Abstract
This Selected Issues paper examines from an empirical standpoint the impact of fiscal aggregates on the evolution of output and the real effective exchange rate in the United Kingdom from the late 1970s to the present. It finds that the size of the dynamic fiscal multipliers is small, and often statistically nonsignificant. The paper also finds that the direction of the impact of taxes and government consumption, but not of social transfers, is, if anything, the reverse of that predicted by standard Keynesian models.
II. Why Has U.K. Household Consumption Been so Strong?1
A. Overview and Introduction
1. This study constructs a dynamic model of household consumption in the United Kingdom to analyze its recent behavior and to assess its prospects. The recent strength of household consumption in the United Kingdom is explained to a considerable extent by income gains over the recent past, though steady gains in house prices have also played a role. The wealth effect from house prices appears to dominate that from financial wealth in the short run, but the difference diminishes in the long run. Confidence factors and the ability to borrow against collateral (reflecting mortgage equity withdrawal) appear to be influencing consumption in the short run. The model suggests that household consumption in the United Kingdom should prove quite resilient to moderate shocks stemming from asset price declines, but the prospects for consumption do depend—among other factors—on orderly developments in the housing market.
2. Despite the marked fall in equity prices in the United Kingdom since March 2000, household consumption has remained remarkably resilient (Figure 1). Growth of household consumption has been underpinned by increases in personal incomes, which in turn have reflected steady increases in earnings and strong employment gains over the past few years (Figure 2). Consistent with smoothing behavior, household consumption has been less volatile than personal income. Despite the substantial decline in equity prices, continued strength in house prices has helped sustain the pace of consumption, while, at the same time, household indebtedness has risen markedly (middle and lower panels of Figure 1).
3. This study addresses the following questions:
What are the main determinants of household consumption in the United Kingdom? Are wealth effects among them, and which asset prices are most relevant?
More specifically, have strong gains in housing wealth been among the main factors behind the recent strength of consumption? In addition, has the responsiveness of consumption to housing wealth increased in recent years?
Has rising consumer borrowing—including mortgage equity withdrawal—been a contributing factor to the recent strength of consumption?
What are the prospects for consumption should a major decline in asset (particularly house) prices take place?
United Kingdom: Household Indicators, 1987-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; Bloomberg; and National Statistics (ONS).1/ In terms of gross disposable income.United Kingdom: Household Indicators, 1987-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; Bloomberg; and National Statistics (ONS).1/ In terms of gross disposable income.United Kingdom: Household Indicators, 1987-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; Bloomberg; and National Statistics (ONS).1/ In terms of gross disposable income.
United Kingdom: Labor Market Indicators, 1993-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: National Statistics (ONS).United Kingdom: Labor Market Indicators, 1993-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: National Statistics (ONS).United Kingdom: Labor Market Indicators, 1993-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: National Statistics (ONS).4. Numerous studies of household consumption in the United Kingdom have pointed to the importance of income and wealth variables in explaining the behavior of consumption in the long run, and to a variety of other—primarily wealth and confidence—variables in explaining short-run consumption dynamics.2 Recognizing the potentially different impact on consumption of gains in various asset classes, some studies have explicitly separated wealth effects in an effort to assess their relative importance.3 While the methodology and potential explanatory variables in the analysis of consumption have been largely established in the literature, the questions that each study addresses do not necessarily reflect the issues noted above. Low interest rates in recent years and rising housing wealth have fueled secured household borrowing (including mortgage equity withdrawal) and may have been a contributing factor to the recent strength of consumption. Should the value of the collateral decline or interest rates rise sharply, this factor could potentially impact consumption adversely. It is thus a valid empirical question whether, and to what extent, mortgage equity withdrawal influences the short-run behavior of consumption. However, only a handful of studies have attempted to assess the impact of mortgage equity withdrawal on consumption by modeling explicitly the ability of households to borrow against physical collateral.4
5. This study aims to contribute to the understanding of U.K. household consumption in the following respects. First, the study differentiates explicitly among various asset classes to account for the impact on consumption of differences in liquidity and realization of gains. While wealth decomposition is nothing new in studies of consumption, many have either used data on disaggregated financial wealth only or have employed price indices as proxies for wealth, thus abstracting from changes in the actual stock of wealth. Second, the study models explicitly the short-term impact on consumption of household borrowing secured on dwellings to assess the role of mortgage equity withdrawal. Finally, the study examines whether the gains in house prices in recent years have been accompanied by a larger influence of housing wealth on household consumption decisions, thereby raising the prospect of a large shock to consumption should a major adjustment of house prices take place.
6. This study formulates a model of household consumption in the United Kingdom that is reduced to a parsimonious single-equation representation to describe the dynamic behavior of household consumption. To put the econometric formulation in perspective, Section B provides a brief overview of the theoretical foundation of the model. Section C uncovers an equilibrium long-run relationship between household consumption and its fundamental determinants, and in the process evaluates the impact of individual factors on the behavior of household consumption over the long run. Section D describes a consumption equation that captures both short- and long-run dynamics, and performs experiments to assess the impact on household consumption of large shocks to its determinants. Section E summarizes the results. Finally, Section F contains concluding remarks.
7. The model, which is intuitively appealing, fits the data remarkably well. The main results can be summarized as follows:
By far, the principal determinant of household consumption in the long run is personal disposable income; wealth effects play a secondary—though still important—role.
The influence of housing wealth on household consumption is much larger than that of financial wealth in the short run, but the difference diminishes in the long run.
The boost to household consumption from the availability of borrowing secured on dwellings (a proxy for mortgage equity withdrawal) is strong but short-lived: secured borrowing tends to raise consumption strongly in the very short run, but suppresses it in the long run (as should be expected of any gross liability).5
Among the short-run influences on household consumption, variables capturing consumer confidence play a prominent role.
The impact on consumption growth of a large (say, 10 percent) correction in house prices would be relatively muted and short-lived, but much larger and protracted declines of house prices could potentially cause household consumption to contract for a few quarters.
B. The Theoretical Model
8. The theoretical foundation of the estimated model is provided by the vast literature on the life cycle/permanent income hypothesis of consumption.6 Under this hypothesis, planned consumption Cp is a positive function of total resources, which in turn are the sum of human and other net wealth:
Cp = f(Human Wealth, Wealth)
Given that planned consumption is unobservable, actual consumption at time t, CONSt, and planned consumption are related as follows:
CONSt = ft(Human Wealth, Wealth) + εt
Furthermore, human wealth—represented by the present discounted value of labor income—is unobservable, but can be proxied by some function of contemporaneous labor income INCOt. In addition, other net wealth can be broken down in its two components, net housing wealth, HOU_Wt, and net financial wealth, FIN_Wt. We can therefore derive the following log-linear long-run household consumption equation:7
ln(CONSt) = β0 + β1ln(INCOt) + β2 ln(HOU_Wt) + β3 ln(FIN_Wt) + θt
9. The pure form of the life cycle/permanent income hypothesis of consumption has not fared well in empirical tests. Consequently, researchers have tried to augment the theoretical model by including additional explanatory variables. Such variables typically include a real interest rate (to capture intertemporal substitution effects), the inflation rate (to capture uncertainty as well as the real depreciation of non-indexed financial assets), and the unemployment rate (to capture uncertainty surrounding future income). Some of these variables are expected to explain better the short-run dynamics of consumption (inflation and unemployment), while others (such as the real interest rate) are expected to enter the consumption decision over the longer run.
C. Estimation of the Long-run Household Consumption Function
10. Using quarterly data for 1987:Q4 - 2001:Q3, a long-run cointegrating relationship (interpreted as a steady-state equilibrium) was estimated between household consumption and its fundamental determinants: disposable income, net housing wealth, net financial wealth, and the real interest rate.8
11. Figure 3 (upper panel) presents a decomposition of the long-run cointegrating relationship, revealing the relative contributions of the fundamental determinants of consumption.
12. The statistical evidence suggests that:
There is a stable long-run relationship between household consumption in the United Kingdom and its fundamental determinants. This relationship satisfies the theoretical requirement of homogeneity of order one (i.e., the sum of the estimated coefficients of income and wealth is equal to one).9
Household consumption over the long run is highly sensitive to developments in disposable income, the long-run elasticity being 0.85.
Consumption appears to be more sensitive to changes in net housing wealth than to changes in net financial wealth over the long run.
Some intertemporal substitution takes place, but the small long-run elasticity of consumption with respect to the real interest rate suggests a very small effect.
Much of the strength of equilibrium consumption since the mid-1990s—and especially since 1998—is due to growth in real disposable income, with housing and financial wealth gains playing a secondary role (see Figure 3, upper panel). The relative influence of housing wealth appears to have increased somewhat in 2001, dominating the negative effect from the decline in equity prices.
United Kingdom: Long-run Equilibrium, and Actual and Fitted Values of Consumption, 1990-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff calculations.1/ Variables have been scaled so that they have a zero mean over the estimation period.United Kingdom: Long-run Equilibrium, and Actual and Fitted Values of Consumption, 1990-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff calculations.1/ Variables have been scaled so that they have a zero mean over the estimation period.United Kingdom: Long-run Equilibrium, and Actual and Fitted Values of Consumption, 1990-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff calculations.1/ Variables have been scaled so that they have a zero mean over the estimation period.The next step is to combine the long-run relationship with short-run influences in a single dynamic equation of consumption.
D. A Model of Household Consumption
Error-correction model
13. Deviations of consumption from its long-run equilibrium levels do not always reflect disequilibria; they could also reflect temporary factors and adjustment lags. To capture the short-run dynamics, household consumption was modeled in an error-correction representation, using—in addition to the variables mentioned above—the unemployment rate and loans to households secured on dwellings (in constant prices). The unemployment rate is a proxy for uncertainty surrounding future income (capturing precautionary savings) and is treated as a consumer confidence indicator: other things constant, an increase in the unemployment rate would cause consumption to contract. The level of borrowing by households secured on dwellings attempts to capture the short-run impact of mortgage equity withdrawal, which some researchers have suggested that has been a contributing factor behind the recent strength of consumption.10 Theory prescribes a negative sign for this factor over the long run (as is the case for any gross liability), but its sign in the short run is an open empirical question.
14. Starting from a general specification, that includes several lags and variables, and reducing it to a parsimonious representation with the aid of appropriate tests, the estimation yielded the following error-correction model of household consumption:11
R-BAR2 = 0.730 σ^ = 0.0036
15. Virtually all estimated coefficients have the anticipated signs, and the equation passes a battery of diagnostic tests. Tests for parameter stability and for the presence of structural breaks confirmed that the results are robust (Figures 4 and 5).12 Furthermore, the estimated model fits the data well, suggesting that the recent strength of consumption can be explained adequately by the variables included in the analysis (see lower panel of Figure 3).13
United Kingdom: Parameter Stability, 1992-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff estimates.United Kingdom: Parameter Stability, 1992-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff estimates.United Kingdom: Parameter Stability, 1992-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff estimates.
United Kingdom: Tests for Structural Breaks, 1992-2001 1/
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff calculations.1/ Test values in panels two through four are scaled by one-off critical values from the F-distribution at the 1 percent probability level as adjustment for changing degrees of freedom. Test values below 1.0 cannot reject the null hypothesis.2/ Points outside the 2 standard-error region are either outliers or are associated with coefficient changes.3/ One-step forecast test of the null hypothesis of constant parameters.4/ Chow tests of the null hypothesis of no difference between the N-periods-ahead and one-period ahead forecasts.5/Chow tests of the null hypothesis of no difference between the one-period-ahead and N-periods-ahead forecasts.United Kingdom: Tests for Structural Breaks, 1992-2001 1/
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff calculations.1/ Test values in panels two through four are scaled by one-off critical values from the F-distribution at the 1 percent probability level as adjustment for changing degrees of freedom. Test values below 1.0 cannot reject the null hypothesis.2/ Points outside the 2 standard-error region are either outliers or are associated with coefficient changes.3/ One-step forecast test of the null hypothesis of constant parameters.4/ Chow tests of the null hypothesis of no difference between the N-periods-ahead and one-period ahead forecasts.5/Chow tests of the null hypothesis of no difference between the one-period-ahead and N-periods-ahead forecasts.United Kingdom: Tests for Structural Breaks, 1992-2001 1/
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: IMF staff calculations.1/ Test values in panels two through four are scaled by one-off critical values from the F-distribution at the 1 percent probability level as adjustment for changing degrees of freedom. Test values below 1.0 cannot reject the null hypothesis.2/ Points outside the 2 standard-error region are either outliers or are associated with coefficient changes.3/ One-step forecast test of the null hypothesis of constant parameters.4/ Chow tests of the null hypothesis of no difference between the N-periods-ahead and one-period ahead forecasts.5/Chow tests of the null hypothesis of no difference between the one-period-ahead and N-periods-ahead forecasts.Dynamic simulations
16. How much did the strength of consumption growth in 2001 depend on increases in house prices’? A dynamic simulation of the above error-correction model—which involved holding housing wealth constant at its end-2000 level during 2001—indicates that consumption growth would have slowed, but held up at a sustainable pace of around 3 percent (Figure 6).14 This confirms the result from decomposing the cointegrating relationship that much of the recent strength in consumption derives from steady increases in real disposable income (see Figure 3).
United Kingdom: Real Household Consumption, 2000-01
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/Assumes unchanged housing wealth in 2001 from the end-2000 level. All other variables assume their actual values.2/ Fitted values of the error-correction model.United Kingdom: Real Household Consumption, 2000-01
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/Assumes unchanged housing wealth in 2001 from the end-2000 level. All other variables assume their actual values.2/ Fitted values of the error-correction model.United Kingdom: Real Household Consumption, 2000-01
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/Assumes unchanged housing wealth in 2001 from the end-2000 level. All other variables assume their actual values.2/ Fitted values of the error-correction model.17. Dynamic simulations were also performed to test the response of consumption to large, counterfactual shocks to its determinants. Each determinant was subjected to a structured shock and the depth and duration of the impact on consumption was observed (Figures 7 and 8).15 The experiments suggest that consumption is quite resilient to relatively large adverse shocks to its determinants, though the extent and duration of the impact on consumption growth does vary considerably among the controlled variables.
United Kingdom: Dynamic Simulation of Consumption—Shocks to Income, Housing and Financial Wealth, 1998-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes a decline in disposable income of 2.6 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in housing wealth of 8.9 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.3/ Assumes a decline in financial wealth of 11.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.United Kingdom: Dynamic Simulation of Consumption—Shocks to Income, Housing and Financial Wealth, 1998-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes a decline in disposable income of 2.6 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in housing wealth of 8.9 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.3/ Assumes a decline in financial wealth of 11.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.United Kingdom: Dynamic Simulation of Consumption—Shocks to Income, Housing and Financial Wealth, 1998-2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes a decline in disposable income of 2.6 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in housing wealth of 8.9 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.3/ Assumes a decline in financial wealth of 11.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.
United Kingdom: Dynamic Simulation of Consumption—Shocks to Unemployment and Secured Liabilities, 1998–2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes an increase in the unemployment rate of 2.3 percentage points between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in the stock of secured liabilities of 2.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.United Kingdom: Dynamic Simulation of Consumption—Shocks to Unemployment and Secured Liabilities, 1998–2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes an increase in the unemployment rate of 2.3 percentage points between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in the stock of secured liabilities of 2.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.United Kingdom: Dynamic Simulation of Consumption—Shocks to Unemployment and Secured Liabilities, 1998–2001
Citation: IMF Staff Country Reports 2002, 046; 10.5089/9781451814163.002.A002
Sources: Bank of England; National Statistics (ONS); and IMF staff estimates.1/ Assumes an increase in the unemployment rate of 2.3 percentage points between 1998:Q4 and 1999:Q4, and unchanged values thereafter.2/ Assumes a decline in the stock of secured liabilities of 2.4 percent between 1998:Q4 and 1999:Q4, and unchanged values thereafter.18. The counterfactual simulations should be interpreted with caution because they are based on partial analysis. With given paths for the explanatory variables, the simulations preclude feedbacks between variables. For instance, it is likely that a decline in housing wealth of the magnitude assumed in the experiment (close to 10 percent) would be accompanied by other developments (such as erosion of confidence) that could have a larger impact on consumption than the one suggested by the experiments.
E. Summary of Results
19. The main results can be summarized as follows:
Household disposable income does not appear to have a statistically significant influence on household consumption in the short run. This result suggests substantial consumption smoothing, characteristic of an economy with relatively few liquidity-constrained individuals.16
Consumer confidence variables (specifically the unemployment rate) seem to play an important role in explaining the short-run dynamics of consumption: the estimated coefficient implies that, if unemployment were to rise from its current level of about 5 percent by half a percentage point to 5.5 percent within a quarter (a 10 percent increase), the immediate impact on quarter-on-quarter consumption growth would be a decline of roughly 0.4 percentage points.17
The boost to consumption from the availability of credit secured on dwellings appears to be strong but short lived. The immediate impact on consumption of changes in secured household liabilities is positive (positive coefficient of contemporaneous secured liabilities), but the reversion to long-run behavior begins after one quarter (negative coefficient of lagged secured liabilities).18
The combined short-run sensitivity of consumption to net housing wealth is much larger than that of net financial wealth.19 This seems to suggest that households tend to regard recent gains in housing wealth as more permanent than those in financial wealth (mainly stock market gains).
The adjustment of consumption to deviations from the long-run equilibrium is relatively slow, pointing, once again, to considerable consumption smoothing: the coefficient of the error correction term suggests that it takes roughly 7 to 8 quarters for household consumption to fully respond to a shock and reach its new equilibrium. The dynamic simulations confirmed this pattern.
The estimated coefficients of the model exhibit remarkable stability throughout the sample. This suggests that the influence of housing wealth and secured borrowing by households has not risen in recent years and that their contribution to the recent strength of consumption reflects their rising levels rather than an increase in the sensitivity of consumption to these factors.
The initial response of consumption to a change in disposable income is slow (reflecting smoothing), but gathers momentum as consumers increasingly realize that the income change is permanent rather than temporary. The dynamic simulations suggest that, over the long run, consumption is primarily responsive to changes in disposable income, and to a lesser extent, housing wealth. In the short run, changes in housing wealth and unemployment (and to a lesser extent secured liabilities) appear to be important factors.
Consumption growth should prove quite resilient to modest shocks stemming from asset price declines. Consumption grew robustly in 2001 despite the fall in equity prices, and simulations suggest that, while consumption growth that year was bolstered by the increase in housing wealth, much of its strength reflected the underlying gains in disposable income. However, a major decline in house prices could potentially have a significant impact on consumption in the short run, but the effect would be mitigated somewhat over the long run once consumption reaches its new, lower equilibrium. A roughly 10 percent permanent decline in real housing wealth over a year would moderate quarter-on-quarter consumption growth substantially, but only for a short period, and it would reduce the level of consumption by about 1 percent in the long run (based on the estimated long-run elasticity).20
F. Concluding Remarks
20. The strength of household consumption in the face of the decline in equity prices and large gains in U.K. housing prices has raised questions about its sustainability. This study aimed to uncover both the short- and the long-run influences on consumption and to assess its prospects. The results are robust, the estimated model has a dynamic structure and appealing economic interpretation, and performs well in explaining the historical data.
21. The recent strength of consumption reflects to a significant extent cumulated gains in disposable income, and, to a lesser extent the carry-over of wealth effects. Among wealth effects, housing wealth appears to have a larger influence than financial wealth, primarily in the short run, but the sensitivity of consumption to changes in housing wealth does not appear to have increased in recent years. Borrowing secured on dwellings appears to exert a strong positive influence on consumption in the very short run, but its influence is short-lived and its overall contribution over a longer period becomes negative.
22. The response of consumption to modest shocks (stemming, for example, from a correction in the housing market) would be relatively modest and gradual. Nonetheless, major and protracted declines could potentially have a significant impact, especially when accompanied by erosion of confidence.
APPENDIX
Why Has U.K. Household Consumption Been so Strong?
23. This appendix describes a model of household consumption in the United Kingdom based on quarterly data for 1987:Q4-2001:Q3.
A. Data
24. The following series were used in this study (notation in parentheses):
Consumption (CONS): Total final consumption expenditure of households and non-profit institutions servings households (NPISHs) in 1995 prices; seasonally adjusted.
Income (INCO): Gross disposable income of households and NPISHs in 1995 prices: seasonally adjusted.21
Net housing wealth (HOU_W): The difference between total residential assets of households and NPISHs and household and NPISH debt (secured on dwellings) to banks, building societies, and others; divided by the consumption deflator and seasonally adjusted.22
Net financial wealth (FIN_W): The difference between total financial assets of households and NPISHs and household and NPISH unsecured debt; divided by the consumption deflator and seasonally adjusted.
Real interest rate: Three-month deposit rate (annualized) deflated by the actual annual inflation rate in the preceding 12 months.
Unemployment rate (UNEMP): Unemployment rate (in percent), International Labor Organization definition; seasonally adjusted.
Secured liabilities of households (SEC_LIAB): Total household and NPISH debt (secured on dwellings) to banks, building societies, and others; divided by the consumption deflator and seasonally adjusted.
B. Integration
25. To determine the appropriate estimation procedure, Augmented Dickey-Fuller (ADF) tests for nonstationarity of the above variables were carried out, which showed that each variable is integrated of order one (Table 1). ADF tests (not shown) of the null hypotheses of integration of higher order rejected the null. All variables are thus stationary in first differences, and cointegration analysis among the level variables is required.
ADF Statistics Testing for a Unit Root
ADF Statistics Testing for a Unit Root
| Variable | |||||
|---|---|---|---|---|---|
| cons | inco | hou_w | fin_w | real_int | |
| ADF(2) | ADF(1) | ADF(4) | ADF(0) | ADF(0) | |
| Ho: 1(1) | 2.23 | -0.12 | -1.83 | -1.40 | -1.88 |
ADF Statistics Testing for a Unit Root
| Variable | |||||
|---|---|---|---|---|---|
| cons | inco | hou_w | fin_w | real_int | |
| ADF(2) | ADF(1) | ADF(4) | ADF(0) | ADF(0) | |
| Ho: 1(1) | 2.23 | -0.12 | -1.83 | -1.40 | -1.88 |
C. Cointegration
26. The Johansen procedure found evidence of the following long-run relationship between household consumption in the United Kingdom and its fundamental determinants:23
All estimated coefficients of the selected vector have the anticipated signs.24
27. The estimated relationship in (A.l) was used to test two hypotheses. First, the hypothesis of homogeneity of order one between household consumption, income, and the wealth variables was tested (i.e., the sum of the coefficients of income and the wealth variables is equal to one). The test of the hypothesis yielded the following statistic (p value in square brackets):
X2(1) =1.312 [0.252]
Based on the large (well in excess of 0.05) p value of the statistic, the null hypothesis cannot be rejected, and the restricted long-run relationship becomes:
Second, two hypotheses were tested jointly: homogeneity of order one, and equality of the coefficients of the wealth variables. The test of the joint hypothesis yielded the following statistic:
X2 (1)-2.885 [0.236]
The joint null hypothesis cannot be rejected, and the following restricted long-run relationship results:
28. Although the restricted cointegrating vector in (A.3) cannot be rejected by the data, it is not very appealing for two reasons. First, the coefficient of the real interest rate enters with a counterintuitive positive sign. Second, the coefficient of income is much larger than known empirical estimates of the long-run elasticity of household consumption with respect to income, which are usually in the range 0.8 to 0.9. Consequently, on purely economic grounds, the long-run relationship estimated in (A.2) was the one selected.25
29. Table 2 reports the tests for the presence of cointegrating vectors in the Johansen procedure, as well as the feedback coefficients and their standard errors corresponding to the cointegrating vector in (A.2).
Johansen Test of Existence of Long-run Relationships, and Feedback Coefficients 1/
Standard t-ratios are reported in parentheses. Feedback coefficients represent the response (adjustment) of the respective variable to a deviation of consumption from the long-run equilibrium estimated in (A.2).
Asterisk denotes significant test statistic at the 5 percent level. Based on the trace statistic, the Johansen procedure uncovered a single cointegrating vector, the one in (A.2).
Johansen Test of Existence of Long-run Relationships, and Feedback Coefficients 1/
| Trace 2/ | |||||
| Ho: rank=0 | 74.163 [0.020] * | ||||
| <=1 | 43.050 [0.131] | ||||
| <=2 | 20.403 [0.407] | ||||
| <=3 | 7.8226 [0.492] | ||||
| <=4 | 0.0062 [0.937] | ||||
| cons | inco | hou_w | fin_w | real_int | |
| Feedback coefficient: | -0.156 | 0.137 | 0.713 | -0.059 | 2.885 |
| (-2.51) | (1.13) | (2.01) | (-0.11) | (0.73) |
Standard t-ratios are reported in parentheses. Feedback coefficients represent the response (adjustment) of the respective variable to a deviation of consumption from the long-run equilibrium estimated in (A.2).
Asterisk denotes significant test statistic at the 5 percent level. Based on the trace statistic, the Johansen procedure uncovered a single cointegrating vector, the one in (A.2).
Johansen Test of Existence of Long-run Relationships, and Feedback Coefficients 1/
| Trace 2/ | |||||
| Ho: rank=0 | 74.163 [0.020] * | ||||
| <=1 | 43.050 [0.131] | ||||
| <=2 | 20.403 [0.407] | ||||
| <=3 | 7.8226 [0.492] | ||||
| <=4 | 0.0062 [0.937] | ||||
| cons | inco | hou_w | fin_w | real_int | |
| Feedback coefficient: | -0.156 | 0.137 | 0.713 | -0.059 | 2.885 |
| (-2.51) | (1.13) | (2.01) | (-0.11) | (0.73) |
Standard t-ratios are reported in parentheses. Feedback coefficients represent the response (adjustment) of the respective variable to a deviation of consumption from the long-run equilibrium estimated in (A.2).
Asterisk denotes significant test statistic at the 5 percent level. Based on the trace statistic, the Johansen procedure uncovered a single cointegrating vector, the one in (A.2).
Only the feedback coefficient in the consumption equation is statistically different than zero, suggesting that the single cointegrating vector (A.2) enters only one equation (the consumption equation) in the vector autoregression, and that the adjustments to deviations from equilibrium tend to bring consumption back to equilibrium (negative feedback coefficient).
30. The results of the test for weak exogeneity (i.e., that the feedback coefficients of inco, hou_w, fin_w, and real_int in Table 2 are jointly equal to zero) are the following:26
LR test of restrictions: x2(5) = 5.0797 [0.4062]
The hypothesis of weak exogeneity of inco, hou_w, fin_w, and real_int cannot be rejected. Thus, a more parsimonious single-equation estimation could be used without any loss of information about the cointegrating vector.
D. Single-equation Modeling (Error Correction)
31. This section introduces the long-run dynamics established in (A.2) into a single-equation, conditional, and parsimonious model for U.K. household consumption that encompasses both short- and long-run dynamics. The short-run dynamics are derived from the following vector of changes in the log-levels of the variables used so far in the analysis:
Is = {Δt-j};j = 0, 1…
where vt-j is the vector of all variables (contemporaneous and lagged) used so far, with the addition of two new stationary variables, orthogonal to the existing regressors. These are:
UNEMP = Unemployment rate
SEC_LIAB = Loans to households secured on dwellings (in constant prices and seasonally adjusted).
32. An error correction model for household consumption in the United Kingdom was estimated using quarterly data over 1988:Q1-2001:Q3.27 Estimation began from a general specification with several variables and lags, which also included the vector Is and the deviations of consumption from the long-run relationship (A.2) established above. Subsequently, parameter tests were performed (mostly zero restrictions) to reduce the model to a more manageable form. Below is the resulting specification for household consumption and the relevant statistics (t-ratios are shown in parentheses below the estimated coefficients) and diagnostic tests (p values are shown in brackets next to the estimated statistics):
R-BAR2 = 0.730, DW = 2.28, σ^ = 0.0036
Autocorrelation tests:
AR-1−4 F(4, 43) = 1.385 [0.255]
AR-1−3 F(3, 41) = 0.610 [0.613]
AR-1−2 F(2, 43) = 0.208 [0.813]
AR-1−1 F(1, 45) = 0.301 [0.586]
AR-1−1 F(4, 39) = 0.636 [0.640]
Heteroskedasticity tests:
Xi^2 F(14, 32) = 0.329 [0.985]
RESET F(1, 46) = 0.273 [0.604]
Normality test:
Non-normality x2 (2) = 0.194 [0.908]
33. The estimated equation fits the data well (see lower panel of Figure 3). Moreover, the model passes a battery of diagnostic tests. The hypotheses: of no serial autocorrelation up to fourth order; normality of the residuals; and homoskedasticity could not be rejected. The estimated standard error of the regression (0.0036 or 0.36 percent quarter-on-quarter consumption growth) is relatively low. Finally, the coefficient of determination of 0.73 is relatively high considering that variables are seasonally adjusted and expressed in changes.
34. In addition, the model passes a series of diagnostic tests for misspecification and structural breaks. First, tests for parameter constancy showed that the estimated coefficients are remarkably robust and that their standard errors diminish over time, suggesting correct specification of the estimated model (see Figure 4).28 The tests suggest that the sensitivity of consumption to housing wealth and secured liabilities has not increased in recent years. Second, a series of diagnostic tests confirmed the absence of structural breaks (see Figure 5). The upper-left panel of Figure 5 shows that the errors of one-period-ahead forecasts are white noise with constant variance. The remaining panels show that, at 1 percent level of confidence, the model does not exhibit any structural breaks at any subset of the period under study, estimated in either ascending or descending chronological order. These tests, too, suggest that the sensitivity of consumption to housing wealth and secured liabilities has not increased in recent years.
35. Tests for the exclusion of relevant variables showed that neither the inflation rate—as proxy for uncertainty and the capital loss to non-indexed financial assets due to inflation—nor an explicit nominal policy interest rate—again as proxy for uncertainty—belong in the dynamic equation for a reasonable number of lags and for the period under study.29
References
Ando, A., and F. Modigliani, 1963, “The Life Cycle Hypothesis of Saving: Aggregate Implications and Tests,” American Economic Review, Vol. 103, pp. 55–84.
Bank of England, 2000, Economic Models at the Bank of England: September 2000 Update, (London: Bank of England).
Boone, L., N. Girouard, and I. Wanner, 2001, “Financial Market Liberalisation, Wealth and Consumption,” OECD Economics Department Working Paper No. 308, (Paris: Organisation for Economic Co-operation and Development).
Byrne, J., and E. P. Davis, 2001, “Disaggregate Wealth and Aggregate Consumption: An Investigation of Empirical Relationships for the G7,” NIESR Discussion Paper 180, (London: National Institute of Economic and Social Research).
Church, K. B., P. N. Smith, and K. F. Wallis, 1994, “Econometric Evaluation of Consumers’ Expenditure Equations,” Oxford Review of Economic Policy, Vol. 10(2), pp. 71–85.
Davey, M., 2001, “Mortgage Equity Withdrawal and Consumption,” Bank of England Quarterly Bulletin, Spring 2001, pp. 100–103.
Deaton, A., 1992, Understanding Consumption, (Oxford: Clarendon Press).
Hendry, D. F., and J. A. Doornik, 1999, Empirical Econometric Modeling Using PcGive, (West Wickham: Timberland Consultants Ltd.).
Johansen, S., 1988, “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, Vol. 12, pp. 231–254.
Johansen, S., 1995, Likelihood-based Inference in Cointegrated Vector Autoregressive Models, (Oxford: Oxford University Press).
Ludwig, A., and T. Sløk, 2002, “The Impact of Stock Market and House Prices on Consumption in OECD Countries,” IMF Working Paper WP/02/1, (Washington: International Monetary Fund)
Prepared by Dimitri Tzanninis.
Church et al (1994) present a survey of U.K. consumption functions.
For recent studies, see Byrne and Davis (2001) on the United Kingdom, and Boone et al (2001) and Ludwig and Sløk (2002) on a group of OECD countries, including the United Kingdom.
For example, Boone et al (2001).
Mortgage equity withdrawal is the part of household borrowing secured on dwellings that is not invested in them, but is available for reinvestment or consumption. See Davey (2001).
See Ando and Modigliani (1963) and the survey of literature provided in Deaton (1992).
Theory does not prescribe a functional form for consumption. It is therefore an empirical question whether a log-linear representation is appropriate.
All variables are expressed in real terms. Lower case letters denote logarithms of the variables introduced above. Therefore, the estimated coefficients can be interpreted as long-run elasticities. See the Appendix for a detailed discussion of the series used, the statistical tests, and the estimation results.
The estimated long-run relationship is similar to the one published by the Bank of England in the September 2000 update of its economic model (Bank of England, 2000): const = 0.890*labor_incomet + 0.110*total_wealtht – 0.003*real_intt
See, for example, Davey (2001).
The notation Δ denotes first differences in the logarithms of the variables, which can be interpreted as the quarter-on-quarter growth rates of the underlying variables. Standard t-ratios are reported in parentheses. Only significant coefficients are reported. ECM(cons)t-i is the lagged deviation of actual consumption from the long-run relationship derived in (1) above; together with its coefficient, it represents the error-correction term capturing the adjustment of consumption to deviations from its long-run equilibrium.
The in-sample forecast errors for 2000-01 are within the standard error of the regression. See also footnote 14 below.
Given that recent national income accounts data (including consumption) tend to be revised, the results for 2001 are necessarily tentative.
Each explanatory variable was subjected to a negative shock in 1999:Q4, equivalent to two standard deviations below the average year-on-year historical rates of change (this implied an increase in the unemployment rate). The variable was interpolated linearly between 1998:Q4 (the last actual value) and 1999:Q4 (the period where the full force of the shock was felt), and remained unchanged thereafter. All other explanatory variables assumed their actual values. The starting point of the simulation was selected to allow the dynamics to play out fully by the end of the period (2001:Q3).
See Deaton (1992), Chapter 7.
This result is based on a partial analysis, which does not allow for the impact of an increase in unemployment on the other variables. In addition, it applies only to small changes.
Boone et at (2001), using different methodology and semi-annual data, also found a positive association of contemporaneous equity withdrawal and consumption in the United Kingdom.
The dynamic equation estimated by the Bank of England, though different in the variables included and in their definition, broadly confirms this result. The result is also consistent with other empirical work. See, for example, Boone et al (2001) and Ludwig and Sløk (2002) who used data on OECD countries.
Such a shock (the precise simulated shock is a 8.9 percent decline in real housing wealth) would indeed be sharp and a rare event (occurring about once every ten years for a normal distribution).
Gross disposable rather than labor income was used for the following reason. Equations relying on labor income exhibited positive feedback from disequilibrium in the consumption equation (see Appendix, Section C, and Table 2), thereby exhibiting a tendency to develop bubbles in consumption that were contained only through a large negative feedback from disequilibrium in the financial wealth equation. While this produced a statistically stable system, in the sense that bubbles in consumption were eventually contained by sharp falls in financial wealth, the result was counterintuitive, and thus disposable income was used.
Residential assets account for about 90 percent of total physical assets of households in the United Kingdom. The series on residential assets was used for its intuitive appeal since it is easier to associate its movements with developments in the housing market. Nevertheless, the series is available only with annual frequency (so is the total physical wealth series). Consequently, the series was interpolated using information from the Halifax house price index and additions to household net wealth to derive a quarterly series of housing wealth.
See Johansen (1988 and 1995). Estimation and testing were carried out in PcGive Professional v10b; see Hendry and Doornik (1999).
Only one cointegrating vector was uncovered.
The theoretical requirement of homogeneity of order one is more stringent than that of equality between the long-run elasticities of household consumption with respect to net housing wealth and with respect to net financial wealth.
An additional restriction maintained is that of homogeneity of order one. In essence, this is a joint test of weak exogeneity and homogeneity of order one.
The first observation (i.e., 1987:Q4) was discarded because it was an outlier: the financial wealth variable was considerably smaller than its trend value reflecting the correction of global equity prices that took place in October 1987.
The absence of serial correlation was also an indication of correct specification.
Theory prescribes a real interest rate in household consumption functions. However, some empirical models of household consumption in the United Kingdom have found a strong short-run influence on consumption stemming from a nominal interest rate, not necessarily a policy rate (for example, Bank of England, 2000). Presumably, a nominal interest rate captures consumer-confidence factors, which have already been included in the dynamic equation estimated above.
