Estimating Spillover Effects in Property and Casualty Insurance Consumption

Abstract

The determinants of insurance consumption have been extensively studied, yet spatial correlations are rarely considered within this framework. In this article, we discuss several channels through which spatial dependence may arise and test for spatial dependence using six years (2009–2014) of province, city, and firm-level data from China. Results suggest that spatial spillover effects are large and have the potential to seriously bias marginal effect estimates if neglected. Specifically, when regions experience similar changes in determinants, marginal effect estimates in spatial models are nearly 1.5 times that implied by aspatial models. Additionally, we investigate the sources of the spatial dependence and find that cross-border spillovers occur within and between firms.

ACKNOWLEDGMENTS

We thank the editor and three anonymous reviewers for their valuable comments and suggestions. We also thank Professor Peng Shi for his contributions to the early stage of this work. The authors declare no conflict of interest.

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Notes

1 See, for instance, Outreville (2013) for an excellent overview of 85 empirical papers examining the relationship between insurance consumption and economic development.

2 For example, the U.S. Census Bureau reports that the proportion of residents commuting across state borders for work in another state is quite high in several jurisdictions, including Delaware (16.4%), the District of Columbia (25.2%), Maryland (18.3%), New Hampshire (17%), New Jersey (14%), Rhode Island (15.6%), and West Virginia (12.1%). The inbound commuter rate for the District of Columbia is especially notable, with 72.4% of all DC workers living in a different state (McKenzie 2013).

3 In addition, we examine the general robustness of parameter estimates to the omission of spatially correlated variables by excluding groups of regressors from our analysis. These results, shown in Table OA2 of the online appendix, suggest little change in spatially lagged dependent variable estimates when groups of highly significant variables are excluded from the model.

4 The Herfindahl–Hirschman Index is a measure of market concentration calculated by squaring and summing the market shares of all firms. Lower values indicate more competitive markets, while higher values indicate more concentrated markets.

5 Short-cycle courses are often practically based and occupationally specific. They are designed to prepare students to enter the labor market.

6 Regions are not considered neighbors to themselves. As a result, diagonal elements of the spatial weight matrix equal zero.

7 This analysis uses Stata’s user-written command xsmle to estimate all models. This command was written by Federico Belotti, Gordon Hughes, and Andrea Piano Mortari and estimates spatial panel models using quasi-maximum likelihood. For details about the command, we refer readers to the accompanying 2017 paper by Belotti, Hughes, and Mortari. xsmle is preferred to Stata’s built-in spatial panel command, spxtregress, because the former allows for the estimation of robust standard errors, while the latter does not. Coefficient estimates using xsmle are identical to those using spxtregress.

8 Effects on insurance consumption diminish as long as $\left|\rho \right|<1.$

9 Here, we assume the use of an adjacency weight matrix. For other types of weight matrices, distances between regions may also be important.

10 The sole exception to this statement is when increasing from two regions to three regions.

11 One could also control for region-level factors by including relevant explanatory variables. In this analysis, Equation (8) is estimated using city-level data, for which socioeconomic data are not consistently available.

12 Specifically, the sum of $\mathit{W}{\mathit{y}}_{\mathit{t}}$ and $\mathit{M}{\mathit{y}}_{\mathit{t}}$ is the same for all firms within a given region-year and thus is collinear with region-year fixed effects.

13 We use “province” to collectively refer to China’s 31 provinces, municipalities, and autonomous regions. The Constitution of the People’s Republic of China places municipalities (Beijing, Chongqing, Shanghai, and Tianjin) and autonomous regions (Guangxi, Inner Mongolia, Ningxia, Tibet, and Xinjiang) on the same administrative level as provinces. Although these jurisdictions are different from provinces and from each other in various ways, we account for that variation within our analysis.

14 See Section 4.4 for a discussion of these techniques.

15 We restrict our analysis to these firms because our model specification requires a balanced panel—a city can only be included in our analysis if all insurers write premiums in that city in all years. When using China’s three largest insurers, 289 of China’s 344 subprovincial cities are usable. If other firms were included, the number of usable cities would decline substantially.

16 In 2014, population data are missing for 55 of China’s 344 prefecture-level cities. In other years, the number of missing values is higher. As such, we are unable to construct measures of city-level population density for these areas.

17 Country-level studies must account for such factors. However, doing so can be challenging because these factors are often difficult to measure and positively correlated with one another.

18 The chi-squared statistic in the Hausman test is 72.45, suggesting the inclusion of province fixed effects. The F statistic in a test of year dummies is 17.10, suggesting the inclusion of time fixed effects.

19 Residual diagnostics for all models are shown in Figures OA1 and OA2 of the online appendix. Residual histograms suggest only minor departures from normality for our preferred model (Model 2). Our use of robust standard errors likely accommodates this issue. Plots of residuals versus fitted values do not indicate the presence of heteroskedasticity.

20 This analysis is warranted given the distribution of auto premium density observed in Figure 2. In examining the map, it appears that Beijing, Tianjin, and Shanghai may be the epicenter of the spatial spillovers.

21 Here, we focus on variables that are consistently different from zero at a 5% significance level.

22 Note that the inclusion of spatial errors in Models 2 and 4 does not alter the computation of direct, indirect, and total effects. As discussed in Section 4, direct, indirect, and total effects are a function of the spatial lag parameter, ρ, and a regressor’s estimated coefficient, β, but not the spatial error parameter, λ.

23 Recall that Model 2 appears to best represent the true data generating process. If we instead consider Model 4 results (our second-best fitting model), direct, indirect, and total effects are even more pronounced.

24 Recall that city-year fixed effects are infeasible, given their collinearity with the spatially lagged variables.

25 Subsequent tests (not shown) confirm this result.