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From |
Erasmo Giambona <e.giambona@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Economic Significance and Logged Independent Variables |

Date |
Wed, 8 Jul 2009 16:15:06 +0200 |

Thanks Austin for all the great ideas and suggestions. I think I have addressed some of the issues that you raise. I hope you don't mind to elaborate a bit more on the skewness concern. I thought that skewness could be the cause of the problem. However, I am really working with several sub-samples (extracted from the same sample) with similar skewness. I find that the coefficient changes drammatically only for one of the sub-samples. Could this also be due to some outliers? Thanks, Erasmo On Wed, Jul 8, 2009 at 3:41 PM, Austin Nichols<austinnichols@gmail.com> wrote: > Erasmo Giambona <e.giambona@gmail.com> : > > The change in coefficients is common in highly skewed variables, but > you have much larger problems. For starters, you are explaining y/x as > a function of x, which leads to division bias (see e.g. Borjas, 1980). > Also, I doubt Debt/Total Assets is really constrained to lie in > [0,1], since outstanding debt can exceed assets (also, how do you > count loans from the firm, which could count as negative debt). Also, > if your dependent variable is constrained to the unit interval, linear > regression is almost certainly inappropriate; see e.g. > http://www.stata.com/support/faqs/stat/logit.html or -ssc inst locpr- > for a graphing tool to see the likely functional form in a > cross-section; for the panel case, see > http://www.stata.com/meeting/snasug08/abstracts.html#wooldridge > > More importantly, what is the direction of a causal effect here? If a > firm issues bonds worth $100, they have $100 more debt and $100 cash > on hand, increasing y/x (as long as y/x<1 as you claim) and increasing > x, leading to a positive correlation. But why are they issuing debt? > It's not because they have higher assets (that is an outcome as well), > it's because the marginal value of investment exceeds the interest > rate. The positive correlation is not causal, not even close. Or > should we read that as Total Net Assets, i.e. are you subtracting Debt > from Total Assets? In that case, I am sure Debt/NetAssets is not > constrained to lie in [0,1], since debt can certainly exceed assets > less debt. > > Borjas, George J. “The Relationship Between Wages and Weekly Hours of > Work: The Role of Division Bias,” Journal of Human Resources, Summer > 1980, pp. 409-423. > > On Wed, Jul 8, 2009 at 9:09 AM, Erasmo Giambona<e.giambona@gmail.com> wrote: >> Dear Statalist, >> >> I have a panel dataset for a sample of publicly listed firms. >> >> I am fitting the following model using OLS: Debt/Total Assetsi = a + >> b*ln_Total_Assets + control variables + firm dummies + year dummies + >> ei. - where i is a subscript for firm i. >> >> The dependent variable is total Debt divided by Total Assets (both >> expressed in millions), which is a ratio ranging between 0 and 1; >> ln_Total_Assets is the natural logarithm of total assets. >> >> The output of the above regression shows that ln_Total_Asset is >> statistically significant at the 1% level. This variable has also a >> huge economic effect. In fact, a 1 standard deviation increase in >> ln_Total Assets causes Debt/Total Assetsi to increase by 0.15 (while >> its average is 0.202). >> >> Then, I run Debt/Total Assetsi = a + b*Total_Assets + control >> variables + firm dummies + year dummies + ei. This model differs from >> the above one only because I am not logging Total_Assets. In this >> case, I find that Total Assets is still highly statistically >> significant at the 1% level. However, its economic effect is >> negligible. In fact, a 1 standard deviation increase in Total Assets >> causes Debt/Total Assetsi to increase by 0.0002 (while its average is >> 0.202). >> >> I can see that logging a variable can make a difference on its >> economic effect. However, changing the economic effect from 0.15 to >> 0.0002 seems really a big difference. Can somebody provide some hints >> on why this might be happening? Is that an indicatio that there might >> be something special about the structure of my data? >> >> I would really appreciate any suggestions. >> >> Thanks, >> >> Erasmo > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Economic Significance and Logged Independent Variables***From:*Erasmo Giambona <e.giambona@gmail.com>

**Re: st: Economic Significance and Logged Independent Variables***From:*Austin Nichols <austinnichols@gmail.com>

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