Inter-industry and Intra-industry Switching as Sources of Productivity Growth STRUCTURAL CHANGE OF FINLAND’S ICT INDUSTRIES

Structural change is an important driver of productivity growth at the aggregate level. While previous productivity decompositions account for the contributions of market entry and exit, they overlook continuing firms that switch from one industry to another. We develop an improved productivity decomposition that accounts for both intra-industry and inter-industry switching, is applicable to both static and inter-temporal settings, and ensures consistent aggregation of firm level pro - ductivity to the industry level. The proposed decomposition is applied to Finland’s information and communication technology (ICT) industry in the first two decades of the 21st century. This industry experienced major structural changes due to the rapid downfall of Nokia, the world’s largest mobile phone manufacturer at the beginning of our study period. Our results reveal that the sharp decline of labor productivity was associated with the structural changes, whereas the surviving firms that continued in the same industry managed to improve their productivity. Our results indicate that industry switching can dampen or enhance the productivity impacts of structural change, especially during the times of crisis and recession.

Tulostemme mukaan työn tuottavuuden lasku toimialatasolla aiheutui rakennemuutoksesta, sen sijaan samalla alatoimialalla jatkavien yritysten tuotavuus kehittyi suotuisammin.Tuloksemme myös osoittavat, että toimialan vaihtaminen voi yhtäältä vaimentaa, toisaalta myös vahvistaa rakennemuutoksen tuottavuusvaikutuksia, erityisesti kriisien ja laskusuhdanteen aikana.Schumpeter (1939) coined the term "creative destruction" to describe how market competition leads to the continuous replacement of inefficient producers with more productive ones.He also noted that during recessions, the least productive and least innovative units are more likely to be scrapped, which can help to increase productivity and foster new growth.However, the traditional approach of measuring productivity growth using balanced panel data of continuing firms ignores the impact of structural change through entry and exit on productivity growth.1 Baily et al. (1992) and Griliches and Regev (1995) were the first to introduce structural change decompositions of productivity growth that considered not only the continuing firms, but also the contributions of firm entry and exit.Following Olley and Pakes (1996), another line of studies distinguishes the contribution of resource reallocation across firms, which is also related to creative destruction.Competition favors high productivity firms, which tend to grow larger than low productivity firms.Note that the market share of a low productivity firm may initially shrink and eventually reach zero, resulting in a market exit.Several subsequent studies, such as Maliranta (2003), Böckerman and Maliranta (2007), Diewert and Fox (2009), Hyytinen and Maliranta (2013), Holm (2014), and Maliranta and Määttänen (2015) have extended the Olley-Pakes productivity decomposition to incorporate entry and exit.

Introduction
In previous productivity decompositions cited above, firms are classified into mutually exclusive groups of continuing firms, exiting firms, and new entrants.Conventional interpretations often associate market entry with startups and market exit with bankruptcy.However, Bernard et al. (2010) show empirically that continuing firms frequently enter new markets by adding new products to their multiproduct portfolio.Similarly, market exit can occur through consolidation of production lines.In light of their findings, Kuosmanen and Kuosmanen (2021) argue that pooling continuing firms that introduce a new product (e.g., Apple introducing iPhone) together with genuinely new startups can blur the interpretation of productivity decompositions.Analogously, a multiproduct firm that refocuses its operations on more profitable product lines (e.g., Nokia selling its mobile phone division to Microsoft and focusing on mobile networks) is different from a firm that closes down completely.To address this issue, Kuosmanen and Kuosmanen (2021) introduced a novel structural change decomposition of productivity that ensures consistent aggregation of firm-level productivity measures to the industry level.This approach is applicable to both static and inter-temporal settings, and does not depend on the arbitrary choice of market shares or employment shares as firm weights.
The methodological objective of this paper is to refine the structural change decomposition by Kuosmanen and Kuosmanen (2021) by drawing a sharper distinguishing between intra-industry and inter-industry switching.The distinction is based on standard industry classifications, such as NACE, used in the European Union (Eurostat, 2008).2By intra-industry switching we refer to a change in a firm's four-digit or five-digit industry class within the same two-digit industry division.For example, a firm changing NACE class from 2620 to 2630 within division C26 is considered as an intra-industry switch.Inter-industry switching, on the other hand, refers to a situation where the firm's two-digit industry division changes.For example, a firm changing NACE class from 2620 to 6210, thereby changing from division C26 to J62, is considered as an inter-industry switch.This distinction is important because conventional productivity decompositions focusing on a specific two-digit industry division tend to misclassify inter-industry switching as either entry or exit, while intraindustry switching is typically pooled together with the continuing firms.
Our empirical objective is to examine the impact of structural changes on the productivity development of Finland's information and communication technology (ICT) industry during the first two decades of the 21 st century.This industry went through significant structural changes during our study period, associated with the changing fortunes of Nokia, the flagship of Finland's ICT sector.
Nokia was the world's largest mobile phone manufacturer in years 1998-2008, but since the introduction of iPhone in 2007, Nokia's market share started to decline rapidly, which led to the sale of Nokia's mobile phone division to Microsoft in 2014.The rapid growth and downfall of Nokia had a significant impact on the entire supply chain of subcontractors throughout the country (e.g., Simonen et al., 2020), which also influenced the labor markets for software developers, engineers, and other highly skilled professionals.
To gain a deeper understanding of the labor productivity development in Finland's ICT industry, we apply the proposed structural change decomposition method to comprehensive firm-level register data of Statistics Finland, which covers virtually all firms in Finland.For the sake of completeness, we consider both ICT manufacturing (NACE division C26) and ICT services (NACE division J62) because the structural changes occurring in the ICT manufacturing caused major spillovers in the ICT service industries as well (e.g., Ali-Yrkkö et al., 2021).We find that the major productivity decline in these industries was associated with the structural change, whereas the surviving firms that continued in the same industry managed to improve their productivity.Our results also suggest that industry switching can either dampen or enhance the productivity impacts of structural change, particularly during the times of crisis and recession.
The remainder of the paper is structured as follows.In Section 2, we provide a brief explanation of the phenomenon of intra-and inter-industry switching among firms, which serves as a means of entry and exit.In Section 3, we introduce our proposed method of structural change productivity decomposition.In Section 4, we detail the data used in this study and provide some descriptive statistics.In Section 5, we apply the structural change decomposition to the Finnish ICT industries.
Finally, in Section 6, we offer a concluding discussion and suggestions for future research.

Industry switching as a form of entry and exit
Dynamic models of oligopoly that incorporate sunk entry costs, stochastic technological progress, and endogenous exit decision-making have gained significant attention in the literature.These models, first introduced by Jovanovic (1982), Hopenhayn (1992), Ericson and Pakes (1995), and Olley and Pakes (1996), 3 examine how firms maximize their expected net present value of future profits by competing with incumbent firms and potential entrants in the future.The entry and exit decisions made by firms depend on their perceptions of future market structures, which are based on current information.These decisions ultimately shape the future market structures.Ericson and Pakes (1995) established a Markov perfect Nash equilibrium in which firms' perceptions of the distribution of future market structures align with the objective distribution of market structures generated by the firms' choices.Olley and Pakes (1996) describe the endogenous exit rule implied by their dynamic oligopoly model as follows: "a firm compares the sell-off value of its plant to the expected discounted returns of staying in business.If the current state variables indicate continuing in operation is not worthwhile, the firm closes down the plant."(p.1273).In other words, market exit occurs as a voluntary liquidation decision as the firm updates its perceptions of future profits.In reality, market exit often occurs involuntarily through bankruptcy.Murto and Terviö (2014) address this possibility by introducing a model that includes forced exit due to liquidity constraints.In this model, firms may be forced to exit the market due to a lack of liquidity, even if it would still be profitable to stay in business.Therefore, the firm must optimally manage its cash reserves to cope with the liquidity constraint.They show that the equilibrium state of the market may result in either too much or too little exit depending on the specific assumptions of the model.
In the context of this study, Bernard et al. (2010) present the most relevant theoretical work, introducing a general equilibrium model that incorporates endogenous entry and exit of firms, and multiproduct firms that can switch products over time.Their model assumes a continuum of products and independent distributions for consumer tastes.The firm's expected profits across the continuum of products equal the sum of the expected profits from each product, minus the fixed headquarters cost.The general equilibrium of the model includes steady-state product switching, as well as firm entry and exit.In each period, some new firms will incur the sunk entry cost and enter the market if their productivity is above the zero-value cutoff.Firms will exit endogenously if their productivity falls below the zero-value cutoff or exogenously due to force majeure considerations.
In Bernard et al. (2010)'s model, there are two mechanisms that drive continuing firms to switch products. 4The first mechanism is stochastic shocks to consumer tastes, which can cause fluctuations in the profitability of individual products, leading continuing firms to either discontinue some previously produced products or introduce new ones.The second mechanism is stochastic productivity shocks, which can also result in product switching.An increase in productivity can expand the range of products produced, while a decrease can contract it.Unlike previous dynamic models of endogenous entry and exit, Bernard et al. (2010)'s model allows existing firms to enter new markets and exit existing ones without closing down through liquidation or bankruptcy.The authors suggest that product switching can contribute to reallocation of resources toward their most efficient use.
In practice, empirical analysis of market entry and exit is typically conducted using comprehensive register data that covers nearly all firms or establishments within a specific industry or sector. 5 Industry classification systems, such as NACE, provide essential information for determining which firms and plants belong to the industry being studied (cf., e.g., the Appendix to Olley and Pakes, 1996).In the system of national accounts, all of a firm's activities are assigned to a single NACE class based on its principal economic activity, even if in reality the firm operates in multiple industries that span different NACE classes or divisions.The firm's principal economic activity is the activity that contributes most to the firm's total value added (see Eurostat, 2008).
While the firms must report themselves which NACE class is their main economic activity, this does not mean that firms can arbitrarily change their NACE code.In Finland, he Statistics Finland is 4 Other plausible reasons for product switching include drastic changes in government regulations (e.g., product bans), taxes and tariffs, transportation costs, and the security of supply concerns.It may also be influenced by factor markets and intermediate inputs, such as affordable energy and availability of skilled workers. 5In the empirical part of their paper, Bernard et al. (2010) examine the frequency of product switching in the US manufacturing.They found that half of firms change their mix of five-digit SIC products every five years, and 28% of firms operate in multiple five-digit classes, while 10% operate in multiple two-digit divisions.also actively following and updating the industry classification if necessary.For example, the Statistics Finland conducted a targeted survey to nearly 300 firms involved in the video games business in 2019. 6As a result, the industry classification of approximately 30 software firms was corrected.Majority of these firms were switched from the Computer programming activities (6201) to the Publishing of computer games (5821) or the Other software publishing (5829).
Product switching and industry switching are closely related but distinct concepts.Product switching can sometimes result in a change in a firm's industry classification code (such as NACE code).It is important to note that market entry and exit that occurs through switching of a firm's NACE classification is not always the binary decision described in the theoretical models.In fact, industry switching can occur gradually as a growing production line becomes more significant and overtakes the previous principal economic activity as the main source of value added. 7Paradoxically, a firm can continue to supply the same amount of a product to the market, but the NACE code changes if another product overtakes as the principal economic activity in terms of value added.In this respect, it would be misleading to classify such a firm as a market exit.These observations highlight the need to separate intra-industry and inter-industry switching, both from the continuing firms in the same NACE class and the genuine entry and exit.

Aggregation of firm productivity to industry level
In this paper, we focus on labor productivity, stressing that the proposed decomposition is directly applicable to other productivity measures such as total factor productivity (TFP), green TFP, or carbon productivity.Labor productivity of firm i in period t is defined as the ratio of value added (yit) and labor input (lit), formally, The industry is simply the aggregate of all Nt firms operating in period t; note that Nt can change over time due to market entry, market exit, and industry switching.Aggregate labor productivity of the industry in period t is defined as 6 For further information, see the website: https://www.stat.fi/uutinen/industrial-classification-of-video-gameenterprises-is-reviewed-enterprises-transferred-from-programming-to-publishing 7To avoid frequent changes that do not reflect a substantial change in economic reality, a stability rule has been established for multiproduct firms (Eurostat, 2008).According to this rule, the industry code is changed when the current principal economic activity has accounted for less than 50% of the value added for at least two consecutive years.
where Yt is the total value added of the industry in period t and Lt is the total labor input of the industry.
To link the firm-level and the industry-level, it is helpful to restate labor productivity of the industry as a share-weighted average of firm-level productivity measures, formally, where is the employment share of firm i in year t.Note that the use of employment shares guarantees consistent aggregation of firm-level labor productivity indicators to the industry level. 8

Static Olley-Pakes decomposition
To quantify the contribution of resource allocation on productivity, Olley and Pakes (1996) reformulate equation ( 3) as where ̄ and ̄ denote the averages of firm productivity and market share, respectively, and   =   − ̄ and   =   − ̄ denote the differences from the mean.Since the market shares must sum to one,   ̄ = 1, and hence equation (4) simplifies to . (5) The right-hand side of equation ( 5) decomposes the industry-level productivity into two components: the first one is the unweighted mean productivity of all firms and the second one represents allocation of resources across firms.Note that the second component can be equivalently stated as This representation emphasizes the interpretation of this component as a measure of allocative efficiency.When resources are reallocated from low productivity firms to high productivity firms, the covariance of market shares and productivity increases, resulting in a positive contribution to 8 In general, it is not self-evident that any firm-level productivity measures can be consistently aggregated to industrylevel (e.g., Blackorby and Russell, 1999;Zelenyuk, 2006;Kuosmanen and Kuosmanen, 2021).Clearly, if consistent aggregation is possible, then industry-level productivity must be a share weighted average of the firm-level productivity measures, as in (3).Other averages, such as the geometric mean or harmonic mean, would be inconsistent with the summation of the firm-level inputs and outputs to the aggregate level of the industry.
productivity growth of the industry.Kuosmanen and Kuosmanen (2021) note that the covariance term can be equivalently stated as the difference This means that is possible to calculate the allocation component without using the share weights   because the aggregate productivity   can be calculated using equation ( 2) and the average productivity ī does not depend on the share weights.

Static and intertemporal decompositions with entry, exit and industry switching
The standard approach for measuring the impact of entry and exit on productivity change is to divide the sample of firms into groups of continuing firms, entering firms, and exiting firms, as discussed in previous studies by Baily et al. (1992), Griliches andRegev (1995), andFoster et al. (2001).However, several attempts have been made to reconcile this approach with the Olley-Pakes decomposition, as seen in the works of Maliranta (2003), Böckerman and Maliranta (2007), Diewert and Fox (2009), Hyytinen and Maliranta (2013), Holm (2014), and Maliranta and Määttänen (2015).To ensure consistent aggregation of firm-level productivity measures to the industry level, reduce sensitivity to share weights, and decompose both the level and change of industry productivity, this study utilizes and expands upon the approach proposed by Kuosmanen and Kuosmanen (2021).
Our objective is to measure the contributions of market entry, exit, and industry switching on the level and change of productivity of a specific two-digit industry division (denoted by D) over a chosen study period [t, t+k], where t is the base period t and t+k is the target period.It is important to note that the length of the study period can affect the results; as the study period becomes longer, the shares of entering, exiting, and switching firms will increase.Consequently, the contribution of structural change may appear insignificant in a one-year period but may become more prominent over a longer period of 5-10 years, as seen in previous studies such as Holm (2014) and Kuosmanen and Kuosmanen (2021).
Recall that the total number of firms in the two-digit industry division D in period t is Nt.The division D can be further divided into multiple three-, four-, or five-digit classes cl = 1,…,CL.Given complete data of all firms operating in the base period t and the target period t+k, we can identify the following subsets of firms in period t: The same nested structure applies in period t+k.We will utilize this nested structure to measure the contributions of industry switching and exit on the level of productivity in period t.
First, we measure the contribution of intra-industry switching using the following differences in the sub-sample averages where the subscripts indicate the relevant subset of firms and the time period.The rationale of using unweighted subsample means is similar to that of equation ( 7) related to the Olley and Pakes (1996) decomposition.Note that the only difference between the subsets E(t) and C(t) concerns those firms that switch to another five-digit class within the same two-digit industry division of interest between periods t and t+k.Equation (9a) reflects the selection effect before the intra-industry switch has taken place, whereas equation (9b) captures the productivity difference after the switches have occurred.
Next, the contribution of inter-industry switching is similarly measured as the following differences in the sub-sample averages The rationale is directly analogous to that of equations ( 9a) and (9b).The difference between the subsets S(t) and E(t) concerns those firms observed in division D in period t, which will exit industry D by switching to another industry division by period t+k.Similarly, the difference between the subsets S(t+k) and E(t+k) reflects those firms that entered division D by switching from another division between periods t and t+k.
Finally, the contributions of market entry and exit are measured by the sub-sample averages The difference between the subsets A(t) and S(t) concerns those firms observed in division D in period t, which will close down completely by period t+k.Similarly, the difference between the subsets A(t+k) and S(t+k) reflects new startups that entered division D between periods t and t+k.
The following proposition demonstrates that the components introduced above add up exactly to productivity at the industry level.
Proposition 1: Productivity of industry D in periods t and t+k is obtained as the sum of the following components: The static decomposition has an additive structure that reflects the nested structure of the subsets and the fact that any industry is composed of its firms.This additive structure is also present in the Olley-Pakes equation ( 5).However, it is important to note that equation ( 5) is not suitable for log productivity measures, as the use of logarithms would violate the aggregation rules (2) and ( 3).
The static decomposition of the base period productivity takes into account firms that have exited the industry D, whether through inter-industry switching to another division or market exit by period t+k.In contrast, the static decomposition of the target period productivity captures firms that have entered the industry D through inter-industry switchers and new startups.The key difference between intra-industry switching and inter-industry switching is that the intra-industry switchers remain within industry D throughout the study period.While the productivity levels of the interindustry switchers can be computed in both periods t and t+k, we do not attribute their productivity to industry D when they operate in another division according to the industry classification.
Productivity cannot be computed for firms that are inactive, such as exiting firms and new entrants.
The static decompositions of the productivity levels in the base period and the target period can be directly extended to the intertemporal decomposition of productivity change as follows: Proposition 2: Productivity change of industry D from period t to period t+k can be decomposed as: (contribution of reallocation).
The intertemporal decomposition (13) begins by analyzing the productivity change of firms that continue to operate within the same industry class.The incremental contributions of structural changes are measures using the differences in the growth rates of the subsets of firms.This intertemporal decomposition (13) relies on the nested structure of subsets, which allows for an additive formulation of the incremental contributions, similar to the static decompositions (12a) and (12b).This structure allows for a clear and logical representation of the different sources of productivity change over time.
We see decomposition (13) as a logical way to extend the static Olley-Pakes decomposition of the productivity levels to the intertemporal setting of productivity change over time.Several previous studies cited in the Introduction have tried to bridge this gap, but as Kuosmanen and Kuosmanen (2021) note, most of the previous formulations use log productivity measures, which violates the aggregation rules (2) and (3). 9 9 One could argue that the minimum requirement for any meaningful decomposition of aggregate productivity is that the components add up to the industry productivity, but unfortunately most previous attempts fail this condition.Our aim is Related to the previous point, Bruhn et al. (2021) criticize the typical practice of using logtransformed productivity measures in productivity decompositions.They argue that the use of logs may lead to inaccurate aggregate growth rates as well.In this respect, we stress that our decomposition (13) does not depend on the use of logarithms, and therefore, we do not need to exclude observations with zero or negative values.This is practically important particularly during times of major crisis in the industry, as firms may experience a decline in demand for their products or services, leading to a decrease in revenue and an increase in costs.This can cause firms to incur losses, and as a result, their value added may be temporarily negative.Note that such negative values are included when the value added of the industry is computed, so it would be inconsistent to exclude negative values at the firm level.
The key advancement of the decompositions presented in (12a), ( 12b) and ( 13) compared to the work of Kuosmanen and Kuosmanen (2021) is the distinction between intra-industry switching and inter-industry switching, utilizing the nested structure of industry classification systems such as NACE.Furthermore, we provide more rigorous definitions and formally demonstrate the validity of both static and dynamic decompositions.The proposed decompositions are useful, but not the only possible methods for analyzing structural change components.Other types of firm subsets, such as domestic versus foreign-owned firms or urban versus rural firms, may also benefit from using a similar nested structure.The current study focuses on a single study period [t, t+k], but it may be beneficial to examine multiple overlapping periods, such as using a rolling window.These extensions are left as promising avenues for future research.
The intertemporal decomposition (13) has a limitation in that it does not distinguish between the contributions of market entry and market exit.The component ∆ essentially captures the net effect of both entry and exit, but it is challenging to separate the two as entrants are not observed in period t and exiting firms are not observed in period t+k.Previous decompositions by Baily et al.
(1992), Griliches andRegev (1995), andFoster et al. (2001) have attempted to specify counterfactuals to distinguish between entry and exit.While it may be possible to further decompose ∆ by using a counterfactual benchmark, it may be more practical to report the net effect on productivity change in the intertemporal decomposition.Note that one can always complement the intertemporal decomposition with additional information from the static decompositions (12a) and (12b), which do allow for the separate analysis of the contributions from market entry (  + ) and market exit not to criticize flaws of the specific previous work here, but rather stress the importance of consistent aggregation in a constructive manner.

𝐸𝐸𝐸𝐸𝐸𝐸( 𝑡𝑡).
Additionally, one can examine the data to determine if a large wave of market entry or market exit has occurred, and take this into account in the interpretation of the net contribution ∆.

Data and variables
The till the first quarter of 2015.These recessions mainly occurred within the second subperiod of our study, but also spanned the beginning of our third subperiod.
Labor productivity at the firm level is calculated using value added, employment (measured in full-time equivalent units), firm identity, and reporting year.Value added is deflated by the GDP price deflator, and only firms with at least one full-time employee are included.In contrast to the commonly used log-based decompositions, our calculations do not impose any restrictions on value added, allowing for positive or negative values.

Intra-industry and inter-industry switching
To understand the frequency of intra-industry and inter-industry switching, we next examine the relative sizes (percentage share of a cohort) of the following five subgroups of firms: 1) Firms that remain in the same five-digit industry class throughout the time period, 2) Firms that switch sub-industry within the same two-digit industry (intra-industry switching), 3) Firms that switch to a different two-digit industry division (inter-industry switching), 4) Firms that close down (exiting firms), 5) New entrants during the time period (entering firms).
Table 1 reports the relative shares of these subgroups calculated for each six-year period, with the shares reported for the first and last year of the period.The shares of inter-and intra-industry switching firms are presented separately.The shares of the entering and exiting firms were relatively large in all considered periods.In ICT services (J62), over half of the observations in 2006 and roughly half in 2012 were new firms established in the previous five years.In contrast, the exit group was larger than the entry group in all periods for ICT manufacturing (C26), while it was the opposite in ICT services (J62).This highlights the broader shift in the Finnish ICT sector from manufacturing to services, as reflected in the number of firms shown in the bottom rows of Table 1.
Table 1.Relative shares of continuing, inter-and intra-industry switching, entering and exiting firms (% of the yearly cohort).The shares of firms that switched industries varied across the three periods.The most frequent periods of switching were the first second subperiods.For instance, almost 10 percent of ICT manufacturing firms in 2007 had switched to another two-digit NACE division by 2012.Although industry switches are less frequent than entry or exit, their impact on productivity can be significant since firms that switch industries tend to be larger than new startups, as illustrated below in Table 2.
Notably, the number of inter-industry switches typically surpassed intra-industry switches in both industries across all periods.Table 2 provides additional information on the number of employees and the age of firms in each subgroup.The median values are presented for each subgroup of firms in the ICT manufacturing and ICT service industries.The median values show that the inter-industry switching firms were generally larger and older than those that remain in the same industry.For example, in 2018, the median firm age of inter-industry switching firms was 20 years for ICT manufacturing firms and 15 years for ICT service firms.These observations further support our argument that the industry switchers should not be pooled together with startups and discontinuing firms.
The last two columns of entering and exiting firms include empty cells to highlight the fact that the entering firms are not observed in the first year of the subperiod, whereas the exiting firms are no longer observed in the last year of the subperiod.Note further that the Statistics Finland does not allow us to report median values or averages of subgroups with less than 5 observations.Since the subgroup of intra-industry switchers in period 3 was smaller than this threshold, we use NA in Table 2 to indicate that these statistics could be computed but are not available.

Productivity levels by subgroup
We proceed to compare the levels of labor productivity among the five subgroups introduced in the preceding subsection.Table 3 presents the average levels of labor productivity, expressed as 1000 euros per worker (in constant prices of 2010), in the first and last years of the three subperiods.The aim of this table is to demonstrate the variations in productivity levels among these subgroups.Recall from Section 3 that the average productivity figures are not directly comparable across the three subperiods due to major revisions of the Financial Statement Data Panel by Statistics Finland in 2006 and 2013, but also the composition of subgroups changes from one period to another due to industry switching, entry and exit.
Consider first the ICT manufacturing industry (NACE division C26).During the initial period 2000-2006, the subgroup of intra-industry switchers within the ICT manufacturing had the highest labor productivity.After the consolidation during the second subperiod, the average labor productivity of continuing firms surpassed that of industry switchers during the last subperiod.
During the crisis period 2007-2012, the ICT manufacturing attracted inter-industry switchers from other NACE divisions, who had a higher productivity compared to continuing firms in the same industry.However, during the first and the third subperiod, the inter-industry switchers joining from other industry divisions to the ICT manufacturing had notably lower labor productivity than the firms that left the ICT manufacturing and moved to another NACE division.Analogously, the average labor productivity of the genuinely new startups was lower than that of exiting firms in both the first and third periods.Worse yet, the average productivity of entering firms was negative in the latter two periods, supporting our argument that new startups are very different from industry switchers.Note that the conventional productivity decompositions that employ logarithms would have to exclude a large number of startups with negative value added during their first years of operation, which might cause sample selection bias and portray a too rosy picture of the contribution of startups.Next, consider the ICT service industry (NACE division J62) presented in the bottom part of Table 3.Like the ICT manufacturing, the intra-industry switchers had the highest average productivity in all years, excluding 2007.The inter-industry switchers had lower productivity compared to continuing firms in the first period and the last year of the second period, while they had similar productivity in the last period.Entering firms had higher productivity than exiting firms only in the first period, declining thereafter.In the last period, continuing firms had lower average labor productivity compared to both intra-industry and inter-industry switchers.

Labor productivity decomposition in levels
While the average labor productivity levels presented in Table 3 exhibit distinct patterns for each subgroup over the study period, to assess the impact of structural changes on the productivity of ICT manufacturing and service industries, we next apply the systematic productivity decomposition developed in Section 3, which also takes into account the Olley-Pakes reallocation effect.Table 4 presents the results of the decomposition of labor productivity levels in the first and last years of the three subperiods, with Panel A displaying the results for ICT manufacturing and Panel B for ICT service industries.
The first five rows of Panel A and B of Table 4 present the components of the labor productivity decomposition in the same order as on the right-hand side of equation ( 12).The starting point is the average labor productivity of firms that remain in the same industry.The values in the first row of Table 4 match those in Table 3.However, the average labor productivity of this subgroup differs from the ICT manufacturing and service industries' labor productivity, represented by the lefthand side of equation ( 12).To account for this difference, the structural effects are shown on rows 2 to 5 of Table 4.The ICT manufacturing industry experienced a positive impact on labor productivity from intraindustry switching, particularly in the first and second periods, where 3-4 percent of firms switched within the industry.Inter-industry switching had a mixed impact, being negative in 2006 and 2018 when the shares of switching firms were 11 and 6 percent, respectively.The effect of entry and exit was positive only in 2007 and 2012 (during the financial crisis) and negative in the other four years.
The positive values of the Olley-Pakes covariance term indicate a positive correlation between labor input and productivity, which suggests that resource allocation seems relatively efficient in these industries.Despite positive impacts from industry switching and resource allocation, the overall labor productivity of the ICT manufacturing industry declined over time.
For the ICT service industry, intra-industry switching had mainly positive impacts, except in 2007.Inter-industry switching had a negative effect in the first two subperiods but turned positive in the last subperiod.Entry and exit had a consistently negative impact, appearing to worsen over time.
The Olley-Pakes component had a positive impact thought the study period, indicating efficient resource allocation.Unlike the ICT manufacturing industry, the labor productivity of continuing firms closely resembles the ICT service industry's labor productivity, which had a slight increase followed by a decline over time.

Intertemporal decomposition of labor productivity
In this section we apply the intertemporal productivity decomposition developed in Section 3 to examine the average yearly change of labor productivity in the three subperiods.Table 5 summarizes the results of the two ICT industries for the three time periods considered.
The ICT manufacturing industry (NACE class C26) is analyzed in the upper part of Table 5.
The first row indicates the average labor productivity growth in the subgroup of continuing firms that remain in the same five-digit industry class.The table indicates that continuing firms experienced a yearly average growth of over 3 percent in the first period, declined during the crisis, and returned to positive growth in the final period.These average productivity figures can be considered as the baseline productivity change in the absence of structural changes.
The impact of intra-industry switching on productivity growth in the ICT manufacturing industry was positive in the first and third periods, but negative in the second.Meanwhile, interindustry switching had a positive effect on productivity growth during the crisis, but a negative impact before and after it.Inter-industry switching caused a negative contribution of nearly one percentage point in the first period and 1.4 percentage points in the third period.Recall from Table 3 that the average productivity level of firms that switched from the ICT manufacturing to other industry divisions was higher than that of firms that joined the ICT manufacturing from other industry divisions.
The net impact of entry and exit was negative in the first and third periods but positive in the second period, with a particularly strong negative impact during the last period.Recall from Table 3 that exiting firms had higher average productivity compared to entering firms in the first and third periods.However, the largest factor causing industry-level productivity decline was the negative Olley-Pakes reallocation effect in the first two periods, with a further decline during the crisis.This negative effect suggests that Nokia's crisis had a greater impact on larger firms compared to smaller was positive in the first and third periods, but became negative during the crisis years of the second period.
The bottom row of the lower panel of Table 5 shows the annual average of the aggregate productivity change of the ICT service industry.The strong positive productivity growth in the first period declined during the second period's crisis years and did not recover in the third period.In summary, the results of Table 5 demonstrate that industry switching can significantly affect aggregate productivity, especially during crisis periods.

What if industry switching is ignored?
We noted above that previously structural change decompositions often grouped firms that switch industries with startups and bankrupt firms.To clarify the interpretation of structural change components, Table 6 presents the productivity decompositions for the same ICT industries as in Table 5, but now disregards industry switching.As a result, the intra-industry switcher subgroup is combined with continuing firms in the same industry, while the inter-industry switcher subgroup is merged with the entering and exiting firms.One noticeable difference between Tables 5 and 6 is the change in average productivity of continuing ICT services firms (J62) from positive to negative during the third period.Table 5 shows almost 0.2 percent yearly productivity growth for continuing firms in the same industry class, while Table 6 suggests a decline due to the negative impact of intra-industry switching.Pooling the intraindustry switchers with continuing firms in the same industry class can result in a false representation of productivity growth.Intra-industry switching should be viewed as a component of structural change rather than being attributed to the continuing firms in the same industry division.
While inter-industry switching implies exit from one industry division and entry to another, the inter-industry switchers are established firms that continue to operate.The decomposition of the Finnish ICT industries reveals that the contribution of inter-industry switching can have a different sign than the genuine entry and exit, which thereby offsets the influence of structural change.Our study demonstrates that it is possible to differentiate inter-industry switchers from genuine entrants and exits, as well as intra-industry switchers from continuing firms within the same industry.This distinction provides a clearer understanding of the effect of structural change on productivity growth.

Conclusions
This study presents an improved decomposition method to analyze the impact of structural change on productivity growth.The proposed method extends the work of Kuosmanen and Kuosmanen (2021) by introducing a distinction between inter-industry and intra-industry switching.This distinction is important because conventional productivity decompositions tend to misclassify industry switching as either entry or exit, depending on whether the industry of interest gains or loses the switching firm.By differentiating between these two types of switching, the proposed method provides a more nuanced understanding of the dynamics of productivity growth by capturing the contributions of firms that are entering and exiting the market, as well as those that are switching between industries.
We applied the proposed decomposition method to firm-level register data spanning the period of 2000 to 2018 in the Finnish ICT manufacturing and ICT service industries.The results indicate that structural change had a significant effect on the productivity growth of these industries over the first two decades of the 21st century.The analysis revealed contrasting impacts of intra-industry and inter-industry switching on productivity growth during different time periods.Moreover, the study found that labor allocation among firms improved during the period of 2013-2019, while the contribution of firm entry and exit remained negative.These findings offer valuable insights into the complex relationship between structural change and productivity growth and showcase the usefulness of the decomposition technique in capturing the contributions of firms entering and exiting the market, as well as those switching between industries.
This study opens up several interesting avenues for future research.Firstly, the decomposition based on nested subsets of firms could be applied to other types of subgroups of firms or units, for example, the ownership structure (e.g., nested subsets of public, private, domestic and foreign owned firms).Secondly, the decomposition can be adapted from labor productivity to other relevant productivity measures, such as TFP, green TFP, or carbon productivity.Thirdly, the aggregation of firm-level productivity to the industry level can be further extended to cover multiple levels of aggregation from industry classes to industry divisions and further to the entire economy.Multiple level decomposition could also include regional productivity accounts aggregated to the national economy, to examine the reallocation of resources between regions.Finally, the empirical study could be extended to other industries and countries to gain a deeper understanding of the relationship between structural change and productivity growth.
)  + = C (+) + ( + ) + ( + ) + (  + ) + ( + ) (12b) Note that the final component ALL on the right-hand side of equation (12a) and (12b) represents the Olley-Pakes covariance term, which represents the allocation of resources across firms.The sum of the first four components on the right-hand side is equivalent to the unweighted sample average of all firms, similar to the Olley-Pakes equation (5).By introducing the additional components, our aim is to differentiate the incremental contributions of intra-industry switching, inter-industry switching, and market entry and exit on productivity.
analysis of the study uses the Financial Statement Data Panel of Statistics Finland covering 2000-2018.The data is collected from corporate financial statements and provides detailed information on the financial accounts and balance sheets.The panel contains yearly financial statement information of essentially all firms in the Finnish business sector.The firms are classified into industries using the Finnish industry classification TOL 2008, which aligns with European NACE classification for the first four digits. 10Our analysis focuses on two ICT industries: Manufacture of computer, electronic and optical products (C26) and Computer programming, consultancy and related activities (J62).The ICT sector underwent major structural changes due to the Great Recession and European debt crisis of 2007-2008.To understand these changes, we analyze productivity over three time periods: 1) 2000-2006 (the growth period), 2) 2007-2012 (the Great Recession), 3) 2013-2018 (the follow-up recession and slow recovery).The choice of these time periods is justified by three reasons.First, considering longer periods than yearly changes allows us to better capture the productivity impacts of structural changes, such as entry/exit and industry switching (cf., e.g.,Holm, 2014).Second, major revisions to the Financial Statement Data Panel by Statistics Finland in 2006 and 2013 may impact data comparison across the three subperiods.Third, the second subperiod encompasses the Great Recession (2007-2009), which began with the subprime mortgage crisis in the USA and led to the European Debt Crisis.Further, Finland experienced two recessions according to quarterly real GDP data: the first one from the first quarter of 2008 till the second quarter of 2009, and the second one from the second quarter of 2012

Table 2 .
Median firm size (employees in full-time equivalent) and age (years) of continuing, interand intra-industry switching, entering and exiting firms.

Table 3 .
Average levels of labor productivity (1000 € per worker, in 2010 prices) for different groups of firms.Note: The averages of less than 5 observations cannot be reported, and are hence indicated by NA in the table.

Table 4 .
Structural change decomposition of the levels of labor productivity in the Finnish ICT industries.Labor productivity is measured as value added (euros, prices of 2010) per labor input (full-time equivalent).The figures with less than 5 observations are not reported in the table.

Table 6 .
Alternative structural change decomposition that ignores industry switching.