Forecasting building permits with Google Trends

For example, Strauss (2013) finds that building permits outperform other standard leading indicators of overall economic activity, such as interest rates and oil prices in most US states.

In the USA, the federal agency in charge of collecting these data from granting government agencies is the US Census Bureau, which provides a monthly estimate through the Building Permits Survey. See more information in the data section.

Arouba and Diebold (2010), for example, stressed the importance of having higher frequency, real-time data to monitor macroeconomic variables. Also, the term nowcasting—which was coined by Giannone et al. (2008)—was introduced in the literature to refer to their methodology to update forecasts of lower-frequency variables, such as quarterly GDP, as higher-frequency relevant information appears, such as monthly industrial production.

Naturally, Google Trends has also been used in other research areas, such as oil spending (Yu et al. 2019) youth unemployment (Naccarato et al. 2018) and macroeconomics, for example to forecast inflation and consumer confidence (Niesert et al. 2019), just to name a few. For a review of the use of Google Trends in research during the last decade, see Jun et al. (2018).

We are only interested in the aggregated number of building permits in the USA, which present no missing data.

To see the exact dates of data releases, see https://​www.​census.​gov/​construction/​bps/​schedule.​html.

D’Amuri and Marcucci (2017) clarify this point. They present the following equations for calculating the Google search index (GI):Google also scales the index as follows: \({\text{GI}}_{T,r} = \frac{100}{{{\text{max}}_{t} \left( {S_{T,r} } \right)}}S_{T,r}\). D’Amuri and Marcucci (2017) interpret GI as the probability of a random user of the r location searching in Google for a particular term during a week.

It is also important to mention that D’Amuri and Marcucci (2017) show that the effects of sampling errors in Google Trends are quite negligible when applied to unemployment data.

Examples of this literature are, to name a few, Ginsberg et al. (2009) who select 45 queries over 50 million search terms using out-of-sample goodness of fit for illness data; and Scott and Varian (2014) who use Bayesian methods to automatically select predictors of initial claims and retail sales.

Of course, it is possible to use both simultaneously: for example, using the first method to narrow down some terms, and use judgment to discard terms that are most likely spurious. Examples of this approach are Fondeur and Karamé (2013), Choi and Varian (2012) and D’amuri and Marcucci (2017).

For our preferred search queries, we find high correlations between building permits and each of these variables, with and without seasonal adjustment. The lowest correlation is 0.86 for the query “new housing development” while the highest is 0.96 for the seasonally adjusted query “real estate exam.”

See a complete list of requisites to become a realtor in https://​www.​kapre.​com/​resources/​real-estate/​how-to-become-a-real-estate-agent.

Notice that estimates of the drift terms are removed from Table 7.

The penalty for the number of parameters is much higher with BIC than with AIC in estimation windows of 50 observations.

Here, \(\gamma \left( L \right)\) and \(x_{t}\) are defined as in expression (4).

Table 8 in “Appendix” shows estimates and diagnostic statistics of models (10) and (12) for building permits and the four different Google search queries under consideration. We have removed, again, estimates of the drift terms. We observe that our SARIMA specifications seem to offer a better representation of the data relative to our models (3) and (5). In particular, all the coefficients shown in Table 8 are statistically significant at usual levels, the Schwarz criterion are lower in Table 8 relative to the comparable figures in Table 7 and also the Durbin Watson statistics are closer to 2. This last point is indicating that SARIMA specifications seem to be more successful at removing the excess of first order autocorrelation in the errors relative to our simple specifications in (3) and (5). Finally, while the coefficients of determination show an important degree of heterogeneity, relative to our univariate linear specifications, we observe that SARIMA models tend to produce a higher coefficient of determination for our Google search queries, and a slightly lower one for building permits. This is the only aspect in which the basic linear model in (3) seems to be slightly better than the SARIMA specification in (9) and (11).

When recursive or expanding windows are used instead, the size of the estimation window grows with the number of available observations for estimation. For instance, the first nowcast is constructed estimating the models with R observations, whereas the last nowcast is constructed estimating the models with T observations.

Simulation evidence carried out by Clark and McCracken (2013) and Pincheira and West (2016) show that normal critical values tend to work well when multistep-ahead forecasts are constructed using the iterative method, at least when the data generating process is not very persistent. This is very important because in this paper we use the iterative method for the construction of multistep-ahead forecasts.

We use the word “lags” in parenthesis because we are also including in expression (1) contemporaneous terms of the search queries.

Let us recall that in nested environments the CW test removes a term that should be zero in population under the null hypothesis, but that is not zero in finite samples. Tables 4, 13, 14, and 15 corroborate this prior as the corresponding t-statistics of the GW/DMW test are always lower than the comparable t-statistics of the CW test.

The pairwise Pearson correlations of the 15 series for “real estate exam” fluctuate between 0.97 and 0.99. For "new construction," all correlations are at least 0.99. For "new housing development,” the correlation factors are between 0.90 and 0.96. Finally, the correlations for “new home construction” fluctuate between 0.97 and 0.99.