movements in asset and debt values have a protracted influence on output, which, in the case of omission, would be captured by the other coefficients and may impact on estimations of government spending multipliers and tax multipliers alike. Asset price changes may affect consumer spending via wealth effects, an increase in confidence and credit-worthiness (Eschenbach and Schuknecht 2004; Poterba 2000). According to IMF (2012a), recessions are more severe and more protracted if they were preceded by strong increases in household debt, falling much slower than asset prices when the bubble
bursts. Dynan (2012) shows that gross wealth effects alone cannot account for the
decline in consumption and argues that households’ leverage ratio additionally drags private spending. Fiscal expansions could foster the deleveraging, but would show no positive effect in the data. Controlling for households’ wealth and debt movements may help identify the counterfactual development without the fiscal stimulus.
As will be laid out below, the omitted variable bias could be neglected if a time series with correctly identified fiscal shocks were available and these would be uncorrelated with asset prices or credit markets. However, with imperfect identification or correlation with financial markets, omission of these variables amplifies the wrong measurement of fiscal multipliers, because credit and asset market movements can have considerable effects on aggregate demand that would be captured by fiscal multiplier estimations without having anything to do with fiscal policies. Financial cycles influence GDP over and above what is generally recognized as business cycle swings (Borio 2012).
Given the discussion so far, the ratio of private wealth to debt is chosen as a catch-all variable to identify financial cycles. Budget variables should have a stronger correlation with the wealth-to-debt ratio than with any single asset or credit variable.
Figure 5.1 shows the de-trended wealth-to-debt ratio of households (households’ total
assets-to-total liabilities ratio) and the CAPB-to-GDP ratio. The most striking co-
movements of these two variables are between 1997 and 2010. These two cycles represent the new economy boom and the housing bubble as well as their respective busts. Both were accompanied by a broad increase in stock prices. There is a number of other co- movement phases: the early eighties to the early nineties, the mid seventies and the late sixties.
5.4 A Formal Framework
To phrase the arguments in a more formal way, the simple static model in Perotti (2011) is extended in the following. The model consists of two simplified equations, one for the
5.4 A Formal Framework 120
Figure 5.1:CAPB-to-GDP Ratio vs. De-trended Households’ Total Assets-to-Total Lia- bilities Ratio -8 -6 -4 -2 0 2 4 -12 -8 -4 0 4 8 12 60 65 70 75 80 85 90 95 00 05 10
CAPB/GDP (left axis) HHTATL gap (right axis)
(Source: CBO, FRB Flow of Funds and authors’ own calculations)
change in the unadjusted primary balance as a share of GDP (s0) and one for the change in the log of real GDP per capita (y). The first equation reads
∆s0 = (αsy+ βsy)∆y + (αsf + βsf)∆f + εs. (5.1)
Unadjusted primary budget surplus depends on truly exogenous changes to the fiscal stance by the policymaker (εs), on y via automatic stabilizers αsy and via endogenous
discretionary (countercyclical) reactions (βsy), and on the log of the household wealth-
to-debt ratio (f ) via automatic αsf and endogenous discretionary βsf reactions.
Next, the cyclically-adjusted primary balance stripped of automatic stabilizers is de- fined: ∆s = ∆s0− αsy∆y. Moreover, we follow Blanchard and Perotti (2002) who argue
that, due to recognition and implementation lags by the policy maker, the contempo- raneous endogenous discretionary components are zero (βsy = βsf = 0) when quarterly
data are used. Equation (5.1) thus shrinks to
∆s = αsf∆f + εs (5.2)
which includes the truly exogenous shocks to the budget (εs), but also the disturbances
5.4 A Formal Framework 121
then ∆s is a false identification of the fiscal stance εs.
The second equation is a simplified GDP reaction function:
∆y = −γysεs+ γyf∆f + εy (5.3)
Output reacts through the representation of the fiscal multiplier3 γys to changes in
the fiscal stance, through γyf to changes in the wealth-to-debt ratio and to orthogo- nal business cycle shocks εy that may capture all other changes. Note that a negative
sign is imposed before γysεs, since fiscal multipliers are usually defined as the GDP
reaction to a fiscal expansion, while a positive εs is a surplus, i. e. a fiscal contrac- tion. Unlike Perotti, who models his financial market variable as white noise positively correlated with economic activity, the wealth-to-debt ratio f is given a more pivotal role and is modelled as a non-stochastic variable. f also affects output in order to al- low for the case of an omitted variables bias. The arguments presented above imply Cov(∆f, ∆y), Cov(∆f, ∆s) > 0. In the following, we isolate the biases caused by the identification problem when αsf∆f 6= 0 and the omitted variable bias when γyf∆f 6= 0.
5.4.1 Identification Bias
Isolating the identification bias by setting γyf∆f = 0 and allowing for αsf∆f 6= 0 would
give the following data-generating process for ∆yIB:
∆yIB = −γysεs+ εy (5.4)
When ∆s is generated by 5.2 but is erroneously taken as a measure of the fiscal stance (∆s = εs) an OLS regression of ∆y on ∆s, which should represent the impact of a fiscal contraction, estimates the alleged multiplier
ˆ γysIB= −Cov(∆s, ∆y IB) V ar(∆s) = − P i(∆si− ∆s)∆yiIB P i(∆si− ∆s)∆si . (5.5) 3
In general, γij is an elasticity, whose scale can be different from that of a fiscal multiplier k. For the
5.4 A Formal Framework 122
Inserting equation (5.2) in the numerator and rearranging yields
ˆ γysIB = − P i(εs− εs+ αsf∆f − αsf∆f )∆yiIB P i(∆si− ∆s)∆si = − P i(εs− εs)∆yiIB+ P i(αsf∆f − αsf∆f )∆yIBi P i(∆si− ∆s)∆si = −Cov(εs, ∆y IB) V ar(∆s) − Cov(αsf∆f, ∆yIB) V ar(∆s) . (5.6)
Next, we isolate the true multiplier, γys, in order to show its biased estimation in ˆγys.
Using the information that the true multiplier must be
γys= −Cov(εs, ∆y)/V ar(εs) (5.7)
and substituting into (5.6), yields
ˆ γysIB = γys V ar(εs) V ar(∆s)− αsf Cov(∆f, ∆y) V ar(∆s) (5.8)
Both terms show how the estimation of the multiplier with the CAPB is downward- biased in the presence of movements of f through false identifications. The first term lowers the value of the estimated multiplier against its true underlying value because the variance of εs is likely to be smaller than the variance of ∆s. The second term must
be positive when Cov(∆f, ∆y) > 0 and αsf = Cov(∆f, ∆s) > 0, which are plausible assumptions, given the discussion above. Via the negative sign the second term decreases the estimated multiplier as compared to the true one.
5.4.2 Omitted Variable Bias
The model can also be used to isolate the omitted variable bias explained in section 5.3. By assuming away the identification problem by setting αsf = 0 and allowing for γyf∆f 6= 0, ∆s would be generated by
∆s = εs, (5.9)
so the CAPB would rightly identify the fiscal stance. ∆y would be generated by equation 5.3, but omitting an important variable, one would estimate