# A subregional panel data analysis of life insurance consumption in Italy.

ABSTRACTWe propose a subregional panel approach to the determinants of life insurance development, with new methodological tools, applied to Italian data. Our sample has enough variability in observables and less unobserved heterogeneity than cross-country ones, but is potentially affected by spatial dependence and serial correlation. We propose an encompassing estimator, showing that the spatial diffusion process of life insurance is driven by idiosyncratic shocks in neighbors. Our results partly reconcile the aggregate perspective with survey evidence supporting, in contrast to international studies, a negative link between education and risk aversion, and identifying the positive effect of young dependents predicted by theory.

INTRODUCTION

Empirical research on the determinants of life insurance consumption has followed two main routes. One, based essentially on microdata from surveys on households, consumers, and various subsets of the population (students, married couples, retired people), has investigated life insurance demand from a microeconomic perspective, in order to evaluate empirically the theoretical conclusions derived from saving theory and in particular from the life-cycle hypothesis; see, for example, the recent contribution by Liebenberg, Carson, and Dumm (2012) and the literature survey therein. The other main empirical perspective has been that of aggregate market development, usually drawing on cross-sections or panels of countries. In this latter case, the focus has usually been on the determinants of aggregate market turnover, sometimes labeled "demand" but perhaps more appropriately described as "consumption," as its observed values are the outcome of a market equilibrium between demand and supply.

Besides their interest to insurance scholars, practitioners, and market players, aggregate approaches to the analysis of life insurance consumption find a broader motivation in policy issues pertaining to its role in the financial system and in the aims, scope, and sustainability of the welfare state. Moreover, the importance of insurance for economic growth has been extensively analyzed in the literature, both as a component of a broader financial system (King and Levine, 1993) and in a stricter sense, as in Outreville (1996) and Ward and Zurbruegg (2000). In particular, Arena (2008) provides evidence of a causal link from the development of the life insurance market in a country to its economic growth. As regards public welfare, life insurance has a role in supporting, or even substituting, it. In fact, countries relying substantially on the private sector for the provision of old age benefits typically have very large ratios of life insurance revenues to GDP, as it is the case for Japan, the United Kingdom, Belgium, or South Korea. A third function of life insurers is related to their role as institutional investors. As such, they help the efficient allocation of resources by investing the technical reserves associated with insurance activity. The financial component of life insurance is actually very important because the time span of contracts is so long that the accumulated reserves reach substantial amounts. (1)

The importance of insurance in the Italian economy is geographically very diverse. Unlike what happens with nonlife insurance (see Millo and Carmeci, 2011), the Italian life insurance market as a whole is comparatively well developed by European standards, but striking regional differences persist, the South of the country being generally underdeveloped with respect to the North and Center (see Figure 1, left panel). Moreover, life insurance density is highly correlated in space, with a striking similarity between clusters of nearby provinces (see Figure 1, right panel).

The aim of this study is twofold. From the analysis of the Italian life insurance market across a short panel of Italy's provinces (i.e., NUTS3 regions; see the "Data Description" section) we will assess the determinants of market development in the particular Italian case, characterized by an extremely uneven geographical distribution of insurance density. Moreover, generalizing our findings, we will bring new evidence to the empirical literature on aggregate insurance demand. In this latter respect, we will pay special attention to some research questions that are still largely undecided, as those regarding the effect on life insurance purchases of some demographic characteristics: education, family size, and number of young dependents (Zietz, 2003).

As regards the first point, we motivate the choice of a subregional perspective as a mean of eliminating some problems found in cross-country analyses, in particular, the presence of sources of variation that tend to overshadow all others and that are potentially prone to multicollinearity. Indeed, our sample of Italian provinces is homogeneous as regards systemic characteristics, yet it has enough variability to allow the identification of other determinants of insurance consumption. Moreover, some drivers that are problematic to define or observe can be safely omitted from the empirical analysis because they do not vary over provinces, and their time variation can be easily absorbed by time effects: life insurance prices, that is, all kinds of policy loadings, which unlike what happens with nonlife insurance are set at the national level; and financial returns on life insurance in force, which again derive from centralized financial management and do not change with the province where the policyholder resides. With respect to cross-country samples, a subregional panel analysis provides an environment with reduced unobserved heterogeneity while retaining a fair amount of variability in observable characteristics. On the converse, from the beginning it raises issues of cross-sectional dependence, which combine with well-known issues of insurance data like serial correlation (Beenstock, Dickinson, and Khajuria, 1986). In this article, we propose and apply a new maximum likelihood spatial panel estimator capable of taking into account regional heterogeneity as well as spatial and serial correlation, extending the work of Anselin (1988), Case (1991), and Baltagi et al. (2007) in order to encompass all these features. As expected, we find evidence of both spatial and serial correlation. Moreover, thanks to our encompassing specification we are able to discriminate between spatial correlation in the dependent variable and in the errors. We find only evidence of the latter, meaning that idiosyncratic shocks to insurance consumption propagate to neighboring regions. The evidence of serial correlation is in turn consistent with the previous literature (see Beenstock, Dickinson, and Khajuria, 1986). Our results, while confirming that the diffusion of life insurance depends on economic development, per capita savings, and demographic factors, reconcile to some extent the aggregate perspective with survey evidence. Regarding demography, unlike previous international studies (Beck and Webb, 2003) but in line with the theoretical predictions of Lewis (1989) and previous survey evidence (reviewed in Liebenberg, Carson, and Dumm, 2012), we are able to document the positive influence of the ratio of young dependents. Also contrary to most results from the literature on international insurance development, but again in agreement with some microeconometric evidence (Duker, 1969; Anderson and Nevin, 1975; Auerbach and Kotlikoff, 1989), life insurance is negatively correlated with schooling, supporting the view that better education fosters financial risk taking. Moreover, we assess the importance of supply factors and of some environmental variables, finding that the density of insurance agencies has a substantial positive effect but that of bank counters has none, and that the general level of trust is supportive of life insurance consumption, while the rule of law, unlike what happens in international samples (Ward and Zurbruegg, 2002) and the Italian nonlife sector (see Millo and Carmeci, 2011), is not influent.

In the next section, we review the literature in order to define the subject and sketch previous empirical findings. In the third section, we describe the data set, review the model and discuss the reasons for expecting the presence of heterogeneity and correlation in space and time. The fourth section presents the random effects specification with spatially lagged dependent variable and serially and spatially correlated errors; then outlines the estimation method; lastly, discusses the results. The last section concludes.

LITERATURE REVIEW

In the unifying framework first developed by Yaari (1965) and Hakansson (1969), the demand for life insurance is attributed to a person's desire to bequeath funds to dependents and provide income for retirement. In the case of term life, according to the extension of this scheme by Lewis (1989), it is also a function of the number, personal characteristics, and preferences of the beneficiaries, that is, in most cases, of family composition. The primary function of life insurance can therefore be characterized as "income" protection, meaning either "income of one's dependents" against premature death of the insured, or "lifetime income of the insured" in the case of lower earnings, for example, after retirement. Beenstock, Dickinson, and Khajuria (1986) term the first life protection and the second income protection. They add another function that is typical of insurance: pure saving, the element not related to human life but only to the investment yield. These categories roughly correspond in standard practice to term life, annuities and pensions, and capitalization, although distinctions are blurred in the life products that are actually sold. Most endowment policies sold in Italy, for example, have an important term life component, entitling the beneficiaries to payment of face value upon death of the insured. (2)

According to Outreville (1996, p. 265), the consumer of life insurance maximizes a utility function depending on wealth, the income stream, a vector of interest rates, and a vector of prices including the insurance premium rate. As Beck and Webb (2003) put it, "This framework posits the demand for life insurance to be a function of wealth, expected income over an individual's lifetime, the level of interest rates, the cost of life insurance policies (administrative costs), and the assumed subjective discount rate for current over future consumption." The relevant literature is too vast to be summarized here: in his comprehensive review of the literature on insurance and economic growth, Outreville (2013b) counts 85 papers "most of them examining the demand for life insurance." In the following, we will only mention results that bear a direct relevance to our analysis.

Studies on microdata (usually household income or consumer expenditure surveys) from the international literature over the last 40 years are summarized in table 1 of Liebenberg, Carson, and Dumm (2012). While generally confirming the positive association with income, they weakly support the idea that life insurance consumption be declining with age but are inconclusive as regard the effect of education (often significant but with changing signs) or that of young dependents (mostly nonsignificant).

Many cross-country comparisons find a positive influence from income and schooling (Beenstock, Dickinson, and Khajuria, 1986; Browne and Kim, 1993; Beck and Webb, 2003) and a negative effect of inflation (Beenstock, Dickinson, and Khajuria, 1986; Browne and Kim, 1993; Outreville, 1996; Ward and Zurbruegg, 2002; Feyen, Lester, and Rocha, 2013). The positive income effect is undisputed in applied research. The expected effect of education on insurance purchases is less obvious, although most (Truett and Truett, 1990; Browne and Kim, 1993; Li et al., 2007; Feyen, Lester, and Rocha, 2013) see it as positively related to risk awareness (and hence to life insurance consumption). A different view, equally plausible and consistent with some empirical findings from survey data (Duker, 1969; Anderson and Nevin, 1975; Auerbach and Kotlikoff, 1989) but scarcely considered so far in the literature on insurance development, inversely relates education to risk aversion; in this light, more education can be expected to raise the willingness and the capacity to manage risks, and therefore to associate with lower insurance purchases; see the survey in Outreville (2013a) (see also Outreville and Szpiro, unpublished, cited in Browne, Chung, and Frees, 2000). A puzzling result, by Browne and Kim (1993), is that although being a substitute for life insurance, social security expenditure is in turn positively correlated with it.

The related aspects of mean age of the population (Beenstock, Dickinson, and Khajuria, 1986; Truett and Truett, 1990), life expectancy (Beenstock, Dickinson, and Khajuria, 1986; Outreville, 1996), and old dependency ratio (Beck and Webb, 2003; Feyen, Lester, and Rocha, 2013) have also been found positive and significant. Only two studies separate between young and old dependency ratios: Beck and Webb (2003), consistently with the positive effect of an ageing population, find a positive coefficient for the share of old dependents and a negative one for that of the young, while they are both positive in Feyen, Lester, and Rocha (2013). In general, and unsurprisingly, most characteristics of developed countries (wealth, high life expectancy, good education, monetary stability) tend to be associated with another feature of advanced economies: a well-developed life insurance sector. The issues posed by this multicollinearity and the way they have been dealt with will be discussed in the next paragraph.

Urbanization (or its complement, the share of rural population) has been included as an explanatory variable by Outreville (1996) and Beck and Webb (2003) because it is assumed to positively impact the insurers' production function, as the concentration of consumers in space simplifies the distribution of products; it is nevertheless found not significant. Feyen, Lester, and Rocha (2013) argue in favor of using population density instead of urbanization, which they do, finding a significant and positive effect and observing that this variable has been neglected by most previous research.

The literature has also reserved little attention to another theoretically important determinant of life insurance purchases, what Beck and Webb (2003) call the "vector of interest rates," that is the rates of return on life insurance reserves and those of competing financial products as stocks, mutual funds and in particular safe assets as government and corporate bonds. Hence, as Outreville (2013b, p. 20) aptly observes, life insurance purchases should depend from the spread between the former and the latter. Unfortunately, the rates of return on life insurance reserves at country level are not readily observable and therefore the few studies considering interest rates have simply included (real) government bond yields (Outreville, 1996; Li et al., 2007) or lending rates (Beck and Webb, 2003), finding conflicting results: either a positive (Beck and Webb, 2003), a negative (Li et al., 2007), or no effect (Outreville, 1996). In this respect, we conclude that data problems have to date hindered researchers from correctly approaching an important determinant of life insurance consumption. The interest rates issue further motivates our subnational approach, which will be the subject of the next section.

Motivating a Subnational Perspective

Studies on international insurance have recently been drawing on ever bigger data sets, growing both in geographical scope and in the time dimension. While the latter may pose methodological problems (essentially concerning nonstationarity and spurious regression issues), the growth in geographical coverage has generally been considered a positive feature, as indeed it enriches the informative content of the given sample.

In this respect, though, the cross-country perspective raises big concerns as regards individual heterogeneity relating to institutional, regulatory, social, and other factors that are generally unobservable or difficult to quantify and take into account. Moreover, a number of relevant indicators of development tend to go together and to be all higher in some countries, those who, in the words of Zingales (2003), "seem to be doing the right thing in many dimensions," having better legal enforcement, a higher level of trust, less corruption, a more efficient and independent judicial system, and better developed financial markets, just as others (see the discussion in Outreville, 1990) are characterized by high inflation, low education, a prevalently agrarian workforce, and a monopolistic insurance market. Thus, "[e]ach institution taken individually has a positive effect on economic growth. Yet there are too many (highly correlated) variables and too few countries to be able to reliably identify the effect": collinearity makes establishing statistical relationships difficult. Hence, Guiso, Sapienza, and Zingales (2004) analyze the causal link between financial development and growth from a regional perspective, observing that the level of political, regulatory, and financial integration reached within Italy can be considered an upper bound for which a set of countries will ever be able to attain. So in analyzing Italian data from a subregional perspective, we are confident that the systemic factors will be as homogeneous as possible, while at the same time the variability of other regressors will be high.

Past studies in the insurance development literature have acknowledged the heterogeneity problem (Browne and Kim, 1993; Outreville, 1996; Beck and Webb, 2003; Li et al., 2007) proposing the separation of developing from developed countries as a solution. Yet the homogeneity hypothesis, explicitly stated by Li et al. (2007), that focusing on OECD countries "avoids mixing different country characteristics and heterogeneous consumer demand" still seems overoptimistic to us. Some systemic characteristics, in fact, differ just as wildly within OECD countries as they do between these and the rest of the world. Some examples follow.

In the specific case of insurance, a major source of systemic differences between countries, which often "eats up" all the cross-sectional variability, are social security systems outsourcing old-age welfare to the private sector, which gives rise to the world's biggest life insurance markets in terms of penetration over GDP (South Africa, the United Kingdom, Japan, and South Korea). In general, the features of the social security system play a major role in explaining life insurance: countries with extensive public coverage for old age used to have lower levels of life premium income, so that comparisons between countries with different social security systems are often not meaningful unless the heterogeneity is controlled for, for example, by exploiting time variation in a panel setting, although the time variation is often very small with respect to the cross-sectional one.

An inflation-ridden past history, as, within Li et al.'s (2007) sample, in Turkey or Mexico, in turn depresses public trust in traditional savings products, such as many kinds of life policies: Outreville (1996), in an extensive study of life insurance markets in developing countries, considers the expected inflation rate and the presence of a monopolistic market structure or of barriers to entry of foreign competitors, unsurprisingly observing a negative effect (on inflation; see also Beck and Webb, 2003, and the case of Brazil in Babbel, 1981). Religious beliefs, as shown by Grace and Skipper (1991) and Browne and Kim (1993), are another key determinant of the low insurance consumption in many countries, especially Islamic ones. Browne and Kim find a positive relationship between life insurance consumption and income, literacy, and the type of legal system. In turn, Ward and Zurbruegg (2002) find a positive influence of the rule of law in both an Asian and an OECD sample. Beck and Webb (2003) add also the degree of development of the banking sector, finding a positive effect on the subsample of developing countries. Possibly for the reasons given above (see also the discussion in Hussels, Ward, and Zurbruegg, 2005), education, young dependency ratio, life expectancy, and the size of social security do not prove significant in their setting. (3) Many of these influential factors have little or no time variability; therefore, they cannot be included in a fixed effects analysis. If they are, as in Feyen, Lester, and Rocha (2013), then estimation must omit individual fixed effects, subject to the very strong assumption that the variables included actually account for all of the individual heterogeneity. One modeling possibility, in such cases, is to introduce group fixed effects together with individual (here, country) random effects, as will be discussed later.

Consumption or Demand: The Role of Supply

Some of the studies cited (Browne and Kim, 1993; Zietz, 2003; Li et al., 2007) indifferently use the terms consumption and demand to indicate the total yearly premium volume of a market, while in our opinion, only the first term is adequate as indicating an equilibrium market outcome resulting from the interplay of supply and demand. As a logical consequence of this imprecise wording, they estimate one reduced-form equation, equating (per capita) premium volume to a number of explanatory regressors, then take the resulting coefficients as measures of the influence on insurance demand, which is not necessarily true unless supply is infinitely elastic at a given price, a heroic assumption especially in a cross-country setting. Browne and Kim (1993, p. 620) actually devote some words to the possible effects of supply on price and, although declaring them "beyond the scope of the ... study," include one price proxy in one of their equations.

To our knowledge, only Beenstock, Dickinson, and Khajuria (1986) and Outreville (1996) explicitly formalize a supply schedule, making it dependent on the cost and risk conditions faced by life insurance providers: interest rates, life expectancy, and either on market structure variables (financial development, market openness vs. monopolistic behavior) as in Outreville or on the prices of substitute products, as in Beenstock, Dickinson, and Khajuria. Beck and Webb (2003) in turn discuss the importance of including supply factors, and name some environmental characteristics (quality of human resources, property rights protection) as influencing the insurers' cost function.

Beck and Webb (2003), after noting the usual impossibility of observing price and quantity separately in insurance data sets, stress the importance of the missing price variable and adopt two solutions to account for it. The first is including a number of "supply-side factors that are likely to affect the ability of insurers to market and distribute policies cost-effectively: urbanizaton, monetary stability, bureaucratic quality, the rule of law, corruption and banking sector development." The second is to include country fixed effects in their panel analysis, so as to control for that part of the unobserved heterogeneity that is country specific and time invariant. Still, Beck and Webb's solution is prone to the bias from omitted, time-variant regressors (e.g., price can hardly be assumed time invariant over 36 years) and limited by the fact that most of the assumed determinants of supply can also be thought to influence demand.

In our analysis, we rather choose to start from the terse formalization in Beenstock, Dickinson, and Khajuria (1986), who explicitly model equilibrium revenue, the observable variable, as price times quantity eliminating the need for a problematic price proxy, such as the ratio of total expenditures on life insurance premiums to the amount of life insurance in force used by Browne and Kim (1993, p. 624). Nevertheless, their model still considers the price of competing types of life coverage. In this respect, we observe that in a subregional setting the price of each life insurance product, measured as policy loadings and commissions, is cross-sectionally invariant, as the products sold are the same nationwide. Therefore, only time variations must be accounted for, which are absorbed by time fixed effects. The same goes for the problematic interest rate spread between insurance reserves and market rates: insurers are nationwide players who invest on international markets; hence, the polcyholder's region of residence makes no difference in this respect. (4)

EMPIRICAL SETTING

As anticipated, we take Beenstock, Dickinson, and Khajuria's (1986) model as our reference. They analyze life insurance in 10 industrialized countries over 12 years (see also their companion paper on nonlife Beenstock, Dickinson, and Khajuria, 1988), basing their specification on the decomposition into life protection, income protection, and saving. A priori, they postulate that demand for life protection depends on life expectancy, parental dependency, age, the price of insurance, the general price level, and the level of social security transfers received by the population; supply from insurance price, life expectancy, the real rate of interest, age, and the price of pension products (because capacity-constrained insurers face a tradeoff between supplying life or pension insurance). In their framework, the demand for pensions in turn depends on income, life expectancy, the price of pension policies, the general price level, parental dependency, and social security payments; supply from prices of both insurance categories (for reasons given above), age and the real rate of interest. Lastly, supply of and demand for the saving element of insurance depend on aggregate saving and on a vector of interest rates.

We adopt their formalization, augmented by some significant variables from other studies, and purged of those invariant at national level. Personal disposable income has generally been proxied by means of GDP or GNP, a suboptimal solution due to data limitations (see the discussion in Browne and Kim, 1993, p. 622). We directly observe aggregate disposable income (ryd). We add bank deposits per capita (rbankdep) as a proxy for the stock of wealth. (5) Including this together with the yearly flow of income, usually not an option in international databases, allows us to test the combination of two effects: that on life protection, which should be negative according to the theoretical prediction of Lewis (1989), and that on saving products, which should obviously be positive. We use three measures of dependency: young and old dependency ratio (ydeprat, odeprat), the ratio of non-working-age people, respectively, younger (under 14) and older (over 65) divided by the labor force (1564), are meant to control for young and old dependents; the female participation rate to the workforce (partrate) for dependent spouses. We consider social security payments (socialsec) as the sum of three different kinds of provisions: old age pensions (ss.oldage), pensions to surviving spouses (ss.surv), and inability transfers (ss.inab). (6)

The general price level is unfortunately unobservable, as in Italy there are no comprehensive price statistics at provincial level. Yet the role of inflation in cross-country surveys is in distinguishing countries where a long history of inflation has permanently discouraged long-term commitments to saving products from those where it has not: in this respect, we are confident that Italy's provinces can be considered homogeneous and the general price level discarded from our analysis. Regarding the price of insurance, although the focus is on equilibrium revenue, the price of pensions still enters the supply function of life protection suppliers and the reverse. In general, as Schlesinger (2000) notes, "it is often difficult to determine [even] what is meant by the price and the quantity of insurance.... [T]he fundamental two building blocks of economic theory have no direct counterparts for insurance." Here, the difficulty of (defining and) observing the "price" of insurance coverage, a key limitation of cross-country studies, may be considered irrelevant as products are designed on a nationwide basis and therefore average policy loadings can be taken as uniform across provinces, if not for some possible composition effects. Both interest rates on saving products and the return rates insurers are able to obtain from investing their reserves are determined on a national or international basis, so that we can safely consider them cross-sectionally invariant in our setting.

In Beenstock, Dickinson, and Khajuria's (1986) formalization, total premium income V for the three categories of life insurance products "life protection" ([V.sub.1]), "pension plans" ([V.sub.2]), and "saving" (S) (see the beginning of this section) can be expressed as V = [P.sub.1][Q.sub.1] + [P.sub.2][Q.sub.2] + S where, according to the equilibrium solutions in their paper and considering our choice of regressors,

[V.sub.1] = [F.sub.1] (ryd, family, odeprat, ydeprat, partrate, socialsec) [V.sub.2] = [F.sub.2] (ryd, odeprat, socialsec) S = [F.sub.3] rbankdep)

plus the control variables. Like Beenstock, Dickinson, and Khajuria, we are not able to observe the three components separately; therefore, we will estimate one model for V as a whole.

With respect to Beenstock, Dickinson, and Khajuria's (1986) specification, we add two supply-side variables: the densities of the two main distribution channels, bank counters (bankcount) and insurance agencies (agencies), over population (in thousands). Rather than by Beck and Webb's (2003) finding on bank development, which regards developing countries, this inclusion is motivated by the widespread belief that life insurance be "sold rather than bought," meaning that the ability of salespeople is a powerful force in shaping demand (see Bernheim et al., 2003). A different explanation could be that selling points density reduces the cost of searching for an appropriate policy, but the high standardization of life products and the diffusion of selling points are so high as to make the searching costs explanation less plausible. (7) In this light, in an alternative specification, we consider population density, which as claimed by Feyen, Lester, and Rocha (2013) (and hypothesized as well by Outreville, 1996; Beck and Webb, 2003 for the related measure of urbanization) should capture how the concentration of customers in space simplifies the distribution of products. The theoretical support for the inclusion of population density in a model of life insurance consumption is nevertheless comparatively weak as opposed to nonlife, where population density can be seen as a proxy for risk conditions regarding a number of perils, from theft to motor accidents.

We also add education (school), which might capture the degree of financial sophistication and risk awareness of the population, and the general level of trust based on survey data. Education is unlikely to be relevant here as a measure of human capital in the insurers' production function, as claimed by Outreville (1996) and Beck and Webb (2003), considering that production takes place at the national level.

In the spirit of Hofstede (1995), we acknowledge the influence of cultural values in the purchase of insurance and the need to account for them, although in our more homogeneous setting this is probably mitigated. As noted in Ward and Zurbruegg (2000), the argument in Fukuyama (1995) that a higher level of trust facilitates economic transactions is readily applicable in insurance (see also de Meza, Irlenbusch, and Reyniers, 2010; Guiso, 2012). A survey-based measure of trust (trust) is therefore added to the model.

Finally, an index of judicial inefficiency (lawinef) is added, consistent with the findings of La Porta et al. (1998) on the influence of the legal environment on financial development and the specific results of Ward and Zurbruegg (2002) regarding Asian insurance markets (see also the discussion in Beck and Webb, 2003). The index is the average length of civil trials from Guiso, Sapienza, and Zingales (2004).

Data Description

We draw on Italian data collected at the provincial level over the years 1996-2001. In the following, we refer to the (then-) 103 Italian administrative units called province, corresponding to level 3 in the NUTS (Nomenclature of Territorial Units for Statistics) classification by Eurostat. We also refer to macroregions, which divide the territory into five aggregates: North-West, North-East, Center, South, and Islands. The dependent variable, Life insurance density in euro per capita, comes from the Italian regulatory body, Isvap. As observed, it takes much different values across Italian provinces, being generally lower in the South of the country. All of the last 20 regions in the overall ranking come from the South and Islands; all but one of the first 20 are northern regions. Besides high spatial differentiation, insurance density shows a high degree of spatial correlation, (8) as shown by Figure 1.

The situation is much alike for most of the possible determinants of insurance consumption, although clustering is less apparent. Spatial dependence is confirmed by the spatial correlation Moran's I test reported in Table 2.

The description and sources of the regressors included in the model can be found in Table 1, some descriptive statistics in Tables 2 and 3. All monetary variates are expressed in real terms using 2000 as the base year by deflating them with the official national price index from Istat, the Italian statistical institute.

Heterogeneity and Correlation in Space and Time

Our setting poses a number of specification problems, mostly related to heterogeneity and dependence in time and space. To control for unobserved heterogeneity in space we add both macroregional fixed effects and provincial random effects. As Wooldridge (2002, p. 288) notes, this is a sort of middle ground between FE and RE analysis, a way of dealing with regressor-related heterogeneity while retaining most of the efficiency of a random effects estimator. Anyway, adding provincial fixed effects would not be an option in this setting, where cross-sectional variability is the main focus of the study and some regressors are very persistent or even time invariant altogether. The limited time dimension of our study also allows to include time dummies to account for time shifts of all those factors that have been omitted because they are cross-sectionally invariant, like policy loadings (the "price" of insurance) and investment returns.

As Beenstock, Dickinson, and Khajuria (1986) observe, serial correlation is very likely to be an issue in life insurance data because of the considerable slice of recurring payment policies, so that any shock to premiums in one given province and year is bound to persist in subsequent years, albeit with decreasing intensity. This time-decaying kind of serial correlation is different from, and may coexist with, the time-invariant error persistence given by individual error components: the first accounting, as observed, for the (limited) persistence of a shock whose memory is eventually lost, the second for a permanent unobserved individual feature.

Spatial correlation can arise as a meaningful characteristic of the data-generating process, if justified by the economic model, or as a specification and measurement problem, typically due either to the so-called aggregation bias, "a mismatch between the spatial unit of observation and the spatial dimension of the economic phenomena under consideration" (Anselin and Bera, 1998, p. 239), or to the omission of a spatially correlated regressor. It can be modeled as a spatial diffusion process in the dependent variable (spatial lag), whereby the outcome in each province influences those of neighbors, and/or in the errors (spatial error), meaning that idiosyncratic shocks in one place partly propagate in space toward neighboring ones. In our case an influence of life insurance purchases in one province on neighbors is difficult to justify, while the spatial diffusion of shocks is a plausible hypothesis, as shocks to demand or supply will hardly follow the administrative boundaries according to which the data have been collected.

SPECIFICATION AND ESTIMATION

Beside the inclusion of macroregional and time fixed effects, the peculiar features of our problem require the estimation of a model with individual (provincial) random effects (9) and both serial and spatial correlation in the idiosyncratic error. Moreover, the nature of the spatial correlation is unclear and therefore it is not possible to choose a priori between the two common specifications of spatial lag (where the dependent variable premultiplied by a spatial contiguity matrix is added to the right-hand-side regressors) and spatial error, where it is the idiosyncratic error term that is spatially lagged.

Specification

Case (1991) estimates a model nesting both spatial specifications in order to account for any possible source of spatial effects and, after estimation of the full model, discriminate via a Wald test. Building on the general approach of Anselin (1988) and on analytical results from Baltagi et al. (2007), we augment Case's specification with a time-autoregressive term in the remainder of the idiosyncratic error:

y - [lambda] ([I.sub.T] [cross product] W)y + X[beta] + u u = ([I.sub.T] [cross product] [mu]) + [epsilon] [epsilon] = [rho]([I.sub.T] [cross product] W)[epsilon] + v [v.sub.t] = [psi][v.sub.t - 1] + [e.sub.t], (1)

where y is the nT x 1 response vector, X is the nT x k matrix of regressors, and v is the nT x 1 vector of autocorrelated error terms, all stacked by year and then province; W is an iixii spatial weights matrix representing the relative position of units in geographical space, and as such assumed exogenous and time invariant. More precisely, here W is a binary contiguity matrix with ones corresponding to neighboring provinces, zeros elsewhere, standardized so that the row sums are all one. (10) [micro] is an n x 1 vector of individual random effects with elements [[mu].sub.i] ~i.i.d. N(0, [[sigma].sup.2.sub.[mu]); and [I.sub.T], [1.sub.T]/ respectively, a T x T identity matrix and a T x 1 vector of ones; [v.sub.t] and [e.sub.t] are n x 1 vectors. As for the estimands, [beta] is the vector of parameters of interest, [lambda] and [rho] are the spatial autoregressive and spatial error coefficients, and [psi] is the (time) autoregressive coefficient for the remainder error term vt. The error terms [epsilon], v, and [e.sub.t] are normally distributed and X, [micro], and [e.sub.t] are assumed to be mutually independent. As observed, this specification is meant to control for individual heterogeneity ([phi]), for serial error correlation deriving from the persistence in time of idiosyncratic shocks ([psi]), and for two possible kinds of spatial diffusion processes: in the dependent variable ([lambda]) and in the idiosyncratic shocks ([rho]). As a variance ratio, [phi] is constrained to be positive. According to the previous literature (Beenstock, Dickinson, and Khajuria, 1986), [psi] is expected to be positive too, and significantly so. On the contrary, as observed above there are no compelling reasons to hypothesize a diffusion process in the dependent variable (translating into [lambda] > 0). The expected sign of [rho] is less clear-cut; as observed above, a positive spatial correlation in errors would show evidence of shock propagation across space, and is the most likely outcome; but a negative one, which could be associated with local cross-border spillovers due to aggregation bias (see Millo and Carmeci, 2011, p. 5.1), is also a possibility.

Estimation

We estimate the model as specified in Equation (1) by two-step maximum likelihood (ML); see Millo (Forthcoming) for computational details. Coefficient estimates are reported in Table 6 and will be discussed in the next section. Of the spatial lag and error covariance parameters (Table 4), the former turns out not significant while the spatial error parameter is significant and rather large, indicating a spatial diffusion process in the errors. Random effects and serial correlation are in turn, respectively, not significant and highly significant, pointing to time-decreasing error persistence rather than time-invariant individual effects. As for the time and macroregional fixed effects (Table 5), the former are significant and almost linearly increasing, while of all the macroregional effects South and Islands turn out very similar, and much different from the rest of Italy. In general, estimation results indicate that neglecting spatiotemporal correlation would have led to inefficient estimation of the vector [beta] of the parameters of interest, but at the same time, they show some directions for admissible simplification of the model, which will be pursued below.

The model shows strong serial correlation in the errors (0.68), as expected, confirming the persistence of idiosyncratic shocks discussed above. By contrast, the evidence of a random effects structure is weak: the variance of the individual error component, picking up that part of the heterogeneity not yet accounted for by macroregional fixed effects, is estimated at 33 percent of the idiosyncratic error variance and not significant. As for the spatial parameters, the Wald test for spatial lag versus spatial error correlation implicit in the encompassing model favors the second, which is significant and substantial (0.39), while the spatial lag coefficient is not significantly different from zero (Table 4).

It is worth noting that in our case separate estimation of a spatial lag or a spatial error model would yield significant spatial terms in each case (results omitted). The encompassing model instead allows us to discriminate between the two cases, avoiding misleading conclusions. Our evidence favors a diffusion process in the errors whereby idiosyncratic shocks propagate to a certain extent to neighboring provinces; on the contrary, as expected, outcomes in one province do not seem to influence those of neighbors.

Discussion of Estimation Results

According to the diagnostics for the full model, the specification is to be reduced to a pooled model with spatial and serial correlation in the errors, and neither random effects nor an SAR term. The statistical admissibility of this reduction is supported by a joint likelihood ratio test ([chi square](2) = 2.68, P-value = 0.26). Estimation of this reduced specification yields slightly higher serial correlation (0.73) and lower spatial correlation (0.25) in the errors. Results for the coefficients in [beta] are reported in Table 6 as Model 0.

As expected, disposable income is a very significant positive driver of life insurance consumption, confirming all previous evidence: higher income flows lead to increased insurance purchases. We attribute this to both life protection and income protection products, for the reasons discussed above. An alternative specification (Model 1 in Table 6) substituting GDP for disposable income (see the discussion in Browne and Kim, 1993, p. 622) confirms the positive result, although predictably yielding a much lower estimate for the elasticity. Fit statistics empirically support the theoretical preferability of disposable income and hence of Model 0 as our maintained specification. (11)

Our proxy for aggregate wealth, the per capita amount of bank deposits, is significantly positive too, a less obvious result. As observed, based on the model of Lewis (1989) wealth should exert a negative effect on life protection insurance (the well-endowed are better protected from loss of breadwinners' income risk) while according to Beenstock, Dickinson, and Khajuria (1986), it is positively related to saving products. Our analysis seems therefore to capture the effect of wealth on the saving-related part of life premiums, while not finding any evidence in favor of Lewis's (1989) effect.

Social security expenditure, which should in theory substitute for income protection, is negative (contrary to what happens in cross-country comparisons) but not significant: the effect of public welfare seems statistically not discernible in a homogeneous setting, but shows the expected negative sign. Regarding social security as a proxy for wealth, as used by Browne and Kim (1993), the availability of a better measure (bank deposits; see above) highlights its inappropriateness: the latter is, as observed, significant and positive just as one would expect, while social security retains its negative sign and a very similar value if bank deposits are removed from the model (see Model 2). We conclude that the hypothesis of social security as a substitute for private life insurance is consistent with, albeit only weakly supported by, our data, and that the use of social security as a proxy for wealth is unwarranted.

Regarding dependency indicators, the only significant one is the young dependency ratio: the presence of young dependents is associated with life insurance purchases, confirming the predictions of Lewis (1989). On the contrary, neither the share of the elderly nor the labor force participation rate or the average number of family members seem to play a role once we have controlled for the share of the young. The signs of the coefficients on family size and participation rate are, respectively, positive and negative, as expected, reflecting their correlation with the number of dependents, while old dependency is very close to zero. Hence, while providing evidence in favor of the life protection function theory of Lewis (1989), our data do not support the conjecture in Beck and Webb (2003, p. 13) (the elderly are assumed to buy more of both life protection and savings products) neither the opposite, life-cycle view (the elderly are dissaving). Again, this is in sharp contrast to international evidence in Beck and Webb (2003), where life insurance is directly related to the share of the old and inversely to that of the young. A different approach (Beenstock, Dickinson, and Khajuria, 1986; Browne and Kim, 1993; Outreville, 1996) considers (average) age as a proxy for life expectancy. As the argument goes, (1) people expecting to live "longer" would be inclined to buy more annuities (income protection life insurance, in our framework) because they would earn benefits for a "comparatively longer" time (Beenstock, Dickinson, and Khajuria, 1986), or (2) people expecting to die "earlier than average" should buy more life protection insurance. Therefore, average age should have a positive effect on the former, a negative one on the latter. At the national aggregate level, we consider this reasoning a fallacy: insurance will typically be priced according to national mortality tables, that is, to average life expectancy, so that annuities will be more expensive where people tend to live longer, life protection where life expectancy is shorter, offsetting the effect that is unsurprisingly never (12) found significant in empirical studies (see also Li et al., 2007, p. 641). Yet this reasoning might become relevant in our subregional setting (as it is a fortiori for individual data): if prices are set according to national average mortality, provinces (individuals) with longer life expectancy should actually find income protection products relatively cheap, and the opposite for life protection. Moreover, given the preponderance of annuities' revenue over that of life protection policies, if this theory holds we would expect the positive effect to prevail. Average age is therefore added to an alternative specification (Model 3) because of collinearity with dependency ratios. For the above reasons, we consider the negative and significant observed effect as due to negative correlation with the (omitted) share of young dependents. While it might also be seen as consistent with argument (2), it sure is evidence against (1).

Schooling in turn proves negative and significant at the 1 percent level. As observed, many (Truett and Truett, 1990; Browne and Kim, 1993; Li et al., 2007; Feyen, Lester, and Rocha, 2013) see education as positively related to risk awareness (and hence to life insurance consumption). Our evidence supports instead the minority view that relates education to the willingness and the capacity to manage risks, implying that better educated people are able to better diversify their portfolios, holding a greater variety of (possibly riskier) assets and thus reducing the slice of safe assets as life insurance.

Among other controls, judicial inefficiency is insignificant. As this is the main distinctive character in an otherwise homogeneous legal environment, this finding contradicts the applicability of the general arguments of La Porta et al. (1998) to the life insurance case and of the specific findings of Ward and Zurbruegg (2002) to the Italian one. Moreover, this finding is strikingly dissimilar from the sharp negative effect of judicial inefficiency on nonlife insurance in Millo and Carmeci (2011), which testifies to the appropriateness of trial length as an efficiency measure. We conclude that property rights protection, and in general the rule of (civil) law, is not an important determinant of life insurance purchases in an advanced democracy, the difference with respect to nonlife being consistent with the lesser amount of litigation involving life contracts. Trust is a positive driver, as also found by Guiso (2012) for nonlife insurance and by Guiso, Sapienza, and Zingales (2004) for financial development at large.

As for supply controls, despite the current trend toward the preminence of bancassurance in life distribution, the density of bank counters is not significant at all. The density of insurance agencies proves instead to be an important positive factor, suggesting that tied agents are still a crucial force in shaping the market. The density of overall population, unlike what happens in nonlife insurance (see Millo and Carmeci, 2011), is not significant, (13) which is unsurprising, considering that (as observed in the third section) the case for its inclusion is much different and comparatively weaker. While a good predictor of risk conditions in nonlife, the role of population density as facilitating life insurance distribution via the concentration of consumers in space is not confirmed by our evidence, irrespective of the inclusion of the other two distribution variables. We conclude that in an urbanized and, on average, densely populated country such as Italy, life insurance consumption does not depend on the generic concentration of people in space or on the density of bank counters, but does indeed benefit from a denser network of dedicated agents.

Lastly, as observed, all relevant interest rates (both the financial yields on life insurance reserves and those of competing financial products) are invariant over provinces. The lending rate is the only observable financial yield to vary with the insured's province of residence. The reasons for including it in the model are unclear but, as its effect was positive and significant in Beck and Webb (2003), in order to control for the possibility that customers consider the spread between the interest rate on financing and the one they can get from investing, we include the cost of borrowing, which shows considerable territorial variability, in an alternative specification (Model 5). As expected, the estimated coefficient is not significant.

CONCLUSIONS

We approach the empirical investigation of life insurance consumption in Italy from a subregional perspective. The highest disaggregation level for which data are available is that of 103 provinces, which we observe over the years 1996-2001. This setting allows analyzing some of the determinants of insurance development in an environment that is highly integrated in other respects (legal, religious, monetary, fiscal) and free from the systemic differences that may overshadow some relationships of interest in cross-country studies. Moreover, some specification issues (most notably, the measurement of insurance prices and financial yields) turn out to be irrelevant because there is no variation at the cross-sectional level, and the common time variation can be easily accounted for. Lastly, we are able to distinctly observe disposable income and a good proxy for wealth and savings (bank deposits), disentangling their effects instead of proxying for both through GDP or GNP as usually done in the literature. An overview of the literature on insurance consumption provides the foundation for our model specification. Three economic functions of life insurance are discussed: protection of dependents in case of death, protection of one's own income stream in case of survival, and pure saving. Based on this, we identify appropriate explanatory variables and proceed to a descriptive analysis, showing evidence of spatial dependence and heterogeneity. We discuss some methodological issues arising from considering data from observational units inside an integrated market instead than from different countries, that is, spatial correlation, and from peculiar features of insurance, such as serial correlation. Together with the need to allow for individual random effects, these issues require a new maximum likelihood estimator for random effects panels with spatial lags, spatial and serial correlation, implemented elaborating on the work of Anselin (1988), Case (1991), and Baltagi et al. (2007) as described in Millo (Forthcoming).

Consistent with previous evidence, we confirm the positive influence of disposable income. Using bank deposits as a proxy for wealth, we identify a positive effect, which we see as related to the savings component of premiums; the latter possibly offsets the expected negative effect on life protection, which does not show up in the data. The ratio of young dependents to people of working age captures the need for life protection, while the substitution effect of social security payments, although showing the expected sign, is not significant. The positive coefficient of the density of the distribution network and that of trust (as defined by Guiso, Sapienza, and Zingales, 2004) point to important supply effects, to some extent validating the common wisdom that "insurance is sold, not bought." Lastly, and contrary to most previous research, the effect of the education level of the population turns out negative, a finding that we attribute to the role of education in fostering risk understanding and managing capabilities, driving customers towards riskier kinds of assets and away from the safe and moderate returns that characterize most life policies. In other words, better education seems to have been associated with disintermediation, reducing the perceived need for insurers' professional risk management and guarantees. Yet one must bear in mind that the time span of our sample has seen a bullish stock market throughout. To which extent the experience of the subsequent 10 years of recurring financial crises may have modified this attitude in the Italian public is an interesting subject for future research. As for the reasons of the extremely uneven geographical distribution of life insurance density in Italy, the model successfully explains spatial correlation and macroregional heterogeneity within two clusters of macroregions: the Center-North (North-West, North-East, and Center) on one side, and the South and Islands on the other. Nevertheless, an unexplained difference in outcomes remains between the two. A better explanation of the Italian "insurance divide" will be another subject for further work.

DOI: 10.1111/jori.12023

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(1) According to CEA, the European insurers' association, in 2000 the ratio of life insurance reserves on GDP (a common measure of the sector's importance) reached 97 percent in the United Kingdom, 69 percent in Sweden, 67 percent in Switzerland, 51 percent in France, 26 percent in Germany, and 16 percent in Italy.

(2) There is no clear correspondence between the theoretical functions of life insurance and the Italian official classification, according to which the actual composition of life insurance sold in Italy in 2000 was: traditional endowment and annuities plus term life (Class 1) 44.2 percent; unit- and index-linked policies (Class 3) 42.3 percent; capitalization (life-independent endowment) (Class 5) 13.3 percent; pension plans (Class 6) 0.2 percent.

(3) More precisely, they are significant in the cross-section but are not in the panel sample.

(4) The lending rate is the only observable financial yield to vary with the insured's province of residence. Although excluding it from the maintained model for lack of theoretical support, as a robustness check we added it to an alternative specification.

(5) We verified the appropriateness of deposits as a proxy for wealth drawing on a new database from the Bank of Italy (see Albareto et al., 2007), comparing our data on bank deposits with their estimates of household wealth for the year 1998. On a per capita, cross-region basis, the correlation between bank deposits and real assets was 0.92, with financial wealth 0.80, both significantly positive at the 1 percent level. Province-level data are not available.

(6) It is notorious that inability pensions are used as an improper state subsidy to some poorer parts of Italy by tacitly lowering requirements and controls, although both the economic and geographic dimensions of the phenomenon are unclear.

(7) Nowadays, the banks' share in the distribution of life policies is steady at 50 percent of premiums, while the Post Office is gaining ground at the expense of tied agents. Financial promoters and company staff hold a minor and quite steady slice. The strategies of the supply side play a major role in driving revenues of one channel over the other or those of life insurance over competing financial products from the same groups.

(8) Tests and diagnostic plots for spatial correlation as well as spatial models are based on a spatial weights matrix constructed according to the principle of queen contiguity (i.e., provinces are considered neighbors if they share a common border or vertex; see LeSage, 1999). According to common practice, the matrix has been row-standardized. Reggio Calabria and Messina, divided by the Messina Strait, have been considered contiguous.

(9) For another application of the same specification strategy to insurance data, see Millo and Carmeci (2011), beginning of sixth section.

(10) Standardizing the row sums of the W matrix allows for an intuitive interpretation of the spatial lag of a variable X as, for each determination [x.sub.i], the (arithmetic) average of the values X takes in the set of neighboring locations J; in our panel context, the generic element of the spatial lag WX is then W[X.sub.it] = [[summation].sub.j [member of] J] [w.sub.ij] [x.sub.jt]. Different choices for W are possible, and are common in the literature: especially distance-based weights, where distance can be geographic or defined according to some economic measure. The choice of the contiguity matrix is one of the most controversial subjects in spatial econometrics (see Anselin, 1988, p. 19). Binary contiguity has the advantage of simplicity, of imposing a minimum of a priori structure and of making the interpretation of a spatial lag straightforward as the average value of neighbors; therefore (Anselin, 1988, p. 21), it is often preferred for spatial error structures and in general where the focus is on testing for spatial effects rather than on precisely estimating a theoretically well-defined spatial process.

(11) Given that Model 0 and Model 1 have the same number of parameters to be estimated, (minus) the maximized log likelihood can be interpreted as an information criterion, such as, for example, AIC or BIC.

(12) A partial exception is the reduced model in Outreville (1996, table 3).

(13) Actually, it is significant at 5 percent in Model 1, but as discussed above, Model 0 was preferred to Model 1 in terms of model fitting.

Giovanni Millo is at the Research and Development Department at Generali S.p.A., via Machiavelli 3, 34132 Trieste, Italy. Millo can be contacted via e-mail: giovanni_millo@generali. com. This article is a thoroughly revised version of Chapter 2 of the author's doctoral dissertation at DEAMS, University of Trieste. The views expressed are solely his own and do not necessarily reflect those of his employer. Gaetano Carmeci is at the Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche (DEAMS) at the University of Trieste, piazzale Europa 1, 34127 Trieste, Italy. The author gratefully acknowledges financial support from MIUR-PRIN (2005--Prot. N. 2005132539-002). The authors would like to thank for his precious insights into the Italian life insurance market Roberto Menegato; for useful comments and suggestions at various stages of this work: Giacomo Pasini, Annapaola Lenzi, Elisa Tosetti, Roberto Cannata, and participants to the following conferences: Spatial Econometrics Association, Cambridge 2007; European Regional Science Association, Liverpool 2008; Applied Statistics Conference, Bled 2008; Italian Congress of Econometrics and Empirical Economics, Ancona 2009; and to internal seminars at DEAMS, University of Trieste. They are also grateful to two anonymous reviewers for constructive comments, which helped to improve the article. All the computations in the article are done inside the R open-source environment for statistical computing (R Development Core Team, 2012), using the splm add-on package for spatial panel data econometrics (Millo and Piras, 2012) and, for spatial dependence tests, the spdep package (Bivand, 2012). This article has been prepared as a dynamic document with the Sweave utility (Leisch, 2002) according to the principles of literate statistical practice.

TABLE 1 Description and Sources of Regressors Description Source ryd Real per capita disposable income 1st. Tagliacarne rgdp Real per capita value added 1st. Tagliacarne rbankdep Real bank deposits per capita Bank of Italy socialsec Real per capita social security 1st. Tagliacarne payments family Average number of family members Istat odeprat Old dependency ratio Istat (over 65 to 15-64) ydeprat Young dependency ratio Istat (under 14 to 15-64) age Average age Istat partrate Labor participation rate of people 1st. Tagliacarne aged 15-64 school Share of people with second-grade Istat schooling or more lawinef Judicial inefficiency: years to settle [17] a civil case trust Survey results to the question "Do you World Values trust others?" Survey bankcount Bank counters per 1,000 inhabitants Bank of Italy agencies Density of insurance agencies per 1,000 Isvap inhabitants density Population density in 1,000/[km.sup.2] Istat rirs Real interest rate on borrowing 1st. Tagliacarne TABLE 2 Summary Statistics; Range, Inequality (Gini's Coefficient), and Spatial Correlation Tests (Moran's I) for the Year 2000 Min. Italy Max. Gini Moran ryd 8,232.91 13,420.02 18,838.51 0.12 12.45 *** rgdp 10,051.70 17,564.85 28,650.07 0.14 11.64 *** rbankdep 3,878.30 8,388.58 21,981.67 0.20 8.69 *** socialsec 1,026.69 2,103.23 6,218.51 0.21 9.70 *** family 2.05 2.60 3.07 0.05 11.00 *** odeprat 16.22 26.78 36.54 0.10 9.40 *** ydeprat 13.55 20.30 28.79 0.11 12.92 *** age 35.46 41.43 46.09 0.04 11.71 *** partrate 35.47 47.85 58.08 0.05 9.48 *** school 34.32 41.85 50.00 0.05 11.66 *** lawinef 1.44 3.79 8.32 0.20 7.29 *** trust 3.03 3.26 3.62 0.02 7.88 *** bankcount 0.22 0.52 1.01 0.20 11.81 *** agencies 0.13 0.38 0.59 0.15 11.92 *** density 36.95 244.92 2,646.92 0.46 1.52 ([dagger]) rirs 2.98 4.99 7.68 0.10 10.70 *** Note: ([dagger]) = significant at 10 percent; *** = significant at 0.1 percent. TABLE 3 Macroregional Averages, Year 2000 N-W N-E Center South Islands ryd 15,600.56 15,559.07 14,243.68 10,396.13 9,793.90 rgdp 20,475.58 21,815.82 18,354.19 12,677.81 12,368.46 rbankdep 10,201.66 10,514.48 9,088.06 5,568.43 5,303.25 socialsec 2,960.79 2,369.16 2,030.48 1,497.97 1,258.35 family 2.39 2.48 2.58 2.85 2.79 odeprat 28.18 27.97 29.57 23.84 22.84 ydeprat 17.74 17.76 18.48 24.72 24.46 age 42.83 42.68 42.78 38.98 38.84 partrate 49.87 51.88 48.20 43.96 43.64 school 43.54 43.88 44.63 39.01 35.83 lawinef 2.89 2.86 3.71 5.14 4.76 trust 3.32 3.30 3.24 3.20 3.19 bankcount 0.61 0.71 0.54 0.31 0.36 agencies 0.45 0.45 0.42 0.28 0.26 density 301.84 250.97 204.35 270.67 149.61 rirs 4.47 4.43 4.60 6.01 5.76 TABLE 4 Error Variance Parameters (Top) and Spatial Autoregressive Coefficient (Bottom), as in Equation (1) Pr(> [absolute Estimate Std. Error t-Value value of t]) [phi] 0.3301 0.2773 1.1902 0.2340 [psi] 0.6800 0.0513 13.2605 0.0000 *** [rho] 0.3884 0.0973 3.9936 0.0001 *** [lambda] -0.1456 0.1126 -1.2930 0.1960 Note: [phi], ratio of random effects variance to idiosyncratic error variance; [psi], the (time) autoregressive; [rho], spatially autoregressive error coefficient; [lambda], spatial lag coefficient. *** = significant at 0.1 percent. Standard errors are based on estimates of the numerical Hessian. TABLE 5 Time and Macroregional Fixed Effects' Estimates and Diagnostics Pr(> [absolute Estimate Std. Error z-Value value of z]) year97 0.3561 0.0273 13.0586 0.0000 *** year98 0.8551 0.0386 22.1295 0.0000 *** year99 1.2342 0.0483 25.5661 0.0000 *** yearOO 1.4463 0.0579 24.9902 0.0000 *** yearOl 1.5490 0.0677 22.8959 0.0000 *** NorthWest 0.0987 0.0745 1.3253 0.1851 NorthEast -0.0910 0.0674 -1.3494 0.1772 South -0.5207 0.0900 -5.7848 0.0000 *** Islands -0.5405 0.1098 -4.9232 0.0000 *** Note: *** = significant at 0.1 percent. Standard errors are based on the GLS step at optimal values of spatial and covariance parameters. TABLE 6 Estimation Results Model 0 Model 1 Intercept -7.372 ** -2.153 log(ryd) 1.303 *** -- -- log(rgdp) -- -- 0.72 *** log{rbankdep) 0.185 * 0.252 ** log(socialsec) -0.082 -0.066 log(family) 0.279 0.137 odeprat 0.001 0.011 ([dagger]) ydeprat 0.023 * 0.017 ([dagger]) log(age) -- -- -- -- log(partrate) -0.035 -0.082 log(school) -0.707 ** -0.814 *** log(lawinef) -0.001 0.01 log(trust) 1.02 ([dagger]) 0.827 log(bankcount) 0.02 -0.004 log(agencies) 0.168 * 0.149 ([dagger]) log(density) 0.028 0.053 * log(rirs) -- -- -- -- logLik 336 -- 328.9 -- Obs 618 -- 618 -- n 103 -- 103 -- T 6 -- 6 -- Model 2 Model 3 Intercept -7.464 ** -0.974 log(ryd) 1.524 *** 1.405 *** log(rgdp) -- -- -- -- log{rbankdep) -- -- 0.237 * log(socialsec) -0.086 -0.124 log(family) 0.285 0.067 odeprat -0.003 ydeprat 0.022 * -- -- log(age) -- -- -1.403 ([dagger]) log(partrate) -0.03 -0.255 log(school) -0.75 ** -0.784 ** log(lawinef) -0.019 -0.001 log(trust) 1.018 ([dagger]) 1.237 * log(bankcount) 0.064 0.031 log(agencies) 0.178 * 0.143 log(density) 0.034 0.023 log(rirs) -- -- -- -- logLik 333.4 -- 178.3 -- Obs 618 -- 412 -- n 103 -- 103 -- T 6 -- 4 -- Model 4 Model 5 Intercept -8.706 *** -7.05 * log(ryd) 1.348 *** 1.406 -- log(rgdp) -- -- -- -- log{rbankdep) 0.211 ** 0.263 ** log(socialsec) -0.083 -0.133 log(family) 0.285 0.182 odeprat 0.001 -0.002 ydeprat 0.017 ([dagger]) 0.021 ([dagger]) log(age) -- -- -- -- log(partrate) -0.009 -0.231 log(school) -0.631 ** -0.822 ** log(lawinef) 0.002 0.003 log(trust) 1.259 * 1.38 * log(bankcount) -- 0.005 log(agencies) -- 0.149 log(density) 0.018 0.027 log(rirs) -- 0.02 logLik 333.2 -- 178.5 -- Obs 618 -- 412 -- n 103 -- 103 -- T 6 -- 4 _ Note: Model comparison. The dependent variable for all models is the log of per capita life insurance premiums. ([dagger]) = significant at 10 percent; * = 5 percent; ** = 1 percent; *** = 0.1 percent. Standard errors are based on the GLS step at optimal values of spatial and covariance parameters.

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Author: | Millo, Giovanni; Carmeci, Gaetano |
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Publication: | Journal of Risk and Insurance |

Article Type: | Abstract |

Geographic Code: | 4EUIT |

Date: | Jun 1, 2015 |

Words: | 11881 |

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