[Hussain Sulaimani]

Good morning everyone,

I have an inquiry, please.

I estimated the model that explains freight flow (Flow_ij) by using ppmlhdfe command. Thereafter, I predicted freight flow (pr_Flow_ij) by using predict command as follows:

ppmlhdfe Flow_ij lnTEU_it GDP_jt lnDistance_ij d_Rail_ij d_Redsea_i lnBunkerRate_t lnFreightRate_t, vce(cluster ID) d(newvar1) 

predict pr_Flow_ij, mu 

The freight flow originated from 4 ports (i) to 13 provinces (j) for the period 2006-2018. I noticed that the total freight flow (e.g. sum of predicted flows from the 4 ports to A province in a specific year) varies considerably from the actual one. In other words, non of the estimates summed to the actual province totals. as shown in the example below.

actual flow year Port A Port B Port C Port D total annual 2001 563,400 100 0 563,500 2002 672,500 0 0 672,500 2003 913,400 0 0 913,400 2004 926,200 200 0 926,400 2005 940,700 0 0 940,700 2006 1,003,100 0 0 1,003,100 2007 1,045,300 0 0 1,045,300 2008 1,076,800 0 0 1,076,800 2009 1,075,700 34,200 0 0 1,109,900 2010 1,269,900 59,800 0 0 1,329,700 2011 1,288,700 80,600 0 0 1,369,300 2012 932,100 84,900 0 0 1,017,000 2013 990,600 110,000 0 0 1,100,600 13,068,200 predicted flow year Port A Port B Port C Port D total annual 2001 884,352 27,833 4,546 916,731 2002 912,977 29,815 8,401 951,192 2003 1,023,809 34,223 10,654 1,068,687 2004 931,028 31,854 11,039 973,921 2005 1,100,573 35,674 13,220 1,149,468 2006 1,177,734 39,208 15,681 1,232,623 2007 1,376,118 40,863 20,048 1,437,030 2008 1,325,111 38,929 20,002 1,384,042 2009 1,301,724 77,291 45,346 24,225 1,448,586 2010 1,261,080 111,610 46,129 24,117 1,442,936 2011 1,246,122 112,726 43,460 26,113 1,428,421 2012 1,203,509 121,631 41,309 28,658 1,395,106 2013 1,297,077 146,315 43,332 31,280 1,518,005 16,346,749

I am interested to have a similar or very close actual and predicted total flow.
My question is: How to constrain the flow estimates to the total known (actual) value? I know that I can set a fixed effect for provinces. but if I do so, I won't be able to use the IV of (GDP_it) which explains province attribute.

Thank you,
Hussain Sulaimani