Partial Adjustment Model

Firstly, download the excel file called " japan_interest " from this page.

Then creates a Workfile like  below which starts at cell E9 and the variables are m1, m2, irate, cpi and ip.

We postulate the following long run desired money demand function: 

log(M*_t) = b₀ + b₁log(irate_t) + b₂log(ip_t) + u_t

Since M*_t is unobservable, how can we deduce the coefficients for this long run desired equation. We can do it through the  postulated "Partial Adjustment" hypothesis as:

 log(Mt)- log(Mt-1) = c [log(M*_t) - log(M_t-1)]

Through substitution, we can have the observable short run money demand function as: 

log(M_t) = cb₀ + cb₁log(irate_t) + cb₂log(ip_t) + (1-c)log(M_t-1) + cu_t

or  log(M_t) = r₀ + r₁log(irate_t) + r₂log(ip_t) + r₃log(M_t-1) + v_t

Then, we can run regression and get coefficients for short run money demand function which will be use to deduce for coefficients of long run money demand function. The equation specification is

The regression result is:

Estimated log(M_t) = -0.178782  - 0.23416log(irate_t) + 0.209937log(ip_t) + 0.842745log(M_t-1)

Then, to test whether it is serial correlation in the regression, Durbin h test can be used:

Durbin h* =(1-DW/2)[n/1-(n*Var(r₃)]

h* = (1- 0.5*2.606624)*[245/(1-245(0.036132)²)]^1/2 = -5.756

Since h* < -1.96, thus at the 5% significant level we reject the H_o that there is negative first-order autocorrelation.

In EVIEWS, we can use the pre-programmed Breusch-Godfrey (BG) test, also know as the Lagrange multiplier (LM) test to test whether there is any high-order autocorrelation within the model. Simply. by choosing "View", "Residual tests", " Serial Correlation LM Test", 

and set "Lags to include" is "1", then the result is:

As you can see, the computed Chi-square is 30.08481 which is very large and its probability is also close to 0,  we can conclude that there may exist a higher-order series correlations in the autoregressive model. (Remark: Since a high-order autocorrelation may exist in the model, we should use other methods to remove it , but it is out of our scope.)

For finding the desired long run coefficients, b₀, b₁ and b₂ of the money demand function, the calculation are as following:

since (1- c)  = 0.842745 and c = 0.15725

b₀ = -0.178782 / (0.15725) = -1.1369

b₁ = -0.023416 / (0.15725) = -0.1489

b₂ = 0.209937 / (0.15725) = 1.3350

The estimated desired long run money demand equation is:  

log(M*_t) = -1.1369 - 0.1489 log(irate_t) + 1.3350 log(ip_t)

The End