# regression coefficient expected to be negative but it is always positive

In my research project I have to do a regression of the financial risk on the business risk of the year before. As a reference, I have a paper showing the results for several countries. The paper states that, for the country I am interested in, the coefficient of the regression is negative. their year span :1995-2008

I have to perform the same analysis at region level for the country I am interested in. I find a negative lagged correlation coefficient. However, the coefficient in my regression is positive and significant. My year span:2000-20014.

Should I not have a negative coefficient as in the country-level regression (paper). Thank you.

• Without knowing more about the underlying science it is difficult to be sure but as a general principle why would you always expect to repeat the results of the past? Things can change. Authors may have been wrong. – mdewey May 13 '16 at 20:53
• Thank you for your answer. The project is about risk balancing in farm households: high business risk should result in Low financial risk. Besides, as my overall negative coefficient is negative, I assumed the regression coefficient should be negative as well. – shenice May 13 '16 at 20:59
• Perhaps you need to give us some more details about the various models involved here? – mdewey May 13 '16 at 21:11
• The model is the following: log(FR)=b1*log(BR)+b2*log(cost of debt)+b3*log(asset profitability)+b4*log(area)+b5*age+year_dummies+region_dummies+farm_types_dummies log(BR),log(cost of debt) and log(asset profitability) are lagged by 1 I have 7 farm types and 13 regions. – shenice May 13 '16 at 21:14

## 3 Answers

It is in fact possible for groups of cases in which a relationship is in one direction to exhibit an apparent relationship is in the opposite direction when all the data is analyzed together. This is called Simpson's paradox.

Such coefficient reversals are quite common in my expirience. It often depends on simple things like the fact that you are using a differen time interval than the original authors. I would simply change the years you are using a couple of times and see what happens to the coefficient.

Furthermore, the reason might be the source of the data. Where is the data from in the study you are referring to? Wheres does your data come from? Is it seasonally adjusted? Look at simple correlations in the data and so on.

The difference might also come from the controls you are using. Just play around with the data: Start with only the variable you are interested in at righthand side..Is the coefficient already positive? If not, add further controls one by one to see where the reversal in sign happens.

• Thank you for your reply. The reference study data and mine are from the same source. I have tried using another proxy for the business risk: the reference paper uses the coefficient of variation of the NOI and I have another paper where they use an asset-based measure. And with that proxy my coefficient is negative. So I don't really know how to explain this – shenice May 14 '16 at 6:00

Do you receive the same negative coefficients when you fit the model with the 1995-2008 span? Which coefficients are negative? Could you send the link for the data?