This Selected Issues paper describes a variety of methodologies for estimating a country’s potential output level and presents empirical estimates for Sweden. The paper explains why these methods produce a variety of results, some of which are more plausible than others. The paper looks more closely at one aspect of growth in potential output: how it has been affected by the structural policy improvements of the past several years. The paper examines the pattern of output and unemployment over time to separate permanent changes from cyclical and other temporary changes.


This Selected Issues paper describes a variety of methodologies for estimating a country’s potential output level and presents empirical estimates for Sweden. The paper explains why these methods produce a variety of results, some of which are more plausible than others. The paper looks more closely at one aspect of growth in potential output: how it has been affected by the structural policy improvements of the past several years. The paper examines the pattern of output and unemployment over time to separate permanent changes from cyclical and other temporary changes.

II. productivity growth in Sweden: has there been a recent structural change?9

A. Introduction

1. In recent years there has been considerable debate on whether productivity growth in Sweden has begun to return to the levels experienced before the 1970s. Over the 1970-93 period, Swedish labor productivity growth (1.37 percent per annum) was considerably below the average among OECD countries (1.73 percent), and this led to a fall in rank from third place to seventeenth among the richest OECD countries in terms of PPP adjusted GDP per capita.10 While a number of research papers have charted the steady decline in Swedish performance over this period, disagreement remains about the nature of the underlying factors behind the decline. In particular, although many argue that the rapid rise in the government sector and the attendant increase in taxes were the major culprits in the relative decline in total factor productivity, small changes to other controlling factors can have significant effects on the results (see in particular Agell, 1998).

2. Rather than entering into this debate directly, the objective of this paper is more modest in considering whether a structural shift has occurred to productivity growth in Sweden in the 1990s in response to the improved government finances, increased central bank independence, and EU accession. The main focus of the paper is, therefore, to identify proper cyclical variables that can eliminate cyclical movements in productivity and allow proper inference on whether the long-term productivity performance of Sweden has improved. Section B of the paper discusses the standard measure of total factor productivity (TFP) in a Swedish context, section C presents a discussion of the variables chosen to control for cyclical movements in TFP, section D tests whether a structural change has occurred to Swedish TFP during the 1990s and section E presents an estimate of potential output growth based on the TFP estimates obtained in this paper.

B. Estimates of Total Factor Productivity

3. The standard way of measuring total factor productivity is to assume two factor inputs, labor and capital, and constant returns to scale technology. Under these conditions TFP growth is represented as follows:


where Y is real GDP, H is total hours worked, K is the gross real capital stock and the coefficient a is the average labor share over a particular historical period.

4. In this analysis, we propose using government expenditure variables as determinants of changes in total factor productivity in line with the current literature in this area (see below). In order to minimize potential endogeneity problems between TFP growth and government expenditure, we shall focus on TFP growth in the private sector in this paper. Total TFP growth will be determined as the weighted sum of the private and public components. In Sweden, total factor productivity growth in the public sector has averaged about zero over the period 1971-1998, although it has picked up over the recent period (Figure 1, Chart 1). The working assumption in this paper is that future TFP growth in the public sector will be zero.11

Figure II-1.
Figure II-1.

Sweden: Total Factor Productivity Growth and Growth in Factor Inputs

Citation: IMF Staff Country Reports 1999, 115; 10.5089/9781451835922.002.A002

Source: Statistics Sweden; and staff estimates.

5. TFP growth in the private sector is defined according to equation (1) with Y representing real GDP in the private sector measured in 1991 prices, H is total hours worked in the private sector, K is the gross real capital stock in the private sector and the coefficient a is the average labor share over the 1970-98 period. Since data on the real capital stock are currently available only through 1995, estimates through 1998 were obtained using the following formula and assuming that depreciation was constant in relation to the capital stock at the average level over the 1991–94 period.


where I is gross investment in period t and lambda is the average depreciation rate over the 1991–94 period.

6. Figure 1, Chart 2 presents the calculated TFP growth rate in the private sector and the aggregate GDP growth rate over the 1970–98 period. This chart reveals the large cycles in TFP growth with peaks in 1973, 1979, 1984 and 1995, all coinciding with peaks in output growth. Until the mid–1980s, labor and capital were not very sensitive to the cycle, and movements in TFP growth over this period can generally be explained by the pattern of output growth (Figure 1, Chart 3). However, since the mid–1980s, working hours in the private sector have become much more responsive to the cycle, rising rapidly in the late 1980s in response to the boom in domestic demand and falling during the severe recession of the early 1990s.

7. To explain the movements in TFP growth, particularly over the 1970–85 period, it is useful to briefly describe the movements in real GDP. The peak in productivity growth in 1973 was associated with the strong competitive position of firms with moderate wage increases during the early 1970s facilitating strong investment and production. However, in the mid-1970s, significant wage increases were triggered by imported price increases in connection with world-wide inflation and by increases in payroll taxes. As a result, the growth of product real wages far outpaced the growth of labor productivity leading to a loss of competitiveness and export market shares. A number of discretionary exchange rate devaluations were undertaken to restore competitiveness (1976, 1977,1981,1982), and nominal wage increases returned to levels experienced prior to the mid-1970s. Following the 1982 devaluation, the government obtained a tacit understanding from the labor unions that they would accept the pending real wage losses without claiming compensation. This agreement improved the business environment leading to sizeable production and productivity increases in the mid-1980s.

8. In the late 1980s, the terms of trade improved considerably for Sweden as a result of the oil price decline and the surge in world market prices for paper and pulp, and this improvement led to strong net export growth which spilled over into domestic demand. This stimulus was amplified by easier access to credit following the financial deregulation of the mid-1980s and by rising wealth attributable to higher asset prices. However, the tightening of monetary policy and the extensive tax reform during 1990–91 raised real after tax lending rates to historically high levels and contributed to the sharp drop in property and bank share prices. In response, households began to consolidate their financial positions by cutting back on consumption, and businesses became less favorable toward new investment. These events led to the sharp recession of 1991–93. Since then, output has recovered strongly, associated with the positive effects on net exports of the large exchange rate depreciation of 1992 and more recently, the improving sentiment in the household sector.

9. Since 1993, Sweden’s total productivity growth has averaged about 2 percent per annum. However, this is not an appropriate estimate of structural productivity because productivity is usually very strong during the early stages of an upturn with firms reluctant to rehire until clear evidence of the upswing is visible. Therefore in order to properly evaluate whether a structural improvement has taken place in recent years, it is necessary to control for the cycle.

C. Cyclical Controls

10. Macroeconomists have struggled with the issue of separating trend from cycle for a long time and still have not developed a clear consensus on the issue. A popular way of constructing the trend is by fitting a piecewise linear spline through the logarithm of GDP in years with similar levels of unemployment. The rapid increase in unemployment since the late 1980s precludes adopting this method for Sweden, An alternative view of output movements is that all fluctuations are the results of the dynamic effects of permanent shocks, so that actual and trend outputs are equivalent. In this case, movements in GDP result from the accumulation of shocks, each of which is on average positive, and has large permanent effects on output. Under these conditions, there is no sense in which recessions or expansions are temporary, or that cyclical fluctuations can be defined.

11. This paper assumes that cycles occur in economic activity and tries to find variables that are sensitive to the cycle and are projected to have only temporary effects on productivity. In identifying such variables the paper takes its cue from the literature on leading indicators, that identifies stock prices, the money supply, and the term structure of interest rates as variables that lead the cycle (see “Lahiri and Moore, 1991” and “Estrella, 1998” for a detailed discussion of these variables). This paper also considers coincident variables such as the unemployment rate because it is less interested in leading indicators than in variables that comove with output. However, it is recognized that including contemporaneous variables makes the analysis subject to problems of simultaneity.

12. In terms of the hypothesized effects of the cyclically-sensitive variables on TFP growth, an increase in the spread between the long-term and short-term interest rates would be expected to put upward pressure on the economy leading to an increase in output and TFP growth.12 However, as output responds, the interest rate spread would also be expected to decline. Increases in the money supply and in the stock price index would normally imply future increases in output and productivity. Finally, because output adjustment is more rapid than the adjustment of labor input early and late in the cycle, an increase in the unemployment rate would tend to be negatively correlated with total factor productivity growth. However, this effect comes from the unemployment rate responding to changes in TFP growth so that the assumption of exogenous regressors is questionable in this case: there appears to be causality both ways between the unemployment rate and TFP growth.

13. During the recession of the early 1990s, total hours worked in the private sector fell by a cumulative 12 percent. Moreover, in contrast to the experience during a similar recession in the early 1970s, hours worked in the public sector did not adjust to compensate for the significant reduction in hours worked in the private sector. As a result, the aggregate unemployment rate shot up dramatically, leading a number of commentators to argue that a structural shift had taken place in the unemployment rate (Figure 2, Chart 2). This paper does not address the magnitude of this structural shift, but rather nets out contemporaneous effects by regressing the unemployment rate on time dummies for the period 1991-93 and constructs a variable that excludes these effects.13 This was also done for the ratio of government expenditures to GDP (to be discussed later in the paper).

Figure II-2.
Figure II-2.

Sweden: Cyclical Variables

Citation: IMF Staff Country Reports 1999, 115; 10.5089/9781451835922.002.A002

Source: Statistics Sweden.

D. Test for Structural Change

14. Total factor productivity began to rise rapidly in 1994 following the recession, coinciding with the adoption of an inflation target by the Riksbank (1993), the announcement in 1994 of a consolidation program to achieve fiscal balance by 1998, and Sweden’s accession to the European Union in 1995. Given that both structural and cyclical effects were present at this time it is necessary to isolate cyclical effects to determine whether any structural change has taken place. To accomplish this, the estimate of TFP growth was regressed on a constant, a dummy for the 1994–98 period, the change in the adjusted unemployment rate, the interest rate spread, and the growth in the broad money supply (M3) and in the Swedish stock index. Two lags of the dependent variable were also included to mitigate problems of autocorrelation.

15. The estimates in Table 1 indicate that both the interest rate spread and the adjusted unemployment rate are significant and have the correct signs whereas the growth in the money supply and in the stock price index have low explanatory power. Turning to the main hypothesis of interest, the dummy for the period after 1993 is insignificant, indicating the absence of a structural change in total factor productivity over this period when cyclical factors are included in the specification. It is possible, however, that the specification suffers from multicollinearity. To address this drawback the growth in the money supply and in the stock price index were excluded from the specification (Column 2). Now, the P-value of the constant term rises considerably, although it is still insignificant at the 10 percent significance level. Moreover, the dummy variable for 1994–98 is still insignificant.

Table II-1.

Sweden: Determinants of Total Factor Productivity 1/

article image

Probability values in parentheses; an asterisk indicates that the coefficient is significant at the 10 percent level.

16. The above analysis has assumed that once cyclical effects have been netted out, TFP growth is constant over time. In contrast, an extensive literature on long-term determinants of TFP growth has emphasized variables such as structural changes in government expenditure, R&D expenditures, and education enrollment. Smith (1975) and Gould (1983) find a significantly negative effect on GDP growth from changes in government consumption and investment spending among OECD countries. More recently, Grier and Tullock (1989) also find a significant negative effect. Hansson and Henrekson (1994) distinguish between the effects of government consumption and investment on TFP growth in the private sector and find that while changes in consumption expenditure have significant negative effects on TFP growth, the change in government investment has no effect. R&D is hypothesized to influence TFP growth because it fosters the development of new products. Consistent with this assumption, Fagerberg (1988) and Gittelman and Wolff (1994) find that the growth in civilian R&D has significant effects on growth in developed countries. Moreover, Coe and Helpman (1995) relate TFP convergence rates across countries to the domestic and foreign stock of R&D expenditures and find significant effects from both domestic and foreign sources. Human capital variables such as educational attainment have also provided significant explanatory power in equations explaining international productivity differences, although the effects are more muted in a sample of OECD countries compared with a broader range of countries (see Barro and Sala-I-Martin for a detailed discussion of this issue).

17. This study next incorporates some of these effects by adding the change in the ratio of government expenditures to GDP and the change in the real capital stock of the public sector to the cyclical variables identified above.14 Of course, government expenditure has a strong cyclical component but it is assumed that this component is controlled for in the regression through the inclusion of the interest rate spread and the change in the unemployment rate.15 Column (3) in Table 1 indicates that both the change in the government expenditure ratio and the change in the capital stock of the public sector have significant effects on TFP growth with the 1 percent per annum decline in the expenditure ratio over the past few years generating a 0.3 percentage point increase in TFP in the long-run and the average annual growth rate in the government capital stock of about 1¾ percent over the past few years providing an additional TFP growth impetus of about 0.75 percentage points. Tests were also conducted to discover whether an additional effect could be found for these variables over the 1994-98 period by interacting both variables with a time dummy. However, column (4) reveals that no significant effect was found.

18. It could be argued that regressing the expenditure ratio on a component of private GDP could lead to simultaneity bias because of supply constraints: the higher the ratio of public expenditures to GDP, the lower the available resources for the private sector. This concern can be mitigated by substituting the ratio of government expenditures to nominal GDP with the growth in real government expenditures relative to an estimate of 2.2 percent for potential output growth.16 Of course, this analysis must be qualified because of the circularity of including an estimate of potential output growth in the process of estimating potential output growth as mentioned previously. Column (5) reveals that the estimates are broadly similar with the interest rate spread and the expenditure variable significant at the 5 percent level. The main difference between the specifications is in the size of the coefficient on the expenditure variable. Whereas a 1 percentage point decline in the expenditure ratio would lead to a 0.3 percent increase in TFP growth, a 1 percentage point decline in real government spending relative to the long-run potential growth rate of the economy is estimated to raise TFP growth by about half that much.

E. Long Term Potential Output Growth

19. To obtain a long-run estimate of TFP growth it is necessary to make assumptions about the value of the interest rate spread in steady state and about the future profiles of the expenditure GDP ratio and the growth in the capital stock of the public sector. Figure 1, Chart 2 presents the interest rate spread over the 1970–98 and reveals that the average interest rate spread is about 100 basis points. Assuming that this interest rate spread continues into the future, this variable would contribute about 0.1 percent per annum to long-term TFP growth. According to the government, the ratio of government expenditures to GDP is projected to decline by about 1¼ percent per annum over the next four years to 57½ percent of GDP in 2002. That decline would provide a growth impetus of about 0.4 percent of GDP per annum to the private sector. The capital stock of the public sector is projected to grow at an annual rate of about 1½ percent over the next few years, providing an additional GDP impetus of about 0.65 percent per annum. These estimates combined yield a total private sector growth effect of 1.15 percent. Converting this estimate in terms of the whole economy would yield an annual increase of 0.95 percent assuming a private sector output weight of about 82 percent and the assumption of zero productivity growth in the public sector. A projected increase in the working age population of about 0.2-0.3 percent over the next few years and annual increases of about 3 percent in the capital stock would, therefore, yield a potential output growth rate of about 2.15 percent per annum.17 Once the economy settles at a level in which the ratio of government expenditures to GDP is constant and the working age population remains stable, potential output growth would be estimated to fall to about 1.7 percent.

20. A comparable potential output growth estimate was obtained based on the specification using growth in real government expenditures. Assuming a 1 percentage point annual increase in real government expenditures over the 1999–2002 period and a 1½ percent rate of increase in the capital stock of the public sector, the private sector TFP growth rate would amount to about 0.8 percent per annum and would contribute to a potential output growth rate of 2 percent per annum. Over the long term, assuming that real government expenditures grow in line with economic capacity and that the working age population remains stable, potential output growth would again fall to about 1.7 percent per annum.

21. The estimates in this paper must be considered as tentative because of the prevalence of endogeneity problems. For example, many of the variables used to control for the cycle are endogenous in and of themselves (e.g. the unemployment rate, the interest rate spread). Moreover, while the endogeneity of the government expenditure variables has been mitigated by focusing on TFP growth in the private sector, an appropriate estimate for TFP growth in the public sector remains open. While there are considerable merits in using a structural approach to estimating potential output growth as against purely statistical methods, the drawbacks of the approach must clearly be recognized.


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Prepared by Alun Thomas.


The public sector includes both general government and parastatal enterprises. Because most government output has no measurable market value, output is valued conventionally by the cost of inputs. The variation in public-sector TFP, therefore, primarily reflects changes in composition and in parastatal productivity.


This prediction is based on the assumption that movements in the spread are driven by movements in the short rate so that a more accomodative monetary stance would be expected to support output. Analyses that consider determinants of turning points in the economy generally find that an increase in the spread lowers the likelihood of a future recession (Estrella 1998).


It must be recognized, however, that longer-term effects may still be present.


The public sector capital stock was extended through 1998 using the method outlined above for the private capital stock.


An alternative way of isolating the structural component of government expenditure would be to correct for movements in the output gap. However, this adjustment would require pre existing measures of potential output which we are trying to calculate in this paper.


The estimate for potential output growth corresponds to the estimate obtained below.


This is only slightly below the latest estimate from the Riksbank at 2.3 percent per annum.

Sweden: Selected Issues
Author: International Monetary Fund