optimal control of fiscal policies for austria: applications of a stochastic control algorithm

NonlinearAnalysis. Theory, Merhodr & Applications, Vol. 30, No. 2, pp. 1051-1061, 1997 PRX. 2nd World Congress of Nonlinear Analysts

Q 1997 Elsevier Science Ltd

PII:SO362-546X(97)00134-X Printed in Great Britain. All tights reserved

0362-546X197 fl7.00 + 0.00

OPTIMAL CONTROL OF FISCAL POLICIES FOR AUSTRIA: APPLICATIONS OF A STOCHASTIC CONTROL ALGORITHM

REINHARD NECK? and SOHBET KARBUZ$

TDepartment of Economics, University of Osnabrueck, D-49069 Osnabrueck, Germany, and fUTESAV, Mecidiye Cad. 7/50 Mecidiyekby, Istanbul, Turkey

Key words and phrases: Optimum control, stochastic control. economics, fiscal policy, sensitivity analysis, simulation, nonlinear econometric model.

1. INTRODUCTION

Optimum control theory has been applied to various problems of economics in order to yield insights into the qualitative properties of economic policies to be conducted on a national or regional level or on the level of an individual firm or household. Most of this work has used simple mathematical economic models with one or two state variables only. Except for linear-quadratic control problems, virtually no analytical solutions are available for multivariable stochastic models. For practical policy problems, on the other hand, more complicated nonlinear relations between a fairly large number of politically relevant variables have to be taken into account in policy planning. This is particularly true when the influence of uncertainty on the formulation of an optimal policy is to be investigated, which is important due to the limited knowledge about the exact relations between economic variables. Therefore, numerical results are desirable for such a purpose, which should be based on econometric models estimated from actual data for the economy to which economic policies are to be applied.

In this paper, we apply an optimum control approach to a problem of quantitative economic policy. We determine numerically optimal budgetary policies for Austria for the nineties by minimizing an intertemporal objective function subject to the constraints given by an econometric model. The model, called FINPOW, is a medium-size macroeconometric model for Austria. It relates policy and exogenous variables to objective variables of Austrian economic policies, such as the rate of unemployment, the rate of inflation, the growth rate of real GDP, the current account and the budget deficit. Moreover, we postulate an objective function for Austrian policy-makers over the years 1995 to 2000, which penalizes deviations of objective variables from their desired values. The exogenous variables of the model are forecast over this planning horizon using time series methods. Next, we calculate optimal stabilization policies over this time horizon using the stochastic control algorithm OPTCON. In the present paper, we concentrate on the question how optimal policies are affected by assumptions about uncertain model parameters, taking the structure of the model and the forecasts for the exogenous variables as given. The results indicate that considerable differences between optimal policies can arise, depending primarily upon the amount of covariation between different parameters of the model.

2. THE ECONOMETRIC MODEL FINPOL3

The model FINPOL3 is based on traditional Keynesian macroeconomic theory in the sense of conventional IS-LM/aggregate demand-aggregate supply models. It is an updated and re-specified version of our model FINPOLl, which we have used for several optimization experiments; see, e.g., [l]. Stochastic behavioral equations for the demand side include a consumption function, an investment function, an import function and an interest-rate equation as a reduced-form money market model. Prices are largely determined by aggregate demand variables. Disequilibrium in the labor market, as measured by the excess of unemployed

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persons over vacancies, is modelled to depend on the real GDP growth rate and the rate of inflation, embodying both an Okun’s law-type relation and a rudimentary Phillips curve, The main objective variables of Austrian economic policies, such as real GDP, the labor market disequilibrium variable (related to the rate of unemployment), the rate of inflation, and the ratios of the balance of payments and of the federal net budget deficit to GDP, are related directly or indirectly to those fiscal policy instruments which are used as control variables, namely to federal budget expenditures and revenues,

The model, which is dynamic and nonlinear, was estimated first by OLS and then by simultaneous equations estimation methods using annual data over the period 1965 to 1994. Data have been obtained from the Austrian Institute of Economic Research (WIFO). The estimates and test statistics together with ex-post simulation results suggest that the model provides a reasonable account of the development of economic variables in the recent past. Here we use the estimates of the parameters obtained by three-stage least squares; the software package PC TSP, Version 4.2B has been used for estimating and simulating the model. These estimation results together with the statistical characteristics of the regressions are given below. Values in brackets denote estimated standard deviations. R2 is the coefficient of determination, SE is the estimated standard error of the equation,

LIST OF VARIABLES FOR THE MODEL FINl’OL3

Endogenous Variables CR, 14 MRt Rt YRt w pvt YDRt PW ot RR, MlR, PMV,

pyt “Nt YRo/ot LBRt

4 G Rt TRt PGt vt Gt Tt NDEFt DEFO/ot

yt FDt FDO/q LBRO/ot

real private consumption real fixed investment real imports of goods and services nominal rate of interest (long-term bond yield) real gross domestic product at market prices real total aggregate demand general price level (total demand deflator) real disposable personal income rate of inflation real rate of interest real stock of money supply relative price of imports domestic price level (deflator of GDP at market prices) labor market excess supply (unemployed minus vacancies as percentage of dependent labor force) growth rate of real GDP at market prices current account (real exports minus real imports of goods and services) real autonomous expenditures real public consumption real public sector net tax receipts (including social insurance contributions etc., minus subsidies) deflator of public consumption nominal total aggregate demand nominal public consumption nominal public-sector net tax receipts federal net budget deficit federal net budget deficit as percentage of GDP nominal GDP at market prices federal debt federal debt as percentage of GDP current account as percentage of GDP

Yohy Instrument Variables NEX, federal budget net expenditures BINt federal budget tax receipts

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Exogenous Non-controlled Variables XRt real exports of goods and services IIRt real inventory changes (including errors and omissions from the national accounts statistics) PM, import price level (deflator of imports of goods and services) Ml, nominal stock of money supply Ml DXDt correction term for federal debt changes

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EQUATIONS OF MODEL FINPOL3

CRt = 0.523 CRt-1 + 0.447 YDRt - 2.768 RRt + 9.664 (0.127) (0.118) (1.034) (5.403)

R2 = 0.998 SE = 6.941

IRt = 0.710 IRt-1 + 0.270 VRt - 0.223 VRt-1 - 3.624 RR, + 18.488 (0.104) (0.042) (0.489) (1.562) (9.197)

R2 = 0.988 SE = 7.303

MRt = 0.481 MR,-1 + 0.197 VRt - 1.362 PMV, + 60.588 (0.098) (0.036) (0.718) (86.008)

R2 = 0.995 SE = 13.367

Rt = 0.505 Rt-1 - 0.019 MIRt + 0.004 YRt + 0.351 PV%t + 2.038 (0.100) (0.008) (0.001) (0.057) (0.928)

R2 = 0.690 SE = 0.585

YRt = CRt + IRt + GRt + ARt - MRt

VRt= YRt + MRt

PVt = (YRt / VRt) PY, + (MRtiVRt) PMt

YDRt = YRt - TRt

PV%t = ((PVt - PV,1) / PVt-1) 100

RRt = R, - PW~

MIRt = (Ml, / PVt). 100

PMVt = (PM, / PVt) . 100

PY, = 0.914 PYtml + 0.009 YRt + 0.050 PMt - 3.565 (0.021) (0.002) (0.017) (1.161)

R2 = 0.999 SE = 0.778

IJN, = 0.737 LJNtwl - 0.386 YRo/ot - 0.168 PVyq + 2.610 (0.079) (0.047) (0.074) (0.513)

R2 = 0.950 SE = 0.445

(2.1)

(2.2)

(2.3)

(2.4)

(2.5)

(2.6)

(2.7)

(2.8)

(2.9)

(2.10)

(2.11)

(2.12)

(2.13)

(2.14)


YRO/ot=((YRt-YRt-l)/YRt-1)’ 100

LBRt = XRt - MRt

ARt = XRt + IIRt

GRt=(Gt/PGt). 100

TRt=(Tt/PYt). 100

PGt = 0.845 PGt,1 + 0.010 VRt + 0.084 PVt - 5.807 (0.050) (0.003) (0.054) (2.080)

R2 = 0.999 SE = 1.074

Vt = VRt PVt / 100

G, = 0.035 Vt + 0.43 1 NEX, (0.014) (0.059)

R2 = 0.998 SE = 5.877

(2.15)

(2.16)

(2.17)

(2.18)

(2.19)

(2.20)

(2.21)

(2.22)

Tt = 0.546 Tt-1 + 0.345 BINt + 0.097 VRt - 56.995 (0.063) (0.068) (0.019) (14.902)

R2 = 0.998 (2.23)

SE = 8.667

NDEF, = NEX, - BINt (2.24)

DEFO/ot = (NDEFt / Yt) 100 (2.25)

Yt = YRt PYt / 100 (2.26)

FDt = FDt- 1 + NDEFt + DXD, (2.27)

FDO/ot = (FD, / Yt) 100 (2.28)

LBRO/q = (LBRt / YRt) 100 (2.29)

3. THE OPTlh4UM CONTROL APPROACH

In the theory of quantitative economic policy, macroeconomic policy problems are often considered as problems of optimizing an intertemporal objective function under the constraints of a dynamic system which is subject to various kinds of uncertainties. Stochastic optimum control theory has been used in several studies to determine optimal policies for econometric models. Here we use the algorithm OPTCON, developed in [2]; it determines approximate solutions of stochastic optimum control problems with a quadratic objective function and a nonlinear multivariable dynamic model under additive and parameter uncertainties. The objective function is quadratic in the deviations of the state and control variables from their respective desired values. The dynamic system is required to be given in a state space representation. Apart from the additive error term, a constant vector of unknown (and hence stochastic) parameters enters the system equations. As input for the algorithm, the user has to supply the system function, the initial value of the state vector, a tentative path for the control variables, the expected value and the covariance matrix of

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the stochastic parameter vector, the covariance matrix of the additive system noise, the weight matrices of the objective function, and the desired paths for the state and control variables.

For our simulation experiments, we choose the planning horizon as 1995 to 2000. Among the variables whose deviations from desired values are to be penalized, we distinguish two categories: First, there are five “main” objective variables which are of direct political relevance in assessing the performance of the Austrian economy. These are the rate of inflation (PV”/9), the labor market excess supply variable (UNt) as a measure for involuntary unemployment, the rate of growth of real GDP 0, and the current account (LBR%t) and the federal net budget deficit (DEF%t), both as percentages of GDP. In all experiments, 2% p.a. is considered as the desired rate of inflation (PV%t,), 4% p.a. as the desired real growth rate (YR%t), and the desired levels for labor market excess supply (UNt) and the current account (LBR%t) are set equal to zero. Thus, we want to achieve equilibrium in the labor market and in the external relations. The choice of a positive rate of inflation is motivated by high rates of inflation in the past, which make complete price stability (PV%t = 0) seem to be an unrealistic goal for the near future. The desired value for the real growth rate is above the average of the last twenty years, but in line with the long-term growth performance of the Austrian economy after World War II. For the deficit variable, we assume that the aim is to consolidate the federal budget deficit gradually such that the desired value of DEF0/9 is reduced by 0.5 percentage points each year, from the historical value of 4.67% in 1994 down to 1.67% in 2000.

Second, we introduce a category of “minor” objective variables. These include real private consumption (CRt), real private investment (IRt), real imports of goods and services (MRt), the nominal rate of interest (Rt), real GDP (YRt), real total aggregate demand (VRt), the domestic price level (PYt), the price level of public consumption (PGt), nominal public consumption (Gt), and nominal public-sector net tax revenues (Tt), as well as the policy instrument (control) variables federal budget net expenditures (NEXt) and federal budget tax receipts (BINt). We take 1994 historical values of these “minor” objective variables (except for Rt) to be given and postulate desired growth rates of 4% p.a. for the planning horizon for all real variables, desired growth rates of 2% p.a. for the price level variables, and desired growth rates of 6% p.a. for the nominal variables. The rate of interest Rt has a desired constant value of 6 for all periods. There are two reasons for including these “minor” objective variables: First, assigning to them the above desired values shall reflect the aim of the hypothetical policy-maker of stabilizing the economy in the sense of achieving smooth growth paths for real and nominal variables, i.e. some kind of “balanced growth” of total demand and its components. Second, this device serves as a substitute for imposing inequality constraints on state and control variables to prevent erratic fluctuations of these variables which are not possible in reality due to various rigidities in the economic system which cannot be adequately captured by our model.

In the weight matrix of the objective function, all off-diagonal elements are set equal to zero, and the main diagonal elements are given weights of 10 for the “main” objective variables and of 1 for the “minor” objective variables. The state variables that are not mentioned above get weights of zero, thus being regarded as irrelevant to the hypothetical policy-maker. The weight matrix is assumed to be constant over time.

The algorithm OPTCON assumes the values of the non-controlled exogenous variables to be known in advance for all time periods of the planning horizon. In addition, starting values are required for the control variables for all time periods to initialize the iterative determination of their optimal values. For a simulation over a future planning horizon, projections (forecasts) of the exogenous (controlled and non-controlled) variables are needed. Here we use extrapolations of these variables for the years 1995 to 2000 calculated from linear stochastic time series models of the ARMA (mixed autoregressive-moving average process) type. After several trials and applying the usual diagnostic checking procedure for the time series under consideration, we decided to model federal budget expenditures (NEXt) by an ARMA (2,3) process, federal budget revenues (BIbIt) by an ARMA (2,2) process, the import price level (PM3 by an ARMA (1,l) process, real exports of goods and services (XRt) by an ARMA (3,3) process, the inventory change variable IIRt by an ARMA (1,l) process, and money supply (Mlt) by an ARMA (2,l) process. The correction term variable DXDt was set equal to zero over the planning horizon.

The forecasts from these time series models imply an average growth rate of 5.5% for the fiscal policy variables. The extrapolation implies that the federal budget deficit (NDEFt) grows moderately from 99.5 billions AS in 1995 to 118.8 billions AS in 2000, which is an optimistic forecast. The development of the


foreign sector variables PMt and XRt is also optimistic: PMt grows by less than 1% p.a., and XRt grows by 4% p,a. on average. IIRt is positive and nearly constant. Money supply Ml, grows by 6.5% p.a. on average.

4. THE DETJZRhJJNISTIC AND THE STOCHASTIC OPTIMUM

As a first step, the model was simulated over the years 1995 to 2000 using the extrapolations of all (control and non-controlled) exogenous variables from the time series models as input. This amounts to a dynamic forecast of the endogenous variables of the model; no optimization is involved in this projection, which serves as a reference for comparison with the optimization runs. Next, we performed two optimization experiments as detailed in the previous section. Here again the projections of the non-controlled exogenous variables from the time series models are used as inputs, being assumed to be known for certain, but the values of the policy instruments are determined endogenously as (approximately) optimal under the assumed objective function. For a deterministic optimization run, we assumed all parameters of the model to be known for certain, This amounts to a neglect of uncertainty of all policy effects. For a fully stochastic optimization run, on the other hand, only deterministic paths for the non-controlled exogenous variables were assumed, but the estimated covariance matrices of the parameters and of the additive disturbances of the model, which are obtained from the 3SLS estimation, are taken into account when calculating optimal policies. In this case, the expected value of the same quadratic objective functional is minimized.

As can be seen from Table 1, the projection scenario forecasts a fairly constant inflation rate (PV%t) of about 2.5%, relatively high growth of real GDP (YR%t), diminishing involuntary unemployment (UN3 and a federal budget deficit growing slower than GDP (DEF%t), implying only minor growth of the debt--o-GDP ratio FD’/ot. Some fluctuations occur along the projected growth path of the Austrian economy, especially in real income and unemployment. The current account exhibits a growing deficit

year

1995 1996 1997 1998 1999 2000

NEXt B w PV%t UN, YRo/ot LBRO/ot DEF0/9

769.925 670.429 2.383 4.286 2.793 -0.983 4.066 813.893 709.808 2.570 3.773 4.060 -1.222 3.960 854.013 749.461 2.416 4.092 2.320 -1.827 3.770 902.264 791.639 2.524 3.779 3.694 -1.937 3.729 949.580 835.462 2.506 3.664 3.400 -2.185 3.605 1000.270 881.451 2.499 3.615 3.311 -2.466 3.521

Table 1. Projected values of instruments and dynamic forecasts of “main” objectives.

In spite of this already optimistic picture of the future development of the Austrian economy provided by the projected forecast, there is still some scope for optimal stabilization policy, as can be seen from the optimization experiments (Tables 2 and 3). Optimal fiscal policies are more countercyclical than projected ones and imply smoother time paths of the endogenous variables of the model. In particular, for those years where the projection forecasts lower than desired growth, federal budget expenditures (NEXt) are higher than in the projection and federal budget revenues (BINt) are lower. The reverse is true for the year 1996, where the projection scenario implies higher growth of real GDP. To compensate for expansionary budget expenditures, budget revenues increase faster over the entire planning horizon. The overall effects on policy objective variables are favorable: Unemployment, though initially higher, comes down to lower values than in the projection, the current account deficit and the budget deficit are eventually lower, real GDP growth is higher, and the rate of inflation is virtually unaffected by this relatively expansionary fiscal policy design.

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year NEX, BW PVYq UN, YRD/9 LBRO/ot DEFD/9

1995 789.285 672.909 2.422 4.879 3.813 -1.238 4.85 1 1996 824.079 721.674 2.572 4.022 4.548 -1.027 3.960 1997 882.422 766.342 2.490 3.861 3.360 -1.620 4.175 1998 929.493 814.704 2.553 3.509 3.939 -1.786 3.882 1999 986.307 861.199 2.550 3.356 3.665 -2.129 3.954 2000 1048.852 905.979 2.550 3.293 3.536 -2.5 19 4.223

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Table 2. Optimal values of instruments and “mam” objectives, deterministic optimum

year NEXt BlNt PV%t UN, YRo/q LBRO/ot DEFO/q

1995 790.933 671.251 2.430 4.846 3.895 -1.257 4.984 1996 823.105 723.069 2.564 4.040 4.439 -1.033 3.869 1997 881.683 767.970 2.489 3.873 3.366 -1.619 4.126 1998 928.723 818.119 2.544 3.547 3.868 -1.764 3.744 1999 984.786 865.204 2.539 3.407 3.608 -2.083 3.785 2000 1046.506 909.042 2.540 3.343 3.508 -2.45 1 4.072

Table 3. Optimal values of instnancnts and “mam” objectives, fully stochastic optimum

There is not much difference between the deterministic (Table 2) and the fully stochastic (Table 3) optimization run. Optimal values of budgetary policy variables are close in these two experiments, with more expansionary policies (higher NEX,, lower BIN3 in 1995, and more restrictive policies (lower NEXt, higher BIN,) in 1996, 1998, 1999. and 2000 in the fully stochastic optimum; in 1997, both NEXt and BIN, are higher in the stochastic optimization run. Price levels and real variables (hence also nominal aggregates) show slightly lower growth over the entire planning period in the stochastic than in the deterministic optimum. The optimal value of the objective function is 23,187.8 in the deterministic experiment and 32,504. I in the fully stochastic one; hence the costs of uncertainty are about 40% of the deterministic minimum costs.

5. OPTIMAL POLICIES UNDER DIFFERENT ASSUMPTIONS ABOUT STOCHASTIC PARAMETERS

The similarity between the optimal deterministic and stochastic paths of budgetary policies seems to imply that optimal policies are reliable even when neglecting parameter uncertainty. This is somewhat astonishing. because previous theoretical and numerical studies using simple macroeconomic models have shown that uncertainty generally matters in the design of optimal stabilization policies. Therefore we would like to know whether our result holds true also when only some parameters of the model are treated as stochastic, with the other ones remaining dctermmistic. WC introduce different assumptions about parameter uncertainties into our model FINPOL3 in order to assess the influence of various kinds of uncertainty on the design of future optimal budgetary policies. In particular, we want to investigate the effects of making several key parameters determining fiscal and monetary policy multipliers uncertain. All the experiments described below start from the specification of the objective function assumed for the deterministic optimum and described in Section 3.

As our model FlNPOL3 was estimated by 3SLS, we have an estimate of the entire parameter covariance matrix. To concentrate upon the effects of uncertainty of some key parameters, we neglect the variance and covariance estimates of the other parameters. However, it turns out that taking into account or not covariances between different parameters may be crucial for optimal policies. Therefore, in each of our


experiments, we calculated three versions of optimal budgetary policies. For Version A, only the variances of the parameters being regarded as stochastic were taken into account and all covariances were neglected. In this case, the parameter covariance matrix is diagonal, with non-zero elements in the main diagonal only for the stochastic parameters. Version B takes into account also the covariances between the parameters with non-zero variances. For Version C, in addition all covariances between the stochastic parameters and all other parameters (which still have zero variances) are given non-zero values. In this way, we want to study effects of correlations between parameter estimates on the design of optimal policies. Estimates for parameter variances and covariances were always taken from the estimated parameter covariance matrix obtained from the 3SLS estimation. Results can be compared either to the deterministic optimum or to the fully stochastic optimum (which is very similar to the deterministic one, anyway).

For the first of these stochastic experiments, some parameters which determine the monetary policy multiplier are regarded as stochastic. These are the coefficient of the real rate of interest in the investment equation (2.2) and the coefficients of real money supply and of real GDP in the interest rate equation (2.4). Although money supply is exogenous in the version of the model used here and monetary policy itself is not affected by this experiment, it is interesting whether there are consequences of the effects of monetan/ policy becoming more uncertain upon budgetary policies. The results of these experiments show that the edCects on fiscal policies are minor. For all three versions, optimal paths of policy instruments are again close to the deterministic optimum.

The picture changes when we still take the same three coefficients as random as before, but *add the marginal propensity to consume as a fourth stochastic parameter. This is the coefficient of real disposable income in the consumption equation (2. I), which is important for the transmission of fiscal policy effects to demand-side variables, as is well known from Keynesian macroeconomic theory. In this case, both monetary and fiscal policy multipliers are made uncertain, and we explore the effects of uncertain demand-side policies on the optimal design of future budgetary policies. The results show considerable deviations from the previous experiment and from the deterministic and the fully stochastic optimum. In Versions A (see Table 4) and B (which gives very similar results), federal budget expenditures are lower and federal budget tax receipts are much higher, hence budgetary policies follow a more restrictive course. The federal budget is consolidated, mainly from the revenue side (by higher taxes), and shows even a surplus in 1995 and 1996. Also the current account comes close to being balanced. On the other hand, growth of real GDP for most years and over the entire planning period is lower than in the previous experiments. Labor market excess supply (UNt) is always higher, inflation (PV’/,, and budget deficit (DEF%t) are always lower than previously, The optimal value of the objective function rises to about f i f ty times its deterministic value (1,162,437.7 in Version A), indicating extremely high costs of this kind of uncertainty.

year

1995 1996 1997 1998 1999 2000

NEXt BWt

756.385 794.250 8 12.768 823.355 879.970 862.455 925.835 908.424 973.695 941.908

1032.978 952.761

PVYq

2.118 2.369 2.294 2.366 2.393 2.487

UN, YRyq LBRO/ot DEFyq

6.053 0.902 -0.540 -1.628 5.165 3.915 0.261 -0.426 4.847 3.076 0.074 0.666 4.310 3.830 0.180 0.619 3.922 3.796 -0.036 1.057 3.418 4.320 -0.539 _ 2.481

Table 4. Optimal values of mstruments and “main” objectives, monetary and fiscal policy multipliers stochastic (Version A)

These results seem to suggest that uncertain policy multipliers render a more restrictive budgetary policy optimal. Version C of the same experiment, however, gives a completely different impression (Table 5). Now both federal budget expenditures and tax receipts (except in the last year) are (in some years considerably) more expansionary than in the deterministic optimum. Except for the last year (2000), the deficit variable


DEFO/ot is much higher than in the deterministic case. This boosts real GDP growth (YR”/s) up to 6.9% in 1995 and to 5% in 1996, but afterwards and over the entire planning period real GDP grows slower than under the optimal policies of the deterministic case. Unemployment (UNt> is lower than in the deterministic optimum until 1998 and higher aftenvards; exactly the opposite is true for inflation (PV%& The deficit of the current account is higher than in the deterministic optimum in every year. The minimum value of the objective function is very high again.

year NEX, BW PWq UN, YRo/9 LBRyq DEF0/9

1995 827.580 549.223 2.744 3.622 6.931 -1.942 11.231 1996 841.376 632.725 2.766 2.897 4.977 -2.267 7.754 1997 891.898 702.788 2.647 3.039 3.275 -3.147 6.581 1998 936.776 781.152 2.625 3.175 3.201 -3.330 5.076 1999 986.118 859.808 2.510 3.606 2.395 -3.404 3.897 2000 1032.639 923.259 2.412 4.072 2.055 -3.297 3.207

Table 5. Optimal values of instruments and “main” objectives, monetary and fiscal policy multipliers stochastic (Version C).

year

1995 1996 r 1997 1998 1999 2000

NEXt

747.006 801.028 866.290 911.000 958.222

1017.849

w YR0/9 LBRyq DEFO/ot

6.110 0.761 -0.505 -1.441 5,172 4.006 0.296 -0.467 4.831 3.130 0.095 0.508 4.284 3.864 0.185 0.427 3.898 3.807 -0.044 0.839 3.406 4.306 -0.550 2.195

Table 6. Optimal values of instruments and “main” objectives, fiscal policy multipliers stochastic (Version A).

From the results of the three versions of the previous experiment, we have to conclude that it makes a big difference for the design of optimal budgetary policies whether correlations between parameters are taken into account or not. This impression is confirmed by the results of our next experiment, where we assume the coefficients relating to monetary policy to be known for certain and investigate the effects of making only fiscal policy multipliers uncertain. To do so, we take as stochastic parameters the marginal propensity to consume (as before) and the coefficients of federal budget expenditures (NEXt) in the equations determining public consumption (2.22) and of federal budget receipts (BIN3 in the public-sector tax equation (2.23). The results of this experiment with uncertain fiscal policy effects parallel those of the experiment with both fiscal and monetary policy effects being uncertain. In Version A of this experiment (Table 6), again optimal NEXt values are lower and optimal BINt values are higher than in the deterministic optimum, resulting in a more restrictive budgetary policy. The values of both instruments are lower than in the case where monetary policy effects are also uncertain. The results for the endogenous variables are similar as in Version A of the previous experiment; the minimum value of the objective hnction is still higher (1,204,394.0). Version B gives similar results, but here BINt and especially NEXt are higher than in Version A, which makes the impact of budgetary policy slightly less contractionary and yields a lower minimum of the objective function. The results of Version C (Table 7) are again completely different from those of Versions A and B and are similar to those of Version C in the previous experiment. Except for the last year of the planning period,


budgetary policies act in a very expansionary way. The optimal value of the objective function is very high again (1,103,084.6)

year

1995 1996 1997 1998 1999 2000

NEXt BW PV%t

828.710 547.959 2.750 842.593 630.724 2.772 892.769 699.963 2.652 937.214 776.73 1 2.632 985.860 853.371 2.518

1031.751 916.940 2.419 I w YRo/g

3.599 6.989 2.869 5.003 3.012 3.288 3.147 3.220 3.574 2.420 4.041 2.071 I

LBRO/q

-1.955 -2.293 -3.184 -3.379 -3.465 -3.371 --

DEFO/ot

11.321 7.866 6.702 5.228 4.080 3.359

Table 7. Optimal values of instruments and “main” objectlves, fiscal policy multipliers stochastic (Version C).

The extent to which optimal budgetary policies and their performance depend upon the amount of correlations between the stochastic parameters of the model can also be seen from the results of our next experiment. Here we assume all estimated parameters of the model to be stochastic but neglect their covariances, i.e., we only take into account the estimated own variances of the 36 parameters. This can be regarded as Version A of a fully stochastic optimization experiment; Versions B and C are identical to the fully stochastic optimum described before. Results are shown in Table 8. Again, optimal budgetary policies are dramatically different from both the deterministic ones and the tilly stochastic ones with pairameter covariances taken into account. They are even more restrictive than those in Version A of the experiment with stochastic fiscal policy multipliers. High federal budget tax revenues and low federal budget expenditures combine to create a budget surplus for all but one year. A severe recession is created in 1995, with real GDP falling by more than 7% and labor market excess supply jumping up to more than 9%. Intertemporal trade-offs are exploited to some extent, because UNt comes down to 1.6% until 2000, inflation remains low, and the current account has a big surplus in every year, but the overall performance is again deteriorated, with an optimum value of the objective fimction of 5,396,446.9. We have to conclude that neglecting parameter covariances in stochastic optimization problems results in optimal policies which are heavily biased as compared to the “true” (approximate) fully stochastic optimum with parameter covariances taken into account

year NEX, BIN, PV%t UN, YRO/ot LBRO/q

1995 611.669 986.183 1.267 9.296 -7.135 1.615 1996 705.921 959.128 1.954 7.811 3.437 3.918 1997 783.906 962.178 1.951 6.65 1 3.606 4.427 1998 831.696 969.944 2.156 5.064 5.414 4.516 1999 898.778 960.3 12 2.400 3.411 6.560 3.555

L 2000 1011.186 942.847 2.744 1.607 7.926 1.730

DEFO/ot

-17.637 -11.301

-7.5 16 -5.396 -2.191 2.181

Table 8. Optimal values of instruments and “main” objectives, fully stochastic optimum, Version A


6. CONCLUDING REMARKS

In this paper, we have used a medium-size macroeconometric model of the Austrian economy to calculate optimal budgetary policies for the years 1995 to 2000 for a given objective function. In particular, we have investigated the effects on optimal budgetary policies of making some parameters uncertain that are important for the transmission of policy effects. The results show that optimal budgetary policies for the particular model employed are very sensitive with respect to stochastics affecting fiscal policy multipliers and especially to correlations of these parameters with other ones. On the other hand, if the full covariance matrix of the parameters is taken into account, optimal policies are similar to those obtained in the deterministic case. We interpret this result as showing the reliability of optimal policy recommendations when the full covariance matrix is either taken into account or totally neglected, i.e., deterministic optimal policies can be relied upon even in a world of uncertainty. On the other hand, neglecting correlations between model parameters leads to policy recommendations which ought not to be presented to policy-makers as they are seriously flawed. This result is important for practical policy advisers, because often econometric models are estimated by OLS, hence no estimate for the entire parameter covariance matrix is available. In this case, results based on deterministic optimization are to be preferred to those based on rudimentary stochastics.

ACKNOWLEDGI-MENT

Financial support from the “Jubilaeumsfonds der Oesterreichischen Nationalbank” (project no. 5 126) is gratefully acknowledged. Karbuz acknowledges support from the Institute for Advanced Studies, Vienna.

REFERENCES

1 NECK R. & KARBUZ S., Optimal budgetary and monetary pohcies under uncertainty: A stochastic control approach, Annals oJOpera)iow Resecrrclr 58, 379 - 402 (1995)

2. MATULKA J. L NECK R., OPTCON. An algorithm for the optlmal control of nonlmear stochastic models, A~?rtnls o/ Operatiot~s Resemdt 37, 375 - 401 (1992)

optimal control of fiscal policies for austria: applications of a stochastic control algorithm

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