Abstract
This Selected Issues paper on Hungary presents an empirical analysis of the leading indicators for inflation and models the determinants of inflation. It summarizes current knowledge about the behavior of inflation and thus underpins the subsequent discussion of possible changes to the current nominal anchor framework. The paper analyzes the growth potential and fiscal issues affecting that potential, and the external constraint. The paper suggests that some relatively stable econometric relationships can be found, despite the considerable structural and policy changes that occurred during the 1990s.
III. Wage–Price Dynamics in Hungary12
A. Introduction
52. The dynamics of wage and price adjustment are of interest to analyze alternative disinflation strategies. The magnitude and timing of nominal exchange rate effects on inflation, the flexibility of wages with respect to unemployment, and the degree of nominal inertia in wage growth, are among the key factors shaping the size and timing of real exchange rate responses to disinflation. To investigate these issues, this chapter presents a model of Hungarian inflation based on the theoretical structure for wage and price setting of Layard, Nickell, and Jackman (1991).13 Variants on such models are commonly used, including the supply–side of the OECD’s INTERLINK model (Turner et al, 1996). Section B outlines the long–run model specification, section C covers the estimation technique and results, while section D discusses system properties. Given the short sample available, and the extent of structural change in goods and labor markets in Hungary, the results reported are preliminary. Section E concludes by discussing potential extensions to this research.
B. Model Specification
53. The system has three equations, a wage equation based on bargaining theory, a consumer price equation being a mark–up over marginal costs and tradable goods prices, and an equation linking domestic producer prices to foreign prices, as Hungary is a small open economy. The model embodies the Balassa–Samuelson effect, as real wages reflect aggregate labor productivity growth, and if this exceeds productivity growth in the nontraded goods sector, inflation in nontraded goods prices will exceed that in traded goods, producing a real appreciation on a CPI basis.
Consumer prices
54. The price of regulated goods has risen sharply in real terms, primarily to bring domestic energy prices in line with production costs, contributing substantially to inflation measured by the official CPI. Therefore, a core measure of the CPI is modeled, excluding regulated goods and also seasonal foods. This core CPI depends on the domestic currency price of tradable consumer goods, and on the price of nontradable consumer goods that are set as a mark–up (that may be demand sensitive) over marginal costs in the non–traded goods sector, or in logs:
| where: | pc = Hungarian core CPI |
| pct* = foreign price of tradable consumer goods | |
| e = exchange rate (price of foreign currency) | |
| oil = crude oil price, and other commodities if relevant | |
| d = demand indicator (nontrending) | |
| mcn = marginal cost in nontradable sector |
| where: | pc = Hungarian core CPI |
| pct* = foreign price of tradable consumer goods | |
| e = exchange rate (price of foreign currency) | |
| oil = crude oil price, and other commodities if relevant | |
| d = demand indicator (nontrending) | |
| mcn = marginal cost in nontradable sector |
55. The restriction on the marginal cost coefficient of (1) ensures long–run nominal homogeneity in the levels of prices and costs.14 Martin (1997) shows that with a CES production function (elasticity of substitution a) that marginal cost is given by:
| where: | wn = gross average wage in nontraded goods sector |
| lpn = labor productivity in nontraded goods sector |
| where: | wn = gross average wage in nontraded goods sector |
| lpn = labor productivity in nontraded goods sector |
In the Cobb–Douglas case where σ=1, marginal cost equals unit labor costs, but otherwise the coefficient on wages and labor productivity need not be equal.
Producer prices
56. The PPI includes the prices of pre–dominantly traded goods, but also includes the domestic price of energy. Administered price hikes each January have aimed to bring Hungarian energy prices in line with world prices over time. The specification for producer prices must therefore include dummy variables for this impact in addition to the domestic currency price of foreign producer goods and commodities:
| where: | ppi = Hungarian PPI |
| ppi* = foreign price of producer goods |
| where: | ppi = Hungarian PPI |
| ppi* = foreign price of producer goods |
Gross Wages
57. Moghadam and Wren–Lewis (1994) derive a wage equation from bargaining theory, where real consumption wages in equilibrium depend on labor productivity, payroll taxes and other components of the wedge between the real wage of employees and firms, unemployment benefits or some other indicator of the “fallback position” of employees, and labor market conditions affecting bargaining power, e.g., the unemployment rate.
| where: | w = average gross wage |
| lp = aggregate labor productivity | |
| pt = wedge between gross and net wage, due to payroll taxes | |
| reg = wedge between total and core CPI, due to regulated prices and indirect taxes | |
| ub = unemployment benefit | |
| u = unemployment rate or other labor market indicators |
| where: | w = average gross wage |
| lp = aggregate labor productivity | |
| pt = wedge between gross and net wage, due to payroll taxes | |
| reg = wedge between total and core CPI, due to regulated prices and indirect taxes | |
| ub = unemployment benefit | |
| u = unemployment rate or other labor market indicators |
58. As discussed by Greenslade et al (1998a), under the classic “right–to–manage” bargaining model, it would be expected that δ1 = 1, while δ2 = δ3 = 0, so that employees would bear the full effects of changes in these wedges in the long–run. The model makes no explicit allowance for the wage guidelines of the Interest Reconciliation Council. The rapid decentralization of wage bargaining has made these guidelines less relevant over time, and there is a technical difficulty that no guidelines were issued in 1992 and 1995.
C. Equation Estimates
59. All data are clearly nonstationary in levels, and standard tests reject a unit root in differences, though at seven years the sample span is rather short for such tests. Given the system of equations, and the nonstationarity of the data, estimation using the maximum likelihood method of Johansen (1988) appears most appropriate. However, this preliminary work estimates each equation separately, using the single–step estimation of the unrestricted ECM form of Banerjee et al (1986). Inder (1993) finds that this estimator avoids the finite sample bias that afflicts the Engle–Granger (1987) two–step procedure, and that it also gives precise estimates and valid t–statistics even in the presence of endogenous variables.
60. The core CPI equation is presented in Appendix II and Figure 4, with variable names and descriptions in Appendix I. In the long–run, the core CPI is estimated to have an elasticity of 0.70 with respect to nominal wages, a 0.22 elasticity to the foreign CPI, and a 0.08 elasticity to the price of motor fuels. The influence of wage growth on official CPI inflation will be somewhat lower, as a substantial component of regulated prices—which have a 17.3 percent weight in the CPI basket 1998—are set according to world energy prices. Note that industrial wages are used in the CPI equation. Though an estimate of the nonindustrial wage was made to proxy wages in the nontraded goods sector, Figure 5, this variable performed less well.
Core CPI Equation
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Core CPI Equation
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Core CPI Equation
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Hungary: Productivity, Wages, and Energy Prices, 1990–98
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Central Statistical Office and staff calculations.Hungary: Productivity, Wages, and Energy Prices, 1990–98
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Central Statistical Office and staff calculations.Hungary: Productivity, Wages, and Energy Prices, 1990–98
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Central Statistical Office and staff calculations.61. Labor productivity in the nontraded goods sector was initially proxied by a estimate using total GDP excluding manufacturing, Figure 5. However, perhaps due to the recorded productivity fall early in the sample, this variable did not perform as well as a simple time trend. The time trend has an annual contribution of negative 2.9 percent, well above the roughly 1 percent rate of productivity growth in the nonmanufacturing sector over 1992’H1 to 1998’H1. Further refinements to the productivity calculation, for example by excluding government output and employment, may be needed to produce a variable that better reflects productivity in relation to the goods and services that are included in the CPI.
62. The Austrian CPI was the best proxy found for tradable consumer goods in Hungary, from a search covering also German and U.S. prices. This finding implies that the exchange rate to the German mark (to which the Austrian schilling has been pegged during the 1990s) has the dominant role in consumer price determination. The U.S. dollar has a role in the equation through its impact on motor fuels prices.15 The estimated long–run effect of the motor fuels price is about 2 percent greater than its weight in the core CPI, indicating some indirect price effects. Though it was expected that international prices of agricultural products would affect the CPI, in practice indices of commodity prices were not found to be significant. The price of regulated goods, both with and without the estimated VAT contribution, was also not found to affect the core CPI in the long–run. Finally, no effect from demand was detected, which may reflect statistical problems with the retail sales data used to proxy demand.
63. Making the plausible assumption that motor fuels prices are linked to the exchange rate in the long–run, the estimated “passthrough” elasticity of the core CPI with respect to the exchange rate is 0.3, that is, other factors unchanged, a 1 percent depreciation leads to a core CPI increase of 0.3 percent. Figure 6 (top panel) shows this adjustment is rapid, being completed within 12 months, reflecting the relatively high estimated error correction coefficient.
Hungary: Wage-Price Model Simulations
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Staff calculations.Hungary: Wage-Price Model Simulations
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Staff calculations.Hungary: Wage-Price Model Simulations
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Staff calculations.64. The producer price equation is presented in Appendix III and Figure 7. In the long–run the Hungarian PPI is estimated to reflect German producer prices with an elasticity of 0.43, U.S. producer prices with an elasticity of 0.39, and crude oil prices with an elasticity of 0.18. The dummies for the January adjustment of regulated prices are negative in years when the contribution is smaller that the normal seasonal impact, which is estimated at 2.4 percent over 1992 to 1998. The exchange rate dynamics are faster than suggested by the error correction coefficient, with three–quarters of an exchange rate shock passed into the PPI within 12 months, Figure 6 (middle panel), due to the dynamic terms in the exchange rate basket and lagged PPI inflation. Therefore, nominal exchange rate shocks have only a relatively short–lived effect on the real exchange rate on a PPI basis.
65. To reflect the typically annual frequency of wage negotiations, the wage equation presented in Appendix IV and Figure 8 models the 12 month growth rate of real wages.16 The restriction that the coefficient on labor productivity be unity was accepted, with this long–run relationship evident in Figure 9. Real wages were found to be quite sensitive to the rate of unemployment, with a 1 percentage point increase in the unemployment rate estimated to have a negative 1.2 percent effect on real wages in the long–run. This corresponds to an elasticity of -0.12 at a 10 percent rate of unemployment, consistent with the -0.11 elasticity estimated by Kertesia and Kollo (1996) on cross–sectional data in 1994 and 1995. The unemployment effect is stronger in the short–run, at about negative 1.9 percent for rises in unemployment in the last 12 months. Nonlinearities in the unemployment effect were not evident when logarithmic and quadratic functional forms were evaluated.
Real Wages and Labor Productivity
(Log Scale, left and right scales differ only in intercept)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Real Wages and Labor Productivity
(Log Scale, left and right scales differ only in intercept)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Real Wages and Labor Productivity
(Log Scale, left and right scales differ only in intercept)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
66. No effect from the wedge between producer and consumer prices was detected, which may partly reflect problems in the PPI series, including the high weight of energy prices in the PPI. Similarly, no long–run effects from payroll taxes or regulated prices were found, implying that changes in these are fully borne by employees. The effect on industry wages of the unemployment benefit, the minimum wage, and public sector wages, remains to be examined.
67. This equation explains the adjustment of real rather than nominal wages, with nominal wage growth calculated by adding the recent core CPI inflation rate. Inflation surprises, as proxied by the change in the inflation rate relative to rates in the recent past, were found to have a relatively short–run effect on real wages.17 Nominal wage adjustment therefore appears to involve a degree of informal indexation for recent inflation, or in other words, a reasonably rapid catchup in nominal wages to preserve real wages. The implication is that nominal wage inflation will slow soon after a slowing in CPI inflation, which may well account for the fall in nominal wage inflation seen in the second half of 1998 despite falling unemployment and steady productivity growth. Attempts to model nominal wage growth using the standard Phillips–curve approach of backward–looking inflation expectations, including a combination of past inflation and the announced inflation targets, were not successful.
D. System Properties and Forecasting
68. Only the wage and core CPI equations are needed for the system, as the PPI was not found to affect wages as allowed for in the theoretical model. The two equation system is homogenous in the nominal exchange rate in the long–run, with Figure 6 (bottom panel) showing that wage–price adjustment to a 10 percent depreciation is virtually complete after three years. Twelve months after the depreciation the core CPI level has risen by about 5.6 percent, with the wage response adding 2.6 percent to inflation over the direct passthrough effect of the exchange rate. While the exchange rate shock initially affects the CPI more than wages, after three months wages begin to catch–up with consumer price inflation, and after 12 months wages lead the inflation.
69. The key simulation of interest is the real exchange rate impact of changes in the nominal exchange rate. For the two equation system, this is just the mirror image of the simulation reported on Figure 6 (bottom panel). With a 5.6 percent price response after 12-months, the real exchange rate on a CPI basis will have changed by only 4.4 percent, down from the initial 10 percent shock. Similarly, with nominal wages responding by 5.8 percent after 12 months, only 4.2 percentage points of the initial shock to the real exchange rate on a ULC basis will remain. However, the simulation is incomplete, as the feedback from the real exchange rate on activity and unemployment, and therefore on wages, is omitted. As a real appreciation will likely slow activity and increase unemployment, wage growth and therefore price inflation would be lower, unwinding the real appreciation. So this partial simulation likely overstates the real exchange rate effects of a change in the nominal exchange rate.
70. An initial evaluation of forecasting performance of the system is reported in Figure 10. This dynamic simulation of the core CPI and wage equations over a two–year within sample period, (using actual data for the exchange rates, labor productivity, foreign prices, and the unemployment rate) is quite accurate, with the standard deviation of errors in the annual inflation rates being 0.4 percent for the core CPI and 2.0 percent for wages in industry. However, true out–of–sample projections will also be subject to errors in projecting unemployment, energy prices, and other variables exogenous to these equations, along with potential structural changes and parameter uncertainty. While standard tests showed no evidence of structural instability, a re–estimation of the core CPI and wage equations until 1997:6 produced a higher core CPI elasticity to wages (0.775 compared to 0.701), and lower elasticities on foreign prices. The corresponding out–of–sample core CPI projections were too high by 2.6 percent after 12 months.
Dynamic Simulation of 12-month Inflation Rates
(June 1997 to June 1998)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Hungarian Central Statistical Office and staff calculations.Dynamic Simulation of 12-month Inflation Rates
(June 1997 to June 1998)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Hungarian Central Statistical Office and staff calculations.Dynamic Simulation of 12-month Inflation Rates
(June 1997 to June 1998)
Citation: IMF Staff Country Reports 1999, 027; 10.5089/9781451817843.002.A003
Source: Hungarian Central Statistical Office and staff calculations.E. Conclusions and Extensions
71. Equations for the core CPI and for the PPI were estimated, and found to have both long–run properties consistent with the theoretical models, and dynamics broadly consistent with prior beliefs. The core CPI equation reinforces the view that slowing wage inflation is the key to slowing CPI inflation, and also finds that the nominal exchange rate has a significant direct impact in the near–term.
72. In the long–run, real wages were found to have a relationship with labor productivity and unemployment consistent with theory. However, the dynamics of nominal wage adjustment showed less inertia than might have been expected from the history of nominal wage growth, see Figure 11. Taking this property at face value might suggest that an exchange-rate based disinflation faces little risk of a significant and sustained real appreciation that would undermine the trade balance. However, this conclusion could be misleading if the accompanying fall in interest rates stimulated demand, reduced unemployment, and boosted pressure on real wages. A full model is needed to draw sound policy conclusions. There is also the possibility that the apparent informal wage indexation or rapid “real–wage catch–up”, may tend to weaken at lower inflation rates, or it may function more strongly for inflation rises than inflation falls. In either case, the real exchange rate response to an exchange rate based disinflation would be larger than suggested above. Nevertheless, the standard tests of specification do not reveal problems with the wage equation, and it fits the data relatively well, suggesting that the finding of low inertia in nominal wages at least merits further investigation.
73. As mentioned, further analysis would ideally be conducted using a systems approach to estimation, perhaps using the procedures of Greenslade et al (1998b) to ensure the identification of cointegrating vectors with a structural economic interpretation, given the small data sample available in Hungary. There may be the possibility to improve data in a number of areas, including labor productivity. Data from the Labor Force Survey could be used to test for different effects from short–term and long–term unemployment. Additional variables that might be investigated include alternative measures of demand and labor market tightness, agricultural commodity prices, the unemployment benefit, the minimum wage, and public sector wages. Thorough testing of the forecasting performance of a further developed wage–price system would be needed to have adequate confidence in applying it to make inflation projections that might guide monetary policy formulation.
References
Banerjee, A., J. Dolado, D. Hendry, G. Smith (1986) “Exploring equilibrium relationships in econometrics through static models: Some Monte Carlo evidence”, Oxford Bulletin of Economics and Statistics, 48, 253–277.
de Brouwer, Gordon and Ericsson, Niel (1995), “Modeling Inflation in Australia” Research Discussion Paper 9510, Reserve Bank of Australia.
Engle, Robert and Clive Granger (1987) “Cointegration and error correction: Representation, estimation, and testing”, Econometrica, 55, 251–276.
Greenslade, Jennifer, Brian Henry, Richard Jackman (1998a) “A Dynamic Wage-Price Model for the UK”, Discussion Paper 10–98, London Business School.
Greenslade, Jennifer, Brian Henry, Richard Jackman (1998b) “On the Identification of Cointegrated Systems in Small Samples: Practical Procedures with and Application to UK Wages and Prices”, Project Link Conference, Rio de Janeiro, September.
Inder, Brett (1993) “Estimating long-run relationships in economics: A comparison of different approaches”, Journal of Econometrics, Vol. 57, 53–68.
Johansen, Soren (1988) “Statistical analysis of cointegrating vectors”, Journal of Economic Dynamics and Control, Vol. 12, 231–54.
Kertesia, Gábor and Köllô, János, 1997, “The Birth of the ‘Wage Curve’ in Hungary 1989–95,” paper presented to the Labor Markets in Transition Economies Conference, University of Michigan.
Layard, Richard, Steven Nickell and Richard Jackman (1991), Unemployment: macroeconomic performance and the labor market, Oxford University Press.
Martin, Christopher (1997) “Price Formation in and Open Economy: Theory and Evidence for the United Kingdom, 1951–1991”, Economic Journal, September.
Moghadam, Reza and Simon Wren-Lewis (1994) “Are Wages Forward Looking?”, Oxford Economic Papers, 46, 403–424.
Turner, Dave and Pete Richardson and Sylvie Rauffet (1996) “Modelling the Supply Side of the Seven Major OECD Economies”, OECD, Working Paper No. 167.
van Elkan, Rachel (1996) “Inflation Inertia in Hungary”, in Moghadam et al “Hungary—Selected Issues”, IMF Staff Country Report No. 96/109.
APPENDIX I: Variables
Note that SA denotes seasonally adjusted.
Endogenous variables:
| PCSA | Nonregulated CPI excluding fruit and vegetables (CPI items 140, 141, 142) |
| PPISA | Hungarian PPI |
| WIGSA | Monthly average gross earnings in industry (inc. payroll taxes of employee). |
| PCSA | Nonregulated CPI excluding fruit and vegetables (CPI items 140, 141, 142) |
| PPISA | Hungarian PPI |
| WIGSA | Monthly average gross earnings in industry (inc. payroll taxes of employee). |
Exogenous variables:
| PA | Austrian CPI (Harmonized CPI from 1995:1) |
| PPIG | German PPI |
| PPIUS | United States PPI |
| PMF | CPI component for motor fuels (CPI item 541) |
| OIL | Crude oil, average spot price in US$ |
| EUS | Forint per U.S. dollar, monthly average |
| EDM | Forint per DM, monthly average |
| EB | Forint per basket, 70 percent DM, 30 percent U.S. dollar |
| URSA | Official unemployment rate. |
| LPT | Trend labor productivity (GDP/Employment from Labor Force Survey). Quarterly GDP calculated by cubic–spline of annual data until 1996, then using CSO four–quarter growth rates. Quarterly data is seasonally adjusted, and monthly labor productivity is interpolated. The trend is computed using a Hodrick–Prescott filter with a smoothing parameter of 1600. |
| LPNMT | Trend labor productivity in non–manufacturing. Calculated as for LPT, but excluding NBH data on manufacturing GDP and employment from the totals. |
| SUP | Estimate of surprise in core CPI, due to the difference between inflation in the current quarter, and average inflation in the previous three quarters. SUP = ln(PCSA) -ln(PCSA)-3 - (ln(PCSA)-3 ln(PCSA)-12)/3 |
| PA | Austrian CPI (Harmonized CPI from 1995:1) |
| PPIG | German PPI |
| PPIUS | United States PPI |
| PMF | CPI component for motor fuels (CPI item 541) |
| OIL | Crude oil, average spot price in US$ |
| EUS | Forint per U.S. dollar, monthly average |
| EDM | Forint per DM, monthly average |
| EB | Forint per basket, 70 percent DM, 30 percent U.S. dollar |
| URSA | Official unemployment rate. |
| LPT | Trend labor productivity (GDP/Employment from Labor Force Survey). Quarterly GDP calculated by cubic–spline of annual data until 1996, then using CSO four–quarter growth rates. Quarterly data is seasonally adjusted, and monthly labor productivity is interpolated. The trend is computed using a Hodrick–Prescott filter with a smoothing parameter of 1600. |
| LPNMT | Trend labor productivity in non–manufacturing. Calculated as for LPT, but excluding NBH data on manufacturing GDP and employment from the totals. |
| SUP | Estimate of surprise in core CPI, due to the difference between inflation in the current quarter, and average inflation in the previous three quarters. SUP = ln(PCSA) -ln(PCSA)-3 - (ln(PCSA)-3 ln(PCSA)-12)/3 |
Dummies:
| Trend | Time trend |
| D9X:Y | Dummy equal to 1 in year 199X, month Y, 0 otherwise |
| DL9X:Y | Dummy equal to 1 until and including year 199X, month Y, 0 otherwise |
| Trend | Time trend |
| D9X:Y | Dummy equal to 1 in year 199X, month Y, 0 otherwise |
| DL9X:Y | Dummy equal to 1 until and including year 199X, month Y, 0 otherwise |
APPENDIX II: Core Equation
Dependent variable: ΔlnPCSA
Sample: 1992:1 to 1998:7, 8 variables and 79 observations
| Variable | Coefficient | Std. Error | t-value |
| ECMC-1 | -0.18642 | 0.02843 | -6.557 |
| ΔlnPCSA-3 | 0.27979 | 0.08859 | 3.158 |
| ΔlnPMF | 0.02496 | 0.01341 | 1.861 |
| DL93:3 | 0.00703 | 0.00143 | 4.931 |
| Variable | Coefficient | Std. Error | t-value |
| ECMC-1 | -0.18642 | 0.02843 | -6.557 |
| ΔlnPCSA-3 | 0.27979 | 0.08859 | 3.158 |
| ΔlnPMF | 0.02496 | 0.01341 | 1.861 |
| DL93:3 | 0.00703 | 0.00143 | 4.931 |
Error-correction term:
| ECMC = | lnPCSA- | [0.70131 lnWIGSA (15.996) | + 0.21610 * ln(PA*EDM) | |||
| + | 0.082593 lnPMF (1.967) | -0.0024465 Trend (-31.991) | - | 8.4743 ] (-21.332) | ||
| R2 = 0.553 | S.E.E.= 0.26 percent | DW=1.61 | ||||
| Normality: | Chi2(2) = 1.0493 [0.5918] | |||||
| Autocorrelation: | F(5,66) = 1.0713 [0.3843] | |||||
| Heteroskedasticity: | F(11,59) = 1.9615 [0.0492]* | |||||
| ECMC = | lnPCSA- | [0.70131 lnWIGSA (15.996) | + 0.21610 * ln(PA*EDM) | |||
| + | 0.082593 lnPMF (1.967) | -0.0024465 Trend (-31.991) | - | 8.4743 ] (-21.332) | ||
| R2 = 0.553 | S.E.E.= 0.26 percent | DW=1.61 | ||||
| Normality: | Chi2(2) = 1.0493 [0.5918] | |||||
| Autocorrelation: | F(5,66) = 1.0713 [0.3843] | |||||
| Heteroskedasticity: | F(11,59) = 1.9615 [0.0492]* | |||||
Comments on statistical properties:
The equation marginally fails the heteroskedasticity test, possibly reflecting the clustering of larger residuals earlier in the sample. Tests of stability do not detect problems once the dummy for the first 15 months of the sample is included, possibly reflecting the relative price adjustments early in the transition. The high t—statistic on the error correction coefficient rejects the null hypothesis of no cointegration at 1 percent significance, using Dickey–Fuller critical values.
APPENDIX III: Producer Price Equation
Dependent variable: ΔlnPPISA
Sample: 1992:1 to 1998:6, 12 variables and 78 observations
| Variable | Coefficient | Std. Error | t-value | |||
| ECMP-1 | -0.05845 | 0.01685 | -3.469 | |||
| ΔlnEB | 0.14588 | 0.03500 | 4.168 | |||
| Δ2 lnOIL | 0.01420 | 0.00515 | 2.755 | |||
| ΔlnPPISA-1 | 0.35349 | 0.06252 | 5.655 | |||
| D92:1 | -0.02153 | 0.00378 | -5.672 | |||
| D94:1 | -0.02171 | 0.00378 | -5.744 | |||
| D95:1 | 0.02198 | 0.00366 | 6.007 | |||
| D97:1 | 0.01138 | 0.00382 | 2.978 | |||
| D98:1 | -0.00728 | 0.00384 | -1.894 |
| Variable | Coefficient | Std. Error | t-value | |||
| ECMP-1 | -0.05845 | 0.01685 | -3.469 | |||
| ΔlnEB | 0.14588 | 0.03500 | 4.168 | |||
| Δ2 lnOIL | 0.01420 | 0.00515 | 2.755 | |||
| ΔlnPPISA-1 | 0.35349 | 0.06252 | 5.655 | |||
| D92:1 | -0.02153 | 0.00378 | -5.672 | |||
| D94:1 | -0.02171 | 0.00378 | -5.744 | |||
| D95:1 | 0.02198 | 0.00366 | 6.007 | |||
| D97:1 | 0.01138 | 0.00382 | 2.978 | |||
| D98:1 | -0.00728 | 0.00384 | -1.894 |
Error–correction term:
| ECMP = ln PPISA - | [ 0.43331 ln(PPIG*EDM) + (3.945) | 0.17860 ln(OIL*EUS) (2.727) | |
| + 0.38809*ln (PPIUS*EUS) | -4.6514 ] (-36.160) | ||
| R2 = 0.841 | S.E.E.= 0.36 percent | DW = 2.00 | |
| Normality: | Chi2(2) = 0.78361 [0.6758] | ||
| Autocorrelation: | F(5,61) = 0.08646 [0.9941] | ||
| Heteroskedasticity: | F(15,50) = 0.56113 [0.8901] | ||
| ECMP = ln PPISA - | [ 0.43331 ln(PPIG*EDM) + (3.945) | 0.17860 ln(OIL*EUS) (2.727) | |
| + 0.38809*ln (PPIUS*EUS) | -4.6514 ] (-36.160) | ||
| R2 = 0.841 | S.E.E.= 0.36 percent | DW = 2.00 | |
| Normality: | Chi2(2) = 0.78361 [0.6758] | ||
| Autocorrelation: | F(5,61) = 0.08646 [0.9941] | ||
| Heteroskedasticity: | F(15,50) = 0.56113 [0.8901] | ||
Comments on statistical properties:
No specification problems are detected. The null hypothesis of no cointegration is rejected at 5 percent significance, using Dickey–Fuller critical values for the t–statistic on the error correction coefficient. Chow–tests and recursive parameter estimates do not indicate instability.
APPENDIX IV: Gross Wage Equation
Dependent variable: Δ12 ln(WIGSA/PCSA)
Sample: 1992:1 to 1998:6, 6 variables and 78 observations
| Variable | Coefficient | Std. Error | t-value |
| ECMW-12 | -0.8521 | 0.08042 | -10.956 |
| Δ12 URSA | -1.8760 | 0.25942 | -7.231 |
| Δ12 URSA-12 | 1.2091 | 0.10201 | 11.852 |
| SUP | -0.5958 | 0.20467 | -2.911 |
| Variable | Coefficient | Std. Error | t-value |
| ECMW-12 | -0.8521 | 0.08042 | -10.956 |
| Δ12 URSA | -1.8760 | 0.25942 | -7.231 |
| Δ12 URSA-12 | 1.2091 | 0.10201 | 11.852 |
| SUP | -0.5958 | 0.20467 | -2.911 |
Error–correction term:
| ECMW = | In(WIGSA/PCSA) | -[In LPT | -1.2147 URSA (-3.444) | + 5.3260 ] (131.637) | ||
| R2 = 0.871 | S.E.E. = 1.21 percent | DW = 1.37 | ||||
| Normality: | Chi2(2) = 4.3397 [0.1142] | |||||
| Autocorrelation: | F(5,67) = 1.4898 [0.2049] | |||||
| Heteroskedasticity: | F(8,63) = 1.5785 [0.1493] | |||||
| ECMW = | In(WIGSA/PCSA) | -[In LPT | -1.2147 URSA (-3.444) | + 5.3260 ] (131.637) | ||
| R2 = 0.871 | S.E.E. = 1.21 percent | DW = 1.37 | ||||
| Normality: | Chi2(2) = 4.3397 [0.1142] | |||||
| Autocorrelation: | F(5,67) = 1.4898 [0.2049] | |||||
| Heteroskedasticity: | F(8,63) = 1.5785 [0.1493] | |||||
Comments on statistical properties:
No specification problems are detected. The null hypothesis of no–cointegration is rejected at 1 percent significance, using Dickey–Fuller critical values for the t–statistic on the error correction coefficient. Chow-tests and recursive parameter estimates do not indicate instability.
Prepared by Craig Beaumont.
van Elkan (1996) estimated an error-correction model for CPI inflation based on an empirical long-run cointegrating relationship amongst consumer prices, industry wages, the nominal effective exchange rate, and broad money. This chapter also reports estimates of error-correction models, but for a system of price and wage equations, where the long-run relationships reflect the theoretical structure outlined below. The money stock does not feature in this analysis as under a pegged exchange rate regime it is largely endogenous.
de Brouwer and Ericsson (1995) provide a full discussion of the specification and estimation of this type of equation.
The crude oil price performed poorly, possibly reflecting the substantial past divergences between domestic petroleum prices and crude oil prices, Figure 5.
An equation for monthly wage inflation had a similar long-run solution, but a lack of persistence in its dynamics meant that the implied 12-month wage inflation showed swings not seen in the actual series.
The SUP variable used is the difference between current quarter inflation and the average quarterly inflation in the previous three quarters. This formula was arrived at from a general-to-specific search on changes in the inflation rate at various frequencies. The change in the inflation rate is also used by Turner et al (1996) to estimate nominal inertia.
