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4 when are pell grants most effective we next assess

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4.When Are Pell Grants Most Effective?
4.1.Multipliers in Recessions and ExpansionsOur first estimation compares the multiplier of Pell grants during episodes when the economy is inexpansion to when it is in recession. Recent evidence suggests that fiscal spending generally has agreater effect on output when the economy is in recession.23If this holds for Pell grants, they couldform a particularly effective tool to stabilize macroeconomic activity. We estimate the followingequation to test this:Ym,t-Ym,t-2Ym,t-2=F(zm,t-1)βREm,t-Em,t-2Ym,t-2+[1-F(zm,t-1)]βEEm,t-Em,t-2Ym,t-2+φm+ψt+γ0Xm,t+μm,t,(5)23Examples includeAuerbach and Gorodnichenko(2012),Corsetti et al.(2012),Ilzetzki et al.(2013),Blanchard andLeigh(2013),Jordà and Taylor(2016), andBerge et al.(2020).Ramey and Zubairy(2018) do not find state-dependencein a historical sample with news shocks about defense spending.16
whereβRandβErespectively capture the multiplier in recessions and expansions, whileF(zm,t) isa continuous function that strictly decreases with lagged biannual growthzt1.This equation is also known as a smooth transition model, which we borrow from the literatureon the state-dependent effect of fiscal and monetary policy on economic activity.24The 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 towardsβEwhile it weights moretowardsβR. FollowingTenreyro and Thwaites(2016),F(zm,t) is a logistic function:F(zt)=expθ[zm,t-μm]σm·1+expθ[zm,t-μm]σm·,(6)whereμmdetermines the fraction of the sample in which the metropolitan area is in recession,σmgives the standard deviation of biannual growth in whileθdetermines how stark the demarca-tion between recessions and expansions are (e.g., for a lowerθ, the weight of observations is moreequally split betweenβEandβR).μmis calibrated such that each area is in recession 20% of thesample, which matches the percent of quarters that the economy is in recession at the nationallevel according to the NBER. We calibrateθto 3 in line withTenreyro and Thwaites(2016).Results are presented in Table6. Recession multipliers representβRin equation (5) while ex-pansion multipliers representβE. The recession (expansion) should be interpreted as the 2-yeareffect of a relative increase in Pell grants on relative income growth if growth is initially at itslow-est(highest) level in the dataset. The actual multiplier of an increase in Pell grant disbursementsdepends on how close growth is to either of these levels. The estimations of columns I to V areestimated with two-stage least squares regressions. Pell grant disbursements at the MSA level areinstrumented with disbursements at the national level, multiplied byF(zm,t-1) for the first termand 1-F(zm,t-1) for the second term. Column I contains the base specification that controls formetropolitan and year fixed effects as well as an area-specific time trend. Column II adds controlfor the share of students in the population while column III adds the other non-financial control

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