(-1) 0.840727 345.3397

(0.16585) (32.6895)

[ 5.06924] [ 10.5642]

PIDOMESTIC(-1) -7.522969 -1238.059

(1.31409) (259.013)

[-5.72484] [-4.77991]

C -624.6280 -352319.6

(131.294) (25878.6)

[-4.75747] [-13.6143]

Error Correction: D(DLS) D(GDP) D(CONSENT) D(PIDOMESTIC)

CointEq1 -0.087126 -1.310316 -0.752511 -0.016387

(0.03805) (10.6109) (0.21696) (0.00627)

[-2.28981] [-0.12349] [-3.46850] [-2.61509]

CointEq2 0.000316 -0.123061 -0.001585 4.82E-05

(0.00020) (0.05454) (0.00112) (3.2E-05)

[ 1.61563] [-2.25614] [-1.42120] [ 1.49597]

D(DLS(-1)) 0.239486 35.02476 1.454408 -0.029682

(0.15763) (43.9577) (0.89878) (0.02596)

[ 1.51932] [ 0.79678] [ 1.61820] [-1.14340]

D(DLS(-2)) -0.113142 22.30902 0.152244 0.001768

(0.16567) (46.1998) (0.94462) (0.02728)

[-0.68295] [ 0.48288] [ 0.16117] [ 0.06482]

D(DLS(-3)) 0.156774 -27.36019 0.370964 -0.017493

(0.15664) (43.6818) (0.89314) (0.02580)

[ 1.00087] [-0.62635] [ 0.41535] [-0.67813]

D(DLS(-4)) 0.128427 42.62697 -0.143566 0.046587

(0.14463) (40.3344) (0.82470) (0.02382)

[ 0.88794] [ 1.05684] [-0.17408] [ 1.95586]

D(GDP(-1)) 0.000130 0.118840 0.003525 4.27E-05

(0.00037) (0.10380) (0.00212) (6.1E-05)

[ 0.34815] [ 1.14491] [ 1.66082] [ 0.69676]

D(GDP(-2)) 0.000193 0.007038 0.002379 6.52E-05

(0.00037) (0.10243) (0.00209) (6.0E-05)

[ 0.52447] [ 0.06871] [ 1.13572] [ 1.07823]

D(GDP(-3)) 0.000468 0.015970 0.001642 2.83E-05

(0.00033) (0.09310) (0.00190) (5.5E-05)

[ 1.40194] [ 0.17154] [ 0.86282] [ 0.51531]

D(GDP(-4)) 2.16E-05 0.890051 0.000352 3.44E-06

(0.00034) (0.09461) (0.00193) (5.6E-05)

[ 0.06355] [ 9.40752] [ 0.18201] [ 0.06162]

D(CONSENT(-1)) -0.057579 44.41051 -0.128162 -0.003001

(0.06261) (17.4592) (0.35698) (0.01031)

[-0.91970] [ 2.54367] [-0.35902] [-0.29102]

D(CONSENT(-2)) -0.066064 33.57194 0.020893 0.001181

(0.05468) (15.2474) (0.31176) (0.00900)

[-1.20830] [ 2.20181] [ 0.06702] [ 0.13117]

D(CONSENT(-3)) -0.017503 21.20179 0.152667 -0.003753

(0.04248) (11.8471) (0.24223) (0.00700)

[-0.41201] [ 1.78963] [ 0.63025] [-0.53638]

D(CONSENT(-4)) 0.012376 14.66215 0.210645 0.004571

(0.02810) (7.83662) (0.16023) (0.00463)

[ 0.44041] [ 1.87098] [ 1.31463] [ 0.98770]

D(PIDOMESTIC(-1)) 1.209503 412.5680 0.925190 0.619721

(0.88909) (247.940) (5.06951) (0.14642)

[ 1.36039] [ 1.66398] [ 0.18250] [ 4.23248]

D(PIDOMESTIC(-2)) 0.437685 -303.5912 -11.05572 -0.067530

(1.07281) (299.176) (6.11712) (0.17668)

[ 0.40798] [-1.01476] [-1.80734] [-0.38222]

D(PIDOMESTIC(-3)) -1.060077 179.0560 -6.118109 -0.228047

(0.95429) (266.124) (5.44131) (0.15716)

[-1.11085] [ 0.67283] [-1.12438] [-1.45106]

D(PIDOMESTIC(-4)) -0.937314 -543.9680 -4.354184 -0.209890

(0.90725) (253.005) (5.17307) (0.14941)

[-1.03314] [-2.15003] [-0.84170] [-1.40478]

R-squared 0.633543 0.904778 0.673666 0.738878

Adj. R-squared 0.460494 0.859812 0.519564 0.615571

Sum sq. resids 26443.66 2.06E+09 859737.7 717.1915

S.E. equation 27.10251 7558.094 154.5367 4.463405

F-statistic 3.661056 20.12135 4.371559 5.992167

Log likelihood -243.8550 -547.9153 -337.8584 -146.4544

Akaike AIC 9.698332 20.95983 13.17994 6.090903

Schwarz SC 10.36133 21.62282 13.84294 6.753897

Mean dependent 3.648148 3346.574 -5.844444 0.018519

S.D. dependent 36.89872 20186.29 222.9534 7.198770

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At this moment I would like to ask whether the steps of estimating this VECM is correct?

If not, could someone provide some guide on how should I do for the estimation?