Monetary policy and capital accumulation processes: how did the FED react to the transition phases?

ABSTRACT

The present paper is related to the recent discussion about the efficiency of the Reserve Federal Bank on investment decisions. Our aim is not to propose an optimal policy rule but rather to appreciate and to understand the link between the monetary interventions of the FED and capita/accumulation processes. Therefore, we propose to adopt a Smooth Transition Regression Model to take account of structural changes in capital stock for the sole equipment and computer goods. We analysed two periods (1967-1981 and 1982-1997) that correspond to the policy changes of the Federal Reserve Bank occurring in the early eighties. We conclude to a strong heterogeneity of the exogenous variables between the periods, and above all, to a modification of the effects of monetary policy during the transition phases. In fact, the different results over the two periods could be explained by the instability of the relation linking the decisions of the FED to investment expenditures.

1. INTRODUCTION

The present paper is related to the recent discussion about the role of the Reserve Federal Bank (FED) on investment decisions. More particularly, some authors argue that monetary interventions produce few effects on capital accumulation dynamics for the sole equipment and computer goods. Nevertheless, this result requires an econometric investigation that takes account of structural changes, and precisely, the important increase of equipment and computer investment expenditures during the 90's. Therefore, our goal in this paper is not to consider an optimal definition of the FED's monetary rule, but rather, to understand and to appreciate the interactions between monetary interventions and capital accumulation process. We then consider capital stock accumulation in USA for the sole equipment and computer goods, over two periods, (1967-1981 and 1982-1997) that correspond to the policy changes of the FED, occurring in the early eighties. Formally, we use Smooth Transition Regression models (STR models) to appreciate the relation between the monetary intervention and the investment dynamics

2. LINEAR ECONOMETRIC MODELS FOR INVESTMENT DYNAMICS

The basic model we use to study the capital stock adjustments is the one introduced by Tevlin and Whelan (2000). This model considers the adjustment costs of the capital stock between two periods, and the deviations separating the effective stock from the optimal one.

Formally, the estimated equation takes the following form:

[K.sub.t] = [alpha] + [[lambda].sup.*] [K.sub.t-1] + [N.summation over i=0] [[beta].sub.i] [Y.sub.t-1] + [N.summation over i=0] [[gamma].sub.i] + [R.sub.t-1] + [u.sub.t] (2) with [K.sub.t]: the capital stock; [Y.sub.t]: GDP; [R.sub.t]: the capital cost

This equation is estimated over two periods, 1967-1981 and 1982-1997, that take account the policy changes of the FED, occurring in the early 80's. The cost of capital is calculated from the Hall-Jorgenson formula. The data we use for capital stock, price indexes and GDP are taken from NIPA tables. The short-term real interest rate is then calculated as the difference between the short-term nominal interest rate and the expected inflation (i.e. measured by the average inflation rate over the last three years). In accordance with the Neoclassical Theory, we obtain an inverse relation between the variations of cost of capital and the variation of equipment and computer expenditures (See Tables 1 and 2), even if this coefficient is quite small. The coefficient of output is significantly positive, whatever the periods.

The estimation of this linear model points out a small but significantly elasticity of the stock of capital with respect to the output, whatever the period. On the other hand, the cost of capital divides these two periods. Precisely, the cost of capital appears to be significant only over the period 1967-1981. It is surprising, especially if we consider the fiscal policy changes. In fact, from 1986 (US Tax Reform), the Marginal corporate income tax rate have been decreased by 10%. This fiscal policy is favourable to an increase of investment expenditures. However, and for the same period, the Investment Tax Credit have been stopped. Considering the compensatory evolution of the real components of the cost of capital (i.e. ITC and MCITR), we think that the evolution of the cost of capital depends mainly on the evolution of the real interest rate. The following graph (Graph 1) seems to confirm this hypothesis.

Contrary to S. Tevlin and K. Whelan (2000), we take the short-term real interest rate as the relevant variable. In fact, the following << modified >> model differs from the model developed by S. Tevlin and K. Whelan (2000) for two main reasons: first, we choose the short-term real interest rate as the relevant monetary variable instead of cost of capital calculated by using Hall-Jorgenson Formula. Moreover, we introduce a liquidity constraint through the Cash Flow/Capital Stock ratio. We think that liquidity constraint influences the self-financing of the firms. According to J. Hicks (1973), self-financing capacities contribute to capital accumulation process. The estimated equation of this modified model then takes the following form:

[DELTA][K.sub.t] = c[(1).sup.*] [DELTA][K.sub.t-1] + c[(2).sup.*] [DELTA][Y.sub.t] + c[(3).sup.*] [DELTA][r.sub.t] + c[(4).sup.*] [DELTA]CF. (3) With: [DELTA][K.sub.t]: Variations of capital stock; [DELTA][Y.sub.t]: Variations of output; [DELTA][r.sub.t]: Variations of real interest rate and [DELTA]CF: Variations of liquidity constraints.

At this stage, it is not appropriate to present the result of the estimation of those models. Whatever the model, the Cusum Square tests reveal instability of the coefficients, in other words, the estimated equations are affected by structural breaks. Within this framework, a potential structural break of the estimated equation occurs when the evolution of the coefficients exceeds the interval of confidence (called the << stability corridor >>). A simple look at the graphs is then sufficient to conclude to instability of the coefficients (See Graph 2-5).

Therefore, this Squares Cusum Tests reveal instability of the parameters, whatever the periods or the models. In other words, these tests reject the null hypothesis of stability of the coefficients. The breaks we observe within the corridor stability have justified the development of a non-linear model. We implement a Smooth Transition Regression Model (STR model) to introduce the changes of regimes of the capital accumulation process. Effectively, STR models introduce transition functions that take account of structural changes.

3. TRANSITION PHASES OF CAPITAL ACCUMULATION PROCESS AND MONETARY POLICY

According to T. Terasvirta (1994) and D. van Djik and al (2000), STR models present the following general form:

[y.sub.t] = [A + [B.sup.*]G([s.sub.t] ; [gamma] ; c)] + [[epsilon].sub.t]. Where, [y.sub.t]: the dependant (endogenous) variable; A et B : the parameters vectors ; G ([s.sub.t] ; [gamma] ; c) : a continuous function taking its values between 0 and 1 ; [gamma] : the speed of changes of the constitutive values of the transition function (i.e. if [gamma] is high then transition is fast from one regime to another) ; [[epsilon].sub.t] : a white noise ; c: the regimes' change threshold ; [s.sub.t]: the lagged endogenous variables, or the exogenous variable, or else a function of lagged endogenous variables. To select a relevant STR model, we applied the methodology introduced by T. Terasvirta (1994) that is a series of embedded (overlapping) tests. From this methodology, we conclude that using an STR model is a relevant strategy to describe the dynamic process of capital accumulation, and more particularly LSTR1 models (equation (5)).

The generic model we implement is thus as follows:

[DELTA][k.sub.t] = c[(1).sup.*] [DELTA][k.sub.t-1] + c[(2).sup.*] [DELTA][Y.sub.t] + c[(3).sup.*] [DELTA][R.sub.t] + c[(4).sup.*] [DELTA]CF

{Linear Component}

+

[(c[(5).sup.*] [DELTA][Y.sub.t] + c[(6).sup.*] [DELTA][R.sub.t] + c[(7).sup.*] [DELTA]CF).sup.*](1 + exp{(-c[(8).sup.*][([k.sub.t-1] - c(9))}).sup.-1]

{Non linear Component} (8)

with, c(1) to c(4) the coefficients of the linear model; c(5) to c(7) the possible parameters of the function ; c(8) = [gamma], the speed change of the constitutive values of the transition function; c(9) = c, the regimes' change threshold ; the other variables are identical to those of the basic model.

To our opinion, it is important to notice that the transition functions reflect essentially the changes of the speed of the capital accumulation process. Indeed, the linear restriction tests do not conclude to the rejection of the non-null hypothesis of the constant parameter of the transition function. Comparing the transition functions does not offer any insight about changes of growth regimes, but only about dynamic reactions of the accumulation processes. We thus have the following relations:

* The speed of adjustment increases when the transition function tends to 1.

* Conversely, the speed of adjustment decreases when the transition function tends to 0.

This transition functions confirm the radical change of the shape of the equipment and software accumulation process, in the early 80's. More precisely, the first period (1967-1981) exhibits a deceleration of the transition function, while the second period (1982-1997) is characterized by a continuous acceleration of the accumulation process. Moreover, and as a general feature, we notice a strong heterogeneity of the capital accumulation processes over the two periods. We observe that both the nature and the importance of the exogenous variables differ between 1967-1981 and 1982-1997. Even if the variations of GDP are always significant over the two periods, we should note that both interest rate and liquidity constraint are significant on the linear component of the model (i.e. on the long-term accumulation process) only since 1982. Thus, the different impacts of the interest rate and the liquidity constraint confirm the Squares Cusum Tests about the variability of those parameters. On the non-linear component, we should note that USA exhibits different speeds of adjustment of the capital stock. In fact, the variables that are involved in the transition functions are not substitutes and are calibrated differently. Precisely, the real interest rate is directly implicated in the deceleration of the speed of equipment and computer expenditures over the period 1967-1981. On the other hand, and over the period 1982-1997, the real interest rate is not a significant variable, while the speed of capital accumulation increases. Those contrasted results over the two periods could be explained by the evolution of the stability of the relation linking the decisions of the Federal Reserve Bank to investment expenditures.

e. Instability of the relation (1967-81): the variations of the interest rate are directly involved in the observed changes of the speed of capital accumulation. This means implicitly that the monetary interventions have generated some distortions over the reactions of investment expenditures. Such distortions are captured by a strong variability of the transition function. One can note that the observed instability jointly came with a deceleration of the speed of capital accumulation dynamics over the 1967-1981 period. Liquidity constraints are also significant over the same period. In other words, monetary policy could generate important and lasting effects during the transition phases by affecting the speed of adjustment of capital stock.

f. Stability of the relation (1982-97): the variations of the interest rate become neutral over the observed changes of the speed of capital accumulation. This means implicitly that monetary interventions are no more a primary cause for the distortions of the transition function. One can note that the period of stability correspond to an acceleration of the speed of capital accumulation dynamics over 1982-1997 period. Within this period, the observed changes of the speed of capital accumulation are thus linked to the evolution of non-monetary variables (variations of the amounts of sales) and to exogenous shocks. The monetary policy produces a priori a neutral effect on the capital adjustment processes. This neutrality could be interpreted as a good management of the liquidity constraints of firms. The Neo-Austrian analysis (Hicks, 1973; Amendola-Gaffard, 1998) considers in fact, that during the transition phases, firms are affected by an increase of those liquidity constraints, because of the temporal dimension of production process and the irreversibility of investment. According to this theory, it is probable that the FED has fitted its interventions to the implementation of the new capital processes over 1982-1997 period.

4. CONCLUSION

A theme of this paper is that monetary policy is a relevant component of the capital accumulation processes. We explored the monetary impact both on the long-term process and on the transition phases. In fact, the STR models we used reveal that the influence of the monetary policy on the investment decisions is very different since the early eighties. Indeed, during the period 1967-1981, the monetary policy was directly implicated in the observed deceleration of the speed of the capital accumulation. We assume that the variations of short-term interest rate were not appropriate with the economic conditions, because they contributed to destabilize the reactions of economic decision-makers, by generating some distortions over the investment expenditures. Unlike, since 1982, the variations of the interest rate are correlated with a substantial increase of equipment and computer stock, and moreover, with an acceleration of the speed of the capital accumulation. Therefore, the STR models confirm the idea of change in the monetary regime of the FED, occurring in the early eighties. The stabilization of the reactions of firms, that is, the decrease of the variability of transition phases seems, to be a serious task for monetary policy. Furthermore, that research program will be making significant progress toward the development of a framework that will consider the appropriate monetary rule associated with the durability of investment decisions.

TABLE 1

Period 1967:04 - 1981:04   Coefficients   Student Error   t-Statistic

C(1)*[DELTA]
  ([K.sub.t-1])             0.9           0.05             34.75780
C(2)*[DELTA](Output)        0.3           0.1              5.415574
C(3)*[DELTA](Cost of
  Capital)                 -0.03          0.01             -11.67294

[R.sup.2]                   0.60          Akaike info criterion
Ajusted [R.sup.2]           0.58          Schwarz criterion
Durbin-Watson stat          2.03          Prob(F-statistic)

Period 1967:04 - 1981:04    Prob.

C(1)*[DELTA]
  ([K.sub.t-1])             0.00
C(2)*[DELTA](Output)        0.00
C(3)*[DELTA](Cost of
  Capital)                  0.04

[R.sup.2]                   -7.28
Ajusted [R.sup.2]           -7.15
Durbin-Watson stat          0.00

TABLE 2

Period 1982:01-1997:03      Coefficients   Student Error    t-Statistic

C(1)*[DELTA]([K.sub.t-1])   0.89           0.03             27.38741
C(2)*[DELTA](Output)        0.15           0.035257         4.448857
C(3)*[DELTA](Cost of
  Capital)                  -0.008         0.005            -0.790739

[R.sup.2]                   0.86           Akaike info
                                             criterion      -10.06
[R..sup.2] Ajuste           0.85           Schwarz
                                             criterion      -9.96
Durbin-Watson stat          1.90           Prob(F-statis-
                                             tic)           0.00

Period 1982:01 - 1997:03    Prob.

C(1)*[DELTA]([K.sub.t-1])   0.0000
C(2)*[DELTA](Output)        0.0000
C(3)*[DELTA](Cost of
  Capital)                  0.13

[R.sup.2]
[R..sup.2] Ajuste
Durbin-Watson stat

TABLE 3

Period 1967:04 - 1981:01     Coefficients   Student Error   t-Statistic

C(1)*[DELTA]([K.sub.t-1])    0.92           0.037           24.31475
C(2)*[DELTA](Output)         0.15           0.055           2.73
C(3)*[DELTA](Real
  Interest Rate)             0.002          0.004           0.47
C(4)*[DELTA](Cash-Flow)      0.014          0.013           1.09
C(5)*[DELTA](Cash-Flow)      0.325          0.047           6.85
C(6)*[DELTA](Real Interest
  Rate)                      -0.026         0.007           -3.66
C(7)                         1486.626       1456.205        1.02
C(8)*[DELTA]([K.sub.t-1])    0.023471       0.00078         29.89

[R.sup.2]                    0.84           Ajusted [R.sup.2]   0.82
Durbin-Watson stat           2.44           Prob(F-statistic)   0.00

Period 1967:04 - 1981:01     Prob.

C(1)*[DELTA]([K.sub.t-1])    0.0000
C(2)*[DELTA](Output)         0.0086
C(3)*[DELTA](Real            0.64
  Interest Rate)
C(4)*[DELTA](Cash-Flow)      0.28
C(5)*[DELTA](Cash-Flow)      0.00
C(6)*[DELTA](Real Interest   0.00
  Rate)
C(7)                         0.31
C(8)*[DELTA]([K.sub.t-1])    0.00

[R.sup.2]
Durbin-Watson stat

TABLE 4

1982:01 - 1997:03            Coefficients   Student Error   t-Statistic

C(1)*[DELTA]([K.sub.t-1])    0.88           0.034           25.55
C(2)*[DELTA](Output)         0.24           0.039           5.96
C(3)*[DELTA](Real
  Interest Rate)            -0.011          0.0057          -1.83
C(4)*[DELTA](Cash-Flow)      0.034          0.010           3.33
C(5)*[DELTA](Output)        -0.097          0.053           -1.82
C(6)                         3940.861       12419.46        0.317313
C(7)*[DELTA]([K.sub.t-1])    0.01           0.000528        18.65206

[R.sup.2]                    0.89           Ajusted [R.sup.2]   0.88
Durbin-Watson stat           1.93           Prob(F-statistic)   0.00

1982:01 - 1997:03             Prob.

C(1)*[DELTA]([K.sub.t-1])     0.00
C(2)*[DELTA](Output)          0.00
C(3)*[DELTA](Real Interest
  Rate)                       0.07
C(4)*[DELTA](Cash-Flow)       0.00
C(5)*[DELTA](Output)          0.07
C(6)                          0.75
C(7)*[DELTA]([K.sub.t-1])     0.00

[R.sup.2]
Durbin-Watson stat

REFERENCES

M. Amendola, J.L. Gaffard (1998): Out of Equilibrium, Oxford, Clarendon Press.

R. Clarida, J. Gali & M. Gertler (1998), "Monetary Policy Rules and Macroeconomic Stability: Evidence and some theory", in N.B.E.R. Working Paper [n.sup.o] 6442, March 1998.

J. Hicks (1973), Capital and Time, Oxford Clarendon Press.

T. Terasvirta (1994), "Specification, estimation and evaluation of smooth transition autoregressive models", in Journal of the American Statistical Association, 89, p. 208-18.

D. van Dijk, T. Terasvirta, & P.H. Franses (2000), "Smooth Transition AutoRegressive Models--A Survey of Recent Developments", Econometric Institute Research Report EI2000-23/A.

C.D. Romer & D.H. Romer (1989), "Does Monetary Policy Matter? A new test in the spirit of Friedman and Schwartz", N.B.E.R. Macroeconomics Annual 1989.

C.D. Romer (1999), "Changes in Business Cycles: Evidence and Explanations", in Journal of Economic Perspectives, 13, Spring, p. 23-44.

S. Tevlin & K. Whelan (2000), "Explaining the Investment Boom of the 1990s", Working Paper Series N.B.E.R., March 2000.

Author Profile

Dr. Frank Paolucci earned his Ph.D. at the University of Nice-Sophia Antipolis in 2003. Currently, he is professor at the IUT of Cannes.