QUESTION 1: How to regress company data, i.e. sales (X) against GDP (Y) for 10 years (n = 10)?  Since the model is a simple regression resulted from single X (independent variable) and Y (dependent variable), the model is a straight forward linear regression:

(1)   Y = B0 + B1X1 + e

... where Y = company data (quantitative, i.e. sales, etc.); B0 = slope or average value of Y absent X; X = GDP value; and e = forecast error. The hypothesis statements are: H0: B1 = 0 and HA: B1 not = 0. If B1 = 0, you have a failed model. Don't do anything further. Your hunch about the relationship between the company value and GDP did not pan out. If B1 not = 0, then go to next step to find the correlation coefficient between X and Y. Since Y and X are assumed to be quantitative in this case, Pearson r is used, thus:

(2)   r = B1(Sx / Sy)

... where r = correlation coefficient ranging with a range of -1< r 1.83 = significant relationship. Compare the value resulted from equation (3) to 1.83; conclude.

SIDE ISSUE: 200 COMPANIES. How to treat them? These 200 companies cannot be lumped together. They are individual companies. If you want to make a "general statement" about these 200 companies, you must prove that they are homogeneous, i.e. no significant difference. Depending on what value do you use in the measurement for the companies, i.e. sales, expenses, etc. They might not be homogeneous. In that case, you run individual tests using (1), (2) and (3) and conclude: [1] significant or [2] not significant according to the result of (3). Then score significant = yes = 1 and not significant as no = 0. From there, run binomial distribution test for significance of the findings to come to a general conclusion for the entire group of 200 companies.

STARTING POINT: This may be a starting point. Further variations in methodology may also be introduced. Is regressing company value (data) against GDP a valid model? This question was not asked.

Try to include companies from different countries. If the firms are all from the same country, macro GDP will not provide additional information. In fact, it could not be distinguished from common time effects. Probably, one alternative is to use sectorial GVA instead of overall GDP. This would work, given that not all the firms are from the same industrial sector.

You may have macroeconomic data that does not mean that given the characteristics of the sample (N much larger than T) considers one microeconometric model. If estimates a microeconometric model with panel data is due on the following questions. That econometric problem you want to solve by using a micro panel (ommited varible problem, unobserved heterogeneity, etc). When you solve these problems must choose the most appropriate estimator, as fixed or random effects or GMM estimator if you use lags of the dependent variable.

QUESTION 1: How to regress company data, i.e. sales (X) against GDP (Y) for 10 years (n = 10)?  Since the model is a simple regression resulted from single X (independent variable) and Y (dependent variable), the model is a straight forward linear regression:

(1)   Y = B0 + B1X1 + e

... where Y = company data (quantitative, i.e. sales, etc.); B0 = slope or average value of Y absent X; X = GDP value; and e = forecast error. The hypothesis statements are: H0: B1 = 0 and HA: B1 not = 0. If B1 = 0, you have a failed model. Don't do anything further. Your hunch about the relationship between the company value and GDP did not pan out. If B1 not = 0, then go to next step to find the correlation coefficient between X and Y. Since Y and X are assumed to be quantitative in this case, Pearson r is used, thus:

(2)   r = B1(Sx / Sy)

... where r = correlation coefficient ranging with a range of -1< r 1.83 = significant relationship. Compare the value resulted from equation (3) to 1.83; conclude.

SIDE ISSUE: 200 COMPANIES. How to treat them? These 200 companies cannot be lumped together. They are individual companies. If you want to make a "general statement" about these 200 companies, you must prove that they are homogeneous, i.e. no significant difference. Depending on what value do you use in the measurement for the companies, i.e. sales, expenses, etc. They might not be homogeneous. In that case, you run individual tests using (1), (2) and (3) and conclude: [1] significant or [2] not significant according to the result of (3). Then score significant = yes = 1 and not significant as no = 0. From there, run binomial distribution test for significance of the findings to come to a general conclusion for the entire group of 200 companies.

STARTING POINT: This may be a starting point. Further variations in methodology may also be introduced. Is regressing company value (data) against GDP a valid model? This question was not asked.

Please refer to

http://www.federalreserve.gov/pubs/feds/1997/199703/199703pap.pdf.

in the first instance, is it econometrically right to regress company data on aggregate data such as GDP? please throw more light then the problem of the different between N and T can be looked into .

You might want to have a look at

https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_modelling_of_Time-Series_Cross-Sectional_and_Panel_Data

and the resources  at

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

The actual placing of the GDP observations in the spreadsheet of your Panel depends on how it is arranged.

Where we have added Macro-economic avariables to a panel analysis we have just added them as another column in the panel.

If the Panel is by company and several vaiables just add it as the last variable for the correct year; this involves 10 entries for 1 company.  Repeat this for each company.  It is a bit repititous but won't take to long for 200 companies.  If you can write a little visual basic it is even quicker.

As final comment you might want to use some other measures like inflation, unemployment rate, exchange rate.  Best to collect them all and do it at once.

@Stuart Thanks for the detailed answer. Can you please attach spreadsheet containing an example?