ONE RESPONSE TO FRUSTRATED ECONOMIC POLICY:

A Paper Prepared for

A Staff Seminar

National Bureau of Economic Research

New York, New York

November 16, 1973

Glenn E. Burress

Visiting Professor of Economics University of Texas of the Permian Basin

Odessa, Texas 79762

*I am indebted to Hyman P. Minsky for encouragement and helpful criticism. Thanks are also due Milton Friedman, Laurence H. Meyer, Paul Hodges, and Sam Keeley. None has seen this entire draft.

Supporting Documents:

Table 1

Selected Data on Origins of Annual Changes in Personal Saving
and Their Consistency With Theory, 1953-72

Table 2

Estimates of Consumption Function:
Houthakker-Taylor Model(1) with Annual Data(2)

Table 3

Estimates of Selected Values of the
Installment Debt Variables 1953-72

Table 4

Errors in Estimating Changes in Saving via Installment Debt with Equation (3)* with Particular Reference to Periods of Significant Short-run Change, 1953-72

Appendix A

Forecasting Record with the Installment Debt Model

Appendix B

Implications for Further Research

Figure 1

Chart: Evaluations of the Habit Hypothesis

Figure 2

Annual Changes in Selected Installment Debt Components of Personal Saving

References

Footnotes

Frustration of economists with the consumption function as a tool for planning policy, both private and public, is widespread. But that frustration is so recent that examples must be cited from comments of scholars in the press rather than their publications in literature. A recent comment in Business Week by James Pierce, Division of Research and Statistics at the Federal Reserve Board of Governors, not only underscores the problem to which this paper is addressed, but also at least hints at a solution developed here. With respect to efforts of researchers to explain and estimate the impact of Federal Reserve policy, Pierce said, "The world is much more complicated than the world of theory—the theories of monetarists and the Keynesians ... There are fundamental changes going on in the economy that we don’t yet understand. The people who were born in the baby boom of World War II are causing shifts in the demand for things such as washing machines, TV sets, automobiles, and housing. We don’t know enough yet about their habits to adjust the consumption function in our models...At times our models make me very uneasy." (underlining added)

The problems with consumption functions and econometric models identified by Pierce can be illustrated with data that will be a focal point of this paper. Recent data, as represented by regression coefficients in econometric models, suggest little reason to quarrel with traditional theory. The regression coefficients suggest that during recessions and recoveries, personal saving (saving) not only rises and falls with personal disposable income (income), but that saving rises and falls faster than income, i.e., that the short-run marginal propensity to consume (SR-MPC) is less than the long-run marginal propensity to consume (LR-MPC). But when the same data used to compute the regression coefficients are examined directly, they tell a dramatically different story. These data show that saving fell, rather than rose in calendar years 1968, 1969 and 1972 -- as well as in early 1973. And saving rose as income fell in the 1970 recession.

One thesis of this paper is that a prerequisite to explaining what is viewed as a recent pattern, is recognition that it is not a new pattern at all. During both the 1955 and 1959 recoveries, saving fell rather than rose when income rose rapidly. And the saving-income ratio fell rather than rose in the 1962 recovery. Moreover during both the 1958 and 1961 recessions, saving rose rather than fell as income fell, and the saving-income ratio rose rather than fell in the 1967 mini-recession.¹ These data are shown in Table 1.

If the pattern of inconsistencies has persisted for two decades, one must ask why the inconsistencies have gone unnoticed. Why was traditional theory still used for unsuccessful forecasts of saving in both the 1972 and 1973 Economic Reports of the President" after earlier failures. The same question should be asked of the 1973 forecast of the Research Seminar in Quantitative Economy at the University of Michigan. That is, in November 1972 the RSQE forecast that disposable income would rise at about the same rate as in 1955, 1959 and 1968.² In each of those years the absolute level of saving fell. Why, one must ask, did the Michigan econometric model, fitted to these same past data, fail to pick up the past relationships and instead produce a forecast that the saving ratio would increase by more than one-third and the level of saving by more than l5-billion in the first half of 1973?

It is the thesis here that continued use of traditional theory so long after it ceased to be consistent with data can be explained by an unwitting conspiracy between an error in traditional theory of the consumption function and an error in standard econometric interpretations. The alternative offered here rejects both traditional theory and econometrics. The alternative focuses on adjustments associated with the role of consumer durables, as Pierce suggests it must. But it appears that Pierce errs in suggesting that the need for these adjustments is a product of the recent entry into the marketplace by the new breed of consumers born of the postwar baby boom. Rather the need for modifying consumption function theory dates from the early 1950s. It was required at that time by a new combination of (1) mild fluctuations, (2) Moderate growth of durables and (3) rapid growth of consumer installment debt used to finance durables.

II.

It is well-known that data for the 1930s and 1940s when fluctuations were severe are consistent with traditional theory. But not only for the last two decades, when fluctuations were mild, are the data inconsistent with traditional theory. On the contrary, data for the 1920s, when fluctuations were also mild, likewise appear inconsistent with consumption functions in both textbooks and sophisticated econometric models. It is suggested here that if these data are to be explained, theory must allow for a distinct difference in the consumer’s reaction to short-run changes in income, depending on whether fluctuations are mild or severe. Traditional theory was a response to data for the 1930s and 1940s when fluctuations were severe. It is suggested that Keynes’ 1936 "fundamental psychological law" [p.96] and Duesenberry’s 1949 "fundamental psychological postulate" [p.84] can still be expected to explain data when fluctuations are severe. The new model offered here is a response to more recent data and can be expected to explain data when fluctuations are mild. This model is not a striking departure from the old, although to many this appears, at first, to be the case. Some signs are reversed. Values of some parameters are significantly different. But the critical variables in the new model can be traced directly to variables implicit in the traditional model. There is a link between the old and the new.

The following sections review traditional theory and methodology and develop an alternative, attempting throughout to bridge the old and the new. In Appendix A the new approach is shown to provide some reconciliation of the recent debate between monetarists and fiscalists mentioned by Pierce. This is brought out in the context of a review of successful forecasts based on the new approach, made for precisely those years when forecasts based on traditional theory most seriously led policy astray. Implications for further research appear in Appendix B.

The traditional approach to explaining measured SR-MPCs that exceed the LR-MPC is, of course, to look to non-income or perhaps even non-economic determinants of spending. This approach follows, of course, from the a priori assumption that the SR-MPC is less than the LR-MPC.

The hypothesis one cites from the literature to explain why the SR-MPC is less than the LR-MPC depends on whether the dependent variable in the consumption function is spending or the flow of utilities. If spending is the dependent variable, the habit hypothesis, first proposed explicitly by Keynes but overlooked, and attributed to Duesenberry and Modigliani [Burress, December, 1972], is the most widely accepted explanation. If the flow of utilities is the dependent variable, the life cycle and permanent income hypotheses, proposed by Modigliani and Brumberg and Friedman, are widely accepted explanations. Many view the latter hypotheses as superior to the habit hypothesis when, in fact, they are not alternatives to the habit hypothesis because their dependent variable is not spending, but the flow of utilities. The life cycle and permanent income hypotheses can be viewed as alternatives only if they are supplemented with specification of the relationship between the flow of utilities (from durables) and spending (on durables). Problems in the usual implicit specification are discussed in Appendix B.

The most recent careful statement of the Keynes-Duesenberry-Modigliani hypothesis is the 1970 work of Houthakker and Taylor (HT). It is reasoned that if spending is habit-forming, outlays cannot be cut as fast as income during a recession as consumers defend the habitual standard of living established in the past. Therefore the saving-income ratio falls in a recession. Then in a recovery, because spending is habit forming, outlays cannot rise as fast as income and the saving-income ratio therefore rises. In what follows, this traditional formulation will be rejected in favor of the assumption that during recessions and recoveries one should assume spending is postponable or not habit-forming.

If spending can be postponed, one might expect consumers to react to falling income in a recession by postponing some outlays. In that case, it is plausible that spending might fall faster than income—especially if the reduction in income is as modest as in post-war recessions. As a result, the saving-income ratio will rise as income falls. Then in the recovery, outlays that were postponed in the recession are accelerated. In that case, it is plausible that spending might rise faster than income and the saving-income ratio will fall as income rises. As already noted, data for the 1930s and 1940s are consistent with the habit hypothesis, but data for the last two decades in Table 1 are not. On the other hand, data for the last two decades are consistent with the notion that spending is postponable or not habit-forming, but data for the 1930s and 1940s are not.

Using the model developed by HT, a test of the hypothesis that there was a shift in the relative importance of habit- and non-habit-forming categories since the 1930s and 1940s will be offered shortly. But before summarizing the HT model, a different approach will be outlined. If one uses estimates of rates of depreciation of consumer durables outlined in Harberger, et. al., it seems clear that during most mild recessions (especially if consumer durable demand has been rising rapidly), durable demand falls, but remains above replacement level. This means the stock of durables rises in most recessions. That the stock of durables rises in a recession is important because it suggests the flow of utilities from the durable stock rises as demand and income fall. This, in turn, suggests that it is inappropriate to assume consumers are under any pressure to maintain spending in order to defend the habitual level of consumption of durables attained in the past because the current level of consumption exceeds the past level.

During most mild recessions, real per capita spending on services and non-durables also rises. This suggests then that if one may use the real per capita flow of utilities from durables plus real per capita spending on non-durables and services as a proxy for the standard living, the standard of living rises in mild recessions as spending falls. Needless to say, this casts serious doubt on a keystone of the habit hypothesis, namely, the notion that defense of the past living standard will induce saving to fall faster than income in a recession. Yet this notion has remained at the core of reasoning of work extending from Keynes in 1936, Duesenberry and Modigliani in the 1940s, Houthakker and Taylor in 1966 and 1970, and Eckstein and Green in 1972.

Perhaps there follows from this a compelling need to treat consumer durables separately. Some comments on the logic of this position appear in footnote ³. A major reason for focusing on the aggregate function is to provide a bridge between the old and the new. But, as explained in the footnote, the focus of the alternative approach on changes in personal saving has much in common with both the aggregate and disaggregate approaches.

The HT model provides a sensitive test of whether a given category of spending or aggregate spending is habit-forming or postponable. Hence for a first approximation, the HT model will be used to test the hypothesis that there has been a shift in the relative importance of habit- and non-habit-forming categories over the last 40 years.

The notion that current spending, c(t), depends on current income, y(t), and a stock or state variable, s(t) -- the habit hypothesis—translates into estimating equations by HT as follows:

c(t) = a + bs(t) + gy(t)

where b is the stock coefficient and g is the marginal propensity to consume. The implication of the sign of the stock coefficient for various components of aggregate spending as well as for the aggregate is important. Where the stock coefficient is positive, that category of spending can be considered habit-forming and the SR-MPC is less than the LR-MPC. In such cases, high levels of past expenditures, cet. par., will induce higher current spending. Where the stock coefficient is negative, that category of spending can be considered non-habit forming and the SR-MPC exceeds the LR-MPC. In such cases, high levels of past expenditures will, cet. par., depress current spending. For this paper it is obvious that the sign of the stock coefficient when the model is fitted to aggregate data is of even more interest than the notion that some categories of total spending are habit-forming and some are postponable. If the stock coefficient for the aggregate is positive, the result is consistent with the habit persistence hypothesis. If the stock coefficient for the aggregate is negative, serious questions about the habit persistence hypothesis are raised.

The basic equation of the model given above is expressed in continuous time and treats all equations as holding exactly. HT then translate into discrete time and derive the corresponding equation for estimation which, aside from measurement errors, takes the form:

They show that when this equation is fit to data, the stock coefficient, b, the SR-MPC, and the LR-MPC are computed as follows

It should be emphasized that the SR-MPC is not A₂, but is provided by the above computation. So computed, the value of the SR.MPC should be the same with both quarterly and annual data. However, as HT point out, the computed values of the SR-MPC from quarterly data are significantly lower than from annual data and they are unable to explain why this is true.

Using this model, HT report values of these variables for both 1929-64 (0mitting 1942-46) and 1947-64 with annual data for total spending. As is evident in the first two lines of Table 2, data for these two periods yield positive stock coefficients and SR-MPCs that are less than LR-MPCs. This appears to confirm traditional theory. Indeed HT indicate this is what the model "was designed to represent" (p.282). The values of these same variables were computed for 19147-72, as well as for 1928-48. Results are reported in lines 3 and 4 of Table 2 and these too are consistent with the HT thesis and inconsistent with the notion proposed in this paper, namely, that there has been a shift in relative importance of habit- and non-habit-forming categories. These data appear, then, to raise serious doubts regarding the main thrust of this paper.

But surely this result must be questioned. That is, Commerce data since the mid-fifties in Table 1 used by HT suggest the saving-income ratio rose in recessions and fell in recoveries, a result that requires the measured SR-MPC to be systematically greater than the LR-MPC. But the HT econometric model, which appears to fit well, suggests that for the 1947-72 period the saving ratio followed precisely the opposite pattern, a pattern that requires the measured SR-MPC to be less than the LR-MPC. That is, the standard econometric approach to these data provides a computed result which appears to be inconsistent with much if not most of the data used to make the computations. Moreover, the discrepancy is not evident in the error term. The methodological issues raised by this result are explored by this author elsewhere (Burress, Sept. 1972). But even more serious questions can be raised in a more direct manner using data reported in Table 2. Annual data indicate that for most postwar periods, equal to or greater than the 17 years (1947-64) reported by HT, this same regression model, "designed to represent" the habit hypothesis, produces negative stock coefficients and values of the SR-MPC that exceed the LR-MPC. Indeed there are 45 possible postwar periods equal to or greater in length than the 17 years reported by HT. Results are inconsistent with the habit hypothesis for 25 of these 45 cases. The data for all 25 periods are also in Table 2. Partial results of computations for 187 postwar periods computed are reported in Figure 1. ^{(See footnote 4)}

This report, suggesting the SR-MPC ordinarily exceeds the LR-MPC or that the stock coefficient is negative, is consistent with the data on the saving-income ratio and measured SR-MPC in recessions and recoveries since the mid-fifties. But if one focuses on the annual data, it appears that, although the measured annual MPC has exceeded the LR-MPC in half the last 18 years, it is also true that it has been less than the LR-MPC half the time (Table 1.) That is, for private planning and public policy, it appears that the assumption that the SR-MPC exceeds the LR-MPC might have generated as many problems as were generated by the assumption that the SR-MPC is less than the LR-MPC. Before pursuing a model that might enable one to predict when the SR-MPC is greater than and less than the LR-MPC, it is important, especially in terms of the problem of testing the alternative model, to comment on some econometric problems which emerge from a study of Table 2 and Figure 1. One problem is illustrated by conflicting reports for many periods, such as 1955-64. For example, if one seeks clues to spending-income relationship for the 1955-64 decade from the HT report for 1947-64, it would appear that for 1955-64 one should assume the SR-MPC is less than the LR-MPC. In terms of the saving-income relationship, it appears that increased income induced increased saving. On the usual assumptions regarding statistical significance, it would follow that one might disregard periods in which saving and income moved in opposite directions as random errors, unlikely to be repeated, and not worthy of serious study.

But it so happens that this line of reasoning leads to precisely the opposite conclusion from an interpretation of the same regression model fit to 1955-72. Note that 1955-72 is equal in length to the 1947-64 period reported by HT. It differs in that it starts, rather than ends, with the ten years in question, 1955-64. But the 1955-72 data suggest that , for 1955-64, one should assume increased income induced reduced saving. Again on the usual assumptions, it would follow that one might disregard contrary data within the period as random errors, unlikely to be repeated, and not worthy of investigation.

This raises issues extending beyond the standard econometric approach to short-run behavior in the consumer sector. As for the consumer sector, it is suggested that the standard linear econometric approach to the consumption function is inappropriate; that it asks the wrong questions of non-linear relationships. It is suggested that the appropriate question is not whether one should assume the SR-MPC is greater than or less than the LR-MPC for some period, such as 1955-64. Nor is the question whether one should assume total spending postponable or habit-forming over such periods. Rather a more appropriate question or approach to postwar data is why does the SR-MPC tend to be inflated in recessions and recoveries and why does the SR-MPC tend to be lower in other years?

More generally, one might ask the following three questions. First, why is the SR-MPC inflated when the rate of change of disposable income is inflated (postwar recoveries) or moderately negative (postwar recessions)? Second, why does the SR-MPC remain reasonably near the LR-MPC when the rate of change in disposable income is near its trend? Finally, why does the SR-MPC assume values suggested by traditional theory when fluctuations are severe? The proposed answer to the first question is that non-habit-forming categories dominate changes in total spending in recessions and recoveries. The proposed answer to the second question is that in the absence of significant short-run deviations of the rate of change in income from its trend, there is little reason to assume short-run deviations in spending from its trend. This implies a more narrow definition of the short-run than is customary, but one that is implicit in early equations of Duesenberry and Modigliani.⁵ The proposed answer to the third question is that when fluctuations are severe, habit-forming categories loom so large relative to the total spending that they dominate changes in the total.

Perhaps an even more important question is why these questions are not suggested by the standard econometric approach to the data. The answer is simple. It is that for defining and computing the MPC, the chronological order in which data are generated is critical. But for computing the regression coefficients, the chronological order in which data are generated is not even relevant. Another way to approximate the problem is that the regression coefficient essentially averages past relationships, but what is relevant for the short-run can be viewed as the marginal relationship. Strictly speaking, this is true only when the intercept is suppressed—as it often is in consumption function work.. But this leads one to expect the standard economic approach to be successful only when the marginal value happens to be near the average value.

If this is true, one may ask why the slope of the original Keynesian consumption function was consistent with data on the measured MPC in the 1930s. The suggested reason the measured MPC was depressed in the 1930s is probably because habit-forming categories dominated total spending and this tended to depress the SR-MPC measured from period to period. Why, then, one may ask, did the regression coefficient of the Keynesian function also happen to be depressed? Clearly, the reason the slope or regression coefficient of early Keynesian functions was depressed was, not because that coefficient bore any relationship to data on the ratio of changes in spending to changes in income (the measured or observed MPC) but because the saving-income ratios were unusually depressed in the 1930s and inflated in the 1940s. This pattern of saving income ratios—or consumption-income ratios—flattened the consumption function. Indeed, if one either includes both the 1930s and early 1940s (computing 1929-7l) or excludes both (computing 1947-7l), the regression coefficient in the simple Keynesian function matches the apparent long-run MPC. It follows then, that the relative slopes of the long-run consumption function and the so-called Keynesian short-run function as it appears in texts are in a relationship to be explained not by analysis, either economic nor statistical. Rather it is explained by the unusual sequence of historical events of the 1930s and 1940s.

To the extent that the long-run is a representation of past short-runs and the short-run is a change at the margin, it is clear that the regression coefficient, at least in consumption function work, is more closely related to the long-run than the short-run. This explains what HT called the unexplained "fundamental inadequacy" of the short-run component of their model: It overestimates in downturns and underestimates in upturns (p. 284). If regression coefficients used to compute SR-MPCs in the HT model are more closely related to the long-run than short-run, one would indeed expect them to overestimate in downturns and underestimate in upturns. In 1961 Burress offered the same explanation for the pattern of errors in the Chow model for forecasting short run changes in auto demand. That is, Burress found nearly perfect rank correlation (0.9 to 1.0) between short-run forecasting errors in Chow’s model and deviation of observations from an independently computed trend. This is precisely what one would expect of a model designed to forecast long-run values. It is important to note that both Chow and HT differentiate between those parts of their models designed for estimating long-run and short-run values.

If one assumes such regression coefficients often better estimate long-run values than short-run values, it becomes clear there emerged in the literature an unwitting conspiracy of an error in interpretation of econometric models and an error in consumption function theory. In the 1961 study, Burress argues that, a priori, one would expect the habit hypothesis to explain the relationship between changes in spending and income over the long-run when fluctuations are mild. That is, even if spending on durables can be postponed, it cannot be postponed indefinitely without, as a result of depreciation, some ultimate pressure to maintain the services from durables at the habitual level. Hence, if (1) the regression coefficient is more closely related to the long-run than to the short-run, and if (2) the task of theory has been to explain regression coefficients rather than short-run changes, and if (3) the habit hypothesis can be expected, a priori, to explain the long-run and not the short-run, it is easy to see why the habit hypothesis has long been considered consistent with the data when this ‘was not the case.

Given a short-run change in income, the attempt to explain and forecast the response of consumers may focus on either the change in spending or saving. The search for clues on the deviation of observed/from expected values first focused on saving data as reported in the flow of funds. Needless to say, there vas no expectation that all inconsistencies would be explained. But it was soon clear that a substantial portion of these inconsistencies with traditional theory were associated with installment debt variables. Indeed as suggested in Table 1, if changes in observed personal saving are adjusted to remove the influence of installment debt, the adjusted data are far more consistent with traditional theory. It would appear then, that the modifications in traditional theory required to explain observed data must be related, either explicitly or implicitly, to data on installment debt. This is the rationale of what follows.

There have been numerous studies of installment debt over the past 50 years. An excellent review of the literature prior to the mid-1950s was offered by Homer Jones in the six-volume Federal Reserve study, Consumer Installment Credit, in 1957. Since then significant studies have been made by Enthoven in 1957, McCracken, Mao, and Fricke in 1965, Evans and Kisselgoff in 1966. None of these attempts a specification of the relationship between installment debt and the SR-MPC.

In the data on installment debt over the past 50 years, there are direct counterparts to data on spending which suggest that habit-forming categories dominated changes in total spending when fluctuations were severe and that nonhabit-forming categories dominated changes in the total when fluctuations were mild. That is, quarterly data reported by McCracken et al for the 1930s suggest that consumers react to severe downturns by borrowing more as they finance outlays that cannot be postponed. These data suggest consumers also react to recoveries from severe downturns by borrowing less as they apparently repay what was borrowed. The resulting negative cyclical income elasticity e, of extensions E, tends to reduce the saving-income ratio in downturns and inflate the saving-income ratio in upturns. A positive value of e for changes in assets doubtless reenforces this tendency for the saving-income ratio to follow the script provided by traditional theory.

When fluctuations are mild, there is little reason to believe e for asset changes is not likewise positive, the primary difference between the pattern of assets changes in severe and mild fluctuations being the amplitude of changes. But in the case of debt, the data suggest that during mild fluctuations, consumers react to recessions by borrowing less, not more, as they postpone outlays that are not habit-forming. Moreover, these data suggest consumers react to rising income, not by borrowing less, but by borrowing more as outlays that had been postponed are accelerated. In short, the data suggest that as the consumer moved from severe fluctuations of the 1930s and 1940s to mild fluctuations in more recent years, the sign of e of E changed from negative to positive.

In severe fluctuations, the stock coefficient in the HT model is positive, e of E is negative, and, therefore, e of saving is positive or the SR-MPC is less than the LR-MPC. But during mild fluctuations, the stock coefficient in the HT model is negative, e of E is positive, and therefore e of saving is negative or the SR-MPC exceeds the LR-MPC.

The effort to estimate these parameters encountered the same problems noted in the report of the HT model above. For example, using the technique for estimating e employed by Harberger, et al, e of E was positive for both the period before and after the early 1950s. Likewise e of PS was positive for both periods, despite data on period-to-period change which suggest e of PS was positive in the 1930s and 1940s and negative over the past 20 years. Nearly a decade ago it vas shown that what Harberger and others report as cyclical income elasticity actually measures long-run elasticity (Burress, June 1964). Needless to say, this is consistent with econometric problems reported earlier. For these reasons, the alternative model developed below offers a different approach to the data.

Traditional theory has not actually postulated that installment debt tends to reduce saving in downturns and increase saving in upturns. Although that may be implicit, it is more accurate to suggest that installment debt variables have been neglected. To develop the rationale of the alternative model and make explicit its relationship to traditional work, it will prove useful to explore the conditions under which installment debt variables would, cet. par. , have no influence on the change in personal saving from one period to the next and therefore, no influence on the LR-MPC or SR-MPC. This could be viewed as implicit in traditional theory.

Where PS(t) denotes personal saving in t and _PS(T) = PS(t)-PS(t-1), the initial objective of what follows is to determine the conditions, in terms of the behavior of extensions of installment debt, under which, cet. par. , _PS(T) = _PS(t-1). Let E(t) denote the level realized extensions in t and let E*(t) denote the level of extensions in t required if _PS(T) - _PS(t-1) = 0, cet.par.. In that case, installment debt is neutral with respect to the change in saving. In terms of data in Table 1, if E(t) = E*(t), the value in column three is zero. Put differently, installment debt variables are neutral or play no role in the change in column one. Clear understanding of this point is critical.

It will prove useful to focus on the relationship between the change in extensions, LE(t) = E(t) - E(t-1) and the requirement for neutral extensions, E*(t) - E(t-1), denoted _*E(t). If the realized change in extensions, E(t), is less than _*E(t), cet. par., saving will rise. If _E(t) exceeds _*E(t), then saving will fall. Once an expression for _*E(T) is derived, it will be easy to trace its cyclical pattern. Then by superimposing the cyclical pattern of _E(t) on the cyclical pattern of _*E(t), it will be easy to see why the behavior of installment debt tends to produce saving behavior consistent with traditional theory when fluctuations are severe, but a pattern inconsistent with traditional theory when fluctuations are mild. Experience has demonstrated that an understanding of _*E(t) as well as its second difference, (_*)²E(t) also provide useful forecasting tools.

PS(t) Personal saving as defined in national income accounts

_PS(t) PS(t) - PS(t-i)

E(t) Extensions of consumer installment credit as defined and reported by the Federal Reserve Board of Governors

R(t) Repayments on consumer installment credit as defined and reported by s

_I(t) Change in consumer installment credit outstanding between end of t-1 and end of t as defined and reported by same

_SI(T) That part of _PS(T) due to installment debt behavior = _I(t) - _I(t-1)and reported for 1953-72 in column three of Table 1

E*(t) The level of extension required in t so that _SI(T) = 0, or, cet. par. _FS=O.

_*E(T) E*(t) - E(t-1) or the change in extensions between t-1 and t which, if realized, would provide _SI(T) = 0 or play no role in _PS between t-1 and t. In terms of Table 1, the value in column 3 is zero.

E(t) Change in extensions between t-1 and t or E(t) - E(t-1)

k Effective maturity of installment debt outstanding implied by

k = [E(t)+E(t-l)+E(t-2)+¼ +E(t-k+l)]/R(t).

PDSI(T) Predetermined saving or repayments in t on extensions prior to t, i.e.,

PSDI(T) [E(t-l)+E(t-2)+E(t-3)¼ E(t-k+l)]/k.

(I) _I(t) - _I(t-1) [E(t) - R(t)] - [E(t-1) - R(t-1)]

Where maturity is defined as k, one may write:

(2) R(t) = [E(t) + E(t-1) + E(t-2) + E(t-3) + ¼ + E(t-k+l)]/k

Substituting (2) in (1), (1) can be rewritten:

(3) _I(t) - &I(t-1) = (k-1/k)E(t) - E(t-1) + (1/k)E(t-k).

Clearly I(t) - I(t-1) = 0, the condition provided in the case where _E(t) _*E(t), if and only if:

(4) E(t-1) (k-1/k)E(t) + (1/k)E(t-k).

To solve for _*E(t), multiply through by (-k)/(l-k) and rearrange, yielding:

(5) _*E(t) = 1/k-l[E(t-1) - E(t-k)].

_*E(t) is predetermined at the end of t-1 by E(t-1) and E(t-k). Where repayments on E(t) is t are (1/k)E(t), one may express _SI(T) as

(6) _SI(T) - (k-1/k)[_*E(t) - E(t)].

Because _*E(t) is predetermined at the end of t-1, it follows that part of _SI(T) is therefore predetermined at the end of t-1. If _*E(t) = _*E(t-1), the predetermined component of _SI(t) will equal zero. But if _*E(t) ¹ _*E(t-1), the predetermined component of _SI(T) will be:

(7) PD_SI(T) = (k-1/k)(_*E(t) - _*E(t-1)]

= [(k-l)/(k2-k)] [_E(t-1) - _E(t-k) ]

= _²PSI(t).

As this is written, most work with these relationships has been with data since 1952 when fluctuations were mild and the observed SR-MPCs appear to have exceeded the LR-MPCS. However before turning to those results, consider the probable relationships during severe fluctuations. For the sake of argument, assume (1) that consumers borrow only during severe downturns, (2) that such downturns last only one period, (3) that consumers pay off their debts during a recovery following the downturns, and (4) that another severe downturn follows each period of recovery.

Examination of (5) shows why _*E(t) would tend to be depressed in downturns, inflated in recoveries. But _E(t) would be inflated in downturns, depressed in recoveries. In that case, _SI(t) would rise most in downturns, fall most in recoveries. The relationship between _*E(t) and _E(t) is consistent with traditional theory and is illustrated in Schematic 2A in the bottom of Figure 2.

Turning to the case of mild fluctuations, the results of fitting (2) and (5) to 1953-72 data when k is 3 years appear in Table 3. Results of fitting (3) to the same data appear in Table 4, with particular reference to the fit of these second differences in installment debt outstanding during periods of recession and recovery. It is of interest to note that (3) fits better, in both relative and absolute terms, during periods of recession and recovery. This is in striking contrast to the fit of regression models which, as Houthakker and Taylor point out [p. 284], have the least satisfactory fit during such periods. For an approach that focuses on the short-run, this point is critical.

Examination of (5) shows that when fluctuations are mild and consumers react to recessions by borrowing less and to recoveries by borrowing more, _*E(t) will tend to reach a peak value in recession and a trough value in recoveries. But _E(t) will reach its trough value in recessions and peak value in recoveries. This then, would tend to produce the largest value of _SI(T) in recessions, tending to increase saving when income is falling. This will also produce the lowest value of _SI(t) in recoveries, tending to depress saving when income is rising. These relationships in an economy that fluctuates continuously between recession and recovery are illustrated in the schematic 2B. Note that in that case, the SR-MPC might always exceed unity.

This need not lead to an explosive system. Even if the SR-MPCs always exceeded unity, the LR-MPC could still remain below unity. Put differently, even if the SR-MPS were always negative, the LR-MPS could be positive. This would be true if the two following conditions were met. First, if the increases in income in recoveries exceeded reductions in income in recessions. Second, if the increases in saving in recessions exceeded the reductions in saving during recessions. Both are realistic assumptions—at least for periods of recession and recovery over the past 20 years or so. Hence the possibility that the SR-MPC might always exceed unity may be more than a far-fetched a priori possibility if recessions and recoveries are short and follow one another.

The economy does not, of course, oscillate continuously between short recessions and recoveries. Nevertheless, it is clear that when fluctuations are mild, _SI(T) will tend to rise most in recessions, tending to increase personal saving most when income is falling. Then _SI(T) will tend to fall most in recoveries, tending to reduce personal saving most when income is rising. Hence one would expect, a priori, a result which might contradict the traditional case. Of course, whether _SI(T) dominates _PS(T) is not an a priori question. It must be settled by the data. Data in Table 1 suggest that it often does. But it is not suggested that all deviations of PS from expected values are explained by this approach.

This analysis neglects the influence of PD_SI(t). PD_SI(T) can be viewed as restraint (if positive) or stimulant (if negative) that is not unlike an expected change in the full employment legislated in advance by Congress. That is, the stimulant or restraint in t is determined in advance of t. It can effect the economy in t, but it is independent of events in t. In particular, PD_SI(t) can affect _E(t). But _E(t) cannot affect PD_SI(t)

Where k is 3 years, PD_SI(T) undergoes predictable oscillations for four years once a recession is introduced. PD_SI(T) will reach its lowest value the year after a recession, helping bring on a recovery. In that case an inflated SR-MPC may, in part, be explained by PD_SI(t). Indeed in some recovery periods, the reduction in PD_SI(T) exceeded the reduction in PS, suggesting the SR-MPC may not have exceeded the LR-MPC if PDASI(T) had not been negative.

The second year after a recession PD_SI(T) is typically positive because _E(t) in (T) is so large. Then in the third year after recession, especially if _E(t-1) is large, PD_SI(T) tends to reach a peak value because the second term in (7), _E(t-3), refers to the change in extensions in the last recession when they were depressed. If the third year after a recession should be a period of weakness in the economy, PD_SI(T) may contribute to further weakness. The 1970 recession is an example. If the third year after a recession is one of strength, PD_SI(T) will tend to cause saving to rise more or fall less than it might otherwise. The first published application of the model was such a case [Burress, September, 1964]. The current year, 1973, is another example.

It does not follow, of course, that values of PD_SI(T) are significant. The values are recorded in Table 3. But it must be concluded that if the magnitude of changes in personal income taxes, as part of recent explicit fiscal policy formulations, have been significant, the values of FD_SI(T) must be considered significant. A review of behavior of PD_SI(T) in the context of recent fiscal policy as well as the forecasting record of the past ten years appears in Appendix A. Some reconciliation of competing interpretations of recent data offered by monetarists and fiscalists also appears in that review.

Because most forecasts missed the first half 1973 by wide margins, there is considerable detail in Appendix A on forecasts for that period with particular emphasis on how an assumed high cyclical income elasticity of extensions combined with increased _PDSI to generate a forecast that the level of first half saving would rise, but that the rise would be so modest that the saving rate would fall. As compared to calendar year 1972 data which were used in the -forecast (in response to questions from Business Week), personal saving rose less than $1-billion in the first half of 1973 and the saving rate fell from 6.2 to 5.9 percent in each of these two quarters [Burress, May 14, 1973 and October 15, 19731.

To conclude, it may prove useful to offer a partial summary in the form of a more formal statement of the thesis of this paper under conditions of mild fluctuations and then add comments on problems of estimation. John Carlson and on e of his students, Jim Nunns, suggested a formulation that is only a slight variant of the following:

Assume: (8)

and (9)

Substituting (9) in (8) yields:

Simplifying notation: (10)

Differencing: (11)

Dividing through by _Y (t), assuming _Y(t) ¹ 0: (12)

Equation (12) provides, of course, an accelerator model of the SR-MPC which appears to be a good summary of the thrust of a major thesis of this paper. That is, the term _²y/_y will. be positive, producing an MPC value greater than C₁ whenever the change in income, _Y, either: (1) has just gone from positive to negative; (2) is negative and Y is falling faster; (3) has just changed from negative to positive; or (4) is positive and getting larger. That is, the accelerator effect through income will tend to inflate the MPC during recession and recovery.

The final term, _²PDSI(t)/_Y(t) = PD_SI(t)/_y(t) produces an accelerator effect on the MPC which permits generalization only after a recession is introduced. As already noted, only then does _²PDSI undergo relatively predictable oscillations. Once there is a recession, this effect will join the acceleration of income to inflate the MPC during a recovery. Indeed, as mentioned above, in several postwar recoveries, the MPC would have remained below unity—indeed even below the LR-MPC—if it had not been for the reduction in _²PDSI that comes in a recovery period. Then, in the second and third years after a recession, _²PDSI(t) tends to depress the MPC progressively—assuming income increases. One may also expect a modest propensity to inflate the MPC in the fourth year after the recession—assuming k is three years and income continues to rise. After the fourth year following a recession, _²PDSI(T) remains near zero until another recession.

While this paper is being circulated to readers at the Staff of the NBER, (10), (11) and (12) will be estimated. It takes little experience in estimating equations such as (11) and (12) to predict poor fits. In addition, there is the problem of ratios in (12) as well as interdependence of variables acting through _Y(t). Inasmuch as (11) and (12) are a direct result of merely Differencing (10) and dividing by a common term, the usual procedure would be to suggest one should only estimate (10) and derive coefficients for use in (12).

But there are serious problems. In the first place, and at a practical level, several years experience explaining and forecasting the MPC suggests neither the level of income nor PDSI in (10) has played a significant role. But if these are eliminated from the equation, it is suggested, as mentioned above, that the fit will be poor.

It is further suggested, however, that standard procedure in this situation—using estimated coefficients in (10) as proxies for coefficients in (11) and (12) -- carries with it the same econometric problem discussed in the context of the Houthakker-Taylor model in Part III. That is, the chronological order in which the economy generates data used to complete differences in (11) and (12) is absolutely critical. Levels of the variables are not relevant. But, as a rule, the chronological order in which the economy generates data used to compute coefficients in (10) is not even relevant. It is the level of the variables that is relevant. Only in the case where the ratios between period-to-period differences in (11) and (12) do not deviate significantly from the corresponding regression coefficients in (10) would it be appropriate to use the coefficients in (10) as proxies for the corresponding coefficients in (11) and (12). In language used earlier, only when the marginal values do not deviate from average values would it be appropriate to employ such a proxy relationship. But in that case one could question whether one should concern oneself with short-run analysis. The short-run is significant and of interest primarily because these marginal values differ from the average or long-run values.