Table 7: Linear probability models for the effect of TFP and sales on the probability of observing a missing value in t+1

|Dependent variables: for each country<br>|A. Missing in TFP<sup>1</sup><br>a dummy taking value 1 if we<br>|observe all la<br>|bor, materials, ca<br>|pital and sales<br>|
|---|---|---|---|---|
|Explanatory variables|India|Turkey|South Africa|Tanzania|
|log TFP (t+1)|0.0168*<br>[0.0091]|0.0183**<br>[0.0084]|0.0212<br>[0.0180]|0.0281<br>[0.0250]|
|ICvariables <sup>3</sup>|Yes|Yes|Yes|Yes|
|Constant|Yes|Yes|Yes|Yes|
|Industry/region/size dummies|Yes|Yes|Yes|Yes|
|Observations|1476|426|454|87|
|R-squared|0.27|0.07|0.19|0.32|
|<br>Dependent variables: for each country<br>|B. Missing in sales<sup>2</sup><br>a dummy taking value 1 if we<br>|observe sales<br>|<br>||
|Explanatory variables|India|Turkey|South Africa|Tanzania|
|log sales (t+1)|0.0063*|0.0069|0.0079|0.0033|
||[0.0033]|[0.0043]|[0.0083]|[0.0144]|
|ICvariables <sup>3</sup>|Yes|Yes|Yes|Yes|
|Constant|Yes|Yes|Yes|Yes|
|Industry/region/size dummies|Yes|Yes|Yes|Yes|
|Observations|1894|677|564|155|
|R-squared|0.17|0.05|0.16|0.14|

1 Missing in TFP takes value 1 if we observe all sales, materials, labor and capital, and 0 otherwise. 2 Missing in sales takes value 1 if we observe sales and 0 otherwise. 3 The set of IC variables of equation (1) is also included. Both TFP and sales are used before imputing missing values. Significance given by robust standard errors allowing for clustering by industry and region *** 1%, **5%, * 10%. Source: Authors’ estimations with ICSs data.

The results of both equations for missingness in TFP and sales are in Table 7. Under endogenous sampling when the pattern of missing values is correlated with sales or TFP and if we were able to observe everything, we should expect a positive relation between contemporaneous TFP/sales and the missingness problem before controlling for other determinants such as IC and D variables. As a consequence, the relation between missingness ‘yesterday’ and TFP/sales ‘today’ should also be positive. Table 7 supports this view for TFP (see Table 7 panel A) and for the cases of India and Turkey, where the <sup>ˆ</sup> 1<sup>_a_</sup> is positive and therefore more productive firms in year t+1 are associated with a higher probability of being able to keep track of proper accountability on output and inputs in past years. Note that we find this relation even before controlling for IC and D effects. However, the <sup>ˆ</sup> 1<sup>_a_</sup> for South Africa and Tanzania do not indicate any significant association between TFP and missingness in these countries. On the other hand, in the case of sales (panel B) we only observe a positive and significant effect of <sup>ˆ</sup> 1<sup>_a_</sup> in India, although the effect in Turkey is no longer significant. In South Africa and Tanzania the effect remains non-significant.

Therefore, Table 7 points to a plausible endogenous selection problem between missingness and TFP in India and Turkey, with the endogenous sampling selection problem corroborated in the case of sales in India but not in Turkey. On the opposite side, the analysis does not support this view in South Africa and Tanzania, neither in the case of sales nor TFP. Nonetheless, Table 7 does not allow us to conclude that there is a self-selection problem in India and Turkey, nor that the MDM is MAR in South Africa and Tanzania. At this point caution is a requisite. All we are able to say is that we have four different patterns of data generating mechanisms. For some of them we find evidence of a more likely self-selection problem and under which we can test the performance of the various imputation methods, including the Heckman models.

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