historical context of impulse response-convolution
Stanley: Thanks for your input. Your answer led me to the "brilliant" idea of googling myself. Based on the link below, I think one can define the birth of convolution as sometime between 1760-1900 depending on how one defines birth. https://pulse.embs.org/january-2015/history-convolution-operation/.

Either way, it seems that Koyck was unaware of it since  he came  up with his model in the 1950's. He would have had a much easier time using the DSP framework in his derivation but he came up with the model without impulse response or convolution which is quite impressive in itself. I'm gonna check this answer but your mention of Mr. Heavside is appreciated.