Food Prices and Overweight Patterns in Italy



Table 2: Estimated cointegrating vectors with price indices at regional (2a) and national (2b) levels
and theoretical restrictions imposed

Specification 2a - Regional price index.

w1

w2

logP1

logp2

logp3

Income

Intercept

Vector of cointegration (1)

-1

0

0.0106

0.0452

-0.0558

0.0946

0.1456

(0.0022)

(0.0171)

(0.0155)

(0.0454)

(0.0945)

[4.938]

[ 2.644]

[-3.594]

[2.081]

[1.526]

Vector of cointegration (2)

0

-1

0.0452

0.0368

-0.0820

-0.0237

0.0837

(0.0171)

(0.0061)

(0.0169)

(0.0561)

(0.0629)

[2.644]

[5.954]

[-4.829]

[-0.422]

[1.331]

Theoretical restrictions:

LR test

d.f.

p-value

Symmetry

1.3972

(1)

[0.2371]

Symmetry and homogeneity

10.39

(3)

[0.015]

Specification 2b - National price index.

w1

w2

logpι

logp2

logp3

Income

Intercept

Vector of cointegration (1)

-1

0

0.0118

0.0503

-0.0621

0.0493

0.1245

(0.0024)

(0.0108)

(0.0139)

(0.0295)

(0.1045)

[4.9089]

[4.6567]

[-4.4667]

[1.6712]

[1.1919]

Vector of cointegration (2)

0

-1

0.0503

0.0322

-0.0825

-0.0124

0.0237

(0.0108)

(0.0056)

(0.0630)

(0.0137)

(0.0562)

[4.6567]

[5.6929]

[-1.4732]

[-0.9028]

[0.4221]

Theoretical restrictions:

LR test

d.f.

p-value

Symmetry

6.46

(1)

[0.011]

Symmetry and homogeneity

33.754

(3)

[0.000]

Notes: Standard errors in round brackets; student’s t-test in square brackets. Degrees of freedom and
p-values of LR tests in round and square brackets, respectively.

Table 3: Residual serial correlation of the vector error correction model in equation (7)

VEC Residual Portmanteau Tests

VEC Residual Serial Correlation LM Tests

Lags

Q-Stat

Prob.

Adj Q-Stat

Prob.

df

LM-Stat

Prob

1

7.6456

-

7.7191

-

-

46.424

0.1144

2

20.253

-

20.571

-

-

42.455

0.2127

3

42.478

0.2120

43.451

0.1837

36

37.933

0.3812

Note: Q-statistics and adjusted Q-statistics are shown with small sample correction for residual serial
correlation up to specified order h (see Liitkepohl, 1991, for details). Also shown: LM test statistics for
residual serial correlation up to specified order (see Johansen, 1995, for details). Under null hypothesis
of no serial correlation, statistic tests are
χ2 distributed. Degrees of freedom are k2 (p - h) and k2 ,
respectively, where
k is number of endogenous variables of V AR and p is V AR lag order.

39



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