## **Item Nonresponse**

Another challenge in estimating total factor productivity is dealing with item nonresponse: i.e., sampled firms do not answer specific questions of the survey. For example, respondents may answer the employment question but not sales. To reduce item non-response, the Enterprise Surveys team follows a strict quality control process that identifies non-responses and contacts firms to complete the data.

Despite this effort, like many other firm-level datasets, the ES also suffers from item nonresponse in variables needed to calculate TFPR. One way to handle the item nonresponse is through imputation. For example, in the U.S. Census Bureau’s 2007 manufacturing data 73% of observations have imputed data for at least one variable used to compute TFPR (White et al. 2018). While item non-response may be consequential for most analysis, we do not attempt to address it in the data. We do not employ any of the available imputation or re-weighting methods that assume that data “missingness” is not ignorable and is related to underlying firm characteristics (Little & Rubin 2019). Additionally, the survey (probability) weights included in the data are agnostic to item non-response and the missingness of productivity estimates: weights are not re-adjusted or scaled to account for this missingness.

We exclude observations missing any one of the main production function variables (i.e., sales, labor, capital, or materials). Additionally, note that in cases of negative value-added, logarithms cannot be defined, and thus these observations are not included. This leaves 50,754 observations in 134 countries .

# **3 Estimating Firm-Level Total Factor Productivity**

We begin with a Cobb-Douglas production function (1) for ease of exposition. Throughout this paper, all lowercase variables denote the natural logarithms of the corresponding uppercase variables, representing raw, level values.

Where firm-level value-added ( _vai_ ) is a function of inputs of capital ( _ki_ ), and labor ( _li_ ). Firms’ (logged) TFP is estimated as a sum of the constant and the residual, i.e., _tfpi_ = _β_<sup>ˆ</sup> 0 + ˆ _εi_ . We refer to the above model as value-added specification (VAKL). In addition to VAKL, TFP is also estimated using gross-output specification (YKLM) where _vai_ in (1) is replaced with _yi_ , output in terms of total revenues, and the right-hand-side has an additional input variable, expenditure on material inputs ( _mi_ ).<sup>5</sup> The coefficients _βk_ and _βl_ estimate the elasticities of capital and labor, respectively. Throughout, we will denote estimated elasticities by _θ_<sup>ˆ</sup> _input_ ( _i.e., θ_<sup>ˆ</sup> _l_ ), where _input ∈ k, l, m_ .

While analytically straightforward, this estimation of TFP bears several caveats. First, ordinary least squares estimates of equation (1) may suffer from a simultaneity problem: firms’ input choices may be guided by their productivity (Marschak & Andrews 1944). Several methods have been developed in order to address this endogeneity problem (Olley & Pakes 1996, Levinsohn & Petrin 2003, Ackerberg et al. 2015). In these methods, past input decisions (for instance the choice to invest in capital) are

> 5Note that other versions of (1) are also possible, e.g. YKL, or YKELM with E for Electricity. We do not analyze these here as adding a fourth input into a translog production function substantially increases the number of parameters to be estimated.

4