Margins Interpretation: When coefficients are very small

[Imtiaz Ahmad]

I used xtprobit to estimate the impact of risk-aversion(estimate), firms size (lntotalassets), and inventory to sales ratio (linv_sales) on export status of firms. I have also used an interaction term risk-aversion*firmsize and i.sectors and i.years as follows:

xtprobit exporter lntotalassets estimate estimate_size linv_sales i.sectoren i.year if avgestimate<0,pa vce(robust)

Note that it is estimated only for risk-taking firms " avgestiamte<0"

The Dataset looks like this:
"Spinning, Weaving, Finishing of Textiles" "(Colony) Sarhad Textile Mills Ltd." 2003 0 6.42859
"Spinning, Weaving, Finishing of Textiles" "(Colony) Sarhad Textile Mills Ltd." 2004 0 6.423734
"Spinning, Weaving, Finishing of Textiles" "(Colony) Sarhad Textile Mills Ltd." 2005 0 6.422103
"Spinning, Weaving, Finishing of Textiles" "(Colony) Sarhad Textile Mills Ltd." 2006 0 6.401873
"Spinning, Weaving, Finishing of Textiles" "(Colony) Sarhad Textile Mills Ltd." 2007 0 6.382574
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 1999 1 5.797273
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2000 1 5.738184
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2001 1 5.727824
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2002 1 5.701447
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2003 1 5.69944
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2004 1 6.194814
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2005 1 6.265092
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2006 1 6.237729
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2007 1 6.256276
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2008 1 6.156852
"Spinning, Weaving, Finishing of Textiles" "(Colony) Thal Textile Mills Ltd." 2009 1 6.123591

The problem is that coefficients are very small

exporter Coef.	Std. Err. z	P>z	[95% Conf.	Interval]
lntotalassets .0093449	.0043098	2.17	0.030 .0008979	.0177919
estimate .002572	.0010758	2.39	0.017 .0004635	.0046805
estimate_size -.0001785	.0000749	-2.38	0.017 -.0003252	-.0000318
linv_sales .0030466	.0014534	2.10	0.036 .000198	.0058952

and there fore margins at means as well

dy/dx Std.	Err. z	P>z	[95% Conf. Interval]
lntotalassets	.0029151	.0014068	2.07 0.038 .0001578	.0056723
estimate	.0008023	.0003333	2.41 0.016 .000149	.0014557
estimate_size	-.0000557	.0000238	-2.34 0.019 -.0001024	-9.01e-06
linv_sales	.0009504	.0004518	2.10 0.035 .0000649	.0018358

My Question is:

Are these coefficients and margins very small?
Can I interpret the margins i.e. .0029151 as " 400% or 4 times higher firm size increase the probability of exporting by 2.9%"
Note: the distribution of total assets is such that the max value is about 15 times higher than average value in the dataset..





The attached figure shows the impact of lntotalassets at various estimate(risk-aversion is estimated using following code:
margins, dydx(lntotalassets) at(estimate=(-800(20)600)) vsquish noatlegend
marginsplot, ylin(0)

The is only small impact of lntotalassets on probability of exporting. Since the firm size in the dataset vary too much, can we say this is still significantly larger impact if we are considering a firm which is 4 time larger than average firm?