Lessons from forecast averaging residential investment

This policy brief summarises three key lessons for policymakers, modellers, and forecasters from recent work on forecasting real housing investment (Cañizares Martínez et al., 2023a and 2023b). Our study offers a new approach to conditionally forecast residential investment in the largest euro area countries and the euro area. We estimate many models using a wide set of determinants and select the 50 best performing models. This forecast averaging approach addresses considerable model uncertainty in the case of residential housing investment. 

In a nutshell, our forecast averaging approach is based on selecting among many model equations the best performing ones in terms of four in- and out-of-sample selection criteria. The first selection criterion is the existence of a co-integration relation between residential investment and three long-run drivers: Tobin’s Q, income, and credit. All three long-run drivers can be measured in different ways, and we therefore consider three to five different measures of each. A novelty is that among the income measure we also consider a housing affordability index, which combines the joint impact of income, house prices, and mortgage rates in one variable. This results in 119 long-run equations of which we only keep those that show a cointegration relationship. As potential short-term drivers we not only consider the earlier mentioned three categories, but also four other groups: mortgage interest rates, macroeconomic variables, demographic and wealth series, and unemployment rate and uncertainty. Again, various measures of each group are considered, in total 15 series. To further select among the more than 100,000 potential equations, we apply an autocorrelation test as a general model misspecification test (second selection criterion), the individual significance of Tobin’s Q and income long-run coefficients (third selection criterion or restrict them to one in an alternative restricted model specification we consider), and at least a 10% out-of-sample forecast outperformance of an AR benchmark (fourth selection criterion). Three lessons emerge from our forecast averaging tool.

The first lesson is that forecast averaging is powerful. It steers forecasters and is evidencing the accuracy of forecast averaging in practice in the face of modelling uncertainty. This lesson confirms previous successes of forecast averaging that date back decades ago (Wang et al., 2022). Our forecast averaging approach consistently beats a battery of ambitious benchmark models (see Figure 1). The root mean squared errors (RMSE) of the averaged forecasts across the top 50 restricted equations relative to the RMSE of benchmarks is in all cases clearly below one. Among the benchmark models the model using building permits as only leading factor is performing comparatively well. Keeping an eye on building permits developments might thus be insightful for the residential investment outlook.

The second lesson is that long-run restrictions can help in enhancing forecasts of residential investment. This lesson of the usefulness of long-run restrictions should please forecasters as it improves the narrative of residential investment projections. The long-run restrictions of Tobin’s Q and income to one result for all countries in a much larger number of equations that fulfils the four selection criteria. The long-run restrictions also substantially improve the residential investment forecasts for Spain and the Netherlands. In those two countries real residential investment did not behave like a normal distribution, reflecting a boom-bust pattern in the sample. Figure 2 plots the long-run misalignment of real residential investment according to Tobin’s Q and real disposable income both restricted to one for the largest euro area countries and the euro area. Most notable is a steep increase in the Italian misalignment, following the introduction of the Italian Superbonus scheme in July 2020 (Financial Times, 2023; Ruggieri et al., 2023).

The third lesson is that country heterogeneity is key for modelling and thus forecasting residential investment. This lesson helps policymakers on implementing country-specific housing market policies and guides modellers on improving housing investment models. In fact, marked country heterogeneity in the drivers of residential investment exists. For example, Tobin’s Q is not cointegrated with residential investment in France and Italy. Moreover, housing affordability as income measure is especially relevant in Spain and the Netherlands. The estimated long-run credit sign also varies across countries. A negative long-run credit coefficient as found for Germany and Spain might be a signal of debt overhang. At the same time, short-run credit effects have been positive. Changes in mortgage interest rates are significantly adversely affecting residential investment growth in France and Italy. The finding of cross-country diversity in the drivers of residential investment is consistent with well-known structural differences across European housing markets. A broader implication of this lesson is that residential investment modellers and forecasters should not assume that another institution’s housing model or block will easily fit their modelling purposes. Instead, country-specific modelling approaches are needed.