Panel data problems: singular matrix and hausman test

[trangnguyen]

Hello, I am doing my thesis and having problems with panel data analysis. My topic is the determinants of capital structure so I make a regression of leverage level (Leverage) on some independent variables ( profitability, tangibility, business risk, non-tax shield, size, growth, gdp and inflation) and year dummy variables. GDP and Inflation are different cross-time but not cross-section. Data from 2000 to 2013 includes 672 companies. I want to use both fixed effect and random effect for following equation:
leverage c growth(-1) profitability(-1) size(-1) tangibility(-1) tax(-1) business_risk(-1) inflation(-1) gdp(-1) year_01 year_02 year_03 year_04 year_05 year_06 year_07 year_08 year_09 year_10 year_11 year_12 year_13

There are some below problems:
- Singular matrix error:
+ For full window period, even I drop year dummies for 2000, 2001 and 2002, I cannot get the result. Does this mean I need to keep drop more variables? In that case, which one should I drop?
+ For 2008-2013 period, I cannot include any dummies
- Hausman test: there is an error: "Cross-section test variance is invalid. Hausman statistic set to zero"
If anyone can help me with those. Thank you in advance