# Capital diversion in Vietnamese state-owned enterprises

Cuong Le-Van, Ngoc-Anh Nguyen, Ngoc-Minh Nguyen, Phu Nguyen-Van

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Cuong Le-Van, Ngoc-Anh Nguyen, Ngoc-Minh Nguyen, Phu Nguyen-Van. Capital diversion in Vietnamese state-owned enterprises. Fulbright Review of Economics and Policy, 2023, 3 (2), pp.221-229. 10.1108/FREP-05-2023-0019. hal-04384629

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# Capital diversion in Vietnamese state-owned enterprises

Vietnamese state-owned enterprises

Cuong Le-Van

CNRS, PSE, Paris, France and

TIMAS, Thang Long University, Hanoi, Viet Nam

Ngoc-Anh Nguyen

Development and Policies Research Center, Hanoi, Viet Nam

Ngoc-Minh Nguyen

Development and Policies Research Center, Hanoi, Viet Nam and
OECD, Paris, France, and

Phu Nguyen-Van

Economix-CNRS & University of Paris Nanterre, Nanterre, France;
UMT Business School, University of Management and Technology,

Ho Chi Minh City, Viet Nam and

FERDI, Clermont-Ferrand, France

Received 25 May 2023
Revised 2 August 2023
Accepted 2 August 2023

## Abstract

**Purpose** – The authors estimated the hidden overhead (capital diversion or wasteful use of capital) of Vietnam state-owned enterprises (SOEs).

**Design/methodology/approach** – The authors used a panel data set of 10,200 Vietnam SOEs observed over the period 2010–2018. The authors modeled and estimated the hidden overhead by using a stochastic production frontier. The hidden overhead parameter is modelled as the technical inefficiency in the production function.

**Findings** – Vietnam SOEs are very capital intensive. The hidden overhead (or the wasteful use of capital) is very high with an average rate of 69%.

**Research limitations/implications** – Alternative estimation methods should be used to account for endogeneity in production inputs. Lack of comparison with the Vietnam private firms.

**Originality/value** – The paper proposes an original way to quantify hidden overhead (or capital diversion) in the Vietnam SOEs. The finding (a capital diversion rate of 69% on average) is astonishing. It calls for an urgent and profound reform of the Vietnam SOEs.

**Keywords** Productivity, Stochastic production frontier, Hidden overhead

**Paper type** Research paper

**JEL Classification** – E20, O53, P20

© Cuong Le-Van, Ngoc-Anh Nguyen, Ngoc-Minh Nguyen and Phu Nguyen-Van. Published in *Fulbright Review of Economics and Policy*. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licenses/by/4.0/legalcode

The authors are grateful to Le Viet Phu, Pham Hoang Van, Tran Nam Binh and participants at the VNUA seminar (Hanoi, 2018) and the FUV conference "From Economic Theory To Economic Policy: Contributions of Ngo Van Long" (Ho Chi Minh City, 2023) for their very constructive and useful comments. This paper partly corresponds to our previous work, entitled as "Some Issues on the Vietnam Economic Growth" (Le et al., 2019), and posted on the BETA Working Paper series repository (WP n.2019-36). The usual caveat applies.

<figure><img src="image_2.png" /></figure>

Fulbright Review of Economics
and Policy
Emerald Publishing Limited
2635-0173
DOI 10.1108/FREP-05-2023-0019
# 1. Introduction

When the Vietnam War ended in April 1975, Vietnam was one of the poorest country in the world. By the mid-1980s, Vietnam GDP per capita was stuck between 200 USD and 300 USD. In recent years, Vietnam became one of the important emerging economies with growth of 6–7% and a GDP per capita around 2,000 USD in 2017. The volume of goods trade is around 200% of the GDP. This shows Vietnam economy is very open. The important question is how Vietnam economy can go further.

Van Thang and Freeman (2009) showed there is a negative correlation between state-owned enterprise (SOE) growth and private sector growth. There is an evidence that SOEs are ‘crowding-out’ the private sector in Vietnam. Similarly, Nguyen and Van Dijk (2012) found that corruption hampers the growth of Vietnam’s private sector but is not detrimental for growth in the state sector. For Yoshino (2018), if the Vietnamese government has made efforts for several years to promote the reform of SOEs, this process cannot be completed since it will be required for the introduction of regulations and systems to correct opaque financial situation and management techniques of SOEs. Nguyen et al. (2016) showed that corruption generally has a negative effect on economic growth and that investment is the most important transmission channel. For Vietnam, the authors quantified that investment accounts for about 63% of the total effect.

Previous studies on the misallocation effect of state ownership policy in Vietnam, such as Bach Ngoc Thang (2019), modeled capital misallocation effect as the difference between actual TFP and efficient TFP (when distortions are absent). Bach Ngoc Thang (2019) found that commercial and subsidized credit can reduce a capital distortion for all firms, but awarding more commercial and subsidized credit to the SOEs, compared to private firms, mitigates this reduction effect.

In the same vein, Le Phan (2022) calculated capital misallocation effect as the difference between actual TFP and the undistorted first-best level of aggregate TFP in the absence of all distortions. Le Phan (2022) underlined that the most severe source of capital misallocation comes from policy distortions (besides adjustment costs and uncertainty), accounting for 81% of capital misallocation in Vietnam and causing an aggregate TFP loss of 110% compared to the undistorted level. Moreover, among different policy distortions, state ownership policy accounts for 38% of loss in aggregate manufacturing TFP.

In this paper, we consider a “wasteful” use of capital in Vietnamese SOEs and model it as the distance from the actual production to the production frontier by applying the well-known literature on stochastic production frontier. Even if we do not provide explanation for this capital diversion, our paper is much in the spirit of the literature on lobbying for protection by Ngo Van Long and coauthors (Van Long & Soubeyran, 1996; Hillman, Van Long, & Soubeyran, 2001, 2003), following that less efficient firms invest their resource to lobbying for protection measures (like tariff). In this case, we can say that part of firm capital is diverted into “political capital”.

We use a census conducted over the period 2010–2018 by the General Statistics Office (GSO) of Vietnam. In this census, we have the data of 10,200 SOEs concerning the values of their outputs, their capital stocks and the labor costs. The average value of the ratios [Value of the capital stock/Labor cost] is 42.07. The Vietnam average real interest rate in 2013–2018 is 5.19% [1]. If we take the capital depreciation rate equal to 0.05, the average value of the ratio [Investment cost/labor cost] is therefore [2]

$$ (0.052 + 0.05) \times 42.07 = 4.29. $$

We now consider the profit rates of these SOEs. The profit rate $r(\pi)$ is defined by
$$r(\pi) = \frac{\text{value of the revenue} - \text{investment cost} - \text{labour cost}}{\text{value of the revenue}}$$

There are 9,030 SOEs (about 77% of observations) that made positive profit (the average profit rate is positive and equals 1.85%). Their ratio [Investment cost/labor cost] equals 25.59 on average. The mean of their capital coefficients (i.e. ratio between capital and output) is 165.41 which is quite high. The remaining 2,621 firms with a negative profit (their average profit is -11.77%) have a much higher ratio [Investment cost/labor cost]: it equals 32.78. Their average capital coefficient is impressive, 533.78.

This shows that the Vietnamese SOEs are very capital intensive. Some of them are extremely capital intensive. In developed countries, the ratio [Investment cost/labor cost] is 0.5. So, is there maybe a waste of physical capital for Vietnamese SOEs? It is well known that when a Vietnamese SOE asks for say 1 billion of VND for its purchase of capital, it will receive (1-λ) billion. But it has to declare receiving 1 billion, λ billion VND have been diverted. The number λ is called by us “hidden overhead”. Our purpose is to estimate λ. Note that the period of study covers some most important anti-corruption trials concerning some big SOEs in Vietnam, such as the shipbuilding conglomerate Vinashin, the national shipping company Vinalines, the petroleum conglomerate PetroVietnam and the PetroVietnam Construction Joint-Stock Corporation PVC, etc. (Malesky & Phan, 2019).

The main findings of our paper are:

(1) Using a census conducted by GSO in 2010–2018 for 10,200 Vietnam SOEs, we found that they are very capital intensive.

(2) Around 9,030 SOEs make profit, the average profit rate is around 1.85% whereas 2,621 SOEs make losses with the average profit rate of -11.77%

(3) Regarding the issue of “hidden overhead”, we found that the average rate of hidden overhead (λ above) is 69% for the whole sample. If we consider the 9,030 SOEs which make profits (20,804 observations), the average value hidden overhead is relatively the same (68%). However, for the 2,621 SOEs who make losses (3,689), it rises up to 74%.

The rest of the paper is organized as follows: Section 2 presents a simple model to deal with the capital diversion issue on Vietnamese SOEs. Section 3 presents the data. Section 4 discusses estimation results and show there exists an over utilization of the physical capital. We also question the issue of diversion of the capital in these SOEs. This diversion may be due to a waste of capital stocks or to a special form of bribery we call “hidden overhead”. Section 5 concludes the papers with several remarks.

## 2. A simple modeling of capital diversion

We check the diversion issue. Let $λ_{it}$ denote the rate of waste (or bribery) in terms of physical capital of firm $i$ at year $t$. The effective production function of firm $i$ at period $t$ is actually

$$Y_{it} = A[(1 - \lambda_{it})K_{it}]^{\alpha}N_{it}^{\beta}e^{\varepsilon_{it}} \quad (1)$$

which includes a white noise disturbance ($\varepsilon_{it}$).

Taking the logarithm of equation (1) gives
$$ \ln Y_{it} = \alpha_0 + \alpha_K \ln K_{it} + \alpha_N \ln N_{it} + \varepsilon_{it} - \underbrace{[-\alpha_K \ln(1 - \lambda_{it})],}_{u_{it}} \quad (2) $$

where $\alpha_0 \equiv \ln A$. The new residual term corresponds to $\varepsilon_{it} - u_{it}$. Remark that $u_{it} \ge 0$ because $0 \le \lambda_{it} \le 1$.

Following the literature on stochastic frontier production (e.g. Kumbhakar & Lovell, 2000), $u_{it}$ corresponds to the well-known stochastic technical inefficiency. Besides the normal distribution assumption for $\varepsilon_{it}$, we need an additional assumption about the distribution of $u_{it}$ in order to calculate the maximum likelihood estimator of the model. For instance, we assume that $u_{it}$ follows a truncated normal distribution $N^+(\mu, \sigma_u^2)$ with truncation point at 0. We note that $\mu = z'_{it}\psi$ corresponding to exogenous determinants (included in $z_{it}$) of inefficiency (or capital diversion). Thus, our model corresponds to the inefficiency effects models of Battese and Coelli (1995) and its estimation can be performed by maximum likelihood.

The technical inefficiency $u_{it}$ can be estimated by $\hat{u}_{it} = E(u_{it}|\varepsilon_{it} - u_{it})$ (following Jondrow, Lovell, Materov, & Schmidt, 1982).

$$ \hat{u}_{it} = E(u_{it} | \varepsilon_{it} - u_{it}) = \tilde{\mu}_{it} + \tilde{\sigma} \left[ \frac{\phi(-\tilde{\mu}_{it} / \tilde{\sigma})}{\Phi(-\tilde{\mu}_{it} / \tilde{\sigma})} \right], \quad (3) $$

where $\tilde{\mu}_{it} = [-(\varepsilon_{it} - u_{it})\sigma_u^2 + \mu\sigma_e^2]/\sigma_s^2$, $\tilde{\sigma} = \sigma_e\sigma_u/\sigma_s$, $\sigma_s = (\sigma_e^2 + \sigma_u^2)^{1/2}$. Note that $\phi(\cdot)$ and $\Phi(\cdot)$ are, respectively, the density and the cumulative distribution function of the standard normal distribution.

When an estimation of technical inefficiency ($u_{it}$) and output elasticity of capital ($\alpha_K$) are available, one can recover an estimate for the hidden overhead ($\lambda_{it}$):

$$ \hat{\lambda}_{it} = 1 - \exp\left(-\frac{\hat{u}_{it}}{\alpha_K}\right). \quad (4) $$

In the following, we only discuss the Cobb–Douglas production case [3]. It is important to note that the source of inefficiency may also come from a “low effort” in labor in the sense that the production function could be $Y_{it} = AK_{it}^a[(1 - \gamma_{it})N_{it}]^\beta e^{\varepsilon_{it}}$ instead of (1). However, Mauro (1995) found that corruption lower private investment but does not deter public investment, suggesting that public investment has a different purpose than returns to capital. Our observation above about the very high capital intensity of Vietnamese SOEs seems to be consistent with Mauro’s finding, therefore supporting our capital diversion-based modeling.

### 3. Data

We observe that Vietnamese SOEs are very heterogeneous and that this heterogeneity has to be accounted in estimations. We deal with this issue in several ways. Firstly, the proposed modeling is a panel inefficiency model of Battese and Coelli (1995) with takes into account the panel dimensions. Secondly, exogenous determinants of inefficiency correspond to some firm heterogeneities related to their export activities, scale, sectoral and year dummies. Finally, the analysis is also performed on different subsamples based on capital-output ratio.

Table 1 reports main descriptive statistics for firm production $Y$, capital stock $K$, labor $L$. We also calculate the ratio of capital in production $K/Y$. The data on these variables are in values (i.e. in monetary terms): we employ capital costs, labor costs and revenue for $K$, $L$ and $Y$, respectively. As a result, the ratio $K/Y$ represents the share of capital value in revenue. We
observe a very large heterogeneity in the sample as the ratio *K/Y* can vary from 0.0001 to 1.368 × 10⁶ with a mean of 220.82. To have a more detailed view on this heterogeneity, we consider two subsamples: one with *K/Y* ≤ 20 and another with *K/Y* > 20. The first subsample includes 9,726 firms with a quite reasonable average *K/Y* (2.29) while the second subsample only contains 787 firms with a very high average *K/Y* (4141.96) (see Tables 2 and 3) [4]. Tables 4 and 5 report the distribution of firms by sector and the distribution of firm size, respectively. Note that in order to avoid a too small sector; we define two dummies “Agriculture, Forestry, Fishing and Mining and Quarrying”, on the one hand, and “Electricity, Gas, Water Supply and

<table><thead><tr><th>Variable</th><th>Obs</th><th>Mean</th><th>Std. Dev</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>K</td><td>24,493</td><td>1894.285</td><td>25357.08</td><td>0.001</td><td>1282304</td></tr><tr><td>L</td><td>24,493</td><td>51.459</td><td>297.079</td><td>0.004</td><td>16600.17</td></tr><tr><td>Y</td><td>24,493</td><td>944.976</td><td>6135.086</td><td>0.0001</td><td>275040.9</td></tr><tr><td>K/Y</td><td>24,493</td><td>220.821</td><td>12903.76</td><td>0.0001</td><td>1367856</td></tr></tbody></table>

**Note(s):** Data on 10,200 SOEs over the 2010–2018 period. *K*, *L* and *Y* are in billion VND
**Source(s):** Data from the GSO Enterprise Census, table by the authors

<table><caption>**Table 1.**
Descriptive statistics
on SOEs</caption><thead><tr><th>Variable</th><th>Obs</th><th>Mean</th><th>Std. Dev</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>K</td><td>23,200</td><td>1766.011</td><td>25353.74</td><td>0.001</td><td>1282304</td></tr><tr><td>L</td><td>23,200</td><td>53.466</td><td>305.003</td><td>0.008</td><td>16600.17</td></tr><tr><td>Y</td><td>23,200</td><td>994.927</td><td>6299.463</td><td>0.033</td><td>275040.9</td></tr><tr><td>K/Y</td><td>23,200</td><td>2.295</td><td>3.102</td><td>0.0001</td><td>19.99</td></tr></tbody></table>

**Note(s):** Data on 9,726 SOEs over the 2010–2018 period. *K*, *L* and *Y* are in billion VND
**Source(s):** Data from the GSO Enterprise Census, table by the authors

<table><caption>**Table 2.**
Descriptive statistics
on SOEs, subsample
with *K/Y* ≤ 20</caption><thead><tr><th>Variable</th><th>Obs</th><th>Mean</th><th>Std. Dev</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>K</td><td>1,293</td><td>4113.539</td><td>25070.44</td><td>0.278</td><td>418665.3</td></tr><tr><td>L</td><td>1,293</td><td>17.025</td><td>65.103</td><td>0.004</td><td>976.456</td></tr><tr><td>Y</td><td>1,293</td><td>81.547</td><td>738.807</td><td>0.0001</td><td>19100.97</td></tr><tr><td>K/Y</td><td>1,293</td><td>4141.962</td><td>56036.1</td><td>20.003</td><td>1367856</td></tr></tbody></table>

**Note(s):** Data on 787 SOEs over the 2010–2018 period. *K*, *L* and *Y* are in billion VND
**Source(s):** Data from the GSO Enterprise Census, table by the authors

<table><caption>**Table 3.**
Descriptive statistics
on SOEs, subsample
with *K/Y* > 20</caption><thead><tr><th>Sectoral dummies</th><th>Frequency</th><th>Percentage</th></tr></thead><tbody><tr><td>Agriculture, Forestry, Fishing, Mining and Quarrying</td><td>3,821</td><td>15.60</td></tr><tr><td>Manufacturing</td><td>4,913</td><td>20.06</td></tr><tr><td>Electricity, Gas, Water Supply and Construction</td><td>5,304</td><td>21.66</td></tr><tr><td>Others</td><td>10,455</td><td>42.69</td></tr><tr><td>Total</td><td>24,493</td><td>100.00</td></tr></tbody></table>

**Note(s):** Data on 10,200 SOEs over the 2010–2018 period
**Source(s):** Data from the GSO Enterprise Census, table by the authors

<caption>**Table 4.**
Distribution of firms
over different sectors</caption>
Construction”, on the other hand, as two aggregate sectors (the former is the reference category) which are comparable to Manufacturing (3,821 and 5,304 observations versus 5,304 observations). The largest group is the remaining sectors with 10,455 observations. Finally, we define “Small and very small firms” dummy for firms with fewer than 200 employees (reference category), “Medium firms” for firms having between 200 and 300 employees and “Large firms” for firms with more than 300 employees. Following this definition, the small and large firm groups are of similar size (10,490 and 10,253 observations).

## 4. Estimation results

Table 6 reports estimation results of model (2) using maximum likelihood and firm-level clustered standard errors. We observe that output elasticities of capital and labor are 0.47 and 0.55, respectively, corresponding to a constant returns to scale (CRS) production function (the z-statistic for the CRS hypothesis equals 1.62 with the *p*-value = 0.11).

It is also shown that technical inefficiency depends on several variables like export activity, sectoral dummies, firm size and year dummies. Export dummy has a negative and significant (at the 5% level) coefficients, indicating that exporting firms are more efficient than non-exporting firms. This is rather intuitive as exporting firms should be sufficiently competitive in order to entry and stay in international markets. We also obtained the negative impacts of sectoral dummies on technical inefficiency. It means that firms operated in all economic sectors are more efficient than the reference group (agriculture, forestry, fishing, mining and quarrying sector). Moreover, medium-size and large-size firms are more efficient than small and very small firms (as both firm size dummies are negative and significant). Finally, all the year dummies coefficients are positive and significant, except 2014–2015, representing the deterioration of firm technical efficiency over the period of study compared to the reference year 2010.

Figure 1 presents the distribution of $\lambda_i$ for the full sample, over a range between 0.24 and a value close to 1. The average inefficiency value is 0.690 (also very close to the median, 0.692) indicates a very high rate of capital diversion for the Vietnamese SOEs. The most “efficient” (or rather the least inefficient) firms has a hidden overhead of 0.24 (minimum value of $\lambda$), which is still a high amount. The figure also shows the existence of an important group of firms (more than 10% of observations) that have a $\lambda$ very close to 1, meaning that these SOEs wasted almost all their capital during 2010–2018.

## 5. Concluding remarks

This paper estimates the technical inefficiency of the Vietnam SOEs during the period 2010–2018. The result is indicative of a very high “hidden overhead” in physical capital, 69% on average. Thus, even without a comparison with private firms, this astonishing finding

<table><caption>**Table 5.**
Firm size</caption><thead><tr><th>Size dummies</th><th>Definition</th><th>Frequency</th><th>Percentage</th></tr></thead><tbody><tr><td>Small</td><td>Small and very small firms</td><td>10,490</td><td>42.83</td></tr><tr><td>Medium</td><td>Medium firms</td><td>3,750</td><td>15.31</td></tr><tr><td>Large</td><td>Large firms</td><td>10,253</td><td>41.86</td></tr><tr><td>Total</td><td></td><td>24,493</td><td>100.00</td></tr></tbody></table>

**Note(s):** Data on 10,200 SOEs over the 2010–2018 period

**Source(s):** Data from the GSO Enterprise Census, table by the authors
<table><thead><tr><th>Variable</th><th>Coefficient</th><th>Robust Std.Err</th></tr></thead><tbody><tr><td><em>Production function</em></td><td></td><td></td></tr><tr><td>In Capital</td><td>0.471**</td><td>0.012</td></tr><tr><td>In Labor</td><td>0.544**</td><td>0.017</td></tr><tr><td>Intercept</td><td>1.446**</td><td>0.099</td></tr><tr><td><em>Inefficiency determinants</em></td><td></td><td></td></tr><tr><td>Export</td><td>-33.351**</td><td>12.244</td></tr><tr><td><em>Sectoral dummies</em></td><td></td><td></td></tr><tr><td>Manufacturing</td><td>-72.646**</td><td>26.862</td></tr><tr><td>Electricity, Gas, Water, Construction</td><td>-33.775**</td><td>12.250</td></tr><tr><td>Others</td><td>-44.183**</td><td>16.149</td></tr><tr><td><em>Firm size dummies</em></td><td></td><td></td></tr><tr><td>Medium</td><td>-34.105*</td><td>13.787</td></tr><tr><td>Large</td><td>-26.354**</td><td>9.903</td></tr><tr><td><em>Year dummies</em></td><td></td><td></td></tr><tr><td>2011</td><td>26.715**</td><td>10.055</td></tr><tr><td>2012</td><td>33.853**</td><td>12.302</td></tr><tr><td>2013</td><td>7.877*</td><td>3.925</td></tr><tr><td>2014</td><td>5.597</td><td>4.233</td></tr><tr><td>2015</td><td>3.496</td><td>3.747</td></tr><tr><td>2016</td><td>9.850**</td><td>4.923</td></tr><tr><td>2017</td><td>16.882**</td><td>6.338</td></tr><tr><td>2018</td><td>14.707**</td><td>5.559</td></tr><tr><td>Intercept</td><td>-44.765*</td><td>17.903</td></tr><tr><td>σ<sub>e</sub></td><td>1.009**</td><td>0.012</td></tr><tr><td>σ<sub>u</sub></td><td>7.967**</td><td>1.512</td></tr><tr><td>Log-likelihood</td><td>-39.470</td><td></td></tr><tr><td>Number of firms</td><td>10,200</td><td></td></tr><tr><td>Number of observations</td><td>24,493</td><td></td></tr></tbody></table>

Note(s): Estimation performed by maximum likelihood with firm-clustered standard errors. Reference group for sectoral dummies is “Agriculture, forestry, fishing, mining and quarrying” sector. Reference group for year dummies is 2010. Reference group for firm size is “Small and very small firms”. Significance level: \*p < 0.05, \*\*p < 0.01

Source(s): Table by the authors

Vietnamese state-owned enterprises

<caption>Table 6. Estimation results of the Cobb-Douglas production frontier</caption>

suggests the need for an urgent and profound reform of the Vietnam SOEs in order to reduce their wasteful use of capital.

Some further investigations are necessary in order to deliver a more precise calculation of hidden overhead. One the one hand, an alternative production function such as the CES function would be more general than the Cobb-Douglas one considered here. In this regard, some more advanced econometric techniques could be employed to account for the endogeneity of input variables (similarly to the TFP estimation literature). On the other hand, a similar exercise can be applied to private firms in order to have a comparison between public and private sectors. This analysis could tell us, other things being equal, whether a campaign to privatize state-owned companies would be appropriate in Vietnam.
<figure><img src="image_3.png" /><figcaption>Figure 1. Distribution of $\hat{\lambda}_i$</figcaption></figure>

Source(s): Figure by the authors

Notes

1. See the link https://data.worldbank.org/indicator/FR.INR.RINR?locations=VN&most=desc=true

2. Let qK be the value of the capital and wN the value of total wages. q, w are, respectively, the price of the capital and labor wages. If r is the real interest rate and δ is the capital depreciation rate, then the ratio [Investment cost/labor cost] is $\frac{(r+\delta)qK}{wN}$

3. In case of translog production function, the regression equation becomes

$$ \ln Y_{it} = \beta_0 + \beta_K \ln K_{it} + \beta_N \ln N_{it} + \beta_{KK} (\ln K_{it})^2 + \beta_{NN} (\ln N_{it})^2 + \beta_{KN} \ln K_{it} \ln N_{it} + \varepsilon_{it} \\ - \underbrace{\{-(\beta_K + 2\beta_{KK} \ln K_{it} + \beta_{KN} \ln N_{it})\ln(1-\lambda_{it}) - \beta_{KK}[\ln(1-\lambda_{it})]^2\}}_{u_{it}}, \quad (5) $$

This specification implies the endogeneity of ln Kᵢᵢₜ and ln Nᵢᵢₜ as E(ln Kᵢᵢₜuᵢᵢₜ) ≠ 0 and E(ln Nᵢᵢₜuᵢᵢₜ) ≠ 0. Hence, alternative methods would be more appropriate to estimate this specification but this will completely change the nature of our paper (see Van Beveren, 2012). Indeed, while the methods advocated by Olley & Pakes (1996), Levinsohn & Petrin (2003) and Wooldridge (2009) can allow to estimate the TFP (represented by β₀) derived from this production function, it seems that the hidden overhead parameter cannot be easily identified.

4. It is normal that the two subsamples give a number of firms (9726 + 787 = 10513), exceeding the total number of available firms in our sample (10,200) because the ratio K/Y can vary and crosses the threshold of 20 over the period of study.

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**Further reading**

The General Statistics Office of Vietnam GSO (2014). Vietnam enterprises census 2014.

The General Statistics Office of Vietnam GSO (2015). Vietnam enterprises census 2015.

**Corresponding author**

Phu Nguyen-Van can be contacted at: pnguyenvan@parisnanterre.fr

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