Economic Significance

[Raja Hasan]

Hi, I have a large dataset.

The dependent variable is Y and independent variable is X and there are other control variables.

Here, Y = log(std of P)
and X = sum of (standardize value of a and b)

Considering I know mean and std of Y and X, how will I explain economic significance?

Could anyone please help me?

[Maarten Buis]

Economic significance just means that you consider the parameter big enough that it has a noticeable and meaningful impact on the (economic) process you are studying. So at it's core it is a subjective evaluation of the parameter. You look at the parameter, you think about what that parameter actually means for the process you are studying, you compare it with what you already know, and you decide whether or not you think that it is a big effect or a small effect. Important is that you can argue why you think that. For example, because the effect is about as big as another well known effect that is routinely considered big.

[Joro Kolev]

Further to what Maarten said, it is hard to talk of economic significance in your case as you have already standardised everything.

[Raja Hasan]

Hi Joro,
Yes. That is hard. That's why I am not sure how I will calculate economic significance in this case. If I have Y= P, (where p=return/total asset) then I can calculate something like following.

Coefficient of X multiply by sample mean std of X

And then explain it like the following
A one-standard-deviation increase in X is associated with a increase/decrease in P of (2% --just an example) percent of total assets.

I am not sure if use log of P instead of Raw value, how will I calculate the significance? This is where I need help.

Maarten Buis

Can you tell me how I can solve this problem?

[Joro Kolev]

Probably I did not say it right. When you are standardising your variables, you are moving away from economic significance. What I mean by "hard" is that when you standardised, you lost the economic significance interpretation.

If you standardise both your regressor and regressand, this is equivalent to beta weights regression, here:

. sysuse auto, clear
(1978 Automobile Data)

. reg price mpg, beta

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     20.26
       Model |   139449474         1   139449474   Prob > F        =    0.0000
    Residual |   495615923        72  6883554.48   R-squared       =    0.2196
-------------+----------------------------------   Adj R-squared   =    0.2087
       Total |   635065396        73  8699525.97   Root MSE        =    2623.7

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|                     Beta
-------------+----------------------------------------------------------------
         mpg |  -238.8943   53.07669    -4.50   0.000                -.4685967
       _cons |   11253.06   1170.813     9.61   0.000                        .
------------------------------------------------------------------------------


. summ price

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       price |         74    6165.257    2949.496       3291      15906

. replace price = (price - r(mean))/r(sd)
variable price was int now float
(74 real changes made)

. summ mpg

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
         mpg |         74     21.2973    5.785503         12         41

. replace mpg = (mpg-r(mean))/r(sd)
variable mpg was int now float
(74 real changes made)

. reg price mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     20.26
       Model |  16.0295484         1  16.0295484   Prob > F        =    0.0000
    Residual |   56.970452        72  .791256278   R-squared       =    0.2196
-------------+----------------------------------   Adj R-squared   =    0.2087
       Total |  73.0000004        73  1.00000001   Root MSE        =    .88953

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -.4685967   .1041111    -4.50   0.000    -.6761384   -.2610549
       _cons |  -3.76e-09   .1034053    -0.00   1.000    -.2061347    .2061347
------------------------------------------------------------------------------

.

The interpretation in beta weights regression is that one standard deviation increase in mpg leads to -.4685967 standard deviations increase in price.

There is no economic significance here, everything is in unitless measures of standard deviations.

[Raja Hasan]

Joro Kolev
Thank you very much for providing example. Will it be same if we calculate 5 year rolling std of price and then use log of std_price? In my case, I have done the same with my dependent variable.

[Raja Hasan]

Joro Kolev

Is my calculation and explanation in #4 correct? In this case, the dependent variable is not standardize. Only independent variable is standardized.

[Joro Kolev]

I think yes, if you only standardise the independent variable.

Say you run

log (P) = a + b* Standardised X + e

then the interpretation would be that "One standard deviation increase in X leads to b*100 percent increase in P".

Joro Kolev

Is my calculation and explanation in #4 correct? In this case, the dependent variable is not standardize. Only independent variable is standardized.

[Raja Hasan]

Joro Kolev
That's awesome. Thank you very much.