HAUSMAN TEST MAY NOT BE THE BEST TO START WITH: The Hausman test uses the linear model as its basis for the test.The linear model is presented as: Y = bX + e where X is the vector of regression, b is a coefficient of X and e is the error term. In this case, the problem does not come from whether one select random or fixed effect, the focus should be X. What was used for X? There are 21 years---this means sample size is 21. There are 24 nations, is it that you are comparing foreign bank entry in 24 countries? If that is the case, you would also have: Y1, Y2, ..., Y24 which you try to explain over a period of 21 years. if you Hausman test results insignificant, it means that your choice of X does not explain Y in Y = bX + e. What are your current Xi? Not knowing what is/are your Xs is difficult to answer.

SUGGESTION: Run the regression of Y = bX + e for each country and for each X one at a time and check its significance level. Instead of Hausman test, I suggest conventional t-test (assume the data passes normality test in Anderson-Darling and that Y is quantitative and X also quantitative) thus:

(1)   r = b(Sx / Sy)

... where r = Pearson correlation coefficient for Y and X; Sx = standard deviation of X; and Sy = standard deviation of Y. The test of significance follows:

(2)   tr = r(sqrt(n - 2) / sqrt (1 - r2)

... where n = 21 years. rund single regression one-by-one to verify which X is significant. First run simple regression on all Xi to obtain:

(3)   Y = B10 + B11X + ei

Verify that B11 is significant. Drop the ones that are not significant. Select all those that are significant, then run regression among these Xs to verify their mediation effect:  

(4)   Y = B20 + B21X + ei

Verify that B21 is significant. Next regress the dependent variable on both mediator and independent variable X, thus:

(5)   Y = B30 + B31X + B32Me + e

 Verify that B32 = significant. Note that B31 < B11 due to mediation effect. Following this approach, you might have interesting finding with your current data set. To complete the process, you would also want to see if there is a moderation effect, thus:

(6)   Y = g0 + g1X1 + g2X2 + g3X1X2 + e

This would give a complete picture: knowing what is mediating and moderating the value of Y. This approach would give more information than what Hausman would provide because Hausman is based on a linear argument Y = bX + e.

I am grateful to you Mr. Paul for a depth explanation. 

but I would like to clarify my question for some more input from you.

I am studying on finding the determinants for foreign banks entry into India after liberalization. I found out that there are foreign banks in India from 24 countries. so, I have panel for 24 countries and 21 years which is unbalanced. As X is the independent variable which consists of five macroeconomic factors like FDI, GDP, Interest rate Differentials, NIM and Domestic Savings. I have collected the available data for all these variables.

When I ran Panel OLS by selecting none in the panel option -effect specification- cross section, I got three variables significant. But when i applied fixed or random effect, all the variables are insignificant even at 10% level. 

So In case i don't select any effect under Panel option in E view. am I prove something. (Note: the study takes hypothesis where the heteroscedasity for cross section variable does not matter).

UNBALANCED: This is not a problem. This issue was resolve long ago in joint probability writing. The "balance" you referred to was termed K x K (in Pearson's time when he first introduced tetrachoric correlation); it was later made K x L (post Pearson when polychoric correlation was introduced) in order to accommodate situations where row > column and vice versa. you don't have a problem here.

INDEPENDENT VARIABLES: FDI, GDP, interest rate differentials, NIM and Savings. The objective is foreign bank entry into India. Let's take a look.

(i) Can FDI explain international banks entry? Actually, foreign banks entering a country will bring capital with them. Most countries have minimum capital requirement law which foreign banks must maintain. This may have been registered as part of FDI already. using FDI to explain foreign bank entry may run into issue of "double accounting.

(ii) Can GDP explain foreign bank entry? This is a tricky one. You might had to "lag" GDP one year back because prior year's GDP is used by foreign bank in assessing country entry. GDP can explain, but you have to look back one year prior for the current year's bank entry.

(iii) Interest rate differential may a logical choice. if India pays 7.5% and banks in the US are paying 2.5%. Note that although there is an interest rate differential that would lead to a jump in conclusion that foreign banks must come because of high interest rate; however, this variable itself is a function. Foreign banks must exchange US dollar to Indian Rupee to earn high interest rate in India. Once interest is earned, it is paid in Rupee. There is India income tax to pay plus adjustment must be made for inflation average about 6.9%, netting only 0.60% in real earning. See link below.

(iv) NIM ---- not sure what is this one. Net import?

(v) Savings rate of India is 26% and is on a downward trend. See link below. The prospect does not seem positive.

PRELIMINARY SIGNIFICANT TEST RESULTS: individual runs shows 3 variables significant, when combine none shows significant. This is an interesting finding; in fact, a learning experience. It is a prima facie evidence that there is a mediation effect among the variables. This happens very often. Through such an approach you have discovered for yourself a new method of "model testing." Now one must go back to step one and re-think variable selection that would explain foreign bank entry.

Foreign banks enters an foreign market for any number of reasons: (i) tax treatment, (ii) revenue from banking transactions in emerging market, (iii) foreign presence for the sake of going international because everyone else had gone international (herding effect); (iv) speculating for the potential take-off, i.e. India and China are economic regional powers; (v) diversification; etc. Try to look into these possibilities and run the same test as you did. You are on the right track for testing; just need to explore more variables.

http://www.inflation.eu/inflation-rates/india/historic-inflation/cpi-inflation-india-2014.aspx

http://data.worldbank.org/indicator/NY.GDS.TOTL.ZS

My Dear, An attached file will help you..

what is option best from the panel data for analysis the moderating variable, if the secondary data

Dear Friend, first of all, to choose the fixed or random effect, first of all, you should applied the Hausman test, then your p value less than alpha level (0.05), you should select the fixed effect, if your p value is insignificant, you should select the random effect. As far as the GMM, before run GMM you should be checked heterscadecity, endogeniety problems, if you found such problems, you can run GMM by selecting the instruments variables