The analysis of Klein`s model„ The economic fluctuations in the United States 1921-

1941” (1950)

Prepared by:Aleksander Rzewuski

Roman Gąsowski

Few words about Lawrence R. Klein

born in 1920 in Omaha, Nebraska in Jewish family

1947 the book The Keynesian Revolution established him as one of the foremost scholars on Keynesian economics

In 1980 he was awarded the Nobel Memorial Prize in Economic Sciences

The goal of our presentation

Introduction of Klein’s model Estimation for data covering

American economy in the period of 1921-1941

Analysis of the results Estimation of the model for

contemporary data (1970-2000) Comparison and final conclusions

Background for Klein’s model

One of the first models to explain the economy as a whole

Published in 1950

It includes years of Great Depression till the beginning of American participation in World War II

All variables are measured in billions of dollars

Structural form of the model

Endogenous variables of the model are: Consumption – Ct

Wages in private sector – Wp

Investments – It Capital stock – Kt

GNP – Xt

Profits in private sector – Pt

Structural form (cont’d)

Exogenous variables are: Government expenditure – Gt

Wages in public sector – Wg

Taxes – Tt

Lagged variables: Pt-1, Kt-1, Xt-1

Equations of the model

Ct = α 1 + α 2Pt + α 3Pt-1 + α 4 (Wp +Wg) + u1t

Wp = γ 1 + γ 2Xt + γ 3Xt-1 + γ 4t + u3t

It = β 1 + β 2Pt + β 3Pt-1 + β 4Kt-1 + u2t

Kt = It + Kt-1

Xt = Ct + It + Gt

Pt = Xt – Wp – Tt

Three-stage least squares regression ---------------------------------------------------------------------- Equation Obs Parms RMSE "R-sq" chi2 P ---------------------------------------------------------------------- c 21 3 .9443305 0.9801 864.59 0.0000 wp 21 3 .7211282 0.9863 1594.75 0.0000 i 21 3 1.446736 0.8258 162.98 0.0000 ----------------------------------------------------------------------

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- c | p | L1 | .1631439 .1004382 1.62 0.104 -.0337113 .3599992 -- | .1248904 .1081291 1.16 0.248 -.0870387 .3368194 wp_plus_wg | .790081 .0379379 20.83 0.000 .715724 .8644379 _cons | 16.44079 1.304549 12.60 0.000 13.88392 18.99766 -------------+---------------------------------------------------------------- wp | x | -- | .4004919 .0318134 12.59 0.000 .3381388 .462845 L1 | .181291 .0341588 5.31 0.000 .1143411 .2482409 year | .149674 .0279352 5.36 0.000 .094922 .2044261 _cons | -287.2233 53.4488 -5.37 0.000 -391.9811 -182.4656 -------------+---------------------------------------------------------------- i | p | -- | -.0130791 .1618962 -0.08 0.936 -.3303898 .3042316 L1 | .7557238 .1529331 4.94 0.000 .4559805 1.055467 k1 | -.1948482 .0325307 -5.99 0.000 -.2586072 -.1310893 _cons | 28.17785 6.793768 4.15 0.000 14.86231 41.49339 ------------------------------------------------------------------------------ Endogenous variables: c wp i wp_plus_wg x p Exogenous variables: L.p L.x year k1 g wg t ------------------------------------------------------------------------------

Interpretation Estimates of all parameters look very

reasonable The point estimates are not sufficient The signs of the parameter seem to be

expectable in the context of economic theory

Most of the coefficients are significant] Coefficient of determination (R2) for all

equations is very high

Observed level of GNP (solid line), simulated level of GNP (dotted line)

As many economists pointed out the model does not track the historical data well

However it can be used to simulate various policies

Possible way of policy simulation

Change the value of government expenditure in one year holding all other levels of g and all other variables fixed

Run the estimation with altered data and compare new „under shock” values of GNP with those obtained before

Observe the difference in GNP and conclude policy recommendation

Analogous analysis of contemporary data

Data set covers the period of 1970 – 2000

The data were gathered from World Development Indicators database and from Bureau of Economic Analysis of U.S. Department of Commerce

All variables are measured in billions of dollars

Three-stage least squares regression ---------------------------------------------------------------------- Equation Obs Parms RMSE "R-sq" chi2 P ---------------------------------------------------------------------- c 30 3 76.55733 0.9982 21791.42 0.0000 wp 30 3 52.79923 0.9973 12318.64 0.0000 i 30 3 22.7667 0.9179 322.08 0.0000 ----------------------------------------------------------------------

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- c | p | L1 | -1.976323 .6102105 -3.24 0.001 -3.172313 -.7803319 -- | 2.711593 .6818255 3.98 0.000 1.37524 4.047946 wp_plus_wg | 1.312336 .0587717 22.33 0.000 1.197146 1.427527 _cons | -186.1593 28.9765 -6.42 0.000 -242.9522 -129.3664 -------------+---------------------------------------------------------------- wp | x | -- | 1.123226 .1578403 7.12 0.000 .813865 1.432588 L1 | -.6039088 .1601588 -3.77 0.000 -.9178143 -.2900034 year | -45.23511 7.061766 -6.41 0.000 -59.07592 -31.3943 _cons | 89054.35 13910.47 6.40 0.000 61790.33 116318.4 -------------+---------------------------------------------------------------- i | p | -- | .0512894 .3611802 0.14 0.887 -.6566108 .7591897 L1 | .4434355 .4515954 0.98 0.326 -.4416753 1.328546 k1 | -.130268 .069566 -1.87 0.061 -.2666149 .006079 _cons | 17.08937 10.72621 1.59 0.111 -3.933628 38.11236 ------------------------------------------------------------------------------ Endogenous variables: c wp i wp_plus_wg x p Exogenous variables: L.p L.x year k1 g wg t ------------------------------------------------------------------------------

Interpretation

Coefficient of determination (R2) is even higher

Most of the parameters are significant at the level of 1%

Model tracks the economy indicators well

Final conclusions Both models follow the reality well

Do they give any predictions?

Only policy simulation

Pioneer work and the cornerstone in the evolution of econometrics

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