Productivity estimation

Consider a Cobb-Douglas production function (in logs) for firms 𝑖𝑖 at a time𝑡𝑡 where 𝑦𝑦𝑖𝑖𝑖𝑖

is output, 𝑙𝑙𝑖𝑖𝑖𝑖 is labour, 𝑘𝑘𝑖𝑖𝑖𝑖 is capital and 𝑚𝑚𝑖𝑖𝑖𝑖 is material inputs as follows:

9 _{As discussed in Greenaway and Kneller (2007b), foreign investors with knowledge of international}

markets might not have to deal with these start-up costs. In this regard, the FDI regime becomes important, in that allowing for foreign ownership can help reduce the sunk costs problem.

10 _{Exporting firms are systematically different from non-exporting firms in various ways. The former are}

larger, more productive and more skill- and capital- incentive. They use more varied input mix and pay higher wages than the latter (Bernard et al. 2012). Many studies from various countries have provided evidence. A simple and well-known model by Bernard and Jensen (1999) has been replicated in many articles and case studies.

𝑦𝑦𝑖𝑖𝑖𝑖 =𝛽𝛽𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖 +𝛽𝛽𝑘𝑘𝑘𝑘𝑖𝑖𝑖𝑖+𝛽𝛽𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖+𝜔𝜔𝑖𝑖𝑖𝑖+𝑣𝑣𝑖𝑖𝑖𝑖 (3.1)

where 𝜔𝜔𝑖𝑖𝑖𝑖 captures productivity and 𝑣𝑣𝑖𝑖𝑖𝑖 is the standard 𝑖𝑖.𝑖𝑖.𝑑𝑑error term capturing

unanticipated shocks to production and measurement error. We can then derive the

total factor productivity (TFP) 𝜔𝜔�𝑖𝑖𝑖𝑖as a residual 𝜔𝜔�𝑖𝑖𝑖𝑖 =𝑦𝑦𝑖𝑖𝑖𝑖− 𝛽𝛽̂𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖− 𝛽𝛽̂𝑘𝑘𝑘𝑘𝑖𝑖𝑖𝑖− 𝛽𝛽̂𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖. We

hypothesise that TFP depends, amongst other things, on whether or not the firm was exporting in the previous year:

𝜔𝜔�𝑖𝑖𝑖𝑖 =δ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑖𝑖,𝑖𝑖−1+φ𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡𝑒𝑒𝑒𝑒𝑙𝑙𝑐𝑐+𝜗𝜗𝑖𝑖𝑖𝑖+𝜀𝜀𝑖𝑖𝑖𝑖 (3.2)

where 𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡𝑒𝑒𝑒𝑒𝑙𝑙𝑐𝑐 denotes industry dummy and year dummy and 𝜗𝜗𝑖𝑖𝑖𝑖 is firm-level

specific aspects that impact on productivity and 𝜀𝜀𝑖𝑖𝑖𝑖 is pure random error.

3.3.1.1. Bias in production function estimation

The usual practice involves a two-step approach, where the TFP is first derived from Equation 3.1 and then regressed on prior exporting status and other controls with

Equation 3.2. If the 𝜔𝜔𝑖𝑖𝑖𝑖 is uncorrelated with the regressor, the productivity function

can be estimated using ordinary least squares (OLS). However, the correlation between the factors and possible unobserved effects that include productivity may affect the coefficients of the factors, thus biasing the estimated TFP. If the unobserved effects are time-invariant firm characteristics, then a fixed-effect estimation could reduce the bias. However, there is another source of endogeneity that might not be solved. If export status is correlated with inputs, then omitting the export dummy from the production function regression could yield inconsistent input coefficients and productivity estimates. In that case, incorporating export status in the function might reduce the bias. Substituting the export decision in Equation 3.1 and, following Van

Biesebroeck (2005), assuming that productivity evolves according to an autoregressive process, yields the dynamic model:

𝑦𝑦𝑖𝑖𝑖𝑖 =𝛾𝛾𝑦𝑦𝑖𝑖𝑖𝑖−1+𝛽𝛽𝑘𝑘𝑘𝑘𝑖𝑖𝑖𝑖 +𝛽𝛽𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖+𝛽𝛽𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖+𝛿𝛿𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑖𝑖𝑖𝑖−1+𝜑𝜑𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡𝑒𝑒𝑒𝑒𝑙𝑙𝑐𝑐+𝜔𝜔𝑖𝑖𝑖𝑖 +𝑣𝑣𝑖𝑖𝑖𝑖 (3.3).

In Equation 3.3, the export propensity is treated as an endogenous variable. To solve this problem, some studies apply a generalised method of moments (GMM) technique

to obtain input coefficients 𝛽𝛽𝑘𝑘,𝛽𝛽𝑙𝑙,𝛽𝛽𝑚𝑚 and productivity estimates 𝜔𝜔𝑖𝑖𝑖𝑖 that are free from

simultaneity bias.

Another issue that may appear in estimating production function parameters is selection bias. This bias is due to the relationship between productivity shocks and the probability of exit from the market. If a firm’s profitability is positively related to its capital stock, then a firm with more capital can be expected to produce greater future profits. The negative correlation between capital stock and the probability of exit, for a given productivity shock, will cause the coefficient on the capital variable to be biased downward unless we control for this effect. We can solve this problem by following a method suggested by Olley and Pakes (1996) in which it is assumed that productivity

shocks 𝜔𝜔𝑖𝑖𝑖𝑖 follow the first order Markov process and capital is accumulated by firms

through a deterministic dynamic investment process. Profit maximisation yields an investment demand function that depends on state variables capital and productivity, as well as export participation, an additional state variable, as suggested by De Loecker

(2007) and Amiti and Konings (2007), 𝐼𝐼𝑖𝑖𝑖𝑖 = 𝑖𝑖(𝑘𝑘𝑖𝑖𝑖𝑖,𝜔𝜔𝑖𝑖𝑖𝑖,𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑖𝑖𝑖𝑖). Inverting the

investment function gives an expression of productivity as a function of state variables:

capital, decision to export and investment, 𝜔𝜔𝑖𝑖𝑖𝑖 = ℎ(𝑘𝑘𝑖𝑖𝑖𝑖,𝐼𝐼𝑖𝑖𝑖𝑖,𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑖𝑖𝑖𝑖). It is assumed

substituting the productivity expression in (3.1), we can express the production function as:

𝑦𝑦𝑖𝑖𝑖𝑖 = 𝛽𝛽𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖 +𝛽𝛽𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 +𝜙𝜙(𝑘𝑘𝑖𝑖𝑖𝑖,𝐼𝐼𝑖𝑖𝑖𝑖,𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡𝑖𝑖𝑖𝑖) +𝑣𝑣𝑖𝑖𝑖𝑖 (3.4).

Equation 3.4 can be estimated using the procedures discussed in Yasar,

Raciborski and Poi (2008). In the first step, we obtain consistent estimates of 𝛽𝛽𝑙𝑙 and

𝛽𝛽𝑚𝑚. In the second step of the estimation procedure, the probability that a firm exits

from the sample is determined by the probability that the end-of-period productivity falls below an exit threshold. And in the third step, the coefficients of the state variables are estimated using nonlinear least squares.

The preferable model in this paper is that based on the Olley and Pakes methodology because this procedure takes account of the simultaneity between input choices and productivity shocks, as well as the sample selection bias of surviving firms. The model also incorporates the firms’ decisions to enter international markets via exporting.

3.3.1.2. Price difference effects

There is a possibility of bias in the TFP measurement due to price effects. Since physical quantities are rarely observed, it is very challenging to measure the physical TFP accurately. Most studies use sales to replace output, but the TFP estimates from this strategy may also contain firm-level mark-ups (Amiti & Konings 2007). Keller (2010) argues that the use revenues, capital spending and input expenditures instead of physical quantities of output, capital and intermediate inputs may confound higher productivity with higher mark-up. Katayama, Lu and Tybout (2009) argue that productivity estimations using these data might not reflect the technical efficiency, but

might be correlated with policy shocks and managerial decisions in misleading ways. The standard solution in the literature is by deflating firm-level sales in the hope of eliminating price effects. However the standard solution can still potentially bias the coefficients of inputs if they are correlated with price errors, and it generates productivity estimates that contain price and demand variation (De Loecker 2011). De Loecker et al. (2016) try to control for unobserved prices and demand shocks to separate revenue productivity and physical productivity by using multi-product firm- level data during trade liberalisation episodes.

One alternative way of dealing with the issue is by adjusting the exporter’s output. If information about revenue from the domestic market and export market is available, we can adjust the output by using the deflator gained from world price and

domestic price data. If total revenue can be defined as 𝑌𝑌_{𝑖𝑖𝑖𝑖}𝑇𝑇𝑇𝑇𝑖𝑖 _{= 𝑌𝑌}

𝑖𝑖𝑖𝑖𝐷𝐷𝑇𝑇𝑚𝑚+𝑌𝑌𝑖𝑖𝑖𝑖𝐸𝐸𝐸𝐸𝐸𝐸, then we

can obtain the proxy for output with this following expression:

𝑦𝑦𝑖𝑖𝑖𝑖𝑇𝑇𝑇𝑇𝑖𝑖=𝑌𝑌𝑖𝑖𝑖𝑖 𝐷𝐷𝐷𝐷𝐷𝐷 𝐸𝐸_{𝑖𝑖𝑖𝑖}𝐷𝐷𝐷𝐷𝐷𝐷+ 𝑌𝑌_{𝑖𝑖𝑖𝑖}𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸_{𝑖𝑖𝑖𝑖}𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑌𝑌_{𝑖𝑖𝑖𝑖}𝐷𝐷𝐷𝐷𝐷𝐷 𝐸𝐸𝐷𝐷𝐷𝐷𝐷𝐷+ 𝑌𝑌_{𝑖𝑖𝑖𝑖}𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤 (3.5).