Does fiscal policy affect interest rates? Evidence from a factor-augmented panel

3.1 Data

Our database contains real-time semi-annual forecasts of macroeconomic and fiscal variables taken from the December and June issues of the OECD’s Economic Outlook, (EO), and covering the period from 1989 to 2013. The countries included are 17: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, Norway, Netherlands, Spain, Sweden, UK and US.

In our dataset, the projected horizon of the forecast is always one year ahead. So for example, for the June and the December issue of each year t, we collect the projections for year t+1.^[4] The June and the December issues of the EO release forecasts with different information sets. Following the terminology of Beetsma and Giuliodori (2010), the December issue contains a forecast related to the planning phase of the budget law, while the June issue contains a forecast related to its implementation phase. In spite of this difference, we pool them together to achieve higher degrees of freedom. However we checked that splitting the sample according to the June or December issue does not affect our main results.^[5]

As for the dependent variable we use the realized ten years yield on sovereign bonds (r_it). We construct this variable using the value of the interest rates observed in the month after the release of the forecast: January for the December issue and July for the June issue. This approach is useful because the forecasts on fiscal variables are likely to take into account current market conditions and the level of interest rates. Under the assumption that financial markets are forward looking and are able to incorporate rapidly all the available information, sampling interest rates after the release of the forecasts reduces the issue of reverse causality.^[6] Data on interest rates are taken from Datastream (Appendix A).

As indicators of fiscal stance, we use the expected primary deficit (pdef) and the expected public debt (debt) all measured as shares of previous period GDP.^[7] We use primary the deficit instead of total deficit to avoid the problem of reverse causality (since total deficit contains also the total interest payments), while debt is measured as the total gross financial liabilities of the general government.^[8]Table 1 reports the descriptive statistics of the variables of interest.

Finally, following Ardagna, Caselli, and Lane (2007), we include the expected short term interest rate^[9] (stnr) and the expected inflation rate (infl) – to net out of the long-term interest rate the expectations on future monetary policy stance and the inflation premium. We also include the expected GDP growth rate (growth) to control for the cyclical stance.^[10]

3.2 Properties

The importance of the cross-sectional correlation among our variables of interest can be observed when looking at the behavior of long-term interest rates in our sample (Figure 1). We have grouped the countries from the right in the following way: first are the Scandinavian countries (Norway, Sweden, Denmark); then the EMU countries (Finland, Ireland, Italy, Spain, Austria, Belgium, Netherlands, France, Germany); then the Anglo-Saxon countries (Australia, Canada, the UK) and finally Japan and the US. Long-term interest rates are higher at the beginning of the sample in all countries. Starting from 1994, there appears to be a strong convergence, with an especially marked reduction of the interest rates in the peripheral EMU countries (Ireland, Italy, Spain). Nevertheless, the convergence is observed also outside the EMU. Interest rates remain low throughout the 2000 particularly so in Japan, and they begin to diverge only during the crisis.

Figure 1:

Long-term interest rates 1989–2013.

Behavior of long-term nominal interest rates on 10 years government bonds for the countries in our sample. The sample runs from 1989 to 2013.

This evidence is in line with the hypothesis that countries might be subject to the same shocks causing a co-movement in interest rates. To verify the importance of common factors, we test for the presence of cross-sectional dependence in long-term interest rates and the macroeconomic variables of interest using Pesaran’s (2004)CD test. For a panel of N countries, the test statistic is constructed from the combinations of estimated correlation coefficients. Under the null of cross-sectional independence the statistic is distributed as a standard Normal. For all the variables in our sample we find strong evidence of cross-sectional dependence (Table 2).^[11]

We also conducted standard stationarity tests (Table 3). We first implement the Pesaran’s (2007) test for panel unit root and we find indication that almost all the variables can be treated as stationary. There is mixed evidence with respect to the fiscal variables, particularly the public debt. We therefore implement the Moon and Perron’s test (2004) which accounts for multifactor structure, which gives evidence of stationarity for all the variables.^[12] We thus conclude that all the variables in our panel can be treated as stationary.

4.1 The econometric model

Let r_it and x_it be, respectively the long-term interest rate and a set of observable variables, with (i=1, …, N; t=1, …, T). When looking for the determinants of interest rates the natural starting point is a linear model of the type:

where the country intercepts α_i capture time invariant heterogeneity across countries. This is the equation estimated for example by Reinhart and Sack (2000) in a panel of 20 OECD countries. The estimates of the β coefficients are however unlikely to be informative of the effect of x_it on r_it if these are influenced by a set of unobserved global factors. This is the case for open and integrated economies where there exist common sources of fluctuations – such as common business cycle, common monetary policy. A common shock would in fact jointly determine the reaction of monetary and fiscal authorities across countries and hence the level of interest rates. Following Giannone and Lenza (2008) we therefore assume a factor structure of the type:

in which observable quantities {r_it, x_it} are a function of a set of q unobservable global factors {ftk}k=1q with heterogeneous impact in each country {λkir, λkiX}k=1q, ∀i: 1, …, N.

Given this data generating process, an accurate estimate of the effect of macroeconomic and fiscal policy variables on interest rates should be based on the idiosyncratic components only:

Equation (3) cannot be estimated because the idiosyncratic components {ritID, xitID} are unobservable, but we can use (2) to substitute the idiosyncratic component in (3) and rewrite the equation in terms of observable quantities and global factors:

By taking explicitly into account the global factors {ftk}k=1q, (4) allows us to estimate the relationship between the idiosyncratic components of the variables of interest. Consistent estimates of the common factors, allow an estimation of the β by standard panel techniques. In the next Section we show that these can be obtained extracting principal components from the set of observable variables of equation (4), {r_it, x_it}_i=1, …, _N;_t=1, …, _T. This estimation technique goes under the name of FAP.

When the data generating process is represented by the system in (2), we can obtain unbiased estimates of the coefficients β only if we allow the factors to have heterogeneous impact across countries (δ_ki≠δ_kj). This aspect has been often ignored in previous studies. In fact, when tackling the issue of common unobserved factors the literature has mainly pursued different paths. The first approach (Chinn and Frankel 2007) consists of finding an a priori observable variable (or a subset of variables) which might affect contemporaneously the interest rates across countries, and introduce it directly in the panel:

where the variable (z_t) is the vector (or matrix) of identified common factors. Alternatively, unobserved factors have been accounted for by introducing time effects. This would lead to the estimation of the following model (Ardagna, Caselli, and Lane 2007):

This is equivalent to assuming that in each time period there is a common shock which affects homogeneously countries’ interest rates.

Differently from the FAP specification in (4), equations (5) and (6) impose homogeneous effects of the global factors, represented either by the common regressors z_t or by the time effects τ_t. If however the unobserved factors have truly an heterogeneous effect across countries, then the country specific components will become part of the error terms of (5) and (6). Therefore, if the factors are correlated with the observable variables- as implied by (2) – equations (5) and (6) will suffer from endogeneity and produce biased estimates.

4.2 Estimation strategy

To obtain consistent estimates of the sets of unobservable factors we follow Giannone and Lenza (2008) and use principal components. This is a general procedure that can be applied whenever in a linear regression the variables have a factor structure. It consists of taking the entire set of dependent and independent variables for all the N cross sections and, after stacking them together in a single matrix, apply principal components.

Hence to estimate the unobserved factors of equation (4), we collect all the variables {r_it, x_it}_{i=1, …, N;t=1, …, T} in a matrix W^r:

Wr=[rit1, …, ritN; xit1, …, xitN]

If the elements xitj have dimension T*k the matrix W^r will be of dimension T*(N(k+1)).^[13] The Principal Component Analysis (PCA) of W^r produces set of N(k+1) orthogonal vectors which are the eigenvectors obtained from the eigenvalue-eigenvector decomposition of the covariance matrix of W^r. The eigenvectors are linear combinations of the columns of W^r. However, under the assumptions that common factors are pervasive and that idiosyncratic shocks are not pervasive, the eigenvectors are a consistent estimate of the common factors, with consistency achieved as the dimensions of W^r increase. Of all the N(k+1) eigenvectors extracted from W^r we keep the first q, which are the ones associated with the highest proportion of explained variance. This procedure ensures that the q factors are indeed those elements which explain the bulk of the correlation among all of our data series and are therefore responsible for their observed co-movements.

The first two eigenvectors explain 69 percent of the panel variance with the third one contributing for less than 10 percent (see Table 4).

Following Giannone and Lenza (2008), we therefore take into consideration only the first two factors. Using these two estimated vectors we can rewrite equation (4) as:

Notice that, while we allow the response to the common factors (δ_ik) to vary across country, we impose the coefficients β to be common to keep the results consistent with those obtained in previous studies. The economic interpretation of the estimated factors f^1t and f^2t is important for the scope of our analysis. In Appendix A we show that these two elements can be related to macroeconomic aggregates: the average monetary policy and the average fiscal policy stances of the countries in our sample.

Although having estimated elements in the regression introduces a further source of uncertainty, which normally requires to bootstrap the standard errors, we rely on the result by Giannone and Lenza (2008), Bai (2004) and Bai and Ng (2006) who show that with a relatively large number of countries there is no generated regressor problem.^[14] However, we also perform a robustness check estimating the FAP with bootstrap standard errors as in Gonçalves and Perron (2013).^[15]

The FAP is however not the only methodology proposed in the literature. Other types of estimator developed to tackle the issue of common unobservable factors and cross-sectional dependence are Pesaran’s (2006) Common Correlated Effect (CCE), and Bai’s (2009) Interactive Fixed Effects (IFE) and Greenaway-McGrevy, Han, and Sul (2012) estimator. In Technical Appendix B we show that our main results are preserved if we employ these alternative estimation techniques.^[16]

5.1 Baseline model

In this section we present the results from the estimation of equation (7). The results are reported in Table 5. To control for possible structural breaks in the coefficients as a result of the crisis, we report in the first three columns the results excluding the observations before the year 2008, and in the last three columns the results including the latest sample. In the table, columns 1, 2, 4 and 5 use standard panel techniques, while columns 3 and 6 presents the results of the FAP estimation. In particular, we first estimate equation (7) using only country fixed effects α_i (columns-FE), then we include also time fixed effects τ_t (columns-2FE) and finally we include both fixed effects and estimated factors (columns-FAP).^[17] At the bottom of each table we include, as a further specification test, the value of the CSD statistic, which is Pesaran’s (2006) test for cross-sectional dependence^[18] applied to the residuals of the estimated equation.

We first discuss the results for the pre-crisis period. Our results show that, when we account for cross-sectional dependence, the impact of domestic variables on long-term interest rates diminishes significantly. We start by looking at the role of fiscal policy. The positive correlation between fiscal variables and long-term interest rates previously found in the literature is not robust when we account for cross-sectional dependence. A standard FE estimator shows that a one percentage point increase in the expected primary deficit to GDP ratio increases interest rates by around 11 basis points, while a 1 percent increase in the expected debt to GDP ratio increases interest rates by around 1.9 basis points (column 1). However, the large value of the CSD statistic (43.04) for the residual, indicates that the regression is misspecified.

Looking at columns 2 and 3 we first notice the importance of accounting for common factors. For both estimators, the CSD statistic falls markedly compared to the FE, but the FAP performs better against the 2FE (–3.42 vs. –3.34). The response of long-term interest rates to domestic fiscal policy diminishes in both cases. When we allow for heterogeneous response to global shocks with the FAP (column 3), the primary deficit becomes statistically insignificant, while the effect of public debt remains significant. As for the magnitude, the effect is smaller than the standard FE estimator (column 1): a 1 percent increase in public debt increases long-term interest rates by around 1 basis point.

The coefficients on the other variables also decrease significantly in magnitude. The coefficient on short-term interest rate decreases when using the FAP, indicating that, accounting for cross-sectional dependence, long-term interest rates are less responsive to domestic monetary policy. The result confirms the findings in the literature that central banks have been progressively losing effectiveness in stirring long-term rates. Giannone, Lenza, and Reichlin (2009), show how in the recent decades long-term interest rates have become more disconnected from country-specific monetary policy stances. The coefficient on GDP growth remains positive but becomes marginally significant. Finally, we find that coefficient on expected inflation becomes insignificant.

We now briefly discuss the results obtained when including the more recent sample. We confirm the importance of accounting for global factors, but the FAP again performs better than the 2FE as shown by the improvement in the CSD statistics (from –2.10 to –1.23). The coefficients on fiscal and monetary policy are almost unaffected, with short-term rate, deficit and debt maintaining similar magnitude and significance. Including the latest crisis changes the significance and signs of the coefficient on GDP growth which becomes negative and ceases to be statistically significant. This shows how growth expectations have started to play a stronger role in assessing fiscal sustainability, with downturns impacting negatively borrowing costs.

5.2 Time variation in the domestic components

In this section we check how the importance of the domestic (idiosyncratic) components has been changing over time. We have shown that, when controlling for global factors, coefficients on domestic variables weaken. We first provide evidence on the changing contributions of the common factors to the total variance in the data. We then show the evolution of the coefficients in the main regression over time and check for possible breaks.

In Figure 2 we compute the variance explained by the first three global factors using a rolling window of 20 periods.

Figure 2:

Rolling window estimates – principal components.

The figure report a 20 period rolling window estimate of the proportion of variance explained by the first three principal components.

The figure shows that the share of variance explained by the first three global factors tends to be relatively stable over the sample period, with three principal components explaining between 70 and 80 percent of the variance in the data. We notice that the share of variance explained by the first principal component diminishes over time until the crisis, while the share of variance explained by the second factor increases. After the crisis, the share of variance explained by the first principal component increases up to 60 percent indicating a stronger co-movement of macroeconomic and financial variables in heightened market turmoil, a result found also in different markets (Longstaff et al. 2011; Eichengreen et al. 2012).

We now analyze the time varying effect of domestic fiscal variables.^[19] We re-estimate (7) using rolling regressions with a window of 20 periods.^[20] We can therefore follow the evolution over time of the coefficients on domestic primary deficit and public debt, and analyze more clearly how the crisis has affected the stability of these coefficients (Figure 3).

Figure 3:

Rolling window estimates – long-term interest rates.

The figures report the rolling window estimates for expected deficit and expected debt obtained from estimating equation (7) with a 20 period rolling window. Dashed lines represent two standard deviation confidence bands.

There is a clear downward trend in the coefficients up until the crisis, indicating weakening influence of domestic variables on interest rates. After the crisis, there is a temporary increase in the importance of domestic fiscal policy. While fiscal deficits do not have any impact through the more recent period, the coefficient on public debt increases but the uncertainties around its estimates also increases due to the large variation observed in debt during this period. We have further analyzed the role played by the crisis by testing for structural breaks in the coefficients interacted with a crisis dummy. The results, available in Technical Appendix B, provide evidence the coefficient on a measure of fiscal sustainability – the “deficit gap” defined as in Faini (2006) – has increased after the crisis. This evidence suggests a possible re-pricing of risk in the aftermath of the global financial crisis [see Sgherri and Zoli (2009) for evidence on the EMU].^[21]

5.3 Comparison with existing literature

The results so far indicate that, when we account for heterogeneous response to global shocks: (1) long-term interest rates remain positively related only to public debt; (2) there is mild evidence of increased importance of domestic fiscal policy in the crisis. Our results stand partly in contrast with previous literature. In particular, past studies have found a significant effect of public deficits on long-term interest rates (Ardagna, Caselli, and Lane 2007). We show in this paper that properly accounting for global factors and cross-sectional dependence in the estimation is crucial to understand this result. The omission of such factors leads to overestimating the impact the idiosyncratic component of fiscal policy. Beside lower impact of public deficits, we also find that the effect of public debt on long-term interest rates is smaller compared to previous estimates. Laubach (2009) for instance, finds that a 1 percent increase in public debt to GDP leads to an increase in long-term interest rates by 3–4 basis points. We find that the impact is close to 1 basis point. While we cannot directly compare our estimates to Laubach’s (2009) due to differences in the underlying datasets and specifications used in the estimation, we can refer to Laubach’s analysis (2009) to reconcile our results with economic theory. Within the neoclassical growth model, under the assumption that roughly two-thirds of the increase in public debt is offset by domestic savings, Laubach (2009) shows that a 1 percent increase in public debt to GDP leads to an increase in real interest rates by 2.1 basis points.^[22] Recent evidence has however challenged this assumption on the degree crowding-out. Giannone and Lenza (2008), using a Feldstein-Horioka regression, show that less than one-fifth of savings in developed countries are retained for domestic investment. Once a lower degree of crowding-out is assumed, we can reconcile our estimates with theory, and generate effects of public debt on real interest rates in the range of 1 basis point (Table 5, columns 3 and 6).^[23]

Our results show that the domestic components of fiscal policy play a smaller role in determining long-term interest rates, once we account for global factors. Previous literature has in fact recognized that, in financially integrated economies, “global fiscal policy” should more prominently explain fluctuations in long-term interest rates compared to domestic fiscal policy. Faini (2006) for example, analyzes the effect of a “global fiscal expansion” for EMU countries. He finds that the effects on interest rates of domestic fiscal policy shocks are rather small compared to those caused by a global fiscal expansion: a change in domestic surplus leads to a 5 basis points reduction of interest rates, while a change in the EMU surplus leads to a 41 basis points decrease in interest rates. Ardagna, Caselli, and Lane (2007) analyze the impact of the world fiscal stance, measured as both the aggregate primary deficit and the aggregate debt, on a sample of OECD countries. They find that, depending on the specification, the world deficit leads to increase in interest rates between 28 and 66 basis points, while world debt increases interest rates between 3 and 21 basis points. Similar results can be found in Claeys, Rosina, and Suriñach (2012).^[24] In all cases, the effects are found to be statistically significant and much larger than those of domestic fiscal shocks. Our estimation strategy is well suited to capture the importance of global factors estimated through principal components. The lack of an economic interpretation of what these principal components represent is a possible drawback of the estimation strategy. While a formal analysis of what can constitute these global factors is beyond the scope of this paper, to provide some economic interpretation to these factors, we relate our results to the existing literature and use the FAP estimator to analyze the magnitude and the cross-country differences in the coefficients related to the global factors.

As a first step we plot the principal components against macroeconomic aggregates. We find that the first principal components resemble a measure of aggregate global monetary policy. The second principal component should be a variable which is driven by the same common shocks but not collinear with the monetary stance. As discussed in Technical Appendix A, we find that indeed there is a strong correlation with global fiscal policy stance, a result which is in line with the empirical specifications chosen by the previous literature.^[25] To estimate the effects of these global factors we re-estimate equations (7) replacing the estimated factors with their economic interpretation. As discussed in Technical Appendix B we use the average expected primary deficit^[26] and the average expected short term rate of the countries in our sample. The estimated coefficients on the global factors are indeed quantitatively important and highly heterogeneous across countries (see Table 6). In line with previous literature, average deficit is by far more important than the idiosyncratic fiscal components. Its average effect is in fact around 20 basis points, which is more than ten times larger than the effect of an increase in idiosyncratic primary deficit. However, contrary to previous literature, the results are highly heterogeneous across countries (F-test rejects hypothesis of homogeneity at less than 1%). Suggestively, coefficients are higher for countries which were less financially integrated at the beginning of the sample or which were characterized by macroeconomic and institutional weaknesses (Figure 4).

Figure 4:

Determinants of the cross-country dispersion of the effects of global deficit.

The figures report the estimated country specific effect of global deficit. They are correlated with measures of initial capital markets integration, current account imbalances and economic and institutional fragility.