Illustrating changes in the Structure of the Malaysian Economy Empirically

Illustrating changes in the Structure of the Malaysian Economy Empirically

∆X = X1 – X0

= R[E1 – E0) + µ1(D1 –D0) + µ1(A1 – A0)X0 + (µ1 - µ0) (A0X0 + D0) ]

whereby;

∆X = change between 2 years (eg 2010 & 2000; 1990 & 1970)

= changes in domestic demand & changes in export & changes in technological efficiency (or inefficiency?)

in other words:

we can see whether the Economy is export-led or or whether it is domestically-driven or whether technology is a key driver of the economy .....

So there you go - you can prove many things using numbers

 

METHOD FOR STRUCTURAL DECOMPOSITION OF OUTPUT

In an open Leontief system, the basic material balance between supply and demand can be written as:

                  X = D + W + E – M                                                                                          (1)

Where X, D, W, E and M are respectively vectors of gross output, domestic final demand, intermediate demand, export demand, and import.

Noting that the intermediate demand of i^th sector can be determined by by multiplying the input-output coefficients by total sectoral output as  W = AX (where A is the matrix of input coefficients), while the import ratio can be computed as import to total domestic supply as m_i = M_i /(D_i + W_i) Chenery 1979).

Because import ratio, m_i = M_i /(D_i + W_i)

Therefore, M_i = m_i (D_i + A_iX_i)

Equation (1) can be written as:

                  X = D +AX + E – m (D + AX)

                 = (I – m) D + (I – m) AX + E                                                    (2)

By putting µ = I – m (where µ represents the diagonal matrix of domestic supply),

                  X = µD + µAX + E                                                 

                  X – µAX = (µD + E)

                  X (1 - µA) = (µD + E)

                  X = (I- µA)^-1(µD + E)                                                                (3)

By taking “∆ decomposition measure” (utilized by Kubo and Robinson 1979), and because R =  (I- µ₁ A₁)^-1

                  ∆X = X₁ – X₀

                       = R(µ₁D₁ + E₁) – X₀

    = Rµ₁D₁ + RE₁ – X₀           

    = Rµ₁D₁ – Rµ₁D₀ + Rµ₁D₀ + RE₁ – RE₀ + RE₀ – X₀     

                     = Rµ₁(D₁ – D₀) + Rµ₁D₀ + R (E₁ – E₀ ) + RE₀ – X₀         

                = Rµ₁∆ D + R∆E + Rµ₁D₀ + RE₀ – X₀

The last three terms of the above expression can be expanded as follows:

         Rµ₁D₀ + RE₀ - X₀

                = Rµ₁D₀ + RE₀ - RR^-1 X₀  

                = Rµ₁D₀ + RE₀ – R (I - µ₁ A₁ )X₀

                        = Rµ₁D₀ + RE₀ – RX₀  + Rµ₁ A₁ X₀

 = Rµ₁ A₁ X₀   + Rµ₁D₀  – R (X₀  – E₀)

 = Rµ₁ A₁ X₀ - Rµ₁A₀X₀  + Rµ₁ A₀ X₀ + Rµ₁D₀  – R (X₀  – E₀)

= Rµ₁ (A₁ -A₀) X₀  + Rµ₁ A₀ X₀ + Rµ₁D₀  – R (X₀  – E₀)

              = Rµ₁∆AX₀  + Rµ₁ (A₀ X₀ + D₀)  – R (X₀ – E₀)

From equation (1),

                  X = D + W + E – M                 

i.e.           X – E = D + W – M

Therefore,

                  (X₀ – E₀) = D₀ + W₀ – M₀

                                    = (D₀ + A₀X₀ ) – m₀ (D₀ + A₀X₀)

                                    = (1 – m₀) (A₀X₀ + D₀)

                                    = µ₀ (A₀X₀ + D₀)

Therefore...

                  ∆X            = X₁ – X₀

                  = Rµ₁∆ D + R∆E + Rµ₁D₀ + RE₀ - X₀

= Rµ₁∆ D + R∆E + Rµ₁∆AX₀  + Rµ₁ (A₀ X₀ + D₀)  – Rµ₀ (A₀X₀ + D₀)

= Rµ₁∆ D + R∆E + Rµ₁∆AX₀  + R (µ₁ – µ₀) (A₀ X₀ + D₀)

= Rµ₁∆ D + R∆E + Rµ₁∆AX₀  + R∆µ(A₀X₀ + D₀)   

 = R [µ₁∆ D + ∆E + µ₁∆AX₀  + ∆µ(A₀X₀ + D₀)]   

From equation (4), the decomposed ∆X can be expressed as follows:

∆X = Rµ₁∆D represents the change in domestic demand

        + R∆E represents the change inn export demand

        +Rµ₁∆AX₀ represents the change in intermediate demand

       + R∆µ(A₀X₀ + D₀) represents the change in import substitution

The decomposition equation can be defined by using initial year structural coefficients and terminal year weights as follows:

∆X            = X₁ – X₀

= R [µ₁∆ D + ∆E + µ₁∆AX₀  + ∆µ(A₀X₀ + D₀)]   

Because:

∆D = (D₁ –D₀), ∆E =  (E₁ – E₀),  ∆A = (A₁ – A₀),  ∆µ =  (µ₁ - µ₀),  therefore:

∆X            = R [µ₁(D₁ –D₀) + (E₁ – E₀) + µ₁(A₁ – A₀) X₀ + (µ₁ - µ₀) (A₀X₀ + D₀)]

Where subscripts 0 and 1 designate the initial year and terminal year, respectively.