# Financial-cycle ratios and multi-year predictions of GDP: Evidence from the
United States

Graziano Moramarco University of Bologna, Department of Economics - Piazza
Scaravilli 2, 40126 Bologna, Italy.
E-mail<EMAIL_ADDRESS>
###### Abstract

Using a large quarterly macroeconomic dataset over the period 1960Q1-2017Q4,
this paper documents the usefulness of selected financial ratios from the
housing market and firms’ aggregate balance sheets for predicting GDP in the
United States over multi-year horizons. A house price-to-rent ratio adjusted
for the business cycle and the liabilities-to-income ratio of the nonfinancial
noncorporate business sector provide the best in-sample fit and out-of-sample
forecasts of cumulative GDP growth over horizons of 1-5 years, outperforming
all other predictors as well as popular high-dimensional forecasting models
and forecast combinations.

##  1 Introduction

Investigating financial cycles and macro-financial linkages is essential for
understanding business cycles. Following the global financial crisis and the
Great Recession, the interactions between asset price dynamics, balance sheets
and real economic activity have become increasingly important ingredients of
macroeconomic analysis (see, e.g., Taylor and Uhlig [eds.] 2016; Gertler and
Gilchrist 2018; Mian and Sufi 2013, 2014a, 2014b). In particular, house prices
and credit have received a great deal of attention and have been argued to
provide “the most parsimonious description of the financial cycle” (Borio
2012). Empirical research has delivered substantial results on the predictive
potential of financial-cycle variables for business cycles (e.g., Mian and
Sufi 2014b; Jordà, Schularick and Taylor 2014). However, comprehensive
comparative evaluations are still needed to determine whether any specific
indicators, among those related to credit, balance sheets and housing, stand
out as effective predictors of output.

This paper offers a novel assessment of the predictive power of financial-
cycle indicators for U.S. real GDP over the period from 1960 to 2017. We
conduct an extensive evaluation using a dataset of 262 quarterly indicators,
which combines the FRED-QD macroeconomic database (McCracken and Ng 2015) with
additional variables, mostly housing and credit-cycle indicators. We find that
selected financial-cycle ratios are especially important to predict U.S.
cumulative GDP growth over horizons of three or more years. A house price-to-
rent ratio calculated over the aggregate stock of owner-occupied housing and
corrected for business-cycle fluctuations (Contessi and Kerdnunvong 2015;
Davis, Lehnert and Martin 2008) provides the best in-sample fit of multi-year
GDP growth. Also, this cyclically-adjusted price-rent (CAPR) ratio and the
liabilities-income ratio of the nonfinancial noncorporate business sector
(NNBLI) provide the best out-of-sample forecasts (both direct and iterated) at
all horizons between 1 and 5 years.111Interestingly, the nonfinancial
noncorporate business sector includes the activities associated with tenant-
occupied housing, which further strengthens the predictive role of the housing
market. Except for these two ratios, the predictive importance of housing and
credit indicators appears sensitive to the choice of the evaluation criteria
(in-sample fit or out-of-sample forecast accuracy) and the prediction horizon.

We also show that forecasts produced by single-predictor models using the best
financial-cycle ratios outperform those of large forecasting models like Large
Bayesian VARs, LASSO VARs and factor models, as well as forecast combinations
of a large number of macroeconomic variables.

This paper relates to other comparative evaluations of predictors of economic
activity using large datasets (e.g., Stock and Watson 2003; Banerjee,
Marcellino and Masten 2005; Marcellino, Stock and Watson 2003; Rossi and
Sekhposyan 2014), in particular those that assess the predictive power of
financial variables. In their seminal paper, Stock and Watson (2003) focus on
the role of asset prices (broadly defined) for forecasting GDP growth and
inflation in the United States and other countries, and provide a
comprehensive review of the early literature on this topic. More recently,
Claessens and Kose (2017) have surveyed the literature on asset prices and
macroeconomic outcomes. Based on this literature, the evidence on the
predictive power of financial variables for GDP growth is mixed. Some
variables, such as the term spread, exhibit good forecast performance, but
only in specific periods (Stock and Watson 2003; Chauvet and Potter 2013). The
paper also relates to the literature on cycles in credit, housing and equity
markets, and their relationships with business cycles (e.g., Claessens, Kose
and Terrones 2011; Drehmann, Borio and Tsatsaronis 2012; Borio 2012; Piazzesi
and Schneider 2016). In a series of influential contributions, Mian and Sufi
(2013, 2014a, 2014b, 2018) provide extensive evidence on the prominent role of
housing wealth and household debt in the recent financial crisis, the Great
Recession and the subsequent slow recovery. Jordà, Schularick and Taylor
(2013,2014,2016) provide stylized facts on the relationship between long
trends in credit and business cycles in advanced economies. Finally, this
paper relates to the literature on valuation ratios, such as stock market
price-earnings ratios (Campbell and Shiller 1998, Shiller 2015) and house
price-rent ratios (Sommer, Sullivan and Verbrugge 2011, Contessi and
Kerdnunvong 2015). Campbell (1999) provides theoretical justification for
using the stock market price-dividend ratio to forecast output growth, but
empirically finds that the variable shows no clear predictive ability.
Campbell and Shiller (1998) introduce the cyclically-adjusted price-to-
earnings (CAPE) ratio, smoothing out spikes due to expansions and recessions.
Using the same methodology, Contessi and Kerdnunvong (2015) construct the
cyclically-adjusted house price-rent (CAPR) ratio, and use it to test for
bubbles in the housing market.

Our paper is the first to show the outstanding predictive power of the CAPR
and NNBLI ratios for U.S. GDP in recent decades. Figures 1(a) and 2(a) plot
the log CAPR ratio and the NNBLI ratio and compare them with the cumulative
real GDP growth rate over the following 20 quarters.

The remainder of the paper is structured as follows. Section 2 presents the
data. Section 3 shows the results of in-sample evaluation. Section 4 presents
the (pseudo-)out-of-sample evaluation. Section 5 concludes.

##  2 Variables and data

Our analysis is conducted using a large quarterly dataset (262 macroeconomic
and financial variables) over the period 1960Q1-2017Q4. The dataset combines
the FRED-QD dataset222Available at
https://research.stlouisfed.org/econ/mccracken/fred-databases/. This paper
uses the 2018-06 vintage and the associated labels for variables. with the
variables reported in Table 1(a), which include a variety of financial-cycle
indicators (total credit to the non-financial sector, the credit-GDP ratio,
households’ mortgage debt and mortgage-income ratio, real house price growth
and price-rent ratios, the ratio of residential fixed investment to GDP, real
stock market prices and the cyclically-adjusted price-earnings ratio, and
households’ interest payments as a fraction of disposable income), as well as
leading indicators (the OECD composite leading indicator and business
confidence index) and the comprehensive National Financial Conditions Index
(NFCI) by the Chicago Fed to capture a variety of other financial factors.
Table 1(a) also indicates the data transformations used for these additional
variables. The FRED-QD dataset is made of 248 variables, which cover in detail
a wide spectrum of macro areas. McCracken and Ng (2015) classify the variables
into 14 groups: National Income and Product Accounts (NIPA); Industrial
Production; Employment and Unemployment; Housing; Inventories, Orders, and
Sales; Prices; Earnings and Productivity; Interest Rates; Money and Credit;
Household Balance Sheets; Exchange Rates; Stock Markets; Non-Household Balance
Sheets; Other. We apply the data transformations suggested by McCracken and Ng
(2015) to the FRED-QD raw data, the only adaptation being the use of year-on-
year instead of quarter-on-quarter changes/growth rates. Table 2 lists the
subset of FRED-QD variables that will be reported among the best predictors of
GDP in the following sections. In the results, uppercase labels will identify
variables from FRED-QD and lowercase labels the additional set of variables,
as shown by Tables 1(a) and 2.

The cyclically-adjusted price-to-rent ratio (CAPR) (Contessi and Kerdnunvong
2015) from Table 1(a) is the housing-market counterpart of the popular
cyclically-adjusted price-to-earnings ratio (CAPE) proposed by Campbell and
Shiller (1998) for the equity market, which is constructed by dividing the
real S&P 500 index by the 10-year moving average of real earnings on the
index. Accordingly, the CAPR ratio is calculated by dividing real house prices
by the 10-year average real rents:

$CAPR_{t}=\frac{HPI_{t}}{\frac{1}{40}\sum_{i=1}^{40}R_{t-1}}$

where $HPI_{t}$ denotes the house price index in real terms at time $t$ (in
quarters) and $R_{t}$ is the imputed real rent at time $t$. Following Davis et
al. (2008) and Contessi and Kerdnunvong (2015), we use prices and rents
measured on the aggregate stock of owner-occupied houses.333See Davis et al.
(2008) for methodological details. The raw data on house prices and rents over
the period 1960Q1-2018Q2 are available on the website of the American
Enterprise Institute at https://www.aei.org/historical-land-price-indicators/.
To calculate the CAPR before 1970Q1, the time series of rents is extrapolated
backward from 1960Q1 using the quarterly growth rate of the rent of primary
residence, as released by the U.S. Bureau of Labor Statistics and provided by
the FRED website (https://fred.stlouisfed.org/). The homeownership rate in the
United States in the period 1965-2017 ranged between 63% and 69% (see
https://www.census.gov/housing/hvs/index.html). Asset price-to-earnings ratios
seem particularly suitable for investigating the effects of asset booms and
the associated financial vulnerabilities on economic fluctuations. They are
generally monitored by investors to detect market overheating and have been
used by researchers to test for bubbles (e.g., Shiller 2015; Phillips et al.
2015; Diba and Grossman 1988; Contessi and Kerdnunvong 2015).

##  3 In-sample evaluation

Following Stock and Watson (2003), the in-sample evaluation of predictive
power is conducted using autoregressive distributed lag (ARDL) models for
multi-period cumulative GDP growth rates. More specifically, we predict the
$h$-quarter-ahead cumulative GDP growth rate, with $h=4,12,20$, using a
bivariate model that includes one predictor at a time plus lags of GDP growth.
We also consider results for $h=28$, which corroborate those obtained for
$h=20$ and are not reported here to save space. The economic significance of
alternative predictors is then evaluated using the $R^{2}$ of the regressions.

The ARDL regressions are as follows:

$y_{t}^{h}=\beta_{0}+\beta_{1}(L)y_{t-h}+\beta_{2,i}(L)x_{i,t-h}+u_{t}$ (1)

where $y_{t}^{h}$ is the log approximation of the cumulative GDP growth rate
over a period of length $h$, i.e., $y_{t}^{h}=\ln(GDP_{t})-\ln(GDP_{t-h})$,
$y_{t}$ is the log approximation of the year-on-year GDP growth rate at time
$t$, i.e., $y_{t}=\ln(GDP_{t})-\ln(GDP_{t-4})$, $x_{i,t}$ is the $i$-th
candidate predictor, $u_{t}$ is the error term, $\beta_{0}$ is a constant,
$\beta_{1}(L)$ and $\beta_{2,i}(L)$ are lag polynomials, such that
$\beta_{1}(L)y_{t-h}=\sum_{j=1}^{p}\beta_{1,j}y_{t-h+1-j}$ and
$\beta_{2,i}(L)x_{i,t-h}=\sum_{j=1}^{q}\beta_{2,i,j}x_{i,t-h+1-j}$.

The models are estimated using data in the time range 1974Q1-2017Q4. The
starting date is chosen so as to ensure that 95% of the time series have no
missing data in the sample (shorter series are excluded here but will be used
in the out-of-sample evaluation of section 4). To ensure perfect comparability
of $R^{2}$, the lag length is fixed across models. In particular, both $p$ and
$q$ are set to 5 to adequately account for serial correlation in quarterly
time series.

Table 3(a) reports the $R^{2}$ of the regressions. Predictors are listed in
descending order of $R^{2}$ and only the best 10 are reported for each value
of $h$, out of the 262 predictors in the dataset. The cyclically-adjusted log
price-rent ratio (label: $capr$) dominates over longer horizons. It is the
best predictor for $h=12,20$ and the second best for $h=4$. The OECD composite
leading indicator ($cli$) is a particularly strong predictor over short
horizons. It ranks first for $h=4$, then it gradually falls down the ranking
as the horizon increases (5th for $h=12$, 9th for $h=20$). Most of the top
positions are occupied by financial-cycle indicators. The noncorporate
liabilities-income ratio or NNBLI (FRED-QD label: NNBTILQ027SBDIx) is the
third best predictor for $h=4,12$, after CAPR and the unadjusted price-rent
ratio ($pr$), and the fifth best predictor for $h=20$. Private residential
fixed investment, both as a share of GDP and in growth rates (labels: prfi_gdp
and PRFIx, respectively), performs especially well over the 4-quarter horizon,
while the mortgage/income ratio (mortg_inc), households’ liabilities and net
worth relative to disposable income (LIABPIx and NWPIx), and the credit/GDP
ratio (cred_gdp) are effective predictors over longer horizons.

Among the other variables, the unfilled orders for nondurable goods (AMDMUOx)
feature in the top 10 for $h=4,12$, while the inventories to sales ratio
(ISRATIOx) for $h=12,20$.

The usefulness of the log CAPR appears even more remarkable if the lag orders
$p$ and $q$ are selected by the Bayes information criterion (BIC) (we first
select $p$, then $q$ conditional on $p$, given the maximum lag length of 5).
In this case, it is the best predictor at all horizons (results are not
reported).444The comparatively good performance of financial-cycle ratios such
as $capr$, $mortg\\_inc$ and $cred\\_gdp$ over long horizons is robust to the
inclusion of a deterministic time trend in GDP growth. In this case, $capr$ is
still the best predictor for $h=12$ and the third best predictor for $h=20$,
while $cred\\_gdp$ and $mortg\\_inc$ rank first and second, respectively, for
$h=20$.

A question to be addressed is to what extent the results depend on the
specific data transformations used here for the FRED-QD dataset, which are
based on the recommendations by McCracken and Ng (2015). As a robustness
check, we consider the results obtained when all ratios and rates are not
transformed, i.e., taken in levels. The top positions in the $R^{2}$ rankings
remain unchanged in this case.

##  4 Out-of-sample evaluation

The second part of the analysis evaluates the forecasting power of the
predictors out of the estimation sample. To this aim, we track direct and
iterated forecasts over time using a recursive-window scheme.555We also
consider rolling windows of various fixed lengths (40, 60 and 80 quarters).
However, the lowest mean square forecast errors are generally achieved in the
recursive-window case, so we report this in the paper. Direct forecasts are
made using multi-period ARDL models, while iterated forecasts are produced by
bivariate VAR models. The forecast horizons are the same as in the in-sample
evaluation, i.e., 4, 12 and 20 quarters (again, $h=28$ is considered but not
reported as it only strengthens the main results for $h=20$). Time series of
forecasts over different horizons are constructed for each one of the
competing models and then used for comparison. In particular, predictors are
evaluated using the mean square forecast errors (MSFE) computed over the
period 1990Q1-2017Q4. Given the maximum forecast horizon of 20 quarters, this
implies setting the ending point of the shortest estimation window to 1985Q1,
which is accommodated by moving the starting point to an earlier date than in
the previous sections, namely 1968Q2.666As the maximum number of lags is set
to 5, this specific start date is chosen to ensure that all the VAR and the
one-step ARDL models are estimated using data as far back as 1967Q1, which is
the first quarter in which data are available (after transformation) for at
least 90% of the time series in the dataset. Concerning the multi-step ARDL
models, the range of data used for estimation will depend on the relevant
horizon. Given the unbalanced nature of the dataset, the actual starting date
of the sample will adjust to the availability of the time series used for
estimation. In sections 4.1 and 4.2, which consider one predictor at a time,
all predictors are used regardless of the length of the respective time
series. Therefore, when interpreting the results it should be kept in mind
that a fraction of the predictors have fewer observations available for
estimation than others. To ensure that the MSFE is computed over the same
timespan for all predictors, only variables that have sufficient data to
produce forecasts for 1990Q1 should be considered. However, even if the
variables with an insufficient number of observations are included in the
evaluation, none of them ranks among the best performing predictors reported
in sections 4.1 and 4.2. The high-dimensional models presented in sections 4.4
exclude from estimation those variables (21 in total) whose time series start
after 1967Q1 (as they would lead to discard observations for all other
regressors), while the 14 predictors with the shortest time series (which do
not have enough data to make direct forecasts for as early as 1990Q1, at least
over the longest horizon) are excluded from forecast combinations.

Competing models are initially estimated on the shortest sample 1968Q2-1985Q1
and used to make forecasts for the interval 1986Q1-1990Q1. Then the sample is
recursively expanded by one quarter at a time and the estimation and
forecasting steps are repeated in each iteration.

###  4.1 Direct forecasts: ARDL models

The first out-of-sample evaluation procedure is based on direct forecasts
produced by bivariate ARDL models as in (1), in which the lag lenghts $p$ and
$q$ are selected recursively using the BIC. Let $\widehat{y}_{i,t+h|t}^{h}$
denote the direct out-of-sample forecasts of $y_{t+h}^{h}$ made by the model
with the $i$-th predictor, estimated on data up to time $t$:

$\widehat{y}_{i,t+h|t}^{h}=\widehat{\beta}_{0}^{(t)}+\widehat{\beta}_{1}^{(t)}(L)y_{t}+\widehat{\beta}_{2,i}^{(t)}(L)x_{i,t}$
(2)

and let $\widehat{u}_{i,t+h|t}=y_{t+h}^{h}-\widehat{y}_{i,t+h|t}^{h}$ denote
the forecast error incurred by the model at time $t+h$. The $i$-th predictor
is ranked based on the following MSFE:

$MSFE_{i,h}=\frac{1}{T_{1}-h-T_{0}+1}\sum_{t=T_{0}}^{T_{1}-h}\left(\widehat{u}_{i,t+h|t}\right)^{2}$

where $T_{0}$ is the end date of the shortest sample and $T_{1}-h$ is the end
date of the longest sample.

Table 4(a) reports the MSFE of the ARDL models relative to the benchmark AR,
i.e., model (1) without the terms associated with $x_{i}$ and with the lag
length $p$ selected recursively by the BIC. Table 6(a) shows the root mean
square forecast error (RMSFE) of the benchmark AR (direct forecasts). The log
CAPR ratio is by far the best predictor over long horizons ($h=20,28$) and the
second best predictor for both $h=4$ and $h=12$. The NNBLI ratio is the most
effective predictor for $h=4,12$ and the second best predictor at a 5-year
horizon. Forecast gains over the benchmark are substantial: the log CAPR ratio
and the NNBLI ratio achieve MSFE values as low as 0.29 (log CAPR for $h=20$)
and 0.32 (NNBLI for $h=12$). For $h=4$, NNBLI has a relative MSFE of 0.54.
Such results are all the more remarkable if one considers that only two
variables have MSFE values lower than 0.8 for $h=4$, only 4 variables for
$h=12$ and only 5 variables for $h=28$. The absolute RMSFE also helps
appreciate the forecast performance of CAPR and NNBLI. In terms of 20-quarter
cumulative GDP growth, the RMSFE of CAPR is 3.32%, corresponding to an average
annual error of 0.66 percentage points of GDP growth for 5 years. For $h=12$,
the RMSFE of NNBLI is 2.50%, corresponding to an average annual error of
0.83%.

Other top performers include the unfilled orders for nondurable goods
(AMDMUOx) (for $h=4,12$), the OECD composite leading indicator ($cli$) (for
$h=4,12,20$), the unadjusted price-rent ratio ($pr$) (for $h=4,20$),
industrial production of consumer goods (IPCONGD) (for $h=4,12,20$), the ratio
of households’ net worth to disposable income (NWPIx) (for $h=4,12$) and the
inventories to sales ratio (ISRATIOx) (for $h=20$).

###  4.2 Iterated forecasts: VAR models

The second out-of-sample approach uses VAR models to compute multi-step-ahead
iterated forecasts of GDP. Evaluation of predictors is conducted using models
that include only real GDP growth and one predictor at a time. The $i$-th VAR
can be written as:

$\widetilde{y}_{t}^{(i)}=a_{0}^{(i)}+\sum_{j=1}^{p}B_{j}^{(i)}\widetilde{y}_{t-j}^{(i)}+\varepsilon_{t}^{(i)}$
(3)

where $\widetilde{y}_{t}^{(i)}$ is the vector containing the year-on-year
growth rate of real GDP and the $i$-th predictor at time $t$, $a_{0}^{(i)}$ is
a $2\times 1$ vector of constants, $B_{j}^{(i)}$ is a $2\times 2$ matrix of
coefficients, $\forall j=1,\dots,p$, and $\varepsilon_{t}^{(i)}$ is a $2\times
1$ vector of error terms. The lag length $p$ is recursively selected by the
BIC for the whole system and the maximum length is again fixed at 5.

Predictors are ranked based on the performance of the VARs in terms of
forecasts of the $h$-period-ahead GDP level:

$MSFE_{GDP}^{(i,h)}=\frac{1}{T_{1}-h-T_{0}+1}\sum_{t=T_{0}}^{T_{1}-h}\left(\ln(GDP_{t+h})-\ln(\widehat{GDP}^{(i)}_{t+h|t})\right)^{2}$

where $\ln(\widehat{GDP}^{(i)}_{t+h|t})$ is the forecast of the log GDP level
for period $t+h$ obtained from model $i$ by cumulating the growth rate
forecasts over time.

Table 5(a) reports the MSFE of the best 10 VAR models for each horizon,
relative to the benchmark AR.777In this case the benchmark AR follows
specification (3). Table 6(a) shows the RMSFE of the iterated forecasts from
the AR model. The top positions remain largely unchanged with respect to Table
4(a). Once again, the log CAPR is the best predictor for $h=20$ and ranks
second for $h=4,12$. The NNBLI ratio is still the most useful predictor for
$h=4,12$.

Just as in Table 4(a), the forecast gains provided by CAPR and NNBLI over the
benchmark AR are substantial for every $h$. In particular, for $h=12$ the
relative MSFE of NNBLI is 0.34, corresponding to an absolute RMSFE of 2.31%
(an annual average of 0.77 percentage points of GDP growth). For $h=20$, the
log CAPR gives a relative MSFE of 0.40 and an absolute RMSFE of 3.56% (annual
average: 0.71%). For $h=4$, the relative MSFE of NNBLI is 0.55, corresponding
to an absolute RMSFE of 1.3%.

As for the other top predictors, once again private residential fixed
investment (as a share of GDP) ranks highly over the shorter horizon of 4
quarters, while the OECD composite leading indicator ($cli$) and the unfilled
orders for durable goods (AMDMUOx) rank highly over all horizons.

###  4.3 Further remarks

Like in Section 3, as a robustness check we also consider forecasts obtained
using all ratios and rates in levels. The top positions in the ranking of
direct (ARDL) forecasts are unaffected. In the case of iterated (VAR)
forecasts, two ratios, namely the ratios of net worth to disposable business
income for the nonfinancial noncorporate and corporate business sectors (FRED-
QD labels: TNWBSNNBBDIx and TNWMVBSNNCBBDIx, respectively), provide comparable
results to those produced by CAPR and NNBLI. However, the two net worth-income
ratios perform poorly in direct forecasts, therefore their forecasting power
is not as robust as that of CAPR and the NNBLI.

As shown in Sections 4.1 and 4.2, forecasts based on the best predictors
provide large gains in accuracy compared to forecasts from the benchmark AR
models. To determine if the predictive content of the variables is
statistically significant, we use the ENC-F test by Clark and McCracken (2001,
2013), which is suitable for comparing nested models and has been shown to
have comparatively high power among forecast encompassing and accuracy tests
(Busetti and Marcucci 2013). The test results indicate that both the log CAPR
and the NNBLI ratio have significant predictive content at all horizons.

Importantly, conducting forecast evaluations over sub-samples, we find that
the good predictive performance of CAPR and NNBLI is not simply determined by
global financial crisis period.

###  4.4 Comparison with high-dimensional forecasting models and forecast
combinations

Finally, we assess whether the forecasts produced by the best single-predictor
models are outperformed by those produced by methods that pool all available
information. We consider three models that use all predictors at the
estimation stage: (i) a Large Bayesian VAR (LBVAR) using the approach by
Bańbura et al. (2011), (ii) a LASSO VAR, i.e., a VAR estimated using a LASSO
penalty, and (iii) a factor model using principal components (a VAR model for
GDP growth and a set of principal components extracted from all predictors).
The three models reflect different approaches to the problem of high
dimensionality. The LBVAR approach retains all the available predictors in the
forecasting model, applying a shrinkage method that does not restrict any
coefficient to be exactly zero. The LASSO VAR performs variable selection by
setting a subset of coefficients exactly to zero. The principal component
approach reduces the dimension of the model by summarizing the dataset of
predictors into a small number of factors. We estimate the LBVAR and LASSO VAR
using grids of values for the shrinkage/penalty parameters and report the best
results for each forecast horizon.888The LBVAR model is estimated using a grid
of possible values for the shrinkage parameters $\lambda$ and $\tau$, using
the notation by Bańbura et al. (2011). In particular, the values considered
for $\lambda$ lie in the range [0.0001, 0.1], while $\tau$ can assume values
$\tau=10\lambda$ and $\tau=100\lambda$. The value $\tau=100\lambda$ generally
provides better forecast performance and is used to report the results. As for
the LASSO VAR, using $\lambda$ to denote the penalty parameter of the LASSO
estimator, we consider
$\lambda=0.00025,0.00050,0.00075,0.00100,0.00125,0.00150$.  As for the factor
VAR, for each horizon we select the number of factors that gives the best
forecasts. For all models, we produce iterated forecasts of GDP using the same
recursive-window scheme as in previous sections.

We also consider information pooling at the forecasting stage, by calculating
forecast combinations. Forecast combinations find widespread application in
the forecasting literature (Elliott and Timmermann 2016, Chauvet and Potter
2013) on the grounds that individual models are likely to be misspecified and
that combining forecasts from different models should increase efficiency
compared to individual forecasts. Measuring the performance of combined
forecasts helps give a sense of how useful it is in practice to establish
rankings of predictors. If combined forecasts turn out to outperform forecasts
from every individual model, then the information contained in poorly-ranking
predictors should not be discarded. We combine the iterated forecasts produced
by single-predictor VAR models using two different weighting schemes. Let
$w_{i}$ denote the weight assigned to model $i$ and $M$ the number of models
to be combined. The simplest approach consists in using an equal-weighted
average of the forecasts, i.e., $w_{i}^{equal}=1/M$. There is ample empirical
evidence that equal weighting performs well for point forecasts (e.g., Stock
and Watson 2003) and often outperforms more sophisticated weighting strategies
(Elliott and Timmermann 2016, Smith and Wallis 2009). The second approach is
Bayesian model averaging (BMA). In particular, since the value of the BIC for
model $i$ provides an asymptotic approximation to its marginal likelihood, the
BMA weights are approximated by
$w_{i}^{bma}=\exp(-0.5BIC_{i})/\left[\sum_{i=j}^{M}\exp(-0.5BIC_{j})\right]$.
The weights are computed recursively across estimation windows.

In addition, we report the performance of forecasts produced by a major
forecasting institution, the International Monetary Fund (IMF).999The IMF
forecasts are particularly suitable for comparisons in this context, as they
cover horizons from 1 to 5 years. In the case of other major forecasters,
comparisons would necessarily have more limitations in terms of horizons. For
instance, the Fed Greenbook forecasts cover a maximum horizon of 2 years. The
OECD publishes annual forecasts for the following year and long-term
projections in 10-year steps. The Survey of Professional Forecasters (SPF)
includes quarterly forecasts up to 4 quarters ahead, annual forecasts for the
next three years but only starting from the 2009Q2 survey, and 10-year annual
average forecasts. However, as OECD (2014) points out, “the profile and
magnitude of the errors in the GDP growth projections [over 2007-2012] of
other international organizations and consensus forecasts are strikingly
similar”. 101010The IMF World Economic Outlook (WEO) provides forecasts in the
form of annual growth rates up to 5 years ahead. We convert them into
4-quarter-ahead, 12-quarter-ahead and 20-quarter-ahead forecasts of the GDP
level using the following approach: (i) we take the Spring issues of the WEO;
(ii) we consider the last quarter of the year prior to each issue as the
starting value for forecasting; (iii) we apply the annual forecast growth
rates to the starting value to compute forecasts of the GDP level and (iv) we
assign each resulting value to the last quarter of the relevant forecast year.
For example, the annual forecast growth rate for 1990 published in the 1990
Spring issue is used to compute the 4-quarter-ahead forecast for 1990Q4 based
on historical data up to 1989Q4, the annual rates up to 1992 are used to
compute the 12-quarter-ahead forecast for 1992Q4 based on data up to 1989Q4,
and so on.

Table 7(a) reports the relative MSFE of all these forecasting models/methods.
No model nor forecast combination scheme outperforms the single-predictor
models using CAPR and NNBLI at any forecast horizon. Also, unlike the small
models using the best financial-cycle predictors, all models/combinations in
Table 7(a) provide their best results relative to the benchmark AR at the
shorter (4-quarter) horizon.

Figure 3(a) compares the iterative forecasts produced right before the global
financial crisis of 2007-2009 by single-predictor VAR models using CAPR and
NNBLI and the forecasts by the IMF.

##  5 Conclusions

A strong emphasis on the role of macro-financial linkages has permeated
macroeconomics in recent years. Financial cycles (in particular housing and
credit cycles), building up in the background of business cycles and
interacting with them through a variety of mechanisms, are now recognized to
have profound and potentially disruptive effects on economic activity. This
paper provides new results on the role of financial-cycle indicators for
predicting U.S. real GDP, especially over medium-term horizons. The results
highlight the predictive power of specific financial ratios. In a comparative
evaluation of a large dataset of macroeconomic and financial indicators, a
valuation ratio from the housing market (the cyclically-adjusted house price-
rent ratio, or CAPR) and an aggregate balance-sheet ratio (the ratio of
liabilities to income in the nonfinancial noncorporate business sector, or
NNBLI) emerge as the most powerful predictors of cumulative GDP growth over
horizons beyond 1 year. Compared to all other predictors, the performance of
the CAPR and the NNBLI ratios is remarkably stable across horizons and robust
across in-sample and out-of-sample evaluation. A number of other financial-
cycle indicators, such as the credit-to-GDP ratio, the household debt-to-
income and net worth-to-income ratios, and residential fixed investment, show
valuable predictive content for specific horizons and evaluation methods.
Small forecasting models that include the best financial-cycle indicators
outperform high-dimensional models and forecast combinations that exploit all
predictors.

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Figure 1: CAPR ratio and multi-year GDP growth (a) Notes: The figure shows the log cyclically-adjusted house price-to-rent (CAPR) ratio (left axis) and the cumulative growth rate of real GDP over the following 20 quarters (right axis) in the United States, from 1960Q1 to 2012Q4. Data on house prices and rents are available at the website of the American Enterprise Institute (https://www.aei.org/historical-land-price-indicators/) and are based on Davis et al. (2008). The GDP data are from the FRED-QD dataset (McCracken and Ng 2015), available at https://research.stlouisfed.org/econ/mccracken/fred-databases/. See section 2 in the text for more details. Figure 2: NNBLI ratio and multi-year GDP growth (a) Notes: The figure shows the nonfinancial noncorporate business sector liabilities-to-income (NNBLI) ratio (left axis) and the cumulative growth rate of real GDP over the following 20 quarters (right axis) in the United States, from 1960Q1 to 2012Q4. The data are from the FRED-QD dataset (McCracken and Ng 2015), available at https://research.stlouisfed.org/econ/mccracken/fred-databases/. Table 1: Additional variables label | description | data source | source label | transformation
---|---|---|---|---
bci | OECD Business Confidence Index | OECD | — | $x_{t}$
cli | OECD Composite Leading Indicator | OECD | — | $x_{t}$
sp500 | Real S&P500 index growth | Shiller | — | $\ln(x_{t})-\ln(x_{t-4})$
cape | Cyclically adjusted price/earnings ratio | Shiller | — | $\ln(x_{t})$
cred | Real credit growth | FRED | CRDQUSAPABIS/CPIAUCSL | $\ln(x_{t})-\ln(x_{t-4})$
cred_gdp | Credit/GDP ratio | BIS | — | $x_{t}$
hpi | Real house price growth | Shiller | — | $\ln(x_{t})-\ln(x_{t-4})$
pr | Price/rent ratio | AEI | — | $\ln(x_{t})$
capr | Cyclically-adjusted price/rent ratio | AEI; FRED |  —  ; CUUR0000SEHA, CPIAUCNS | $\ln(x_{t})$
mortg | Households’ real mortgage debt growth | FRED | HHMSDODNS/CPIAUCSL | $\ln(x_{t})-\ln(x_{t-4})$
mortg_inc | Households’ mortgage/income ratio | FRED | HHMSDODNS/DSPI | $x_{t}$
prfi_gdp | Private residential fixed investment/GDP ratio | FRED | PRFI/GDP | $x_{t}$
pip_inc | Personal interest payments/income ratio | FRED | B069RC1/DSPI | $x_{t}$
nfci | Chicago Fed national financial condition index | FRED | NCFI | $x_{t}$
(a) Notes: Shiller = http://www.econ.yale.edu/~shiller/data.htm; AEI =
American Enterprise Institute, https://www.aei.org/historical-land-price-
indicators/, based on original data by Davis et al. (2008) (using the Case-
Shiller price index after 2000). Table 2: Best performing FRED-QD variables

label | description
---|---
AAA | Moody’s Seasoned Aaa Corporate Bond Yield© (Percent)
AHETPIx | Real Average Hourly Earnings of Production and Nonsupervisory Employees: Total
AMDMUOx | Real Value of Manufacturers’ Unfilled Orders for Durable Goods Industries (Millions of 2012 Dollars), deflated by Core PCE
B021RE1Q156NBEA | Shares of gross domestic product: Imports of goods and services (Percent)
CONSPIx | Nonrevolving consumer credit to Personal Income
DOTSRG3Q086SBEA | Personal consumption expenditures: Other services (chain-type price index)
FEDFUNDS | Effective Federal Funds Rate (Percent)
GS1TB3Mx | 1-Year Treasury Constant Maturity Minus 3-Month Treasury Bill, secondary market
HNOREMQ027Sx | Real Real Estate Assets of Households and Nonprofit Organizations (Billions of 2012 Dollars), deflated by Core PCE
IPCONGD | Industrial Production: Consumer Goods (Index 2012=100)
IPNCONGD | Industrial Production: Nondurable Consumer Goods (Index 2012=100)
ISRATIOx | Total Business: Inventories to Sales Ratio
LIABPIx | Liabilities of Households and Nonprofit Organizations Relative to Personal Disposable Income (Percent)
MORTGAGE30US | 30-Year Conventional Mortgage Rate© (Percent)
NNBTILQ027SBDIx | Nonfinancial Noncorporate Business Sector Liabilities to Disposable Business Income (Percent)
NWPIx | Net Worth of Households and Nonprofit Organizations Relative to Disposable Personal Income (Percent)
PCECC96 | Real Personal Consumption Expenditures (Billions of Chained 2009 Dollars)
PRFIx | Real private fixed investment: Residential (Billions of Chained 2009 Dollars), deflated using PCE
REVOLSLx | Total Real Revolving Credit Owned and Securitized, Outstanding (Billions of 2012 Dollars), deflated by Core PCE
S&P: div yield | S&P’s Composite Common Stock: Dividend Yield
TLBSNNCBBDIx | Nonfinancial Corporate Business Sector Liabilities to Disposable Business Income (Percent)
UNRATESTx | Unemployment Rate less than 27 weeks (Percent)
USMINE | All Employees: Mining and logging (Thousands of Persons)

(a) Notes: The table reports the subset of variables from the FRED-QD dataset
(McCracken and Ng 2015) that rank among the best predictors of GDP in this
paper (see Sections 3 and 4.) See Section 2 for more details on data
transformations.

Table 3: Regression $R^{2}$ of single-predictor ARDL models

| $h=4$ | $h=12$ | $h=20$
---|---|---|---
1 | cli | 0.4323 | capr | 0.6253 | capr | 0.6797
2 | capr | 0.4032 | pr | 0.5710 | pr | 0.6534
3 | NNBTILQ027SBDIx | 0.3607 | NNBTILQ027SBDIx | 0.5647 | LIABPIx | 0.5787
4 | prfi_gdp | 0.3487 | AMDMUOx | 0.5544 | mortg_inc | 0.5780
5 | pr | 0.3474 | cli | 0.5050 | NNBTILQ027SBDIx | 0.5503
6 | DOTSRG3Q086SBEA | 0.3326 | mortg_inc | 0.4545 | ISRATIOx | 0.5291
7 | nfci | 0.3273 | LIABPIx | 0.4439 | cred_gdp | 0.5284
8 | PRFIx | 0.3245 | ISRATIOx | 0.4426 | NWPIx | 0.4736
9 | AMDMUOx | 0.3203 | cred_gdp | 0.4181 | AAA | 0.4669
10 | IPCONGD | 0.3098 | NWPIx | 0.4075 | CONSPIx | 0.4444

(a) Notes: For each $h$, the dependent variable is the $h$-quarter cumulative
GDP growth. Estimated on data from 1974Q1 to 2017Q4. Please refer to Tables
1(a) and 2 for a description of the variables. Table 4: Direct forecasts by
single-predictor ARDL models: mean squared forecast errors

| $h=4$ | $h=12$ | $h=20$
---|---|---|---
1 | NNBTILQ027SBDIx | 0.5376 | NNBTILQ027SBDIx | 0.3223 | capr | 0.2860
2 | capr | 0.7202 | capr | 0.5151 | NNBTILQ027SBDIx | 0.4293
3 | AMDMUOx | 0.8180 | cli | 0.6170 | pr | 0.4576
4 | pr | 0.8335 | AMDMUOx | 0.7760 | ISRATIOx | 0.7739
5 | cli | 0.8505 | NWPIx | 0.8228 | cli | 0.7847
6 | IPCONGD | 0.8601 | cred_gdp | 0.8588 | LIABPIx | 0.8639
7 | NWPIx | 0.8677 | UNRATESTx | 0.8590 | UNRATESTx | 0.8657
8 | IPNCONGD | 0.8701 | IPCONGD | 0.8651 | AHETPIx | 0.9012
9 | PCECC96 | 0.8805 | FEDFUNDS | 0.8755 | MORTGAGE30US | 0.9037
10 | prfi_gdp | 0.8862 | B021RE1Q156NBEA | 0.8757 | IPCONGD | 0.9125

(a) Notes: Out-of-sample MSFE for the $h$-quarter-ahead cumulative GDP growth
rate, relative to the benchmark AR (Table 6(a), direct forecasts). All models
are estimated recursively (shortest sample 1968Q2-1985Q1, longest sample
1968Q2-2016Q4). MSFE computed over the period 1990Q1-2017Q4. Please refer to
Tables 1(a) and 2 for a description of the variables.

Table 5: Iterated forecasts by bivariate VAR models: mean squared forecast
errors

| $h=4$ | $h=12$ | $h=20$
---|---|---|---
1 | NNBTILQ027SBDIx | 0.5467 | NNBTILQ027SBDIx | 0.3391 | capr | 0.4034
2 | capr | 0.7066 | capr | 0.5347 | NNBTILQ027SBDIx | 0.4849
3 | pr | 0.7575 | pr | 0.6853 | pr | 0.5260
4 | AMDMUOx | 0.8043 | cli | 0.7093 | HNOREMQ027Sx | 0.7992
5 | TLBSNNCBBDIx | 0.8298 | AMDMUOx | 0.7530 | AMDMUOx | 0.8075
6 | prfi_gdp | 0.8366 | UNRATESTx | 0.8362 | UNRATESTx | 0.8109
7 | cli | 0.8726 | USMINE | 0.8577 | ISRATIOx | 0.8135
8 | S&P: div. yield | 0.8754 | IPNCONGD | 0.8585 | B021RE1Q156NBEA | 0.8158
9 | IPCONGD | 0.8762 | B021RE1Q156NBEA | 0.8719 | cli | 0.8273
10 | cape | 0.8907 | GS1TB3Mx | 0.9028 | REVOLSLx | 0.8385

(a) Notes: Out-of-sample MSFE for the $h$-quarter-ahead cumulative GDP growth rate, relative to the benchmark AR (Table 6(a), iterated forecasts). All models are estimated recursively (shortest sample 1968Q2-1985Q1, longest sample 1968Q2-2016Q4). MSFE computed over the period 1990Q1-2017Q4. Please refer to Tables 1(a) and 2 for a description of the variables. Table 6: Root mean squared forecast error (RMSFE) of benchmark AR |  | $h=4$ | $h=12$ | $h=20$ |
---|---|---|---|---|---
direct forecasts |  | 0.01764 | 0.04402 | 0.06211 |
iterated forecasts |  | 0.01739 | 0.03974 | 0.05611 |
(a) Notes: Out-of-sample RMSFE for the $h$-period-ahead real GDP level. The model is estimated recursively (shortest sample 1968Q2-1985Q1, longest sample 1968Q2-2016Q4). The RMSFE is computed over the period 1990Q1-2017Q4.  Table 7: High-dimensional models and forecast combinations: mean squared forecast error forecasting model/method |  | $h=4$ | $h=12$ | $h=20$ |
---|---|---|---|---|---
LBVAR |  | 0.780 | 0.976 | 0.968 |
LASSO VAR |  | 0.901 | 0.946 | 0.993 |
Factor model |  | 0.917 | 1.138 | 0.931 |
Forecast combination (equal weights) |  | 0.932 | 0.998 | 1.009 |
Forecast combination (BMA weights) |  | 0.954 | 0.996 | 1.009 |
IMF |  | 0.762 | 1.005 | 1.326 |
(a) Notes: The table shows out-of-sample mean square forecast errors (MSFE)
for the $h$-quarter-ahead cumulative GDP growth rate, relative to the
benchmark AR (Table 6(a), iterated forecasts). The forecasting models/methods
considered are: a Large Bayesian VAR (LBVAR) (Bańbura et al. 2011); a VAR
estimated using a LASSO penalty (LASSO VAR); a factor model using principal
components of predictors; combinations of forecasts from single-predictor VAR
models, using equal combination weights and Bayesian model averaging (BMA)
weights; forecasts by the International Monetary Fund (IMF). See Section 4.4
for more details. The MSFE are computed over the period 1990Q1-2017Q4.

Figure 3: Forecasting the crisis: a comparison (a) Notes: The figure compares
multi-year forecasts of U.S. GDP produced right before the global financial
crisis of 2007-2009. The green solid line and the yellow dashed line identify
the iterated forecasts produced by bivariate VAR models using the CAPR and
NNBLI ratios, respectively, estimated on data up to 2007Q2. The red dashed
line represents the forecasts contained in the Fall 2007 World Economic
Outlook by the IMF.