Antonia López-Villavicencio

Maria Cervini Pla

Antonia Lopez-Villavicencio

The mental health consequences of globalisation *

Keywords: JEL Classification: F60, I1, C33 Mental Health, globalisation, anxiety, depression

Micro evidence for employed workers has led to the claim that globalisation, i.e. higher trade exposure, has far-reaching implications for mental health problems in some advanced countries. Evidence for other aspects of globalisation at the cross-country level is scarce. Using information on depression and anxiety, combined with proxies for different dimensions of globalisation, we undertake a detail analysis in a large sample of countries. We go beyond the simple impact of globalisation in observable labor market outcomes and show that more globalized counties experience higher mental distress than less globalized countries. In particular, we show that even though trade globalisation reduces mental health disorders at the country-level, the positive influence of social globalisation prevails over the economic dimension. Hence, our results complement documented consequences of globalisation on mental health outcomes by showing that factors involving cross-border movement of cultures and openness of media play a major role.

Introduction

Today, about 970 million people around the world suffer from a mental or substance use disorder. In particular, according to WHO's Global Burden of Disease 2017, the largest number of these people had an anxiety or depression disorder (around 4 and 3.3 percent of the global population, respectively). Twenty percent of workers in the OECD countries currently suffer from some form of mental disorder and 50% of people experience mental health problems at least once over their lifetime [START_REF] Colantone | Globalization and mental distress[END_REF]). Moreover, even though mental health disorders are still significantly under-reported, particularly at lower incomes where data is scarcer, it is estimated that almost three-quarters of the global burden of disease worldwide occurs in low-and middle-income countries.

Mental disorders are not limited to a small group of predisposed individuals but are a major public health problem with noticeable economic consequences. Indeed, it is projected that, between 2011 and 2030, the cumulative economic output loss associated with mental disorders would be around US$ 16.3 trillion worldwide, making the economic output loss related to mental disorders comparable to that of cardiovascular diseases, and higher than that of cancer, chronic respiratory diseases, and diabetes (see [START_REF] Trautmann | The economic costs of mental disorders: Do our societies react appropriately to the burden of mental disorders?[END_REF]). Moreover, evidence suggests that there is a negative correlation between prevalence of particular mental health disorders (depression and anxiety have been the most widely assessed) and self-reported life satisfaction. This suggests that life satisfaction and happiness tends to be lower in individuals experiencing particular mental health disorders. Mental health is also known to be an important risk factor for the development of substance use disorders (either in the form of alcohol or illicit drug dependencies).

A recent literature associates the prevalence of mental disorders for employed workers in advanced economies with the process of globalisation. Even though much of this work is rather limited in its geographical scope and/or in their concept of globalisation, i.e. flow of goods, it is useful in delineating the sorts of factors that link mental health to the forces of globalisation. For instance, [START_REF] Colantone | Globalization and mental distress[END_REF] suggest that, by increasing competitive pressures, trade can carry significant mental health problems for exposed workers in the U.K. In particular, they document that import competition worsens mental distress by inducing greater job displacement, lower wage growth and a reduction in job satisfaction due to heavier workload, greater job insecurity and gloomier expectations about the future. In a similar vein, [START_REF] Lang | The effects of import competition on health in the local economy[END_REF] provide evidence that Chinese import competition, i.e. the "China syndrome", in local labor markets tends to worsen stress, anxiety, and depression in the U.S. Evidence focusing explicitly on the effects of globalisation on mental health in emerging economies has been com-paratively limited so far. A useful exception is [START_REF] Crozet | Looking for the Bright Side of the China Syndrome: Rising Export Opportunities and Life Satisfaction in China[END_REF] that using data from the China Family Panel Studies they look at the other side of "China syndrome" and investigate the repercussions from enhanced exports on Chinese well-being. Their results show that enhanced export opportunities improve life satisfaction of the local population. However, they do not observe any negative effects on mental health following rapid export growth.

In this paper, we make several novel contributions to the literature. First, we consider globalisation as a comprehensive, multidimensional process that covers not only economic, as it is usually the case, but also social and cultural aspects. Understanding globalisation as a multidimensional process is closer to the common usage and definitions of the term than an individual indicator like trade openness, and helps to account for the possibility that the comprehensive concept may be more than the sum of its constituent parts (e.g. [START_REF] Lang | The effects of import competition on health in the local economy[END_REF]). Relying on this aggregate concept of globalisation also allows us to avoid possible collinearity and simultaneity problems with multiple interrelated dimensions of globalisation (e.g., trade, capital flows, technology diffusion, liberalization policies).

The influences of individual factors on mental health are then addressed separately. Disentangling the multidimensional concept of globalisation is also important. Indeed, globalisation is a complex network of interrelated processes which could impact mental health of a nation's population in opposite directions. For instance, trade globalisation might be seen as a work-related risk factor for individuals working in an industry exposed to a stronger foreign competition. However, it is important to keep in mind that mental disorders are not limited to this group of individuals. Cultural or social cross-communication are key factors in the breakdown of boundaries in the world that might impact mental health more generally than just in exposed workers [START_REF] Kelly | Globalisation and psychiatry[END_REF]). In particular, it is suggested that modalities such as the internet, film and television, are factors that play a key role in enhancing globalisation, can lead to identity confusion among individuals and be a source of stress (e.g. [START_REF] Bargh | The Internet and Social Life[END_REF], [START_REF] Arnett | The Psychology of Globalization[END_REF]). Yet, globalisation also implies increasing levels of trade in health services, such as movement of health workers, medical tourism, and foreign direct investment, all of them with potentially positive effects of mental distress. Therefore, we consider the following aspects: economic flows (trade and financial), social flows (migration, exports of technology and trade in personal services) and social liberalization indicators (access to telephone, television and internet). The influences of these individual factors on mental health in the total population should be addressed separately, while keeping in mind the fact that one group of processes very often amends the other.

Second, we rely on a large sample of countries, allowing us to go beyond a case study with a simple comparison of national conditions. Our analysis explores the influence of globalisation on mental health worldwide and, separately, for advanced and emerging countries. This distinction is important since most of the consequences of globalisation may be totally different for these two groups of countries. Indeed, the literature provides evidence of a positive link between trade and mental distress in some western countries. The arguments is that the changing nature of work, i.e. the increasing fragmentation of the labour market, the demand for flexible contracts, increased job insecurity, a high work pace, long and irregular working hours, low control over job content and process, and low pay, together with new occupational hazards related to the globalisation process act as acculturative stressors (e.g [START_REF] Colantone | Globalization and mental distress[END_REF] or [START_REF] Lang | The effects of import competition on health in the local economy[END_REF]). However, there are potential mechanisms working in the opposite direction, particularly in emerging countries. For instance, globalisation, in theory, intends to provide more jobs, specially for low-income workers in developing countries, and this work in return can contribute to lower distress among the population. While the precise impact of different manifestations of globalisation in developing countries is hard to predict, it may at least be conceivable that data tell a different story compared to western countries.1

Overall, the process of globalisation clearly has both negative and positive results and it is likely to create both losers and winners. Since there is no clear a priori effect of globalisation on mental distress at the country level, the sign and magnitude of the effects are thus open to empirical investigation. To the best of our knowledge, this is the first paper that put together data covering 67 countries for the 1990-2016 period, providing the largest data set that can be used in empirical studies linking globalisation and mental health.

Our results show that, at the multidimensional level, there is a positive relationship between globalisation and both depression and anxiety. However, unlike previous studies based on employed workers, this study finds that trade globalisation reduces depression and anxiety at the country level. The overall positive effect is then explained by a strong, positive, influence of the social component of globalisation. Indeed, factors linked to cross-border movement of cultures and openness of media, e.g. migration, telephone subscriptions, the share of households with a television and individuals using internet, etc, prevail over the economic dimension. In sum, our findings suggest that globalisation appears to be neither the magic solution to improve life conditions, as some proponents would claim, nor an unmanageable risk for mental distress, as others have sought to portray it. Our paper provides complexity and diversity of the outcomes.

In what follows, Section 2 reviews the existing literature that represent the point of departure for our analysis. Section 3 introduces the data set and presents some descriptive statistics. The empirical analysis is found in the sections that follow. Section 5 presents the results. Finally conclusions are presented in Section 6.

Evidence on globalisation and mental health

There is a broad literature that analyses the effects of globalisation on labour market outcomes, in most cases using micro data. For example, [START_REF] Autor | The China Syndrome: Local Labor Market Effects of Import Competition in the United States[END_REF] explore the effect of rising Chinese import competition between 1990 and 2007 on US local labour markets. They find that rising imports cause higher unemployment, lower labor force participation, and reduced wages in affected local labour markets. [START_REF] Mcmanus | The effects of import competition on worker health[END_REF] explore how the international trade affects occupational safety in US manufacturing industries. Using Chinese import growth in 1996-2007 as a shock of competition, they find that import competition increase work place injuries, especially at small firms that are most affected by foreign imports.

Regarding mental health, most of the research also relies on micro data. For example, [START_REF] Bechtel | Income Inequality And Mental Health-Empirical Evidence From Australia[END_REF] analyse the causal relationship between income inequality and mental health in Australia. They find that mental health is only adversely affected by the presence of relative deprivation to a very small degree. Using data for the UK, [START_REF] Dustmann | The Effect of Local Area Crime on Mental Health[END_REF] explore the effect of local crime rates on the mental well-being of the population and find that crime causes considerable mental distress of residents, especially property crime. Another example is [START_REF] Farré | Feeling useless: the effect of unemployment on mental health in the Great Recession[END_REF] that show strong connection between unemployment and mental disorders using data from the Spanish Health Survey. Exploiting the collapse of the construction sector to identify the causal effect of job loss, they find that an increase of the unemployment rate by 10 percent due to collapse of the sector, raised mental disorders in the affected population by 3 percent.

The relationship between globalisation and mental health is more scarce. As far as we know, most of the literature relies on survey data for employed workers in some advanced economies. For instance, using Danish data on individuals' health and Danish matched worker-firm data, [START_REF] Hummels | No Pain, No Gain: The Effects of Exports on Effort, Injury, and Illness[END_REF] find that when firm exports rise for exogenous reasons, the hazard rates of worker-level stress, injury and illness increase.2 Recently, [START_REF] Colantone | Globalization and mental distress[END_REF] study the effect of import competition on workers' mental distress using information on mental health of workers from the British Household Panel Survey combine with measures of import competition in more than 100 industries over 1995-2007. They provide evidence that an increase in import competition has a positive, statistically significant, and large impact on mental distress. In particular, for a one standard deviation increase in import competition, a worker would need a yearly monetary compensation of 180 British pounds to make up for the ensuing utility loss. They detect that import competition worsens mental distress through greater job displacement, lower wage growth, a reduction in job satisfaction due to heavier workload, greater job insecurity and gloomier expectations about the future, in terms of career progression and overall financial perspectives. Similarly, [START_REF] Lang | The effects of import competition on health in the local economy[END_REF] show that average mental, physical, and general health worsens for employed workers in local U.S. labor markets exposed to greater import competition from China.3

For emerging economies, also using micro data, [START_REF] Crozet | Looking for the Bright Side of the China Syndrome: Rising Export Opportunities and Life Satisfaction in China[END_REF] explore the inverse of the China syndrome: they analyse the extent to which increased export opportunities have influenced well-being of Chinese workers. The analysis is based on panel data covering approximately 25,000 adults across 122 Chinese localities in 2010, 2012 and 2014. Their results show that perceived life satisfaction has improved significantly when local export markets have increased, beyond improving local GDP per capita and individual incomes. However, they fail to find evidence of deteriorating physical and mental health following greater exposure to international markets as suggested by [START_REF] Hummels | No Pain, No Gain: The Effects of Exports on Effort, Injury, and Illness[END_REF]. Similarly, [START_REF] Tanaka | Exporting Sweatshops? Evidence from Myanmar[END_REF] provides evidence that exporting has large positive impacts on working conditions for workers in Myanmar. In particular, exporting leads to the adoption of better fire safety and health management, improvement in interactions with unions (including allowing unions), and increases in wages. As in [START_REF] Crozet | Looking for the Bright Side of the China Syndrome: Rising Export Opportunities and Life Satisfaction in China[END_REF], there is no evidence on the causal effects of exporting on mental health.

Data and Conceptual Issues

In this section we present the main variables that we use for the empirical analysis. We start by presenting the measurements of mental health. We then describe the different indicators for globalisation as well as the control country-level factors.

A. Mental Health

The data currently available from population-based surveys on mental health are often limited to a few specific mental health disorders. Fortunately, the Institute for Health Metrics and Evaluation (IHME) from the University of Washington provides estimates of the prevalence of a wide range of mental health disorders across all age groups based on a wide variety of data sources and a set of assumptions in their IHME's Global Burden of Disease (GBD). This is currently one of the only sources which produces global level estimates across most countries on the prevalence and disease burden of mental health. 4We concentrate on the prevalence of depression and anxiety for 65 countries over the 1990-2016 period. According to the World Health Organization (WHO) depressive disorders are characterized by sadness, loss of interest or pleasure, feelings of guilt or low self-worth, disturbed sleep or appetite, feelings of tiredness, and poor concentration. Depression can be longlasting or recurrent. Anxiety disorders, in turn, refer to a group of mental disorders characterized by feelings of anxiety and fear, including generalised anxiety disorder (GAD), panic disorder, phobias, social anxiety disorder, obsessive-compulsive disorder (OCD) and post-traumatic stress disorder (PTSD). As with depression, symptoms can range from mild to severe. The duration of symptoms typically experienced by people with anxiety disorders makes it more a chronic than episodic disorder. As seen in tables 1 and 2, prevalence of depression vary by country, from a low of 2.3% in Poland to 5.6% of the population in Morocco in average over the studied period. In the case of anxiety, a 2.0% of the population is affected in Vietnam compared to 8.7% in New Zealand. Note that the prevalence also differs by country group, the average depression and anxiety being both higher in advanced economies. 5

B. globalisation

We first use the composite index of of globalisation as proposed by [START_REF] Dreher | Does globalization affect growth? Evidence from a new index of globalization[END_REF]. This widely used index combines economic, social and political dimensions to measure the concept in a multidimensional way. 6 One of the great advantages of this index (The KOF index) is that it provides a comprehensive concept of globalisation that considers the interaction and integration among people rather than a more narrow term to refer only to international trade. It also allows us to disaggregate the social and economic dimension of globalisation that we use for the subsequent analysis. The index takes values from 1 to 100 with high values indicating high level of globalisation. Tables 1 and2 provide averages over the 1990-2016 period for each country. As expected, the globalisation indicator is larger in advanced than in emerging countries (81.3 and 63, respectively). Within the advanced countries, Belgium presents the highest indicator and Greece the lowest (87.8 and 75.01, respectively). Regarding emerging countries, the differences are even larger, with Singapore averaging 80.3 and Laos with a low 36.

One of the advantages of the globalisation index is that it can be decompose into economic globalisation and social globalisation. In particular, economic globalisation includes i) trade, hidden import barriers, mean tariff rate, taxes on international trade (in percent of current revenue) and ii) financial globalisation that captures foreign direct investment, portfolio investment, international debt, income payments to foreign nationals, investment restrictions and capital account openness. On the other hand, social globalisation includes: i) interpersonal, factors such as international voice traffic, transfers, international tourism, migration, telephone subscriptions, freedom to visit and international airports; ii) informational factors as Patent applications, number of international students, share of households with a television set and individuals using the internet and, iii) cultural factors capturing trade in cultural goods, trademark applications, trade in personal services, number of Mc-Donald's restaurants and IKEA stores, gender parity expenditure on education and civil freedom.

As Tables 1 and2 show, social globalisation is higher in both groups of countries compared to economic globalisation. For advanced countries, the social globalisation index is 81.7, while economic globalisation is 73.7. In the case of emerging countries, both social and economic globalisation are lower than for advanced economies (58.3 and 55.8, respectively). We can also observe that there seems to be a high correlation between the two dimensions of globalisation: countries that have high economic globalisation, in general, present high social globalisation. However, we observe countries with a higher index of economic globalisation than social globalisation like Luxembourg or Vietnam, and on the other side countries with a higher social globalisation index compare to economic globalisation like Australia or Colombia. 7 The relationship between globalisation and mental health is shown in Figures 1 and1. The figures on the left show the relationship between globalisation and depressions and figures at the right show that between anxiety and globalisation. In Figure 1 each point represents a combination of a country in a given year. Figure 2 shows relationships between the average globalisation score and average mental health for a given country. These figures seem to indicate a positive relationship between the broad concept of globalisation and mental distress. Let us now investigate these links in more detail.

C. Additional Variables

The factors involved in mental health are many and varied. In addition to the aforementioned indicators of globalisation, we include a series of control variables, most of them borrow from the psychology and sociology literature or from micro-oriented studies: the natural logarithm of GDP per capita (in constant US dollars), the percentage of urban population (% of total), the percentage of industrial employment (% of total employment) and the unemployment rate. In all cases, data was extracted from the World Bank's World Development Indicators.

The relationship between a country's GDP and mental health is ambiguous. Some studies conclude that richer countries tend to have a higher proportion of the population with mental problems (Ayelet Meron Ruscio (2017)). However, it could be argue that rich countries have more ability to reduce mental disorders through a wide array of mechanisms such as improved capacity to purchase and provide health care -including mental health-, increased government welfare policies, and higher levels of educational attainment, presumably leading to better mental health behavior [START_REF] Knapp | Economic barriers to better mental health practice and policy[END_REF]).

We also controlled for urbanization and industrialization. The arguments to do so are several. First, there is evidence that urbanization leads to a massive increase in behavioral disturbance as well as depressive and anxiety disorders. The proposition is that breakdown of families, overcrowded physical environments, high levels of violence and accidents, insecure tenure and poor housing, social deviance, competition, class conflict, poverty or economic disparity, among other factors, could be traced to many of the social processes accompanying urbanization and industrialization (see [START_REF] Harpham | Urbanization and mental health in developing countries: A research role for social scientists, public health professionals and social psychiatrists[END_REF], [START_REF] Marsella | Urbanization, mental health, and social deviancy: A review of issues and research[END_REF], [START_REF] Bibeau | Cultural psychiatry in a creolizing world: questions for a new research agenda[END_REF], among others). Moreover, access to the natural environment and outdoor spaces are believe to reduce stress, anxiety and depression (e.g. Beyer, et. al. and Reklaitiene, et. al.). However, the opposite relationship can also be justified since urbanization may provide better access to proper sanitation and health -including mental health-care services (See [START_REF] Ruhm | Are Recessions Good for Your Health?[END_REF] and [START_REF] Ruhm | Are Recessions Good for Your Health?[END_REF]).

Finally, we also include the unemployment rate. Indeed, unemployment is one of the most important determinants of physical and mental health. A number of theoretical contributions justify a positive relationship. For instance, in his life-span development theory [START_REF] Erikson | Identity and the Life Cycle[END_REF] postulates that healthy emotional well-being among adults depends on the capacity to economically contribute to the family and, more generally, the society. Alternatively, [START_REF] Jahoda | Employment and Unemployment: A Social-Psychological Analysis[END_REF] and [START_REF] Warr | Work, Unemployment and Mental Health[END_REF] claim that unemployment negatively affects mental health since it prevents a person from obtaining the non-monetary benefits of work -such as a structured day, shared experience and opportunities of creativity and mental development. A large body of empirical studies, such as [START_REF] Linn | Effects of unemployment on mental and physical health[END_REF], Kim, et. al or Farré, Fasani, and Mueller (2018), also report a negative association between unemployment and a mental health.

Empirical Implementation

Starting with the most parsimonious model, we are primarily interested in how mental health is affected by various manifestations of globalisation:

M H it = α i + δ t + βGlob it-1 + βX it-1 + ε it ; i = 1, . . . , C, t = 1, . . . , T, (1)
where M H it represents one of the dependent variables of interest (i.e., depression, anxiety) in country i for period t -C and T are the number of countries and time periods, respectively-, Glob denotes globalisation, X the vector of control variables described above, α i and δ t are full sets of country fixed effects and period fixed effects, respectively and ε is the error term. The parameter of interest is β, the causal impact of globalisation on mental health.

Unavoidably, our strategy undergoes from several limitations. Most of them are data-related. Indeed, using aggregate cross-country level data rather than individual level data impede us to use information on the objectively measured mental health status of each individual and to control for relevant individual-level characteristics such as education, age or household size, etc. These are features that should increase the analytical precision. Having said that, by using country-level information of depression and anxiety, we are able to go beyond the purely economic effects in terms of employed workers and, therefore, to draw some major causal claims about our findings.

Moreover, examining the causal effect of globalisation on mental health is challenging and some potential problems need to be taken into account: unobserved heterogeneity and possible endogeneity of different explanatory variables. Unobserved heterogeneity is based on the circumstance that even a careful selection of determinants cannot ensure that all differences between the countries under consideration are adequately accounted for. If these unobserved characteristics correlate with the dependent variable or the control variables under consideration, the explanatory power of unobserved characteristics may falsely be assigned to other determinants. Thus, unobserved heterogeneity can result in distorted OLS estimates for all determinants. For this reason, fixed effects models were used in the analysis. These control for differences between the countries that can assumed to be approximately constant over the observed period of time.

Endogeneity problems can occur when interdependencies exist between the dependent variable and one or more determinants. Reverse causality, however, should not be an issue in our case, because a country's globalisation process is unlikely to be driven by the current realization of mental distress. However, all independent and control variables are lagged by one year to mitigate the possibility of simultaneity or reverse causality bias.

Results

We now present the empirical results. We start by showing the influence of the broad concept of globalisation on mental distress. We then "unpack" the overarching concept of globalisation into its constituent parts.

globalisation and mental health: baseline

The baseline estimates of eq.( 1) are reported in Table 5.1. 8 In columns (1) and (3), we show estimates of a parsimonious specification, in which depression or anxiety are regressed only on the globalisation indicator, the (log) GDP per capita and individual and time fixed effects. These results show that globalisation induces a significant increase in mental distress, the coefficients β being positive and significant. The regression results can be interpreted as follows: If the globalisation index rises by one standard deviation, the percentage of the population with depression or anxiety increases by about 0.03 and 0.04 percentage points respectively (which is around an increase of 1% in the proportion of people with this problem). However, as this association may in part be driven by country-level confounding, it is also important to consider its robustness by including relevant controls. In column ( 2) and ( 4), we show that the adding of country level controls reduces the magnitude of the association, although the parameters for the globalisation dummies remain positive and significant at the 5% level.

Looking at the effect of the main control variables, higher income per capita is associated with lower mental distress, reflecting probably rich countries' ability to reduce mental disorders through a wide array of mechanisms, including improved capacity to purchase health care, increased government welfare policies, and higher levels of educational attainment, presumably leading to better personal mental health behavior. On the contrary, a higher proportion of the population employed in industry relates to higher mental distress risk. Interestingly, the unemployment rate and a high proportion of people residing in urban areas have opposite effects on depression and anxiety: an increase of the scores are associated with higher depression risk but lower anxiety.

The table also shows some interesting results in terms of the differences between emerging and advanced economies. The results in column ( 5), ( 7), ( 9) and ( 11), without controls for any factors except country and time dummies and GDP per capita, indicate that greater globalisation is associated with a lower (higher) risk of being mentally distressed in emerging (advanced) countries. Even though controlling for individual covariates reduces the magnitude of the association, the signs remain the same, except in the case of depression in emerging countries which becomes non significant. These results suggest that globalisation may be perceived as an opportunity in emerging countries, reducing anxiety and depression.

Decomposing globalisation Measures

As we mentioned above, the first goal of our study is to analyse the causal impact of globalisation. Our empirical approach is thus tailored to answering this question. Its applicability to testing individual channels might be more limited given the collinearity and simultaneity problems that bias estimates when the effects of numerous interconnected dimensions of globalisation (e.g., trade, capital flows, migration, etc) are tested simultaneously.9 Keeping this in mind, we can still gain further insight on the effects of globalisation by unpacking the aggregate index into its two main components, economic and social globalisation, and add them, one at the time, and then together, to the baseline regressions. These gradual steps allow us to provide more robusts results. Indeed, on the other hand, we avoid collinearity between different subcomponents. On the other hand, putting these scores together in the same model help us to consider the more realistically hypothesis that the different aspects of the globalisation process occur simultaneously. Note also that given the evidence of heterogenous effects of globalisation across sub groups of countries, we perform the subsequent analysis distinguishing advanced and emerging countries. Table 5.2 presents the main results. Columns (1), ( 2), ( 5), ( 6), ( 7), ( 8), ( 11) and ( 12) in Table 5.2 assess the influence of economic globalisation on mental distress. The results indicate that, in general, a higher score is associated with lower depression or anxiety in emerging economies, even when we add country control to the models. However, our empirical analysis does not reveal a significant effect of economic globalisation on advanced countries.

In Table 5.2 we also consider the association between social globalisation and mental distress. It is evident that this dimension has the most stable and pronounced association with both depression and anxiety, as adding different sets of control variables changes the magnitude of the association only slightly. This result remains valid even when we consider both globalisation indices together. Depending on the specification, a one standard deviation on the social globalisation index is associated with an increase the share of the population with a mental distress between 0.04 and 0.18.

The final step of our analysis consists of a further disaggregation of the economic and social dimensions of globalisation in order to better understand the underlying mechanisms. Therefore, economic globalisation consists of trade and capital flows and tariffs and import barriers. Social globalisation, in turn, captures individuals' exposure to external ideas, people, and information flows and is disaggregated into interpersonal (telephone, traffic, tourism, etc), informational (internet users, televisions per capita) and cultural (ikea and McDonald's, gender parity, etc) proximities. Even though some aspects of the index may appear problematic (i.e. the idea that the number of McDonald's is an appropriate measure of cultural proximity), in the absence of other comprehensive measures of globalisation we rely on these measures as by far the best existing measures of globalisation. Table 5.2 present the estimated coefficients of our variables of interest.10

The results for emerging economies, which are presented in panel (A) in table 5.2, show that higher trade integration reduces mental distress in most specifications but may constitute a risk-factor for depression in emerging economies. Although, arguably, the biggest attention has so far been directed at the negative impact of trade flows in mental health for employed workers, our results show that, at the country level, trade globalisation process may reduce the risk of mental disorders.

Finally, in table 5.2 we also present the results related to the disaggregation of social globalisation. In line with the results of the previous Section, individuals' exposure to external ideas, people, and information flows are strongly positively related to greater mental disorder risk, particularly in advanced countries. This result may suggest, for instance, that excessive or "maladaptive" use of phones, internet, television, etc. may lead to greater incidences of depression and anxiety in users. It is, however, tricky to parse out whether or not excessive social globalisation causes these symptoms, or rather if it just exacerbates existing depression and anxiety.

Conclusions

Mental disorders are an important public health problem in our society with noticeable economic consequences. Globalisation has often be held responsible for attenuating mental health disorders. The existing evidence for this claim, however, consists mostly of case studies linking some economic aspects of globalisation, i.e. trade integration, and some labour market outcomes for employed workers in advanced countries. Quantitative measures of the range of potentially very different globalisation-related drivers involved have not been examined so far. In this paper we explore the association between two expression of mental disorder, namely depression and anxiety, with globalisation. Importantly, we disentangle the economic and social dimensions of globalisation in order to provide a richer analysis.

Using aggregate country level data we find that the relationship between mental distress and globalisation depends on the specific dimension of globalisation. Indeed, we find that greater globalisation is associated with more depression and more anxiety. In particular, if the globalisation index rises by one standard deviation, the percentage of the population with depression or anxiety increases by about 0.03 and 0.04 percentage points, respectively. In addition to our main result, our analysis generates findings worthy of further examination. First, we find that our main results are driven by social globalization. Specifically, while the social globalisation dimension appear strongly positively related to mental distress, the same is not apparent for economic globalisation. This is a rather surprising finding, given the focus of most of the literature on the link between mental distress of employed workers and economic -trade-globalisation.

Second, exploring the differences between emerging and advanced countries, we observe that higher globalisation is associated with greater mental problems in advanced countries. However, this is not the case in emerging economies. This is related to the fact that in these countries, higher economic globalisation is associated with lower anxiety and depression, counteracting the negative effect of social globalisation. In the advanced countries, in turn, there is no effect of economic globalisation; we only observe that higher social globalisation is associated with greater mental problems.

If globalization is having a significant impact on the risk of mental health as our results show, then there is a need for additional mechanisms able to protect mental health during the globalizing process. Moreover, given that social globalisation seems to be the main driver of mental distress, our results merit further research to gain knowledge on the specific mediating mechanisms related to the cross-border movement of cultures and openness of media.

Annex

Figure 1 :

 1 Figure 1: Depression, Anxiety and globalisation. Overall

Figure 2 :

 2 Figure 2: Depression, Anxiety and globalisation. Country averages

  errors in parentheses. Estimations include country and time fixed effects. ***, **, * = indicate significance at the 1, 5 and 10% level.

  errors in parentheses. Estimations include country and time fixed effects. ***, **, * = indicate significance at the 1, 5 and 10% level.

  errors in parentheses. Estimations include country and time fixed effect and the following control variables: (log) GDP per capita, unemployment rate, percentage of the population employed in the industry and percentage of the population living in urban areas.. ***, **, * = indicate significance at the 1, 5 and 10% level.

Table 1 :

 1 Average Depression and Anxiety in the period. Advanced countries

	Mental health globalisation	Depression Anxiety globalisation Economic globalisation Social globalisation	4.80 6.54 77.75 63.52 82.21	3.43 5.36 85.87 79.07 84.37	3.88 5.22 87.83 85.77 82.09	4.03 5.22 80.94 65.87 86.07	3.96 5.34 87.04 79.83 88.17	3.90 6.64 84.09 74.80 82.00	3.51 5.31 86.20 80.79 85.77	3.52 5.13 79.33 69.17 74.97	5.20 3.73 83.44 77.37 82.34	4.38 6.69 83.44 72.92 80.32	4.17 4.63 86.39 77.48 85.07	4.21 5.76 75.08 63.88 73.61	4.29 5.77 82.03 87.96 83.59	3.47 5.28 69.91 65.88 84.49	3.49 5.51 78.29 65.29 73.95	3.09 3.54 69.60 52.28 72.96	3.81 5.33 82.99 89.41 88.07	4.09 6.82 86.95 85.78 80.65	3.75 7.64 83.67 74.40 88.13	4.10 8.66 75.69 70.93 81.60	4.71 5.36 77.70 71.82 72.40	4.58 5.32 86.81 78.87 86.52	4.74 6.74 78.11 61.61 79.56	4.05 5.70 81.27 73.72 81.69
			Australia (AUS)	Austria (AUT)	Belgium (BEL)	Canada (CAN)	Switzerland (CHE)	Germany (DEU)	Denmark (DNK)	Spain (ESP)	Finland (FIN)	France (FRA)	Great Britain (GBR)	Greece (GRC)	Ireland (IRL)	Island (ISL)	Italy (ITA)	Japan (JPN)	Luxembourg (LUX)	Netherlands (NLD)	Norway (NOR)	New Zealand (NZL)	Portugal (PRT)	Switzerland (SWE)	United States (USA)	Group mean

Table 2 :

 2 Average Depression and Anxiety in the period. Emerging countries

	Mental health globalisation	Depression Anxiety globalisation Economic globalisation Social globalisation	3.64 6.24 64.50 43.22 61.11	2.92 3.58 72.39 67.26 65.60	3.17 4.24 55.31 49.48 48.58	3.71 6.07 54.54 36.98 50.40	4.21 6.24 69.61 63.61 64.12	3.44 3.18 55.32 41.65 40.78	2.32 2.62 54.34 42.07 53.49	3.31 5.29 69.81 66.43 78.16	2.80 3.45 78.81 73.99 76.97	2.93 4.26 56.06 41.08 55.50	3.18 4.26 61.71 53.06 43.44	4.28 2.96 73.23 81.10 75.40	3.25 3.55 67.19 59.39 72.14	2.95 3.45 78.44 73.65 73.73	2.62 3.26 58.30 54.76 40.79	3.79 3.29 50.67 32.53 34.31	4.11 3.05 71.58 67.32 78.55	2.90 3.79 68.77 51.39 73.69	2.90 4.16 36.43 41.41 31.02	4.29 2.92 66.99 68.41 68.64	3.72 2.94 64.63 70.82 68.67	5.62 4.96 59.09 50.59 48.71	2.75 3.09 61.07 50.01 58.39	3.32 4.38 73.82 72.94 70.43	3.43 3.76 48.92 36.57 29.09	2.32 4.24 59.83 52.66 49.86	2.78 3.23 61.58 57.39 50.79	2.29 3.44 71.29 55.51 68.66	2.87 5.99 53.43 46.53 49.89	2.35 3.22 67.00 53.99 60.91	3.79 2.94 64.59 46.09 59.36	3.30 2.89 53.76 45.34 37.85	3.69 3.67 80.30 91.59 82.24	2.68 3.40 59.37 54.69 67.36	2.48 3.44 74.49 68.31 76.01	3.19 3.46 69.87 63.71 75.57	3.08 3.29 63.59 61.19 54.91	3.91 5.01 62.48 55.86 51.25	3.81 3.82 64.62 51.76 54.45	3.44 6.26 66.92 56.29 65.32	2.91 2.03 47.03 51.02 34.08	3.72 4.01 59.29 48.63 55.45	3.29 3.89 63.00 55.81 58.31
			Argentina (ARG)	Bangladesh (BGR)	Bolivia (BOL)	Brazil (BRA)	Chile (CHL)	China (CHN)	Colombia (COL)	Cyprus (CYP)	Czech Republic (CZE)	Ecuador (ECU)	Egypt (EGY)	Estonia (EST)	Croatia (HRV)	Hungry (HUN)	Indonesia (IDN)	India (IND)	Israel (ISR)	South Korea (KOR)	Laos (LAO)	Lithuania (LTU)	Latvia(LVA)	Morocco (MAR)	Mexico (MEX)	Malaysia (MYS)	Pakistan (PAK)	Peru (PER)	Philippines (PHL)	Polonia (POL)	Paraguay (PRY)	Romania (ROU)	Rusia (RUS)	Senegal (SEN)	Singapore (SGP)	Serbia (SRB)	Slovakia (SVK)	Slovenia (SVN)	Thailand (THA)	Tunisia (TUN)	Turkey (TUR)	Uruguay (URY)	Vietnam (VNM)	South Africa (ZAF)	Group mean

Table 3 :

 3 Impact of globalisation on mental health

Table 4 :

 4 Impact of economic and social globalisation on mental health by country groups

Table 5 :

 5 Impact of decomposed economic and social globalisation index on mental health

Table 6 :

 6 Multicollinearity diagnostics: Variance Inflation Factors

	Variable	Advanced Emerging
	Variable	countries countries
	Unemp. rate	1.377	1.171
	Urban pop.	1.698	2.489
	Tertiary edu.	1.864	3.462
	Emp. in ind.	3.003	1.683
	(log) GDPPC	3.502	10.634
	Trade	3.119	2.942
	FDI	3.663	2.486
	Migration and other interpersonal	5.288	5.415
	Technology exp. and other informational	2.333	8.235
	Telephone and other Interpersonal	2.006	3.302
	Trade in personal services and other cultural 2.095	6.546
	TV, internet and other Informational	3.080	6.442

Notes: This table presents the Variance Inflation Factors. Minimum possible value = 1.0. Values > 10.0 may indicate a collinearity problem

Even though the link between globalisation and mental health in emerging economies is unexplored in the literature, there is evidence showing that globalisation, in particular tighter trade linkages, has improved social conditions and contributed to a reduction in inter-state wars in in recent decades in emerging market economies (e.g.[START_REF] Black | Importing Equality? The Impact of Globalization on Gender Discrimination[END_REF] and[START_REF] Lee | Does Trade Integration Contribute to Peace?[END_REF]).

According to[START_REF] Hummels | No Pain, No Gain: The Effects of Exports on Effort, Injury, and Illness[END_REF], a 10% exogenous increase in exports increases women's rates of depression by 2.5%, and hospitalizations due to heart attacks or strokes by 15%. Furthermore, men and women have higher injury rates. They also show that men and women work longer hours and take fewer sick-leave days.

 3 Lang, McManus, and Schaur (2019) find that moving a region from the 25th percentile to the 75th percentiles of import exposure corresponds to a 7.8% increase in the morbidity of poor mental health and also corresponds to adding about 3 days of poor mental health per year for the average adult.

The GBD acknowledges the clear data gaps which exist on mental health prevalence across the world: despite being the

5th largest disease burden at a global level (and within the top three across many countries), detailed data is often lacking. This is particularly true of lower income countries. Moreover, the range of epidemiological studies the IHME draw upon for global and national estimates are unequally distributed across disorders, age groups, countries and epidemiological parameters.5 Since many people experience both conditions simultaneously (comorbidity), it is inappropriate to simply add these two figures together to arrive at a total for common mental disorders.

See Gygli, Haelg, Potrafke, and Sturm (2019) for a full description of the KOF index.

[START_REF] Oberlander | Globalisation and national trends in nutrition and health: A grouped fixed-effects approach to intercountry heterogeneity[END_REF] find high correlation between both dimensions -economic and social-in each country. Meanwhile,[START_REF] Olivier | Globalization and the dynamics of cultural identity[END_REF], analyzing the effect of globalisation on diet, predicts that both dimensions have different and opposite effects.

We normalize the globalisation indicators by its overall standard deviation for ease of interpretation

In order to rule out that coefficients are unstable because of multicollinearity, we checked the variance inflation factor (VIF). When the models contain the sub-indices they do not exhibit a VIF substantially larger than the rule of thumb of

The specifications include all the control variables (not presented in the tables to save space).


Tim Friehe
email: tim.friehe@uni-marburg.de

Eric Langlais
email: eric.langlais@parisnanterre.fr.

Elisabeth Schulte
email: elisabeth.schulte@uni-marburg.de.

Product liability when cumulative harm is incurred by both consumers and third parties

Keywords: Product liability, Cumulative harm, Environmental harm JEL Code: K13

Traditional law and economics analyses of product liability assume that expected harm is proportional to usage. This paper builds on Daughety and Reinganum (2013a, 2014) by assuming that harm increases and is convex in usage. In contrast to previous contributions, we analyze liability rules when not only consumers but also third parties incur harm. We show that the social ranking of liability rules previously established for the case in which only consumers suffer harm (strict liability dominates no liability and negligence)may be reversed if third party harm is sufficiently important.

Introduction 1.Motivation and Main Results

Product liability makes manufacturers of defective products liable for harm caused and is an important, much analyzed, topic in the USA. A lively debate about its application in general and potential welfare ranking of specific liability rules continues in policy and academic circles (e.g., Polinsky and Shavell, 2010a;2010b;[START_REF] Goldberg | The Easy Case for Products Liability Law: A Response to Professors Polinsky and Shavell[END_REF]. In the traditional model, which assumes that fully informed, homogeneous consumers incur expected harm that is proportional to output, optimal product safety is independent of output, and the market outcome (including equilibrium product safety) is independent of the liability rule put in place (see, e.g., the survey by Daughety and Reinganum, 2013b). Daughety andReinganum (2013a, 2014) highlight that many realistic circumstances do not match the proportionality assumption and show that assuming cumulative harm instead has radical consequences for the results obtained under different liability rules. In their framework, the level of product safety and the level of output are inextricably linked and different liability rules yield very different market outcomes. Strikingly, Daughety andReinganum (2014, DR 2014 in the following) establish that a firm subject to negligence prefers to be strictly liable and that welfare is higher under strict liability than under no liability, which leads them to argue in favor of strict liability.

In addition to dropping the assumption of proportionality of expected harm to output, it is realistic to consider a product may harm not only consumers but also third parties (i.e., parties with no contractual relationship with the firm). Third-party effects can result from the widespread usage of the product in a neighborhood, through leakages, emissions, disseminating effects etc., as well as from the accidental event itself that also induces consumers' harm (e.g., via flying debris). Consider, for example, the use of glyphosate by farmers for agricultural weed control. Glyphosate is currently the most widely used herbicide in the world [START_REF] Dias | Glyphosate use in agriculture and birth outcomes of surrounding populations[END_REF]. Glyphosate supposedly harms both human health (as it is classified by the International Agency for Research on Cancer as probably carcinogen) and the environment (as it kills populations of insects such as bees). Third-party effects may stem from, for example, food consumption or exposure to spraying of fields.1

This paper analyzes the performance of different product liability regimes when cumulative harm is incurred by both consumers and third parties. We thereby generalize the analysis by DR 2014 as they focus on the scenario in which the product may cause harm only to consumers. We seek to describe how different liability regimes (no liability, strict liability, and negligence) influence privately optimal care and output choices by a monopolistic firm, whose product may harm consumers as well as third-party victims.

Our results show that the previously established ranking of liability rules (with strict liability dominating the other regimes) may be reversed. First, we show that no liability can, in specific circumstances, produce the outcome that occurs under strict liability. To obtain this finding in our framework, second-party harm must be as important as thirdparty harm. Relative to strict liability, no liability implies two distortions which are exactly offsetting each other when second-party harm is as important as third-party harm. Second, and more importantly, we delineate circumstances in which negligence yields higher welfare than strict liability. In order for negligence to possibly dominate strict liability, third-party harm must be more important than second-party harm.

Related Literature

Our paper considers different product liability regimes when both consumers and third parties incur cumulative harm. There is a vast literature on product liability (see, e.g., the surveys by Daughety andReinganum 2013b, and[START_REF] Geistfeld | Products Liability[END_REF]. The traditional setup considers perfectly competitive firms, identical risk-neutral consumers, costless trials, and that both care costs and expected harm are proportional to output. The traditional framework delivers the key finding that strict liability, negligence, and no liability are all equally efficient when consumers are perfectly informed about care and do not misperceive risk (e.g., [START_REF] Shavell | Strict Liability Versus Negligence[END_REF]). The rationale is that the consumers' willingness to pay introduces the concern for the minimization of the expected harm when it would otherwise be missing from the firm's profit maximization. In that standard framework, when harm is incurred by third parties instead of by consumers, strict liability and negligence are equally efficient whereas no liability produces an inefficient outcome (e.g., [START_REF] Shavell | Economic Analysis of Accident Law[END_REF].

In our paper, the firm may be liable for both harm to consumers and harm to third parties (including the environment). In the previous literature, liability of firms for harm to third parties was usually separated from liability of firms for harm to consumers. The former has been studied in relation with various issues including liability sharing (Hansen and Thomas 1999;Watabe 1999), or extended liability and the judgment proofness problem [START_REF] Boyer | Environmental risks and bank liability[END_REF]; more recent work has focused on the incentives to adopt green innovations (Endres and Friehe 2011a,b), or the interplay with competitive distortions (Charreire and Langlais 2018).

For our analysis and results, it is important that we consider cumulative harm, thereby building on [START_REF] Marino | Monopoly, Liability and Regulation[END_REF] and Daughety andReinganum (2013a, 2014). Our contribution to this branch of literature is the consideration of the scenario in which harm is incurred not only by consumers but also third parties. This is particularly interesting because the driving force in this context, namely that the marginal expected harm exceeds the average expected harm per unit of output, is only relevant to the extent that it affects consumers, but not third parties.

Plan of the Paper

In Section 2, we present the framework used for our analysis. In Section 3, we first derive the benchmark featuring the socially optimal levels of product safety and output, and we propose a benchmark for a second best allocation. Next, we address the relative performance of the potential arrangements of no liability, strict liability, and negligence. We conclude in Section 4.

Model

Our model builds on DR 2014 who use a representative consumer framework. Specifically, we consider a risk-neutral monopolist serving a market described by a linear (inverted) market demand gross of any harm P (q) = a -bq, where q denotes output and a and b are positive parameters. This (inverted) demand results from maximizing a quasi-linear utility gross of any harm, U = aq-bq 2 /2+r, subject to the budget constraint, y = r+P q where r represents a numeraire good and y exogenous income. The firm incurs a cost C(q, x) = c(x)q, where x denotes product safety and c (0) = 0 = c(0), c > 0, and c > 0 for all x > 0.

Product safety influences the expected harm caused to the representative consumer and/or a third party. For simplicity, we follow the presentation in DR 2014 and assume that the total expected harm can be described by H(q, x) = γh(x)q 2 , where h(0) > 0 and, for any x, h (x) < 0 < h (x). Importantly, we assume that γ = α + β where α ≥ 0 (β ≥ 0) scales up consumer (third-party) harm. Put differently, we have B(q, x) = αh(x)q 2 represent the level of harm that buyers incur, and T (q, x) = βh(x)q 2 denote the level of harm that third parties suffer. In DR 2014, the assumption is that α = 1 and β = 0. We follow DR 2014 in assuming that H is convex.

The timing is such that, in Stage 1, the firm determines the level of observable product safety and the level of output in view of the consumer's decision-making in Stage 2, as represented by the market demand function. In Stage 3, after any accident, the firm is made to compensate any harm when it is judged liable in (socially and privately) costless litigation.

Analysis

We will first derive the socially optimal levels of product safety and output, and introduce our benchmark for the second best solution. Next, we describe market outcomes when the firm faces no liability, is subject to strict liability, or optimizes under a negligence rule with a well-defined product safety standard.

Benchmarks

First Best: Welfare Optimum

Welfare can be defined by the sum of consumer's utility gross of harm less the total harm incurred and the firm's cost of care. Thus, we obtain

W (q, x) = a - b 2 q -c(x) q -γh(x)q 2 (1)
as the specification of welfare for the framework laid out in Section 2.

The social planner maximizes welfare by the choice of output and product safety. The first-order conditions for an interior solution at levels (q

W , xW ) are 2 a -bq = 2γh(x)q + c(x) (2) -h (x)γq = c (x). (3)
The marginal benefit from an additional unit of output balances the marginal costs comprising the marginal harm created for consumers and/or third parties and the cost of care. With respect to the level of product safety, we find that the marginal reduction of total expected harm per unit of output should be equal to the marginal costs of care per unit of output.

In contrast to the traditional framework, the optimal level of product safety depends on the level of output.

We denote the first-best output level conditional on product safety by q W (x) and state it explicitly as

q W (x) = a -c(x) b + 2γh(x)
.

The first-best product safety conditional on output is denoted by x W (q), cannot be stated explicitly, and solves equation (3). Both functions are positively sloped (for q W (x) this holds at least at product safety levels that solve the condition; see the appendix).

In terms of notation, we distinguish between first-best levels of output and product safety, (q W , xW ), and functions giving the socially optimal level conditional on a specified level of the other variable, (q(x) W , x(q) W ). Clearly, we have (q W , xW ) = (q(x W ) W , x(q W ) W ).

2 See our appendix for second-order conditions for this problem and the ones presented below.

Second Best: Taking Market Power as Given

When we want to compare privately optimal incentives to socially optimal incentives under any liability arrangement, we must distinguish between two reasons for a possible departure of the market outcome from the social planner's ideal outcome:

First, we consider a monopolist whose marginal benefit from raising output is described by the marginal revenue which falls short of the social marginal benefit. Specifically, the monopolist considers a -2bq while the social planner considers a -bq. This aspect is independent of the liability regime and will be relevant to how both privately optimal choices compare to socially optimal choices when harm is cumulative. Below, we will refer to secondbest outcomes when we mean outcomes that are socially optimal taking the monopolistic output distortion as given. To clarify, what we label second-best outcomes maximizes

W (q, x) = (a -bq -c(x))q -γh(x)q 2
instead of W from Section 3.1.1. The social planner is restricted by having a deviation in terms of the objective function imposed on her.3

The second-best product safety level is the first-best level for a given level of output,

x W (q). The second-best output level as a function of care differs from the first-best level only due to the output distortion. Specifically, second-best output (i.e., the output level that solves (2) when the private marginal revenue a -2bq replaces the social marginal benefit a -bq) is given by qW

(x) = a -c(x) 2b + 2γh(x)
.

Using first-best product safety x W (q) and second-best output qW (x) leads to second-best levels of output and product safety denoted by (q W SB , xW SB ).4

The second reason for a possible departure of the market outcome from the social planner's ideal outcome, in addition to the market power distortion, results from how the total harm is represented in the firm's trade-off. The firm considers harm and how product safety can lower harm either because consumers care about it or because the firm is made to compensate harm. This second potential cause of a deviation between socially optimal incentives and privately optimal incentives is dependent on the liability regime and thus of prime interest below.

Care and Output Under No Liability

Under no liability, total harm remains with the consumer and/or the third party. This influences the consumer's willingness to pay derived in Stage 2. Considering the marginal effects flowing from the maximization of Ũ = aq -bq 2 /2+ y -P q -αh(x)q 2 , that is, expected payoffs taking account of the budget constraint and the expected harm, we can assert that

P (q) = a -bq -2αh(x)q
is the relevant (inverted) market demand for the firm to consider in the first stage.

In Stage 1, the monopolist chooses output and product safety in order to maximize

Π N L (q, x) = (a -bq -2αh(x)q -c(x))q. ( 4
)
Under no liability, the privately optimal level of product safety conditional on output, x N L (q), and the privately optimal level of output conditional on product safety, q N L (x), satisfy:

a -2bq = 4αh(x)q + c(x) (5) -h (x)2αq = c (x) (6)
As is clear from (5), under no liability the firm perceives the marginal output costs stemming from the change in the consumer's willingness to pay to be 4αh(x)q. In contrast, marginal harm amounts to 2γh(x)q. Stating the privately optimal (conditional) level of output under no liability explicitly, we get

q N L (x) = a -c(x) 2b + 4αh(x)
.

This level will generally depart from both the first-best and second-best (conditional) output levels, except for some combinations of parameters as we explain below.

Under no liability, the firm is concerned only about harm incurred by the consumer and not about harm incurred by the third party. The information about the marginal benefit from product safety is transmitted to the firm via the change in the consumer's willingness to pay which only reflects the repercussions for the consumer. This suggests that, from a social standpoint, the firm will invest too little in product safety. Similarly, when it comes to the output level, the firm takes into account negative effects absorbed by the consumer but not those absorbed by the third party which suggests that output will be excessive.

However, we find that no liability can induce the second-best (conditional) output and the first-best (conditional) product safety when α = β as in that case 4α = 2γ in condition ( 5) and 2α = γ in condition (6).

The intuition for this result runs as follows. The fact that harm is cumulative and borne by the consumer means that the consumer deducts marginal expected harm from her willingness to pay. Marginal expected harm exceeds average harm in the case of cumulative harm and thus leads to the firm's over-weighting of consumer harm. With α = β, we are describing circumstances in which this over-weighting exactly offsets the missing incorporation of third-party harm.

We summarize in:

Proposition 1 (i) Assume that α = β. Then, no liability induces the second-best outcome, that is, we obtain q N L (x) = qW (x) and x N L (q) = x W (q) in terms of conditional output and care levels. In terms of equilibrium levels, we obtain xNL = xW SB and qNL = qW SB . (ii) Assume that α > β. Then, in terms of conditional output and care levels, q N L (x) < qW (x) and

x N L (q) > x W (q). In terms of equilibrium levels, we obtain xNL > xW SB and qNL < qW SB . (iii) Assume that α < β. Then, in terms of conditional output and care levels, q N L (x) > qW (x) and x N L (q) < x W (q). In terms of equilibrium levels, we obtain xNL < xW SB and qNL > qW SB .

Proof. Claim (i) is obvious. The first part of Claims (ii) and (iii) follow directly from the statements of conditional output levels and the first-order conditions for product safety. The second part of Claims (ii) and (iii) uses the comparative statics results from the appendix.

Starting from a benchmark with α = β and then increasing (decreasing) the level of β (which leaves the solution under no liability unaffected as it depends only on α but changes the second-best outcome) means that -in the second-best outcome -output will decrease (increase) whereas product safety will increase (decrease). As a result, when the level of β increases (decreases), the unchanged output under no liability will exceed (fall short of) the second-best level and the product safety level will fall short of (exceed) it.

Undoubtedly, we are describing a knife-edge result because α = β will presumably not hold in the majority of cases. However, the result is important because it points out that the performance of no liability in the cumulative harm framework is much better than previously considered. In Case (ii) of Proposition 1, the third-party harm that we introduce is not important enough to overthrow the pattern described in DR 2014. Case (iii) reported in Proposition 1 makes it possible to have either q N L (x) < q W (x) or q N L (x) > q W (x), that is, the (conditional) output under no liability may be less than or greater than first-best (conditional) output. The (conditional) privately optimal level of output under no liability being greater than the (conditional) first-best level of output requires b < 2(β -α)h(x).

Furthermore, using conditions (3) and ( 6), we can state that

x N L (q) = x W 2α γ q , (7)
which means that the product safety level that results under no liability is equal to the first-best product safety level, xNL = xW , when the output levels relate in a specific way to each other (namely qNL = γ 2α qW ). Using conditions (2) and ( 5), we can write

q N L (x) = b + 2γh(x) 2(b + 2αh(x)) q W (x),
and deduce that the no liability regime can induce the firm to choose the socially optimal safety level only in the case considered by DR 2014, that is, γ = α = 1 > β = 0, as in this case the no liability output is equal to one half of the socially optimal output.

Care and Output Under Strict Liability

Under strict liability, total harm is shifted from the consumer and the third party to the firm. The consumer's willingness to pay derived in Stage 2 thus can be stated as

P (q) = a -bq.
In Stage 1, the monopolist chooses output and product safety in order to maximize

Π SL (q, x) = a -bq -c(x) q -γh(x)q 2 . ( 8
)
The firm bears the average of the total expected harm per unit of output. This contrasts with the case of no liability in two ways. First, the consumer's expected harm enters the firm's maximization problem as the average consumer harm per unit of output (avoiding the double marginalization). Second, under strict liability, the firm thinks not only about consumer harm but also about third-party harm.

The first-order conditions give equilibrium levels qSL and xSL when the firm is strictly liable as solving the system:

a -2bq = 2γh(x)q + c(x) (9) -h (x)γq = c (x) (10)
From this description, it follows that strict liability ensures the attainment of the secondbest outcome. The single distortion relative to the first-best outcome is the artificial output scarcity introduced by the monopolist. We have x SL (q) = x W (q) and

q SL (x) = a -c(x) 2b + 2γh(x) = qW (x).
Proposition 2 Strict liability ensures the attainment of the second-best outcome, that is, we obtain q SL (x) = qW (x) and x SL (q) = x W (q) for any (α, β) in terms of conditional output and care levels. In terms of equilibrium levels, we obtain xSL = xW SB and qSL = qW SB .

= xSL α = β qNL = qW SB = qSL xNL = xW SB = xSL α < β qNL > qW SB = qSL xNL < xW SB = xSL

Comparing Solutions Under No Liability and Strict Liability

In contrast to the analysis laid out by DR 2014, strict liability performs as well as no liability when α = β. However, when α > β, it is clear that strict liability produces better outcomes than no liability (as explained by DR 2014). When, in turn, α < β, it may happen that (conditional) output under no liability is closer to the first-best (conditional) output level than the (conditional) output under strict liability. Higher output is clearly beneficial if

q N L (x) ≤ q W (x), which is the case when b > 2(β -α)h(x).
On the other hand, this benefit comes at the cost of lower product safety, x N L (q) < x W (q). We summarize these rankings in Table 1.

We may consider the level of profits and the level of welfare as a function of τ , a variable that allows us to simulate the change from a regime of no liability (where τ = 0) to a regime of strict liability (where τ = 1). The value functions are

Π(τ ) =(a -bq -c(x))q -(1 -τ )2αh(x)q 2 -τ γh(x)q 2 (11) W (τ ) =(a -b/2q -c(x))q -γh(x)q 2 (12)
where q and x take privately optimal values at a given τ . Accordingly, an increase in τ will -by application of the envelope theorem -be relevant to firm profits according to the direct effect only. As a result, we have that the firm prefers no (strict) liability when β > (<) α and is indifferent otherwise. With respect to welfare, only indirect effects are relevant when τ is changed marginally. When α > β, an increase in τ induces an improvement of both choice variables, as the restricted output grows and the excessive product safety level falls.

When α < β, there is a conflict as increasing τ improves the firm's choice from a social standpoint only with respect to safety. From this argumentation, we get:

Proposition 3 From a welfare point of view, we find that: (i) Strict liability outperforms no liability when α > β. (ii) The two regimes produce the same outcome when α = β. (iii)

No liability may outperform strict liability (at least in selected circumstances) when β > α.

From the firm's point of view, strict liability dominates (is dominated by) no liability when α > (<) β.

Care and Output under Negligence

Any negligence standard allows the firm to choose between the two previously discussed regimes: the firm is strictly liable when it chooses product safety below the due level, and the firm has payoffs as under no liability provided that product safety is weakly in excess of the product safety standard.

From our previous analysis, we deduce that Π SL (q, x) > Π N L (q, x) for any (q, x) if and only if α > β. Thus, if α > β, the firm will certainly not comply with any product safety standard that is excessive from its point of view. From a social perspective, under no liability and α > β, product safety is excessive and the output level too low. Hence, the firm and the social planner are better off under strict liability, or (equivalently) with a product safety standard allowing the firm to operate in an effectively unconstrained manner under strict liability.

In contrast, if α < β, we obtain the following ranking of firm profits

Π SL (q SL , xSL ) < Π N L (q SL , xSL ) < Π N L (q N L , xNL ), (13)
such that the firm is willing to increase the level of care beyond the privately optimal level, if that implies escaping liability. When β > α, it holds that x N L (q) < x W (q) where x W (q) =

x SL (q) (see Propositions 1 and 2). Thus, the social planner can induce the firm to comply with xSL , that is, the first-best level of product safety when the level of output is second-best (i.e., qW SB ). Proposition 1 (iii) implies that, under no liability, the firm will provide output higher than the second-best level of output qW SB if the product safety standard is set at xSL . This increase in output is principally socially desired because the second-best output obtained under strict liability is too low from a social perspective. However, it holds true that the standard xSL is no longer the ideal match for the output higher than qW SB . We deduce that there is scope for improving upon the strict liability outcome using the negligence rule by appropriately choosing the standard of care (possibly as a function of output) in the case α < β. We will focus on these parameter constellations in the following.

Product Safety Standard Independent of Output

Confronted with a standard x ≥ xNL , a compliant firm will choose product safety equal to the standard, and an output level according to:

q N L (x) = a -c(x) 2b + 4αh(x)
.

This (conditional) output is below the socially optimal (conditional) output,

q W (x) = a -c(x) b + 2γh(x) ,
if and only if b > 2(β -α)h(x). A threshold function β(x, α), β(x, α) > α ∀x, exists such that a compliant firm chooses (conditional) output below the first-best (conditional) output when β < β(x, α). We show that, in such a situation, shifting from strict liability to negligence is welfare improving.

Proposition 4 Assume that the product safety standard is xSL and that β < β(x, α). Then, the negligence rule produces higher welfare than strict liability.

Proof. We have explained that the firm prefers to comply with the standard xSL when discussing the ranking in (13). For β < β(x SL , α), the switch from strict liability to negligence induces a higher (conditional) output that is still less than the first-best (conditional) output.

Because we hold the product safety constant, as the firm has no interest in increasing it above the requirement under negligence, we can say that the higher output raises welfare.

As Π SL (q SL , xSL ) < Π N L (q SL , xSL ) < Π N L (q N L (x SL ), xSL ), there is room for demanding an even higher standard of care. In fact, the social planner can choose her favorite combination (q N L (x), x) subject to the compliance constraint:

(a -bq N L (x) -2αh(x) -c(x))q N L (x) > (a -bq W SB (x W SB ) -γh(x W SB ) -c(x W SB ))q W SB , (14)
where the second line represents firm profits under strict liability (which induces the secondbest levels). The social optimum can be reached only in the special case in which b = 2(β -α)h(x W ) and the compliance constraint ( 14) holds for x = xW .

Product Safety Standard as a Function of Output

If we allow the standard of care to be a function of output, the social planner can deter a range of output choices by associating excessive product safety standards with them. In this case, she can induce her favorite combination of (q * , x * ) out of those that satisfy the compliance constraint ( 14) by linking the product safety standard to the output in such a way that (q * , x * ) maximizes the first line of ( 14).

Conclusion

The traditional product liability framework specifies expected consumer harm as being proportional to output. [START_REF] Daughety | Cumulative harm and resilient liability rules for product markets[END_REF] highlight the important implications from assuming cumulative harm instead. The distinction between marginal expected harm and average expected harm is at the heart of the discussion. Out of three liability arrangements (no liability, strict liability, and negligence), they provide convincing arguments for the primacy of strict liability.

Our paper introduces third-party harm into the framework presented by [START_REF] Daughety | Cumulative harm and resilient liability rules for product markets[END_REF] to analyze how this aspect affects previous results. In fact, we establish circumstances in which no liability and negligence can outperform strict liability. This possibility emerges only when third-party harm is relatively more important as a harm category than consumer harm.

Our analysis is kept very simple. For example, we assume linear demand, a quadratic harm function where consumer harm and third-party harm have the same functional form and simply add up, and a monopolistic firm. Nevertheless, the basic insight that third-party harm is an important factor for decisions over liability rules in a context with cumulative harm is more reflective of reality and relevant in more complex settings.

Watabe, A., 1999. The effect of liability-sharing rules in delegating hazardous activities.

International Review of Law and Economics 19, 349-368.

Appendix: Second order conditions and comparative statics Welfare maximization. We follow DR 2014 to establish that any interior solution to the first-order conditions will be a local welfare maximum.

From the maximization of W = aq -b 2 q 2 -c(x)q -γh(x)q 2 (15)

follows:

W q =a -bq -c(x) -2γh(x)q = 0 (16) W x = -c (x)q -γh (x)q 2 = 0 (17)

W qq = -b -2γh(x) < 0 (18)
W xx = -c (x)q -γh (x)q 2 < 0 ( 19)

W qx = -c (x) -2γh (x)q, ( 20
)
where W x denotes the partial derivative of W with respect to x. Using c (x) = γh (x)q, we restate W qx = -γh (x)q > 0. Next, it can be established that W xx W qq -(W qx ) 2 > 0 since (b + 2γh)(c q + γh q 2 ) -(-γh q) 2 > γ 2 q 2 2hh -(h ) 2 > 0,

where the second inequality sign stems from the convexity of H, which implies that h(x)h (x)-2 (h (x)) 2 ≥ 0 for all x.

Condition (16) defines q W (x), where

dq W dx = - W qx W qq > 0, ( 22
)
using the restatement W qx = -h (x)q > 0. Similarly, condition (17) defines x W (q), where

dx W dq = - W qx W xx > 0. ( 23
)
Second-best outcome Consider the case in which the monopolistic quantity distortion is taken as given. We obtain:

W q =a -2bq -c(x) -2γh(x)q = 0 (24) W x = -c (x)q -γh (x)q 2 = 0 (25)

W qq = -2b -2γh(x) < 0 (26)

W xx = -c (x)q -γh (x)q 2 < 0 ( 27)

W qx = -c (x) -2γh (x)q (28)
We are interested in the influence of a change in γ on the second-best outcome (q W SB , xW SB ) and find that dq

W SB dγ = 1 H W qx W xγ -W xx W qγ (29)
and

dx W SB dγ = 1 H W qx W qγ -W qq W xγ , (30)
with W qγ = -2h(x)q < 0 (31)

W xγ = -h (x)q 2 > 0. ( 32
)
More specifically, we derive that

dq W SB dγ = 1 H γ(h ) 2 q 3 -(c q + γh q 2 )2hq < γq 3 H (h ) 2 -2hh < 0, ( 33
)
where the inequality sign stems from the convexity of h, and (34)

dx W SB dγ = 1 H 2γhh q 2 -(2b + 2γh)h q 2 = 1 H (-2bh q 2 ) > 0.

Table 1 :

 1 Ranking of Equilibrium Output and Care under No Liability and Strict Liability

	Scenario Output	Care
	α > β	qNL < qW SB = qSL xNL > xW SB

See, for example,[START_REF] Dias | Glyphosate use in agriculture and birth outcomes of surrounding populations[END_REF] for a study of the potential effects on birth outcomes. Other examples for products that may cause harm to consumers as well as third parties include smoke from tobacco products, potentially exploding smart phones (Samsung Galaxy Note 7), and soft drinks in bottles (e.g., Escola v. Coca-Cola Bottling Co.).

Accepting the firm's market power in our discussion of liability rules is consistent with the argument presented in DR 2014. They explain that the role of product liability is allocating the responsibility for harms due to product failures and not improving market performance in terms of output.

[START_REF] Daughety | Markets, torts, and social inefficiency[END_REF] similarly consider a restricted social optimum in which they take the output distortion that results in settings with market power as given. However, in their setup, the social planner chooses the level of safety taking into account how safety influences equilibrium output levels (i.e., the social planner may strategically distort safety to influence output).