4 when are pell grants most effective we next assess

4. When Are Pell Grants Most Effective?
4.1. Multipliers in Recessions and Expansions
Our first estimation compares the multiplier of Pell grants during episodes when the economy is in
expansion to when it is in recession. Recent evidence suggests that fiscal spending generally has a
greater effect on output when the economy is in recession.
23
If this holds for Pell grants, they could
form a particularly effective tool to stabilize macroeconomic activity. We estimate the following
equation to test this:
Y
m , t
- Y
m , t - 2
Y
m , t - 2
= F ( z
m , t - 1
)
•
β
R
E
m , t
- E
m , t - 2
Y
m , t - 2
‚
+ [1 - F ( z
m , t - 1
)]
•
β
E
E
m , t
- E
m , t - 2
Y
m , t - 2
‚
+ φ
m
+ ψ
t
+ γ
0
X
m , t
+ μ
m , t
, (5)
23
Examples include Auerbach and Gorodnichenko ( 2012 ), Corsetti et al. ( 2012 ), Ilzetzki et al. ( 2013 ), Blanchard and
Leigh ( 2013 ), Jordà and Taylor ( 2016 ), and Berge et al. ( 2020 ). Ramey and Zubairy ( 2018 ) do not find state-dependence
in a historical sample with news shocks about defense spending.
16

where β
R
and β
E
respectively capture the multiplier in recessions and expansions, while F ( z
m , t
) is
a continuous function that strictly decreases with lagged biannual growth z
t
1
.
This equation is also known as a smooth transition model, which we borrow from the literature
on the state-dependent effect of fiscal and monetary policy on economic activity.
24
The specifica-
tion assigns weight to observations based on whether the economy is in recession or expansion.
If last year’s growth was relatively high, the observation weighs towards β
E
while it weights more
towards β
R
. Following Tenreyro and Thwaites ( 2016 ), F ( z
m , t
) is a logistic function:
F ( z
t
) =
exp
‡
θ
[ z
m , t
- μ
m
]
σ
m
·
1 + exp
‡
θ
[ z
m , t
- μ
m
]
σ
m
· , (6)
where μ
m
determines the fraction of the sample in which the metropolitan area is in recession,
σ
m
gives the standard deviation of biannual growth in while θ determines how stark the demarca-
tion between recessions and expansions are (e.g., for a lower θ , the weight of observations is more
equally split between β
E
and β
R
). μ
m
is calibrated such that each area is in recession 20% of the
sample, which matches the percent of quarters that the economy is in recession at the national
level according to the NBER. We calibrate θ to 3 in line with Tenreyro and Thwaites ( 2016 ).
Results are presented in Table 6 . Recession multipliers represent β
R
in equation ( 5 ) while ex-
pansion multipliers represent β
E
. The recession (expansion) should be interpreted as the 2-year
effect of a relative increase in Pell grants on relative income growth if growth is initially at its low-
est (highest) level in the dataset. The actual multiplier of an increase in Pell grant disbursements
depends on how close growth is to either of these levels. The estimations of columns I to V are
estimated with two-stage least squares regressions. Pell grant disbursements at the MSA level are
instrumented with disbursements at the national level, multiplied by F ( z
m , t - 1
) for the first term
and 1 - F ( z
m , t - 1
) for the second term. Column I contains the base specification that controls for
metropolitan and year fixed effects as well as an area-specific time trend. Column II adds control
for the share of students in the population while column III adds the other non-financial control