Natural Resources, Technology Improvements, and Growth

Perez-Sebastian, Fidel; Raveh, Ohad; van der Ploeg, Frederick Article — Published Version Natural Resources, Technology Improvements, and Growth Environmental and Resource Economics Provided in Cooperation with: Springer Nature Suggested Citation: Perez-Sebastian, Fidel; Raveh, Ohad; van der Ploeg, Frederick (2025) : Natural Resources, Technology Improvements, and Growth, Environmental and Resource Economics, ISSN 1573-1502, Springer Netherlands, Dordrecht, Vol. 88, Iss. 8, pp. 2157-2199, https://doi.org/10.1007/s10640-025-01004-x This Version is available at: https://hdl.handle.net/10419/323702 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Accepted: 7 May 2025 / Published online: 24 June 2025 © The Author(s) 2025 Fidel Perez-Sebastian, Ohad Raveh, and Frederick van der Ploeg contributed equally to this work. Extended author information available on the last page of the article Natural Resources, Technology Improvements, and Growth FidelPerez-Sebastian1· OhadRaveh2· Frederickvan der Ploeg3,4,5,6 Environmental and Resource Economics (2025) 88:2157–2199 https://doi.org/10.1007/s10640-025-01004-x Abstract We study, analytically and empirically, how technological changes affect the nexus between resource abundance and economic growth. Our two-sector model indicates that capital-augmenting technological improvements can be contemporaneously contractionary in resource-rich economies, and expansionary elsewhere, due to differences in the size of the elasticity of substitution between labor and capital. In addition, such improvements yield relatively steeper expansionary patterns in resource-rich economies in the longer run. We test these predictions using a panel of U.S. states and counties. Our identification strategy rests on geographically-entrenched differences in resource endowments, and the adoption of plausibly exogenous technology shocks at the national level. Our core estimates corroborate our predictions. First, we document persistent differences in the elasticity of substitution between capital and labor across the natural-resource dimension. Second, we find that an increase in TFP is on impact contractionary in resource-rich states, but is non-contractionary (at worst) in resource-poor ones. Third, we illustrate that in the longer term a positive technology shock expands output and inputs in resource-rich economies relatively more strongly. Our results shed light on hitherto overlooked potential adverse effects of natural resource abundance. Keywords Natural resource abundance · Technology shocks · Input elasticities JEL classifications Q32 · E32 · O33 1 3 F. Perez-Sebastian et al. 1 Introduction Understanding the nexus between natural resources and economic growth has been of perennial interest to economists and policy makers, especially in discussions of the resource curse. The literature so far has highlighted a host of potential transmission channels.1 Little attention, however, has been given to the potential role of technological changes.2 The latter represents a pivotal phenomenon with long-lasting implications for the economy. Nonetheless, the empirical literature still debates the size of the contemporaneous impacts.3 This study examines how resource abundance interacts with technological changes to affect growth. We hypothesize, and demonstrate using U.S. data, that technology improvements induce a contemporaneously divergent outcome on growth in output and labor, across the natural resources dimension. Our results shed light on previously overlooked potential adverse effects of natural resource abundance, and offer one possible reconciliation for the ongoing debate over the opposing contemporaneous effects of TFP shocks on the economy. The notion that the oil and gas sectors tend to be relatively intensive in capital and lowskilled labor has been documented in previous studies (e.g., Michaels et al. 2014). The well-documented capital-skill complementarity hypothesis (e.g., Krusell et al. 2000) then suggests that the elasticity of substitution between capital and labor (hereafter, the ESKL) should be relatively higher in resource-rich sectors. This prediction has been substantiated in a number of cross-sectional studies. 4 Moreover, Raveh (2020) illustrates that these features may translate to the macroeconomic level in economies with a dominant oil and gas sector, noting that resource-abundant economies are consistently more capital-intensive over a period of three decades. We hypothesize that this may similarly extend to the size of the ESKL, positing that it is persistently relatively higher in extractive industries. Importantly, the relative size of the ESKL can be central to understanding the contemporaneous impact of technological changes on economic activity.5 The intuition is simple: a positive technology shock increases the productivity of capital, but it also reduces the need for labor through factor substitution. To examine this analytically, we construct a twosector (extractive and non-extractive) model of economic growth with capital adjustment costs, and economy-wide laborand capital-augmenting technological change. The analytical results indicate that while labor-augmenting technological improvements are similarly expansionary in both sectors, the shortand long-term patterns may differ for capital-augmenting improvements. Specifically, a capital-augmenting technology shock increases the productivity of capital while substituting labor, thus giving rise to involuntary unemployment in the short-run due to capital adjustment costs. These costs result in a gradual conver1 See, e.g., Allcott and Keniston (2018), Arezki et al. (2017), Armand et al. (2020), Brollo et al. (2013), Gylfason et al. (1999), James and Rivera (2022), Tornell and Lane (1999), Torvik (2002), and the references therein. Van der Ploeg (2011) and Venables (2016) provide syntheses of the literature. 2 The literature unveils the potential endogeneity of TFP shocks and innovation to resource abundance (e.g., Kuralbayeva and Stefanski 2013). However, it overlooks the potential role of resource abundance in transmitting the effects of technological changes on the economy. 3 While standard frictionless real business cycle models predict short-term expansionary effects, other canonical macro workhorse models predict the opposite (e.g., Chang and Hong 2006). This inconclusive evidence, along with the other related literature, is reviewed in more detail in the following section. 4 See, e.g., Caballero et al. (1995), Young (2013). 5 The notion that the ESKL parameter is central for understanding the impacts of technological changes dates back to Hicks (1932) and Satō (1975). For a more recent analysis, see Cantore et al. (2014). 1 3 2158 Natural Resources, Technology Improvements, and Growth gence back to full employment. Hence, in the short-term the impact is contractionary if the ESKL is sufficiently high; yet, in the long-term the magnitude of the expansion depends on the initial capital-intensity, thus pointing at the potential divergent outcome across resourcerich and -poor economies. The model also serves to derive sector elasticities and capitaland labor-augmenting technology shocks over time using U.S. industry-level data. Our estimates reveal that extractive industries indeed exhibit consistently higher ESKL than non-extractive sectors, averaging around 0.79 compared to 0.55 for other sectors. The latter underpins our subsequent analysis, in which we empirically examine our main analytical predictions, using an extensive panel of U.S. states and counties, covering the period 1963–2015. Employing plausibly exogenous measures of national technology shocks—the purified U.S. TFP series of Basu et al. (2006) (henceforth, BFK)—and geologically determined cross-sectional state resource abundance from James (2015), we exploit geographic and temporal variation to identify the differential effects of technology improvements across resource intensities. Our empirical strategy hinges on interacting state-level resource endowments with national technology shocks, facilitating causal identification through geographic and temporal exogeneity.6 Our empirical analysis provides robust support for our analytical predictions. We find that positive national TFP shocks, most notably capital-augmenting ones, have a contemporaneously contractionary effect on output and employment in resource-rich states, driven by labor market impacts, whereas it is expansionary or at worst neutral in resource-poor states. Quantitatively, our baseline estimates suggest that a standard deviation increase in TFP decreases the average output of resource-rich states by approximately 0.1% relative to resource-poor states in the short term. Nonetheless, our estimates also show that two to five years ahead, positive TFP shocks lead to relatively stronger expansions of output and inputs in resource-rich states, aligning with our model’s predictions. Finally, we show that these patterns are robust to a battery of robustness tests that consider different treatments, sample restrictions, specifications, and controls. Section 2 reviews related literature and places our contributions within it. Section 3 explains analytically how resource abundance interact with technology shocks to affect growth. Section 4 presents the data, empirical findings, and robustness tests. Section 5 concludes. 2 Related Literature Our contributions relate to three strands of literature. First, natural resource abundance can be a blessing as well as a curse.7 A central aspect is the potential negative impact of resource abundance on productivity and innovation. Among the various channels proposed, natural resource wealth may depress factor productivity (e.g., Gylfason et al. 1999; Krugman 1987; Sachs and Warner 2001; Torvik 2001; Van Wijnbergen 1984), lower human capital (e.g., Bhattacharyya and Hodler 2010; Gylfason 2001; Stijns 2006), and induce special6 This methodology is reminiscent of that adopted in other studies that have also examined the heterogeneous local effects of aggregate shocks, by testing the impact of their interaction, including Liu and Williams (2019), Perez-Sebastian et al. (2019), and Raveh (2020), among others. 7 See the surveys in Van der Ploeg (2011) and Venables (2016) for effects at the national level, and Van der Ploeg and Poelhekke (2016) for effects at the local level. 1 3 2159 F. Perez-Sebastian et al. ization that crowds out innovation and entrepreneurship (e.g., Kuralbayeva and Stefanski 2013; Michaels 2011; Torvik 2002). In contrast, our analytical and empirical setups consider (national) technology shocks that are exogenous to resource abundance at the level of individual states, and advance a novel hypothesis concerning the interaction of resource abundance and technological shocks and its potential impact on shortand long-term growth. We find that improvements in technology are contractionary on impact primarily in resourcerich areas, and are more expansionary, relative to the remaining areas, in the longer term. Our results shed light on hitherto overlooked negative impacts of natural resource abundance. Second, dating back to the seminal contributions of Kydland and Prescott (1982) and Gali (1999), the question of whether technology improvements are contractionary or expansionary has taken a central role in the macroeconomic literature. While standard frictionless real business cycle (RBC) models predict that technology improvements are expansionary in the short-term, sticky-price models predict the opposite.8 The related empirical literature is also inconclusive. For instance, in their seminal work BFK show that technology improvements are contractionary on impact due to decreases in input use, most notably labor. However, Christiano et al. (2004) demonstrate that their correction of the BFK technology measure yields contemporaneously expansionary effects, focusing on labor. More recently, Cantore et al. (2014) highlight that the factor-augmenting nature of shocks and the ESKL are critical in determining the impact of technology shocks on the labor input in both RBC and sticky-price frameworks. We contribute to this literature by analyzing the role of natural resources in the transmission of these shocks. Specifically, our analysis offers one potential reconciliation for the opposing views based on the underlying persistent differences in the ESKL between extractive and non-extractive industries. We observe that the short-term impacts of technology improvements are contractionary primarily in resource-rich areas, where extractive industries hold a significant share of the economy, but are mostly expansionary elsewhere. We show that these patterns arise using BFK’s measure, time frame, and methodology, and that they are applicable also when implementing corrections like those undertaken in Christiano et al. (2004). Further, consistent with previous studies, we show that in the long-term positive technology shocks are expansionary across all areas, albeit more so in resource-rich regions. Third, there is no shortage of studies that provide estimates for the aggregate ESKL (e.g., Doraszelski and Jaumandreu 2013; Klump et al. 2007; Raval 2019). The evidence summarized in Chirinko (2008) point at estimates well below one. Industry-level estimates point at similar magnitudes, albeit with some heterogeneity across sectors (Balistreri et al. 2003; Caballero et al. 1995; Young 2013). Notably, these studies estimate the substitution elasticity in the extractive industry to be amongst the highest, and even the highest under various specifications, relative to the other industries.9 Since estimates pertain to specific samples, we estimate the time series for the ESKL in the oil sector within our sample’s time frame and compare it to the time series for the aver8 However, non-standard RBC models can also generate a negative correlation between hours worked and technology shocks. See, for example, Francis and Ramey (2005). 9 For example, Young (2013) employs the equation system approach proposed by León-Ledesma et al. (2010) and finds a larger average value of this elasticity across the mining and quarrying activities (0.72) than across the rest of sectors (0.63). Furthermore, he estimates that the largest elasticity among the former activities is for the oil and gas extraction industry (0.87). 1 3 2160 Natural Resources, Technology Improvements, and Growth age elasticities of the rest of the economy. We achieve this by employing U.S. industry data to compute the elasticity parameter directly from our analytical framework, which incorporates CES production functions and non-neutral productivity shocks—both essential for the estimation of elasticities (Antras 2004). We obtain estimates consistent with those reported in previous literature: the estimates are below one, and the ESKL in the extractive industry is significantly and consistently higher than the corresponding elasticity for the average of the remaining economy. 3 Technology Shocks in a Two-Sector Economy Here, we analyze the implications of cross-sector differences in resource intensities (tied to differences in the ESKL) for the shortand long-term impacts of productivity shocks. We begin by presenting the basic elements of the model. Next, the predictions are organized into propositions, with the proofs relegated to Appendix A. The section also derives the testable predictions that the subsequent empirical section will focus on. Finally, we conclude by performing a structural estimation of the sectoral ESKL and the bias of technology shocks, and by discussing the implications for resource-rich and resource-poor economies. 3.1 The Environment Consider an economy with two production sectors: extractive ( e ) and non-extractive ( m ). The non-extractive product is the numeraire. The economy is inhabited by a constant population of N individuals that are endowed with one unit of labor. Each period t , individuals supply their labor unit inelastically in exchange for a salary ( wt ). We suppose that capital and output markets are open to the rest of the world. The labor market is closed and labour is internationally immobile. We have a small open economy. Therefore, if pi represents the price of output in sector i , and R is the gross return to capital (i.e., the interest rate plus the depreciation rate), then pm=1 , while the resource price pe and R are constant and given on world markets. Markets are perfectly competitive and firms maximize profits. In the short-run, firms in sector i , with i∈{e, m} , employ productive capital ( kit ) and labor ( nit ) at time t according to the following Leontief production function yit =Ω it min {zktkit,ω itzntnit}, (1) where yit represents output in sector i at period t , zkt and znt provide productivity levels specific to capital and labor, respectively, Ωit is a productivity parameter specific to sector i , and ωit represents the level of effective capital per unit of effective labor.10 New technologies bring labor-augmenting gains when znt rises, and capital-augmenting technical progress when zkt rises. The new vintages also come with particular values of ωit and Ωit . These values result from the long-run, sector-specific ESKL ( εi ) not being equal to zero. Specifically, in the long-run, the production function takes the CES form 10 We could include the stock of natural resources as an additional input in the production functions associated with the extractive activity. Our qualitative predictions would not be affected by this modification if natural resources enter the production function through a Cobb-Douglas form (see Appendix B). 1 3 2161 F. Perez-Sebastian et al. y it = [ (zktkit)1−1/εi+(zntnit)1−1/εi ] ε i εi−1 . (2) We assume that the values of ωit and Ωit result from imposing the fixed input proportions dictated by the solution to the maximization problem faced by firms under the long-run production function given by Eq. (2).11 Finally, following Caballero (1994) and BFK, our framework features investment adjustment costs. In particular, the capital motion equation is given by kit = (1 −δ)kit−1+xϕ it, (3) where xit denotes investment, δ denotes the depreciation rate, kit−1 is the productive capital inherited from the previous period, and ϕ∈(0,1) .12 3.2 Predictions Our first proposition presents the values of ωit and Ωit that drive short-run output and shows how they depend on capital-augmenting productivity zkt , but are determined by the longrun problem. Proposition 1 The optimal level of effective capital per unit of effective labor is ω it = [( zkt R ) 1−εm−1 ]ε i /(1−ε m ) and increases in zkt and decreases in the user cost of capital. The vintage-specific parameter is Ω it = [ 1+ω(1−εi)/εi it ]ε i /(ε i −1) and decreases in zkt . Both ωit and Ωit are independent of znt Proof. See Appendix A. □ 11 Appendix C analyzes a version of the model that includes skilled labor and accounts for sector-specific productivity shocks. The production function displays capital-, skilled-, and unskilled-biased productivity shocks, along with capital-skill complementarity within a CES-nested-in-CES specification. The main conclusion is that results similar to our main findings hold. More specifically, capital-biased and skilled-biased productivity shocks have positive effects on long-run ouptut, and these effects can be amplified by εe . However, this amplification is less likely when shocks originate from unskilled-biased productivity. Negative short-run effects on output are more likely to result from capital-biased than from skilled-biased productivity and, once again, can be amplified by εi . Importantly, unskilled-biased productivity shocks can never cause short-run output losses. 12 For simplicity, the presence of investment adjustment costs in our model are captured through the parameter ϕ . Therefore, we follow a reduced-form approach. For more general forms of introducing investment adjustment costs in macroeconomic models, see Francis and Ramey (2005) for example. 1 3 2162 Natural Resources, Technology Improvements, and Growth Due to the constant input proportions dictated by ωit , the difference between the short and long run lies in the total amount of labor used in production. In the short run, if the capitallabor ratio increases while capital grows slowly due to adjustment costs, the constant input proportions may imply that total labor demand falls short of total labor supply, thus leading to involuntary unemployment.13 However, in the long run, capital accumulates until the economy reaches full employment. Therefore, given that labor moves towards the most productive sector and labor productivity increases in both production activities, technology shocks are always expansionary in the long run. Furthermore, while the impact of labor augmenting technology is independent of the ESKL, capital-augmenting technology shocks tend to generate stronger labor-productivity growth as the ESKL increases. The following proposition summarizes the effects of technology shocks in the long run. Proposition 2 An increase in capital-augmenting productivity zkt or in labor-augmenting productivity znt leads to an increase in labor productivity in both sectors. Furthermore, in the long run, which is characterized by full employment, an increase in zkt or znt yields larger levels of output. Additionally, the change produced by labor-augmenting productivity znt is independent of the ESKL. If capital-augmenting productivity zkt rises, the induced growth of labor productivity in the extractive activity increases with εe if ( z kt /R )1−ε m> 2 and εm<1 , or if zkt/R is sufficiently close to 1 and either εm>1 or both εe and εm are smaller than 1. Proof See Appendix A. □ A corollary to Proposition 2 is that, under the stated parameter restrictions, if εe>ε m , the growth of labor productivity caused by an increase in zkt will be larger in the extractive sector than in the non-extractive sector. This result suggests that economies in which the extractive activity contributes sufficiently more to total output will tend to grow more in the long run in response to an increase in zkt if εe>ε m . As mentioned previously, in the short run, since capital and labor enter the production function in fixed proportions and capital does not move to the new long-run equilibrium immediately, employment can be below N . Importantly, if the economy does not have full employment, the impact of a capitalaugmenting technology shock can be contemporaneously contractionary. The following proposition summarizes these short-run effects. Proposition 3 A positive labor-augmenting technology shock znt can never cause a fall in output. However, because optimal investment in capital decreases with ϕ , if ϕ is sufficiently low, a positive capital-augmenting technology shock zkt can contemporaneously reduce output. In the non-extractive activity, this occurs if εm>1 , but if εm<1 , ymt always increases with zkt . In the extractive sector, sufficient conditions for yet to fall with zkt are εe=εm>1 , or εm<ε e<1 and zkt/R is sufficiently close to 1. 13 In principle, individuals are willing to work at any wage because the labor supply is inelastic. However, ω it ≡z kt k it zntnit is fixed at its long-run value, as established by Proposition 1, which implies that labor demand equals n it =z kt k it zntωit . Therefore, if ωet or ωmt have increased sufficiently, whereas ket or kmt grow relatively slowly, the sum net +nmt can be lower than N in the short run, where N denotes the full-employment level. 1 3 2163 F. Perez-Sebastian et al. Proof. See Appendix A. □ To better understand Proposition 3, note that adjustment costs introduce diminishing returns to investment. Furthermore, for very low values of ϕ , these diminishing returns can be so strong that capital may experience only negligible increases. Thus, in the short run, if the increase in zk causes a sufficiently large reduction of labor per unit of capital, and ϕ is sufficiently low, the fall in the labor demand due to the larger ωi can dominate the positive effect of a higher zk , resulting in a decrease in output.14 Regarding the short-run effect of a change in zn , recall that it neither affects ωi nor Ωi . So, a higher zn only serves to increase the optimal stock of capital, and as a result, output cannot fall in the short run. 3.3 Testable Hypotheses The analysis indicates that a capital-augmenting increase in productivity boosts output in the long-run but may reduce output in the short-run if the ESKL is larger in the extractive sector than in the non-extractive sector. This finding leads to two testable hypotheses. The first one is that a technology improvement in capital in a sector where it is easier to substitute labor for capital will lead to (1) higher output growth in the long-run, and (2) a smaller increase or even reduction of output in the short-run. The second testable prediction is that (3) a labor-augmenting improvement in productivity boosts output both in the short and in the long run. Our strategy to test these hypotheses consists of two steps. We first estimate the ESKL and find that the ESKL is higher for the extractive than for the non-extractive sectors. Armed with this insight, we then proceed to test these hypotheses employing a sample of economies that differ in their degree of natural resource abundance. 3.4 Sectoral Elasticities of Substitution Between Labor and Capital Our analysis thus points at a primary triggering primitive of the sign of technology-shock effects on the economy, namely cross-sectional differences in the ESKL. As noted earlier, there is already some cross-sectional evidence that supports this hypothesis (e.g., Young 2013).15 We now explore the hypothesis that the ESKL is persistently higher in extractive industries. For this, similar to Caselli and Coleman (Caselli et al. 2006), we first derive expressions from the model that allow recovering the productivity and elasticity parameters zkt , znt , εe , and εm , and then estimate them using cross-industry U.S. data. We start from equation (2) and, for the estimation, allow R , wt and εi to vary across time and sectors, while zkt 14 For example, the conditions stated in Proposition 3 for an increase in ymt and a decrease in yet as a consequence of an increase in zkt are fulfilled for εm=0.6 , εe=0.8 , zkt =0.5 , and R=0.2 . The values of εm and εe are the average estimates obtained in Sect. 3.4. The value of zkt is the maximum estimate obtained in Sect. 3.5. Finally, R=0.2 corresponds to the historical S&P 500 average return of 0.10 ( see, e.g., h t t p s : / / w w w . s t e r n . n y u . e d u / a d a m o d a r / p c / d a t a s e t s / h i s t r e t S P . x l s .) minus a 0.02 average annual inflation rate calculated using data from Bureau of Labor Statistics for the U.S. consumer price index from 1998 to 2015, and an average depreciation rate of 0.12 calculated for the same period from Table 1 in Escribá-Pérez et al. (2023). 15 Although we do not consider cross-sectoral differences in adjustment costs, empirical evidence indicates that adjustment costs in extractive industries are significantly higher than in other industries (e.g., Groth and Khan 2010), thus strengthening the suggested mechanism. 1 3 2164 Natural Resources, Technology Improvements, and Growth ployment rate and thus decreases the change in labor, yet in the periods thereafter they expand it. Columns (2) and (3) report results when the sample is split into resource-rich and -poor states, respectively. The outcome for the contemporaneous impact shows that for the resource-rich sub-sample, technological improvements are contractionary, but for the resource-poor sample such improvements are expansionary. Hence, the natural resources dimension is potentially an important aspect in the interpretation of the key results of BFK.33 In addition, the results in columns (2) and (3) further indicate that in the longer term, labor expands more strongly in the resource-rich sample, despite the initial drop. However, Christiano et al. (2004) addressed concerns related to potential endogeneity of the BFK measure. In addition, they considered the level of (rather than changes in) the labor input measure, and found a contemporaneous positive impact of TFP improvements on labor input. Christiano et al. (2004) thus found that TFP shocks are contemporaneously expansionary. In our state-level setting concerns related to the endogeneity of TFP shocks are mitigated given their national perspective. Hence, to illustrate that correcting for the effect of the natural resources dimension may represent a reconciliation between the findings of BFK and Christiano et al. (2004), we re-estimate our results for columns (2) and (3) when the dependent variable (i.e., the unemployment rate) is in levels rather than in changes. The results appear in columns (4)-(5). They are similar to those reported in columns (2)-(3): technology improvements are contractionary in resource-rich and expansionary in resource-poor states. 33 The potential relevance of the natural resources dimension to the interpretation of BFK’s findings has been implied by Bils (1998), who pointed at the potential over-estimating effect of the oil price instrument used in BFK’s analysis. Nonetheless, as will be noted in our main analysis, we illustrate that the observed patterns extend to various measures, and are not specific to those used in BFK. Table 1 TFP shocks and the unemployment rate for resource-rich and resource-poor states, 1980–1996 (revisiting BFK) 1 3 2171 F. Perez-Sebastian et al. 4.4 Core Results on Impact of TFP Shocks We now turn to our core results on the heterogeneous impacts of TFP shocks and how these depend on resource wealth in a more complete and rigorous setting, and with an expanded sample. We estimate various versions of Eq. (4), for each of the three outcome variables. These core results are presented in Table 2. 4.4.1 Effects on Output Starting with output, measured by the Gross State Product (GSP), Column (1) represents our core specification and provides support for our main hypotheses. The estimated value of θ is negative and statistically significant, which indicates that contemporaneous technology improvements indeed induce a stronger negative impact in resource-rich states than in resource-poor states, substantiating the main analytical prediction. In terms of magnitude, under the mean endowment of natural resources, a one standard deviation increase in TFP contracts average output of resource-rich states by 0.1% relative to output of resource-poor states.34 Under an alternative interpretation, given an average resources level, a technological improvement that amounts to the annual mean level (i.e., the average improvement undertaken each year over time) contracts the output level of resource rich states relative to their resource poor counterparts by 0.007%, being the equivalent of about $800 million difference between the two state groups.35 Notably, the magnitude of this estimate of θ suggests that the outcome is not only in relative terms (noting that some states have no resource endowments). Furthermore, it points at a divergent outcome (cf. Table 1). This is also illustrated by columns (2) and (3) of Table 2. In the latter, we estimate a version of Eq. (4) which excludes ν and θ and examines the direct impact of TFP shocks via δ under the two separate sub-samples. This attempts to examine whether the main outcome is the result of a relative effect (resource-rich relative to resourcepoor states), or a direct one driven by resource intensity. We focus on examining the sign, interpreting the magnitude with caution due to the exclusion of the time fixed effects. Fol34 This is computed by multiplying the estimated value of θ by the mean resource endowment and the standard deviation of TFP, and examining the change that this induces in the mean output measure. 35 Similar to the previous case, this is computed by multiplying the estimated value of θ by the mean resource endowment and the annual mean TFP level, and dividing by the mean output level. The monetary value is computed by considering the 0.007% amount of the average annual state output level. Table 2 Resource endowments and effect of technology improvements, 1963–2015 1 3 2172 Natural Resources, Technology Improvements, and Growth lowing the previously outlined division, the sub-sample in column (2) includes states with a per-capita resource endowment above the 25th percentile while the sub-sample in column (3) includes the remaining states with little or no resource endowments. We observe that contemporaneous TFP shocks have a negative and statistically significant impact on output if there are some natural resource endowments. Conversely, if resource endowments are scarce, the impact becomes statistically imprecise with a magnitude close to zero. These outcomes clarify the source of the observed relative difference. They point at a distinct diverging outcome, similar to the patterns noted previously in our BFK exercise reported in Table 1, and consistent with our analytical predictions. 4.4.2 Effects on Unemployment and Capital Columns (4)-(6) and (7)-(9), present an analysis similar to that presented in columns (1)-(3) yet with the labor or capital input proxies (namely, the unemployment rate or investment, respectively) as outcome . Columns (4) and (7) examine the complete sample whereas columns (5)-(6) and (8)-(9) consider the split samples based on the same division used before. For the case of labor, the estimated value of θ in column (4) points at a similar outcome as observed under output. Specifically, technology improvements contract the labor market more strongly if natural resource endowments are high. Similar patterns are also observed in columns (5)-(6), since the estimated values of δ indicate that the contractionary effect occurs only in the group of states that are endowed with significant natural resources. The outcomes in columns (8)-(9) show that investment contracts similarly in both types of environments following a positive TFP shock. This is further confirmed by the outcome in column (7), which points at no statistically distinguishable impact of TFP shocks on investment across resource intensity levels. These patterns, in conjunction with those observed for the effects on labor, are consistent with our analytical predictions given the previously established systematic differences in elasticities of substitution between labor and capital for resource-rich and -poor states, to the extent that the TFP shocks are capital-augmenting. Next, we examine this analytical prediction. 4.5 Effects of Capitaland Labor-Augmenting TFP Shocks Our analytical predictions indicate that capital-augmenting shocks trigger contemporaneous substitution between capital and labor with a magnitude that depends on the size of the elasticities of substitution between labor and capital, hence contracting the labor input in resource-rich states. Here we examine the differential impact of capitaland labor-augmenting TFP shocks. We do so by employing the znt and zkt parameters computed and outlined previously in Sect. 3.5, corresponding to laborand capital-augmenting shocks, respectively. Given the scope of the underlying U.S. industry data, the computed parameters are available annually for the period 1998–2015. We estimate our baseline specification, as per column (1) of Table 2, where now the znt and zkt measures enter in lieu of tfp , separately. The results are presented in in Table 3. Columns (1)-(3) and (4)-(6) examine the case of zkt and znt , respectively. In each case, the first, second, and third column examine the outcome related to the output, labor, and capital measure, respectively. 1 3 2173 F. Perez-Sebastian et al. These results are consistent with our analytical predictions. The estimated values of θ indicate that the differential impact across resource intensity levels is observed only under capital-augmenting shocks, and most notably with respect to output and labor input. This is consistent with the view that capital-augmenting shocks induce substitution between capital and labor more strongly in states where this substitution is stronger, i.e., resource-rich states, as suggested by our model. 4.6 Robustness Tests We now conduct various robustness tests to see whether our core findings survive if we allow for other sectors than natural resources, different aggregate shocks, or different TFP measures, and when the resource measure is interacted with the world oil price. We also examine the level of U.S. counties, and test for robustness using different sample restrictions, controls, and specifications. Tables 4 and 5 present the robustness results when we allow for other sectors than natural resources, or different aggregate shocks, respectively. The other robustness results are presented in Table 6. All specifications follow the core specification, unless otherwise specified, and they cover different time periods (depending on data availability), as stated in the table. 4.6.1 Results with Other Sectors than Natural Resources Our core analysis has focused on one dimension of the industrial composition of states, i.e., resource abundance. To further motivate this focus, we also examine the role of other major sectors. We thus consider the GSP share of four major aggregate sectors: manufacturing, services, agriculture, and wholesale trade.36 To examine how they might affect the impact of 36 Each, as estimated by Young (2013), with a significantly lower ESKL, compared to that estimated for the oil and gas sector (taking manufacturing as an average of its sub-sectors). Table 3 Effects of capitaland labor-augmenting TFP shocks, 1998–2015 1 3 2174 Natural Resources, Technology Improvements, and Growth TFP shocks, we interact them each with tfp and add them separately, and then concurrently, to the core specification. We will focus on output. The results are presented in Table 4. In columns (1)-(4) we add each of the additional interaction terms separately, in conjunction with our interaction term of interest, resource ∗tfp . The outcome in each case indicates that our core results are robust to these inclusions, i.e., the estimated value of θ maintains its sign and precision. The robustness of θ is further observed in the demanding specification undertaken in column (5), in which all interaction terms are added concurrently. Interestingly, while natural resource intensity retains its role in the effects of technology shocks, none of the other major sectors exhibit similar characteristics. In all cases the estimated coefficients on the additional interaction terms have close to zero magnitudes and no statistical significance,37 thus reaffirming the role of natural resources in understanding the effects of TFP shocks on state-level outcomes. 37 Services and agriculture yield marginally precise patterns, but appear in only one of the specifications. Hence, these effects are not robust. Table 4 Results with other sectors than natural resources, 1963–2015 Table 5 Results with different aggregate shocks 1 3 2175 F. Perez-Sebastian et al. 4.6.2 Results with Different Aggregate Shocks Our main hypothesis pertains to the impact of TFP shocks. For identification purposes, we consider aggregate, national TFP shocks, as they are exogenous to each individual state. Nonetheless, their temporal variation may correlate with other concurrent national shocks with heterogeneous impacts across the natural resource dimension, especially as TFP shocks capture noise in aggregate production by construction. To address this, we consider additional national shocks, focusing on the impact of their interaction with the resource measure, in conjunction with the effect of our main interaction term of interest. We consider four additional shocks at the aggregate, national U.S. level: monetary policy shocks, federal tax shocks, news shocks, and business cycles. For monetary shocks, we consider the data series constructed by Tenreyro and Thwaites (2016); considering federal tax shocks, we employ the narrative-based federal tax changes from Romer and Romer (2010); news shocks are represented by the Investment Specific Technology (IST) news shocks of Ben-Zeev (2018); last, business cycles are examined via an indicator that captures whether the U.S. is in a recession, as defined by the U.S. Federal Reserve.38 We interact each measure with resource, and add each separately to the baseline specification, as per as per Column (1) of Table 2.39 The results are presented in Table 5. Columns 1–4 report the outcomes under each aggregate shock, in the order that appears above, respectively. Thereafter, column 5 presents the results of a specification in which all shocks are concurrently included. The estimated coefficients indicate that, consistent with Perez-Sebastian et al. (2019) and Perez-Sebastian and Raveh (2019), resource-rich states have better absorption of contractionary federal tax changes, and interestingly also of national recessions. In addition, consistent with Raveh (2020), resource-rich stats are impacted more strongly by contractionary monetary 38 Each is available for a different sample period, as outlined in the Data Appendix; hence, sample size differs across cases. 39 Similar to TFP , each (non-interacted) aggregate shock is captured by the year fixed effects, and hence excluded. Table 6 Further robustness tests 1 3 2176 Natural Resources, Technology Improvements, and Growth shocks.40 Importantly, however, θ maintains its sign, significance, and magnitude, in all cases, including in the one in which all interaction terms are considered concurrently, thus further motivating the focus on national technology changes in the analysis. 4.6.3 Results at the U.S. County Level While the availability of some of our data is limited at the more granular county level, examining our hypotheses under the measures that are available at the county level enables us to exploit a significantly larger sample of more than 3,000 counties. To measure crosssectional resource endowments at the county level, we employ the plausibly exogenous resource measure constructed by James and Smith (2017). This provides a geologicallybased indicator for counties with reserves of shale gas. We examine the impact of tfp , zk , and zn on county per-capita output, by interacting each of these with the county resource measure. Results are presented in columns (1)-(3) of Table 6, respectively. They indicate that our core result is robust at the county level, as we observe differential effects on output in the case of tfp and zk , but none for zn . 4.6.4 Results for Three Different Alternative TFP Measures Columns (4)-(6) of Table 6 present estimation results for three different types of TFP measures. Our core estimates were done with the BFK measure, primarily in an attempt to create a more direct comparison to the BFK results. The literature, however, offers various measures of technology shocks, each with their own merits and limitations. To examine the validity of our results, we consider three additional data sources of TFP shocks: the FORD series (Francis et al. 2014), the BS series (Barsky and Sims 2011), and the JPT series (Justiniano et al. 2011). Each of the TFP types is interacted with our resource measure and we use these instead of our baseline measure tfp . For each of these three alternative TFP measures, the estimated value of θ maintains its sign and precision. Our core results are thus robust to using these different types of TFP shocks. 4.6.5 Results with Different Sample Restrictions, Controls, and Specifications Columns (7)-(14) of Table 6 present the results of some additional robustness tests that include different sample restrictions, controls, and specifications. First, motivated by the BFK exercise, we re-estimate our core specification prior to 1997 and after 1996, separately. This serves to test the applicability of the BFK case under the complete specification (not directly examined in the previous related sub-section), and examine whether our core results depend on that period. The estimated values of θ in columns (7)-(8) indicate that our core results are apparent in both periods, and that it intensifies in magnitude in the post1996 period. This is consistent with the notion that technology improvements become more capital-oriented over time. Next, we add various additional basic controls that may affect the impact of technology shocks indirectly, consider a specification with state-by-year fixed effects, and test the baseline specification under a different clustering method. In column (9), we include as controls government tax revenues per capita, government expenditure per capita, government 40 The impact of IST news shocks is not robust, as the effect is unstable across specifications. 1 3 2177 F. Perez-Sebastian et al. debt per capita, state unemployment rate, party affiliation of state governor, state inequality, and state population size. These controls account for various potential confounding factors at the state level, including the size of states (population), efficiency and size of states’ public sector (taxes, expenditures, debt), states’ business cycles (unemployment), political incentives of states’ governors (party affiliation), and states’ income polarization (inequality). In column (10) we consider a quarterly-based sample, in which both outcome and resource ∗tfp are quarterly-based (i.e., in this specification t represents a quarter-by-year cell). Such a specification enables adding state-by-year fixed effects, which control for all state-by-year changes, including the state indicators employed in column (9), as well as additional unobserved ones. The sample period in this case is 2005–2015, υt represents quarter fixed effects, and state-by-year fixed effects are included in lieu of ηi .41 In Column (11) we then re-estimate our core specification with a two-way clustering method, where standard errors are clustered by state and year. The outcomes in all cases indicate that our main result is robust to these sensitivity examinations. In columns (12)-(14) we re-estimate our model with three restricted samples. In column (12) we exclude Montana, North Dakota, and Wyoming. Figure 4 indicates that these states are outliers in terms of their resource richness, hence this exclusion enables us to examine the extent to which our core results are affected by them. In column (13) we exclude states with zero resource endowments (e.g., Delaware, Maine, New Hampshire, and Rhode Island). This addresses the potential concern that our core results are driven by states with no resources. In Column (14) we exclude California, New York, and Texas from the sample to test the robustness of our results when the three largest states are excluded. This restriction addresses the concern that our results may be driven by the dominant states. The estimated values of θ in all these cases indicate that our core results are robust to these restrictions on the sample. 4.6.6 Results When Resource Measure is Interacted with the Oil Price Next, we interact the cross-sectional measure of resource endowment (used in our baseline) with the oil price which is plausibly exogenous (James 2015). This measure then enters the estimated equation instead of our core resource measure. We examine the effects of TFP shocks across states, but also within them across time. Column (15) presents the results. The estimated value of θ maintains its sign and significance under this interacted measure. This indicates that the impact of technology shocks does not only depend on the existence of resource endowments, but also on their value. 4.6.7 Results Under State-Level TFP Shocks As a final robustness test, we examine the assumption about the homogeneity of the technological shocks across U.S. states. The baseline empirical analysis adopts this assumption in an attempt to address potential endogeneity concerns, noting that aggregate technological changes are plausibly exogenous to intra-state indicators. Our analytical framework takes a similar perspective under the assumption that TFP shocks are correlated across states due to the intra-federal setting. To examine the robustness of the results to this homogene41 The sample period in this case is limited by the availability of data on Gross State Product at the quarterby-year level. 1 3 2178 Natural Resources, Technology Improvements, and Growth ity assumption, we employ data from Caliendo et al. (2018). The latter estimated changes in measured TFP across U.S. states during two timeframes, 2002–2007, and 2007–2012. First, we note that the correlation of estimates across these two periods is highly positive, motivating the assumption about cross-state similarities in TFP patterns. Second, we adopt their estimates for the first period, as it is closer to the mid-point of our sample period, and consider them as cross-sectional differences in the absorption rate of national TFP changes, hence providing a cross-sectional dimension to the baseline national TFP measure.42 Interacting this cross-sectional TFP measure with the baseline national TFP changes yields a state-level measure, with variations across both dimensions, namely states and time. We then employ this measure in lieu of tfp in the baseline specification. The results in column (16), under this modified specification, indicate that the main results hold and increase in an order of magnitude, thus pointing at the robustness of the analysis to the homogeneity perspective. 4.7 Longer-Term Effects of TFP Shocks Our focus has been on the contemporaneous effects of TFP shocks. However, our analysis in Section 3 also gives insights concerning the dynamic patterns over time. Specifically, we find that resource-rich states should expand more strongly beyond the contemporaneous effect. Hence, we estimate and present the dynamic heterogeneous effects of TFP shocks across states with different levels of natural resources over the course of five years.43 We employ the method of local-projections of Jorda (2005). The method of local projections gives us estimates of impulse response functions separate regressions for each lead over the forecast horizon. The effect of TFP shocks at t+h with h=0,1,...,4 is estimated by regressing dependent variables at t+h on shocks and covariates at time t . Responses thus do not rely on nonlinear transformations of reducedform parameters as in VARs.44 We define ∆t−1xi,t+h≡xi,t+h−xi,t−1 and estimate the sequential equations ∆ t−1 ( outcome ) i,t+h = α h+ β h( outcome ) i,t−1 + γ h( resource ) i + δh ( tfp )t+ θh ( resource ∗ tfp )i,t + ηh i+ νh t+ ϵ i,t+h . (6) The dependent variable is cumulative growth of the outcome variable, ∆t−1(outcome)i,t+h , for different values of h . Our main coefficients of interest are the ones on the resource ∗tfp interaction variable, i.e., θh for the contemporaneous effect h=0 and the different leads h=1,...,4 . These 5 parameters shape the impulse response function, and hence enable us to trace the time profile of the effect of TFP shocks. Figure 5 plots the impulse response functions for each of the outcome variables, together with 95% confidence intervals. For output, the gradual increase in the estimated value of 42 For instance, during the 2002–2007 period the change in measured in TFP in Oregon was twice the size of that in Oklahoma, and three times that in New Hampshire. 43 The length of the examined horizon is based on a 1-year extension of the BFK framework in which the effects of TFP shocks are observed, and measurable over the medium-term horizon of approximately four years. 44 In Appendix B we present VAR estimates, and illustrate that the observed patterns are robust to the estimation method. 1 3 2179 F. Perez-Sebastian et al. θh , as the lead h increases, indicates that after the contemporaneous negative effect of TFP shocks, technology improvements become more expansionary in resource-rich states, most notably starting in the second year, relative to those in resource-poor states. The impulse response functions for labor and capital inputs paint a similar picture. This is evident from the gradually decreasing (increasing) patterns in the unemployment rate (investment), indicating again that positive TFP shocks are more expansionary in resource-rich environments, starting in the second year. These patterns lend support to our analytical predictions, and importantly, they are also consistent with the outcomes noted in the initial BFK exercise in which the observed postcontemporaneous expansionary impacts (noted as well, under the general sample) were stronger for resource-rich states than for resource-poor states. 5 Conclusion We have examined, both analytically and empirically, how technological shocks interact with natural resource abundance to affect growth in output and inputs. We offered a twosector growth model with non-neutral technical progress and adjustment costs to show that cross-sector differences in the degree of substitution between capital and labor can induce corresponding differences in the contemporaneous and long-run reactions to technology improvements, most notably capital-augmenting ones. Using our model and U.S. industry data, we have computed elasticity parameters of different sectors, revealing that the ESKL is persistently higher in extractive industries. We have also computed time series for the capitaland labor-augmenting technology parameters and employed these in our empirical analysis. Fig. 5 Impulse response functions for the effect of TFP shocks. The figure presents the impact of technology shocks interacted with resource endowments on the natural logarithms of real per capita GSP, the unemployment rate, and real per-capita investment over a 5-year horizon, with 95% confidence intervals, following the method of local projections of Jorda (2005). The sample includes the 48 continental U.S. states and covers the period 1963–2015 1 3 2180 Natural Resources, Technology Improvements, and Growth p iy1/εi it [ (zkitkit)1−1/µi+(zsitsit)1−1/µi ] µ i µi−1 (1 − 1 /εi ) − 1 (zkitkit)−1/µizkit = R, (26) p iy1/εi it [ (zkitkit)1−1/µi+(zsitsit)1−1/µi ] µi µi−1 (1 − 1 /εi ) − 1 (zsitsit)−1/µizsit =wst , (27) piy1 /εi it (znitnit) − 1 /µi znit =wnt, (28) where yit is given by Eq. (24). Combining the optimality conditions (26) and (27) gives the optimal ratio of physical capital to skilled labor, so that θ it ≡zkitk ∗ it z sit s ∗ it = ( zkit z sit wst R )µ i (29) Equation (29) implies that θit increases in zkit , decreases in zsit , and is independent of znit . In the same way, the optimality conditions (26) and (28) deliver the optimal ratio of physical capital to unskilled labor, which gives ω it ≡zkitk∗ it znitn∗ it = ( zkit znit wnt R ) εi [ 1+ ( zkit zsit wst R ) 1−µi ] ε i −µ i µi−1 . (30) It is easy to deduce from equation (30) that ωit increases in zsit and decreases in znit . In contrast, since zkit appears twice in Eq. (30), we obtain the first derivative to know how ωit is affected by changes in zkit , namely ∂ωit ∂zkit = ( zkit znit wnt R ) εi zkit [ 1+ ( zkit zsit wst R ) 1−µi ] ε i −µ i µi−1− 1[ εi+µi ( zkit zsit wst R ) 1−µi ]. (31) This last expression is always positive. To summarize, given that εi>µ i , both equations (29) and (30) indicate that the optimal amount of an input relative to another input, both measured in efficiency units, varies directly with relative input productivity levels and inversely with relative input prices. The prices of physical capital and skilled labor are given exogenously. However, the wage rate of skilled labor is endogenous. From equations (28) to (30), applied to the nonextractive sector ( m ), we can derive an expression for the wage of unskilled labor expressed as a function of exogenous variables and parameters, 1 3 2187 F. Perez-Sebastian et al. w nt =znmt   1−      (zkmt R)εm [ 1+(zkmt zsmt wst R)1−µm ] εm−µm µm−1    1−1/µ m +   (zsmt wst )εm[(zsmt zkmt R wst )1−µm +1 ]εm−µm µm−1   1−1/µm   µm µm−1 εm−1 εm    1 1−εm . (32) Therefore, the unskilled-labor wage rate depends only on variables and parameters related to the non-extracted sector. It can be easily shown that wnt increases in znmt , zkmt , and zsmt . Recall that, due to capital-skill complementarity, the optimal efficiency units of physical capital and skilled labor relative to those of unskilled labor increase in zkmt and zsmt . This, along with the fact that there is always some degree of complementarity between the three inputs, implies that an increase in the productivity of any input raises the wage rate. Substituting the fixed input proportions implied by Eqs. (29) and (30) into the long-run production function, given by equation (24), we obtain y it =      [ω µi−1 µi it +(ωit θit ) µi−1 µi] µi µi−1 ( εi−1 εi ) +1      εi εi−1 znitn∗ it , (33) or, alternatively, y it =  ( 1+θ 1−µi µi it ) µi µi−1 ( 1−1 εi ) +ω 1−εi εi it   εi εi−1 zkitk∗ it . (34) Moreover, comparing this last expression to the short-run production function, given now by Eq. (23), we deduce that Ω it =  ( 1+θ 1−µi µi it ) µi µi−1 ( 1−1 εi ) +ω 1−εi εi it   εi εi−1 . (35) Equation (35) indicates that Ωit decreases in both θit and ωit . Therefore, Eqs. (29) and (30) imply that Ωit decreases in zkit , as in the benchmark case. However, in the new version of the model, both znit and zsit also affect it—the former with a positive impact, while the latter has an ambiguous impact. In what follows, we assume that z kit znit w nt R>1 and z kit zsit w st R>1 , since R is constant, but wages tend to increase with the economy. We first analyze the effects of productivity shocks on long-run output. In the long run, all the economy’s available labor is used in production. Therefore, similar to what happens in the benchmark model, because labor is directed to the most productive activity, gains in any input productivity must result in gains in output. However, unlike in the benchmark model, since productivity shocks are now sector-specific, 1 3 2188 Natural Resources, Technology Improvements, and Growth long-run output will tend to increase more significantly in the sector where productivity parameters experience a larger rise. Our next task is to determine how these long-run output gains induced by productivity shocks vary with the elasticities of substitution between inputs ( εi and µi ). The effects on long-run output can be inferred from Eq. (33), which is the relevant one because labor goes back to full employment in the long run, that is, n∗ et +n∗ mt =N . Therefore, we can assume that n∗ it does not vary significantly. We focus on the elasticities of the extractive activity, as we are interested in knowing, for example, how the different effects change when εe increases away from εm . From Eqs. (29) and (30), we see that εe does not affect θet but amplifies the positive effect of zket on ωet . While this suggests a stronger positive effect, the presence of εi within the CES structure of the production function introduces an additional channel—hereafter referred to as the CES channel—through which changes in the elasticity of input substitution influence the overall outcome, leading to ambiguity. This ambiguity implies that, as observed in the benchmark model, the effect operating through input proportion responses may dominate for some subsets of the input elasticity parameters. Moreover, in most cases, when analyzing the impact of εe and µe , the CES channel will deliver the same outcome in our analysis. Therefore, our discussion will henceforth focus primarily on the impact on input proportions, while keeping in mind that the results hold for specific values of the elasticity parameters. Hence, the results so far are similar to those of the benchmark model. An increase in the elasticity of substitution between the capital-skill bundle and unskilled labor in the extractive industry has a clear effect on the input proportion responses, contributing to a stronger positive impact of long-run output to changes in zket . However, this result may hold only for certain values of εe . In contrast, an increase in µe makes ∂θe/∂zket more positive and ∂ωet/∂zket less positive. Equation (33) then suggests a weaker positive effect of capital-augmenting productivity on long-run output when the elasticity of substitution between capital and skilled labor increases in the extractive sector. It is also easy to show that changes in the input elasticity parameters affect the long-run output response to skill-biased productivity shocks ( zset ) in qualitatively the same way as they do for an increase in zket .,47 Regarding the response to znet , as εe rises, ωet falls more, while θet does not vary. As a result, the impact of znet weakens as εe increases, since capital rises less due to its greater substitutability with unskilled labor. Conversely, the impact of znet on long-run output channeled through input proportions strengthens as µet rises. We can thus draw the following conclusions. First, if the extractive industry exhibits a higher elasticity of substitution between capital and unskilled labor (i.e., εe>ε m ), there may exist values of εe and εm for which long-run output in the extractive sector rises more than in the non-extractive industry as a response to the same capitalor skill-biased productivity shock. Second, if the extractive industry has a higher elasticity of substitution between capital and skilled labor (i.g., if µe>µ m ), the opposite effect may occur—namely, longrun output may increase less in the extractive sector than in the non-extractive industry for 47 This can be easily deduce by comparing Eq. (30), which gives ωit θit = ( zsit znit wnt wst ) εi [ 1+ ( zsit zkit R wst ) 1−µi ] ε i −µ i µi−1 . (36) 1 3 2189 F. Perez-Sebastian et al. certain values of µe and µm as a response to an increase in zket or zset . Third, higher values of εe are less likely to amplify the long-run output impact when productivity shocks result from unskilled-biased technical change. Finally, since all these productivity shocks are sector specific, the impact will be stronger in the sector experiencing the greatest productivity increase. Short-Run Effects Let us now analyze the short-run effects for which Eq. (34) is now relevant. The maximization problem that determines the optimal investment in physical capital is max xit { piΩitzkitkit −R t ∑ j=1 (1 −δ)t−jxij −wntnit −wstsit } (37) subject to the motion of capital, which is determined by Eq. (3), and the constant input proportion conditions given by Eqs. (29) and (30). Solving this problems delivers the same solution as the benchmark model, given by Eq. (20), but now Ψ it =p i Ω it −w nt ωitznit −w st θitzsit . Therefore, following the same logic as in the proof of Proposition 3 in Appendix A, we can focus on the particular case where capital adjustment costs are so strong (i.e., ϕ sufficiently small) that the change in the capital input is negligible. In this scenario, Ωitzkit gives the response of short-run output to productivity shocks. From Eqs. (29), (30), and (35), when zkit increases, both θit and ωit increase, pushing Ωit down. This implies that both skilled and unskilled labor decrease per unit of capital. Therefore, as in the benchmark model, capital-augmenting productivity shocks can reduce output in the short run if the decrease in Ωit in absolute value is larger than the increase in zkit . Skill-biased technical change, on the other hand, is less likely—though not impossible— to cause a decrease in short-run output. As zsit rises, ωit increases, but θit falls, making the overall impact on Ωit uncertain. This occurs because, while the amount of unskilled labor per unit of capital falls, the amount of skilled labor increases. Finally, in the short run, the impact of znit on sector i ’s output can only be positive—note that as znit rises, ωit decreases, θit does not vary, and then Ωit increases. We also aim to examine how input elasticities affect the strength of a potential negative short-run effect on output. Therefore, we focus on how the impact of zket and zset varies with εe and µe . As εe increases, ∂θ et ∂zket remains unchanged, but ∂ω et ∂zket increases, potentially strengthening the negative effect on short-run output. The influence of εe on the short-run impact of zset is qualitatively identical to that of zket . Conversely, an increase in µe , raises ∂θ et ∂zket but decreases ∂ω et ∂zket , thus implying that the influence of µe on the short-run response to a zkit shock is ambiguous. In contrast, µe has a well-defined impact on input proportion responses to changes in zsit . When µe increases, ∂θ et ∂zset becomes more negative and ∂ω et ∂zset less positive, making a positive effect of zsit on short-run output more likely. We can summarize the short-run results when there are strong adjustment costs for the capital input as follows. First, capital-biased productivity shocks can negatively affect sec1 3 2190 Natural Resources, Technology Improvements, and Growth toral output in the short run. Furthermore, as in the benchmark model, for certain values of εe and εm , an increase in εe can amplify this negative short-run impact. The influence of µe is less clear, as it affects the capital-unskilled-labor and the capital-skilled-labor ratios in opposite directions. Second, skilled-biased technical change is less likely to generate shortrun output losses due to the increase in the amount of skilled labor. Third, unskilled-biased technical change cannot reduce output in the short run. Finally, since productivity shocks are sector-specific, all these effects will be more pronounce if productivity gains impact the extractive industry more significantly. D. Estimating ESKL and the Productivity Parameters We introduce time and sector subindices when necessary to allow R , wt and εi to vary across time and sectors. Hence, Eqs. (2) and (10) become y et = [ (zktket)1−1/εet +(zntnet)1−1/εet ] εet εet−1 , (38) ket n et = ( zkt z nt )ε et −1( wet R et )ε et , (39) y mt = [ (zktkmt)1−1/εmt +(zntnmt)1−1/εmt ] εmt εmt−1 , (40) kmt n mt = ( zkt z nt )ε mt −1( wmt R mt )ε mt . (41) We can use these to obtain z nt =yit n it ( witnit p it y it ) εit εit−1 ,for i= e, m, (42) and z kt =yit k it ( Ritkit p it y it ) εit εit−1 ,for i= e, m. (43) Finally, equalizing Eqs. (42) and (43) across the two sectors delivers εmt εmt −1= ln ( ymt/kmt yet/ket ) − ln(R et k et petyet ) ln(wetnet petyet )ln ( ymt/nmt yet/net ) ln(Retket petyet ) ln ( wetnet petyet ) ln ( wmtnmt ymt )− ln ( Rmtkmt pmtymt ) (44) and 1 3 2191 F. Perez-Sebastian et al. εet εet −1= ln ( ymt/kmt yet/ket ) +εmt εmt−1ln ( Rmtkmt pmtymt ) ln ( Retket petyet ). (45) Using data for yet , ymt , ket , kmt , net , nmt , wet , wmt , Ret and Rmt , we can thus obtain an estimate of εmt from Eq. (44). Then, taking εmt into Eq. (45) gives εet . Finally, substituting εmt and εet into (42) and (43) gives znt and zkt . We can thus obtain the ESKL for each of the two sectors and the common labor-augmenting and capital-augmenting productivities, at any given point in time. More specifically, the EUKLEMS provides data for the variables required to perform the estimation. Output variables yet and ymt , and the stocks ket , kmt , net and nmt are directly available in the dataset. We compute the salaries wet and wmt by dividing total labor compensations by total hours worked ( nit ). We compute Ret and Rmt by dividing total capital compensations by the total capital stock ( kit ). This is consistent, for example, with the computations undertaken by Caselli and Coleman (Caselli et al. 2006). E. Data We use an annual state-level panel that, unless otherwise specified, covers the 48 continental U.S. states for the period 1963–2015. Real variables are expressed in 2009 prices. Descriptive statistics for all variables are presented in Table A1. Table A1 Descriptive statistics 1 3 2192 Natural Resources, Technology Improvements, and Growth Variable definitions Resource endowment: Recoverable state stocks of oil and natural gas (cross-sectional), normalized by average state income (averaged over 1958–2008). Alaska and Hawaii are excluded. Source: James (2015) Real per-capita Gross State Product (GSP): Real Gross State Product divided by state population. Source: U.S. Census Bureau. Population: State population. Source: U.S. Census Bureau. Real per-capita tax rates: State tax revenues divided by state population. Source: U.S. Census Bureau. Real per-capita government expenditures: Total expenditures of state government divided by state population. Source: U.S. Census Bureau. 1 3 2193 F. Perez-Sebastian et al. Real per-capita state outstanding debt: Total outstanding debt of state government divided by state population. Source: U.S. Census Bureau. Party affiliation of governor: An indicator for the party of the governor; 0 = Republican, 1 = Democrat, 0.5 = non-major party governor. Source: Marty and Grossman (2016). Inequality: Theil Index measure of income inequality. Source: Frank (2009). Unemployment rate: State unemployment rate. Source: U.S. Census Bureau. Real per-capita capital stock: State capital stock divided by state population. Source: Garofalo and Yamarik (2002), including an extension of it available at the second author’s homepage. Fernald TFP shocks: Aggregate, national TFP shocks, aggregated to an annual level. Source: Fernald (2014). Federal tax shocks: Narrative-based federal tax shocks, aggregated to an annual level, and normalized by U.S. GDP; available up to 2007. Source: Romer and Romer (2010). Business cycles: An indicator for whether the U.S. economy is in a recession. Source: U.S. Federal Reserve. News shocks: Investment Specific Technology (IST) news shocks, aggregated to an annual level; available up to 2011. Source: Ben-Zeev (2018). Monetary shocks: Monetary policy shocks a-la Romer and Romer (2004); available for 1969–2007. Source: Tenreyro and Thwaites (2016). JPT TFP shocks: Series of TFP shocks derived from Justiniano et al. (2011). BS TFP shocks: Series of TFP news shocks derived from Barsky and Sims (2011). FORD TFP shocks: Series of TFP shocks derived from Francis et al. (2014). Zk: Capital-augmenting technology shocks. Computed from the model, as described in the text, vis-à-vis data from the EUKLEMS dataset. Source: O’Mahony and Timmer (2009). Zn: Labor-augmented technology shocks. Computed from the model, as described in the text, vis-à-vis data from the EUKLEMS dataset. Source: O’Mahony and Timmer (2009). GSP share of manufacturing: Share of state manufacturing sector in Gross State Product. Source: U.S. Census Bureau. 1 3 2194 Natural Resources, Technology Improvements, and Growth GSP share of services: Share of state services sector in Gross State Product. Source: U.S. Census Bureau. GSP share of agriculture: Share of state agriculture sector in Gross State Product. Source: U.S. Census Bureau. GSP share of wholesale: Share of state wholesale trade sector in Gross State Product. Source: U.S. Census Bureau. F. VAR analysis In Sect. 4.7 of the paper, we have examined the dynamic patterns following the method of local projections (Jorda 2005). To examine the robustness of the observed patterns to the type of estimation method, we undertake an equivalent estimation under a VAR framework. Specifically, we estimate ∆(outcome) i,∆(t−1,t) =α+β(outcome) i,t−1 +γ(resource) i +δ(tfp)t+ j=4 ∑ j=0 θj(resource ∗tfp)i,t−j+ηi+νt+ϵi,t. (46) Here outcome again denotes each of the three outcome variables. The results are presented in Table A2. Columns (1)-(3) examine the cases of GSP, unemployment, and capital, respectively. The observed patterns are qualitatively similar to those under the Jorda (2005) method outlined in Sect. 4.7. We note that upon impact, TFP shocks contract output and labor more strongly in resource-rich than resource-poor states, but there are no such differential impacts on capital. However, specifically from about the second or third years, output, labor, and capital expand more strongly in those same, initially contracted, resource-rich states. These results indicate that the main observed patterns are robust to this alternative estimation method. Table A2 Resource endowments and technology improvements (VAR analysis) 1 3 2195 F. Perez-Sebastian et al. Funding Open access funding provided by Hebrew University of Jerusalem. Open access funding provided by Hebrew University of Jerusalem. Fidel Perez Sebastian acknowledges funding from the Spanish Ministry of Science and Innovation, Projects PID 2019-111208 GB-I00 and PID2023-153032NB-I00. Data availability The data used in this study is available from the authors upon request. Declarations Conflict of Interest The authors have no conflicts of interest to disclose. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Acemoglu D (2002) Technical change, inequality and the labor market. J Econ Lit 40:7–72 1 3 2196