The main interest—besides the purely theoretical one—in discussing Tullio’s paper¹ lies in the fact that it contains implicit and explicit policy recipes for the Italian economy. Therefore, the theoretical and empirical perplexities that the model gives rise to are well worth discussing.

Section I contains the discussion of theoretical aspects, while Section II discusses estimation results and simulations. Reference is made to equation numbers as they appear in Tullio’s paper, and his symbology is used throughout.

I. Discussion of the Theoretical Framework

The model purports to be a real and financial one, and the link between the real sector and the financial sector is provided by the consumption function, one argument of which is real wealth. The real sector, and within it the consumption function, is examined later. The financial sector is based on a general-equilibrium portfolio approach, but the specification of the behavioral functions is not always consistent with it. In fact, the scale variable is not included in all functions: in particular, it is not present in equation (2)—currency—or in equation (8)—the demand for capital stock, which is considered as part of private sector wealth. Furthermore, the demand for financial assets is assumed to be a function of only two interest rates instead of the whole structure.

In several cases it is not clear whether the function concerning a financial asset is a demand or a supply function. For example, in equation (2), ĉ is a quantity demanded whereas c is the existing quantity (supply); therefore, this equation implies that the quantity supplied (by the central bank) adjusts passively to the quantity demanded (by the public), which is a questionable assumption to say the least.

In general, one has the impression that the behavior of the financial sector operators (the banks and the public) is heavily conditioned by the international market and by monetary policy. Let us consider the balance constraint of the banking sector, equation (25). Of the variables on the right-hand side, FINBI is determined exogenously, TBD is determined by the choices of the public, and BB is determined by the portfolio constraint. In principle, BFB is also determined by the regulations of the Bank of Italy. Actually, the net foreign asset position of commercial banks is a variable that allows banks a certain freedom of action. But equation (6), which concerns BFB, seems questionable, since it does not make clear what kind of hypothesis it is meant to represent. In fact, it does not define BFB as completely determined by the Bank of Italy’s regulations; on the other hand, it does not represent the behavior of commercial banks, because in this case it should contain—corresponding to the specification of the other equations of the financial sector—a process of adjustment to a desired level of the actual value of the variable being considered (BFB).

Let us now consider the behavior of the nonbank private sector. Desired deposits are a function of—among other variables—the differential between the exogenous interest rate on deposits and the long-term interest rate (determined by monetary policy), which denotes a scant consideration of the play of demand for and supply of financial assets. Inflationary expectations also play a crucial role, but the equation for their determination—equation (14)—gives an excessive weight to international sources relative to internal sources, which are limited to cyclical factors.

Net foreign assets—equation (5)—are a function of the appropriate interest rates r_F and r_TIT (of which the former is exogenous and the latter is policy determined) and of expectations concerning the exchange rate that are proxied by the deviation of the actual exchange rate from its PPP. The role of the international scale variable, which coexists with the internal scale variable and is represented by a time trend, is crucial and leads to a patent error in the specification of the equation. Since β₁₄ (the elasticity with respect to the internal scale variable f) is constrained to one, $\hat{b}f$ is actually explained as a share of f, and rewriting equation (5’) as

it follows that this share increases, ceteris paribus, according to an exponential trend, which is clearly wrong, because a share cannot exceed one. Incidentally, this equation prevents the model from having a steady state and this—as is well known (Wymer (1976); Gandolfo (1981))—is a symptom of the internal inconsistency of this type of model. Finally, in the balance of payments identity—equation (23)—unilateral transfers are lacking.

Let us now turn to the real sector. First, note that the use of the consumer price index to deflate all current price variables to obtain “real” variables, although consistent with the central role played in the model by real wealth as an explanatory variable in the consumption decisions of households (discussed later), is less suitable where other variables are concerned. Perhaps a more general index, such as the gross national product or the gross domestic product (GDP) deflator, would have been a better choice.

Tullio suggests that the model retains the Keynesian feature that output is demand determined in the short run. Income is determined by identity (26). As the stock of inventories is not considered because of problems with the quality and availability of data, there is no room for the typical Keynesian role of inventories as an adjustment variable.

The role of the short-run behavior of output in the model remains obscure. This behavior is represented by the ratio between the actual and the (exponential) trend value of industrial value added, which is then introduced as an additional explanatory variable in several equations (inflation, (13); expected inflation, (14); imports of nonmanufactures, (12)) without a convincing theoretical explanation. This short-run feature of the model seems to be inconsistent with the consumption function—which is a key item, since the integration between the real and financial sectors hinges on it. Tullio states that this function, which depends on real wealth and the long-run real interest rate, follows Metzler’s (1951) contribution. Unfortunately, this appeal to authority is misplaced: as is well known, Metzler was investigating a model in which income is given at the full employment level, and he explicitly assumed that the amount of real saving out of a full employment income was a function of the interest rate and of the real value of wealth. In Tullio’s model the level of income is variable, so that it is surprising to see that it has been left out of the consumption function (whereas a cyclical term is included, as we said earlier, in other functions); it is all the more surprising if we note that in this way the entire short-run side of the model fails to feed back on the key function of the model, namely, consumption.

As regards the import function, a more satisfactory disaggregation would have been that between final and intermediate goods. In any case, the variable representing the need for imported manufactures should be industrial production rather than industrial value added.

The supply side is based on a Cobb-Douglas production function, which according to Tullio underlies the investment function—equation (8), the price determination—equation (13), and the demand for labor in industry—equation (16). These three equations must therefore be considered together, as it is obvious that they have to be based on the same production function. Although standard neoclassical theory allows one to derive equations (8’)² and (16’)³ easily from a Cobb-Douglas production function, it does not seem possible to perform such a derivation rigorously for equation (13’). Consequently, Tullio’s statement that his price equation is consistent with both the flexible mark-up theory and a Cobb-Douglas neoclassical framework is not correct, and only the mark-up theory can be applied. But, in this case, equation (13’) becomes inconsistent with the other two equations and in particular with equation (16’), at the basis of which lies the maximizing behavior of entrepreneurs in free competition. Further, L in equation (13’) represents labor employed, whereas L in equation (16) represents labor demanded: therefore, the two equations are consistent only if labor employed is always equal to labor demanded (instantaneous adjustment of the supply of labor).

Finally, although the wage-determination equation—equation (15)—is acceptable in itself, it is inconsistent with the other equations of the model, in particular, equation (16). In fact, if the demand for labor is based on the maximizing conditions in a competitive market, it is not correct to drop this hypothesis when passing to the wage-determination equation, which to be consistent should be based on some form of excess demand for labor. (This is the solution correctly adopted, for example, by Bergstrom and Wymer (1976) and Knight and Wymer (1978).)

II. Discussion of the Estimates

There are several sources of perplexities concerning the procedure of estimation and its results. First, consider the choice of excluding from the estimation the constant terms (namely, the γ’s) or at least of not reporting the results concerning them. It is true—as suggested by Wymer (1979)—that in the estimation of this type of model the constant terms can be left out when there are no across-equation constraints on them, but this exclusion cannot be accepted when it implies an incorrect specification of the equations in which the constant terms happen to play a crucial role from the point of view of economic theory. In particular, this is true for equation (10)—export prices—where the importance of γ₁₀ (the ratio between the desired value of p_xm and p_xmw) is obvious; for equation (11)—imports of manufactures—where, as γ₂₆and γ₂₇ are constrained to one and zero, respectively, γ₁₁ is the only parameter left in the functional form of î_m; for equation (16)—demand for labor in industry—because, as both β₃₉ and β₄₀ are constrained to one, γ₁₆ is the only parameter left in the functional form of $\hat{L};$ for equation (17)—the long-term interest rate—where γ₁₇ is the only parameter relating ${\hat{r}}_{TIT}$ to its argument.

Second, although the choice of the parameters to be constrained is often dictated by practical matters (convergency of the iterative procedure, etc.), this choice must be consistent with theory. It is therefore surprising that in the demand functions for financial assets only two of the elasticities with respect to the internal scale variable (β₁ and (β₁₄) are constrained to one, whereas other such elasticities (for example, β₇ and (β₁₀) are not. This disparity has no theoretical basis. Furthermore, either homogeneity of degree one with respect to real wealth (the scale variable) holds for all the functions considered or, if not, some other across-equation constraint on the elasticities must be introduced, given definition (24).

Third, the values of the estimated adjustment velocities of some variables seem too low, and, consequently, the corresponding mean time lags seem too high. Postal savings deposits show a mean time lag (1/α₃) of 4.03 years, net foreign assets (1/α₅) of 3.09 years, and the long-term interest rate (1/α₁₇) of 3.57 years; particularly surprising is the mean time lag of the general price level (1/α₁₃ = 3.21 years). The discovery that prices (and some financial variables) have a slower adjustment velocity than quantities does not seem consistent with the behavior of the Italian economy in the period considered.

Fourth, the way in which the second version of the model (concerning the regime of managed flexibility) is estimated is open to serious objections. Owing to the relatively small number of observations, Tullio assumes that most parameters are the same as in the first version, so that only a few parameters have to be estimated. Apart from objections of an economic nature, the high number of constrained parameters reduces the stochastic nature of the model almost to nil, as is revealed by the fact that the six parameters that are being “estimated” show almost zero standard errors. When the order of magnitude of the ratio of the parameter to the asymptotic standard error is several thousands (ranging from 3,088.71 to 7,379.80), one has reason to doubt whether the procedure or the model is appropriate.

Now let us add a few comments on specific equations. The greatest perplexities concern the results obtained in the estimation of the inflation equation (13). The “contribution” of imported inflation (1 - β₃₄ = 0.737) seems excessive with respect to that of internal sources; and the way in which the cyclical component is allowed for is not satisfactory. In fact, if this component should account for the pressure of demand, the variable chosen $(y_{IND}/{y^{*}}_{IND}{e}^{\lambda /t})$ seems the least suitable, seeing that the variable being “explained” is the consumer price index. On the other hand, the cyclical element in prices is introduced into the equation via a purely statistical effect given by the cyclicity present in y_IND, which seems to be confirmed by the high significance of β₃₃.

As regards inflationary expectations—equation (14), we first note that the constraint α₁₄ = 1.0 is arbitrary; considering the slow adjustment speed of prices, which corresponds to a mean time lag of 3.21 years, an imposed mean time lag of expectations of only one quarter seems all the more inexplicable. Second, the choice of the series to represent II is questionable. This series concerns the inflationary expectations of industrial operators and of experts, whereas the function concerns the expectations of consumers, which are presumably different.

Finally, let us consider the simulations. The results of these seem to confirm the impression that the model is not very representative of the Italian situation. In particular, the negative effect of a once-and-for-all devaluation on GDP, which is of course consistent with the logic of the model (a devaluation increases the price level, which reduces real wealth and therefore consumption), does not seem to correspond to the behavior of the Italian economy in the 1970s. There are no direct effects of the devaluation on industrial production.

Furthermore, it seems unrealistic that a once-and-for-all devaluation still has appreciable effects on prices, GDP, and international reserves after ten years. This result seems to be due to the exceptionally low value of the adjustment speed in the price equation, which—as stated earlier—does not seem to be consistent with the actual behavior of the Italian economy.

III. Conclusion

As treated at length elsewhere (Gandolfo (1981)), the authors firmly believe that small continuous-time disequilibrium models are in principle well suited to deal with medium-term economic and policy problems. For this to be true, however, particular care should be put into the theoretical specification and analysis of the model. Tullio’s model, which belongs to this category of models and for this reason is a step in the right direction, unfortunately is open to both theoretical and empirical criticism that casts serious doubts on the model itself and leads one to consider the policy prescriptions drawn from it to be potentially misleading.