How to determine order(s) of autocorrelation

[Mark Gertsen]

Dear all,

I'm having some trouble with determining the amount of lags I should use in an ARDL model. I am regressing a form of interest rates (x) on the size of the economy (y) of a country. It is very likely that for both dependent and independent variables autocorrelation is present. To adress this, I want to use the ARDL model. However, according to literature (Principles of Econometrics 4th edition, by Hill, Griffiths and Lim), there are a number of subjective criteria for choosing the amount of lags of both variables.

1. Has serial correlation in the errors been eliminated? (this can be checked with a correlogram or LM tests)
2. Are the coefficient signs consistent with expectations?
3. Are the estimates significantly different from zero?
4. Which amount of lags minimize information criteria such as the AIC and SC?

Obs: 420
Countries: 28
Years per country: 15
Strongly balanced panel
To normalise Y, i take logs.

H0 of no first order autocorrelation can be rejected as per:

xtserial logy x

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,      27) =    124.790
           Prob > F =      0.0000

Question 1: which lags do I determine first, those of X or those of Y? Or does it need to be determined simultaneously?

I started off with determining lags of X first, but since it's a panel data set, I cannot use -corrgram- to see how many lags are statistically significant. I have looked at scatter diagrams between x and x_1, x and x_2, x and x_3, but those do not give a definitive answer to the question. I decided to use a correlation table to see which lags (out of 5 to start with) are correlated, but I'm not sure if that's the right way:

           |    x x_1 x_2 x_3 x_4 x_5
-------------+------------------------------------------------------
       x    |   1.0000 
             |
             |
    x_1    |   0.6639*  1.0000 
             |   0.0000
             |
    x_2    |   0.3015*  0.6528*  1.0000 
             |   0.0000   0.0000
             |
    x_3    |   0.1671*  0.2796*  0.6514*  1.0000 
             |   0.0021   0.0000   0.0000
             |
    x_4    |   0.1044   0.1655*  0.2779*  0.6536*  1.0000 
             |   0.0672   0.0036   0.0000   0.0000
             |
    x_   5 |   0.0299   0.1364*  0.1816*  0.2983*  0.6710*  1.0000 
             |   0.6188   0.0225   0.0023   0.0000   0.0000

This suggests lags 1-3 are statistically significant with the x variable. When regressing this however, it does not give me statistically significant results for lag 1 and 2 (where 2 also has an unexpected sign):

Random-effects GLS regression                   Number of obs     =        336
Group variable: Country                         Number of groups  =         28

R-sq:                                           Obs per group:
     within  = 0.0835                                         min =         12
     between = 0.0459                                         avg =       12.0
     overall = 0.0312                                         max =         12

                                                Wald chi2(4)      =      28.26
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     log(y) |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       x     |   .0017694   .0007606     2.33   0.020     .0002787    .0032601
    x_1     |   .0005826   .0009607     0.61   0.544    -.0013004    .0024656
    x_2     |  -.0000425    .000964    -0.04   0.965    -.0019318    .0018468
    x_3     |   .0023062   .0007694     3.00   0.003     .0007982    .0038143
    _cons |    .742227   .0200991    36.93   0.000     .7028335    .7816205
-------------+----------------------------------------------------------------
     sigma_u |  .10615044
     sigma_e |  .02462382
         rho |  .94893718   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Also, I do not seem to be able to use an LM test (-estat bgodfrey- is not valid) or -dwstat2- because I'm using multiple panels.

Question 2: what am I doing wrong with regards to these lags?


As for the lags of Y, I'm running into a similar problem of not being able to test whether the amount of values I choose is correct.


I hope I have been detailed enough. However if there is missing information, I'm very happy to supply it. Thanks in advance for any help!

Mark