United Kingdom: Selected Issues

International Monetary Fund

doi:10.5089/9781451814309.002.A001

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United Kingdom: Selected Issues

Author: International Monetary Fund

Publication Date:: 03 Mar 2006

eISBN:: 9781451814309

Language:: English

Keywords:: ISCR; CR; GDP; consumer spending; price; credit derivative; inflation outcome; policy rule; persistent inflation effect; above-target inflation; Non-energy goods price; Oil prices; Consumption; Global

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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.

Abstract

I. The Impact of Rising Energy Prices¹

In this paper, a variant of the IMF’s Global Economy Model that incorporates energy is used to examine the impact of rising energy prices on the major industrial countries (US, euro area, Japan, UK, and Canada). For all countries except Canada, permanently higher energy prices imply a permanent reduction in supply capacity. While energy price increases lead to a temporary spike in inflation proportional to the energy intensity of consumption, there are no persistent inflation effects provided (i) the monetary authority fully incorporates the negative supply-side implications into the policy setting process and (ii) labor suppliers are not able to resist the required decline in their real consumption wage. If policymakers attempt to support aggregate demand above potential supply, then second-round persistent inflation effects emerge, which are exacerbated if labor suppliers are able to temporarily resist part of the required decline in real wages.

A. Introduction

1. The rise in oil prices since the beginning of 2004 has had an important impact on the United Kingdom and other large industrial countries. Inflation, which had long been subdued, even during the high-tech boom years of the late 1990s, has accelerated in most industrial countries. GDP growth, while still healthy in most industrial countries, has slowed relative to expectation. In this paper, a variant of the IMF’s Global Economy Model (GEM) is used to estimate the contribution of rising oil prices to these developments.

2. The model incorporates energy (oil and natural gas) as a final consumption good as well as a primary input in the production process. Because energy enters the consumption basket directly, increases in energy prices quickly affect household welfare through their impact on the level of consumer prices and thus households’ real wage. 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 costs structures.

3. The analysis of the impact of permanently higher energy prices focuses on three key issues:

the likely implications for the level of economic activity;
the magnitude of the direct impact on headline inflation; and
the mechanisms through which permanently higher energy prices could lead to persistently high inflation.

4. The remainder of the paper is structured as follows. In Section B a brief, nontechnical outline of GEM is presented focusing on how energy is integrated into the model’s structure. The calibration of the model is also outlined in this section. A technical description of the incorporation of energy into GEM is presented in the Appendix. Section C presents some simulation results of a stylized permanent increase in energy prices on major industrial countries. This section also contains the simulation results for the U.K. economy of an increase in energy prices that mimics the increase that has occurred in oil prices since the beginning of 2004 using futures prices to guide the evolution about the shocks expected persistence. The implications of some alternative responses of the monetary authority and wage bargainers are also examined in this section. Some conclusions are offered in Section D.

B. The Global Economy Model – GEM

5. GEM is a large multi-country macroeconomic model derived completely from optimizing foundations. The version used here characterizes the behavior of two countries, home and foreign. The home country is alternatively calibrated to represent the major industrial economies, the United Kingdom, the Euro Area, the United States, Japan and Canada. In each case, the foreign country represents the rest of the world. The model describes the behavior of three types of agents: households; firms; and government. Below, only a brief overview of GEM is presented and the interested reader can look to Laxton and Pesenti (2003) and Hunt and Rebucci (2005) for a more detailed description of the model’s structure and properties.

Households

6. Households are infinitely lived, consume a bundle of goods, are the monopolistic suppliers of differentiated labor inputs to all domestic firms, and own the capital stock. Households exhibit habit persistence in their consumption behavior contributing to real rigidities in economic adjustment. Monopoly power in labor supply implies that the wages households receive contain a markup over the marginal rate of substitution between consumption and leisure. Because wage contracts are subject to adjustment costs, aggregate nominal rigidities arise through the wage bargaining process. Households rent the capital stock to firms in a competitive market. Capital accumulation is subject to adjustment costs that contribute to gradual economic adjustment. Capital and labor are immobile internationally and households only trade short-term nominal bonds internationally.

7. Households consume energy goods directly along with other tradable and nontradable goods. The households final consumption bundle is given by:

A = f (N, Q, M, Q_{E}, M_{E}), (1)

where A is the bundle of final goods consumed by households, N represents nontradable goods, Q represents domestically produced tradable goods, M represents imported tradable goods, Q_E represents domestically produced energy goods, and M_E represents imported energy goods. The function, f, is a constant elasticity of substitution (CES) aggregator.

Firms

8. Firms produce three types of goods: nontradable goods; non-energy tradable goods; and a tradable energy good. Goods are assumed to be differentiated giving rise to market power that enables firms to charge a markup over the marginal cost of production. Non-energy goods prices are subject to adjustment costs that along with slowly adjusting wages gives rise to the gradual adjustment of prices in response to economic disturbances.

9. Firms combine capital, labor and energy to produce the tradable and nontradable goods. The production process is given by:

Y = f (K, L, Q_{E}, M_{E}), (2)

where Y denotes the output of tradable and nontradable goods (N, Q), K is the capital input, L is the labor input, Q_E is the domestically produced energy input, and M_E is the imported energy input. The production technology, f, is assumed to be Cobb Douglas, implying unitary elasticity of substitution among factors of production. However, firms face adjustment costs in both capital and energy that reduce the short-run elasticity of substitution below unity.

10. Energy producing firms combine capital, labor and land to produce the tradable energy good. The production technology is given by:

Q_{E} = f (K, L, L a n d), (3)

where Q_E is domestically produced energy, K represents the capital input, L the labor input, and Land is the known available reserve of energy. The production technology, f, embodies constant elasticity of substitution.

Government

11. Government consumes a bundle of goods identical to that consumed by households. Government spending is financed through a non-distorting tax. The government controls the national short-term interest rate with the objective of providing a nominal anchor for the economy, which here is assumed to be the rate of CPI inflation. Figure 1 contains a simplified pictorial representation of GEM’s structure incorporating energy.

Calibration²

12. The main focus of the calibration has been to achieve two key properties in energy prices:

home and foreign energy prices moving together; and
energy prices that are considerably more volatile over the business cycle than other prices.

13. The elasticities of substitution play a central role in achieving the desired properties. The elasticity of substitution between home and foreign produced energy in both consumption and production is calibrated to be high to ensure the that home and foreign energy prices move together. The calibration of three elasticities of substitution and the importance of the fixed factor in energy production contribute to the desired cyclical volatility in oil prices. First, a relatively low elasticity of substitution between energy and non-energy tradable goods in consumption. Second, standard unitary elasticity of substitution among capital, labor and energy in non-energy goods production (Cobb Douglas) combined with costly adjustment. Third, a low elasticity of substitution among the fixed factor (Land), labor, and capital in the production of the energy good in industrial countries.³ Further, the fixed reserve of energy, Land, is assumed to be the most significant input into energy production.

14. The energy intensities, valued at producer prices, of the major industrial countries have been calibrated to match their levels as of end-2003. The energy intensities that the model has been calibrated to replicate are presented in Table 1. A number of points are worth noting. First, the United Kingdom and Canada are net exporters of energy. Second, for some countries it was necessary to make assumptions about the split between energy as a primary input into production and energy consumed directly by households because of data limitations. Third, the model has not been calibrated to replicate the exact treatment of energy taxes. Value added taxes, however, are important because they affect the transmission of energy price shocks into the CPI. Consequently, for the United Kingdom, a value added tax of 17.5 percent has been included.

Table 1.

Eenrgy Intensities of the Major Industrial Countries

Expressed as a share of nominal GDP (oil and natural gas valued at producer prices)

Source: OECD, IEA Database; and IMF staff estimates.

Table 1.

Eenrgy Intensities of the Major Industrial Countries

Expressed as a share of nominal GDP (oil and natural gas valued at producer prices)

		United Kingdom	Euro Area	United States	Canada	Japan
Production		2.23	0.16	1.50	6.80	0.02
Imports		0.71	1.60	1.26	1.22	1.38
Total available		2.94	1.76	2.76	8.02	1.40
Total use		1.94	1.76	2.72	4.05	1.40
	Input	1.15	1.02	1.23	2.23	0.70
	Consumption	0.79	0.73	1.49	1.82	0.70
Net Exports		0.29	-1.60	-1.22	2.75	-1.38

Source: OECD, IEA Database; and IMF staff estimates.

Table 1.

Eenrgy Intensities of the Major Industrial Countries

Expressed as a share of nominal GDP (oil and natural gas valued at producer prices)

		United Kingdom	Euro Area	United States	Canada	Japan
Production		2.23	0.16	1.50	6.80	0.02
Imports		0.71	1.60	1.26	1.22	1.38
Total available		2.94	1.76	2.76	8.02	1.40
Total use		1.94	1.76	2.72	4.05	1.40
	Input	1.15	1.02	1.23	2.23	0.70
	Consumption	0.79	0.73	1.49	1.82	0.70
Net Exports		0.29	-1.60	-1.22	2.75	-1.38

Source: OECD, IEA Database; and IMF staff estimates.

C. Energy Price Shocks

15. Given the complete market for energy in GEM, the price of energy is the result of the interaction of supply and demand factors. To implement an increase in the price of energy in this paper, factors on the supply side are altered. These factors could be either the markup demanded by the monopolistic suppliers of energy or the available reserve of energy (Land). Preliminary work indicates that the macroeconomic implications are independent of the factor altered. Although the shocks are technically generated by altering the supply side, the interpretation of the shock should be broader, recognizing that the outcome reflects the interaction of demand relative to supply. The increases in energy prices in the 1970s are generally interpreted to have arisen because of the actions of energy producers restricting the supply. Conversely, the increase in energy prices that has occurred recently is generally interpreted as the outcome of demand for energy increasing faster than available supply and this is how the shocks considered in this paper should be interpreted.⁴

An Illustrative Permanent Increase in the Price of Energy

16. To examine the cross-country impact of an increase in energy prices, a 50 percent permanent increase is considered. The impact on GDP and CPI inflation in the major industrial countries, at several horizons, is presented in Table 2 and the dynamic adjustment path for several key macro variables for the United Kingdom, the Euro Area and the United States are presented in Figure 2. These simulations are done assuming that monetary policy follows a standard inflation-forecast-targeting rule given by:

r s_{t} = α_{1} \cdot r s_{t - 1} + (1 - α_{1}) \cdot (r_{t}^{*} + π_{t}^{4} + α_{2} \cdot (π_{t + 4}^{4} - π^{*}) + α_{3} \cdot (y g a p_{t})), (4)

where rs_t is the short-term policy rate, $r_{t}^{*}$ is the equilibrium real interest rate, π⁴ is year-over-year CPI inflation, π^* is the target rate of inflation, ygap is the output gap, and the α_is are response coefficients. For these simulations α₁ = 0.5, α₂ = 0.5, and α₃ = 0.⁵

Table 2.

The Impact of a Permanent 50 Percent Increase in Energy Prices

Table 2.

The Impact of a Permanent 50 Percent Increase in Energy Prices

	United Kingdom	Euro Area	United States	Canada	Japan
	GDP-percent deviation from baseline
Year 1	-0.27	-1.20	-1.08	2.36	-1.09
Year 5	-0.37	-0.97	-0.99	1.55	-0.93
Steady state	-0.61	-1.49	-1.76	0.74	-1.43
	Year-over-Year CPI Inflation (percentage point deviation from baseline)
Quarter 1	0.45	0.39	0.77	0.68	0.36
Quarter 4	0.28	0.27	0.43	0.04	0.15
Quarter 8	-0.16	-0.20	-0.37	-0.11	-0.30

Table 2.

The Impact of a Permanent 50 Percent Increase in Energy Prices

	United Kingdom	Euro Area	United States	Canada	Japan
	GDP-percent deviation from baseline
Year 1	-0.27	-1.20	-1.08	2.36	-1.09
Year 5	-0.37	-0.97	-0.99	1.55	-0.93
Steady state	-0.61	-1.49	-1.76	0.74	-1.43
	Year-over-Year CPI Inflation (percentage point deviation from baseline)
Quarter 1	0.45	0.39	0.77	0.68	0.36
Quarter 4	0.28	0.27	0.43	0.04	0.15
Quarter 8	-0.16	-0.20	-0.37	-0.11	-0.30

17. The negative impact on GDP grows over time for most countries, reflecting gradual adjustment of the supply side of these economy. In Canada, the positive impact that arises because of its large net export position in energy, gradually diminishes over time as aggregate supply in the non-energy sectors adjust. The initial negative impact on GDP reflects lower consumption, lower investment, and lower net exports in net-energy-importing countries (the Euro Area, the United States, and Japan). Consumption declines because of a real decline in households’ consumer wage. Lower investment reflects the response of firms to the permanent increase in a factor cost, energy. Firms want to employ fewer of all factors of production. However, because firms face adjustment cost in capital, and energy, the adjustment to the new desired input mix occurs gradually. As the capital stock falls toward itsnew equilibrium level, real wages continue to fall, tracking the decline in the marginal productivity of labor and consumption continues to moderate according.

18. Although headline CPI inflation spikes up initially, reflecting the energy intensity of households’ consumption bundle, there are no persistent inflation effects. This benign inflation outcome occurs for two important reasons. First, the response of the monetary authority is implicitly accounting for the negative supply-side implications of the shock. The response is based on an inflation-forecast-based policy rule that incorporates the model-consistent, one-year-ahead rate of inflation. By responding to this measure of inflation, the monetary authority is not attempting to support aggregate demand at the level expected prior to the shock. Rational forward-looking households and firms fully understand the policymaker’s reaction function. Second, households accept the permanent change in relative prices and the resulting decline in their real consumption wage, which, along with the policy response, helps to ensure no second round effects.

The Actual Increase in Energy Prices Since End-2003

19. Since end-2003, oil prices have increased by roughly 100 percent. To examine the implications for the United Kingdom, an energy price increase that broadly matches that seen in oil prices over the last two years is simulated. One important feature of the recent energy price increase has been the gradual evolution of expectations regarding its persistence. Looking at futures’ market prices, it appears that at the beginning of 2004, the increase in the price of oil above the 30 dollars a barrel level was thought to be temporary. As prices accelerated throughout the year and into 2005, it appears that expectations of the price rise’s persistence increased. To capture the impact of gradually evolving expectations, the simulations that follow are built up, quarter by quarter, with an energy price shock that matches that seen in the data both in terms of its magnitude and its expected persistence. The left-hand panel in Figure 3 presents the energy price shock considered. The solid line denotes the increase in energy price that occurred over 2004 and 2005 and its expected persistence as of the fourth quarter of 2005.⁶ The dashed lines denoted the persistence of the shock in each quarter of the multi-period simulation. In each period in the simulation experiment, agents’ expectation of the shock’s persistence broadly matches the expected path for oil prices as suggested by futures market prices. The right-hand panel in Figure 3 illustrates the actual increase in oil prices and the futures’ market path.

20. The simulation is run assuming no change in nominal interest rates in the first eight quarters of the shock. Since energy prices started to rise in early 2004, there has been little change in the monetary policy rate in the United Kingdom. The tightening cycle in the Bank of England’s policy rate, prompted by domestic concerns, was complete by summer-2004. Since then, the only move in the policy rate has been a 25 basis point decline in summer-2005. Given that the endogenous policy rule used in the simulations would lead to an increase in the nominal rate as current inflation increases, the interest rate is temporarily fixed at baseline at the start of each of the iterative simulations. The final outcome is that interest rates remain at baseline for the first eight quarters. Beyond that horizon, the endogenous policy rule switches back on.

21. The simulated responses of the key macroeconomic variables in the U.K. economy to the multi-period energy price increase are presented in Figure 4. The peak effect on year-over-year CPI inflation is roughly 0.7 percentage points, which occurs in the fifth quarter. Beyond that horizon, the impact on inflation moderates. Assuming no further increases in oil price beyond the eighth quarter, the impact on year-over-year CPI inflation turns slightly negative before returning toward baseline. Because of the model’s structure, the direct impact of energy price changes are reflected immediately in the CPI. In reality, this pass-through is likely slower and, consequently, the precise quarterly dynamics should not be interpreted too literally.⁷ The initial impact of the shock on GDP is slightly positive as the increase in the real value of exports more than offsets the negative effects on investment and consumption that are quite mild due to expectations that the persistent component of the shock is small. As both energy prices and expectations of its persistence continue to rise, the negative impact on both consumption and investment grows, more than offsetting the positive impact on the energy sector and GDP falls below baseline. After eight quarters, GDP is roughly 0.2 percent below baseline. As firms adjust to the higher factor cost by reducing investment and labor demand, GDP continues to fall further below baseline, reaching -1 percent after 20 quarters and -1.2 percent in the long-run.

22. In the simulation experiment, the monetary authority’s awareness of the supply-side implications and wage bargainers’ acceptance of the required decline in their real consumption wage lead to a very benign inflation outcome. To illustrate how the energy price increase could lead to more persistent inflationary pressures, alternative responses are considered. First, if policymakers model the evolution of the supply-side of the economy as a determinist or highly persistent process, they may only gradually incorporate the supply-side implications into the policy setting process. As illustrated in Orphanides (2000), during the 1970s the real-time estimates of potential output used by the Federal Reserve appeared to considerably overestimate what is now viewed to have been the level of potential output following the first oil price shock in 1973–74. Hunt (2005) illustrates how responding to an overestimate of potential output incorporated into a standard Taylor (1993) rule could have contributed to the secondary burst of persistent inflation that followed initial spike in CPI inflation in 1974–75.

23. To illustrate this point, the simulation experiment is re-run putting a coefficient of unity on the policymaker’s estimate of the output gap in equation 4 (dotted line in Figure 5). The policymaker’s estimate of potential output only gradually incorporates the negative implications for aggregate supply of the permanent increase in a real factor cost.⁸ With monetary policy now aiming to simultaneously stabilize inflation and support aggregate demand at too high a level, a secondary burst of persistent inflation follows the initial spike in CPI inflation generated by the direct effect of higher energy prices. The magnitude and duration of this secondary acceleration in inflation will depend on the speed with which the policymaker learns about the true level of potential output. Faster learning than assumed here would reduce the secondary acceleration. It is interesting to note that nominal interest rates actually rise faster in this scenario than in the base case (solid line in Figure 5) reflecting the important role that expectations can play. Here agents in the model economy understand the policymakers’ error and expectations fuel the acceleration in inflation. Policymakers fall behind the curve resulting in real interest rates that are below those in the baseline.

24. In addition to the inflationary consequences of misperceptions about the level of potential output, the inflation outcome could deteriorate further if workers resist the required decline in their real consumption wage. To illustrate this point, a temporary increase in wage bargainers’ market power is added to the simulation (dashed line in Figure 5). This has the effect of adding some resistance to the decline in the real consumer wage. To capture the fact that this resistance would take time to materialize as workers gradually realize that the rise in energy prices is permanent, the increase in market power is phased in during the third and fourth years of the simulation. In part, this increased market power could arise because of the easier monetary conditions. In this scenario, the secondary burst of inflation roughly doubles in magnitude even though the relative increase in real wages is small. This reflects the fact that with the same view of the potential output process, the policymaker’s error about the output gap increases. This arises because, given the relatively higher real wages, firms adjust the labor input faster, moving more quickly to the long-run equilibrium level of capacity output.

25. The important interaction between labor suppliers’ response to the shock and the monetary authority’s estimate of potential output is highlighted by considering an additional scenario. In this scenario it is assumed that the monetary authority understands the structure of the economy and can compute the flexible-price solution for output. This is the outcome for GDP that would be achieved if there were no nominal rigidities in the economy. This flexible-price level of GDP is then used by the monetary authority as its estimate of potential output. This estimate is in turn used to compute the output gap appearing in the reaction function. Further, this scenario also includes the temporary increase in wage bargainers’ market power (dotted line in Figure 6). When the monetary authority fully understands the supply side of the economy, there is no secondary burst of persistent inflation even if there is a temporary increase in workers’ market power that slows the adjustment in real wages.

D. Conclusions

26. Permanent increases in energy prices can be expected to have a negative impact on the level of GDP in most of the major industrial economies. Underlying the reduction in GDP is a decline in output in the non-energy sectors as firms reduce their production capacity due to the permanent increase in a factor cost, energy. In Canada, however, the positive impact on the energy sector because of Canada’s large net export position more than offsets the negative impact on the non-energy sector. While headline inflation spikes up in proportion to the energy intensity of households final consumption bundle in each country, there are no persistent inflation effects. This favorable inflation outcome arises for two reasons. First, under the inflation-forecast-targeting policy rule, the actions of the monetary authority are based on a complete understanding of the supply-side implications of the shock. Second, labor suppliers accept the required real reduction in their final consumption wage.

27. Despite the positive impact on the energy sector in the United Kingdom, the increase in energy prices that has occurred over the last two years, if sustained, will permanently reduce the level of GDP. The simulation results suggest that, once adjustment is complete, GDP in the United Kingdom will be lower by just over 1 percentage point given the current energy intensity of production and consumption. Firms in the non-energy sector facing a permanently higher factor cost (energy) respond by producing less output by employing fewer of all the factors of production.

28. The simulation results suggest that, in the United Kingdom, the peak in the direct impact on CPI inflation of the recent run up in energy prices will be in the neighborhood of 0.7 percentage points. Although the immediate pass-through structure of the model suggests the peak in CPI inflation should have occurred after 5 quarters, which would correspond to the first quarter of 2005, actual pass-through in the U.K economy is likely to be slower. If, as assumed in the simulation, oil price do not rise any further, it may be that the peak direct effect has already occurred in U.K. headline inflation.

29. If the resulting reduction in aggregate supply is not fully internalized into the monetary policy setting process, persistent above-target inflation can emerge following the initial direct effects on headline CPI inflation. To illustrate how such an event might occur, the simulation analysis incorporated a standard Taylor-type monetary policy reaction function that included a response coefficient on the policymaker’s estimate of the output gap. If that estimate of the output gap is based on a slowly evolving view of aggregate supply, then policy will be set too loosely, fueling inflation as private agents understand the implications of the policymaker’s view.

30. A temporary increase in labor suppliers’ market power, when monetary policy is being guided by a slowly evolving estimate of aggregate supply, can greatly amplify the second round acceleration in inflation. Once wage bargainers come to believe that the increase in energy prices in permanent, they may attempt to recover a portion of the resulting decline in their real consumption wages. An environment in which monetary policy is perceived to be somewhat accommodative may encourage workers to attempt to do this. Although the resulting wage pressures do directly stimulate inflation somewhat, the largest impact comes through its effect on monetary policy. The response of firms to more quickly reduce labor utilization and its resulting implications for aggregate supply increases the magnitude of the monetary authority’s estimate of the extent of excess supply and, consequently, magnifies the excess accommodation in policy settings.

31. For policymakers, effectively communicating their assessment of the negative supply-side implications of permanent increases in energy prices is essential to avoid persistent above-target inflation. The simulations suggest that private agents’ expectations about the level of economic activity that the monetary authority views as being sustainable will have important implications for the second-round inflation effects. In addition to the direct effect that this has on inflation via expectations, it could also increase second-round effects coming through the labor market. This could arise if perceptions about the monetary authority’s preference for output stabilization encourages labor suppliers to resist the required declines in real wages given permanently higher energy prices. If workers are able to temporarily resist the required real wage declines, it is important that policymakers factor this in to their assessment of sustainable economic growth to avoid further exacerbating second-round effects.

APPENDIX Technical Presentation of Energy in GEM

Demand for Energy in Final Good

The integral of the Home final goods producing firms output at time (quarter) t is denoted A_t and can be thought of as capturing Home preferences over the range of goods available for consumption.⁹ The final good is produced with the following CES technology:

\begin{matrix} A_{t} = {{(1 - γ)}^{\frac{1}{ε}} N_{N, t}^{1 - \frac{1}{ε}} + γ^{\frac{1}{ε}} [{(1 - γ_{O A})}^{\frac{1}{ε_{O A}}} {(ν^{\frac{1}{ε_{Q M}}} Q_{t}^{1 - \frac{1}{ε_{Q M}}} + {(1 - ν)}^{\frac{1}{ε_{Q M}}} {[M_{t} (1 - Γ_{M, t})]}^{1 - \frac{1}{ε_{Q M}}})}^{(\frac{ε_{Q M}}{ε_{Q M} - 1}) (1 \frac{1}{ε_{O A}})} \\ + γ_{O A}^{\frac{1}{ε_{O A}}} {{(ν_{O}^{\frac{1}{ε_{Q M O A}}} Q_{O A, t}^{1 - \frac{1}{ε_{Q M O A}}} + {(1 - ν_{O})}^{\frac{1}{ε_{Q M O A}}} M_{O A, t}^{1 - \frac{1}{ε_{Q M O A}}})}^{(\frac{ε_{Q M O A}}{ε_{Q M O A} - 1}) (1 - \frac{1}{ε_{O A}})}]}^{(\frac{ε_{O A}}{ε_{O A} - 1}) (1 - \frac{1}{ε})}}^{(\frac{ε}{ε - 1})} & \begin{matrix} (1) \end{matrix} \end{matrix}

Three intermediate goods and two energy goods are used in the production of the final good A : a basket N_N of domestically-produced nontradables, a basket Q of domestically-produced intermediate tradable goods, a basket M of imported intermediate tradable goods, a basket Q_OA of domestically-produced energy goods and a basket M_OA of foreign-produced energy goods. The elasticity of substitution between tradable and nontradable goods is ε > 0. The elasticity of substitution between the tradable intermediate good and the tradable energy good is ε_OA > 0. The elasticity of substitution between the domestic and foreign tradable intermediate good is ε_QM > 0 and ε_QMOA > 0 is the elasticity of substitution between the domestic and foreign energy good. The parameters γ and γ_OA ∈ (0,1) are the weights on tradable goods and energy respectively in the production of the final good. The parameters v and v_O ∈ (0,1) are the weights on the domestically-produced tradable intermediate good and energy in the final good. These parameters are measures of home bias in consumption. Imports of intermediate goods are subject to adjustment cost Γ_M,t.

Taking prices as given, cost minimization in Home final good production yields the demands for tradable goods and energy as follows:

Q_{t}^{D} = γ {(1 - γ O A)}^{ν} {(\frac{P_{Q, t}}{P_{t}})}^{- ε_{Q M}} {(\frac{P_{X, t}}{P_{t}})}^{ε_{Q M} - ε_{O A}} {(\frac{P_{T, t}}{P_{t}})}^{ε_{O A} - ε} A_{t} (2)

\begin{matrix} M_{t}^{D} = γ (1 - γ_{O A}) (1 - ν) {(\frac{P_{M, t}}{P_{t}})}^{- ε_{Q M}} {(\frac{P_{X, t}}{P_{t}})}^{ε_{Q M} - ε_{O A}} {(\frac{P_{T, t}}{P_{t}})}^{ε_{O A} - ε} A_{t} \\ * \frac{{[1 - Γ_{M, t} - φ_{M} ({\frac{M_{t}}{A_{t}}}_{/}_{\frac{{M_{t - 1}}^{- 1}}{A_{t - 1}}}) ({\frac{M_{t}}{A_{t}}}_{/} \frac{M_{t - 1}}{A_{t - 1}})]}^{ε_{Q M}}}{1 - Γ_{M, t}} & (\begin{matrix} 3 \end{matrix}) \end{matrix}

Q_{O A, t}^{D} = γ γ O A^{v o} (\frac{P_{Q O A, t}}{P_{t}})^{{}^{- ε}{Q M O A}} (\frac{P_{O A, t}}{P_{t}})^{ε_{Q M O A^{- ε} O A}} (\frac{P_{T, t}}{P_{t}})^{ε_{O A^{- ε}}} A_{t}, a n d (4)

M_{O A, t}^{D} = γ γ O A (1 - v_{O}) (\frac{P_{M O A, t}}{P_{t}})^{- ε_{Q M O A}} (\frac{P_{O A, t}}{P_{t}})^{ε_{Q M O A^{{}^{- ε}{O A}}}} (\frac{P_{T, t}}{P_{t}})^{ε_{O A^{- ε}}} A_{t} (5)

Relative prices faced by the final goods firms are given by:

\frac{P_{O A, t}}{P_{t}} = (v_{o} (\frac{P_{Q O A, t}}{P_{t}})^{1 - ε_{Q M O A}} + (1 - v_{o}) (\frac{P_{M O A, t}}{P_{t}})^{1 - ε_{Q M O A}})^{\frac{1}{1 - ε_{Q M O A}}}, (6)

\frac{P_{Q O A, t}}{P_{t}} = (\frac{{\bar{P}}_{Q O A, t}}{P_{t}} + η_{O A} \frac{P_{N, T}}{P_{t}}) (1 + t a x_{O A}), (7)

\frac{P_{M O A, t}}{P_{t}} = (\frac{{\bar{P}}_{M O A, t}}{P_{t}} + η_{O A} \frac{P_{N, t}}{P_{t}}) (1 + t a x_{O A}), a n d (8)

\frac{P_{T, t}}{P_{t}} = ((1 - γ_{O A}) (\frac{P_{X, t}}{P_{t}})^{1 - ε_{O A}} + γ_{O A} (\frac{P_{O A, t}}{P_{t}})^{1 - ε_{O A}})^{\frac{1}{1 - ε_{O A}}}, (9)

where the relative prices of the home-produced, P_Q,t, and foreign-produced, P_M,t, tradable intermediate goods, and the overall relative price of the tradable intermediate good, P_X,t are as given in Laxton and Pesenti (2003). Also, $\bar{P}$ denotes the wholesale or producer price, η_OA represents the number of units of the nontradable good required to distribute a unit of the energy good to the final goods producer, and tax_OA is the rate at which the government taxes the energy good used in final goods production.

There are several important features of this structure worth noting. First, because energy enters the final good directly, energy price shocks will have an immediate impact on headline inflation. However, the presence of a distribution sector in energy, based on Corsetti and Dedola (2002),¹⁰ mutes the impact of changes in the producer price of energy on the final consumption price. In this application, these distribution services represent things like transportation and refining. The more important are these services in the final energy good, the more muted will be the impact of changes in producer prices on final energy prices. Finally, the structure allows for government to tax energy goods. The specification above implies an ad valorem tax, however, alternative formulations which lead to government tax policy muting the impact of changes in the producer price of energy can be easily implemented.

Demand for Energy in Intermediate Goods Production

The CES production technologies in the tradable, T, and nontradable, N, intermediate goods sectors are given by:

T_{t} = Z_{T, t} [(1 - α_{T} - γ_{T})^{\frac{1}{ξ_{T}}} l_{T, t}^{1 - \frac{1}{ξ_{T}}} + α_{T}^{\frac{1}{ξ_{T}}} K_{T, t}^{1 - \frac{1}{{}^{ξ}T}} + γ_{T}^{\frac{1}{ξ_{T}}} [(1 - Γ_{O T, t}) {O_{T, t}]}^{1 - \frac{1}{ξ_{T}}}]^{\frac{ξ_{T}}{ξ_{T^{- 1}}}}, a n d (10)

N_{t} = Z_{N, t} [(1 - α_{N} - γ_{N})^{\frac{1}{ξ_{N}}} l_{N, t}^{1 - \frac{1}{ξ_{N}}} + α_{N}^{\frac{1}{ξ_{N}}} K_{N, t}^{1 - \frac{1}{ξ_{N}}} + γ_{N}^{\frac{1}{ξ_{N}}} [(1 - Γ_{O N, t}) O_{N, t}]^{1 - \frac{1}{ξ_{N}}}]^{\frac{ξ_{N}}{ξ_{N^{- 1}}}}, (11)

where Z denotes the level of productivity, l the labor input, K the capital input, O the energy input, ξ the constant elasticity of input substitution, γ and α are the parameters that determine the shares of energy, and capital respectively and Γ_O is the cost of adjusting the energy input. Taking input prices as given, solving the intermediate goods firms’ cost minimization problem yields demands for the energy input given by:

Q_{O N, t}^{D} = v_{O N} (\frac{P_{Q O, t}}{P_{O N, t}})^{- ε_{O N}} O_{N, t}, (12)

Q_{O T, t}^{D} = v_{O T} (\frac{P_{Q O, t}}{P_{O T, t}})^{{- ε}_{O T}} O_{T, t}, (13)

M_{O N, t}^{D} = (1 - v_{O N}) (\frac{P_{M O, t}}{P_{O N, t}})^{{- ε}_{O N}} O_{N, t}, (14)

M_{O T, t}^{D} = (1 - v_{O T}) (\frac{P_{M O, t}}{P_{O T, t}})^{- ε_{O T}} O_{T, t}, (15)

\begin{matrix} O_{N, t} = γ_{N} {(\frac{P_{O N, t} / P_{t}}{Z_{N, t} M C_{N, t} / P_{t}})}^{- ξ_{N}} \frac{N_{t}}{Z_{N, t}} \\ * {\frac{[1 - Γ_{O T, t} - φ_{O T} (\frac{O_{T, t}}{T_{t}} / \frac{O_{T, t - 1}}{T_{t - 1}} - 1) (\frac{O_{T, t}}{T_{t}} / \frac{O_{T, t - 1}}{T_{t - 1}})]}{1 - Γ_{O T, t}}}^{ξ_{T}}, a n d & (16) \end{matrix}

\begin{matrix} O_{T, t} = γ_{T} {(\frac{P_{O T, t} / P_{t}}{Z_{T, t} M C_{T, t} / P_{t}})}^{- ξ} \frac{T_{t}}{Z_{T, t}} \\ * {\frac{[1 - Γ_{O T, t} - φ_{O T} (\frac{O_{T, t}}{T_{t}} / \frac{O_{T, t - 1}}{T_{t - 1}} - 1) (\frac{O_{T, t}}{T_{t}} / \frac{O_{T, t - 1}}{T_{t - 1}})]}{1 - Γ_{O T, t}}}^{ξ_{T}}, & (17) \end{matrix}

where the parameters v_ON and v_OT denote the degree of home bias in energy demand in the nontradable and tradable intermediate good sectors and the parameters ε_ON and ε_OT denote the elasticities of substitution between domestic and foreign energy in nontradable and tradable intermediate good sectors respectively.

The relative prices faced by the intermediate goods producers are given by:

\frac{P_{O N, t}}{P_{t}} = {(ν_{O N} {(\frac{P_{Q O, t}}{P_{t}})}^{1 - ε_{O N}} + (1 - ν_{O N}) {(\frac{P_{M O, t}}{P_{t}})}^{1 - ε_{O N}})}^{\frac{1}{1 - ε_{O N}}}, (18)

\frac{P_{O T, t}}{P_{t}} = (ν_{O T} (\frac{P_{Q O, t}}{P_{t}})^{1 - ε_{O T}} + (1 - ν_{O T}) (\frac{P_{M O, t}}{P_{t}})^{1 - ε_{O T}})^{\frac{1}{1 - ε_{O T}}}, (19)

\frac{P_{Q O, t}}{P_{t}} = (\frac{{\bar{P}}_{Q O, t}}{P_{t}} + η_{O} \frac{P_{N, t}}{P_{t}}) (1 + t a x_{O}), a n d (20)

\frac{P_{M O, t}}{P_{t}} = (\frac{{\bar{P}}_{M O, t}}{P_{t}} + η_{0} \frac{P_{N, t}}{P_{t}}) (1 + t a x_{0}), (21)

where tax_O is the rate at which the government taxes energy used as an intermediate input, and η_O represents the number of units of the nontradable good required to distribute a unit of the energy good to the intermediate goods firms.

As was the case with the final consumption price of energy, the existence of distribution services in energy used in the production of intermediate goods will mute the impact of changes in the producer price of energy on the prices paid by intermediate goods producers. There is also a role for government tax policy. The level of distribution services and government tax policy can be different in energy used in the production of intermediate goods and energy used directly in the final good. Unlike the case of energy price effects in the final good, the existence of adjustment costs in intermediate goods price setting implies that changes in the price of energy inputs will only be passed slowly into intermediate goods prices. Further, because it is costly for intermediate goods producers to adjust the quantity of energy used in production, the short-run elasticity of substitution between energy and the other two inputs, can be significantly below ξ_N and ξ_T.

Energy Production

The CES production technology for energy is given by:

T_{O, t} = Z_{O, t} [(1 - α_{O} - γ_{O})^{\frac{1}{ξ_{O}}} l_{O, t}^{1 - \frac{1}{ξ_{O}}} + α_{O}^{\frac{1}{ξ_{O}}} K_{O, t}^{1 - \frac{1}{ξ_{O}}} + γ_{O}^{\frac{1}{ξ_{O}}} L A N {D_{t}}^{1}^{-}^{\frac{1}{ξ_{O}}}]^{\frac{ξ_{O}}{ξ_{O} - 1}}, (22)

where Z_O,t denotes the level of productivity, l_O,t denotes the labor input, K_O,t denotes the capital input, LAND_t denotes the fixed factor land, γ_O and α_O are the parameters that determine the shares of land and capital respectively, and ξ_O. is the elasticity of input substitution.

Taking input prices as given, the solution to the energy producer’s cost minimization problem yields real marginal cost in energy production as:

\frac{M C_{Q O}}{P_{t}} = [{\frac{ϕ_{O} (W_{t} / P_{t})^{1 - ξ_{O}} + α_{O} (R_{t} / P_{t})^{1 - ξ_{O}} + γ_{O} (P_{L, t} / P_{t})^{1 - ξ_{O}}}{Z_{O, t}}]}^{\frac{1}{1 - ξ_{O}}}, (23)

where φ_O = (1–α_O–γ_O),W_t / P_t is the real wage, R_t / P_t is the real user cost of capital, and P_L,t / P_t is the real price of land.

In the presence of a distribution sector in energy and monopolistic competition, the producer or wholesale prices of the energy good are given by the following markups over marginal cost:

\frac{{\bar{P}}_{Q O A, t}}{P_{t}} = (\frac{1}{θ_{O} - 1}) η_{O A} \frac{P_{N, t}}{P_{t}} + (\frac{θ_{O}}{θ_{O} - 1}) \frac{M C_{Q O}}{P_{t}} (24)

\frac{{\bar{P}}_{M O A, t}}{P_{t}} = (\frac{1}{θ_{O}^{*} - 1}) η_{O A} \frac{P_{N, t}}{P, t} + (\frac{θ_{O}^{*}}{θ_{O}^{*} - 1}) \frac{M C_{Q O}^{*}}{P_{t}} (\frac{ε_{t} P_{t}^{*}}{P_{t}}), (25)

\frac{{\bar{P}}_{Q O, t}}{P_{t}} = (\frac{1}{θ_{O} - 1}) η_{O} \frac{P_{N, t}}{P_{t}} + (\frac{θ_{O}}{θ_{O} - 1}) \frac{M C_{Q O}}{P_{t}}, a n d (26)

\frac{{\bar{P}}_{M O, t}}{P_{t}} = (\frac{1}{θ_{O}^{*} - 1}) η_{O} \frac{P_{N, t}}{P_{t}} + (\frac{θ_{O}^{*}}{θ_{O} - 1}) \frac{M C_{Q O}^{*}}{P_{t}} (\frac{ε_{t} P_{t}^{*}}{P_{t}}), (27)

where ε_t is the nominal exchange rate and θ_O is the elasticity of input substitution (the lower is the elasticity of input substitution, the greater is the energy producers’ market power and the larger is the markup over marginal cost in energy prices).

Given this structure, the producer price of energy is endogenously determined in GEM. The structure can be calibrated so that the supply of energy is very inelastic and small changes in demand yield large changes in prices. Alternatively, changes on the supply side to either the quantity of land available for energy production or energy producers’ markup over marginal cost can also lead to sharp changes in energy prices.

Nontradable Good Resource Constraint

The resource constraint in the nontradable intermediate good N_t is given by:

N_{t} = N_{N, t} + η (Q_{t} + M_{t}) + η_{O} (Q_{O N, t} + Q_{P t, t} + M_{O N, t} + M_{O T, t}) + η_{O A} (Q_{O A, t} + M_{O A, t}) (28)

In addition, with imports of the intermediate input now going into the production of the final nontraded good, the equations for imports, exports, the trade balance, the current account and the exchange rate must all be modified slightly to account for this. There is also a symmetric set of equations added or modified as outlined above for the foreign sector.

References

Burstein, A., J. Neves, and S. Rebelo, 2000, “Distribution Costs and Real Exchange Rate Dynamics during Exchange Rate Based Stabilizations,” NBER Working Paper No. 7862 (Cambridge, Massachusetts: National Bureau of Economic Research).
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Corsetti, G., and L. Dedola, 2002 “Macroeconomics of International Price Discrimination,” Working Paper, University of Rome III and Bank of Italy, January.
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Hunt, B., 2005, “Oil Price Shocks: Can They Account for the Stagflation in the 1970s?” IMF Working Paper, WP/05/215.
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Hunt, B., P. Isard, and D. Laxton, 2002, “The Macroeconomic Effect of Higher Oil Prices,” National Institute Economic Review, No. 179 (January), pp. 87–103.
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Hunt, B., and A. Rebucci, 2005, “The U.S. Dollar and Trade Deficit: What Accounts for the Late 1990s?” International Finance Vol. 8, No. 3.
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Laxton, D., and P. Pesenti, 2003, “Monetary Policy Rules for Small, Open, Emerging Economies,” Journal of Monetary Economics, Vol. 50, No. 3, pp. 1109–46.
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Orphanides, A., 2000, “Activist Stabilization Policy and Inflation: The Taylor Rule in the 1970s,” Finance and Economics Discussion Paper Series No. 2000–13 (Washington: Federal Reserve Board).
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Taylor, J., 1993, “Discretion Versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, Vol. 39, (December), pp. 195–220.
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Prepared by Ben Hunt.

A more detailed discussion of the calibration of the energy structure in GEM can be found in Hunt (2005).

Cobb Douglas technology is assumed in energy production in the foreign sector.

A rapid increase in energy demand by emerging Asian economies is cited as key driver of the current rise in energy prices. This increase in energy demand by Asian economies reflects several factors and has an impact on the major industrial countries that is not captured in these simulations. Some preliminary work with GEM generating energy price increases from a variety of factors illustrates that positive spillovers can offset some of the negative impact of higher energy prices. The stronger are the industrial countries’ trading links with emerging Asia, the larger are the offsets.

GEM’s representative agent structure combined with the assumption that domestic households own all the capital stock has some important implications under energy price shocks that must be considered carefully. Households in energy producing countries receive a positive wealth shock from the increased returns in energy production when real energy prices rise. The structure of the model is such that households consume out of that wealth with their standard propensities. However, the increased returns in the energy sector are probably not widely spread and the propensity to consume out of the increase in wealth is likely much lower than average. To more accurately portray the likely impact on U.K. GDP, an additional temporary shock to household preferences is include so that in the near-term, U.K. consumption behaves similarly to consumption in the Euro Area. Although this is likely a factor in Canada as well, (and could be a factor for the U.S. because of the level of energy production there) no additional shock has been included. Consequently, the near-term positive impact on GDP in Canada is likely to be more subdued than these results suggest. This is an area that will be addressed more carefully in future work.

For the fourth quarter of 2005, the price and expectations path is matched to that available as of end-October 2005.

Because of the model’s complete choice theoretic framework, there is no scope for making ad hoc changes to the dynamic adjustment properties to more closely match the pass-through properties in the data.

Initially the policymaker’s estimate of potential output is generated putting a weight of 0.95 on the pre-shock level of output and a weight of 0.05 on the post-shock long-run level of output that is achieved once all adjustment has occurred. As the policymaker moves through time the weight on the old level of output gradually declines to zero and the weight on the new long-run level of output gradually increases to unity.

The convention throughout the model is that variables which are not explicitly indexed (to firms or households) are expressed in per-capita (average) terms. For instance, $A_{t} = {(1 / s)}_{o}^{s} A_{t} (x) d_{x}$

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United Kingdom: Selected Issues

Author: International Monetary Fund

Volume/Issue:: Volume 2006: Issue 087

Publisher:: International Monetary Fund

ISBN:: 9781451814309

ISSN:: 1934-7685

Pages:: 138

DOI:: https://doi.org/10.5089/9781451814309.002

Keywords
I. The Impact of Rising Energy Prices1
References

View raw image

Simplified GEM Structure

View raw image

A Fifty Percent Permanent Increase in Energy Prices

(percent or percentage point deviation from baseline)

View raw image

Energy Prices - Simulation and Data

Solid Line - represents actual path and expected path beyond quarter 8.

Dashed Line - represents expected path at each quarter prior to quarter 8.

View raw image

An Energy Price Increase Matching Recent History

(percent or percentage point deviation from baseline)

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Alternative Responses of Monetary Authority and Labor Suppliers

(percent or percentage point deviation from baseline)

View raw image

Responding to the Flexible-Price Output Gap

(percent or percentage point deviation from baseline)

Table 2.

The Impact of a Permanent 50 Percent Increase in Energy Prices

	United Kingdom	Euro Area	United States	Canada	Japan
	GDP-percent deviation from baseline
Year 1	-0.27	-1.20	-1.08	2.36	-1.09
Year 5	-0.37	-0.97	-0.99	1.55	-0.93
Steady state	-0.61	-1.49	-1.76	0.74	-1.43
	Year-over-Year CPI Inflation (percentage point deviation from baseline)
Quarter 1	0.45	0.39	0.77	0.68	0.36
Quarter 4	0.28	0.27	0.43	0.04	0.15
Quarter 8	-0.16	-0.20	-0.37	-0.11	-0.30

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Abstract

I. The Impact of Rising Energy Prices1

A. Introduction

B. The Global Economy Model – GEM

Households

Firms

Government

Calibration2

C. Energy Price Shocks

An Illustrative Permanent Increase in the Price of Energy

The Actual Increase in Energy Prices Since End-2003

D. Conclusions

APPENDIX Technical Presentation of Energy in GEM

Demand for Energy in Final Good

Demand for Energy in Intermediate Goods Production

Energy Production

Nontradable Good Resource Constraint

References

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Inter-American Development Bank

International Labour Organization

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I. The Impact of Rising Energy Prices¹

Calibration²