I think you need to conduct some pre-estimation tests to determine any possible heteroskedasticity or cross sectional dependence in the dataset. You may also read Tsalavoutas et al. 2012, Moundigbaye, William S. Rea, and W. Robert Reed 2018.

you try random effect model.

It may give more intuitive results.

Why a Random effects model? If I have unobservable factors, that are correlated with the X market-to book ratio, then I would get biased SE would I not?

Hello

Your worries are justified. Especially when the modeling concerns variables such as the financial structure, the unmeasurable specificities of the companies are in most cases explanatory variables.

 You do the Hisiao test to determine if the effects of individuals and periods are fixed. By software Stata you use the command xtreg Y X1 X2 X3 .... Xk, fe then you observe the value of the Fisher statistic at the bottom of the regression table F. If its value is higher than the parameterized value, then it is necessary consider fixed effects. You determine next if these effects are random using the Breuch-Pagan test. By Stata, this test is obtained after a regression: xtreg Y X1 X2 X3 ... Xk, re by entering the command xttest0. If the Breuch-Pagan statsitic is greater than the Chi-2 value at the 5% threshold, then you confirm the existence of the panel structure.

The choice between fixed and random individual effects is based on test results like Hausman's. By Stata, after the regression xtreg Y X1 X2 X3 .... Xk, fe you register the model by: estimate store eq1 then you make a reference: xtreg Y X1 X2 X3 .... Xk, re before performing the command: hausman eq1. The result is a Hausman statistic that allows a fixed effects model to be taken if it is greater than the chi-2 value at the 5% threshold.

Once the specification of the individual and temporal effects is complete, it is possible to determine the cause of the non-significance of your explanatory variable. Heteroscedasticity and autocorrelation tests must be done, since the temporal dimension of your panel is large there is a good chance that the residues have a structure AR, MA or others. To make sure you do the regression: xtregar Y X1 X2 X3 .... Xk, fe lbi then look at the Baltagi and wu statistic at the bottom of the results table. This statistic follows a reduced normal centered distribution and if it is greater than 1.96 then the residues may have an AR structure. To be sure of the order of the AR perform a test similar to that of Breuch-Pagan. After regression Y X1 X2 X3 .... Xk, fe / re save the residuals by: predict res, e. You regress the residues on their delays 1, 2, 3, 4 and you stop if after two delays the residues become insignificant: regress res L.res L2.res L3.res L4.res If beyond the second delay (L2.res) the residues are statistically significant, there is a good chance that it is an MA process.

You test the existence of heteroscedasticity and there is a good chance that you will not find it if the number of individuals is low and the number of times is important. After the regression Y X1 X2 X3 .... Xk, fe you enter the command xttest3, or the command xttest1 for the random effects model. For the case of xttest3 there is heteroscedasticity if the Breuch-Pagan statistic is much higher than the parameterized value of Chi-2. There is heteroskedasticity in the random-effects model if the Chi-2 statistic, which assumes that the residue variances are stable, has a higher value than the ch-2 statistic.

If these tests are conclusive then you have the following choices:

Fixed effects model

only autocorrelation of the same order: xtregar Y X1 X2 X3 .... Xk, fe

only heteroscedasticity of the same form: xtreg Y X1 X2 X3 .... Xk, fe vce (robust)

heteroscedasticity and autocorrelation of the same form: xtregar Y X1 X2 X3 .... Xk, fe

heteroscedasticity inter individual, correlation of the residues inter-individuals and which are an MA: xtscc Y X1 X2 X3 .... Xk, fe (estimator of Driscoll and Kray to download by ssc instal xtssc)

Random effects model

only autocorrelation of the same order: xtgls Y X1 X2 X3 ... X4, panels (iid) corr (ar1) (do not use xtgls if the panel period is less than 20 years) otherwise: xtpcse Y X1 X2 X3 ... X4, correlation (ar1) independent

autocorrelation specific to each individual and without heteroscedasticity Y X1 X2 X3 ... X4, panels (iid) corr (psar1)

specific autocorrelation and heteroscedasticity (no correlation between variances of residues): xtgls Y X1 X2 X3 ... X4, panels (heteroskedastic) corr (psar1) (with correlation of residue variances) panels (correlated) corr (psar1)

NB: since your model contains variables delayed by one period, it is advisable to use a dynamic model with a first difference and a type estimator: Arrelano and Bond or Blundell and Bond (xtdpdsys Y L.X1 L.X2 L .X3 ... L.X4, lags (1) artests (2) for which you check the validity by (estat abond) where the residuals of second order will not be statistically significant.

Maybe your main contribution is to do the empirical examination but with a more restrictive and robust methodology

Good luck

Thanks @Zoubir for your very long and detaiæed answer. My main contribution is to test the relationship on the Scandinavian market however, because it has some very different characteristics compared to the US regarding for instance the ownership structure of firms and a less disperse equity market.

However, now two month into the research, I must admit that the econometrics has gotten me very curious and I wish I had time to change my subject to contribute with a more robust method. However, this is not possible at this point in time.

My main concern with using Fixed Effects is, that it only considers within variation. That is fine in testing the short term effect of variations in the marker-to-book on equity issued, which I do.

However, when it comes to the variable of external finance weighted average market to book ratios, the case is different. Here, I want to compare on a cross-sectional basis to test if firms with a high EFWAMB ratio has lower leverage than firms with a small EFWAMB.

I am not sure that the Fixed Effects model can provide me with this answer? What the FE model would give me is a coefficient that predicts the change in current leverage of a change in the EFWAMB?

You're welcome. The purpose of the fixed effects panel structure is only to make the conditions of the tests more binding. The interpretation of the regression coefficient does not change. Using an EF model in your case allows for a negative coefficient associated with the variable EFWAMB (t-1) which will be interpreted as follows:

given the specificities of the companies (corporate culture, management style, stakeholder relations and other unobservable variables) an increase in the ratio (EFWAMB) of 10% leads to a drop in book leverage of an average of 10% * (regression coefficient) and in this case your hypothesis is validated.

I would like to point out that we should treat the heteroscedasticity that is still present in the panels where the number of companies is important. Since each company has its own form of heteroscedasticity, it will be better to use a dynamic model with a first difference of Blundell-Bond type. Heteroscedasticity and possibly autocorrelation are the sources of the lack of significance of your variable (EFWAMB).