Research on China insurance demand forecasting: Based on mixed frequency data model

China’s insurance industry has grown rapidly but remains below developed countries in depth and density despite high aggregate premiums. Given macroeconomic shocks (e.g., pandemic, financial risks) and the stabilizing role of insurance, accurately forecasting insurance demand is important for policy and market planning. The study aims to construct and optimize a mixed-frequency MIDAS regression to assess how monthly macro indicators—Consumer Confidence Index (CCI), Economic Policy Uncertainty (EPU), and Consumer Price Index (CPI)—predict quarterly insurance demand (TID: premium income/GDP). The research questions are: (1) Do MIDAS models using high-frequency macro indicators improve short-term forecasts of insurance demand relative to same-frequency benchmarks? (2) Which indicators and weighting functions best predict TID, especially during COVID-19? (3) Can optimized MIDAS models provide reliable nowcasts and short-term forecasts for China’s insurance demand? The work contributes by applying MIDAS to insurance demand, evaluating internal design choices (weight functions, windows, combination schemes), and producing forward-looking forecasts.

Micro-level studies link insurance demand to life-cycle, financial position, asset portfolio, and demographics (e.g., older households allocate less to life insurance; financial status and portfolios create heterogeneity; married female heads more likely to purchase). From a macro perspective, background risk and macroeconomic volatility influence insurance decisions. The EPU index measures policy uncertainty; prior studies find higher EPU can raise insurance demand. Consumer expectations and disposable income also affect premiums. Hence, CCI, EPU, and CPI are plausible predictors for TID. On forecasting, traditional co-frequency models (AR, ARMA, GARCH, neural nets, GM) require frequency conversion, risking information loss/distortion. MIDAS integrates different frequencies via weighting polynomials, retaining high-frequency information and enabling nowcasting. Extensions include M-MIDAS, U-MIDAS, AR-MIDAS, ADL-MIDAS, FA-MIDAS, RR-/RU-MIDAS, and MF-DFM approaches. MIDAS has been successful in GDP, inflation, energy, and volatility forecasting, often outperforming co-frequency models and enabling timely nowcasts.

Data: Monthly CCI, EPU, CPI from 2006M1–2022M3; quarterly TID from 2006Q1–2022Q1. CCI and CPI from Wind; EPU from policyuncertainty.com. Monthly series seasonally adjusted via X-12-ARIMA. Visual trends and impulse responses indicate short-term impacts of CCI, EPU, CPI on TID. Model: MIDAS regression relates low-frequency TID to high-frequency regressors with polynomial lag weights and includes TID autoregressive term. Generic univariate h-step ahead form: y_t = β0 + β1 B(L^{1/m};θ) x_t^{(m)} + ε_t, with m=3 (monthly to quarterly), K up to 30 monthly lags, and h defining nowcast/forecast horizon. Multivariate MIDAS includes weighted lag polynomials for CCI, EPU, CPI and TID lag: TID_t = β0 + β1 B1(L^{1/3};θ) CCI_t^{(3)} + β2 B2(L^{1/3};θ) EPU_t^{(3)} + β3 B3(L^{1/3};θ) CPI_t^{(3)} + β4 TID_{t-p} + ε_t. U-MIDAS is the unconstrained lag version. Weighting functions tested: Beta, Almon, and Exponential Almon polynomials; parameters and lag orders selected by AIC. Estimation considers potential TID autocorrelation via AR(1). To assess COVID-19 effects, models are re-estimated excluding 2019Q3–2022Q1 and then tested on that period. Forecasting windows: fixed, rolling, and recursive identification are compared. Combination forecasting: aggregate univariate MIDAS forecasts via EW (equal weights), BIC-based weights, MSFE, and discounted MSFE (δ=0.9). Accuracy metric: RMSE over evaluation periods. Benchmarks: same-frequency AR and ARDL models. Nowcasting/forecasting: Full-sample estimates used to generate h=1–12 quarter-ahead paths for 2022Q2–2023Q1 for univariate, multivariate, and combined approaches.

Model selection: Using full sample, optimal univariate specifications by AIC were: CCI: Exp Almon-AR(1)-MIDAS with 3 monthly lags; EPU: U-AR(1)-MIDAS with 7 lags; CPI: Exp Almon-AR(1)-MIDAS with 24 lags. In-sample (excluding COVID-19) optimal lags increased (CCI 6, EPU 24, CPI 30), while weight types remained consistent, suggesting heightened TID sensitivity to these predictors during COVID-19. Benchmark comparison (in-sample prediction over 2019Q3–2022Q1): MIDAS outperformed co-frequency models. RMSEs: CCI AR(1)-MIDAS(3,6): 0.2447; EPU AR(1)-MIDAS(3,24): 0.8645; CPI AR(1)-MIDAS(3,30): 0.3085; Multivariate M(3)-AR(1)-MIDAS (CCI,EPU,CPI): 0.2759; Multivariate M(2)-AR(1)-MIDAS (CCI,CPI): 0.2375; AR(2): 0.4811; ARDL(1,0,0,0): 0.3608. Overall, multivariate MIDAS performed best, especially the M(2) model excluding EPU. Forecast windows: Across h=1–9, MIDAS RMSEs remained generally low (best ≈0.2226; worst ≈1.6118 largely for EPU), confirming stronger short-horizon performance. Rolling and recursive windows typically improved accuracy over fixed windows; optimal window varied by predictor (e.g., CCI favored rolling short-term; CPI favored recursive). Combination forecasting: Combining univariate MIDAS forecasts improved robustness and accuracy; BIC-weighted combinations most frequently yielded the lowest RMSEs (e.g., h=1 rolling BIC RMSE 0.2019), outperforming EW and MSFE/DMSFE in many horizons. Indicator importance: CCI showed the strongest predictive power and stability; EPU forecasts were more volatile and less informative during COVID-19; CPI contributed usefully, and excluding EPU improved multivariate accuracy. Nowcasting/short-term forecasts (2022Q2–2023Q1): Forecasted TID rose from 3.87 (2022Q1) toward pre-COVID levels by 2023, with combined and multivariate models providing stable paths and outperforming univariate projections. The study states recovery to pre-pandemic levels by 2023Q2 (and in conclusion notes 2023Q1), indicating imminent normalization. Policy-relevant result: Consumer confidence was the primary driver of insurance demand variations during COVID-19.

The research question—whether mixed-frequency models leveraging monthly macro indicators can improve and timely forecast China’s quarterly insurance demand—is addressed by consistent evidence: MIDAS models outperform AR and ARDL benchmarks and enable effective nowcasting. The weighting functions and lag structures preserve high-frequency information, which is critical for short-term responsiveness; rolling and recursive estimation capitalize on evolving data, further enhancing accuracy. CCI’s dominance highlights the behavioral channel: shifts in consumer sentiment translate quickly into insurance purchasing behavior, especially under pandemic-related uncertainty. EPU’s weaker predictive effect during COVID-19 suggests that not all macro uncertainty proxies equally inform insurance demand; CPI provides stable complementary information. The improved performance of multivariate and combined forecasts underscores the benefit of diversification across indicators and model specifications. These findings are relevant for insurers and policymakers seeking real-time monitoring and proactive policy responses to demand dynamics.

The paper demonstrates that MIDAS models, optimized by appropriate weighting functions and lag structures, provide superior in-sample predictive accuracy for China’s insurance demand relative to co-frequency AR and ARDL models and are well-suited for short-term forecasting and nowcasting. Rolling and recursive windows enhance performance, and BIC-weighted combination forecasts yield robust accuracy. Among predictors, CCI is the most informative and influential during COVID-19; EPU is volatile and less predictive; CPI remains a stable contributor. Forecasts indicate that TID should recover to pre-COVID-19 levels around 2023, implying positive near-term development. Policy implications: incorporate consumer confidence in insurance policy design; integrate behavioral indicators with mixed-frequency models for real-time demand assessment; and prepare for post-epidemic market expansion through demand- and supply-side reforms. Future research could expand indicator sets, test causal directions, and probe alternative MIDAS weighting schemes and model structures.

The study does not establish bidirectional causality among CCI, EPU, CPI, and TID, nor does it test for potential covariance issues. It also does not systematically assess limitations of different MIDAS weighting functions and their impacts on predictive performance. These constraints limit inference on structural relationships and generalizability across alternative MIDAS configurations, though they do not undermine the main forecasting conclusions.