Abstract
This Selected Issues paper on the United Kingdom reviews the IMF's Global Economy Model, which incorporates energy to examine the impact of rising energy prices on the United Kingdom. The model incorporates energy as a final consumption good as well as a primary input in the production process. With energy entering the production process, increases in energy costs affect overall aggregate supply capacity as firms reduce output and factor-utilization rates given the real increase in their cost structures.
II. The Link Between Private Consumption and the Housing Market11
In the U.K., the cooling of the housing market was accompanied by a sharp slowdown in consumption growth. This paper finds that the main determinants of consumption growth are changes in income and wealth. Changes in housing wealth have an effect on consumer spending on impact, while changes in financial wealth affect consumption only gradually. The results suggest that, between 2001–04, the positive effect of housing wealth growth on consumption was offset by the negative effect of the equity market correction. Looking forward, strong income growth should underpin a sustained pick-up in consumption, in the absence of further negative shocks from the housing market.
A. Introduction
1. The cooling of the housing market in 2004-05 coincided with a sharp slowdown in private consumption growth (Figure 1). This has raised concerns regarding the resilience of consumption in the event of persistent weakness in the housing market. Among industrial countries with significant cumulative house price appreciation since the mid-1990s, the Netherlands was the first to experience an extended period of low house price growth. This was accompanied by a period of very weak consumption growth (see Figure 2 and De Nederlandsche Bank (2004)). More recently, Australia also saw a sharp slowing of both residential asset prices and consumption growth, although domestic activity has been supported by strong commodity export prices.
Real Private Consumption and Real House Price Growth 1/
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics, Nationwide, Halifax, and staff calculations.1/ The house price index is the average of Halifax and Nationwide, deflated by the private consumption deflator.Real Private Consumption and Real House Price Growth 1/
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics, Nationwide, Halifax, and staff calculations.1/ The house price index is the average of Halifax and Nationwide, deflated by the private consumption deflator.Real Private Consumption and Real House Price Growth 1/
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics, Nationwide, Halifax, and staff calculations.1/ The house price index is the average of Halifax and Nationwide, deflated by the private consumption deflator.
Global House Price Developments
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Sources: Haver Analytics; IMF, International Financial Statistics; national sources; OECD, Bank for International Settlements; and IMF staff calculations.Global House Price Developments
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Sources: Haver Analytics; IMF, International Financial Statistics; national sources; OECD, Bank for International Settlements; and IMF staff calculations.Global House Price Developments
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Sources: Haver Analytics; IMF, International Financial Statistics; national sources; OECD, Bank for International Settlements; and IMF staff calculations.2. The degree of sensitivity of consumption to house price developments is a subject of on-going debate in the U.K. Historically there has been a strong correlation between consumption and house price growth. However, the apparent breakdown of the correlation since the early 2000s could be interpreted as diminished sensitivity of expenditure to housing market developments (Figure 1, second panel). A possible alternative explanation is that the sharp equity market correction offset the positive effect of house price appreciation on consumption. In the second half of the 1990s, both housing and financial wealth increased rapidly, while the household savings ratio declined from above ten percent to 4–5 percent of disposable income (Figure 3). The stock market drop in the early 2000s reduced the households’ net financial wealth by an amount equivalent to one year’s disposable income. The decline in total wealth was attenuated by the steady rise in house prices. If household spending is affected by changes in both types of wealth, the puzzle of the weak correlation between housing price growth and consumption growth in recent years could potentially be resolved.
Net Household Wealth and Savings, 1987-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics and staff calculations.Net Household Wealth and Savings, 1987-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics and staff calculations.Net Household Wealth and Savings, 1987-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Source: UK Office of National Statistics and staff calculations.3. This chapter re-examines the determinants of private consumption expenditure suggested by the literature on consumer behavior. The first section reviews the theoretical case for possible effects of changes in household wealth on consumption. The following sections presents the empirical results from a standard error-correction model of consumption, estimated over the period 1987–2005. The estimation results suggest that consumption growth follows closely movements in income, with wealth also playing a role. Changes in housing wealth have a significant effect on consumption both in the short and in the long run, while changes in financial wealth affect consumer spending only gradually.
B. Theoretical Background
4. Most of the literature on consumption behavior is based on the permanent income hypothesis (PIH). The PIH implies that the flow of consumption is chosen via intertemporal optimization given expectations of permanent income, defined as the annuity value of human and non-human wealth. The recent resurgence of empirical interest in that literature is related to importance of assessing the effect of asset prices on the real economy in the context of active monetary policy. Below we review the theoretical case for a possible effect of wealth changes on consumption, and discuss if the impact depends on the type of wealth.12
5. The first channel through which asset prices may affect consumption is the traditional wealth channel. It follows directly from the permanent income hypothesis – an unexpected rise in asset prices increases the wealth of households and their current spending. While this effect is unambiguous in the case of financial asset prices, for housing the case is less clear, since a rise in prices also increases the cost of future housing services (assuming rents move in tandem with house prices). The positive wealth effect for most homeowners could be at least partially offset by negative wealth effects for those that are “short” the housing asset – renters and people intending to buy a larger house. The net effect would depend, among other things, on the share of owner-occupied housing, the age of the population, and the extent to which actual rents move in line with house prices.
6. Second, increases in asset prices expand the collateral available to liquidity constrained households. Mortgage equity withdrawal is a relatively inexpensive source of funds that can be used to boost consumption. The growth of uncollateralized lending also tends to be correlated with asset price cycles. There is strong evidence for the existence of a collateral effect both theoretically and empirically.13 Generally, changes in house prices are expected to have greater influence on consumption than changes in financial assets through this channel. Housing is a widely held asset, while the distribution of financial wealth is heavily skewed toward households in the upper tail of the income distribution, which are less likely to be liquidity constrained. In addition, financial asset prices are more volatile than house prices, therefore shocks to financial wealth are more likely to be perceived as temporary and may not affect borrowing and consumption in the short run. With continuing financial innovation, however, the number of liquidity constrained households may be declining, which could have reduced the strength of the collateral effect over time.
7. Indeed, credit-financed consumption tends to be correlated with asset prices (Figure 4). Aggregate durable goods expenditure, housing prices, and credit growth are highly correlated. The comovement between non-durables consumption and housing prices is much less pronounced, since non-durable goods purchases are less frequently financed by borrowing.
Real Consumption and House Price Annual Growth, 1983-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Real Consumption and House Price Annual Growth, 1983-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Real Consumption and House Price Annual Growth, 1983-2005
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
8. Third, changes in asset prices have an impact on consumer confidence. A sharp slowdown in asset price appreciation may create uncertainty and lead to a decline in investment and consumption. There might be additional channels – for example, Benito and Wood (2005) show that the number of housing transactions affects durables spending. Since transactions tend to be positively correlated with house price movements, the transactions effect will complement any asset price effects on consumption.
9. Finally, asset prices and consumption are affected by common shocks. The above discussion focuses on channels through which changes in asset values can affect consumption. However, asset prices and consumption are jointly determined by individual decisions and their movements will be influenced by common shocks, such as interest rate shocks or changing expectations for future income growth. While it is difficult to estimate separately the liquidity effect, the “pure wealth” effect, and the “common shocks” effect using aggregate data, one could, in principle, distinguish between them using micro data. The evidence from the micro literature is sometimes conflicting, but on balance, research tends to support the hypothesis that asset price movements affect consumption, even after accounting for common shocks.14
10. The analysis in this paper is based on the life-cycle version of the permanent income theory. Gali (1990) has extended the PIH to allow for finite individual life horizons. His model implies a linear long-run relationship between aggregate consumption (C), labor income as a proxy for human wealth (Y), and non-human wealth (see Appendix I for a sketch of the model). Since different types of wealth may have different effects on consumption, in the estimation non-human wealth has been separated into two main components – housing wealth (HW) and financial wealth (FW):
11. A standard error correction model is used in the empirical estimation.15 The above long-run relationship is estimated first, and the short-run movements in consumption growth are estimated in the second step. To keep the analysis manageable, some important temporary factors that can affect real consumption, like oil prices, are not included in the model.
C. Data Issues
12. The permanent income hypothesis applies to the flow of consumption services, which could be different from the measured total consumption expenditure. Consumption expenditure includes spending on non-durable goods, services, and durable goods. The consumption services provided by durable goods and spending on these goods are typically separate events in time. Aggregation over individual durable purchases removes part of this difference, but durables spending remains much more volatile over time than the flow of durables goods services.16 For that reason, in empirical analysis total consumption is frequently proxied by the consumption non-durables and services. That is appropriate, however, only if the share of durables in total expenditure is not changing systematically. This has not been the case in practice – since the mid-1990s, there has been a trend increase in the share of durables in real consumption, reflecting their falling relative price.
13. This study presents estimates of the consumption function using both actual consumption expenditure and a constructed flow of consumption services measure. Hamilton and Morris (2002) have constructed a flow of durable goods services measure for the U.K. by assuming a fixed life for the various categories of durable goods. The results using this measure are comparable to studies for the U.S. that typically use non-durables consumption. However, the model for the flow of consumption services can not be used for short-term growth forecasting since the actual consumer expenditure is much more procyclical and sensitive to asset movements than the smoothed flow of consumption. Therefore, estimates using total consumption expenditure are also presented and used for simulation analysis – the results from this exercise are comparable with most of the earlier consumption studies for the U.K.
14. Statistical analysis of the data is presented in Appendix II. Unit root tests for all series used in the estimation suggest that they are first difference stationary. Next, consumption, income, housing wealth, and financial wealth are tested for cointegration. The maximum eigenvalue and the trace statistics suggest the presence of one cointegrating vector for both total consumption and the flow of consumption services measure.
D. Empirical Estimation
15. A long-run cointegrating relationship between consumption and its fundamental determinants is estimated using three different methods – the dynamic least squares estimator of Stock and Watson (1993), the Johansen cointegration procedure (Johansen, 1998), and the fully modified OLS estimator (Phillips and Hansen, 1990).17 The alternative estimates produce similar long-run coefficients (Appendix II, Table A3). The cointegrating vectors based on the Johansen procedure are presented in Table 1.
Estimation Results for the Cointegrating Vector
Estimation Results for the Cointegrating Vector
| Consumption Flow | Total Consumption | |
|---|---|---|
| Income | 0.66 (0.03) | 0.85 (0.04) |
| Net housing wealth | 0.048 (0.008) | 0.072 (0.010) |
| Net financial wealth | 0.072 (0.015) | 0.075 (0.019) |
Estimation Results for the Cointegrating Vector
| Consumption Flow | Total Consumption | |
|---|---|---|
| Income | 0.66 (0.03) | 0.85 (0.04) |
| Net housing wealth | 0.048 (0.008) | 0.072 (0.010) |
| Net financial wealth | 0.072 (0.015) | 0.075 (0.019) |
16. The main determinant of household consumption in the long run is income, with wealth also playing an important role. The long-run income elasticity and the housing wealth elasticity are both higher for consumption expenditure than for the measure of consumption flow, reflecting the strong pro-cyclical behavior of durable goods expenditure and their high sensitivity to housing market developments. All coefficients are statistically significant and similar in magnitude to the results from earlier studies for the U.K. using the same methodology (Table 2). Various test for constancy of the coefficients show no evidence of instability in the estimated cointegrating relationships (see Appendix II, C).
Estimates of Total Consumption Elasticities for the U.K. from Recent Published Studies
Estimates of Total Consumption Elasticities for the U.K. from Recent Published Studies
| Y | 0.89 | 0.85 | 0.81 | 0.85 |
| HW | 0.05 | 0.10 | 0.08 | 0.07 |
| FW | 0.07 | 0.04 | 0.05 | 0.07 |
| Short run coefficient: d(HW) | 0.12 | 0.14 | 0.30 | 0.14 |
| BOE(2000) | Tzanninis (2002) | Treasury (2003) | Iakova (2006) |
Estimates of Total Consumption Elasticities for the U.K. from Recent Published Studies
| Y | 0.89 | 0.85 | 0.81 | 0.85 |
| HW | 0.05 | 0.10 | 0.08 | 0.07 |
| FW | 0.07 | 0.04 | 0.05 | 0.07 |
| Short run coefficient: d(HW) | 0.12 | 0.14 | 0.30 | 0.14 |
| BOE(2000) | Tzanninis (2002) | Treasury (2003) | Iakova (2006) |
17. The estimates suggest that the strength of the housing market has supported consumption growth in the early 2000s, despite the sharp adjustment of the equity market (Figure 5). In fact, actual consumption expenditure has exceeded the estimated long-run equilibrium level during most of the 2001-2004 period (rather than being below it as a simple comparison of house price growth and consumption growth may suggest). Currently, consumption expenditure is marginally below the estimated equilibrium consumption level.
Actual and Estimated Long Run Equilibrium Consumption
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Actual and Estimated Long Run Equilibrium Consumption
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Actual and Estimated Long Run Equilibrium Consumption
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
18. In the short run, there may be persistent deviations from the estimated long-run equilibrium due to slow adjustment or various temporary shocks that affect consumption. For example, consumers may not respond immediately to wealth shocks if they are not sure whether the shocks are temporary or permanent.18 There could be particular uncertainty in the case of financial shocks since financial asset prices tend to be very volatile.
19. The short-run dynamics of consumption are modeled in an error-correction form. The change in consumption is estimated as a function of changes in income, wealth, and the lagged residual from the long-run relationship (ECT). The change in the nominal interest rate and the lagged change in unemployment are also added to the equation.19 An increase in unemployment creates income uncertainty that can raise precautionary savings (see Benito, 2004). The nominal interest rate captures cash-flow effects and is expected to have a negative effect on consumption.20 The equation was first estimated using instrumental variables techniques (generalized method of moments) to account for the possible endogeneity of changes in consumption, income, and wealth. The set of instruments consisted of lagged changes of income and wealth and all explanatory variables, except for the contemporaneous changes of income and wealth. The Durbin-Wu-Hausman test for endogeneity was applied to compare the estimated coefficients to those from an OLS regression using the same specification.21 Since the coefficients are not statistically different and OLS is more efficient, the results from the OLS estimation are presented (Table 3).
Estimation results for Consumption Growth
Estimation results for Consumption Growth
| Consumption Flow | Total Consumption | |
|---|---|---|
| d(Net housing wealth) | 0.066 | 0.144 |
| (0.020) | (0.030) | |
| d(Income) | 0.070 | 0.181 |
| (0.033) | (0.062) | |
| d(Unemployment rate(-1) | -0.008 | -0.010 |
| (0.002) | (0.003) | |
| d(Nominal Interest Rate) | -0.003 | -0.004 |
| (0.001) | (0.002) | |
| ECT (-1) | -0.170 | -0.207 |
| (0.069) | (0.075) | |
| Constant | 0.004 | 0.003 |
| (0.001) | (0.001) | |
| Sample | 1987:3 2005:3 | 1987:3 2005:3 |
| R2-adj | 0.40 | 0.43 |
| Standard Error | 0.004 | 0.005 |
Estimation results for Consumption Growth
| Consumption Flow | Total Consumption | |
|---|---|---|
| d(Net housing wealth) | 0.066 | 0.144 |
| (0.020) | (0.030) | |
| d(Income) | 0.070 | 0.181 |
| (0.033) | (0.062) | |
| d(Unemployment rate(-1) | -0.008 | -0.010 |
| (0.002) | (0.003) | |
| d(Nominal Interest Rate) | -0.003 | -0.004 |
| (0.001) | (0.002) | |
| ECT (-1) | -0.170 | -0.207 |
| (0.069) | (0.075) | |
| Constant | 0.004 | 0.003 |
| (0.001) | (0.001) | |
| Sample | 1987:3 2005:3 | 1987:3 2005:3 |
| R2-adj | 0.40 | 0.43 |
| Standard Error | 0.004 | 0.005 |
20. The main results are the following:
The short-run income elasticity is relatively small, suggesting substantial consumption smoothing. About 85 percent of the adjustment to income shocks is completed after two years.
Consumption does not respond contemporaneously to changes in financial wealth. That probably reflects uncertainty about the temporary versus the permanent components of shocks to equity wealth.
The short-run sensitivity of consumption to changes in net housing wealth is fairly high – one percent increase in housing wealth can boost private consumption expenditure by about 0.15 percent. The housing wealth elasticity of the consumption flow measure is lower, reflecting the subdued cyclicality of the service flows relative to expenditure. The fact that the estimated short-run elasticities exceed the long-run elasticities could be interpreted as evidence of a strong liquidity channel. Relaxation of liquidity constraints allows more borrowing and stimulates current consumption. However, higher debt payments reduce future consumption.
Changes in unemployment and the nominal interest rate both have the expected negative sign. A quarter percentage point increase in unemployment is associated with a reduction of about ¼ percent in quarterly consumption growth. A twenty five basis point increase in the interest rate will reduce consumption growth by about 0.1 ercentage points. However, this coefficient does not capture the full effect of changes in the interest rates. Both wealth and income respond to interest rates and, in turn, affect consumption growth.
21. Sensitivity analysis suggests that the model is reasonably robust. Estimates of the model in per capita terms, using an interpolated measure of population growth, do not affect the results significantly. Recursive estimates of the parameter coefficients (Appendix II C, Figure A1) show that the coefficients are relatively stable when the sample increases. There is a slight decline in the coefficient on housing wealth over time, which could be consistent with the hypothesis that the strength of the collateral channel has diminished over time. To examine this further, another variable was added to the original consumption growth equation – an interaction of housing wealth growth with a dummy variable, taking a value of one until the end of 1996 and zero after that. The coefficient on that variable was positive, but not statistically significant; while the coefficient on the housing wealth variable declined to 0.11. This suggests that the housing wealth effect has remained significant throughout the period. Finally, non-linearities in the response of consumption to housing wealth growth were added to the model, but these also turned to be insignificant.
E. Dynamic Simulations
22. Dynamic simulations of the model capture well the decline in consumption expenditure over the past year. The equation for total consumption was estimated with data through the first quarter of 2004,22 and consumption growth for the following five quarters was projected out-of-sample. The forecasted growth for the first half of 2005 (solid thin line) is slightly stronger than the actual outcome, but the slowdown relative to early 2004 is evident. Based on the model, the slowdown was driven by weaker income and house price growth.
23. A counterfactual simulation was done to assess the importance of the weakening house price growth. The quarterly growth of net housing wealth over the last year was set at about 2 percent (its average value in 2003). The actual average real housing wealth growth was close to zero in that period.23 The other variables were kept at their actual values. Under this scenario, quarterly consumption growth over 2004Q4-2005Q2 would have been higher by about ¼ percentage points relative to the baseline (dotted line in the text chart above).
24. Finally, consumption growth is projected for a scenario of steady income growth and moderate housing wealth growth for the next five quarters. Real post-tax income is assumed to increase at its average quarterly growth rate over the last two years. Real net housing wealth and real net financial wealth are assumed to grow in line with income, while unemployment and the nominal interest rates are left unchanged. Under these assumptions, quarterly consumption growth is projected to be around 0.6 to 0.7 percent.
25. The simulations and the forecast should be interpreted with caution. They assume a fixed path for the explanatory variables and do not capture any feedback among the variables, which is likely to be important in practice. In addition, the forecast errors of the equation can be fairly high in the short run. This could be due to a number of factors: (i) the model does not capture various one-off shocks that can influence consumption in the short run, (ii) large movements in wealth that are perceived as unsustainable may not affect consumption significantly, and (iii) the estimated elasticities may change over time.
Actual, Forecasted, and Simulated Real Consumption Growth
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Actual, Forecasted, and Simulated Real Consumption Growth
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Actual, Forecasted, and Simulated Real Consumption Growth
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
F. Concluding Remarks
26. The empirical results from this chapter suggest that the main determinants of consumption growth are disposable income and wealth. Changes in housing wealth have a significant effect on consumption both on impact and over the following quarter, while changes in financial wealth affect consumer spending only gradually. Short-term movements in consumption also depend on interest rate changes and labor market developments. As the forecast errors at any particular juncture can be large, predictions from the model should be interpreted with caution. Looking forward, stable income growth should support a sustained pick-up in private consumption expenditure, in the absence of further negative shocks from the housing market and oil prices.
APPENDIX I The Standard Life-Cycle Consumption Model
The representative agent in the model (born at time s) maximizes the expected present discounted value of utility at time t:
max
subject to
where the first equation is the budget constraint and the second is the transversality condition; C is consumption, W is non-human wealth, and YL is labor income, β is the discount rate, and r is the rate of return on wealth.
Assuming quadratic utility and a constant interest rate equal to the discount rate, Gali (1990) shows that the solution to the optimization problem of the individual consumer, aggregated over all consumers alive at time t, gives the following expression for total consumption:
where the error term is the present discounted value of expected future increases in disposable income (in deviations from the mean expected growth rate). For a more detailed exposition of the model, see Gali (1990).
APPENDIX II
A. Data
The following data (in log levels) were used in the analysis:
Consumption (C): Final consumption of households and non-profit institutions serving households (NPISH) in 2002 prices, seasonally adjusted.
Consumption Flow (C_FS): The estimated flow of consumption services from durable and semi-durable goods plus consumption of non-durable goods and services (households only). Deflated by the household consumption deflator, seasonally adjusted.
Income (Y): Total post-tax household income, deflated by the respective consumption deflator, seasonally adjusted.
Net housing wealth (HW): Residential, commercial, industrial and other buildings assets of households and NPISH minus household debt secured on dwellings by banks, building societies and others; deflated by the respective consumption deflator and seasonally adjusted. Residential assets data are available only at an annual frequency – the quarterly figures have been obtained by interpolating the annual data using the ODPM house price index data to revalue the existing stock, and flow data on private sector new dwellings investment. The data on quarterly housing wealth through the end of 2004 has been kindly proved by NIESR and extended by staff for the first three quarters of 2005.
Net financial wealth (FW): The difference between the total financial assets of households and household unsecured debt; deflated by the respective consumption deflator and seasonally adjusted.
Interest Rate (IR): The implied nominal interest rate on total household debt (in percent).
Unemployment Rate (U): Unemployment rate (in percent), International Labor Organization, seasonally adjusted.
House price indexes from Halifax, Nationwide and the Office of the Deputy Prime Minister (ODPM).
B. Unit Root Test and Cointegration Analysis
Augmented Dickey-Fuller tests for non-stationarity of the variables (in log levels) were carried out to determine the order of integration. All variables are found to be stationary in first differences.
Unit Root Tests, 1987:1-2005:3
Unit Root Tests, 1987:1-2005:3
| Variable | Test Specification | Additional Regressors | ADF t-stat |
|---|---|---|---|
| Real Consumption Expenditure | Levels | Constant and trend | -1.049 |
| First Differences | Constant | -3.708 ** | |
| Real Consumption Flow | Levels | Constant and trend | -1.871 |
| First Differences | Constant | -3.918 ** | |
| Real Income | Levels | Constant and trend | -2.647 |
| First Differences | Constant | -12.902 ** | |
| Real Housing Wealth | Levels | Constant and trend | -1.202 |
| First Differences | Constant | -2.427 | |
| Real Financial Wealth | Levels | Constant and trend | -1.741 |
| First Differences | Constant | -8.659 ** | |
| Unemployment | Levels | Constant | -1.933 |
| First Differences | Constant | -2.736 * | |
| Nominal Interest Rate | Levels | Constant and trend | -2.982 |
| First Differences | Constant | -4.258 ** |
Unit Root Tests, 1987:1-2005:3
| Variable | Test Specification | Additional Regressors | ADF t-stat |
|---|---|---|---|
| Real Consumption Expenditure | Levels | Constant and trend | -1.049 |
| First Differences | Constant | -3.708 ** | |
| Real Consumption Flow | Levels | Constant and trend | -1.871 |
| First Differences | Constant | -3.918 ** | |
| Real Income | Levels | Constant and trend | -2.647 |
| First Differences | Constant | -12.902 ** | |
| Real Housing Wealth | Levels | Constant and trend | -1.202 |
| First Differences | Constant | -2.427 | |
| Real Financial Wealth | Levels | Constant and trend | -1.741 |
| First Differences | Constant | -8.659 ** | |
| Unemployment | Levels | Constant | -1.933 |
| First Differences | Constant | -2.736 * | |
| Nominal Interest Rate | Levels | Constant and trend | -2.982 |
| First Differences | Constant | -4.258 ** |
The Johansen procedure was used to test for cointegration of consumption, income, housing wealth, and financial wealth. The lag length of the VAR system used to perform cointegration analysis was selected based on the following criteria:
The trace and the maximum eigenvalue statistic suggest one cointegrating relationship for both total consumption expenditure and the estimated flow of consumption services. T Normalizing the coefficients on consumption to one, the estimated long-run coefficients, based on three different estimators are presented in Table A3.24 The number of lags for the Johansen estimator are set at 2 based on the criteria in Table A2. The Stock and Watson dynamic OLS regression includes the levels of income and wealth, and leads and lags of their first differences. The number of leads and lags is chosen based on the Akaike Information Criterion (which indicates two lags).
Lag Order Selection Criteria
indicates lag order selected by the criterion
Lag Order Selection Criteria
| Lag | FPE | AIC | SC | LR | ||||
|---|---|---|---|---|---|---|---|---|
| 0 | 1.3E-09 | -9.1 | -9.0 | NA | ||||
| 1 | 3.1E-15 | -22.0 | -21.4 | * | 857.9 | |||
| 2 | 2.8E-15 | * | -22.2 | * | -21.0 | 34.9 | * | |
| 3 | 3.2E-15 | -22.1 | -20.4 | 19.4 |
indicates lag order selected by the criterion
Lag Order Selection Criteria
| Lag | FPE | AIC | SC | LR | ||||
|---|---|---|---|---|---|---|---|---|
| 0 | 1.3E-09 | -9.1 | -9.0 | NA | ||||
| 1 | 3.1E-15 | -22.0 | -21.4 | * | 857.9 | |||
| 2 | 2.8E-15 | * | -22.2 | * | -21.0 | 34.9 | * | |
| 3 | 3.2E-15 | -22.1 | -20.4 | 19.4 |
indicates lag order selected by the criterion
Estimates of the Coefficients of the Cointegrating Vector
Estimates of the Coefficients of the Cointegrating Vector
| Total Private Consumption Expenditure | |||
|---|---|---|---|
| Income | Housing Wealth | Financial Wealth | |
| Johansen (1988) | 0.85 | 0.07 | 0.07 |
| Stock and Watson (1993) DOLS | 0.80 | 0.09 | 0.09 |
| Philips and Hansen (1990) FMLS | 0.80 | 0.09 | 0.09 |
| Private Consumption Flow | |||
| Income | Housing Wealth | Financial Wealth | |
| Johansen | 0.66 | 0.05 | 0.07 |
| Stock and Watson DOLS | 0.67 | 0.04 | 0.06 |
| Philips and Hansen FMLS | 0.72 | 0.03 | 0.05 |
Estimates of the Coefficients of the Cointegrating Vector
| Total Private Consumption Expenditure | |||
|---|---|---|---|
| Income | Housing Wealth | Financial Wealth | |
| Johansen (1988) | 0.85 | 0.07 | 0.07 |
| Stock and Watson (1993) DOLS | 0.80 | 0.09 | 0.09 |
| Philips and Hansen (1990) FMLS | 0.80 | 0.09 | 0.09 |
| Private Consumption Flow | |||
| Income | Housing Wealth | Financial Wealth | |
| Johansen | 0.66 | 0.05 | 0.07 |
| Stock and Watson DOLS | 0.67 | 0.04 | 0.06 |
| Philips and Hansen FMLS | 0.72 | 0.03 | 0.05 |
Cointegration Rank Test
(Total Private Consumption)
denotes rejection of the hypothesis at 10% level.
Cointegration Rank Test
(Consumption Flow)
denotes rejection of the hypothesis at 10% level.
C. Model Stability
Examining the stability of cointegrating vectors is a difficult issue. The longest sample available should be used to estimate a truly “long run relationship,” and the sample that we use is already fairly short. Nonetheless, the results from Hansen (1992) tests for parameter instability show no indication of structural break in the estimated relationships (Table A4).
Tests for Parameter Stability
Tests for Parameter Stability
| Cointegrating Vector | ||
|---|---|---|
| Test | c, y, hw, fw | c_fs, y, hw, fw |
| SupF | 10.75 (>0.20) | 8.23 (>0.20) |
| MeanF | 4.12 (>0.20) | 2.71 (>0.20) |
| Lc | 0.14 (>0.20) | 0.13 (>0.20) |
Tests for Parameter Stability
| Cointegrating Vector | ||
|---|---|---|
| Test | c, y, hw, fw | c_fs, y, hw, fw |
| SupF | 10.75 (>0.20) | 8.23 (>0.20) |
| MeanF | 4.12 (>0.20) | 2.71 (>0.20) |
| Lc | 0.14 (>0.20) | 0.13 (>0.20) |
These three tests have been developed specifically for regressions with I(1) processes and all share the null hypothesis of no parameter instability. They differ in the choice of an alternative hypothesis. The first test tries to identify a structural break with unknown timing (typically used to indicate a possible shift in the regime). The second and third tests model the cointegrating vector as a martingale process and are typically used to check whether the specification captures a stable relationship, or one Note: p-values are in parenthesis. that is slowly changing over time. Hansen notes that the lack of cointegration is a special case of the alternative hypothesis considered, so these tests can also be viewed as testing the hypothesis of cointegration (the null) versus to cointegration. All test statistics (shown above) suggest that it is not possible to reject the null of a stable relationship against a number of alternatives that represent various forms of instability.
The recursive residuals from the second stage equation for consumption growth are shown to the right (these correspond to the one-period ahead forecast errors from the equation estimated over increasing subsamples of the data). Points outside the standard error bands are either outliers or indicate possible coefficient changes. Ignoring the beginning of the sample (where only a few observations are used for the estimation), the equation performs least well in the years around 2000, when the peak and burst of the equity price bubble occurred. It is worth noting that the forecast error can be fairly high at times (compared to the average consumption growth rate), so forecasts based on the equation should be treated with caution. Diagnostic tests of the residuals show that the hypotheses of no serial correlation, homoscedasticity, and normal distribution can not be rejected.
Finally, the estimated coefficients from the short-run model for increasing subsamples of the data are shown below.
Recursive Paramenter Estimates
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Recursive Paramenter Estimates
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
Recursive Paramenter Estimates
Citation: IMF Staff Country Reports 2006, 087; 10.5089/9781451814309.002.A002
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Prepared by Dora Iakova.
The focus of this paper is on consumption, even though investment can be influenced by changes in asset prices as well.
See, for example, Aoki et al. (2001) and references therein; and the financial accelerator literature pioneered by Bernanke and Gertler.
See Campbell and Cocco (2005) for evidence for the U.K. and Bostic et al. (2005) for evidence for the U.S. Attanasio et al. (2005) support only the common causality hypothesis.
The model is similar to that used by the HM Treasury (2003), Tzanninis (2002), and the Bank of England (2000).
See Hamilton and Morris (2002) for empirical evidence for the UK, and Caballero (1994) for a theoretical discussion.
All three procedures provide consistent and asymptotically efficient estimates of the long-run coefficients, accounting for the endogeneity of variables and for the serial correlation of the residuals (see Hamilton (1994)).
An interesting recent strand of the wealth literature, following Lettau and Ludvigson (2004), decomposes the unobservable shocks to the consumption system into their permanent and transitory components (see Blake et al. (2003), for the UK). A typical finding is that consumption responds only to permanent shocks, and transitory shocks account for a significant share of the variations in total wealth (especially financial wealth). Unfortunately, the framework is not suitable for forecasting purposes due to the unobservable nature of the constructed shocks. In addition, Koop et al. (2005) shed doubt on the results from this literature with their finding that the magnitude of the role of permanent shocks is difficult to estimate precisely.
These two variables were first regressed on all the other explanatory variables to test for orthogonality. This preliminary analysis confirmed that the nominal interest rate is unrelated to the original regressors. For changes in the unemployment rate, the regression had some explanatory power. Including the residual from this first stage regression in the consumption equation instead of the actual unemployment change did not affect the results significantly, so the latter results are presented.
The Bank of England short-run equation also includes the nominal interest rate in the consumption growth equation.
See Baum et al. (2002) for a description of the test.
The coefficient estimates are practically the same as for the whole sample.
Note that flat net real housing wealth is not equivalent to zero growth in housing prices, since consumer inflation is positive and secured debt is rising.
The theoretically appropriate measure of income that should be used is labor income. Several measures of labor income were constructed and the results were very sensitive to the measure used and the period of estimation, so total disposable income was used instead, in line with most existing studies.
