THE “CROWD OUT” PROBLEM IN STRUCTURAL MODELS OF THE MACROECONOMY
John J. Heim, Ph.D.
Rensselaer Polytechnic Institute and
Visiting Professor, State University of New York at Albany
ABSTRACT: This paper tests the hypothesis that private spending (and borrowing) declines in periods of government deficit growth, due to a “crowd out” effect offsetting government stimulus efforts. The tests use Keynesian structural models of the U. S. economy 1960-2010, into which variables measuring the effects of the government deficit on private borrowing and spending are inserted. Results indicate crowd out completely or almost completely offsets deficit - driven stimulus efforts, even controlling for the state of the economy in which they occur. Extensive tests for endogeneity, stationarity, heteroskedasticity and robustness were undertaken. All testing was done in 1st differences, eliminating nonstationarity and reducing multicollinearity problems by approximately half. Models explained 90 -95% of the yearly changes of consumption and Investment during the 50 year period. Results were robust for tests of different time periods, different structural models, different regression techniques (OLS, strong and weak instrument 2SLS), and different strong 2SLS instruments. Consistency of crowd out effects on borrowing and spending was found. This was important because reduced private borrowing is the mechanism through which crowd out is theorized to affect spending.
THE “CROWD OUT” PROBLEM IN STRUCTURAL MODELS OF THE MACROECONOMY
STIMULUS MODELS USUALLY KEYNESIAN:
· STRUCTURAL
· DEMAND DRIVEN
· SHORT RUN
SIMPLE “KEYNESIAN CROSS” MODEL OF NATIONAL INCOME DETERMINATION: (NO CROWD OUT)
National Income Identity Y = C + I + G + (X-M)
Consumption function C = β(Y-T)
Standard KC Model Y = 11-β ( - βT + I + G + (X-M) )
Of Stimulus Mechanics
Simple IS Curve: Y = 11-β ( - βT - θ r + γ ACC + G + (X-M) )
THE PROBLEM:
· VIRTUALLY IMPOSSIBLE TO FIND ECONOMETRIC EVIDENCE OF A NEGATIVE SIGN ON THE TAX VARIABLE
· (OR A POSITIVE SIGN ON GOVERNMENT SPENDING IN MOST MODELS)
Table 2.1
Tests of Keynesian Models For the Stimulus Effects of Tax Cuts
Model Tax coefficient (t-stat) .
Keynesian Cross:
Y = f T, G, Investment, X-M +.17 (2.2)**
Simple IS Curve Model:
Y = f T, G, ACC, Int. Rate, X-M +.79 (6.6)***
Sophisticated IS Model:
Y = f (T, G, ACC, Interest Rates, Wealth, Tobin’s q,
Exchange Rates, Pop. Growth, Money Supply
Growth ,Consumer Confidence, Depreciation,
Profits, X) + .59 (2.8)***
.
· ** Significant 5% level, *** Significant 1% level. Strong instrument 2SLS, Hausman:
Wald, Sargan, Durban-Watson tests; Newey - West errors, Data in first differences.
POSITIVE SIGN ROBUST FOR VARIOUS PERIODS SAMPLED
§ 1960-2010 1960-2000
§ 1970-2010 1970-2000
GOVERNMENT SPENDING COEFFICIENT SIGNS:
(+) SIMPLE MODELS
(-) SOPHISTICATED MODELS
DOES THIS MEAN STIMULUS PROGRAMS DON’T WORK?
· MAY NOT, BECAUSE OF CROWD OUT
HOW DOES CROWD OUT WORK?
KEYNESIAN CROSS MODEL (WITH CROWD OUT)
Consumption Function C = β (Y-T) + λ (T-G)
Ʌ
|
|
(CROWD OUT FACTOR: GOV’T DEFICIT)
Statement OF Y = 11-β ( (-β+ λ) T + (1- λ) G + I + (X-M))
Stimulus Mechanics Ʌ Ʌ
| |
| |
| |
(Stimulus Effect, Net Of Crowd Out)
SIMPLE “IS” CURVE MODEL (WITH CROWD OUT)
Consumption Function C = β (Y-T) + λ1 (T-G)
Investment Function I = - θ(r)+ γ(ACC) + λ2 (T-G)
Ʌ
|
(CROWD OUT FACTORS)
Statement of Stimulus Y = 11-β ((-β+ λ1+ λ2)T + (1- λ1- λ2) G + γ ACC - θ r +(X-M))
Mechanics Ʌ Ʌ
| |
(Net Stimulus Effects Of -ΔT, +ΔG)
More Sophisticated IS Models: C, I equations Include
additional determinants
PREVIOUS RESEARCH
POPULAR PRESS
· Rising sovereign debt “could crowd out private sector credit growth”
(Chan, NY Times, 2/7/10)
· “Government bond buying by banks is…crowding out, reducing
the supply of consumer and corporate lending”
(Barley, WSJ 2/24/10)
· Crowd Out Relatively Unimportant in Recessions; Stimulus dominates Crowd Out,
· Stimulus Works, If Big Enough; Obama Stimulus Too Small
· Crowd Out Not A Problem In Recessions
(Krugman, NY Times, 9/28/09)
PROFESSIONAL LITERATURE
Spencer and Yohe, (1970)
· Literature Review: Dominant View: Deficits Cause Crowd Out
Ben Friedman (1978)
· Elasticity Of Substitution Between Bonds And Stocks Is Key: When Interest Rates Rise (Due To Gov’t. Borrowing), May Bring Crowd Out (Or Crowd In); Indeterminate Theoretically
· His Empirical results ambiguous.
Gale and Orszag (2004)
Model Tested:
C = f (NNP, NNP-1, Deficit Var.(TT ,or TF, TS&L, GG&S, GTR, Gi,), Gov’t Debt, Tax Rates, Wealth)
Findings:
· Total Tax Cuts Have Net Stimulus Effects On Consumption 1956-2002, (But Not For 1956-92)
· Federal Tax Cuts Have Positive Stimulus , (1956-2002)
· S& L Tax Cuts Have Negative Stimulus, “
· Gov’t Spending On Transfers (Only) Had Pos. Stimulus, “
· Tax rate cuts for labor (but not capital) stimulate consumption “
Methodology
· Not Structural, Not VAR, Not DSGE. OLS, 1st Differences Used
Specification/Estimation Issues:
· What’s the theory? Anything left out necessary to control for?
· Simultaneity of C and NNP? OLS Results likely biased.
· Model Specification May Predetermine Result:
Replace NNP With Disposable Income, 1960-2000, Yields Positive Signed, Statistically Significant Tax Coefficient,
· Recalculate OLS Results For Transfer Payment And Federal/SL Tax Effects For The 1960-2010, , Using Standard Structural Model . Results Change: (+) Tax, (-) Spending Effects
ΔCT =.56Δ(Y-TT) +.64Δ(TF ) +.53Δ(TS&L) -.27Δ(GTrans) - .39Δ(GOther) -10.60ΔPR +.42 ΔDJ-2 +3.60 ΔXRAV
(t =) (13.0) (7.6) (1.9) (-2.2) (-4.1) (-4.4) (5.1) (2.6)
-366.99ΔPOP16 +.011ΔPOP +.78ΔICC-1 +45.26ΔM2AV + .11ΔCB + 19.69 ΔUNEM-0 R2=95.7%
(-1.7) (3.0) (2.6) (5.9) (3.1) (2.8) D.W.=1.8
Conclude:
· Orszag & Gale’s Findings Sensitive To Model Specified, Time period Tested
Montford and Uhlig (2008):
Findings
· Increased Gov’t Spending Reduces Investment. (Crowd Out)
· Decreased Taxes Increase Investment. (Stimulus Theory)
· No Theory Proposed To Reconcile Results,
(Consistent With RBC w/ Backward Bending Labor Supply Curve)
Methodology: VAR
Model
· Consumption or investment: a function of six lagged values of each of ten variables:
· C (or I) = f (GDP, C, P&E Inventory Investment, G, T, Real
Wages, Bank Reserves, PPI index, and GDP deflator.)
· Data: U.S. 1955-2000, quarterly.
· Impulse responses to variables other than the GDP constrained to what the authors considered appropriate signs, regardless of regression results.
· Uhlig (2005, p.383) argued this was common practice to achieve consistency with theoretical expectations
Blanchard and Perrotti (2002)
· Model: VAR
Findings: Same As Montford And Uhlig For Investment
Keynesian Results For, T, G Effects On GDP,
· Method: Difficult To Evaluate
Furceri and Sousa (2009)
Findings: As G Increases As % Of GDP, C and I Fall as a % of GDP
(May Result From Construction Of Hypothesis)
Model: VAR
C/GDP (or I/GDP) = f (Fixed Effects Variable for 140 Countries, 6 Lags of G/GDP)
Heim (2012a, 2012b)
Models: Structural, 2SLS
Findings:
· Both Tax And Spending Deficits Generate Net Crowd Out Effects
· Crowd Out ~ Same In Recession And Non-Recession Periods.
· Possible Explanation: Supply Of Loanable Funds Dropped Faster Than Private Loan Demand For 1981-83 Recessionary Period (Flow of Funds Data)
Models:
CDomestic (or Imports) = f (Disposable Income, Wealth, Prime Interest Rate, T, G, Exchange Rate, Population Size, Consumer Confidence)
IDomestic (or Imports) = f (Accelerator, Tobin’s q Proxy, Prime Interest Rate, T, G, Exchange Rate, Profits, Depreciation Allowances, Capacity Utilization Levels, )
Annual Data 1960-2000
Methods
· Effects On GDP Estimated 2 Ways (IS Curve Method):
§ Inferred from C, I regressions
§ Actual IS curve regression coefficients
DSGE (Euler Equation Models)
Gale and Orszag (2004). Model melds Real Business Cycle and “Rule of Thumb” new Keynesian consumers into one model:
Model
C = f (YGross, Deficit Var.(TF, TS&L, GG&S, ), Gov’t Debt, Wealth, Tax
Rates)
Findings
· Gross Income, Federal Tax Levels, And Wealth Levels Were Significant Stimulus Factors (5% Level)
Methodology:
· (Discussed earlier): everything endogenous, replaced by lagged values, OLS. Results not replicable using structural models)
Non-DSGE Tests of Consumption: DSGE Implications:
Kuznets (1948):
· Current Consumption = 70% Of Current Year Only National Income, 1869-1929, Low S.D.
· 70% Precisely Replicable For The 1960-90 Period (Heim 2008a)
· Reasonably Replicable For 1960-2010 (76.6%) ( “ “ )
Heim (2008b)
Compared Explanatory Power of Consumption Models
· Average Income (Life Cycle/Permanent Income Hypothesis),
· Current Income Only (Keynesian)
Findings:
· Keynesian Models Explained Substantially More Variance (68%) In Consumer Spending. Average income explained about ½ As Much
· Current Income Explained 68% Of Variance, Crowd Out 14%, Wealth 5%, Interest Rates (2%), And Exchange Rates (1%).
(Stepwise Regression- 1st In Method)
KEYNESIAN MODEL
C = f (YDisposable, Deficit (TTotal, GTotal) Wealth, Prime Interest Rate,
Exchange Rates)
LIFE CYCLE/ PERMANENT INCOME MODELS
Adaptive Expectations Version: Same Model as Above , except current income replaced by average income for past 4 years
Rational Expectations Version: : Same Model as Above , except current income replaced by actual average income for next 4 years (or next 4 and past 4 years to combine adaptive with rational expectations)
METHODOLOGY
DATA: U.S. 1960 - 2010 Economic Report Of The President 2011
Flow Of Funds Accounts 2011
Spending And Borrowing Models – Same Determinants Assumed
“Standard Models” Used: Test All Variables Commonly Cited As
Determinants of Consumption Or Investment
Lags:, Chose The Lags Most Systematically Related To The Dependent Variable, If Theory Says Variable Should Be Included
2SLS: To Address Simultaneity Bias
Tests: Hausman Endogeneity: What To Instrument
Wald: Weak Instrument Test
Sargan Endogeneity: Do Instruments Remove It?
Method For Defining Instrument Components: Steps
1. All Exogenous & Lagged Variables In Both Equations Used As Initial Components (Griffiths, Hill, Lim 2011), (Pindyck & Rubinfeld, 1991).
2. Only Six Assumed Endogenous (GDP, T, G, UNEM, PR, ACC)
3. Hausman Tests On These 6 Suspected Endogenous, Using All Others As Hausman 1st Stage Regressors,
4. Hausman Tests On All Others, Using All Others Except The One Being Tested As 1st Stage Regressors
5. All Variables Found Exogenous/Lagged Regressed On Each Endogenous To Obtain Instrument.
6. For Weak Instruments, Add Lagged Versions Of The Endogenous Or Other Variables Used Originally. Continue Until Either F Statistic Was F>= 10, Or At Least One Regressors Had t >= 3.3. (Wald Test)
7. To Ensure Strong Instrument Not Endogenous, Sargan Test Used. Residuals From The Structural Model (With Instruments) Regressed Against Instrument Components Chi Square Used As Test Criteria. If (N)(R2) Χ2(.95,D F) Conclude Endogeneity Eliminated Hausman, Wald And Sargan Tests Used For Every Model Tested.
Data Tested In First Differences To Address Nonstationarity , Serial Correlation Issues.
· All Passed Augmented Dickey-Fuller Unit Root Tests, Except 3.
· The 3 Proved Cointegrated With Spending And Borrowing Dependent Variables (The Dow Jones Average, Population Size And Population Young/Old Ratio Variables)
· 1st Differences Also Reduced Multicollinearity Levels By~ ½, Stabilizing Coefficients
Durbin Watson Tests: Evaluate Serial Correlation. Most Appropriate Test For Small Samples, (Hill, Griffiths & Lim, 2011, P. 355)
Newey West Standard Errors (Heteroskedasticity)
IS Curve Method: Estimate Net Stimulus/Crowd Out Effects On GDP
MODELS TESTED: 24 CONSUMPTION 24 INVESTMENT
OF THE 24 IN EACH GROUP
· 16 SPENDING MODELS: 8 USE 1-VARIABLE DEFICIT,
8 USE 2-VARIABLE DEFICIT
· OF EACH GROUP OF 8, 4 WITH BORROWING DETERMINANT, 4 WITHOUT,
· EACH OF THE GROUP OF 4 USE DIFFERENT BUSINESS CYCLE CONTROLS
· 8 BORROWING MODELS:
· 4 HAVE 1-VARIABLE DEFICIT, 4 HAVE 2-VARIABLE)
· EACH OF THE 4 USE DIFFERENT BUSINESS CYCLE CONTROLS
· EACH OF THE 48 TESTED 3 WAYS
· OLS
· 2SLS (STRONG INSTRUMENT),
· 2SLS (WEAK INSTRUMENT, IF ENCOUNTERED)
· TO ENSURE ROBUSTNESS, RESULTS COMPARED FOR 4 VARYING SAMPLE PERIODS (8 MODELS)
· 1960-2000
· 1960-2010
· 1970-2000
· 1970-2010
TYPICAL MODEL RESULTS (2SLS STRONG INSTRUMENT)
TESTED: DETERMINANTS OF CONSUMPTION (CT), INVESTMENT (IT)
Consumption Investment
Disposable Income (Y-T) Samuelson’s Accelerator (ACC)
Crowd Out Crowd Out
· Taxes (TT) ● Taxes (TT)
· Gov’t. Spending (GT&I) ● Gov’t. Spending (GT&I)
Wealth (DJ) Depreciation Allowances (DEP)
Interest rates (PR) Interest Rates (r)
Exchange Rates (XR) Tobin’s q (DJ as Proxy)
Consumer Confidence (CCI) Profits (PROF)
Population Size (POP) Exchange Rates (XR)
Pop. Age Composition (POP16) Population Size(POP)
Money Supply (M2, M1) Money Supply (M2, M1)
Business Cycle Controls Business Cycle Controls
· Unem. Rate (UNEM) Business Borrowing (IB)
· GDP0, GDP-3
Consumer Borrowing (CB)
CONSUMPTION SPENDING
ΔCT =.50Δ(Y-TT) +.55Δ(TT) -.26Δ(GT&I) -11.81ΔPR +.42 ΔDJ-2 +3.42 ΔXRAV -336.65ΔPOP16 +.012ΔPOP +.36ΔICC-1 +40.86ΔM2AV
(t =) (11.4) (11.4) (-3.7) (-5.1) (5.3) (2.3) (-1.3) (2.6) (1.3) (3.8)
+ .12 ΔCB2 +.04 ΔGDPReal(-3) R2=94.9% D.W. = 1.8 MSE = 25.45 (Eq. 7.1)
(3.1) (1.1)
CONSUMER BORROWING
ΔCB =.34Δ(Y-TT)+.61Δ(TT) -.55Δ(GT&I) -22.89ΔPR-1.62 ΔDJ-1 +24.06ΔXRAV +102.23ΔPOP16 +.005ΔPOP +.12ΔICC-1 -30.82ΔM2AV
(t =) (1.3) (1.8) (-1.7) (-3.7) (-3.4) (2.8) (0.1) (0.3) (0.1) (-0.9)
- .20 Δ(M2-M1)Real -18.54 ΔUNEM R2=58.7% D.W.=2.1 MSE=103.40 (Eq. 7.5.Alt.)
(-1.7) (-0.6)
INVESTMENT SPENDING
ΔIT = +.33Δ(ACC)+.22Δ(TT) -.53Δ(GT&I) + .81ΔDEP +2.39ΔCAP-1 -2.29ΔPR-2 + .10ΔDJ-0 +.13ΔPROF-0+5.87ΔXRAV +.013ΔPOP
(t =) (4.9) (2.0) (-3.4) (3.0)) (1.0) (-0.9) (0.4) (1.9) (2.4) (2.8)
+ .05 Δ(BOR-1) – 12.40 ΔUNEM R2=93.1% D.W.=2.0 MSE=33.05 (Eq. 8.2.Alt.b)
(0.9) (-1.5)
USING STEPWISE REGRESSION: VARIANCE EXPLAINED: (From Eq. 8.3.Alt.a.2 – No bus.cycle var.))
· 1ST IN Method: 64% Explained by (T,G); 2nd In: ACC (17.2%) 3rd In: DEP (4.4%); 4th In:PR-2
(2.5%); 5th In: XRAV (1.6%);6th In: IB(-1) (0.8%);7th In: POP (0.03%);8th In: CAP-1
(0.01%);9th In: PROF (-0.01%);10th In: DJ (-0.07%);
(If ACC entered first, explains 44% of variance; If( T,G) entered second, adds 37%)