Combining the first- and second-stage estimates in column (3) implies that a reduction in the median assignment to the red channel resulted in an increase of 1.7 percent in the number of origin countries from which that firm-product pair imports.<sup>65</sup> The effects of reductions in customs clearance time on the number of imported products are insignificant in column (5). The estimates in column (6) suggest a close to 4.6 percent growth in the number of products among firm-country pairs that saw a reduction in the median allocation to the red channel.<sup>66</sup>

**Table 11. Estimated effect of customs clearance time on the numbers of importing firms,**

**imported products and origin countries**

||<br>Dependent variable is<br>number of importing fir<br>country‐|<br>first‐difference in log<br>ms at HS6 product‐origin<br>year level|<br>Dependent variable i<br>number of origin countr<br>product‐|<br>s first‐difference in log<br>ies at importing firm‐HS6<br>year level|<br>Dependent variable i<br>number of HS6 product<br>country‐|<br>s first‐difference in log<br>s at importing firm‐origin<br>year level|
|---|---|---|---|---|---|---|
||_Clearance time_<br>_measured in days_<br>_‐ 2007‐2012 period_|<br>_Clearance time_<br>_measured in hours_<br>_‐ 2010‐2012 period_|<br>_Clearance time_<br>_measured in days_<br>_‐ 2007‐2012 period_|<br>_Clearance time_<br>_measured in hours_<br>_‐ 2010‐2012 period_|<br>_Clearance time_<br>_measured in days_<br>_‐ 2007‐2012 period_|<br>_Clearance time_<br>_measured in hours_<br>_‐ 2010‐2012 period_|
||IV esti|mation|IV esti|mation|IV esti|mation|
||(1)|(2)|(3)|(4)|(5)|(6)|
|First‐diff. in median clearance time|‐0.587***|‐0.022***|‐0.195***|‐0.011***|‐0.072|‐0.013***|
||(0.077)|(0.003)|(0.027)|(0.002)|(0.071)|(0.005)|
|HS6 product*year fixed effects|Yes|Yes|Yes|Yes|||
|Origin country*year fixed effects|Yes|Yes|||Yes|Yes|
|Firm*year fixed effects|||Yes|Yes|Yes|Yes|
|Observations|94,872|39,709|186,900|77,269|56,890|24,187|
|R‐squared|‐0.258|‐0.16|0.145|0.083|0.516|0.449|
|F‐statistic from first‐stage regression|154|196|491|286|191|102|
|First‐stage coefficient on first‐diff.|||||||
|in median allocation to red channel|0.066***|2.760***|0.084***|2.245***|0.135***|3.429***|
||(0.005)|(0.197)|(0.004)|(0.133)|(0.010)|(0.340)|

Notes: Robust standard errors in parentheses. *** indicates significance at 1% confidence level. The first-difference in median allocation to the red channel and in median clearance time is defined differently across columns: in columns (1)-(2) it is a firstdifference with respect to HS 6-digit product-origin country, in columns (3)-(4) it is a first-difference with respect to importing firm-HS 6-digit product, and in columns (5)-(6) it is a first-difference with respect to importing firm-origin country.

# **7.3 Effects of Dispersion in Customs Clearance Time on Import Values**

The focus on changes in median customs clearance time obscures the effects that reductions in physical inspections may have had on the dispersion of customs clearance time and the potential ensuing effects on import growth. The recent study by Clark _et al._ (2013) focuses on uncertainty as a trade barrier, and the uncertainty about the time needed to clear customs is likely to be an important dimension of uncertainty. To address this issue we calculate the interquartile range in customs clearance time for each firm-HS 6-digit product-origin country within each year.<sup>67</sup> We

> 65 This magnitude is calculated as (e(-0.195*0.084)-1) = 0.017.

> 66 This magnitude is calculated as (e(-0.013*3.429)-1) = 0.045.

> 67 Our choice of interquartile range instead of the standard deviation is aimed at minimizing the influence of transactions with more extreme delays at customs for a given firm-HS 6-digit product-origin country in a given year. It is also preferred, relative to statistics derived from the second moment, because the functional forms that derive those statistics contain the number of shipments in the denominator, and the number of shipments also affects the left-hand-side variable.

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