Land, in terms of floor space used by firms,

Land, in terms of floor space used by firms, is almost omnipresent in economic. On the one hand, land appears as a productive factor (see for example cite{metzemakers_land_2005}, cite{pfluger_trade_2008}) in economic modeling. On the other hand, land is crucial in modeling urban land patterns which in turn is closely related to firms productivity (see cite{duranton_urban_2014} for a review of key models).Along with this important role of land size in economic modeling, land constraints are becoming more and more a big issue in urban cities. According to cite{buhaug_urbanization_2013}, the majority of world population is living in urban areas owing to migration and reclassification of some rural areas into cities. footnote{In 2015, world’s urban population was more than the half of total population. source: The United Nations Population Division’s World Urbanization Prospects}. For cite{hubacek_role_2002}, new infrastructures like roads and many other technological developments may also alter the supply of land. Moreover, as it is well-known, agglomeration forces draw firms as well as workers into cities and thus enforcing urban congestion (see for example cite{gaubert_firm_2017}, cite{lucas_internal_2002}). In addition, others frictions may also be involved on the land market due to historical contingencies, some externalities, as well as asymmetric information and speculation. As a result, land markets might not always function like a perfect market as discussed by cite{hubacek_role_2002}. Along with all these market’s imperfection, cite{needham_land_2000} observed that other motives like local development, local income collection, or specific development charges are many reasons that might also cause authorities to intervene on the land market with regulations. In such a context, firms decisions on the floor space that they use in the area where they operate will merely be conditional on all the above-mentioned constraints. In turn, land size prior decision of firms may also induce some land constraints and thus, be fueling the dynamic. In fact, some empirical evidence of correlation between land regulation and firm decisions may include cite{hilber_origins_2013} who used a model of location choice by household to show that land with more amenities are more populated, more developed and thus adopt tighter land use regulations.\Surprisingly, despite this unquestionable role of floor space used by firms, its influence on firms’ efficiency and productivity has not received much attention. Some researchers have argued that land size of firms is exogenous due in some cases to regulations, suggesting that firms may only have a limited control over the floor space that they are willing to use (cite{combes_production_2016}). Some others had argued that the price elasticity of the demand for land is insignificant (cite{sirmans_capital-land_1979}), inferring thus that its influence on economic matters may be of little importance. Furthermore, since land is typically a factor which is fixed on the supply side and also fixed in the short run on the demand side, hence research framed in the short run have simply ignored land size of firms (see for example ??).\However, many empirical facts might raise some concerns about the role of the floor space used by firms in the economy. For example, cite{metzemakers_land_2005}, while surveying the role of land in economic theory, pointed out the issue of spatial inefficiency and spatial productivity of firms and posited that intensive land use of land may improve social welfare. cite{combes_production_2016} modeled housing production through a function using land and non-land inputs. They used the first order condition of competitive firms that maximize profit with respect to non-land inputs. Thus, they proposed non-parametric estimates of the production with respect to non-land input using data for French firms to estimate the elasticity of the production with respect to non-land input. They estimated an elasticity of 0.8 which is roughly stable for different land size. They also extended their model with land size used by firms as an outcome of the equilibrium, and they derived different results suggesting that parcels size matter. Some other issues like location inefficiency may be of concerns due to land regulation and land constraints. Indeed, in an interesting study cite{cheshire_land_2014} estimated the impact of planning policies on the output of UK supermarket chain. He used a production function where firms’ floorspace is combined with land an capital in a Difference in Difference frame, he analyzed, (i) the extent to which regulation could influence the probability of stores presence and their productivity, and (ii) how stores floorspace is related to production. He found that tighter regulations lead to production loss, lower probability of stores presence and an increase of production per square feet and a reduction of total square feet of store space. These results, suggest that floor space of firms may influence firms’ performance and/or firms’ efficiency through two channels. Firstly, through its direct role as productive input, and secondly, indirectly through agglomeration, selection, and sorting which are well-known to be interconnected to firms productivity (see for example cite{behrens_productive_2014}).\Another concern regarding the potential impact of floor space of firms’ on their productivity might arise through the common approach used in the research related to land used by firms. In empiric, two approaches are basically used to account for floor space of firms in urban studies. Some frameworks used various spatial units data-level like Metropolitan Statistical Area(MSA), Census Blocks, etc. for their research purposes (see for example…..). Some others but very few have looked at land at firm level (see for example cite{brinkman_congestion_2016}, cite{cheshire_land_2014}).  footnote{cite{brinkman_congestion_2016} used Data on employment, residential, worker, wages from 2000 census transportation planning, and 1992 National land cover data base from the US and geological survey for residential/commercial and they processed data at Census track level and combined information with Frankling Auditor office Census track}. Each of this approach might not be without consequences on the derived results. For example, as it is well known, using spatial units may induce the necessity to tackle the issues related to spatial unitsfootnote{see for example cite{anselin_spatial_1988}, Chapiter3, section 3.2 for a technical review of this issue}, whereas it is not the case with firms observational units. However, firms level data including floor space are more difficult to have that spatial units.\Thus, there are several avenues of investigation on the importance of land size used by firms that may be of interest. Some of them may include the following research questions : (i) to what extent the floorspace of firms directly influences firms’ productivity and firms’ efficiency? (ii) to what extent the floorspace of firms influences firms’ location choice, and what is the nexus with agglomeration, sorting and selection, (iii) What are the possible overall welfare implications and consequently the possible political recommendations to land planner and/or land regulators.\ So far in this research area, in addition to cite{cheshire_land_2014} cited above, the studies that seem the most suggestive of this study are those related to (i) housing economics as cite{duranton_urban_2014} who estimated housing production function even though in a partial equilibrium model with no labor in the model, with homogeneity in preferences and constant return to scales as well as exogenous land size used by firms; (ii) cite{pfluger_trade_2008} who studied trade with land as production factor to discuss how a model with land as productive factor could change some widely admitted results. However, these studies do not really focus on how floor space of firms may influence their productivity, their efficiency and thus the welfare.