Simulation of the Klein-Goldberger Model using EViews Robert ...

Simulation of the Klein-Goldberger Model using EViews
Robert Dixon
Department of Economics at the University of Melbourne
The Klein-Goldberger model (1955) is a Keynesian type macroeconomic model of the
U.S. economy over the period 1929-1952. It differs from the earlier model presented by
Klein (Klein's Model I - discussed in another document) in that it includes more detail as
to the commodity composition of expenditure, the composition of employment, the
various sources of income, the determinants of the trade balance and, unlike the early
Klein model, it includes equations describing the behaviour of financial markets. 1
The model as set out below 2 is that discussed in Chapters 2, 3 and 4 of the book by Klein
and Goldberger (1955). We will use it to simulate the period of the Great Depression and
its aftermath, i.e. the period 1929-1941. A summary of the equations of the model is
given on pp. 50-3 of their book and data on the exogenous variables and starting values
for the lagged endogenous variables can be found on pp. 131-3.
The notation used and the 14 behavioural equations for the endogenous variables of their
model using my notation are listed below. You will also find there a list of the identities
used in the model. Note: (i) the symbol used by Klein & Goldberger is given in
parentheses at end of each line and (ii) unless otherwise indicated the data is in U.S. $
bill, in 1939 prices, and (iii) since the equation for the long-term interest rate (LIR) says
that it depends on the short-term interest rate (SIR) lagged up to 5 periods, we have to
supply data on the SIR back to 1924 in order to commence simulation in 1929.
Notation used: 3
AEX Index of agricultural exports, 1939=100 (FA).
AY Real Farm Income (A).
B Real end-of-year corporate surplus (B).
CHWR Year on year change in the index of hourly wages in nominal terms (wt - wt-1).
CONS Real consumption expenditure (C).
CP Real corporate profits (PC).
1
Excellent and brief descriptions are provided in the review article by Carl Christ (1956) and in the paper
by Adelman and Adelman (1959).
2
A slightly larger and revised version of the model is reported in Chapter 6 of their book. I have chosen to
work with the first version of their model.
3
Note I am using CONS for Consumption and DEP for depreciation of physical capital as C and D are
reserved names in EViews.

CS Real corporate savings (SP).
DEP Real capital consumption (D).
DLIR Deviation of long term interest rate from 2% [ ( − 2.
0)
]
= L
i .
DNWY Real gross disposable non-wage income (P + A + DEP - TP - TA).
DY Real aggregate disposable income (Wl + W2+ P + A - TW - TP - TA ).
EX Real exports (FE).
G Real government expenditure (G).
GNP Real Gross National Product (Y+T+D).
GPI Price index of GNP, 1939=100 (p).
GWB Government's Wages Bill in real terms (W2).
H Index of hours worked per year, 1939=100 (h).
I Real gross private domestic capital formation (I).
IM Real imports (FI).
IMPI Index of prices of imports, 1939=100 (PI).
K Real end-of-year stock of private capital (K).
Ll Real end-of-year liquid assets held by persons (L1).
L2 Real end-of-year liquid assets held by businesses (L2).
LIR Long term interest rate (iL).
N Number of persons in the labour force (N)
NCDY Real non-corporate disposable income (Wl + W2+ P + A - TW- TP - SP - TA).
NCP Real corporate profits net of tax (PC – TC).
NE Number of non-farm entrepreneurs (NE)
NF Number of farm operators (NF)
NFDY Real non-farm disposable income (Wl + W2 + P - SP - TW - TP ).
2

NG Number of government employees (NG)
NIT Real net indirect taxes (T).
NU Number unemployed (N - NW - NE - NF).
NW Number of wage and salary earners (NW).
P Real non-wage non-farm income (P).
PCSIR Percentage change in the short-term interest rate [ ( ) ) ]
* i i
100 i − .
PLI Index of labour input in private sector (h(NW - NG + NE + NF)).
PSO Real output of the private sector (Y + T + D - W2).
POP Number of persons in the United States (NP).
PWB Wages-bill of the private sector in real terms (W1).
R Excess reserve of banks as a percentage of total reserves (R).
SIR Short-term interest rate (iS).
TA Net taxes on farm income in real terms (TA).
TC Corporate income taxes in real terms (TC).
1 1 /
st − st−
st
TP Net taxes associated with non-wage non-farm income in real terms (TP).
TW Net taxes associated with wage and salary income in real terms (TW).
TIME time index, measured in years, 1929=0 (t).
WR Index of hourly wages (w).
Equations in the Klein -Goldberger Model: 4
CONS = -34.5+0.62*(PWB+GWB-TW)+0.46*(P-CS-TP) +0.39*(AY-TA)
+0.23*CONS(-1)+0.024*L1(-1)+0.36*POP
I = -16.8+0.76*DNWY(-1)-0.14*K(-1)+0.14*L2(-1)
4 Since EViews will only allow an endogenous variable to appear once on the left-hand side of an equation
in the model, I have written Klein and Goldberger's equation (7) as an expression not for Private Sector
Output but as an expression for the amount of labour input required by the private sector.
3

CS = -2.42+0.86*NCP-0.30*(NCP(-1)-CS(-1))-0.014*B(-1)
CP = -8.34+0.71*P
DEP = 11.46+0.14*((K+K(-1))/2)
PWB = -2.70+0.36*PSO+0.14*PSO(-1)+0.16*TIME
PLI = (PSO+31.98-0.076*((K+K(-1))/2)-1.90*TIME)/2.31
CHWR = 4.11-0.75*NU+0.56*(GPI(-1)-GPI(-2))+0.56*TIME
IM = 2.09+0.0087*DY*(GPI/IMPI)+0.24*IM(-1)
AY = -4.53+0.25*NFDY-0.13*NFDY(-1)+0.0096*AEX
L1 = 0.14*NCDY+(75.0/(DLIR^0.84))
L2 = -0.77+0.24*PWB-0.69*SIR-0.27*(GPI-GPI(-1))+0.64*L2(-1)
LIR = 2.66+0.46*SIR(-3)+0.23*SIR(-5)
PCSIR = 6.42-0.55*R
DLIR = LIR-2.0
GNP = CONS+I+G+EX-IM
K = K(-1)+I-DEP
B = B(-1)+CS
PSO = CONS+I+EX-IM+(G-GWB)
DNWY = P+AY-TP-TA+DEP
NCP = CP-TC
NW = ((PLI-NE-NF)/H)+NG
NU = N-NW-NE-NF
NFDY = PWB+GWB+P-CS-TW-TP
P = PSO-AY-DEP-PWB-NIT
DY = (PWB+GWB-TW)+(P-TP)+(AY-TA)
4

NCDY = DY-CS
SIR = ((PCSIR/100)*SIR(-1))+SIR(-1)
WR = WR(-1)+CHWR
GPI = WR/((PWB+GWB)/(H*NW))
Historical Simulation
The file containing the equations in the Klein-Goldberger model and the relevant data for
the U.S economy over the period 1929-41 is named kg.wfl. It may be downloaded to
your computer and then run using EViews. The model is complicated to solve as it
contains some non-linearities. Don't be surprised if it takes a minute or so to solve the
model and store values of the endogenous variables.
The graph given below depicts actual 5 GNP (solid line) and simulated GNP (dotted line)
over the period 1929-41. Clearly the model tracks actual experience much better than did
Klein's earlier model (Klein Model 1).
120
110
100
90
80
70
60
29 30 31 32 33 34 35 36 37 38 39 40 41
------------------------------
5 I have loaded data for Actual GNP into the workfile under the name AGNP. This is to facilitate
comparisons between simulated and Actual GNP. The data on Actual GNP is not needed in the simulation.
5

References
Adelman, I. and F. Adelman (1959), "The Dynamic Properties of the Klein-Goldberger
Model", Econometrica, 27, pp. 596-625.
Christ, C. F. (1956), "Aggregate Econometric Models", American Economic Review, 66,
pp. 385-408.
Klein, L. R. and A. S. Goldberger (1955), An Econometric Model of the United States
1929-1952, North-Holland.
6