Incorporating price and inventory endogeneity in firm-level sales forecasting

As numerous papers have argued, sales, inventory, and gross margin for a retailer are interrelated. We construct a simultaneous equation model to establish these interrelationships at a firm level. Using publicly available financial data we estimate the six causal effects among sales, inventory, and gross margin. Our results show that sales, inventory, and gross margin are mutually endogenous. In particular, we provide new evidence of the impact of inventory on sales and the interrelationship between gross margin and inventory. We also estimate the effects of exogenous explanatory variables such as store growth, proportion of new inventory, capital investment per store, selling expenditure, and index of consumer sentiment on sales, inventory, and gross margin. We show that our model can be used to benchmark retailers' performance in sales, inventory, and gross margin simultaneously. Finally, we show that our model can be used to generate sales forecasts even when sales were managed using inventory and gross margin. In numerical tests, sales forecasts from our model are more accurate than forecasts from time-series models that ignore inventory and price as well as forecasts from financial analysts.