The Role of FDI in Structural Change: Evidence from Mexico

Foreign direct investment (FDI) flows to Mexico are substantial and play an important role in the Mexican economy since the mid&#8208;1990s. These investments reflect the activities of multinational firms that shape to some extent the economic landscape and sectoral structure in this host country. We illustrate that there is considerable variation in the amounts of FDI and structural change within the country and across time. Based on this, the paper's main purpose is to analyse whether there is a significant impact of FDI on structural change. We conduct an empirical analysis covering the period 2006&#8211;16. We use the fixed&#8208;effects estimator where the unit of observation is a Mexican state for which we calculate structural change from the reallocation of labour between sectors. The results suggest that (if any) there is a positive effect from FDI on growth&#8208;enhancing structural change. This effect depends critically on the lag structure of FDI. Moreover, there is some evidence that the positive effect (a) arises from FDI flows in the industry sector and (b) is present for medium and low&#8208;skilled labour reallocation.


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MÜHLEN aNd ESCOBaR structural change. One attempt of investigating the determinants of structural transformation in a crosscountry setting can be found in McMillan et al. (2014). We explore the driving factors in more detail; in particular, we investigate the role of FDI. Third, the paper at hand contributes to the understanding of the consequences of FDI in a host country. There is a large associated literature that examines the effects of FDI. Yet, the particular focus is different to the one of our work. For example, one strand is interested in the effects of FDI on economic growth. Borensztein, De Gregorio, and Lee (1998) find that FDI may drive economic growth. However, this effect depends on the absorptive capacity of the host country to adopt advanced technologies to benefit from these investments. Another main strand focuses on FDI spillovers (e.g., Fons-Rosen, Kalemli-Ozcan, Sorensen, Villegas-Sanchez, & Volosovych, 2017;Görg & Strobl, 2005;Javorcik, 2004), frequently addressing the effects of the presence of MNEs on domestic firm's productivity levels in FDI host countries. Our work complements the literature as we address the consequences of FDI for the sectoral composition of a particular host country.
Our empirical results suggest that (if any) there is a positive effect from FDI on (productivity) growth-enhancing structural change. This effect depends critically on the lag structure of FDI. Moreover, there is evidence that the positive effect arises from FDI flows in the industry sector and is present for medium and low-skilled labour reallocation.
The rest of this paper is structured as follows. In Section 2, we use descriptive figures to present a detailed portrait of FDI inflows and sectoral patterns in Mexico. This is followed by Section 3 where we investigate the relationship between FDI and structural change at the state level. In Section 4, we extend the analysis and investigate whether and how FDI affects employment changes at the sectoral level. In both Sections 3 and 4, we discuss the methodology first and then present the related results of the regression analysis. Finally, we provide concluding statements in Section 5.

| FDI AND SECTORAL PATTERNS IN MEXICO
First, we show long-run paths of structural change indicators for the Mexican economy as a whole using data from the GGDC 10-Sector Database . Based on these observations, we are able to extract some relevant insights about the development process of the economy. In this context, we apply the common distinction between the broad sectors such as agriculture, industry and services as it provides an appropriate overview. Moreover, we present inward FDI numbers for Mexico using data from the UNCTAD (2018) and place our research question in the long-run context. Second, we change to a subnational perspective and illustrate sectoral patterns as well as FDI inflows related to the Mexican states. This view highlights substantial differences within Mexico. We make use of data from the Instituto Nacional de Estadítica y Geografía (INEGI, 2019). 3 These data are available at different sectoral aggregation levels and offer valuable information. In this regard, we explicitly use data at the two-digit sectoral level in our following empirical investigation since we expect this to be relevant in the context of FDI and structural change. Finally, the descriptive figures serve as a motivation for the regression analysis in the subsequent sections.

| Economy-wide indicators in the long run
In Figure 1, there are undeniable signs for long-run structural change. Most notably, the agricultural employment share decreases significantly over time. Starting in 1950 with almost 60%, the share of agricultural employment relative to total employment goes down to about 14% in 2012. 4 Contrary to this observation, the share of services increases constantly over time and is dominant since the 1970s. The subsector "wholesale and retail trade, hotels and restaurants" makes up the largest fraction in services and grows from 10% to 22% (not reported in the figure). Interestingly, the share of industry sectors (including manufacturing) first increases until 1980, but then remains relatively constant over time ranging between 25% and 30%. Concluding, we note that Mexico appears to be a relatively service-oriented economy in terms of sectoral employment shares since the 1980s.
Overall, the long-run picture mirrors to some extent the rationale of dual economy approaches (e.g., Lewis, 1954;Temple & Wößmann, 2006) where labour moves from a "traditional" sector (agriculture) to "modern" sectors (such as manufacturing or services). In these approaches, the traditional sector is typically characterised by low productivity levels relative to the modern sectors. Especially, in early stages of a country's development process these productivity gaps between sectors can be observed in the data. Given that in this setting labour moves out of the traditional sector towards modern sectors, it is likely to be employed more effectively on average. Such a reallocation of economic activity reflects positive structural change.
However, this story only holds as long as productivity levels remain lower in agriculture than in nonagricultural sectors. Moreover, the marginal effect of positive structural change is supposed to diminish over time. With ongoing labour reallocation towards modern sectors, the labour productivity in agriculture should increase, and other things equal, productivity gaps should tend to decrease in the long run.
Such productivity gaps between sectors are also observable for Mexico. Although employment in agriculture between 1950 and 1970 is considerably high, value added in absolute terms is very low. Moreover, in the full time period 1950-2012 the share of agricultural value added ranges between 5% and 10% only. Figure 2 illustrates labour productivity levels (in terms of value added per employee) for the three broad sectors over time. Obviously, there are large productivity gaps between the "traditional" sector and the two "modern" sectors. Other things equal, a labour reallocation from agriculture towards industry and/or services should lead to positive structural change and contribute to aggregate 4 Data points after 2012 were not available at the time of data extraction. F I G U R E 1 Long-run structural change in terms of sectoral employment. productivity growth in the economy. 5 In the end, the figure indicates a slight tendency for convergence of sectoral productivity levels since the 1980s. Next, we briefly characterise Mexico as a destination country for FDI. Ratios of net FDI inflows relative to GDP are depicted in Figure 3 for the period 1970-2015. 6 FDI became increasingly important over time for Mexico indicated by the solid line. We can observe three periods with different levels of the FDI-GDP ratio. The first period is 1970-79 when the ratio was always lower than 1%. Then, there is a little jump to ratios of around 1% in the years 1980-93. This is followed by a further jump to FDI-GDP ratios of on average 2.75% in the years 1994-2015. 7 As a reference, we take into account the world ratio (dashed line). Overall, the numbers for Mexico are somewhat comparable to those of the world, although there are deviations in some years. We note that FDI inflows play a significant role in the Mexican economy recently.
Finally, we can draw an important conclusion from this subsection and put our analysis in a longrun perspective. Considering the role of the "traditional" sector agriculture over time, the Mexican economy has already experienced a typical first step of structural transformation between 1950 and the mid-1980s. As illustrated in Figure 1, the employment share of agriculture has substantially decreased indicating that economic activity has been shifted towards other "modern" sectors. 8 Since our following analysis is dedicated to recent years starting in the early 2000s, the overall context of our investigation is a relatively service-oriented economy. It is a fact that activities in the "modern" sectors (industry and services) are much more diversified than in agriculture. Thus, we investigate the role of FDI in a setting where potential structural change should be characterised by a reallocation of 5 Indeed, structural change appeared to be positive in the past and contributed to aggregate productivity growth in Mexico. Timmer et al. (2014 ) show this for the period 1975-90 andMcMillan et al. (2014 ) 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Agriculture Industry Services Sectoral value added (in pesos) per employee, 1950-2012 economic activity between the three broad sectors and between subsectors-especially subsectors of industry or services. Since the latter phenomenon appears to be relevant in Mexico, we employ relatively disaggregated data to compute structural change.

| Within-country perspective: State-level figures
Mexico is officially divided into 32 federative entities, 31 states and the capital-Mexico City. Since the level of autonomy is similar for all federative entities, we consider 32 Mexican "states" in the following. Each state is free and sovereign, and has its own congress and constitution (SCJN, 2010). During the 1990s, Mexico's authorities have been working on major structural reforms. First, Mexico undertook important trade liberalisation efforts, which transformed the country from a relatively closed economy to one of the most open in the world. The most important structural reforms included a government-wide deregulation programme, a new competition law, the elimination of price controls and the negotiation of free trade agreements (Gurría, 2000). In 1993, Mexico was the first developing country to sign a free trade agreement with developed countries concluding the North American Free Trade Agreement (NAFTA) with Canada and the United States (Escobar Gamboa, 2013). In addition, the authorities eliminated important restrictions on capital inflows, such as limitations on commercial borrowing from abroad, foreign investment in Mexican securities and foreign participation in domestic money markets (Gurría, 2000). In sum, during that time the country reduced the role of the government as part of the new economic model to promote GDP growth and economic development.
Second, Mexico's authorities implemented a far-reaching fiscal reform to embrace fiscal discipline. Finally, in 1994, the Central Bank of Mexico (Banxico) became independent, and at the end of that year, the exchange rate regime passes from exchange rate bands with managed slippage to free float (Carstens & Werner, 2000).
During the legislative periods between 2000 and 2012, the authorities failed to pass any economic structural reform. However, the process of structural reforms accelerated significantly since 2012 with the Pact for Mexico (OECD, 2015). Indeed, an important set of structural reforms including energy, fiscal, financial, telecommunications, competition, education and labour reforms were approved by the Mexican Congress between 2012 and 2014. Hence, in this paper we focus F I G U R E 3 The relevance of foreign direct investment inflows in the Mexican economy. Mexico World FDI net inflows in % of GDP, 1970GDP, -2015 | 563 MÜHLEN aNd ESCOBaR on a period of legislative stagnation in terms of structural reforms. This is important to note, since most of the reforms in Mexico are also oriented to improve Mexico's FDI attractiveness (Escobar Gamboa, 2013).

| FDI inflows
Foreign direct investment data by state are available on an annual basis. We consider data from 1999 to 2015 and present descriptive numbers in Table 1. 9 In columns (1) and (2), it can be seen that there is a large variation among Mexican states. The average annual inflows between 1999 and 2015 range from roughly 1.3 billion pesos in Chiapas to more than 63 billion pesos in Mexico City. It is quite plausible that the country's capital is the number one FDI destination, since it is the economic centre with many affiliates of foreign MNEs. Total FDI inflows in the capital amount to 1.2 trillion pesos over the full time period (column (2)) which makes up 22% of total inflows to Mexico. Columns (3) and (4) shed some light on two sub-periods and prove that FDI plays a role in all states throughout the considered time horizon. Each column shows the sum of annual inflows of the respective sub-period. In the end, the large differences between the states are of particular interest with respect to the following analysis explaining the variation of structural change within Mexican states. The last three columns refer to the sectoral structure and highlight the differences between agriculture (AGR), industry (IND) and services (SER). Obviously, FDI in agriculture is negligible in all states. Hence, the other two sectors are dominant in terms of FDI activities. The picture is very heterogeneous. In Durango, Hidalgo and Yucatán, there is an almost balanced distribution between industry and services, while in many other states FDI inflows in one sector are dominant (e.g., Aguascalientes or Zacatecas). Across Mexico, FDI in the industry sector is prevalent with 65.8% on average.

| Sectoral employment
As shown in the long-run portray in Section 2.1, Mexico has turned into a relatively service-oriented economy in terms of employment since the 1980s. This is confirmed by the state-level perspective ( Figure 4). The employment share in services (given for the years 2006 and 2016) is dominant in all states, except for Chihuahua (CHI) in 2016. Yet, there is variation across the Mexican states in the sectoral composition. Extreme examples are Mexico City (CMX) and Chiapas (CHS). Mexico City is dominated by the service sector (around 80%) and almost no employment in agriculture, while in Chiapas roughly 45% of the workforce is employed outside the services sector: about 25% in agriculture and about 20% in industry sectors.
A further interesting insight is that the "US border states"-Baja California (BCN), Chihuahua (CHI), Coahuila (COA), Nuevo León (NLN), Sonora (SON) and Tamaulipas (TAM)-have relatively high shares in industry due to high activity in manufacturing (not explicitly shown in this figure) which goes partly back to the "maquiladora" sector.
However, more important for the following analysis of structural transformation are changes in the employment shares which indicate whether economic activity is shifted towards or away from a sector. We get a broad impression by a simple comparison of the years 2006 and 2016-starting and ending year of our period of investigation-for each state (in Figure 4). For the majority of Mexican states, we observe an increase in the service share which is again in line with economy-wide trend. However, our aim is to also take into account the changes in subsectors. Thus, we employ more disaggregated

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MÜHLEN aNd ESCOBaR sectoral data in our following analysis. We consider the North American Industry Classification System (NAICS) and use annual data at the two-digit sector level for all Mexican states. Employing the NAICS two-digit level, we are able to differentiate between 20 sectors. In Figure 5, we show annual (sectoral) employment share changes for selected states and the average of all states. The numbers correspond to the mean of the period 2006-16 in each sector given in percentage points. The values related to the average across all states appear moderate in the graphic. Yet, there are some notable characteristics in manufacturing (sectors 31-33). It seems that employment is shifted away from sectors 31 (food, beverages, tobacco, textiles) and 32 (wood, paper, chemicals, non-metallic products), while sector 33 (metallic and electronic products, machinery, furniture) is on average increasing by 0.1 percentage points per year. We find the largest annual change in sector 33 for Coahuila with 0.8. This implies that within the 10-year period, this sector increases by 8 percentage points which is substantial. A further extreme change is visible for Tabasco. Sector 11 (agriculture) is largely shrinking, while other sectors in this state are increasing, such as construction   (81). The numbers for Mexico City indicate that economic activity is reallocated from industry sectors towards services and public administration (93). Finally, we note that the picture of sectoral employment changes is heterogeneous among the states, which points towards differences in structural change within Mexico.

| Structural change
We calculate structural change from the reallocation of labour between sectors for an economic unit s at time t using Equation (1). In this regard, we follow McMillan & Rodrik, 2011. The indicator is taken from a framework where economy-wide productivity change is decomposed into a within component and a structural change component. 10 Hence, we interpret the indicator in Equation (1) as growth-enhancing structural change: In our case, s refers to a Mexican state. y j,s,t represents the sectoral labour productivity level in sector j in state s in period t. It is measured by (gross) value added per employee. Θ j,s,t is the respective sectoral employment share. The difference between the employment share of t and t−1 indicates a change over time, and thus, it points to a labour reallocation. A positive change signals a shift of economic activity towards the respective sector, while a negative sign indicates a shift in the opposite direction. There are n sectors in the observed economic unit s. The number of n depends on the sectoral aggregation level. As mentioned before, we employ annual data at the NAICS two-digit level for all Mexican states. This level of (dis)aggregation is relatively detailed and ensures a solid calculation of structural change. We argue that this procedure is appropriate for our purpose since it is rather a labour reallocation between subsectors that is relevant in the given context than a labour reallocation between the broad sectors such as agriculture, industry and services.
In Table 2, the values in columns (1), (3) and (5) indicate the average annual structural change for the respective period in Mexican pesos per employee. As a reference, the values in columns (2), (4) and (6) refer to the corresponding growth rates (in %) of each time period; that is, ST s,t of Equation (1) is divided by the state labour productivity of the respective base year t−1. Hence, the growth rates indicate how much structural change contributes to state-level productivity growth. Overall, we observe negative structural change. This is insofar not surprising since Mexico experienced negative productivity growth in the period 2006-16. However, the result indicates that labour reallocation was on average inefficient, that is economic activity moved from more productive sectors to less productive sectors. Considering the state average in the last row, structural change reduces the productivity change by 7,787 pesos (per employee) per year which corresponds to a negative growth rate of 1.94%. The decrease is larger in the sub-period 2006-11 (column (3): 13,331) than in the more recent sub-period 2012-16 (column (5): 2,243).
A comparison of the states reveals considerable differences in the (negative) growth rates. While the reduction in some states such as Nayarit and Sinaloa is only marginal, there is a large negative value for other states such as Chiapas or Hidalgo. A final observation which we have to keep in mind for the 10 Although this framework is typically used for decompositions at the country level within the recent development literature (e.g. McMillan et al., 2014;Timmer et al., 2015), earlier applications are related to micro-level settings (e.g. Haltiwanger, 1997). For formal details on the decomposition framework, see Appendix E. (1) Electronic copy available at: https://ssrn.com/abstract=3621023  (1), (3) and (5) are given as Mexican pesos per employee (MXN/emp) and calculated using Equation (1). As a reference, the values in columns (2), (4) and (6)  following analysis is the result for Campeche. The structural change figures (in pesos per employee) for this state-especially for single years, not reported in the table-document clear outliers. These values are due to large labour productivity levels in the mining sector in Campeche. We consider this fact in the following by providing robustness checks with subsample regressions excluding this state.

STRUCTURAL CHANGE
Our main objective is to investigate the relationship between FDI and structural transformation in Mexico. In particular, we are interested in the issue whether FDI has an impact on structural change.
To analyse this, we run a regression analysis where the unit of observation is a Mexican state.

| Methodology
In terms of the econometric framework, we apply Equation (2): where ST s,t represents structural transformation in (a Mexican) state s and period t. It is calculated based on the indicator introduced in Equation (1) and given in Mexican pesos per employee. It can be interpreted as a measure for effective structural transformation as it contributes to overall productivity growth via labour reallocation across sectors. In Equation (2), the explanatory variable of interest is fdi s,t−k . It captures the presence of MNEs' aggregated activity measured by FDI inflows relative to GDP in a state s at time t−k. We use different lag structures of this indicator since we expect that for a number of FDI projects, it takes some time until the direct investments actually lead to structural change in terms of a labour reallocation. As an example, think of "greenfield" investments. It usually takes a considerable amount of time until labour is employed since potential places of work such as production facilities have to be built first. Moreover, supplementary investments in existing FDI projects that are associated with the provision of additional job opportunities may also attract labour to move. Again, it is plausible that there is a time gap between the point of time when the investment is done and the point of time when workers are actually employed. Especially, if labour moves across sectors such time gaps are likely as barriers and adjustment costs of a job change should be higher on average (compared with changes within a sector). Indeed, the literature illustrates that the time component plays a role for the effects of FDI on employment. There may occur transitory negative effects in the short run and positive effects in the long run (Jude & Silaghi, 2016). In particular for the long-run perspective, many studies suggest positive effects as, for example, unprofitable and least productive firms exit which allows for an efficient labour allocation (Helpman, Melitz, & Yeaple, 2004). Moreover, Hijzen et al. (2013) show that foreign presence leads to job creation.
Given that our dependent variable is calculated from changes between t and t−1, the FDI indicator is tested in lagged values starting with year t−1 up to t−4. Alternatively to aggregated FDI inflows, we also take into account indicators related to FDI in specific sectors. This is explained in detail in Section 3.2.
In principle, FDI stocks rather than FDI flows should be applied as a proxy for the activity of MNEs (Wacker, 2016). However, in the given context, there is a crucial argument to consider the latter. Since the dependent variable (structural transformation) describes a change over time, it is reasonable to assume that its variation is driven by changes in the activity of MNEs (which is more associated with FDI flows) rather than by the level (which is more associated with the FDI stock).
(2) ST s,t = + fdi s,t−k + � X s,t−1 + � Z s,t + s + t + s,t , | 569 MÜHLEN aNd ESCOBaR X s,t−1 in Equation (2) refers to a vector of (time-variant and state-specific) control variables included as lagged values. We consider an indicator that addresses the development level of a state measured by GDP per capita. Additionally, we include the agricultural employment share which represents the status of structural change. States with a high share are supposed to be relatively backwards in terms of structural transformation since a relatively high fraction of labour is bound in the "traditional" sector (McMillan et al., 2014). Z s,t in Equation (2) refers to a vector of (time-variant and state-specific) control variables supposed to affect the dependent variable during its process in period t. We include net national migration (immigrants minus emigrants per 100,000 inhabitants from/to other Mexican states) in order to control for the potential movement of labour between Mexican states. Similarly, we control for international movement of workers by including net international migration (immigrants minus emigrants per 100,000 inhabitants from/to other countries). Moreover, we employ a variable addressing labour market frictions (measured by the number of labour market conflicts) which should account for resulting rigidities in labour reallocation. 11 Finally, we control for period-specific effects t and state fixed effects s . α is the constant, and st is the error term.
In terms of the estimation method, we employ the fixed-effects estimator. Thus, we exploit the panel structure of the data and the within variation in particular. We are able to consider ten (annual) periods of structural change starting with 2006-07 and ending with 2015-16. This time horizon appears to be relatively short when looking at the related literature investigating (long run) structural transformation across countries (e.g., de Vries, McMillan et al., 2014;Timmer et al., 2015). Yet, our perspective is quite different compared with many other studies. One the one hand, considerable FDI inflows are a relatively young phenomenon in Mexico, and thus, potential effects are limited to the recent past. On the other hand, the labour reallocation in response to multinational activity is supposed to occur within a few years. Furthermore, we calculate structural change on the basis of quite disaggregated sectoral data. Hence, we take into account not only a shift of economic activity between agriculture, industry and services (or between nine sectors as, for example, in McMillan et al., 2014) but also within these sectors. Such reallocations between subsectors are expected to play a role in the given context since FDI (or multinational activity, respectively) in a subsector in a Mexican state may be of great economic importance. Taking these aspects into account, the time dimension is appropriate from our point of view. The results of the regression analysis are presented in the following section.

| Baseline estimations
In Table 3, we report our baseline results based on Equation (2). First, we solely include the control variables in column (1). The coefficient of GDP per capita (gdppc) is positive and significant at the 1% level suggesting that higher developed states are more likely to experience positive structural change. All other control variables seem to play no role in explaining structural change as the related estimates turn out to be insignificant.
In the subsequent specifications, we additionally include the variable of interest (aggregated FDI inflows relative to GDP in a Mexican state) with different lag structures. As argued before, we expect that on average FDI activities affect ST with a considerable time lag. In column (2), we use four lags of our FDI indicator. L1 refers to the lag in period t−1, L2 refers to the lag in period t−2 and so on.

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The estimates of the control variables do not change qualitatively. We find negative (insignificant) coefficients for the 1 and 2-year lags. Yet, the estimate of L2 is lower in size. An insignificant estimate is also found for the 3-year lag, but it is positive. Finally, the 4-year lag of FDI turns out to be positive and statistically significant at the 5% level. We take this result as a first evidence that there are effects from FDI on structural change. Moreover, we note that the impact is positive and occurs with a considerable time lag. The latter fact reduces also the probability that this finding is subjected to potential reverse causality issues. Furthermore, to check whether the main finding is biased by potential  (2). Finally, we treat the estimates of column (2) as our baseline result which serves as a point of reference for the following estimations. With respect to our variable of interest, this result suggests that (on average) an increase in the FDI to GDP ratio by 0.1 percentage points would be associated with an increase in the structural change indicator (or productivity change, respectively) by 243.4 Mexican Pesos per employee (i.e., around US$13). Next, we consider further lags of the FDI indicator as the time gap of potential effects may be even larger. This exercise involves some limitations since the number of periods decreases while using higher lags. This is due to a limitation in our state-level indicator of FDI relative GDP which we could not calculate for years before 2003. We simultaneously include lags up to 6 years in column (4). In this case, the full sample decreases by two periods which is associated with a reduction of 64 observations. All estimates for FDI are insignificant under these conditions. L4 and L6 are large in size and positive, while L5 appears to be negative. Since it is likely that there is some correlation bias when including a set of lagged FDI indicators (as shown before), we only include L4, L5 and L6 in a separate regression. It turns out that the 4-year lag is again significant at the 5% level. Although the 5-year lag is negative but insignificant, the 6-year lag is positive and almost significant at the 10% level. Overall, the findings in column (5) show that there are some notable changes compared with the baseline result. However, considering that the number of periods is reduced, they are not contradictory to our main finding. Instead, the estimates are some supportive evidence that FDI has a positive effect on growth-enhancing structural change.
Finally, we investigate whether there are different effects from FDI in particular sectors. It is likely that the effect of aggregated FDI is driven by investments of MNEs that are active in industry or services sectors. To test this hypothesis, we employ alternative indicators of our FDI variable. We include individual indicators for FDI inflows in agriculture (fdi_agr), industry (fdi_ind) and services (fdi_ser), respectively. All three measures are included with their 4-year lag structure. The corresponding coefficients are presented in column (6). The estimate for FDI in agriculture is negative, but insignificant. This is not surprising as we observe hardly any investments in the primary sector documented in Section 2. In contrast, FDI in industry is highly significant (at the 5% level) and positive. Moreover, the size of the estimate is comparable with the coefficients of aggregated FDI in columns (2) and (3). FDI in services seems to play no role although the coefficient is also positive. As shown in a further regression where we solely include the controls and the variable of FDI in industry sectors, the estimate is even significant at the 1% level. We conclude that the positive effect from aggregated FDI on structural change is largely driven by investments in industry sectors.

| FDI, structural change and skill levels
So far, we have considered structural transformation based on the changes in sectoral employment shares-without distinguishing specific types of labour. In the next step, we address this issue and take into account different skill levels of the factor labour. This is relevant in the context of FDI and structural change because standard offshoring examples involve the differentiation of skill groups. That is, MNEs from advanced economies shift particular production steps intensive in relatively low-skilled labour to developing countries (where the costs of low-skilled labour are relatively low). This kind of offshoring behaviour is associated with vertical FDI and can be observed in Mexico, in particular, for the US-Mexico relationship. Findings of Baldwin and Lopez-Gonzalez (2015) suggest that large amounts of FDI flows from the United States to Mexico are associated with the following case: MNEs based in the US offshore production of intermediates or the assembly of goods to Mexican locations and import the (intermediate) output back to the United States for further processing or final selling. 12 Mexico is labelled as "factory economy" in this relationship, providing relatively low-skilled labour for specific production steps. Given that a large amount of Mexican inward FDI comes from the United States, it is worth to consider differences in structural transformation based on employment changes in specific skill groups.
The INEGI data contain information on sectoral employment classified into high-, medium-and low-skilled labour. Thus, we are able to decompose our ST indicator according to these three skill categories and calculate SThskill s,t , STmskill s,t and STlskill s,t . Each indicator is used alternatively as the dependent variable in our econometric model given by Equation (2). The individual calculation of each indicator is similar to Equation (1). For each sector, we multiply the change in the sectoral employment share of the respective skill group with the average sectoral productivity. Afterwards, we take the sum over all sectors. We present the estimation results in Table 4.
First, we include each of the different ST measures as the dependent variable of our baseline specification which includes up to four lags of aggregated FDI. The related results are shown in columns (1)-(3). A comparison of these estimation results reveals striking differences. The outcome suggests that there is no significant effect from FDI on structural change in terms of high-skilled labour reallocation (SThskill), whereas the measures of structural transformation based on medium and low-skilled labour reallocation (SThmkill and STlskill) are positively associated with the 4-year lag of FDI. Hence, the significant effects come again with a considerable time lag. Compared to the baseline estimation result from Table 3 column (2), we note that in column (1) the role of our control variables does not change, while in columns (2) and (3) there are differences. On the one hand, gdppc appears to be negative but only significant for low-skilled structural change. On the other hand, the indicators of migration seem to play a role in explaining the variation of structural change. Net international migration has a positive impact in both regressions, while net national migration has a negative estimate (yet, it is only significant for low-skilled structural change).
Second, we replicate the three estimations but alternatively include the sectoral (4-year lagged) FDI indicators. The results are presented in columns (4)-(6). The previous findings from Table 3 can also be observed here, that is the significant positive effect from aggregated FDI (in columns (2) and (3)) is based on investments in industry sectors as the significant estimates for fdi_ind in columns (5) and (6) suggest. These findings are linked to the discussion on typical offshoring activities described in the beginning of this section. MNEs (that are particularly active in industry sectors) fragment their production process and shift medium or low-skilled intensive production steps to Mexico. That is, they conduct FDI and build up (or buy existing) factories where they employ medium or low-skilled workers. Our results suggest that such activities of MNEs seem to change the economic structure within the locations (states) where they are active and contribute to growth-enhancing structural change in terms of a labour reallocation across sectors.

| Robustness checks
As illustrated in Table 2, Campeche is characterised by extreme values in the structural change indicator compared with all other Mexican states due to large labour productivity levels in the mining sector.

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In addition, as shown in Table 1, FDI inflows to Mexico City make up a large share in total Mexican inflows. Thus, many FDI projects are concentrated in the country's capital. To minimise concerns on potential outlier biases in our estimates, we replicate our baseline estimations from Section 3.2.1 but exclude Campeche and Mexico City from the sample, separately and jointly. 13 Overall, the results are in line with our previous findings from Table 3 and confirm the main outcome. In particular, there is a positive coefficient for the 4-year lag FDI indicator which is also similar in size in most specifications. Although the estimate is slightly below the 10% significance level in the baseline specification, 13 The results are not presented in a regression table but are available upon request. it is highly significant when we redo the regressions based on the specifications shown in columns (3)-(5) of Table 3 with the reduced samples. Moreover, there is again evidence that the effect from aggregated FDI is based on investments in industry sectors. We also test whether FDI from individual source countries (or source country groups) has a significant effect on structural change. The data allow for identifying bilateral FDI, and we separately add an indicator for the most important FDI partners to the baseline specification (instead of the aggregated indicator). As individual countries, we include the United States, Spain, the Netherlands and Japan. With respect to country groups, we consider aggregate FDI of NAFTA partners and OECD countries, respectively. The estimated coefficients are all statistically insignificant suggesting that it is rather aggregate FDI (from various source countries) that plays a role in explaining the variation in structural change.

T A B L E 4
So far, all regressions are based on annual data. This approach may involve potential biases in the results as some variables-such as FDI inflows-may show extreme values in specific years. As a consequence, single observations may drive the overall results. We address this problem by using averaged data in the following estimations. We present results based on 2-year averages in Table 5.
The results in columns (1) and (2) are qualitatively similar to those of our baseline estimations as the coefficients of all control variables and those of the FDI indicators are comparable. In this case, L1 refers to period t−1 which is an average of the 2 years directly before the structural transformation process, while L2 refers to period t−2 which is an average of the years 3 and 4 prior to structural change. Regarding the estimates related to FDI, the one for L1 is negative and insignificant, while the one for L2 is significant and positive. This confirms our main finding. Moreover, there is evidence that the effect from aggregated FDI is driven by foreign investments in industry sectors (column (2)). Regarding the decomposition of structural change with respect to skill levels in columns (3)-(8), we have also supportive evidence for the previous results. Namely, the positive effect from FDI is associated with the reallocation of medium-and low-skilled labour.

| FDI AND SECTORAL EMPLOYMENT CHANGES
We extend our empirical analysis and run sector-state-level regressions. The aim of this exercise is to validate that the positive effect of FDI found in the previous section is associated with a labour reallocation at the sector level as expected. Given that the structural change indicator in Equation (1) is calculated from two sectoral measures, namely (a) labour productivity and (b) employment share changes, we test whether FDI is positively correlated with measure (b).

| Methodology: sector-state-level analysis
Considering Equation (1), any positive contribution to state-level structural change is based on an increase in the sectoral employment share. Thus, as a first step, our strategy is to analyse whether sectoral FDI is associated with a positive change in the employment share. In a second step, we take into account that an overall contribution to growth-enhancing structural change (aggregated over all sectors) rests upon a labour reallocation towards sectors with a relatively high productivity. In this context, we investigate whether sectoral FDI is linked to employment share increases in relative productive sectors. The econometric approach is given as a probit model in the following Equation (3): (3) PR Δ j,s,t > 0 = fdi j,s,t−k + u j,s,t . Notes: *** , ** and * indicate significance at the 1%, 5% and 10% levels, respectively. t-statistics obtained from robust standard errors are displayed in parentheses. All regressions include period-specific dummies not reported. L1 refers to periods t−1, L2 to t−2. All regressions include the full set of 32 states.
We model the dependent variable as a binary indicator which is 1 if the sectoral employment share change (Δ j,s,t ) from t−1 to t is positive and 0 if it is negative. fdi j,s,t−k is the explanatory variable of interest. It captures the sectoral presence of MNEs' activity measured by FDI inflows in a sector j (relative to GDP) in state s at time t−k.

| Empirical results: sector-state-level regressions
We present the first set of probit regressions in Table 6. Starting with columns (1)-(4), we show results related to a pooled probit model. We include the full sample covering all sectors in column (1). It turns out that it is exclusively the 4-year lag of the FDI indicator which is statistically significant (at the 5% level). This indicates that a higher activity of MNEs in a sector is associated with a higher probability that the employment share of this sector is growing.
Next, we split the sample up into the three main sectors and present the results for agriculture in column (2), for industry sectors in column (3) and for services sectors in column (4). Comparing these results, there are only two significant coefficients. On the one hand, it is the 4-year lag FDI indicator estimated for the subsample of industry sectors. This finding is supportive evidence for a previous finding from the state-level analysis. That is, the positive link between FDI and positive employment share changes is evident for industry sectors. On the other hand, the 1-year lag FDI indicator estimated for the subsample of services sectors is also positively significant. This points towards potential immediate effects from FDI in these sectors occurring without a considerable time gap. We replicate all four regressions using the population-averaged probit model and obtain similar results in columns (5)-(8). Finally, we note that the test statistics (in terms of the Wald test p-values) of our regressions for the population-averaged probit model are slightly better for all four samples than those related to the pooled probit model. Hence, we use the former approach in the subsequent steps.
Next, we further investigate whether sectoral FDI is linked to employment share changes in relative productive sectors. In this respect, we differentiate between those sectors that have a labour productivity above the median (in a state in a year) indicated with "High" and those sectors with a productivity below the median labelled with "Low". The related results are shown in Table 7.
In column (1), we consider high-productive sectors within the full sample of 10 years and 608 sector-state pairs. The estimates for the 1 and 2-year lag of FDI are insignificant, while there is negative coefficient for the 3-year lag which is significant at the 10% level. This single finding would suggest that FDI is associated with an employment share decrease in relative productive sectors. Yet, at the same time, we find a positive and significant estimate for the 4-year lag of FDI which is two times larger in size and almost significant at the 5% level. Overall, this indicates that sectoral FDI is positively linked to an increase in the employment share of high-productive sectors.
Considering that we obtain a positive significant estimate for the 4-year lag of FDI in column (1), the same indicator appears to be insignificant for low-productive sectors in column (2). We find a similar result for industry sectors in columns (5) and (6). The positive estimate for the 4-year lag of FDI in high-productive sectors is even significant at a higher level. Taken together, these findings are striking support for our results (and the related interpretation) in the previous section referring to the state-level analysis. It appears to be evident that multinational activity is associated with positive employment share changes in relative productive sectors, and thus, it contributes on average to growth-enhancing structural change within Mexican states. This effect is especially evident for industry sectors implying that multinational activity in industry leads to labour reallocation towards sectors with a higher average labour productivity. Again, this effect is strongly dependent on the lag structure. Thus, effective labour reallocation comes with a time gap in response to FDI.

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In addition to these main findings, we have some evidence for a positive link between multinational activity and the probability of an employment share increase in relatively productive services sectors. However, this estimate is related to the 1-year lag and indicates towards immediate effects. For the sake of completeness, estimation results referring to the agricultural sector are also shown in columns (3) and (4). However, these results have to be treated with caution. First, our type of disaggregation does not account for subsectors within agriculture. Thus, we do not account for potential labour reallocation within agriculture. Second, FDI in this sector is very low or almost absent in many Mexican states as shown in Table 1. Thus, we do not expect significant effects here. Third, the test statistics for both regressions point to uncertain results which may be also a consequence of the first argument that causes a low number of observations.
In a final step, we conduct probit regressions with respect to the different skill levels of labour. That is, we use different dependent variables accounting for sectoral employment share changes in the respective skill group. This procedure extends the analysis of Section 3.2.2, and the results are shown in Table 8. Again, we take into account whether the employment share change occurs in a sector with a relatively high labour productivity level (above the median) or in a low-productive sector. Overall, most of the coefficients are insignificant. Considering high-skilled labour in columns (1) and (2), we find significant negative estimates for the 3-year lag of FDI in the sample of high-productive sectors and for the 1-year lag of FDI in the sample of low-productive sectors. The former estimate suggests that FDI is associated with a decrease in the employment share of high-skilled workers in relative productive sectors, while the latter points to the similar effect in less productive sectors. Taken together, there is no clear finding for the impact of multinational activity on efficient labour reallocation for this skill group. The results for the group of medium-skilled labour in columns (3) and (4)  Notes: *** , ** and * indicate significance at the 1%, 5% and 10% levels, respectively. z-values are displayed in parentheses. The dep. var. is always a binary indicator that is 1 if the sectoral employment share change from t−1 to t for respective skill level is positive and 0 if it is negative. L1 refers to periods t−1, L2 to t−2 and so on.
with a decrease in the employment share of this skill group in less-productive sectors. Thus, due to multinational activity low-skilled labour is reallocated to other sectors that may have a higher productivity (but not necessarily). Finally, considering the results in Table 8, we do not find a clear support at the sector level for our findings from Section 3.2.2 where we have evidence for significant effects from multinational activity contributing to state-level structural change going back the reallocation of medium and low-skilled labour. At the same time, the two sets of findings are not contradicting.

| CONCLUDING REMARK S
We observe considerable FDI inflows in Mexico in the last two decades. Yet, the distribution of these flows is considerably disparate across Mexican states and economic activities. Moreover, there is variation within the states across time and sectors. At the same time, we observe notable structural change in the economy. On average, structural change was (productivity) growth-reducing in the considered time period. However, there is also variation within Mexican states. Taking into account these two phenomena, we analyse whether the activities of MNEs measured by FDI inflows have an impact on effective structural transformation running fixed-effects regressions at the state level.
The results suggest that (if any) there is a positive effect from FDI on growth-enhancing structural change. However, this effect depends critically on the lag structure of FDI and stems from direct investments in industry sectors such as manufacturing. Since the positive (significant) finding is mainly related to the 4-year lag indicator, increases in the effective labour reallocation due to multinational activity occur with a considerable time lag. This is not surprising considering that some FDI projects, in particular greenfield projects, need some time before becoming operational. An example for this is the case of Toyota in Mexico, which announced in 2015 an FDI project of US$1.5 billion for a manufacturing plant in Guanajuato. This factory is supposed to have 2,000 employees but was scheduled to open until 2019.
The results from the sector-state-level analysis verify that the mechanism through which FDI positively affects structural change is indeed a labour reallocation towards more productive sectors. In addition, there is some evidence that it is precisely the reallocation of medium and low-skilled labour that is driven by FDI (in industry sectors).
Finally, FDI inflows appear to play a role in the structural transformation process of the Mexican economy. Regarding that structural change was on average growth-reducing during the considered time period, the positive estimate for FDI indicates that MNEs' activities attenuated this negative process. As a consequence, policymakers aiming at strategies to reverse structural change into a growth-enhancing process in Mexico should encourage FDI-promoting policies, especially in industry sectors. In addition, Mexican authorities could promote policies to ease labour mobility to potentially accelerate the effects of FDI on structural transformation.
Future research may address some of the limitations of our paper. First, we conduct an analysis covering a relatively short period of time. Given that data are available, one could analyse this issue in a long-run context. For Mexico, it would be interesting to also cover the years before and directly after the implementation of NAFTA since FDI inflows increased substantially in response to this event. Second, FDI may not fully measure all aspects of multinational activity. In this regard, one may consider direct measures such as aggregated sales or employees of MNEs in a sector. Another limit is that our findings are restricted to the case of Mexico and as such cannot be generalised to all developing countries. In this regard, a cross-country analysis may lead to richer insights into the role of FDI in structural change. However, one important obstacle to overcome here is the heterogeneity across countries concerning data coverage of FDI, as well as methods of data collection on FDI, labour and | 581 MÜHLEN aNd ESCOBaR productivity at the sectoral level. Alternatively, future research may analyse the case of other countries using data at the subnational level to account for within-country differences. For the calculation of ST, we use gross value added and employment data at the sector state level. The data preparation of these data is described as follows.
Gross value added at the sector state level is taken from the National Accounts of Mexico. These data were retrieved from INEGI's Banco de Información Económica (http://www.inegi.org.mx/siste mas/bie/) INEGI reports from the National Accounts of Mexico the number of workers per economic activity aggregated at the country level. The number of workers corresponds to the number of paid employees. Owners and family workers are not considered by INEGI. The advantage of these data is that it allows for a decomposition into three skill level groups according to educational levels: (a) low-skilled (upon to basic education, primary school); (b) medium-skilled (from secondary to high school); and (c) high-skilled (with a degree higher than high school). These data were retrieved from INEGI's Total Factor Productivity database (https ://www.inegi.org.mx/temas/ ptf/).
To estimate the distribution of the labour units of each sector across Mexican States, we use individual-level data from INEGI's National Survey on Employment (ENOE; https ://www.inegi.org.mx/ progr amas/enoe/15yma s/defau lt.html). More precisely, for each year, each 2-digit sector, and each skill level, we estimate the share of workers for each State. Finally, we combine these shares with the number of workers from National Accounts of Mexico to obtain the number of workers per sector-state pair.

DECOMPOSITION OF PRODUCTIVIT Y CHANGE
The general framework of economy-wide productivity change applied by McMillan and Rodrik (2011) reads as follows: where Y t and y j,t refer to economy-wide and sectoral labour productivity levels in period t, respectively; Θ j,t is the employment share of sector j in period t; Δ denotes changes in productivity or employment shares between the initial periods t−k and t. There are n sectors in the economy. The first term on the right-hand side refers to a within-sector component of productivity change, weighted by the employment share of each sector at the beginning of the time period. The second term refers to productivity change due to the structural transformation component which is calculated as the change in sectoral employment shares weighted by the respective sectors productivity level at the end of the time period. (A1)