Capital Expenditure and Operating Eciency from Vertical Integration in the Global Semiconductor Industry

This paper uses a nonparametric production frontier approach to investigate the operating eﬀiciency differences by the impacts of capital expenditure and business model in the global semiconductor industry. Handling the impact of capital expenditure as fixed input by the directional distance estimator, this study compares the operating eﬀiciencies in the global semiconductor industry between the integrated device manufacturers and the fabless and foundry firms over 1999–2018. The estimation results indicate that vertically integrated manufacturers dominate the semiconductor industry, and the capital-intensive companies operate more eﬀiciently than the asset-light fabless firms on average. disentangling the impact of capital investments comparing the eﬀiciencies between the IDMs and the vertical disintegrated fabless and foundry firms in the semiconductor industry. Data on 470 companies in North America, and are collected to provide a worldwide perspective of the highly globalized semiconductor industry. This the operating eﬀiciencies between the IDMs and the fabless-foundry business models to shed light on which business model will be the market trend and dominate the semiconductor industry in the long run. Based on the capital-intensive feature of the semiconductor industry, this paper chooses a directional distance measure to handle the constraint of CAPEX. At the same time, conditional FDH estimators are used to handle the effects of business model and time in the nonparametric frontier approach. The empirical results provide clear evidence that the fabless firms are operating less eﬀiciently on average. Though the fabless-foundry business model encourages entrance of the fabless startups, the CAPEX barriers accompanying with technical barriers still limit the fields and applications for the fabless firms to growth and development. The IDMs have more room to optimize the operation and lead the technology development with a strategic product roadmap by vertical integration. The fabless-foundry business model is more like a complement of the IDMs to explore a broader scope in the semiconductor industry instead of a sub-stitutional structure change. The IDMs will continuously dominate the semiconductor industry in the foreseeable future.


Introduction
Semiconductors, also referred to as chips or integrated circuits (ICs), are essential components of virtually all modern electronic devices. Since Bell laboratories invented the transistors in 1947 and the first commercial ICs released in the 1960s, the semiconductor industry has been at the forefront of the growth of the digital economy. Prior to the 1980s, integrated device manufacturers (IDMs), which internally perform all of the production processes (e.g., research and design (RD), front-end fabrication, and back-end assembly and test (AT)), dominated the semiconductor industry. As semiconductors with ever-expanding complexity approach the limits of Moore's Law (e.g., see Mack, 2011 andFlamm, 2017), the expenses of manufacturing an inventive chip have become prohibitive for almost all the IC suppliers. These increasing costs stimulated business model innovation and gave birth to the fabless-foundry business model in the mid-1980s. In this new business model, fabless companies dedicate their time to IC design and brand operation. At the same time, pure-play foundries devote themselves to front-end fabrication, and a third group of companies are allotted for back-end outsourced semiconductor assembly and test (OSAT) operations. The fabless-foundry business model has significantly changed the structure of the semiconductor industry over the last few decades.
The structural changes by specialization in the semiconductor value chain is a topic of wide interest (e.g., see Macher et al., 2007, Adner and Kapoor, 2010and Sarma and Sun, 2017. Although the semiconductor industry is both technology-intensive and capital-intensive, much research on the topic of the structural change in the semiconductor industry emphasizes the impact of evolving technologies (e.g., see Macher, 2006, Kapoor and Adner, 2012and Hwang and Choung, 2014, while the impact of capital investments has not been discussed adequately. Simultaneously, vertical disintegration in the semiconductor value chain is accompanied and twisted by the trend of industry globalization (e.g., see Brown et al., 2005), which further increases the complexity of the topic. Recent developments in nonparametric frontier estimation (e.g., see Daraio et al., 2020) provide tools to analyze the operating efficiencies in the semiconductor industry under various types of constraints such as capital investments and the business model. This paper aims to use the Daraio et al. (2020) approach to shed light on disentangling the impact of capital investments and comparing the technical efficiencies between the IDMs and the vertical disintegrated fabless and foundry firms in the semiconductor industry. Data on 470 companies in North America, Europe, and Asia are collected to provide a worldwide perspective of the highly globalized semiconductor industry.
Before jumping into the details of the nonparametric frontier estimation, it is worth tracing the origin and evolution of the fabless-foundry business model in the semiconductor industry. A milestone of the vertical disintegration in the semiconductor industry is the establishment of the Taiwan Semiconductor Manufacturing Company (TSMC) in 1987. Committed to be a long-term non-competitive partner with fabless firms, TSMC is the first and nowadays the largest pure-play foundry worldwide that dedicates to wafer fabrication (e.g., see Hsieh et al., 2002). The drastically reduced burden of capital expenditure (CAPEX) and the reduced barriers to entry by vertical specialization ensure domination of new markets by the fabless firms. The collaboration between the asset-light fabless and the pure-play foundry also provides the more robust protection of intellectual property (IP) rights when the fabless firms pass on their design blueprints to pure-play foundries, which earlier are exposed to the threats of replication and IP theft when fabless firms' ICs are manufactured by their rival IDMs (e.g., see Sarma and Sun, 2017). The entry of new fabless companies, most of which are spinoffs from industry incumbents, spur innovation and propel the diversification of products in various applications. Since the 1990s, fabless firms have had substantial shares or even dominated in most of the fastest-growing market segments (e.g., see Balconi and Fontana, 2011). Nevertheless, despite a trend toward vertical specialization driven by the entry of fabless firms, the vertical integrated IDMs have continued to persist and coexist with the fabless entrants in the semiconductor industry.
Factors that determine production costs and operating efficiencies vary essentially across device types and business models in the capital-intensive and technology-intensive semiconductor industry. On the one hand, manufacturing is capital intensive for leadingedge products such as microprocessors and radiofrequency devices, with steadily rising R&D and equipment expenditures. The slow progress in node technology requires continuous investments in both R&D and advanced fabrication facilities. The uncertainties set high barriers to entry and favor the success of large IDMs, such as Intel, STMicroelectronics, and Texas Instruments, which are able to make risky investments and have a higher chance to foresee and lead the technology evolutions. On the other hand, the major challenges for front-end fabrication and back-end A&T procedures are the heavy CAPEX for cleanroom and costly equipment. The foundries and OSATs seek to optimize productivity by serving many fabless companies to achieve high capacity utilization. In comparison, the fabless companies, many of which are niche startups, getting rid of the burden in setting up, maintaining, and upgrading fabrication facilities, focus on R&D to compete with the IDMs. Hence CAPEX is a crucial factor in the semiconductor industry with a feature of lump sum fixed input.
There has been a long-lasting debate on which business model is operating more efficiently or is more likely to dominate the semiconductor industry. On one side, Monteverde (1995) and Dibiaggio (2007) credit the efficiency of IDMs to the internalization of transaction costs. Ernst (2005), Macher (2006) and Kapoor and Adner (2012) hold the knowledge-based view that the IDMs achieve performance advantages when technological developments involve complex problems. On the other side, Li et al. (2011) show that foundries are becoming technology transferors rather than merely manufacturing capacity providers in the semiconductor industry value chain. Kapoor (2013) proposes and finds that the incumbents who persist with vertical integration increase their emphasis on systemic innovations. Besides the examples shown above that focus on analyzing the impact of technology evolution in the semiconductor industry, this paper plans to emphasize the feature of capital intensive in the semiconductor indus-try and focus on exploring the impacts of CAPEX and business model on operating efficiency.
Taking advantage of a flexible functional form, data envelopment analysis (DEA) is one of the most popular approaches for efficiency estimation. There are rich records for performance evaluation in the semiconductor industry using the DEA approach. For instance, Kozmetsky and Yue (1998) Hung and Lu (2008), Liu and Wang (2008), Lin et al. (2019), the studies contain only 10-25 companies, which may lead to unconvincing results. It also explains why the Free Disposal Hull (FDH) estimator, which is known as an unbiased substitution of the DEA estimator but with a much slower convergence rate, is not widely used in empirical works (e.g., see Wilson, 2018). One solution to mitigate the slow convergence rate problem in nonparametric efficiency estimation is to increase the number of observations by considering the deeply globalized semiconductor industry as an aggregated market. This paper follows this strategy to investigate the impacts of the business model and CAPEX in the highly globalized semiconductor industry through a conditional nonparametric frontier approach. The heterogeneity by CAPEX is treated as a fixed input variable by the directional distance estimator (e.g., see Daraio et al., 2020), while the heterogeneity by the business model is handled by the conditional efficiency estimators (e.g., see Daraio and Simar, 2007). The estimation results indicate that vertically integrated manufacturers dominate the semiconductor industry and the capital-intensive IDMs and OSATs operate more efficiently than the asset-light fabless firms on average.
The paper is organized as follows. Section 2 gives the nonparametric frontier framework and discusses the diagnostics and test statistics for choosing a suitable estimator in this research. Section 3 presents the empirical results and discusses the effect of capital investment and business model in the semiconductor industry. The last section concludes.

The Nonparametric Frontier Model
The economic theory of efficiency in production can be traced to the ideas of Koopmans (1951), Debreu (1951) andFarrel (1957). Consider a production process in which p inputs are used to produce q outputs. The production set describes the set of attainable combinations of inputs and outputs. The efficiency score of a particular production plan (x, y) is then determined by the distance from (x, y) to the efficient frontier or boundary of Ψ (denoted as Ψ ∂ ). There are four kinds of commonly used efficiency measures based on different directions in which the distance is calculated. The most widely used radial measures are the input-and output-oriented Debreu-Farrel measures. Färe et al. (1985) introduce the hyperbolic measure as an alternative to selecting either an input-or output-oriented Debreu-Farrel measures, where input and output quantities are adjusted simultaneously to reach the boundary Ψ ∂ along a hyperbolic path. Note that these three kinds of efficiency measures are all radial measures that allow for only nonnegative values of inputs and outputs. Chambers et al. (1998) propose an additive measure of the technical efficiency, known as the directional distance measure, which considers adding the feasible quantities to a unit's output and simultaneously subtracting proportional quantities from its input. In detail, the directional distance measure is given by which projects the input-output vector (x, y) onto the technology in a specified direction (−d x , d y ) and allows for negative values of x and y. Note that the directional distance measure β(x, y | d x , d y , Ψ) nests both input-and output-oriented Debreu-Farrel measures as special cases by setting the direction vector (d x , d y ) as (x,0) and (0,y), respectively. The flexibility of the directional distance measure also comes from the choices of the directions d x and d y that some directions (but not all) can be set equal to zero to represent non-discretionary inputs or outputs (e.g., see Simar and Vanhems, 2012). This feature of the directional distance measure can represent the impact of a kind of fixed input or output variables, such as CAPEX, which can be categorized into input variables of production but are not under managers' direct control, at least in the short run.
The attainable set Ψ is unobserved in empirical works. Nonparametric methods such as FDH and DEA are developed to estimate the unobservable production set Ψ.

Deprin et al. (1984) define the FDH estimator Ψ FDH as
} denote a random sample of n pairs of inputs and outputs. FDH Baker et al. (1984) propose the varing-returns-to-scale DEA (VRS-DEA) estimator Ψ VRS as the convex hull of Ψ FDH . The corresponding VRS- There is another kind of the DEA estimator, defined as the convex cone of Ψ FDH and called the constant-returns-to-scale DEA (CRS-DEA) estimator. Since the CRS-DEA estimator relies on strong assumption that the returns to scale are everywhere constant, it is less widely used in empirical works.
Therefore, the notation DEA is dedicated for VRS-DEA for the rest of the paper.
Besides inputs and outputs, there exist factors such as differences in ownership, business models, constraints of technology and regulatory, which are typically beyond control of the manager but may influence the production process. These factors (denoted as environmental factors Z ∈ R r ,) may not be independent of (X, Y ), so that the unknown effect of Z must be estimated appropriately. Daraio and Simar (2005) propose a framework to investigate the joint behavior of (X, Y, Z) in probability terms by defining the conditional attainable set as which gives the probability that a firm facing environmental conditions z will dominate the point (x, y). Given Z = z, the attainable set Ψ z is the support of H X,Y |Z (x, y|z).
Introducing environmental factors into (2.2)-(2.3) extend the efficiency scores into their conditional counterparts. For example, the conditional hypobolic measure can be expressed as and the conditional directional distance measure can be expressed as .., n} into (2.7) or (2.8) can derive the estimation of the conditional efficiency scores accordingly. Such a nonparametric estimator of H X,Y |Z (·) may be obtained by standard kernel smoothing, for example, where K(·) is a kernel function with bounded support, h is a vector of bandwidths h = (h 1 , ..., h r ), and r is the number of environmental variables. It is well known that the selection of bandwidth h is of critical importance in kernal smoothing (e.g., see Hall et al., 2004, Bȃdin et al., 2010, Jeong et al., 2010, and Li et al., 2013 for the discussions of choosing the optimal bandwidth by least square cross-validation (LSCV)).
There is a particular case, called the separability condition in Simar and Wilson (2007), where Z has no impact on the boundaries of the Ψ z and Ψ z = Ψ for all z ∈ Z. Wilson (2007, 2011) emphasize that if the separability condition is not hold, naive regression in a second-stage analysis may provide inconsistent estimation.
Alternatively, Bȃdin et al. (2012Bȃdin et al. ( , 2014 suggest a flexible nonparametric location-scale in a second-stage regression, where µ(z) measures the average effect of z on the efficiency, and σ(z) provides additional information on the dispersion of the efficiency distribution as a function of z. Mastromarco and Simar (2015), Cordero et al. (2017), Toma (2020), etc., had used this two-step approach for various empirical studies.

Estimation and Inference
The tradeoff between FDH and DEA estimators for performance evaluation is not trival.
Simar and Wilson (2015) summarize in a survey of the nonparametric frontier models that the FDH and DEA estimators converge to limiting distributions at rates n 1 p+q and n 2 p+q+1 respectively under appropriate assumptions. Hence for a fixed sample size n, the convergence rate slows down with the increasing of dimensionality (p + q), which increases the estimation error accordingly for both the FDH and DEA estimators. A feasible approach to minimize such estimation error (often referred to as the curse of dimensionality) is either to increase the sample size n or to decrease the total dimensions of (p + q). If the sample size n is restricted to a small number by real world constraints, including the market scale and market scope in specific industries, geographical or political restrictions, and the high cost of data collection, dimension reduction may become an attractive solution. Daraio and Simar (2007, pp. 148-150) propose using principal component analysis (PCA) for dimension reduction. Wilson (2018) explains how to use PCA for a mapping for the radial measures. In detail, (p × n) matrix X and (q × n) matrix Y are transformed to (1 × n) matrices Λ ′ x 1 X, Λ ′ y 1 Y by pre-multiplying the first eigenvector Λ x 1 , Λ y 1 of the moment matrices XX ′ and Y Y ′ . Though it is not possible to give a theorem that precisely identifies situations where dimension reduction should be used, Wilson (2018) provides three diagnostics for empirical research. The first diagnostic is to compute the effective parametric sample size m as m ≈ ⌊n 2κ ⌉, where κ = 1 p+q for FDH estimator, κ = 2 p+q+1 for DEA estimator, and ⌊a⌉ denotes the integer nearest a. Hence the criterion of judging the minimum sample size m in parametric estimation can be used as reference in judging the minumum sample size n in nonparametric estimation.
A second diagnostic is to consider the proportion of n observations that yield efficiency scores equal to one. Since FDH estimator converges slower than DEA estimator, a robust diagnostic for the curse of dimensionality should use the FDH efficiency estimator. If more than 25%-50% of the observations yield efficiency scores equal to one, the estimation results are not convincing. A third diagnostic is to exam the ratios R x and R y of the largest eigenvalue of the moment matrices XX ′ and Y Y ′ to the corresponding sum of eigenvalues for XX ′ and Y Y ′ , which provide measures of how close the corresponding moment matrices are to rank-one. For example, if R x = 0.9, then the matrix with dimension reduction Λ ′ x1 X contains 90% of the independent linear information in the original matrix X. In practice, Wilson (2018) proposes standardizing the matrices X or Y before PCA to ensure the inputs or outputs have the same scale, in case of excessive number of inputs or outputs.
After the diagnostics of dimension reduction, Kneip et al. (2015Kneip et al. ( , 2016 use new central limit theorems to construct a test of convexity for the tradeoff between Ψ FDH and Ψ VRS . Note that the main difference of the test statistics by the new central limit theorems in Kneip et al. (2015Kneip et al. ( , 2016 are the bias corrections construced by jackknife estimators (e.g., see Kneip et al., 2016, pp. 441-442). If the null hypothesis of convexity is rejected, the FDH estimator is the only consistent estimator. Alternatively, if the null hypothesis of convexity is not rejected, though it does not imply that the null is true, the DEA estimator may be the preferred estimator because of its faster convergence rate. However, the test of convexity proposed by Kneip et al. (2015Kneip et al. ( , 2016 depends on randomly split the original sample into two independent subsamples for the calculation of the bias terms, which introduces ambiguity in practice. Simar and Wilson (2020, pp. 293-294) develop a generalized bootstrap algorithm that eliminates much of this ambiguity by repeating the random splits a large number of times, which can be used for both the convexity test and the separability test.

Data and Variable Specification
The data are collected from the Sub-Industry of Semiconductors in the Compustat database. In order to provide a global perspective for the semiconductor value chain, I combine data from both the Compustat North America database and the Compustat Global database to cover companies in the industry worldwide. As the semiconductor industry is famous for being a cyclical industry (e.g., see Tan and Mathews, 2010), I gather twenty years of data between 1999-2018 to cover a sufficient period with multiple business cycles in the industry. The reason for the data to begin in 1999 is twofold. A side product of the flexible functional form in the nonparametric frontier approach is a lack of theoretical foundation on the production function. Identifying the inputs and outputs has always been a subject of controversy, either in parametric or nonparametric frontier estimations, without exception in the semiconductor industry.
Hence I sort the most commonly used variables in 37 empirical papers which apply the nonparametric frontier approach for performance evaluation in the semiconductor industry. Besides a few variables which are chosen for specific topics, the commonly used variables in these papers are highly concentrated into two input categories and two output categories. The first input category measures all kinds of variable inputs, including labor, raw material, R&D and sales, and marketing expenditure, while the second input category measures fixed assets. Comparably, the first output category measures revenue and the second output category measures the market value of the firms. Therefore, I specify p = 5 inputs (labor, measured by the number of employees (X 1 ); COGS (X 2 ); R&D expenditure (X 3 ); sales and marketing expenditure (X 4 ) and fixed assets, measured by property, plant, and equipment (PP&E) (X f )) and q = 2 outputs (total revenue (Y 1 ); and shareholders' equity, measured by common ordinary equity (CEQ) (Y 2 )). Since I plan to use the directional distance estimator, I distinguish the notation of the fixed input X f with the other four variable inputs X 1 , X 2 , X 3 , and X 4 . For the output variable Y 2 , I use shareholders' equity instead of the market value of a firm, because the variable of market value is suffering from missing data in the Compustat database, and the variable shareholders' equity is also a widely used proxy for the value of a firm. Table 1  In addition, I specify r = 2 environmental variables (business model (Z 1 ); and time, measured by the years 1999-2018 (Z 2 )). The environmental variable Z 1 is a discrete variable, which categorize the four kinds of business models including fabless, IDM, foundry, and A&T into three groups. The first group contains fabless companies which are labor intensive for chip design, while the second group contains both foundries and OSATs which are capital intensive for fabrication, and a third group contains IDMs which are both labor intensive and capital intensive. The environmental variable Z 2 can either be treated as a continuous variable or a discrete variable, which will be discussed further in the next section. Table 2

Results and Discussion
It is well known that most nonparametric estimators suffer from the curse of dimensionality. Based on the three diagnostics introduced above, the necessity for dimension reduction is unambiguous. With seven dimensions (p=5 and q=2) in the original data, the effective parametric sample size m for the original annual data is small, no matter using FDH or DEA estimators. A slight difference in processing PCA for the directional distance estimator is that PCA is only on the variable inputs and outputs, but not on the fixed input X f . Hence after dimension reduction there remain three dimensions including X (PCA from X 1 to X 4 ), Y (PCA from Y 1 to Y 2 ) and X f . I calculate the values of the largest eigenvalue of the moment matrices of XX ′ and Y Y ′ to the corresponding sum of eigenvalues to be R x = 91.19% and R y = 98.31%, indicating high correlations among the input variables X 1 , ..., X 4 and high correlations between the output variables Y 1 , ..., Y 2 , so that dimension reduction should reduce estimation error. Thus all of the following analyses and results are based on data with dimension reduciton.
Among studies that use nonparametric frontier approach to estimate efficiency and benchmark performance of firms in the semiconductor industry, the vast majority choose DEA estimator, without comparing the pros and cons between FDH estimator and DEA estimator. The DEA estimator is probably a better choice without dimension reduction, as the slower convergence rate of FDH estimator may increase measurement error rapidly with the increasing of dimensions. However, it is worth to reevaluate the tradeoff between FDH estimator and DEA estimator with dimension reduction. The drawback of DEA estimator is imposing convexity on the production set Ψ, while FDH estimator is free of this assumption. As discussed above, the test of convexity versus non-convexity of the product set proposed by Kneip et al. (2016) can be applied to measure this tradeoff. The FEAR package (e.g., see Wilson, 2008) uses a bootstrap algorithm by Simar and Wilson (2020) to extend the Kneip et al. (2016) approach for the convexity test. Table 3 provides results of the convexity test, using the FEAR package and the choosing hyperbolic-oriented measure in (2.2). At 95% confidence level, the null hypothesis of convexity are rejected for over 80% of the 20 years annual data, except 3 years (2009, 2011 and 2012) in hyperbolic-orientation. Simar and Vanhems (2012) link the directional distance measure with the standard hyperbolic measure by a monotonic transformation, so that the results in Table 3 are also valid for the directional distance estimator. Hence I choose FDH estimator for the remainder of the analysis. Daraio et al. (2020) propose a fast and efficient computation of the directional distance measures using FDH estimator. In detail, after monotonic transformation of the data that where ⊘ refers to Hadamard component-wise division of vectors, the FDH estimator in (2.4) can be expressed explicitly as where n is the sample size and i ∈ {1, 2, ..., n}. It is straightforward to extend the expression in (3.2) to the conditional directional distance estimator (e.g., see Daraio et al., 2020, pp. 814) as Therefore, in order to consider a discrete environmental variable such as the business model Z 1 for the estimator in (3.3), the separability condition needs to be examined.
Similarly, in order to consider a continuous environmental variable such as Z 2 (in case Z 2 is treated as continuous) for the estimator in (3.3), the optimal bandwidth h needs to be fixed in advance. Simar and Wilson (2020) propose a bootstrap algorithm which can be used for the separability test on the discrete environmental variable Z 1 . In application to the additive directional distance measure, step [5] in Simar and Wilson (2020, pp. 293) which is originally designed for the radial measures should be revised as and where the directions of d x and d y are chosen commonly as the sample mean of X and Y . The first portion in Table 4 shows the separability test results with respect to the business model Z 1 . Though the test statistics τ 1 and τ 2 not always give the same results, there is strong evidence to reject the separability condition. In other words, each of the three business models in semiconductor industry has its unique production frontier for pooled data.
For the environmental variable Z 2 which represents the years 1999-2018, there is flexibility to either treat it as a discrete variable or as a continuous variable (e.g., see Mastromarco and Simar, 2015). To treat Z 2 as a discrete variable, the 20 years of 1999-2018 can be splitted into ten 2-year groups (two adjacent years as a group), five 4-year groups (four adjacent years as a group) or four 5-year groups (five adjacent years as a group). In this case the separability test with respect to Z 2 is similar to the separability test with respect to Z 1 . Although Z 2 can naturally be treated as 20 individual years, it is not recommended for the directional distance measure here. Since each individual year has around 100-300 observations, the effective parametric sample size m = n 2 3 for the directional distance measure in each year will be a small number and hence increase the measurement error and make this approach less attrative.
Another approach is to treat Z 2 as a continuous variable and using LSCV to determine the optimal bandwidth h by minimizing . (3.6) The optimal bandwidth is h = 5.5 for fabless, IDM, and pooled data, implying the smoothing window of year t is [t-5,t+5], while the optimal bandwidth is h = 7.5 for OSAT with the smoothing window of year t to be [t-7,t+7]. The second portion in Table 4 shows the separability test results with respect to the optimal time Z 2 , while the third portion in Table 4 shows the separability test results with respect to both the business model Z 1 and the time Z 2 . In any case the separability conditions are strongly rejected. Hence the efficiency scores in (3.3) are estimated with separated production frontiers per the restriction of both the conditions Z 1 and Z 2 . Table 5 shows the summary of the efficiency scores conditional on both the business model Z 1 and time Z 2 . Whether the time Z 2 is treated as a discrete variable or a continuous variable, the distributions of the efficiency scores are skewed to the right in all kinds of business models, especially for the fabless firms. Nevertheless, on conditions that Z 2 are treated as a discrete variable, the first quartiles are either equal to zero or very close to zero, no matter how the years are grouped. Based on the second diagnostic in Wilson (2018), it is a sign that the measurement error by slow convergence rate still exist. Choosing a estimation method with larger subsample size is a feasible solution to minimize such measurement error with dimension reduction. Thus a preferred approach is to treat Z 2 as a continuous variable, rewarding faster convergence rate and more accurate estimates. Figure 1 visualizes the trends of the annual mean efficiencies by business model.
Either treating Z 2 as a discrete variable or as a continuous variable, the curves of the annual mean efficiencies for the fabless firms are above the curves for the other business models. This phenomenon is more visable in the bottom right panel, where Z 2 is defined as a continuous variable with more reliable estimates. As higher efficiency score infers lower technical efficiency in the directional distance measure, the curves in Figure 1 imply the fabless firms are operating less efficiently on average. Another interesting discovery is that the curves of different business models in the bottom right panel of Figure 1 tend to converge in 2008, the year of global finanical crisis. It can be interpreted that under extreme conditions the differences in operating efficiency become unconspicuous among business models. Based on the bottom right panel of Figure 1 which produce more accurate estimates, I use new central limit theorem (e.g., see Kneip et al., 2015, pp. 409) to derive 95% confidence interval for the annual mean efficiency curves in Figure 2. The variance for the fabless firms are also higher comparing with the IDMs or OSATs, implying higher risk and uncertainty for the fabless business model. (3.7) In practice, I obtain µ(z) by regressing β(x, y | z) on the environmental variable z and σ(z) by regressing the squared residuals of the preceding regression on z. The upper panel in Figure 3 illustrates the pure efficiency ε(z 1 , z 2 ) that cleanses efficiency scores from the influence of both the environmental factors Z 1 and Z 2 , while the lower panel in Figure 3 illustrates the pure efficiency ε(z 2 ) that cleanses efficiency scores from the influence of only the environmental factor Z 2 . In the upper panel, the curves of ε(z 1 , z 2 ) by different business models twist together with no clear structures, similar to white noise vibrating at small values around zero. On the contrary, in the lower panel, the curves of ε(z 2 ) demonstrate clear separation by business models. Since ε(z 2 ) only cleanses the influence of time, the lower panel in Figure 3 maintains the structure of the differences in technical efficiency by the business model in Figure 1-2. Consequently, the contrast between the upper and lower panels in Figure 3 provides further evidence that the technical efficiencies do vary in the semiconductor by business models, and the asset-light fabless firms are operating less efficiently on average in the past two decades.

Conclusion
The semiconductor industry is famous for the high barriers to entry, especially in

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