Bao-We-Wal Bambe

Jean-Louis Combes

Pascale Combes Motel

• Chantale

Riziki Oweggi
email: chantale_riziki.oweggi@doctorant.uca.fr

Does Climate Change Affect Firms' Innovative Capacity in Developing Countries ?

Keywords: Climate change, Firm innovation, Developing Countries JEL Classifications: D22, O3, Q54

We investigate the impact of climate change on firms' investment in research and development (R&D) in developing countries. The paper relies on two contrasting hypotheses. In the first hypothesis, we speculate an optimistic situation where climate change could induce firms to spend on R&D to both reduce their environmental impact and curb the effects of future climate shocks. In the second hypothesis, we propose a pessimistic scenario where climate change would reduce firms' incentives to invest in R&D. This second hypothesis would mainly be due to tighter conditions for access to finance from lenders, given the increased uncertainty about the firm's future returns in the face of climate change. The empirical results support the second scenario, small firms being more severely affected. Furthermore, we examine the underlying mechanisms and identify financial access as the key channel through which climate change reduces R&D investment.

Introduction

Climate change is one of the most pressing global problems of our time [START_REF] Dessai | Uncertainty and climate change adaptation: A scoping study[END_REF]. Increasingly adverse climatic conditions have created greater systematic risk for companies throughout the global economy [START_REF] Huang | The impact of climate risk on firm performance and financing choices: An international comparison[END_REF]. This is a result of uncertainties created by frequent natural disasters such as droughts, extreme temperatures, floods, landslides, and storms, which are expected to continue rising with global warming [START_REF] Masson-Delmotte | Global warming of 1.5°c[END_REF][START_REF] Kundzewicz | Uncertainty in climate change impacts on water resources[END_REF]. Consequently, profitseeking firms must adapt and deal with these uncertainties to ensure their survival and growth. Such adaptive strategies are particularly possible through innovation, research, and development (R&D).

Contemporary scholars have thoroughly addressed the effects of climate change on diverse sectors of the economy and its negative implications for sustainable development.

Numerous studies emphasize that climate change has grave consequences on economic growth, health, and poverty [START_REF] Noy | The macroeconomic consequences of disasters[END_REF][START_REF] Burke | Global non-linear effect of temperature on economic production[END_REF][START_REF] Hallegatte | Shock waves: managing the impacts of climate change on poverty[END_REF][START_REF] Mejia | The Effects of Weather Shocks on Economic Activity: What are the Channels of Impact? International Monetary Fund[END_REF][START_REF] Solomon | Climate change-a health emergency[END_REF][START_REF] Baarsch | The impact of climate change on incomes and convergence in africa[END_REF]. Other studies have addressed the microeconomic consequences of climate events such as droughts, famine, and floods, especially at the household level. Focusing on developing countries, some of these studies have highlighted various coping strategies applied by households to smooth their consumption in the face of income shocks from climate events. Such strategies include mutual insurance systems, dependence on altruism, credit transfers, seeking wage employment, and selling assets such as livestock and jewellery, among others [START_REF] Quisumbing | Do shocks affect men's and women's assets differently? evidence from bangladesh and uganda[END_REF][START_REF] Ray | Development economics[END_REF].

At the firm level, an emerging branch of literature has brought to light the 'cost of climate change' to firms' operations. Authors find that climate change may negatively affect firm productivity, competitiveness, labour supply, and access to credit [START_REF] Pilcher | Effects of hot and cold temperature exposure on performance: a meta-analytic review[END_REF][START_REF] Graff Zivin | Temperature and the allocation of time: Implications for climate change[END_REF][START_REF] Kling | The impact of climate vulnerability on firms' cost of capital and access to finance[END_REF][START_REF] Cevik | Rogue waves: Climate change and firm performance[END_REF]. Other studies have highlighted the role of product innovation in climate change adaptation [START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF]. This latter branch follows the argument that climate resilience is highly conditional on innovation [START_REF] Denton | Climate-resilient pathways: adaptation, mitigation, and sustainable development[END_REF]. As R&D is one of the determinants of innovation [START_REF] Love | The determinants of innovation: R & d, technology transfer and networking effects[END_REF], some authors have studied the role of R&D and innovation in climate change adaptation and mitigation [START_REF] Blanford | R&d investment strategy for climate change[END_REF][START_REF] Meadow | Moving toward the deliberate coproduction of climate science knowledge[END_REF][START_REF] Bremer | Co-production in climate change research: reviewing different perspectives[END_REF][START_REF] Alam | Does corporate r&d investment affect firm environmental performance? evidence from g-6 countries[END_REF][START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF].

The central interest of this study is the profound nexus between climate change and innovation, and to a great degree, firms' investment in R&D. Our study alludes to the literature on the 'cost of climate change' but also borrows from the latter branch of literature that views R&D as a critical component of climate action. As stated above, literature exists on the implications of R&D on climate change [START_REF] Blanford | R&d investment strategy for climate change[END_REF][START_REF] Meadow | Moving toward the deliberate coproduction of climate science knowledge[END_REF][START_REF] Bremer | Co-production in climate change research: reviewing different perspectives[END_REF][START_REF] Alam | Does corporate r&d investment affect firm environmental performance? evidence from g-6 countries[END_REF][START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF]. However, to the best of our knowledge, we found no existing literature targeting the implications of climate change on firm R&D investment. Allied to the above, developing countries are more vulnerable and less resilient to climate change events [START_REF] Noy | The macroeconomic consequences of disasters[END_REF][START_REF] Fomby | The growth aftermath of natural disasters[END_REF]. Climate change-induced effects, such as natural disasters, are stronger in developing than in advanced countries, as developing countries lack the preconditions to withstand initial shocks [START_REF] Fomby | The growth aftermath of natural disasters[END_REF]. Furthermore, the insurance system in most developing countries is not well established, exposing firms to greater losses in the event of catastrophic climate events [START_REF] Gurenko | Catastrophe risk and reinsurance: a country risk management perspective[END_REF][START_REF] Linnerooth-Bayer | Insurance for assisting adaptation to climate change in developing countries: a proposed strategy[END_REF][START_REF] Barnett | Poverty traps and index-based risk transfer products[END_REF][START_REF] Linnerooth-Bayer | Insurance, developing countries and climate change[END_REF]. Against this background, this paper seeks to study the effect of climate change on firms' innovation through R&D investment, focusing on developing countries.

We question the effect of climate change on firm R&D investment by presenting two contrasting hypotheses. In the first hypothesis, we speculate an optimistic situation where climate change could induce firms to spend on R&D to curb the effects of future climate shocks. In the second hypothesis, we propose a pessimistic view that climate change and its uncertainties reduce R&D investment. In the latter hypothesis, we propose that a possible channel through which climate change could reduce R&D investment is through firms' access to credit, following bank reluctance to lend in periods of climate uncertainty [START_REF] Cevik | Rogue waves: Climate change and firm performance[END_REF]. Next, we discuss three other indirect channels. The first would stem from an increase in public spending to adapt to and mitigate the effects of climate change, which may lead to a crowding-out or a crowding-in effect on private-sector investment. The second channel is based on the Porter hypothesis, whereby the strengthening of environmental regulations in the face of climate change would provide firms with incentives to innovate. The last channel predicts a negative effect of climate change-induced environmental uncertainty on foreign investment, with a potential reduction in technology and innovation transfers by foreign firms. Our empirical results point to a negative effect of climate change on firms' incentives to invest in R&D in developing countries.

This study examines the effect of climate change on firms' R&D investment, using a panel of 103 developing countries over the period 2006-20. Combining firm-level characteristics from the World Bank Enterprise Surveys (WBES) dataset with country-level characteristics, we find that climate change -captured by temperature deviations from the historical average -induces a significant decrease in the probability of R&D investment. We conduct a series of robustness tests that support our results. In addition, we examine some heterogeneity features and find that the negative effect of climate change is amplified for small firms, probably because they have the most difficulty accessing financing, but also because they are often less outward-looking and therefore less likely to benefit from the beneficial externalities of globalization compared to their larger counterparts. Finally, we empirically explore the underlying mechanisms and identify financial access as the key channel through which climate change reduces R&D investment.

The remainder of this paper is organized as follows. The next section provides the conceptual framework. Section 3 discusses our main hypotheses. Section 4 outlines the data. Section 5 details the econometric approach, and Section 6 presents the main results. Section 7 examines the sensitivity of our results. Section 8 explores the main transmission channels. The conclusions and policy implications are presented in the last section.

Background

Extensive literature exists on the global implications of climate change on economic performance. Various authors consider the macroeconomic aspect of climate change and find that climate change manifestations such as extreme temperatures and natural disasters negatively affect economic growth, infrastructure, productivity growth, poverty levels, and health [START_REF] Noy | The macroeconomic consequences of disasters[END_REF][START_REF] Burke | Global non-linear effect of temperature on economic production[END_REF][START_REF] Hallegatte | Shock waves: managing the impacts of climate change on poverty[END_REF][START_REF] Mejia | The Effects of Weather Shocks on Economic Activity: What are the Channels of Impact? International Monetary Fund[END_REF][START_REF] Solomon | Climate change-a health emergency[END_REF][START_REF] Baarsch | The impact of climate change on incomes and convergence in africa[END_REF].

A different strand of literature highlights the micro-economic consequences of climate change, albeit often concentrating on the household level. These studies empirically illustrate the economic losses of climate change and bring to light the various coping mechanisms employed by households in the event of climate uncertainties such as droughts, famine, and floods. For instance, it has been shown that households tend to reduce the use of modern cooking energy in the event of climate shocks, plant low-risk crop varieties in anticipation of climate risks, use assets, savings, mutual insurance, or seek wage employment to smooth consumption [START_REF] Ray | Development economics[END_REF][START_REF] Quisumbing | Do shocks affect men's and women's assets differently? evidence from bangladesh and uganda[END_REF][START_REF] Riziki | Household energy choices under perceived shocks in uganda: Are perceived shocks limiting the energy transition process among households in uganda?[END_REF].

As we approach the Anthropocene epoch, the impact of climate change on the natural environment will become irreversible and climate change events will become severe and unpredictable, causing more uncertainty [START_REF] Gasparin | Slow design-driven innovation: A response to our future in the anthropocene epoch[END_REF][START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF].

Following this logic, a separate strand of literature has focused on the impact of climate change on firms' activities, underscoring 'the cost of climate change' on profit-seeking firms. There is evidence that climate change negatively impacts key firm performance measures such productivity and profitability of businesses [START_REF] Pilcher | Effects of hot and cold temperature exposure on performance: a meta-analytic review[END_REF][START_REF] Huang | The impact of climate risk on firm performance and financing choices: An international comparison[END_REF]Traore and Foltz, 2018;[START_REF] Kling | The impact of climate vulnerability on firms' cost of capital and access to finance[END_REF][START_REF] Pankratz | Climate change, firm performance, and investor surprises[END_REF][START_REF] Cevik | Rogue waves: Climate change and firm performance[END_REF]. Other authors find that these effects are considerably larger in developing countries where industries are more climate-exposed [START_REF] Graff Zivin | Temperature and the allocation of time: Implications for climate change[END_REF]. Moreover, evidence shows that by creating uncertainty about future returns on investment, climate change may lead lenders to tighten lending conditions, thus reducing access to finance [START_REF] Kling | The impact of climate vulnerability on firms' cost of capital and access to finance[END_REF][START_REF] Cevik | Rogue waves: Climate change and firm performance[END_REF].

Given the increasing global temperature that could trigger severe climate events, one set of literature builds on climate uncertainty to study firms' adaptation and mitigation strategies through knowledge co-production among societal actors, innovation, research, and development [START_REF] Meadow | Moving toward the deliberate coproduction of climate science knowledge[END_REF][START_REF] Bremer | Co-production in climate change research: reviewing different perspectives[END_REF][START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF]. A branch of this literature addresses mitigation strategies put forth by firms to reduce their greenhouse gas emissions [START_REF] Su | Does innovation respond to climate change? empirical evidence from patents and greenhouse gas emissions[END_REF]. While this strategy is indeed a step towards zero emissions, it is hardly sufficient on its own to reduce the impacts of climate change, especially at the firm level [START_REF] Kahn | The climate change adaptation literature[END_REF]. The other branch targets product innovation and firm adaptation to changing climatic conditions. However, authors in the field of management highlight the scarcity of literature addressing firms' adaptive strategies in dealing with changing climatic conditions [START_REF] Linnenluecke | Firm and industry adaptation to climate change: a review of climate adaptation studies in the business and management field[END_REF]. One such strategy is firm relocation as an adaptive response to climate change and weather extremes [START_REF] Linnenluecke | Firm relocation as adaptive response to climate change and weather extremes[END_REF]. With regard to innovation, the literature addresses both product and process innovation. In the former, authors find that consumers could either accept or reject, depending on consumer perception of the newly innovated version of the product, especially in the food industry [START_REF] Ramirez | From external information to marketing innovation: the mediating role of product and organizational innovation[END_REF][START_REF] Oliva | Firms adaptation to climate change through product innovation[END_REF]. In the latter, authors find that large firms devote a higher proportion of their R&D expenditure on process innovation than smaller firms [START_REF] Fritsch | Product innovation, process innovation, and size[END_REF]. Further studies found that environment-related process innovations are majorly determined by environmental regulation, as predicted by the Porter hypothesis [START_REF] Porter | Toward a new conception of the environmentcompetitiveness relationship[END_REF][START_REF] Cleff | Determinants of environmental product and process innovation[END_REF].

R&D is one of the key determinants of innovation, together with technology transfer and networking effects [START_REF] Love | The determinants of innovation: R & d, technology transfer and networking effects[END_REF]. In this view, various authors have addressed the role of R&D investment as a strategy for climate change. Authors find that market-based abatement policies are effective mechanisms that encourage knowledge diffusion through R&D [START_REF] Blanford | R&d investment strategy for climate change[END_REF]. Other authors find that R&D investment improves firms' environmental performance by reducing energy consumption and carbon emissions intensities [START_REF] Alam | Does corporate r&d investment affect firm environmental performance? evidence from g-6 countries[END_REF]. However, studies examining the reverse relationship -focusing on the impact of climate change on R&D investment -remain scarce or lacking. This paper addresses this issue, by empirically estimating the impact of climate change on firms' innovative capacity, proxied by R&D investment, in developing countries.

Developing countries often carry the weight of natural disasters, as they are more vulnerable and economically less resilient to climate change than their developed counterparts [START_REF] Noy | The macroeconomic consequences of disasters[END_REF][START_REF] Linnerooth-Bayer | Insurance, developing countries and climate change[END_REF][START_REF] Fomby | The growth aftermath of natural disasters[END_REF]. Moreover, the insurance system in most developing countries is weak [START_REF] Gurenko | Catastrophe risk and reinsurance: a country risk management perspective[END_REF][START_REF] Linnerooth-Bayer | Insurance for assisting adaptation to climate change in developing countries: a proposed strategy[END_REF][START_REF] Barnett | Poverty traps and index-based risk transfer products[END_REF][START_REF] Linnerooth-Bayer | Insurance, developing countries and climate change[END_REF]. Less than a tenth of losses were insured in emerging economy countries, and only 1-2 percent of losses from natural disasters were insured in low-income countries between the period of 1980-2004 [START_REF] Gurenko | Catastrophe risk and reinsurance: a country risk management perspective[END_REF][START_REF] Linnerooth-Bayer | Insurance, developing countries and climate change[END_REF]. Insurance uptake equally improves creditworthiness and promotes investment in productive assets and higher-risk activities [START_REF] Linnerooth-Bayer | Insurance, developing countries and climate change[END_REF]. Such low levels of insurance could exclude firms in developing countries from benefiting from risk reduction strategies and worsen the negative effects of climate change by placing an overbearing recovery burden on firms.

Theoretical predictions

In a nutshell, despite an emerging and growing literature on the impact of climate events on firm performance, so far, very little has been said about the implications of climate change on firms' R&D investment in developing countries. Climate change may influence firms' incentives to invest in R&D through various channels. Some are direct, while others are indirect. This section discusses these mechanisms.

Direct channels

To explore the direct channels through which climate change could affect firms' R&D investment, we postulate two contradictory hypotheses. The first hypothesis is based on an optimistic scenario, in which climate change would encourage firms to invest in R&D as a strategy for mitigating their environmental impact and adapting to future climatic events. Firms can finance their investments (including R&D) through various ways, among others, bank credits, equity financing, savings, personal funds, and remittances.

Most of these options are limited to a great extent. For instance, remittances are mostly used to set up small firms and require transfers from other people [START_REF] Woodruff | Remittances and microenterprises in mexico[END_REF]. Other forms of financing such as personal funds and savings are conditional on having initial finances. Equity financing and venture capitalists only fund a very small fraction of technology-oriented businesses each year [START_REF] Gompers | Equity financing. Handbook of entrepreneurship research: An interdisciplinary survey and introduction[END_REF].

Consequently, despite high interest rates and often tight collateral requirements, bank credit remains an important means of financing businesses in developing countries.

Existing literature has identified access to credit as one of the main obstacles to the development of the private sector in developing countries [START_REF] Chauvet | Financial inclusion, bank concentration, and firm performance[END_REF].

Moreover, as discussed above, it has been shown that by creating uncertainty about the profitability of investment and firms' profits, climate change makes lenders reluctant, thereby reducing the likelihood of granting credit [START_REF] Cevik | Rogue waves: Climate change and firm performance[END_REF]. This is particularly true in developing countries where the insurance system is weak. Yet, access to finance is a major determinant of firm investment, as the empirical literature provides evidence that credit constraints tend to reduce firms' innovation projects (e.g., see [START_REF] Aghion | Credit constraints and the cyclicality of r&d investment: Evidence from france[END_REF][START_REF] Brancati | Innovation financing and the role of relationship lending for smes[END_REF][START_REF] Madrid-Guijarro | Financing constraints and sme innovation during economic crises[END_REF][START_REF] Fombang | Access to finance and firm innovation[END_REF][START_REF] Kaur | Firm innovation and access to finance: firm-level evidence from india[END_REF]. This leads us to the second hypothesis: by tightening access to credit, climate change would reduce firms' R&D investment.

Indirect channels

The indirect channels result from the side effects induced by climate risks. These include government expenditure, environmental stringency, and foreign direct investment (FDI).

First and foremost, climate change may lead governments to increase public spending, in a quest to adopt and mitigate the effects induced by climate risk. These expenditures can be directed towards increasing the capacity of renewable energy by financing hydroelectric, wind, geothermal, and solar power plants [START_REF] Óhaiseadha | Energy and climate policy-an evaluation of global climate change expenditure 2011-2018[END_REF], forest and biodiversity conservation, disaster risk management, agriculture, and food security [START_REF] Philibert | International energy technology collaboration and climate change mitigation[END_REF][START_REF] Eliasch | Climate change: financing global forests: the Eliasch review[END_REF]. A rise in public spending could result in higher interest rates, particularly if public borrowing is financed by the domestic banking sector, which could crowd out private investment -including R&D investment. On the other hand, public spending allocated to infrastructure development and climate change mitigation could improve the business environment and reduce environmental risks, which can be conducive to R&D investment [START_REF] Braese | Resilient infrastructure for thriving firms: A review of the evidence[END_REF][START_REF] Chauvet | Taxation, infrastructure, and firm performance in developing countries[END_REF].

In the face of climate change, the government can tighten environmental regulations as a complementary mitigation mechanism to address environmentally damaging behavior. This can involve, for example, imposing an explicit or implicit price on the use of certain pollutants, greenhouse gas emissions, waste production, etc. This leads us to the second channel: environmental stringency. The Porter hypothesis [START_REF] Porter | Toward a new conception of the environmentcompetitiveness relationship[END_REF] states that stringent environmental regulations should encourage firms to innovate to adhere to environmental policies aimed at mitigating climate change. From this point of view, climate change could indirectly impact R&D investment, through stricter environmental regulations. This effect is all the more plausible for the most polluting firms seeking to reduce their carbon footprint.

Data

Firm-level data

Our analysis combines country-level climate characteristics with firm-level characteristics for a set of 103 developing countries. Firm-level characteristics are drawn from the World Bank Enterprise Surveys (WBES) database. The WBES provide microdata on the performance of formal enterprises, using a representative sample in the manufacturing and services sectors. The surveys are based on a standard questionnaire to ensure comparability from one country to another and from one year to another, and are standardized over time and for all countries (repeated cross-sectional data). We use the latest dataset, covering the period 2006-20, and retain 103 developing countries from available data. Our dependent variable is captured by a dummy equal to 1 if, during the last fiscal year, the establishment spent on R&D, and zero otherwise. More precisely, R&D investment measures a firm's expenditure aimed at achieving a new discovery that may lead either to the development of new products, services or procedures, or to the improvement of existing products, services, or procedures.

We follow the existing literature (see, among others, [START_REF] Chauvet | Financial inclusion, bank concentration, and firm performance[END_REF][START_REF] Chauvet | Aid and growth: evidence from firm-level data[END_REF][START_REF] Kouamé | Structural reforms and firms' productivity: Evidence from developing countries[END_REF][START_REF] Chauvet | Taxation, infrastructure, and firm performance in developing countries[END_REF] and include a series of firm-level controls, such as size, age, and ownership. Firm size is captured by an ordinal qualitative variable equal to 1 for small (less than 20 employees), 2 for medium (between 20 and 99 employees), or 3 for large firms (100 employees and over).

Age measures the length of time an establishment has been in existence, from the year of its formal registration as a start-up. The firm's ownership structure is captured by two distinctive dummy variables equal to 1 if the State or a foreign entity owns part or all of the firm, and zero otherwise. The literature provides evidence that widespread internet adoption or access to telecommunication infrastructures boosts firm performance and innovation performance (e.g., see [START_REF] Harrison | Explaining africa's (dis) advantage[END_REF][START_REF] Paunov | Has the internet fostered inclusive innovation in the developing world?[END_REF][START_REF] Chauvet | Taxation, infrastructure, and firm performance in developing countries[END_REF]. Similarly, as discussed above, it has been shown that access to finance is an important determinant of firm innovation. We therefore include two additional firm-level variables among the controls: access to telecommunication infrastructure and financial access. Access to telecommunication infrastructures is captured by a dummy equal to 1 if the firm has its website, and zero otherwise. Financial access is measured as a dummy variable that takes 1 if the firm has a credit line or an overdraft facility, and zero otherwise.

Country-level data

Climate change is measured at the country level, as annual changes in mean surface temperature, in degrees Celsius, using temperatures between 1951 and 1980 as a baseline (higher values indicate warmer weather compared with the historical average). The variable is from the International Monetary Fund's (IMF) Climate Change Indicators Dashboard. At the country level, we consider as control variables the inflation rateas the literature shows that macroeconomic uncertainty undermines firms' performance, including their ability to invest in R&D [START_REF] Bambe | Inflation targeting and developing countries' performance: Evidence from firm-level data[END_REF]-and the level of education, as knowledge is essential to firms' ability to innovate [START_REF] Acemoglu | Innovation, reallocation, and growth[END_REF][START_REF] Medase | External knowledge modes and firm-level innovation performance: Empirical evidence from sub-saharan africa[END_REF]. The inflation rate and the level of education are from the World Bank's World Development Indicators (WDI) database. The inflation rate is measured as the percentage change in the consumer price index, while the level of education is approximated by the secondary school enrollment rate.

Descriptive statistics and stylized facts

Table 1 provides descriptive statistics on firm and country characteristics for the sample.

The sample is dominated by manufacturing firms (76% of the total sample) compared to the services sector, and is mostly made up of small firms (around 49% of the total sample). On average, 21% of firms operating in the developing countries (DCs) in the sample invest in R&D. This rate is lower in low-income countries -LICs -(about 17%) compared to the whole sample of DCs. Similarly, LICs report a lower rate of access to telecommunications infrastructure (about 24%) than the overall sample of DCs (around 47%). Finally, firms operating in LICs tend to have less access to finance (around 31%) than the overall sample of DCs (around 55%). We then look at the differences in characteristics between manufacturing firms and those in the services sector. On average, a higher proportion of manufacturing firms invest in R&D compared to those in the services sector (23% versus 12%), rely on telecommunications services (49% versus 42%), and have access to finance (56% versus 51%). Looking at the differences by firm size, a higher proportion of medium-sized and large firms (jointly considered) invest in R&D compared to small firms (28% versus 12%), use telecommunications infrastructures (62% versus 28%), and have access to finance (66% versus 40%).

With regard to country-level variables, the data suggest a rise in temperature in developing countries over the period 2006-20 of around 1.03 degrees Celsius compared to the historical average . In other words, this pattern suggests a transition to warmer temperatures. LICs register a slightly higher inflation rate compared to the overall sample of DCs (around 10% versus 7%), and a much lower level of secondary education than the whole sample of DCs (around 34% versus 77%). Figure 1 displays the five-year trend in the proportion of firms investing in R&D and temperature variations in the countries in our sample, over our study period. There is a clear upward trend in temperature, while over the same period, the proportion of firms investing in R&D has fallen significantly. Statistical tests suggest a negative and significant correlation at 1%

between climate change and R&D investment, with a magnitude of around 16%. Table A1 (see Appendix) reports the countries in the sample and the year of the surveys.

Methodology

We as the linear probability model (LPM), probit or logit models. Logit and probit models have serious shortcomings in our design. Indeed, accounting for fixed effects (country, industry, and year) when using such models would be problematic, as a large one would yield inconsistent slope estimates due to the incidental parameter problem [START_REF] Wooldridge | Econometric analysis of cross section and panel data mit press[END_REF]. Moreover, the inclusion of fixed effects would eliminate all observations for which the independent variable perfectly predicts the R&D investment outcome from the analysis (see [START_REF] Zorn | 2019 Sri Lanka 2011 Bangladesh 2007; 2013 Kyrgyz Republic 2009[END_REF][START_REF] Belloc | Earthquakes, religion, and transition to selfgovernment in italian cities[END_REF]. In short, probit and logit models expose us to a serious identification issue. The omission of fixed effects would not allow us to capture unobserved factors specific to each country or industry, or common time-varying shocks, which could be correlated with both climate change and the outcome variable.

Therefore, we rely on the LPM which is appropriate in our design, as it allows us to include a wide range of country, industry, and year-fixed effects to capture unobserved heterogeneity (see [START_REF] Belloc | Earthquakes, religion, and transition to selfgovernment in italian cities[END_REF]. The econometric specification we estimate is the following:

Y i,k,j,t = α + βT emperature j,t + ηX i,k,j,t + + γZ j,t + µ k + ϕ j + ψ t + ϵ i,k,j,t (1)
where Y i,k,j,t is a dummy equal to 1 if the firm i located in the industry k, in the country j invested in R&D in the year t, and 0 otherwise. T emperature j,t is the variable of interest, i.e., climate change, captured at the country level, approximated by an annual rise in temperature using temperatures between 1951 and 1980 as a baseline. X i,j,k,t is a set of time-varying firm-level characteristics described in Section 4, i.e., size, age, ownership, access to telecommunication infrastructure, and financial access. Z j,t includes country-level controls, i.e., the inflation rate and the level of education. µ k , ϕ j , and ψ j account respectively for industry, country, and time-fixed effects, and allow capturing specific characteristics. Country (industry) fixed effects take into account the fact that countries (industries) may differ in many important and permanent unobservable characteristics, which are likely to be correlated with both the country's temperature change and the firms' probability of investing in R&D. Time-fixed effects absorb any potential contemporaneous climate change event for all countries that could affect the probability of the firm investing in R&D. Finally, ϵ i,k,j,t is the idiosyncratic error term. Following [START_REF] Paunov | Has the internet fostered inclusive innovation in the developing world?[END_REF], robust standard errors clustered at the country-industry-year level are applied systematically to account for the fact that the variable of interest is an aggregate variable.

Main findings

The results are presented in Table 2 for our global sample of 103 countries. Columns

[1] and [2] rely on the LPM. In the first column, we consider our baseline model, but exclude fixed effects from the regression. The results show a negative correlation between temperature rises and the probability of a firm investing in R&D. Column [2], which reports our main results, includes country, year, and industry fixed effects among the controls to account for unobserved heterogeneity, as discussed above. The inclusion of fixed effects leads to a drop in the effect of the variable of interest (from 10.9% to 4.7%),

suggesting that the omission of unobserved factors leads to an overestimation of the effect of climate change on the probability of firms investing in R&D. Similarly, there is an improvement in the value of the R-squared (from around 12% to 18%), suggesting that accounting for unobserved heterogeneity in the analysis improves the model's fit.

Our main results (Column [2] of Table 2) suggest a negative and significant impact of temperature change on firms' probability of investing in R&D. More specifically, a 1 degree Celsius increase in temperature compared with the average between 1951 and 1980 reduces the probability of a firm investing in R&D by 4.7%. This effect is economically significant, given that only 21% of the firms in the sample invest in R&D.

With regard to the controls, the results suggest that firm age and size, foreign ownership, access to finance and telecommunications infrastructure, and the level of education are positively correlated with the probability of investing in R&D, in line with the theoretical predictions made in Section 4.

Sensitivity analysis

We conduct a series of robustness tests in subsection 7.1 before exploring some heterogeneity analyses in subsection 7.2.

Robustness

Alternative models

As argued in Section 5, logit and probit models are not suitable for our design, as accounting for fixed effects when using these models is problematic. Furthermore, the results of Columns [1] and [2] of Section 6 show that the inclusion of fixed effects in our study is relevant as it improves the fit of the regression, which strongly reinforces the usefulness of the LPM, at least in our design. Nevertheless, for robustness purposes, we re-estimate our baseline model using probit and logit models, in Columns [3] and [4] of Table 6, respectively. Such an exercise is relevant since it provides a means of estimating the direction and magnitude of the potential estimation bias induced by probit and logit models compared with the LPM. The new estimates suggest that climate change reduces the likelihood of investing in R&D, in both probit and logit models. However, the new coefficients are slightly higher (around 11%) than those provided by the LPM (around 5%), suggesting a slight overestimation of the probit and logit models. This is probably because, as previously discussed, the latter do not account for fixed effects, especially as the new estimates are almost similar to those obtained by LMP when we omit fixed effects from the regression (Column [1] of Table 6). Even so, the new results remain qualitatively similar to those provided by the LPM, which reinforces our conclusions.

Regarding the control variables, the new results suggest a favorable impact of firm age and size, foreign ownership, access to finance, and telecommunications infrastructure on R&D investment, while the effect of education is not robust.

Additional controls

Our main model considers some well-selected controls, as the inclusion of many variables exposes us to multicollinearity and sample size reduction due to missing data. For robustness, we augment our baseline model by including a series of additional controls.

First, we include the logarithm of sales to capture the level of firm performance. Next, as our sample includes a large panel of countries with heterogeneous income levels, we include the logarithm of per capita income to account for this. The literature also highlights the importance of institutions in economic performance [START_REF] Acemoglu | The role of institutions in growth and development[END_REF].

Hence, we control for the quality of institutions, captured by the level of political stability and human rights protection. 1 Third, the world has become increasingly globalized in recent decades, with increasing interaction between countries and sectors that exchange not only goods and services, but also ideas. Firms' participation in global value chains (GVCs) offers them the opportunity to acquire new knowledge, better technologies, and know-how, which can be conducive to R&D innovation [START_REF] Ernst | Global production networks, knowledge diffusion, and local capability formation[END_REF][START_REF] Gereffi | Global value chains in a post-washington consensus world[END_REF]. Therefore, following Del Prete et al. ( 2017) and [START_REF] Reddy | Firm innovation and global value chain participation[END_REF], we capture firms' participation in GVCs by a dummy equal to 1 if the firm exports, imports or

1 The human rights protection variable indicates how the state protects rights and freedoms equally across all social groups (higher values indicate better performance) and is from Our World in Data. The political stability variable measures perceptions of the likelihood of political instability and/or politically motivated violence, including terrorism (higher values indicate better performance), and comes from the Worldwide Governance Indicators (WGI) database.

trades bilaterally with international quality certificates, and 0 otherwise. Fourth, we include the firm's legal status, considering the three most representative statuses in the sample: sole proprietorship, shareholding company with non-traded shares or shares traded privately, and limited partnership, respectively. Fifth, we include an environmental stringency variable, the Environmental Performance Index (EPI).2 As discussed above, given the adverse effects of climate change on economic performance, the government could reinforce its environmental stringency, for example through measures aimed at penalizing environmentally harmful behavior (use of certain pollutants, greenhouse gas emissions, waste production, etc.). The Porter hypothesis [START_REF] Porter | Toward a new conception of the environmentcompetitiveness relationship[END_REF] states that greater environmental stringency may lead firms to adopt more innovative production methods. Sixth, we include energy inflation, as higher energy prices contribute to higher input costs for firms, but can also lead to higher prices for other goods and services. Finally, we also include a linear trend to capture long common movements that could be correlated with climate change and firms' propensity to innovate.

The new results reported in Columns [2]-[12] of Table B1 (see Appendix), where the additional controls are included cumulatively, suggest a robust negative effect of climate change on R&D investment. In addition, the new coefficients of the variable of interest, which range from -2.9% to -3.4%, remain qualitatively comparable to the coefficient of the baseline model (-4.7%). Overall, the effect of the control variables of the baseline model also remains highly robust. With regard to the new controls, the results suggest that firm sales and their participation in GVCs increase the likelihood of investing in R&D.

Alternative subsamples

Our third robustness check consists of re-estimating our baseline model from alternative subsamples. First, we exclude from the sample the years during the COVID-19 pandemic and the 2008-09 global financial crisis, respectively, since these events led to major imbalances in many countries. Next, some outliers could induce bias in our estimates.

Although excluding them from the sample is sometimes considered dealing with this issue, the main problem with such an approach is that it reduces the sample size. We therefore winsorize our variable of interest at 95% to account for outliers. 3 The new estimates reported in Panel A of Table B2 (see Appendix), respectively, remain stable.

Alternative measures

We conduct some additional robustness by considering alternative measures in Table B2 (see Appendix). In Column [1] of Panel B, we consider a dummy equal to 1 if, over the last 3 years, the establishment has introduced a new/significantly improved process or new products/services, and zero otherwise. The results suggest that a 1 degree Celsius increase in temperature relative to the long-term average reduces the probability of a firm introducing a new production process or product by around 6%, which reinforces our conclusions. In Column [2] (Panel B), we re-estimate our baseline model using climate shocks (or temperature volatility) as the variable of interest. We calculate climate shocks from the Hodrick-Prescott (HP) filter, since this approach does not rely a priori on any assumption regarding the presence and nature of the trend in the series. 4 The new estimates yield similar conclusions. Last, we rely on a climatic drought index, the Standardized Precipitation-Evapotranspiration Index (SPEI), provided by [START_REF] Vicente-Serrano | A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index[END_REF]. 5 The SPEI is based on precipitation and temperature data, and has the advantage of combining multiscalar nature with the capacity to include the effects of temperature variability on drought assessment. The literature shows that climate change is associated with an increase in global temperature, but also with an increase in evapotranspiration rates and a decrease in rainfall in certain regions, which has an impact on the severity of droughts [START_REF] Solomon | Climate change 2007-the physical science basis: Working group I contribution to the fourth assessment report of the IPCC[END_REF][START_REF] Vicente-Serrano | A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index[END_REF]. Over our study period, the data suggest a negative correlation between temperature change and the SPEI, with a magnitude of around 30%, suggesting that higher temperatures are associated with lower precipitation. For the sake of comparability with our climate change measure, we construct a dummy equal to 1 for SPEI values indicating extreme drought periods, and zero otherwise. The results reported in Column [3] of Table B2 indicate that extreme drought periods reduce the probability of R&D investment by almost 7%. Finally, it is well known that climate change is associated with frequent natural disasters, such as droughts, extreme temperatures, floods, landslides, storms, etc. Therefore, in the last column, we approximate our variable of interest using the monetary damage (as a percentage of GDP) induced by climate change-related disasters. This variable is taken from the EM-DAT database. The results hold.

Heterogeneity

We now explore some heterogeneity in the relationship between climate change and R&D investment. We consider our main specification, augmented by an interactive term (a significant effect of the interactive term suggests that there is heterogeneity). Among the potential sources of heterogeneity, we consider firm size, export status, and sector of activity (manufacturing vs. services). Firm size is approximated by the level of sales.

More precisely, we consider respective dummy variables equal to 1 if the sales of the firm i in a year t are higher than the first (small firms), second (medium-sized firms), and third (large firms) quartile of all observations for the country j, and zero otherwise.

The results are reported in Table 3, where vector X variables in isolation (without interaction with climate change) and controls are included but not reported for the sake of space. In all cases, the results suggest that climate change reduces the likelihood of investing in R&D. However, when examining the interactive terms between climate change and the potential variable of heterogeneity, we observe that the negative effect of climate change is amplified for small firms, probably because they have the most difficulty accessing finance (as shown in Table 1), but also because they are the most likely to be less outward-looking, and therefore less likely to benefit from the positive externalities of globalization, through technology or skills transfers, compared to larger firms. Finally, with regard to the other factors examined, the results suggest that neither the sector of activity (manufacturing versus services) nor the export status significantly affect the relationship between climate change and R&D investment.

Main transmission channels

This section examines the main channel through which the negative effect of climate change on the likelihood of investing in R&D can be transmitted, i.e., financial access.

Drawing on existing literature (e.g., see, [START_REF] Apeti | Household welfare in the digital age: Assessing the effect of mobile money on household consumption volatility in developing countries[END_REF][START_REF] Bambe | Inflation targeting and private domestic investment in developing countries[END_REF], we adopt a simple two-stage approach to testing the potential channel. In the first two columns of Panel A (Table 4), we report Pearson correlations between R&D investment and financial access.

The results suggest a positive and significant correlation between financial access (both in terms of credit line and overdraft facility) and R&D investment. 6 In Panel B, we report the results of univariate regressions of the potential channel on climate change.

We observe that climate change is associated with a lower probability of access to finance, suggesting that the latter is a relevant channel explaining our results.

Another factor, power cuts, could also play a role. Indeed, it has been shown that high temperatures and heat waves lead to failures in electricity networks and contribute to increased energy losses, reducing the distribution of electricity from power stations to households and firms [START_REF] Schaeffer | Energy sector vulnerability to climate change: A review[END_REF][START_REF] Campbell | Weather-related power outages and electric system resiliency[END_REF][START_REF] Ward | The effect of weather on grid systems and the reliability of electricity supply[END_REF].

Thus, we argue that by affecting firms' energy distribution, heat waves can also indirectly impact firms' innovation. Although Column [3] of Panel B (Table 4) suggests that temperature rise is associated with an increase in the duration of power cuts, the correlation between the length of power cuts and R&D investment, albeit negative, is rather weak (around 3%) and not significant.

To sum up, although the power cuts channel seems to emerge as a potential mechanism explaining our results, we identify financial access as the key channel through which climate change reduces R&D investment. The literature is unanimous on the role of R&D investment in climate action. However, it is equally important to understand the inverse relationship to ensure a multifaceted comprehension of the nexus between climate change and R&D. This study addresses this question, providing empirical evidence of the implications of climate change on firms' R&D investment. Using a large sample of 103 developing countries, we find evidence that climate change reduces the probability of firms' R&D investment. The effect is statistically and economically significant and robust to a wide range of robustness checks.

We also find that the adverse effects of climate change are greater for small firms, and identify firms' access to credit as the key channel through which climate change reduces firms' R&D investment.

Our findings bring to light another 'cost of climate change' for firms in developing countries. Our main conclusion is that climate change appears to be a major impediment to firm innovation in developing countries, through a reduction in R&D investment, as it tends to exacerbate constraints on access to credit. Our result underlines a conundrum given the central role of R&D investment in climate mitigation and adaptation. We highlight important policy implications. It is crucial to promote measures aimed at combating the substantial inertia of climate, in order to limit the adverse consequences of climatic events. This means, among other things, encouraging firms' innovation (through R&D investment) aimed at adapting to and mitigating the effects of climate change.

Moreover, such policies must be complemented by measures to promote access to credit, given that access to credit remains an essential determinant of R&D investment and hence, innovation.

This study uses R&D investment as a proxy for innovation. The data used does not differentiate between green investment and non-green investment in R&D. Future research could explore such a distinction to better understand the effect of climate change on green R&D investment.

Appendix B Robustness

  Last but not least, environmental uncertainty induced by climate change could reduce foreign investors' confidence in the domestic environment of the affected country. This may lead foreign firms to relocate to countries with better climate change adaptation and mitigation strategies, or with relatively less climate uncertainty. Foreign firms' relocation exposes the affected country to the loss of the positive side effects of FDI, such as the transfer of technology, knowledge, know-how, and innovation skills. In other words, by reducing FDI flows to the countries most exposed to climate risk, climate change could hurt R&D investments in these latter countries.

Figure 1 :

 1 Figure 1: Temperature change and the proportion of firms investing in R&D: five-year trend over 2006-20 Notes: Temperature change is measured in degrees Celsius, using temperatures between 1951 and 1980 as a baseline.

Table 1 :

 1 investigate the impact of climate change on firms' innovative capacity in developing Summary statistics

	countries, proxied by R&D investment. The study combines firm-level characteristics
	from the World Bank Enterprise Surveys (WBES) dataset and country-level data, for
	a panel of 103 countries over the period 2006-20. As our dependent variable (R&D in-
	vestment) is binary, the literature suggests using appropriate econometric methods such

Table 2 :

 2 Climate change and firms' innovative capacity

		LPM		Probit	Logit
		[1]	[2]	[3]	[4]
	Temperature change	-0.109*** -0.047***	-0.114***	-0.110***
		(0.009)	(0.013)	(0.009)	(0.009)
	Firm age	0.001*** 2.514e-04*	0.001***	4.944e-04***
		(0.000)	(0.000)	(0.000)	(0.000)
	Firm size	0.056***	0.058***	0.052***	0.049***
		(0.004)	(0.003)	(0.004)	(0.004)
	State	-0.027*	0.018	-0.018	-0.019
		(0.016)	(0.015)	(0.015)	(0.015)
	Foreign	0.045***	0.041***	0.041***	0.038***
		(0.009)	(0.008)	(0.007)	(0.007)
	Financial access	0.102***	0.061***	0.105***	0.102***
		(0.006)	(0.004)	(0.006)	(0.006)
	Website	0.127***	0.100***	0.129***	0.122***
		(0.006)	(0.006)	(0.006)	(0.006)
	Education	-4.031e-04	0.001*	-4.577e-04*	-3.891e-04
		(0.000)	(0.001)	(0.000)	(0.000)
	Inflation	-0.001	0.003	-0.001	-0.001
		(0.001)	(0.003)	(0.001)	(0.001)
	Observations	49010	49010	49010	49010
	R-squared	0.116	0.184	0.1217	0.1215
	Country & Industry & Year FE	No	Yes

This table reports the results of the impact of climate change on firms' innovative capacity (R&D investment). Column [2] displays the baseline results, estimated from the linear probability model (LPM). Columns

[3] and [4]

re-estimate the baseline model using probit and logit models, respectively (the coefficients reported are marginal effects). Robust standard errors are reported in parentheses. The constant is included, but not reported in the table. * p < 0.1, ** p < 0.05, *** p < 0.01

Table 3 :

 3 HeterogeneityThis table reports the results of the heterogeneity effects of the impact of climate change on R&D investment. The equation is estimated by considering the main model augmented by the interactive term. Vector X variables in isolation (without interaction with environmental stringency) and controls are included but not reported for the sake of space. Robust standard errors are reported in parentheses. The constant is included, but not reported in the table. * p < 0.1, ** p < 0.05, *** p < 0.01

		[1]	[2]	[3]	[4]	[5]
	Temperature change (TC)	-0.037*** -0.043*** -0.045*** -0.059*** -0.044***
		(0.014)	(0.013)	(0.013)	(0.016)	(0.013)
	TC * Small firms	-0.013**
		(0.006)
	TC * Medium-sized firms		-0.010
			(0.007)
	TC * Large firms			-0.009
				(0.007)
	TC * Manufacturing				0.014
					(0.011)
	TC * Export status					-0.009
						(0.006)
	Observations	49010	49010	49010	49010	49010
	R-squared	0.184	0.184	0.184	0.184	0.186
	Controls	Yes	Yes	Yes	Yes	Yes
	Country & Industry & Year FE	Yes	Yes	Yes	Yes	Yes

Table 4 :

 4 Transmission channels Panel A reports Pearson correlations between RD investment, financial access, and power cuts. *** indicates significance at the 1% threshold. Panel B reports the effect of climate change on the potential channels, using univariate regressions. * p < 0.1, ** p < 0.05, *** p < 0.01

	Pannel A	[1]	[2]	[3]
		R&D investment R&D investment R&D investment
	Credit line	0.1727***
	Overdraft facility		0.2024***
	Power outages			-0.0027
	Pannel B	[1]	[2]	[3]
		Credit line	Overdraft facility	Power outages
	Temperature change	-0.024**
		(0.010)
	Temperature change		-0.084***
			(0.014)
	Temperature change			0.544**
				(0.221)
	Observations	97671	95982	44493
	R-squared	0.001	0.009	0.0003

Table B1 :

 B1 Robustness: Additional controls

Table B2 :

 B2 This table reports the results of the impact of climate change on firms' innovative capacity (R&D investment), using the linear probability model (LPM). Column [1] displays the baseline results.Columns [2]-[12] report the robustness results, where we include a series of additional controls. Robust standard errors are reported in parentheses. The constant is included, but not reported in the table. * p < 0.1, ** p < 0.05, *** p < 0.01 Robustness: Alternative samples and measures This table reports the results of the impact of climate change on firms' innovative capacity (R&D investment), using alternative samples (Panel A) and measures (Panel B). In Columns [1] and [2] of Panel A, we exclude from the sample the years during the COVID-19 pandemic and the 2008-09 global financial crisis, respectively. In the last column, we winsorize our variable of interest at 95% to account for outliers. In Column [1] of Panel B, the dependent variable is a dummy equal to 1 if, over the last 3 years, the establishment has introduced a new/significantly improved process or new products/services, and zero otherwise. In Column [2], we calculate temperature volatility from the Hodrick-Prescott (HP) filter. In Column [3], relying on the Standardized Precipitation-Evapotranspiration Index (SPEI), we consider as variable of interest a dummy equal to 1 for SPEI values indicating extreme drought periods, and zero otherwise. In the last column, Therefore, in the last column, we approximate our variable of interest using the monetary damage (as a percentage of GDP) induced by climate change-related disasters. Robust standard errors are reported in parentheses. The constant is included, but not reported in the table. * p < 0.1, ** p < 0.05, *** p < 0.01

	016) (0.016) (0.016) (0.016) (0.016) (0.016) (0.018) (0.018) (0.018) Panel A: Alternative samples (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 0.033*** 0.033*** 0.034*** 0.034*** 0.026*** 0.025*** 0.025*** 0.025*** 0.025*** 0.025*** 0.025*** (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.005) (0.005) 0.031* 0.031* 0.027 0.027 0.028 0.025 0.027 0.027 0.027 0.036 0.036 (0.018) (0.018) (0.018) (0.019) (0.019) (0.020) (0.020) (0.020) (0.020) (0.022) (0.022) 0.030*** 0.030*** 0.032*** 0.032*** 0.018** 0.017* 0.017* 0.017* 0.017* 0.016* 0.016* (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) 0.049*** 0.049*** 0.050*** 0.050*** 0.048*** 0.047*** 0.047*** 0.047*** 0.047*** 0.050*** 0.050*** (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) 0.089*** 0.089*** 0.088*** 0.088*** 0.082*** 0.081*** 0.081*** 0.081*** 0.081*** 0.081*** 0.081*** (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) 0.002* 0.002* 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 (0.001) (0.001) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) -0.001 -0.001 -0.000 -0.001 0.001 0.001 0.000 0.000 -0.001 0.000 -0.000 (0.003) (0.003) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.005) (0.005) Temperature change Observations R-squared Controls Country & Industry & Year FE Panel B: Alternative measures Temperature change Temperature volatility Extreme drought Climate-related natural disasters Observations R-squared 2.514e-04* 2.852e-04* 2.852e-04* 2.395e-04 2.408e-04 6.405e-05 5.686e-05 7.060e-05 6.668e-05 6.757e-05 4.080e-05 4.052e-05 (0.000) 0.058*** (0.003) 0.018 (0.015) 0.041*** (0.008) 0.061*** (0.004) 0.100*** (0.006) 0.001* (0.001) 0.003 (0.003) Controls Country & Industry & Year FE	0.011*** 0.011*** 0.011*** 0.010*** 0.008*** 0.007*** 0.007*** 0.007*** 0.007*** 0.007*** 0.007***	(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) -0.048*** -0.047*** -0.050*** -0.041 -0.011 -0.014 -0.014 -0.010 -0.002 -0.002 -0.030 -0.034 -0.033 (0.079) (0.109) (0.123) (0.123) (0.123) (0.123) (0.123) (0.130) (0.132) (0.132) 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) -0.007 -0.020 -0.016 -0.017 -0.018 -0.051 0.037 0.039 (0.125) (0.121) (0.121) (0.121) (0.121) (0.120) (0.152) (0.151) 0.109*** 0.110*** 0.109*** 0.109*** 0.109*** 0.105*** 0.105*** (0.009) (0.010) (0.010) (0.010) (0.010) (0.010) (0.010) -0.013** -0.007 -0.009 -0.009 -0.006 -0.006 (0.005) (0.006) (0.007) (0.007) (0.007) (0.007) 0.012* 0.010 0.010 0.011 0.011 (0.007) (0.007) (0.007) (0.008) (0.008) -0.006 -0.006 -0.004 -0.004 (0.010) (0.010) (0.010) (0.010) -0.002 -0.004 -0.004 (0.003) (0.004) (0.004) -0.007 -0.007 (0.007) (0.007) 5.676e-06 [1] [2] [3] (0.013) (0.013) (0.015) 45940 49010 49010 0.182 0.184 0.184 Yes Yes Yes Yes Yes Yes [1] [2] [3] -0.055** (0.022) -0.079*** (0.020) -0.065** (0.027) 49399 50284 50284 0.242 0.183 0.183 Yes Yes Yes Yes Yes Yes	(0.000)	33766 33766 32424 32329 32329 32213 32213 32213 32213 29930 29930 -0.067* 0.194 0.194 0.198 0.198 0.206 0.206 0.206 0.206 0.206 0.210 0.210 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes (0.035) 50082 0.183 Yes 49010 0.184 Yes Yes
	Firm age	Firm size	State	Foreign	Financial access	Website	Education	Inflation	Sales	Log.GDP per capita	Political stability	Human rights protection	Global value chains	Sole proprietorship	Shareholding (non-traded shares/traded privately)	Limited partnership	Environmental stringency	Energy inflation	Trend		Observations	R-squared	Country & Industry & Year FE

The Environmental Performance Index can range from 0 to 100 (best performance) and captures a country's progress in improving environmental health, mitigating climate change, and protecting the vitality of ecosystems. Source: https://epi.yale.edu/epi-results/2022/component/epi

The results remain robust when we winsorize at 90% or 99%.

We use observed annual temperature data from the World Bank Group (Climate Change Knowledge Portal).

The data is available on the World Bank's WDI dataset.

The WBES defines an overdraft facility as a flexible account that allows firms to draw upon in the event their account balance becomes negative. On the other hand, a credit line is an available amount of credit that the establishment can draw upon or leave untapped.

Senegal 2007; 2014 Indonesia 2009;

Serbia2009; 2013; 2019

Appendix A Sample

Appendix C Figures

Appendix D Variables and their sources


Joseph Halim

Patrick Chartier

Tatyana Basyuk

Tatyana Prikhna

N El'ad

Michel W Caspi

Thierry Barsoum

Cabioc'

Caspi

Michel W Barsoum

Thierry Cabioc

Structure and thermal expansion of (Crx,V1-x

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The Mn+1AXn (MAX) phases (n =1-3) are nanolaminated layered carbides and nitrides, where M is an early transition metal, A is a group A element, mainly from groups 13 and 14, and X is either C or N. [START_REF] Barsoum | MAX Phases: Properties of Machinable Ternary Carbides and Nitrides[END_REF] They have hexagonal crystal structure (space group P63/mmc), where the M atoms are in a near-closed packed arrangement and are interleaved with A-group element layers, with the X-atoms occupying the octahedral sites between the M layers. [START_REF] Barsoum | The MN+ 1AXN phases: a new class of solids: thermodynamically stable nanolaminates[END_REF] There are about 70 MAX phases reported to date, that are classified by their n values as M2AX "211" (n = 1), M3AX2 "312" (n = 2), and M4AX3 "413" (n = 3). [START_REF] Eklund | The Mn+1AXn phases: Materials science and thin-film processing[END_REF] By this time, it is fairly well established that these materials have a unique combination of metal and ceramic properties. For example, they are thermally and electrically conductive, thermal shock resistant, machinable and damage tolerant like metals. In addition, some of them have low densities, high elastic stiffnesses and are oxidation and creep resistant like ceramics. [START_REF] Sun | Oxidation behaviour of Ti3SiC2-based ceramic at 900-1300 C in air[END_REF][START_REF] Zhen | Compressive creep of fine and coarse-grained T3SiC2 in air in the 1100-1300° C temperature range[END_REF][START_REF] Wang | Oxidation behavior of Ti3AlC2 at 1000-1400•C in air[END_REF][START_REF] Qian | Cyclic oxidation of Ti3AlC2 at 1000-1300 °C in air[END_REF] The structures and the properties of MAX phases can be modified, and even tuned, by introducing a fourth, or more, element into their structures. This is especially true here since, isostructural solid solutions can be obtained on the M, A and/or X sites. This compositional degree of freedom has been exploited by some to tailor the MAX phases' properties. For example the oxidation resistance of Ti3SiC2 improves upon the introduction of Al on the A-sites or when Ti atoms are introduced on the M site to create Ti3(Si1-x,Alx)C2 and (Nb1-x,Tix)2AlC solid solutions, respectively [START_REF] Zhang | Improving the oxidation resistance of Ti3SiC2 by forming a Ti3Si0:9Al0:1C2 solid solution[END_REF][START_REF] Salama | Oxidation of Nb2AlC and (Ti,Nb)2AlC in Air[END_REF] . Solid solution hardening effects were also reported for (Vx,Ti1-x)2AlC [START_REF] Meng | Strengthening of Ti2AlC by substituting Ti with V[END_REF] or Ti2AlCxNy [START_REF] Barsoum | Processing and characterization of Ti2AlC, Ti2AlN and Ti2AlC0.5N0.5[END_REF] whereas a solid solution softening effect was noticed for Ti3(Al1-x,Snx)C2. [START_REF] Bei | Synthesis, Characterization, and Intrinsic Hardness of Layered Nanolaminate Ti3AlC2 and Ti3Al0.8Sn0.2C2 Solid Solution[END_REF] More recently, there has been a growing interest in MAX phase solid solutions as a way to achieve new properties. Most notably, it was demonstrated that a promising method to create magnetic MAX phases is to introduce Mn in the structure of MAX phases that do not contain Mn. [START_REF] Meshkian | A magnetic atomic laminate from thin film synthesis: (Mo0.5Mn0.5)2GaC[END_REF][START_REF] Petruhins | Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films[END_REF][START_REF] Mockute | Synthesis and characterization of arc deposited magnetic (Cr, Mn)2AlC MAX phase films[END_REF][START_REF] Ingason | Magnetic self-organized atomic laminate from first principles and thin film synthesis[END_REF][START_REF] Mockute | Solid solubility and magnetism upon Mn Incorporation in the bulk ternary carbides Cr2AlC and Cr2GaC[END_REF] In addition, new ordered MAX phase solid solutions have been recently synthesized [START_REF] Liu | Crystal structure and formation mechanism of (Cr2/3Ti1/3)3AlC2 MAX phase[END_REF][START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF][START_REF] Anasori | Mo2TiAlC2: A new ordered layered ternary carbide[END_REF][START_REF] Anasori | characterization of ordered MAX phases Mo2TiAlC2 and Mo2Ti2AlC[END_REF] and predicted. [START_REF] Dahlqvist | Order and disorder in quaternary atomic laminates from first-principles calculations[END_REF] Indeed, it is more accurate to refer to the ordered n = 2 and n = 3 solid solutions as M 2 ' M " AX 2 and M 2 ' M 2 " AX 3 , respectively, to emphasize the existence of two inequivalent crystallographic sites for the M atoms in these structures (M' being closer to the A atoms). Liu et al. [START_REF] Liu | Crystal structure and formation mechanism of (Cr2/3Ti1/3)3AlC2 MAX phase[END_REF] thus obtained the (Cr2/3Ti1/3)3AlC2 compounds in which the Ti and Cr atoms are on the M' and M" sites, respectively. In the same way, Caspi et al. [START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF] confirmed the strong tendency for the Cr atoms to occupy the M' sites in (Cr0.5V0.5)3AlC2 and (Cr0.5V0.5)4AlC3 solid solutions. Similar behavior was obtained for Mo atoms in Mo2TiAlC2 and Mo2Ti2AlC3. [START_REF] Anasori | Mo2TiAlC2: A new ordered layered ternary carbide[END_REF][START_REF] Anasori | characterization of ordered MAX phases Mo2TiAlC2 and Mo2Ti2AlC[END_REF] Most germane to this work is the fact that the thermal expansions of Cr2(Al1-x,Gex)C solid solutions can be tailored by varying x. For x ≈ 0.75, the thermal expansion coefficients, TECs, of the a-lattice parameters, a-LPs, and c-lattice parameters, c-LPs, were nearly equal. [START_REF] Cabioch | Tailoring of the thermal expansion of Cr2(Alx,Ge1-x)C phases[END_REF] The present contribution builds on these results and deals with solid solutions in the Cr-V-Al-C system, viz.

(Crx,V1-x)n+1AlCn (n = 1, 2, 3) for x = 0; 0.25; 0.5; 0.75; 1.0). This system is of special interest since it is the only system, other than the Ta-Al-C system, [START_REF] Etzkorn | Ta3AlC2 and Ta4AlC3 -single-crystal investigations of two new ternary carbides of tantalum synthesized by the molten metal technique[END_REF] where phases exist for n = 1, 2 and 3. In most other MAX phase systems, only a subset is stable. Previously, Schuster et al. [START_REF] Schuster | The ternary systems: Cr-Al-C, V-Al-C, and Ti-Al-C and the behavior of H-phases (M2AlC)[END_REF] revealed that (Crx,V1-x)2AlC phases can be obtained for 0 ≤ x ≤1. However, for the "312", and "413" phases, only the x = 0.5 solid solutions have to date been synthesized. [START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF][START_REF] Zhou | Zhang New MAX-phase compounds in the V-Cr-Al-C system[END_REF] It is of special interest to study the evolution of the TEC's of these (Crx,V1-x)n+1AlCn solid solutions. In addition to the fundamental scientific interest that knowledge of this property garners, the TEC values can have an important influence on the oxidation resistance of these compounds, and therefore on possible applications. As mentioned above, some of the MAX phases are resistant to high temperature oxidation. For example Ti3AlC2 and Ti2AlC resist high temperature oxidation up to 1400 °C due to the formation of a well adhered, protective Al2O3 scale. [START_REF] Tallman | A critical review of the oxidation of Ti2AlC, Ti3AlC2 and Cr2AlC in air[END_REF] However, Cr2AlC shows cubic rate oxidation and good hot corrosion resistance against molten Na2SO4 up to 1000 °C only. Above that temperature spallation of the Al2O3 layer takes place. [START_REF] Tallman | A critical review of the oxidation of Ti2AlC, Ti3AlC2 and Cr2AlC in air[END_REF][START_REF] Lin | High-temperature oxidation and hot corrosion of Cr2 AlC[END_REF] This spallation occurs due to the TEC mismatch between Cr2AlC (13 K -1 ) and Al2O3 (8 K -1 ). [START_REF] Zhou | On the synthesis and properties of bulk ternary Cr2AlC ceramics[END_REF][START_REF] Engberg | Thermal expansion of Al2O3, BeO, MgO, B4C, SiC, and TiC above 1000 °C[END_REF] In this context, incorporation of V could improve the oxidation resistance of Cr2AlC by decreasing its TEC. The rationale behind this proposition is that V2AlC has a lower TEC (8 K -1 ) than Cr2AlC. As noted above, we already showed that to be the case in the Cr2(Alx,Ge1-x)C system. [START_REF] Cabioch | Tailoring of the thermal expansion of Cr2(Alx,Ge1-x)C phases[END_REF] Here, we use X-ray diffraction to report on the thermal expansions of (CrxV1-x)n+1AlCn solid solutions as a function of both x and n.

Experimental Details

Samples were synthesized by using powder metallurgy techniques. Chromium (-200 mesh, 99.95%, Alfa Aesar GmbH & Co KG Karlsruhe Germany), vanadium (-325 mesh, 99.8%, Alfa Aesar GmbH & Co KG Karlsruhe Germany), aluminum (40-325 mesh 99.8%, Alfa Aesar GmbH & Co KG Karlsruhe Germany) and graphite (<40 µm, Chemwatch) powders were first weighted to obtain the requisite molar compositions. In all cases, an excess of 10 at.% Al was used to compensate for its loss by evaporation during the sintering process. These powders were then mixed for 3 h in a Turbula™ mixer. Cylindrical compacts of 3-4 g in weight, 12 mm in diameter, were obtained by cold pressing the mixed powders in a uniaxial press at a load corresponding to a pressure of 200 MPa.

Ten different starting nominal compositionsall listed in first column in Table 1 -were prepared. These compositions were then heated either pressureless sintered, PS, in a tube furnace under flowing Ar, in the 1400 °C to 1600 °C temperature range or hot-isostatically pressed, HIPed at 1450 °C. Twenty eight different runs-listed in columns 2 and 3 -of varying durations were carried out.

As noted above, several samples were also HIPed. Those are designated by HIP in column 2

in Table 1. In this case, the cold pressed cylindrical samples were sealed under a mechanical vacuum inside borosilicate glass (Pyrex) tubes. The HIP was then heated to 1450 °C and pressurized, using Ar gas, to a pressure of 80 MPa and held at temperature for 4 h, before furnace cooling. The dense compacts were then further annealed for 1 h at 700 °C under Ar flow to relax any internal stresses that may have accrued during the HIPing process.

After a mechanical polishing, all samples were characterized at room temperature, RT, by XRD in a Bragg-Brentano configuration using a diffractometer (B8 Bruker) operating at 40 kV, 40 mA with Cu-Kα radiations with a LynxEye TM rapid detector and a fixed divergence slit of 0.4°. Steps scan of  2 = 0.01-0.02° for 2-3 s per step were typically used for obtaining the RT XRD patterns.

In situ HT-XRD patterns were also obtained for select samples using an Anton-Paar device (Domed Hot Stage for Four-Circle Goniometers (DHS 1100)) with a graphite dome mounted in line in the same X-Ray diffractometer. To accurately determine the temperature of the samples hexagonal boron nitride, h-BN, powder was evenly distributed on the MAX samples' surfaces. h-BN possess a relatively large and well known thermal expansion along it c-axis (c (Å) = 6.6516 Å + 2.74 x 10 -4 T•Å•°C -1 ) [START_REF] Pease | An X-ray study of boron nitride[END_REF] allowing a precise determination of samples' temperatures when the c-LP of h-BN were deduced from Rietveld refinement of the X-Ray diffractograms.

A XRD pattern of a chromia standard powder (NIST 674b) was collected at the same geometrical conditions to generate an instrumental resolution function to account for experimental broadening, and to estimate the systematic uncertainty in the determination of the lattice parameters (LP). Rietveld refinements of all diffractograms were performed using the Materials Analysis Using Diffraction (MAUD) software. [START_REF] Lutterotti | Total pattern fitting for the combined size-strain-stress-texture determination in thin film diffraction[END_REF] At RT, the uncertainty in the LPs is lower than 0.013% and 0.03% for the a and c LPs, respectively; at higher temperatures the uncertainly is lower than 0.03% and 0.07% for the a and c LPs, respectively.

Using the Rietveld refined LPs in the 200-800 °C temperature range, the linear TECs of the phases in this study were calculated by fitting ∆L/Lo, where L is either the a-or c-LPs, and Lo are their values at RT, with a linear fit. This method, however, underestimates the uncertainty in the calculated values, as it ignores the variations on the TECs with temperature. Thus, an average linear method was also used to calculate the TECs using discreet derivatives of the measured data. For more details see Refs. [START_REF] Bentzel | A high-temperature neutron diffraction study of Nb2AlC and TiNbAlC[END_REF][START_REF] Lane | A High-Temperature Neutron Diffraction and First-Principles Study of Ti3AlC2 and Ti3(Al0.8Sn0.2)C2[END_REF]

Results and discussion

Columns 5 to 10 in Table 1 summarize the weight percentages of the different phasesobtained from Rietveld analysis -for all 28 runs carried out in this study. The RT XRD for the HIPed samples are plotted in Fig. 1 whereas a typical result of a Rietveld refinement of a XRD didagram is given in Fig. 2. Before proceeding, it is worth noting that the weight percentages listed in Table 1, are not necessarily fully representative of the average composition of each sample. Said otherwise, they need to be taken with a grain of salt because Al loss from the powdered bed samples is not uniform. For example, Al loss was found to be highest near the surfaces exposed to the Ar gas for the pressureless sintered samples. It follows that the exact fraction of each phase obtained will depend on where exactly the XRD were obtained.

Fortunately, this does not affect any of the conclusions reached herein since the TEC results are obtained from the peaks belonging to each phase.

A perusal of the results listed in columns 5 to 10 in Table 1 indicate that for the PS samples of the 211 composition, the 211 phase is predominantly obtained when the reactive sintering temperature was 1400 °C. Nevertheless, even for this temperature, the lowest used in this study, in some cases and especially for the V-rich compounds, Al-loss resulted in the formation of 413 phases for x = 0 composition, and 312 phases for the x = 0.25 and 0.5 compositions. Annealing at 1500 °C and 1600 °C increased the content of the 413 phase for x=0, confirming the loss of Al, whereas for x=0.25 to 0.75, the 312 and 413 phase contents increased at the expense of the 211 phases, the 413 phase formation presumably coming from an Al loss from the 312 phase.

The results shown in columns 5 to 10 of Table 1 also clearly indicate that for the most part, the phase purity of the HIPed samples were significantly higher than those that were PS. It is for this reason that the HIPed samples were -with one exception -the ones used to determine the HT TECs.

Figure 3 shows which of the (Crx,V1-x)n+1AlCn phases have to date been experimentally observed. As noted above, the existence of 211, 312 and 413 phases with x = 0.5 was already known. [START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF] We show here that the same is true for x = 0.25. However, for x = 0.75, apparently only the 211 and 312 phases exist. In agreement with Schuster et al. [START_REF] Schuster | The ternary systems: Cr-Al-C, V-Al-C, and Ti-Al-C and the behavior of H-phases (M2AlC)[END_REF] , however, 211 solid solutions were obtained for the entire 0  x  1 range. The synthesis of a bulk 312 solid solutions appears to also be possible in a large range of Cr contents, at least 0.25 ≤ x ≤ 0.75. Interestingly, we did not find any evidence for the existence of the end members Cr3AlC2 or V3AlC2. Some of the latter have been synthesized in thin film form, however. [START_REF] Scabarozi | Combinatorial investigation of nanolaminate ternary carbide thin films[END_REF] Finally, Fig. 3 clearly shows that the 413 phases can only be obtained for V-rich compounds, viz. in the x ≤ 0.5 range. A precise determination of the maximum values of x for which the 312 and 413 phases remain stable (and the minimum values of x for the 312 phase) requires a more detailed study.

The situation is more complicated for the C-content since it is difficult to quantitatively determine its composition using XRD or Energy Dispersive X-Ray Spectroscopy, especially in samples containing heavier elements such as Al, Cr and V. However, simple mass balance dictates that when the higher order MAX phases are produced from the 211 phases, the former have to be C-deficient. For example, if one starts with a nominal (Cr1-x,Vx)2AlC stoichiometry, Al loss alone should result in (Crx,V1-x)3AlC2(1-0.25) or (Crx,V1-x)4AlC3(1-1/3) for the 312 and 413 chemistries, respectively. Similarly, the loss of Al from a (Cr1-x,Vx)3AlC2 composition should result in (Cr1-xVx)4AlC3(1-1/9) phase.

We can also note that the formation of an amorphous Al4C3 phase (presumably at the grain boundaries) occurred during the synthesis since an odor of methane, generated by a hydrolysis reaction of Al4C3 (Al4C3 + 12 H2O → 4 Al(OH)3 + 3 CH4), was detected after the sintering process as already observed in the literature. [START_REF] Li | Spontaneous pulverisation of Al4C3 containing MAX bulk ceramics at room temperature[END_REF] The formation of the Al4C3 phase would also contribute to a decrease the amount of C in the 312 and 413 phases. Furthermore, as already discussed in the literature, the 312 and 413 phases in the (Cr1-xVx)n+1AlCn system have indeed been found to be C-deficient. [START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF][START_REF] Etzkorn | V2AlC, V4AlC3-x (x ≈ 0.31), and V12Al3C8: Synthesis, Crystal Growth, Structure, and Superstructure[END_REF] It is thus reasonable to conclude that the 312 and 413 phases synthesized in this study are C deficient. We can also propose that for the same Cr:V ratio, different C-contents can be obtained in the 312 and 413 phases depending on the nominal composition of the reactants and on the annealing temperatures. and this was the case when refining every diffractogram obtained in this study. Nevertheless, some of the uncertainties given in Table 2 are much higher. In fact, slightly different LPs were obtained for the same (Crx-1Vx)n+1AlCn compound depending of its synthesis conditions (nominal composition, temperature, synthesis technique, etc.) and this can certainly be attributed to slight variations in the final MAX phase stoichiometries, especially in light of the variations in C and Al contents alluded to above.

The evolution of the average RT LPs, as functions of x and n are given in Fig. 4. From these results it is reasonable to conclude that: i) Vegard's law appears to apply -for all n -with the LPs decreasing linearly with V-content. Such a linear evolution is generally observed in MAX phases solid solutions when mixing either the M or the A sites. Interestingly, a non-linear behavior is observed for solid solutions on the X-sites in Ti2Al(C,N). [START_REF] Cabioc'h | Structural investigation of substoichiometry and solid solution effects in Ti2Al(Cx,N1-x)y compounds[END_REF] The (Cr0.5,V0.5)2AlC, (Cr0.5,V0.5)3AlC2 and (Cr0.5,V0.5)4AlC3 samples are of special interest here since their LPs were previously studied by neutron diffraction in the 1.5 to 500 K temperature range. [START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF] A combination of the neutron and XRD data obtained herein are shown in Fig. 5. Whereas the LPs remain almost constant (i.e. negligible thermal expansion) below 100 K, above this temperature there is a progressive increase of the slopes of the lines, until a linear increase is observed in the 450-1000 K temperature range. It follows that, the TECs of these compounds can be considered more or less constant in this temperature range. It should also be noted that determining the thermal expansion coefficients of polycrystalline materials in different lattice directions (in the present case the a-and c-axis) with XRD may be affected when exhibiting anisotropic thermal expansion due to the fact that the material remains coherent over the temperature range and hence generates local stresses varying on the scale of the grain size.

The functional dependencies of the TCE's along the a and c-directions on x and n are plotted in Fig. 6a and listed in Table 3. Based on these results the following points are salient: i) For the 312, 413 and the 211 compositions for x > 0.5, a > c. ii) The TEC anisotropies of the 312 phases are significantly higher than those of their 211 and 413 counterparts. iii) At x = 0.5, a ≈ c for the 211 series. At this composition the material would thus not accrue any thermal stresses on cooling or heating. Said otherwise, the material should behave as if it was cubic. iv) The TEC's of the 413 solid solutions are smaller than their 211 counterparts. This is further validated when the average TEC's -av = (2αa+αc)/3 -are plotted as a function of x and n (Fig. 6b). From these results, it is clear that av for 211 > 312 > 413. This result is common in the MAX phase in MAX phases but also, quite surprisingly, it demonstrates that there is no straightforward evolution of the isotropic behavior of the TEC as a function of n.

Figure 1 :

 1 Figure 1: X-ray diffractograms obtained at room temperature for HIPed samples with reactants having a (Crx,V1-x)n+1AlCn stoichiometry + 10 at.% of Al.

Figure 2 Figure 3 :

 23 Figure 2 Rietveld refinement of a X-ray diffractogram obtained at room temperature for a HIPed sample with reactants having a (Cr0.25,V0.75)3AlC2 stoichiometry + 10 at.% of Al and with some h-BN grains randomly dispersed on the surface for temperature calibration. The difference between the experimental and computed data is given below the diffractogram (Rw = 11,3%)

Figure 4 :

 4 Figure 4: Evolution of the room temperature LPs of the (CrxV1-x)n+1AlCn phases as a function of x and n (c parameter was divided by 2(n+2) to allow for easy comparisons between the various phases). The error bars are smaller than the symbol size.

Figure 5 :

 5 Figure 5: Relative variation of the a (a) and c (b) lattice parameters of (Cr0.5V0.5)n+1AlCn phases (n=1,2,3) deduced from neutron diffraction data (ND) measured on two different diffractometers.[START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF]

Figure 6 :

 6 Figure 6: Thermal expansion coefficient of (CrxV1-x)n+1AlCn in the temperature range of 450-1000 K, determined by lattice parameters measurement using XRD (a) along the a and c-directions (αa and αc) (b) average av = (2αa+αc)/3.

Table 2

 2

lists the average RT values of the a and c-LPs, of the different phases synthesized herein as deduced from Rietveld refinement. It is well known that precise values of the LPs can be deduced from Rietveld refinement of X-ray and neutron diffractograms (typically 10 -4 -10 -5 Å)

Table 1 :

 1 Phase contents, in wt.%, deduced from Rietveld refinement analysis of XRD patterns (except * deduced from neutron diffraction data[START_REF] Caspi | Ordering of (Cr,V) Layers in Nanolamellar (Cr0.5V0.5)n+1AlCn Compounds[END_REF] ) for (Crx,V1-x)n+1AlCn samples obtained by different techniques (PS: pressureless sintering under Ar flow; HIP: Hot Isostatic Pressing under 80 MPa of Ar) with various dwell time (DT). 211, 312 and 413 phases correspond to (Crx,V1-

	x)n+1AlCn with n=1,2 and 3 respectively. (Cr,V)C phase corresponds to (Crx,V1-x)C carbide with
	the rock salt structure. The samples used for TEC determination are denoted in bold. The
	uncertainty is typically of 1 wt.%.
	Reactants	Synthesis	T	DT (h)	211	312	413 (Cr,V)C Cr2Al Al2O3 Rwp
		technique	(°C)								(%)
				211
	V2Al1.1C	PS	1400	8	84		8			8	14.7
		HIP	1450	4	95		4			1	17.4
		PS	1500	8	28		66			6	15.7
		PS	1600	8			30	53		16	18.9
	(Cr0.25V0.75)2Al1.1C	PS	1400	8	89	5				6	14.6
		HIP	1450	4	100						14.9
		PS	1500	8	39		53			8	15.2
		PS	1600	8	20	12	35			33	18.1
	(Cr0.5V0.5)2Al1.1C	PS	1400	8	76	24				1	23.5
		HIP	1450	4	91	7				2	19.1
		PS	1500	8	5	92				3	14.1
		PS	1600	8	17	43	11			29	18.7
		*PS	1400	1	96				2	2	5.6
	(Cr0.75V0.25)2Al1.1C	PS	1400	8	100						16.7
		PS	1500	8	94					6	13.4
		PS	1600	8	78	20				2	12.2
	Cr2Al1.1C	PS	1400	8	100						14.9
		PS	1500	8	100						17.5
		PS	1600	8	100						13.2
				312
	V3Al1.1C2	PS	1450	8	10		87			3	16.8
	(Cr0.25V0.75)3Al1.1C2	PS	1450	8		48	49			3	15.8
		HIP	1450	4			100				11.3
	(Cr0.5V0.5)3Al1.1C2	*PS	1500	1	3	95		1	2		5.4
		PS	1450	8		13	60	21		7	13.3
		HIP	1450	4	25	74				1	11.2
				413
	V4Al1.1C3	HIP	1450	4	5		70	25			14.3
		PS	1450	8			21	72		7	20.4
	(Cr0.5V0.5)4Al1.1C3	*PS	1400	3	3	3	81	7	5	1	3.3

Table 2 :

 2 Lattice parameters of (Crx,V1-x)n+1AlCn compounds determined by Rietveld analysis of RT XRD data from samples synthesized in this work. Also listed for comparison are literature values.

	n	x (Cr content)	a (Å)	c (Å)	ref
	1	0	2.918(2)	13.142(1)	This work
			2.9107(6)	13.101(4)	37
			2.909	13.127	25
		0.25	2.9046(6)	13.038(3)	This work
			2.903	13.054	25
		0.5	2.891(1)	12.975(7)	This work
			2.89237(4)	12.9749(3)	19
			2.893	12.970	25
			2.885	12.94	26
		0.75	2.8774(1)	12.886(2)	This work
			2.873	12.928	25
		1.0	2.8643(1)	12.822(1)	This work
			2.866	12.825	25
	2	0.25	2.909(1)	17.848(4)	This work
		0.5	2.8948(5)	17.747(5)	This work
			2.89502(4)	17.7529(3)	19
			2.892	17.73	26
		0.75	2.889(1)	17.657(3)	This work
	3	0	2.9277(6)	22.693(1)	This work
			2.9302(4)	22.745(5)	37
		0.25	2.9187(3)	22.561(1)	This work
		0.5	2.910(2)	22.43(3)	This work
			2.91036(7)	22.4169(9)	19
			2.905	22.39

Table 3 :

 3 Thermal expansion coefficient determined from Rietveld analysis of (Crx-1,Vx)n+1AlCn XRD patterns.

		αa (µK) -1	αc (µK) -1		Anisotropy (αa /αc)	(2αa+αc)/3 (µK) -1	Ref.
			211	Cr2AlC
	Linear fit	13.3	11.7		1.14	12.77	23
			211		(Cr0.5,V0.5)2AlC
	Linear fit	11.4(2)	11.4(2)		1.0(1)	11.4(6)	This work
	Avg. linear	11.2(7)	11.1(6)		1.01(2)	11.2(7)	This work
			211 (Cr0.25,V0.75)2AlC
	Linear fit	10.5(6)	11.1(7)		0.95(11)	10.7(19)	This work
	Avg. linear	10.5(2)	11.0(6)		0.95(1)	10.7(3)	This work
			211	V2AlC
	Linear fit	9.6(2)	9.6(6)		1.0(1)	9.6(10)	This work
	Avg. linear	9.0(1) OK?	9.4(4)		0.9(0.1)	9.1(8)	This work
			312		(Cr0.5,V0.5)3AlC2
	Linear fit	12.7(5)	8.0(3)		1.6(2)	11.1(13)	This work
	Avg. linear	12.6(7)	9.0(2)		1.40(5)	11.0(7)	This work
			312	(Cr0.25,V0.75)3AlC2
	Linear fit	12.0(5)	7.5(5)		1.6(2)	10.5(15)	This work
	Avg. linear	12.0(1)	7.70(2)		1.60(2)	11.0(7)	This work
	413		413	(Cr0.5,V0.5)4AlC3
	Linear fit	10.2(5)	8.8(2)		1.16(8)	9.7(12)	This work
	Avg. linear	10.0(1)	9.0(2)		1.1(3)	9.7(1)	This work
			413	(Cr0.25,V0.75)4AlC3
	Linear fit	9.0(2)	8.6(1)		1.05(4)	8.9(5)	This work
	Avg. linear	9.4(2)	9.9(5)		1.06(3)	9.2(3)	This work
			413	V4AlC3
	Linear fit	9.1(1)	8.65(4)		1.05(2)	8.9(3)	This work
	Avg. linear	9.2(4)	8.8(2)		1.05(3)	9.1(3)	This work

and simply reflects the fact that the thermal expansions of the M-A bonds are typically larger than the MX bonds. Apart from these comments, there are unfortunately little more generalizations that can be reached. Some of the variables that could have been in principle been used to shed more light on these results -such as ordering of the M-atoms and/or C-vacanciesare lacking and must await more in-depth characterization and/or ab initio calculations.

Summary and Conclusions

(Crx, V1-x)n+1AlCn compounds were synthesized, with n =1, 2 and 3, by pressureless sintering and/or HIP. A complete range of solid solution with the MAX phase structure was obtained for n = 1. For n=2, (Crx, V1-x)3AlC2 compounds were characterized only for x varying from 0.25 to 0.75 whereas (Crx, V1-x)4AlC3 were obtained for vanadium-rich compounds (0≤x≤ 0.5). The lattice parameters of all these MAX phases were determined by Rietveld refinement of XRD diagrams obtained for temperatures varying from RT to 800 °C. At RT, the values of the a and c lattice parameters linearly decrease with vanadium content. As a function of the temperature, a linear increase of the lattice parameters was observed above 450K. Thermal expansion coefficients of the different phases were deduced from Rietveld refinement of XRD diagrams obtained at elevated temperatures. As a general trend, the average TEC decreases with the value of n. TEC values vary from 12.8 K -1 to 9.1 K -1 for n= 1, and remain almost constant around 10 K -1 and 9 K -1 for n= 2 and 3 respectively. (Crx, V1-x)2AlC and (Crx, V1-x)4AlC3 solid solutions have almost isotropic TEC (i.e. a ≈ c). On the contrary, for (Crx, V1-x)3AlC2 compounds, an anisotropic behavior is obtained, the TEC along the a-axis being 60% larger than along the c-axis. This study confirms the possibility to tailor TECs by using solid solution effects