Balázs Égert
email: balazs.egert@oecd.org

Nominal and Real Exchange Rate Models in South Africa: How Robust Are They?

Keywords: E31, F31, O11, P17 exchange rate, real exchange rate, nominal exchange rate, commodity, Balassa-Samuelson, productivity, monetary model, stockflow approach, openness, country risk

This paper addresses difficulties in modelling exchange rates in South Africa. Real exchange rate models of earlier research seem to be sensitive to the sample period considered, alternative variable definition, data frequency and estimation methods. Alternative exchange rate models proposed in this paper including the stock-flow approach and variants of the monetary model are not fully robust to data frequency and alternative estimation periods, either. Nevertheless, adding openness to the stock-flow approach and augmenting the monetary model with share prices and the country risk premium improves significantly the fit of the models around the large (nominal and real) depreciation episodes of 2002 and 2008. Interestingly, real commodity prices do not help explain the large depreciations. While these models do a reasonably good job in-sample, their out-of-sample forecasting properties remain poor.

Introduction

South Africa belongs to the group of resource-rich countries where commodities account for a non-negligible share of exports. Most economists would agree and empirical evidence shows that commodity prices are likely to be an important driver of exchange rates of prominent commodity producing and exporting countries [START_REF] Cashin | Commodity currencies and the real exchange rate[END_REF][START_REF] Chen | Commodity currencies[END_REF]Rogoff, 2003, Gruen and[START_REF] Gruen | Why Does the Australian Dollar Move so Closely with the Terms of Trade? Reserve Bank of Australia Research Discussion Papers[END_REF][START_REF] Bailliu | Multilateral Adjustment and Exchange Rate Dynamics: The Case of Three Commodity Currencies[END_REF]. That commodity prices play an important role in long-run real exchange rate movements in South Africa is also largely confirmed in the existing literature (Aron et al., 2000;[START_REF] Chinn | A monetary model of the South African Rand[END_REF][START_REF] Mtonga | The real exchange rate of the rand and competitiveness of South Africa's trade[END_REF] for real gold prices and [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] and [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF] for real prices of the basket of commodities exported by South Africa), even though some cannot confirm the commodity currency finding (Cashin et al, 2002). This paper has several ambitions. First, we revisit the commodity price -exchange rate nexus for the case of South Africa. But a more general objective of the paper is to investigate the stability of exchange rate models with regard to the time period used, economic specification, alternative variable definitions and data frequencies. Also, we would like to find out what explains the rand's large depreciation in 2002 and during the recent financial crisis in 2008 (Figure 1). For this purpose, the models of [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] and [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF] constitute our starting point. 2Source: Author's calculations based on obtained from Datastream. For more details, see the data appendix.

The rest of the paper is organised as follows. Section 2 describes findings of previous research. Section 3 carries out a sensitivity analysis of the models proposed in the literature, Section 4 provides alternative real and nominal exchange rate models and studies their robustness to various economic and econometric specifications. Section 5 finally summarises our findings.

We compare these models to the stock-flow approach to the real exchange rate augmented with commodity prices and country risk premium. We also estimate nominal exchange rate models on the basis of the monetary model. This section seeks to replicate the results reported in [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] and [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]. While we try to follow the modelling choices of the two papers, our comparison is far to be perfect and hence cannot be taken as a genuine replication of the earlier results. Rather, they can be considered as a check whether these results are robust to changes in the estimation setup. Below we discuss the major differences.

We decided to deviate from the modelling choices of [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF] mostly because his real exchange rate model that is estimated against the dollar does not consider the nonstationary properties of the series considered: all variables used in his model are clearly I (1) processes that calls upon cointegration analysis. 3The second major difference to our approach is that Frankel uses data on inflation expectations for the computation of the real interest rate. We use observed inflation rates to calculate forward and backward looking short-term and long-term real interest differentials against the US. On the one hand, we do not have access to the data he used in his paper. On the other hand, it is not clear to what extent inflation expectations generated by a structural model of South Africa that he uses are a good measure of actual inflation expectations of financial market analysts, firms and households.

It is very difficult to reconcile the lagged dependent variable (exchange rate) with a long-term cointegrating relationship. Including the lagged (first differenced) dependent variable is more appropriate in an error correction model. Against this background, we do not consider the lagged dependent variable in the cointegrating vector. [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF] uses a dummy that captures capital account liberalisation in 1994 and an interaction term of the dummy with the interest rate differential. We only include the interaction term in the cointegrating vector but not the dummy variable.

For the real effective exchange rate, our estimations are based on a dataset that has three major differences compared to the dataset used in [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF].

• First, our estimation period starts in 1980:Q1 instead of 1970:Q1 because we could collect data for the five components of the commodity price index (including gold, coal, iron, copper and platinum) starting only in 1980.

• Second, [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] use a variable on the fiscal balance without specifying the exact definition of the series (general or central government or whether it is cash based or not). We have three data series on government balances in South Africa that differ quite substantially. We therefore decided to use the government debt to GDP ratio that is also a proxy for the country risk premium.

• Third, [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] do not provide the countries that constitute the foreign benchmark and the corresponding weights used for the calculation of the effective exchange rate as well as for the effective foreign variables. Hence, we use the (normalised) weights for South Africa's 4 biggest trading partners (USA, euro area proxied by Germany, UK and Japan) published by the South African Reserve Bank (SARB).

The different time spans covered in the two papers and additional observations since the end of 2007 provide three natural benchmark periods for studying model stability: • 1994:q1 to 2009:q1 => sample period that considers changes after capital market liberalisation and that makes the use of dummies to capture that change unnecessary.

Overall, we carry out sensitivity analysis around the following dimensions:

• Time span

• Data frequency (quarterly vs. monthly)

• Variable definition

• Estimation method (for MacDonald and Ricci, 2004)

Estimation issues

We use cointegration analysis to investigate the sensitvity of previous research as the variables considered turn out to be I(1) processes. For the cointegration analysis, we employ dynamic ordinary least squares (DOLS) and the Johansen cointegration technique. Here we briefly describe the two approaches. We use dynamic ordinary least squares (DOLS) to estimate the long-run relationship. [START_REF] Stock | A simple estimator of cointegrating vectors in higher order integrated systems[END_REF] show that DOLS accounts for the endogeneity of the regressors and serial correlation in the residuals by incorporating lags and leads of the regressors in first differences:

t j t i n i k k j j i t i n i i t X X Y ε γ β β + ∆ + + = - = - = = ∑ ∑ ∑ , 1 , , 1 0 2 1 (7)
where k 1 and k 2 denote, respectively, leads and lags. The length of leads and lags is determined on the basis of the Schwarz information criteria. The presence of cointegration is assessed using three methods:

• Residual-based cointegration test where stationarity of the residuals obtained from the long-term relationship ( ) , (

t t i n i i t X Y ε β β + + = ∑ = , 1
- - ∞ + + = T T T p C k β β β
where p and T are the significance level and the sample size respectively, and the betas are parameters of response surface estimates.

• The error correction term as a test of cointegration is used as [START_REF] Kremers | The power of cointegration tests[END_REF] argue that it is more powerful than the residual-based Dickey-Fuller test. • Johansen's trace statistics is used to verify the number of cointegration relationships in a VAR (vector autoregressive) framework

t p i i t i t t Y Y t m m Y ε αβ + ∆ Φ - + + + = ∑ - = - - 1 1 1 ' 1 0 ) ) 1 ( ( (8)
The critical values are tabulated by [START_REF] Osterwald-Lenum | A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics[END_REF] and the test statistics are corrected for small samples if necessary in accordance with [START_REF] Reimers | Comparison of tests for multivariate cointegration[END_REF]. 4

4 Nevertheless, it is known that the trace statistic tend to overreject the null of no cointegration and indicates more cointegrating vectors than [START_REF] Hjalmarsson | Testing for Cointegration using the Johansen Methodology when Variables are Near Integrated[END_REF]. Therefore, we use the trace statistic to see whether or not the series investigated are cointegrated but would worry too much if it would indicate 2 cointegration relationships.

Overall, we will take as an evidence for cointegration if at least two out of the three tests suggest that the variables are cointegrated.

Results of the sensitivity analysis

Tables 1a and1b report the estimation results for the [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF] and [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] models. Before diving into the details, it needs to be emphasised that the real commodity price variable we used reflects the weights and the different commodities included in the real commodity price index used in the two papers (see appendix A) and that we use monthly data in addition to quarterly data used in both papers.

Table 1a shows that for the period 1980:q1 to 2007:q1, the model estimates are comparable to those reported in [START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]. A higher real interest differential is associated with an appreciation of the CPI-and PPI-based real exchange rate, the interaction term has the opposite sign and commodity price increases go hand in hand with a real appreciation. Furthermore, and importantly, the variables seem to be connected via a long-run cointegrating vector. The error correction terms are significantly negative and the trace statistic indicates the presence of one cointegrating vector at the 1% level. Two comments are of order: First, the coefficient estimates on the real commodity price index are substantially higher (between 0.6 and 0.7) than those reported in Frankel (2007) (around 0.15). Second, the fit of the longterm model is around half of that of the model including the lagged real exchange rate.

Looking at the three additional periods, Table 1a suggests that the results do not change much for 1980:q1-2002:q1 but it also shows that cointegration cannot be warranted for the sample running until 2009:q1 and for the period that starts in 1994:q1. These findings remain unchanged when we run the same set of regressions on monthly data.

T nk T / ) ( -
where T is the number of observations, n is the number of variables and k is the lag length.

Table 1b displays results obtained for the [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] modelling framework. While Johansen's trace statistic is able to reject the null of no cointegration at the 1%, the two other tests cannot confirm this result for the benchmark period of 1980:q1 to 2002:q1. Nevertheless, finding cointegration is generally not a problem for the additional periods and when looking at monthly data. For 1980For :q1 to 2007For :q1 and 1980For :q1 to 2009:q1:q1, the question that arises is that there might be more than just one cointegrating vectors as the trace tests indicate the presence of up to 4 cointegrating vectors. Results based on monthly data suggest that the multiple cointegration finding may be less of a problem.

Whereas the lack of cointegration is not a major issue, the sign, significance and stability of the coefficient estimates of the explanatory variables are of major concern. The two variables that are very robust to alternative specifications in terms time span, econometric estimation methods and data frequency are relative GDP per capita and the openness variables. Regarding the other variables, the results show that:

• First, some variables tend to have the wrong sign. For instance, the estimations suggest that an increase in public debt goes in tandem with an appreciation of the real effective exchange rate. This is not very intuitive given that a higher debt and thus a higher country risk should translate into currency depreciation. For the benchmark period of 1980 to 2002, commodity prices have the wrong sign while the sign switches for the remaining alternative periods.

• Second, some variables tend to be statistically insignificant such as net foreign assets.

• Third, estimation results in terms of sign and significance may differ whether the estimations are obtained using DOLS or a VECM. This is for instance the case of openness for three periods at the quarterly frequency: higher openness leads to depreciation on the basis of DOLS estimates and to appreciation using VECM estimates.

• Fourth, data frequency also matters. For 1980 to 2002, the real interest differential has a depreciating effect on the exchange rate when using quarterly data and an appreciating effect if monthly data are used.

Overall, it appears that the real exchange rate model of [START_REF] Macdonald | Estimation Of The Equilibrium Real Exchange Rate For South Africa[END_REF] are not particularly robust to an alternative definition of the country risk variable (replacing government balances by the public debt to GDP ratio), to the shortening of the time span from 1970 to 2002 to 1980 to 2002, to alternative time spans and to a change in data frequency.

Alternative exchange rate models 4.1 Alternative real exchange rate models

We have seen previously that the real exchange rate models proposed in the literature are sensitive to alternative data specifications. The Frankel model is not stable over time and it probably is too narrow in focus while the MacDonald-Ricci model is not very robust across many dimensions probably because the included explanatory variables may be strongly correlated with each other.

Against this backdrop, we estimate real exchange rate models that have a wider focus than the Frankel model and that include a lower number of variables than the MacDonald-Ricci model. A convenient way of doing this is if we use the stock-flow approach to the real exchange rate, according to which the real exchange rate based on the CPI ( CPI Q ) can be linked to the dual productivity differential (PROD) and to net foreign assets (NFA)5

) , , (

/ / - - + - + = COMR NFA PROD f Q CPI
. The basic stock-flow model can be augmented with real commodity prices (COMR). The reduced-form equation used is the following:

(6)
In general, the sign on the productivity variable is not straightforward. NOEM models predict that an increase in productivity in the open sector leads to a depreciation of the real exchange rate of the open sector (positive sign). However, the overall impact depends also on whether this effect is counterbalanced by the traditional B-S effect. The productivity variable of the open sector can also reflect nonprice competitiveness in the open sector and thus lead to a real appreciation [START_REF] Egert | Real exchange rates in small open OECD and transition economies: Comparing apples with oranges?[END_REF].

The sign on net foreign assets is not unambiguous either. Generally, an increase in the net foreign assets position is usually associated with an appreciation of the real exchange rate because of capital inflows related to increasing payments received on net foreign assets (positive sign). However, in emerging market economies, domestic savings may be insufficient to finance the high growth potential. Thus, foreign savings are needed, the inflows of which reduce (increase) net foreign assets (net foreign liabilities) and cause the real exchange rate to appreciate. This implies a negative sign. However, there is a threshold for the net foreign assets position beyond which the sign is likely to switch because the domestic economy has to start servicing its foreign liabilities. Any additional increase in net foreign liabilities would lead to an appreciation of the real exchange rate.

We used three measures for real commodities prices. 1) a price index calculated using the same commodities and weights as in Frankel (2007), 2.) a price index calculated using the same commodities and weights as in MacDonald and Ricci ( 2004) and 3.) the price of gold. All three series are deflated using the US CPI index. A rise in real commodity prices is expected to lead to a real appreciation because it can cause nontradable prices to increase due to a number of reasons linked to the Dutch Disease 6 Table 2a hereafter shows the estimation results for the quarterly and monthly real effective exchange rate models obtained for the four sample periods. Using our criterion of two tests out of three evidencing cointegration, the series are cointegrated for the model including relative GDP per capita, net foreign assets and real commodity prices, irrespective of the time period and data frequency considered. The net foreign assets variable is a very robust driver of the real effective exchange rate as its sign and significance do not change across different time spans and data frequencies even though its size is considerable higher for quarterly data than for monthly data. The GDP per capita variable is always negatively signed but it is not always significant. Finally, a rise in the real commodity price index is found to generate an and because of the appreciation of the nominal exchange rate due to the inflow of export revenues and and FDI going to the commodity sector. appreciation of the rand for three out of four sample sizes but the coefficient estimate for this variable become insignificant for the period from 1994 to 2009. 7 We now add openness to the model (Table 2b). Openness seems to be a very robust driver of the rand's real effective exchange rate. A rise in openness always leads to a real depreciation -an effect usually observed in other empirical studies. Nevertheless, the cointegration finding is rather weak for the period of 1994q1 to 2009:q1. Furthermore, the GDP per capita variable switches sign (quarterly data), or becomes insignificant (monthly data) for this period and net foreign assets become insignificant for the quarterly estimations. 8 When replacing openness with country risk (public debt) in the equations yields unsatisfactory results: 9 7 These results are unchanged when adding a linear trend to the specification. 8 These results are unchanged if we add a linear trend tot he specification. 9 These results are not reported here but are available upon request.

the public debt variable is either insignificant or has a negative sign meaning that higher country risk is reflected in currency appreciation. 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 Notes: *, ** and *** indicate statistical significance at the 10%, 5 % and 1% levels. For the rest, as for Table 1a We now turn to see how the models discussed above are able to track the evolution of the real exchange rate series, in particular the large depreciations around 2002 and 2008. We consider models reported in Table 1a, 2a and 2b. Variants of the MacDonald-Ricci (2004) model are not taken into consideration because of the problems we encountered earlier with regard to the coefficient estimates. Stock-flow models including GDP per capita, net foreign assets and real commodity prices are not capable of explaining the dramatic depreciation around 2002 either. Nevertheless, they do not move as far away from the observed real exchange rate than the Frankel model. 10

Notes: Calculations based on the estimated equations reported in Tables 1a, 2a and 2b.

Alternative nominal exchange rate models

Instead of analysing the real exchange rate, one can also directly look at the drivers of the nominal exchange rate using the monetary model to the exchange rate. The basic monetary model includes relative money supplies, relative real GDP and the interest rate differential: It can be observed that models that are estimated until 2009 stay closer to the observed series than those that are estimated on a sample that stops in 2002 or 2007. This again is an indication that while these models seem to provide a little better in-sample forecasts for the exchange rate at period end, they perform rather poorly in terms of out-of-sample forecasts.

The stock-flow models augmented with openness appear to track exchange rate movements much better than the previous two classes of models. First, the models do a seemingly good job in explaining the large depreciation in 2002. Second, they can explain the evolution of the real exchange rate after 2002 and the depreciation in 2008. Nevertheless, the quarterly model estimated for 1994-2009 is very volatile after 2002, showing the reason of the nocointegration finding for this model. In addition, while overall performing clearly better insample than the models analysed above, the model including openness estimated until 2002 has a worse fit towards the end of the full sample than those estimated until 2007 and 2009

) ( ) ( ) ( * 2 * 1 * t t t t t t t i i y y m m e - + - - - = β β (1)
where t e is the nominal exchange rate, expressed as units of domestic currency units over one unit of foreign currency (an increase means depreciation of the domestic currency). Equation (1) shows that a relative rise in money supply results in a nominal currency depreciation. An increase in relative real income causes a nominal depreciation. Regarding the effects of the interest rate, a rise in the long-term interest rate differential is related to a currency depreciation, in line with the uncovered interest parity condition. The basic monetary model can be extended in various ways to account for additional factors influencing the nominal exchange rate: 10 Note that the Frankel model relates to the real exchange rate against the dollar while the stock-flow model is estimated for the real effective exchange rate. Figure 1 shows, however, that the two series move very closely together. a.) Commodity prices: The standard monetary model can be tailored to capture the features of oil and commodity exporting countries. El Shazy (1989) introduces a wealth term in the money demand function of the net oil exporting domestic economy. The wealth term is related to the real value of oil reserves and is expressed as the relative price of oil exports to that of foreign tradable prices (

β β β + - - - - - = (2)
b.) Balassa-Samuelson effect: The Balassa-Samuelson augmented monetary model can be derived under the assumptions of money market equilibrium and that PPP holds for the open sector (

* T t T t p p e - = ) 11 ) ( ) ( * * NT t T t NT t T t a a a a - - -
. This gives the following relation where a rise in the productivity differential (

) is expected to be associated with a nominal currency appreciation:

)

) ( ) )(( 1 ( ) ( ) ( * * * 2 * 1 * NT t T t NT t T t t t t t t t t a a a a i i y y m m e - - - - - - + - - - = φ β β (3) c.

) Stock prices:

The literature on money demand functions emphasises that omitting asset prices such as stock prices is an important source of instability. [START_REF] Friedman | Money and stock market[END_REF] argues that stock prices can influence money demand in four different ways. The income effect from a rise in wealth implies a positive relationship between stock prices and money as part of the capital gains may be held in liquid assets. The substitution effect can counteract the income effectwhen agents shift their liquid assets into more attractive stocks. The transaction effect says that if an increase in stock prices goes in tandem with higher transaction volumes requires more liquid assets to handle the transactions. The volatility effect occurs if an increase in stock prices is accompanied by more volatility, and if agents reallocate their assets away from more risky assets into less risky liquid assets. Overall, the impact of stock prices on money holdings is ambiguous. Consequently, if integrated into the monetary model, stock prices ( S t p ) can have a negative or positive effect on the nominal exchange rate:

) ( ) ( ) ( * 4 * 2 * 1 * S t
λ β β + - + - - - = ) ( ) ( * 3 * 1 * (5)
Tables 3a to 3d show the estimation results for four variants of the monetary model for the nominal effective exchange rate: the basic monetary model and its versions augmented with real commodity prices, share prices and country risk premium. We do not report estimates for the model that accounts for the Balassa-Samuelson effect because the sign of the Balassa-Samuelson variable (productivity differential) is always positive instead of the expected negative sign implying the effect leading to a nominal depreciation.

A first general observation is that cointegration can be established only for the periods 1980-2007 and 1980-2009 but not for 1980-2002 and 1994-2009, irrespective of the data frequency and model specification considered. There are only two exceptions: the quarterly model including commodity prices for 1994 to 2009 and the monthly model including country risk for 1980 to 2002.

The coefficient estimates of the basic monetary model are always significantly different from zero and are in line with theoretical considerations set out above. An increase in relative GDP is associated with a nominal appreciation, whereas higher relative money supply and interest differential go in tandem with a nominal depreciation. The components of the basic monetary model are very robust to the inclusion of real commodity prices, real share prices or the country risk premium.

As far as the augmented versions of the monetary model are concerned, we can observe that the real commodity price variable is statistically significant with the expected negative sign for 1980-2007 but not for 1980-2009. If real share prices are added, real commodity prices have negative and statistically significant coefficient estimates. Nevertheless, statistical significance decreases again if real share prices are replaced by the country risk premium variable. Real share prices have a positive sign as well as the risk premium variable suggesting that a rise in both variables is associated with a nominal depreciation of the rand. 12We again compare the nominal effective exchange rate estimated on the basis of the above models and the actual exchange rate. Figure 3 depicts the fitted and observed series. 13The basic monetary model seem to track well the overall development of the nominal effective exchange rate. Nevertheless, it fails to capture the two large depreciation periods and the appreciation that occurred between the two episodes. In addition, the quarterly model estimated Concerning the model incorporating share prices, the only major difference is that the model obtained for the period from 1994 to 2009 models well both depreciation periods. The other models perform similarly to the earlier variants of the monetary model presented above.

Finally, the monetary model augmented with the country risk premium fits the data very well after 2004 but it still is not capable of fully explaining the depreciation in 2002. Nevertheless, Figure 3 suggests huge differences for the quarterly and monthly models. The fit of the quarterly models estimated for 1980 to 2002 and 1994 to 2009 are way out of line with the observed exchange rate after 2000. Nevertheless, the fit of the monthly models is much better. Models obtained for 1980-2007, 1980-2009 and 1994-2009 all match the observed data very well after 2003.

Table 3a. Monetary model, nominal effective exchange rate

Quarterly data

Monthly data 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 1980-2002 1980-2007 1980-2009 1994-2009 3a to 3d. [START_REF]Monetary model with country risk -monthly[END_REF][START_REF] Alberola | Quo vadis Euro?[END_REF]1980[START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]1980-20091994-2009 Monetary model with commodity prices -quarterly [START_REF]Monetary model with country risk -monthly[END_REF][START_REF] Alberola | Quo vadis Euro?[END_REF]1980[START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]1980-20091994-2009 Basic monetary model -quarterly [START_REF]Monetary model with country risk -monthly[END_REF][START_REF] Alberola | Quo vadis Euro?[END_REF]1980[START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]1980-20091994-2009 Basic monetary model -monthly [START_REF]Monetary model with country risk -monthly[END_REF][START_REF] Alberola | Quo vadis Euro?[END_REF]1980[START_REF] Frankel | On The Rand: Determinants Of The South African Exchange Rate[END_REF]1980-20091994-2009 Monetary model with country risk -monthly

In this paper, we sought to address the stability and robustness of exchange rate models of the South African rand. Our empirical results showed that real exchange rate models of earlier research were sensitive to the sample period considered, alternative variable definitions, data frequencies and estimation methods. Alternative exchange rate models proposed in this paper -the stock-flow approach and variants of the monetary model -were also found to be not fully robust to data frequency and alternative estimation periods, either. In particular, it was difficult to establish cointegration for all periods considered and some coefficients estimates appeared to be unstable across the time and data frequency dimensions.

Nevertheless, adding openness to the stock-flow approach and augmenting the monetary model with share prices and the country risk premium improved significantly the fit of the models around the large (nominal and real) depreciation episodes of 2002 and 2008. While these models seem to do a reasonably good job in terms of in-sample forecasting, their out-ofsample forecasting properties remain poor.

Furthermore, while our results suggest that real commodity prices are important drivers of the real and nominal exchange rate, we also showed that coefficient estimates of that variable were somewhat sensitive to model specification and other parameters of the estimations and that including real commodity prices in real and nominal exchange rate models did not help too much improve the in-sample fit of the models. In particular, commodity prices cannot explain the large deprecations observed around 2002 and 2008.

Figure 1 .

 1 Figure 1. Real and nominal exchange rate of the South African rand against the effective basket and the USD, 1980:m1-2009:m6 (2000:m1=1)

•

  1980:q1 to 2002:q1 => the MacDonald and Ricci (2004) sample for the end • 1980:q1 to 2007:q1 => the Frankel (2007) sample • 1980:q1 to 2009:q1 => sample period of this paper

Figure 2

 2 Figure 2 shows the fit of the individual models until 2009 even if a model is estimated only until 2002 or 2007. In this case, the fit of the model for the periods of 2002-2009 and 2007-2009 can be thought of as the out-of-sample forecast of the model, while the fit computed for the period for which the model is estimated shows in-sample forecasts. We do not carry out proper forecast accuracy comparisons because we focus on the two large depreciation episodes for which the figures are very informative. The Frankel model can explain only part of the 2002 depreciation episode and it absolutely cannot follow the real exchange rate of the rand vis-à-vis the dollar. This indicates that the out-of-sample forecasting properties of the models estimated until 2002 and 2007 and the insample forecasting properties of the models estimated until 2009 are rather poor.

Figure 2 .

 2 Figure 2. Real exchange rate models, fit vs. actual series, 1980-2009 first row: quarterly data, second row: monthly data

  from 1980:q1 to 2002:q1 appears to systematically underestimate the exchange rate since 2000. The model including real commodity prices does have a slightly improved fit compared to the basic version: while it also misses the depreciation in 2002, it seems to capture a little better the end-period developments of the exchange rate. Nevertheless, this is only true for the estimated obtained for a sample ending in 2009. The models estimated on samples ending in 2002 and 2007 have bad out-of-sample fit.

Figure 3 .

 3 Figure 3. Real exchange rate models, fit vs. actual series, 1990-2009

Table 1a .

 1a Estimation results, Frankel model, real exchange rate against the USD UR is the residual based cointegration test and ECT denotes the error correction term for the DOLS model. JOH r=0 and JOH r=1 are the trace statistics. ECM and LR refer to the error correction model and the long-run relationship estimated using DOLS, respectively. * and ** mean statistical significance at the 10% and 5% levels. All variables are taken in natural logs, the only exception is the real interest differential. SIC is the Schwarz information criterion.

	Notes:
									Quarterly data			Monthly data
								CPI-based PPI-based		CPI-based			CPI-based
								1980-2007	1980-2007	1980-2009	1980-2002	1994-2009	1980-2002	1980-2007	1980-2009	1994-2009
	COINTEGRATION TESTS
	UR							-1.562 (0)	-2.356 (0)	-0.087 (0)	-1.487 (0)	-0.024 (0)	-2.426 (2)	-2.031 (1)	-2.133 (1)	-1.66 (1)
	ECT							-0.096**	-0.14**	-0.031	-0.11**	-0.031	-0.052**	-0.038**	-0.014	-0.033**
	JOH r=0					57.06**	58.23**	44.13*	52.6**	21.67	44.9*	49.14**	52.31**	20.17
	JOH r=1					29.28*	29.08*	19.21	27.75*	2.95	23.03	28.25*	23.48	3.5
	COEFFICIENT ESTIMATES
	C							0.089**	0.072**	0.083**	0.017	0.261**	0.079**	0.106**	0.06**	0.123**
	RIR							-0.029**	-0.036**	-0.037**	-0.039**	-0.039**	-0.034**	-0.023**	0.013**	-0.019**
	RIR*1994					0.018**	0.025**	0.02**	0.026**		0.017**	0.015**	-0.023**
	Commodity					-0.726**	-0.633**	-0.69**	-0.72**	-0.968**	-0.761**	-0.687**	-0.36**	-0.308**
	No. obs					107	107	114	87	59	265	325	352	178
	ECM -	adj -	R	2	0.204	0.217	0.156	0.153	0.167	0.176	0.167	0.171	0.175
	ECM -SIC					-2.594	-2.702	-2.495	-2.525	-2.499	-3.899	-3.846	-3.757	-3.817
	LR -	adj -	R	2		0.599	0.586	0.685	0.7	0.873	0.675	0.559	0.314	-0.371
	LR -SIC					-0.704	-1.093	-0.579	-1.059	-1.318	-1.114	-0.73	-0.284	-0.46

Table 1b .

 1b Estimation results, MacDonald and Ricci model, real effective exchange rate

										Quarterly data
								1980:Q1-2002:Q1	1980:Q1-2007:Q1	1980:Q1-2009:Q2	1994:Q1-2009:Q2
								DOLS	trace	DOLS	trace	DOLS	trace	DOLS	trace
	UR/Rr=0					-1.672	129.5**	-4.549*	105.83** -4.781*	155.61** -3.685	139.74**
	R=1								89.25	76.97**	109.77**	85.97
	R=2								62.69	51.67**	79.33**	52.24
	R=3								38.64	29.16*	50.88**	31.09
	ECT/r=4					-0.01	21.62	-0.242** 10.48	-0.259** 26.47	-0.246** 13.85
	R=5								6.01	1.97	8.21	4.6
	R=6								0.3	0.81	0.18	0
								DOLS	VAR	DOLS	VAR	DOLS	VAR	DOLS	VAR
	C							-0.208	0.052	0.123**	-0.073	0.122**	-0.178	0.077**	-0.282
	RIR							0.076*	-0.037**	-0.014** 0.066**	-0.014** 0.264**	-0.008** 0.044**
	CAPITA					-1.008	2.015**	-1.056** 0.008	-0.994** -3.411	-0.491	-0.876
	OPEN						0.345	-0.891**	0.767**	1.542**	0.72**	10.292** 0.804**	0.577**
	DEBT						-2.386** 0.927**	-0.193** 0.617	-0.176** 1.532	0.104	0.798**
	NFA							-4.833** -0.472	-0.226	1.575	-0.148	4.61	0.587**	1.328**
	Commodity					0.719	-0.658**	-0.152** 0.567	-0.179** 1.92	-0.177	0.759**
	No. obs					63		78	83	45
	ECM -	adj -	R	2	0.26		0.36	0.339	0.28
	ECM -SIC					-2.728		-2.924	-2.887	-2.694
	LR -	adj -	R	2		0.953		0.885	0.894
	LR -SIC					-2.011		-1.947	-1.979
										Monthly data
								1980:M1-2002:M3	1980:M1-2007:M3	1980:M1-2009:M6	1994:M1-2009:M6
								DOLS	trace	DOLS	trace	DOLS	trace	DOLS	trace
	UR/ r=0					-5.824** 139.97** -5.871** 149.49** -5.694** 157.02** -4.239	122.51*
	R=1								88.84	94.46**	101.32**	80.58
	R=2								56.86	58.76	64.98*	46.05
	R=3								33.53	37.04	39.93	27.48
	ECT/r=4					-0.064** 18.01	-0.068** 20.06	-0.073** 20.97	-0.072*	12.28
	R=5								7.45	7.29	6.45	5.41
	R=6								0.1	1.3	0.27	0.24
								DOLS	VAR	DOLS	VAR	DOLS	VAR	DOLS	VAR
	C							0.087**	0.076	0.103**	0.006	0.108**	0.089	0.078**	-0.141
	RIR							-0.011** -0.011	-0.015** 0.001	-0.015** -0.022	-0.01**	0.011
	CAPITA					-1.562** 2.425**	-1.075** 2.159**	-1.006** 2.411**	-0.982	-6.515**
	OPEN						0.764**	-1.604**	0.742**	-2.707**	0.704**	-4.129**	0.747**	-0.656**
	DEBT						-0.565** 0.493	-0.157** -0.595**	-0.132** -1.422**	0.069	0.289
	NFA							-0.053	0.093	-0.045	-0.053	-0.019	-0.568	0.162**	0.239
	Commodity					0.079*	-0.809**	-0.149** -0.576**	-0.183** -0.824**	-0.142*	1.251**
	No. obs					258		318	339	180
	ECM -	adj -	R	2	0.233		0.226	0.236	0.179
	ECM -SIC					-4.006		-3.996	-3.977	-3.858
	LR -	adj -	R	2		0.882		0.889	0.897	0.808
	LR -SIC					-2.172		-2.135	-2.168	-2.265
	Notes: see Table 1a.

Table 2a .

 2a Estimation results, stock-flow model including commodity prices, real effective exchange rate

	Quarterly data	Monthly data

  : *, ** and *** indicate statistical significance at the 10%, 5 % and 1% levels. For the rest, as for Table1a

	COINTEGRATION TESTS
	UR							-2.627 (0)	-3.187 (0)	-3.624 (3)	-1.728 (0)	-3.438 (1)	-3.839	-3.21 (1)	-2.158 (1)
	ECT							-0.177**	-0.201***	-0.129**	-0.203***	-0.072***	-0.074***	-0.05***	-0.061**
	r=0							49**	57.47***	56.85***	57.33***	55.83***	55.01***	49.67**	47.73**
	r=1							25.09	29.53*	29.69**	25.6	24.54	33.37**	26.83*	20.48
	COEFFICIENT ESTIMATES
	C							0.08***	0.075***	0.04*	0.056**	0.095***	0.083***	0.054***	0.049***
	CAPITA					-0.251	-0.107	-0.583***	-2.504*	-0.216**	-0.191***	-0.622***	-1.143
	NFA							1.197***	0.913***	0.954***	0.813***	0.473***	0.406***	0.416***	0.368***
	COMMODITY -0.419***	-0.501***	-0.195***	0.108	-0.468***	-0.462***	-0.188***	-0.064
	No. of obs					84	104	111	60	258	318	339	180
	ECM -	adj -	R	2	0.102	0.12	0.049	0.131	0.092	0.091	0.072	0.111
	ECM -SIC					-2.654	-2.709	-2.622	-2.654	-3.89	-3.879	-3.825	-3.846
	LR -	adj -	R	2		0.768	0.773	0.72	0.444	0.73	0.764	0.717	0.44
	LR -SIC					-1.481	-1.468	-1.205	-1.291	-1.529	-1.564	-1.325	-1.454

Notes

Table 2b .

 2b Estimation results, stock-flow model including commodity prices and openness, real effective exchange rate

	Quarterly data	Monthly data

Table 3b .

 3b Monetary model augmented with real commodity prices Nominal effective exchange rate

	Quarterly data	Monthly data

Table 3c .

 3c Monetary model augmented with real commodity prices and real share prices Nominal effective exchange rate

	Quarterly data	Monthly data
	1980-

Table 3d .

 3d Monetary model augmented with real commodity prices and country risk premium Nominal effective exchange rate

	Quarterly data	Monthly data

Earlier papers are not considered here because the estimation results are obtained for sample periods that stop around the mid-1990s. These papers includeAron et al. (2000) and[START_REF] Mtonga | The real exchange rate of the rand and competitiveness of South Africa's trade[END_REF] for the real exchange rate and[START_REF] Chinn | A monetary model of the South African Rand[END_REF] and[START_REF] Odedokun | The monetary approach to analyzing floating exchange rate behaviour in developing countries: evidence from Sub-saharian African Countries, 1986-1992[END_REF] for the nominal exchange rate.

Unit root and stationarity tests indicate that the series under consideration are nonstationary processes. Results for the data series used in this paper are not reported but are available upon request.

See eg.[START_REF] Faruqee | Long-Run Determinants of the Real Exchange Rate: A Stock-Flow Perspective[END_REF];Aglietta et al.(1998) and[START_REF] Alberola | Outs," and Other Major Currencies in a Panel Cointegration Framework[END_REF][START_REF] Alberola | Quo vadis Euro?[END_REF].

The relative price of nontradables may rise for three reasons. First, as part of the resource movement effect (when a rise in commodity price draws labour and capital from the non-commodity sectors to the commodity sector), nontradable prices increase because of the excess demand for nontradables, which is brought about by a fall in the supply owing to less labor in the nontradable sector. Second, as nominal and real wages increase in the commodity sector, wages will also rise in other parts of the economy provided wages tend to equalize across sectors. As a consequence of wage increases in the non-tradable sector, the relative price of non-tradable goods increases. Third, the relative price of nontradables rises in the event that higher profits and wages in the oil sector and the related tax revenues are spent on nontradable goods and provided the income elasticity of demand for nontradables is positive. This latter effect is also called the spending effect.

For details, seeClements and Frankel (1980) andCrespo-Cuaresma et al (2005a,b).

The coefficient estimates on relative GDP and money supply become unstable if we add a linear trend to the specification.

Figure 3 shows data from 1990 to 2009. See the appendix for fit from 1980 to 2009.

PPI

South Africa: IFS/IMF (via Datastream code: SAI63...F) US economy: IFS/IMF (via Datastream, code: USI63...F) Real interest rate differential (monthly): nominal interest rate deflated by y-o-y CPI, (t+4/t for the Frankel model and t/t-4 for the MacDonald and Ricci model), relative to trading partners Long-term interest rates (long-term government bond yield) (monthly) South Africa: IFS/IMF (via Datastream, code: SAI61...) US economy: IFS/IMF (via Datastream, code: USI61...) Euro area proxied by Germany: IFS/IMF (via Datastream, code: BDI61...) United Kingdom: IFS/IMF (via Datastream, code: UKI61...) Japan: IFS/IMF (via Datastream, code: JPI61...) Real commodity prices (monthly): Frankel definition, weighted nominal prices deflated by US CPI Gold, 56.22%, UK London gold price, Datastream code: UKI..C..A Coal, 18.23%, IMF, http://www.imf.org/external/np/res/commod/index.asp Iron, 8.9%, IMF, http://www.imf.org/external/np/res/commod/index.asp Oil, 9.01%, IMF, http://www.imf.org/external/np/res/commod/index.asp Aluminium, 7.64%, IMF, http://www.imf.org/external/np/res/commod/index.asp MacDonald-Ricci definition, weighted nominal prices deflated by US CPI Gold, 71%, UK London gold price, Datastream code: UKI..C..A Coal, 17.7%, IMF, http://www.imf.org/external/np/res/commod/index.asp Iron, 3.9%, IMF, http://www.imf.org/external/np/res/commod/index.asp Copper, 3.8%, IMF, http://www.imf.org/external/np/res/commod/index.asp Platinum, 3.6%, London Platinum Free Market $/Troy oz, Datastream code: PLATFRE Real gold price: nominal gold price deflated by US CPI Real GDP per capita, relative to trading partners Real GDP (quarterly data, interpolated to monthly frequency if needed) South Africa: Main Economic Indicators/OECD (via Datastream, code: SAOSN029C), NSA US economy: Quarterly National Accounts/OECD (via Datastream, code: USOEXP03D) Euro area proxied by Germany: IFS/IMF (via Datastream, code: BDI99BVRG) United Kingdom: Quarterly National Accounts/OECD (via Datastream, code: UKOEXP03D) Japan: Quarterly National Accounts/OECD (via Datastream, code: JP2EXP03D (prior to 2004, JPGDP...D (after 2004)) Population South Africa (annual): Main Datastream, code: SAI99Z..O US economy (quarterly): Datastream, code: USPOPNIQH Euro area proxied by Germany (quarterly): Datastream, code: BDPOPTOTP United Kingdom (quarterly): Datastream, code: UKESENP.O Japan (annual): Datastream code: JPI99Z..O Net foreign assets (1970:m1 -2007:m3), net foreign assets of the banking sector over nominal GDP Net foreign assets, South Africa, IFS/IMF monetary survey (Datastream code: SAI31N..A) Nominal GDP, if needed interpolated linearly from quarterly to monthly frequency South Africa: IFS/IMF (via Datastream, code: SAI99B.CB) Openness, Export + import of goods over nominal GDP Total trade. Main Economic Indicators/OECD, exports from South Africa and imports to South Africa (via Datastream, exports: SAOXT$03A, imports: SAOXT$09A) Nominal GDP, see net foreign assets Government debt to GDP relative to trading partners Government debt (monthly) South Africa (monthly): Central government debt, Datastream code: SAI99B.CB US economy (quarterly): Gross public debt as % of GDP, Datastream code: USEBQDGD% Euro area proxied by Germany (monthly): Datastream code: BDL99B.CB) United Kingdom (quarterly): Public sector net debt as % of GDP, Datastream, code: UKRUTOQ. Japan (monthly): Datastream code: JPDBTGOVA Nominal GDP (quarterly), if needed interpolated linearly from quarterly to monthly frequency South Africa: IFS/IMF (via Datastream, code: SAI99B.CB) US economy: IFS/IMF (via Datastream, code: USI99B.CB)


Zuzana Brixiova

Balázs Égert

LABOUR MARKET REFORMS AND OUTCOMES IN ESTONIA 1

Keywords: JEL Classification: J08, J64, E24 Labour market reforms, search model, Estonia, OECD countries

The unemployment rate in Estonia rose sharply in 2010 to one of the highest levels in the EU, after the country entered a severe recession in 2008. While the rate declined relatively rapidly in 2011, it remained high especially for the less educated. In 2009, the Employment Contract Law relaxed employment protection legislation and sought to raise income protection of the unemployed to facilitate transition from less to more productive jobs while mitigating social costs. Utilizing a search model, this paper shows that increasing further labour market flexibility through reducing the tax wedge on labour would facilitate the structural transformation and reduce the long-term unemployment rate. Linking increases in unemployment benefits to participation in job search or training programmes would improve the unemployed workers' incentives to search for jobs or retrain and the medium term labour market outcomes. Social protection schemes for the unemployed should be also strengthened as initially intended to give the unemployed sufficient time to search for adequate jobs or retrain for new opportunities.

Introduction

Following a deterioration during the transition to a market economy and the Russian crisis in the 1990s, the labour market outcomes in Estonia improved markedly by the end of 2007. The employment rate exceeded the EU-15 average and participation rates increased. After entering a recession in 2008, Estonia's unemployment rate escalated from 4.1 percent in December 2007 to 19.8 percent in June 2010 -one of the highest levels in the European Union. Even though real GDP grew by almost 9 percent in 2011, unemployment remained about 13 percent. With high unemployment and the large share of low-value added non-tradable sectors including construction, a pressing issue for policymakers became reallocating workers across jobs and sectors to more productive activities, while mitigating fiscal and social costs. Flexibility of the labour market, together with job creation, became important for strong recovery and medium-term outcomes. 1Applying the search frameworks of [START_REF] Mortensen | New developments in models of search in the labour market[END_REF] and [START_REF] Van Ours | Compulsion in active labour market programmes[END_REF] to Estonia, this paper examines the impact of labour market reforms adopted in the country in 2009 and those expected in 2013, in particular deregulating employment protection and raising unemployment insurance.

At the same time, adequate social support for the unemployed was needed to ensure their minimum living standards and opportunities to improve livelihoods.

Main characteristics of the Estonian labour market

The analysis suggests that labour market adjustment from unemployment to increased high value-added activities would be eased if: (i) increases in unemployment benefits were made conditional on participation of the unemployed in active labour market programs, especially retraining and job search; (ii) the employers' social security contributions were reduced, and (iii) increases in minimum wages were contained. The reduction of labour taxation, especially for low-wage workers, could also stimulate job creation.

A simulation exercise based on the labour market matching model with active labour market policies of [START_REF] Van Ours | Compulsion in active labour market programmes[END_REF] illustrates that i) linking unemployment benefits to participation in active labour market programmes reduces unemployment if accompanied by effective job creation incentives; ii) in contrast, lowering minimum wages hampers incentives of the low-wage unemployed to search for jobs, but makes firms more willing to hire, with an ambiguous impact on the overall employment; iii) cuts in firms' social security contributions stimulate firms' incentives to hire.

The paper is organised as follows. Section 2 outlines the main features of the Estonian labour market, and Section 3 presents the search matching model and policy simulations. Section 4 compares the results for Estonia with some stylised facts for OECD countries, while Section 5 concludes.

From 2000 to early 2008, Estonia's labour market outcomes improved markedly: the unemployment rate dropped to close to 4 percent in 2008, its lowest point in 16 years, with long-term and very long-term unemployment rates also falling steadily (Figure1). At the same time, the employment rate and labour force participation increased. While aggregate outcomes improved, large inequalities persisted among regions, ethnic groups, and workers with different skill levels, with unemployment being particularly high among unskilled workers.

The economic boom, reflected also in eventual skill shortages, led to excessive real wage increases during 2005-07, both in the private and public sectors. Subsequently the gap between real wages and real GDP widened. After having risen sharply to 19.8 percent after Estonia fell into a deep recession in mid-2008, the unemployment rate has been declining and reached 13.3 percent in the third quarter of 2011. The structure of employment has also changed, with the share of workers on part-time and temporary contracts gradually rising since 2008 (Figure 1). Differences across skill levels remained: in Q2, 2010 unemployment rate was 32.7 percent for the uneducated population relative to the 18 percent overall rate (OECD, 2011). Besides high unemployment, especially among the less educated workers, the Estonian labour market has the following structural features.

First, it is characterised by a high degree of wage flexibility 3

3 Flexibility reflects how quickly the labour markets adjust to shocks [START_REF] Pissarides | The need for labour market flexibility in a European economic and monetary union[END_REF]. Four elements are typically discussed: i) numerical flexibility, ii) working time; iii) functional flexibility, and iv) the rate at which nominal and real wages respond to changes in supply and demand [START_REF] Eamets | Labour market flexibility and flexicurity[END_REF].

and almost fully decentralised wage setting, with wages being determined mostly within firms. Exceptions are the setting of the minimum wage, wages in the civil service sector set by government regulations, and wages in selected heavily unionized industries (e.g., textiles). 4 According to [START_REF] Rõõm | The principles of wage formation in Estonian companies[END_REF] and [START_REF] Maivali | Managed vs. Free Wage-Setting in Finland and Estonia: Optimizing Outcomes[END_REF], wage adjustments in Estonia are frequent, with substantial cyclical fluctuations and sizeable sectoral dispersion. Yet, wage flexibility declined during the boom period: while until 2004 wage increases reflected closely productivity gains [START_REF] Babecký | Aggregate wage flexibility in the new EU member States[END_REF][START_REF] Rõõm | The principles of wage formation in Estonian companies[END_REF], during 2005-07 real wage increases were largely in excess of labour productivity growth due to labour and skill shortages resulting from rising demand5 Second, until 2009, Employment Protection Legislation (EPL) in Estonia was more rigid than in other Central European countries or the OECD average (Table 1). The rigidity stemmed from: regulation of regular contracts, notably from long notice periods for workers with short tenure; narrow definition of unfair dismissal; and the right to re-employment or high compensation for unfair dismissal.

. At 20 and 40 percent respectively, Estonia's 2007 growth in average earnings (including bonuses and overtime) was among the highest and the increase of the civil sector wage was the highest in the EU (Figure 1).

According to a survey by [START_REF] Dabusinskas | Survey evidence on wage and price setting in Estonia[END_REF], wages were downwardly flexible during the crisis especially relative to other European countries. Specifically, in summer 2009, around 46 percent of Estonian firms already cut wages of their workers and another 40 percent intended to do so. Overall, 30 percent of the labour force were impacted by wage cuts, a far larger share than in other countries surveyed.

6

To address concerns about reduced employees' security due to a lighter EPL, the income protection for the unemployed was to be enhanced through raising the unemployment benefit replacement rate and easing the eligibility for unemployment insurance. Specifically, the unemployment income replacement rate was to be raised from 50 to 70 percent during the first 100 days of unemployment, and from 40 to 50 percent afterwards. Those leaving their jobs voluntarily were also to receive unemployment insurance benefits. However, adoption and implementation of these measures have been postponed to 2013 [START_REF] Leetmaa | EEO Review: Adapting unemployment benefit systems to the economic cycle, 2011 -Estonia[END_REF].This delay is in contrast with measures of some other European countries that increased unemployment support to safeguard adequate living standards.

EPL was eased in 2009: the new Employment Contract Act deregulated comprehensively regular contracts, including i) a reduction in the notice period for redundancy to 15-90 working days, depending on the length of employment; ii) a cut in severance payments, costs of which are shared by the employer and the Unemployment Insurance Fund; and iii) an easing of dismissals and hiring, which facilitates overall mobility and job search of the new job market entrants (OECD, 2004). Estonia's EPL thus became slightly less stringent than in the euro area (Dabusinskas and Rõõm, 2011). 7 Third, before the 2007-08 crisis, expenditures on active labour market policies (ALMPs), as a share of GDP, were very low in comparison to a European or OECD average. ALMPs thus played a minimal role in facilitating workers' employment. Incentives for unemployed workers to search or undergo training were also low. As shown in Figure 1, spending on ALMPs increased markedly to above 3 percent in 2009 from below 1 percent of GDP in 2008.

Fourth, the minimum wage, determined annually by agreement between trade unions and representatives of employers is low, measured by the ratio of the minimum wage to the average wage at around 30 percent. Yet it was increasing very rapidly until 2007. The increases in the minimum wage in these years exceeded both average real wage growth and labour productivity growth, thus pricing out of jobs low-income workers for whom the minimum wage may constitute a binding constraint. The minimum wage is determined annually at the centralised level and covers all employees. According to [START_REF] Rõõm | The principles of wage formation in Estonian companies[END_REF] and other estimates, approximately 6 percent of private sector workers in Estonia earned the minimum wage in 2008. But the influence of the minimum wage on wage formation goes beyond these six percent -for example, in some cases of unionized enterprises (e.g., textile), minimum wages constitute a basis from which wages of all workers are derived and stipulated in collective agreement.

Finally, Table 1 shows the very high tax wedge on labour, which stands in contrast to a modest overall tax burden on income tax and especially on capital gains: Overhead costs, comprising social contribution tax levied on employers accounted for almost 40 percent of wages in 2006 and remained at that level in 2011. The tax wedge is especially high when compared to OECD countries such as Ireland, the USA or the United Kingdom, whose labour markets are similar to Estonia's (OECD, 2011).

A matching model with active labour market policies: application to Estonia

The model

To illustrate the likely medium-term outcomes of reforming labour market institutions, changes in active labour market programmes (ALMPs), unemployment benefits, minimum wages, and employers' social security contributions are examined in a standard search model, applied to Estonia. Specifically, the model outlined below is a somewhat modified version of [START_REF] Van Ours | Compulsion in active labour market programmes[END_REF], which extends the framework of [START_REF] Mortensen | New developments in models of search in the labour market[END_REF] by adding participation in job search and/or training programmes. The application below focuses on the effect of labour market reforms on incentives for the unemployed to search for jobs or to participate in training programmes and for firms to create jobs.

In the model, workers can be either employed in the private sector or unemployed. Unemployed workers receive benefits b, value their leisure as l, and search for jobs or put effort in training with intensity 0 ≥ x while incurring cost

e v A e δ θ η - = -1  (1) xu A e u η θ δ - =  (2)
With normalizing the labour force to 1, that is

u e + = 1
, the steady state equilibrium unemployment decreases with search/training effort and the tightness of the labour market:

x A u η θ δ δ + = (3)
To illustrate the impact of mandatory participation in ALMPs on workers' search/training effort, a scenario where all unemployed workers can receive unemployment benefit only if they participate in the job search assistance or retraining programme is considered. Participation in such programme lowers the value of leisure for the unemployed by fraction V , exceeds the value on unemployment, U V :

        - + - - - + = ) ( 2 ) 1 ( ) 1 ( max 2 U E x U V V x A x l z b V η θ γ σ ρ (4) ) ( E U E V V w V - + = δ ρ (5)
where ρ is the discount rate. Denoting E J as value of filled job and V J as value of vacancy, the corresponding Bellman equations are:

) ( ) 1 ( K J J w y J E V E - - + + - = δ τ ρ (6) ) ( 1 V E V J J A c J - + - = - η θ ρ (7)
Where y is the output from the filled vacancy, τ w is the social employers' contribution tax paid, and K is the severance cost incurred by the firm. Under the standard assumption of free entry into the job creation, value of posting a vacancy is 0 = v J . ( 6) and ( 7) can therefore be reduced to:

A c K w y η θ δ ρ δ τ - = + - + - 1 ) 1 ( (8)
The optimal search/training intensity x can be derived directly from (4):

) ( ) 1 ( U E V V A x - - = η θ σ γ (9)
The search/training effort rises with higher loss of leisure due to participation in the ALMP programme.

To complete the characterization of unemployment outlined in (3), a solution for the tightness of the labour market,θ , needs to be obtained through deriving wages. Regarding wage determination, the model deviates from the standard assumption of Nash wage bargaining. Instead, it assumes that flexible wages move with productivity changes:

y w φ = , where ) 1 , 0 ( ∈ φ
, consistent with the empirical evidence [START_REF] Dabusinskas | Survey evidence on wage and price setting in Estonia[END_REF][START_REF] Babecký | Aggregate wage flexibility in the new EU member States[END_REF][START_REF] Rõõm | The principles of wage formation in Estonian companies[END_REF].

Comparative statics

The comparative statics relevant in the Estonian context are:

Simulation results

The model is simulated using quarterly parameters from existing studies and the Estonian labour market data. Parameters are specified as follows:

Figures

Search intensity Unemployment rate u n emp lo ymen t rat e search in ten sity

Note: Unemployment rate is number of unemployed as % of labour force. For units of consumption good, the price of the consumption good is normalised to one. Mandatory participation represents foregone leisure.

Search intensity Unemployment rate u n emp lo ymen t rat e

Note: Unemployment rate is number of unemployed as % of labour force. For units of consumption good, the price of the consumption good is normalised to one. Source: Author's calculations.

Search intensity Unemployment and vacancy rate (percent) u n emp lo ymen t rate vacan cy rate search in ten sity

Note: Unemployment and vacancy rates are respectively the number of unemployed and vacancies as % of labour force. For units of consumption good, the price of the consumption good is normalised to one. Source: Author's calculations.

Search intensity Unemployment and vacancy rates u n emp lo ymen t rate vacan cy rate vacan cy-u n emp lo ymen t ratio

Note: Unemployment and vacancy rates are respectively the number of unemployed and vacancies as % of labour force. The vacancy/unemployment ratio is the vacancy rate divided by the unemployment rate.

Source: Author's calculations.

Figure 4 illustrates the impact of increases in minimum wages on the low-wage unemployed workers for whom these wages may constitute a binding constraint. While workers would increase their search/training effort because of a higher payoff from working, the positive impact could be more than offset by firms' posting fewer vacancies because of lower profits. Figure 5 illustrates the likely impact of cuts in social contribution tax paid by employers. The direct consequence would be a higher profitability of firms and hence more vacancies/lower unemployment rate, provided that the lost revenues are replaced by less distortionary taxes.

Policy lessons

The above simulation exercise helps us draw several policy conclusions:

• Linking increases in unemployment benefits to participation in job search or training programmes would improve workers' incentives to search for jobs or put effort into training, by reducing the value of being unemployed and improving their chances of finding a job.

• While lower minimum wages would somewhat hamper incentives of the low-wage unemployed to search for jobs or be retrained, firms would be more willing to hire. The unemployment rate could decline as long as the prevailing minimum wage level is binding.

• A lower tax wedge due to cuts in firms' social security contributions would raise firms' payoff from filled jobs, and hence their incentives to post vacancies. Search or training effort of workers would also increase, as their chances of finding jobs would improve. Both the unemployment level and duration would decline.

The transition costs

Although the results presented in the previous section focus on the longer term labour market outcomes, the above measures would also affect the speed of adjustment and the associated transition costs, and hence the political support for reforms. Generally, the speed of adjustment is faster when labour market flexibility is enhanced, underlying for example the importance of reducing the social security tax, especially on low income workers, as a way to ease the recovery and reduce medium term unemployment. [START_REF] Mourougane | Speed of adjustment to selected labour market and tax reforms[END_REF], who examined the length of adjustments to selected structural reforms in the OECD countries, found that the impact of structural reforms takes several years. As reallocating resources (e.g., labour) is costly, the efficiency gains take time to materialize. Effective monetary policy and well functioning financial markets can reduce the adjustment speed and transition cost through, for example, facilitating the access of new firms to credit. According to the authors, the tax wedge on labour, unemployment replacement ratio, and product market regulations play a major role in explaining the evolution of structural unemployment in OECD countries during 1983-2003. Tax wedge and product market regulations also have the largest impact in the short run. The importance of easing employment protection is in accordance with results of [START_REF] Caballero | Effective labour regulation and microeconomic flexibility[END_REF], who found that in countries with strong law enforcement, increasing job security would reduce the annual speed of adjustment to shocks by a third, while subtracting 1% from productivity growth.

While our model illustrations focus on the flexibility aspects of labour market reforms, the experience of other countries from the crisis and other episodes shows that the importance establishing adequate social protection mechanisms that would also help the unemployed search for appropriate jobs or retrain cannot be overstated. Putting differently, too low level of protection may force the unemployed to accept jobs that are not 'good' matches and hence increase the job dissolution rate and transaction costs associated with the job matching process.

Confronting the results with stylised facts from OECD countries

This section seeks to summarise available evidence from OECD countries regarding the impact of labour market reforms aimed to increase flexibility on the level of unemployment. Measures considered are: i.) ALMPs; ii.) the minimum wage; and iii.) the tax wedge.

Active labour market policies and unemployment

Over the medium term, increases in ALMPs would enhance workers' employability and give a larger role to automatic stabilisers. Among various activation approaches, job search assistance or "work first" strategies tend to have a large positive impact and low cost. Long term labour market programmes alone, such as training, often have no or even a negative impact in the short term, but increase employment and earnings 2-3 years after the individuals completed them. Hence mixed strategies combining job search and selective training programme participation seem to be most effective (OECD, 2005a,b).

Well designed and targeted activation policies or training programmes can offset the disincentives due to generous unemployment benefits. For instance, the Danish Flexicurity model, which is based on low employment protection, high expenditures on active labour market policies and generous unemployment benefits conditional on the obligation to take on job offers seems to incentivise firms to create jobs and unemployed persons to take up new job offers. Figure 6 below shows that the combination of extensive ALMP with higher net replacement rates and lower employment protection legislation might go in tandem with lower unemployment rates in OECD countries. Source: Authors' calculations using data obtained from the OECD Note: Vertical axis of the left panel shows an indicator, which is the product of public expenditures on ALMPs as a share of GDP and the long-term net replacement rate of unemployed persons, both measures averages of the period 2000 to 2008. Vertical axis of the right panel is augmented by the effect of the inverted employment protection legislation indicator (EPL). EPL ranges from 1 (least restrictive) to 4 (most restrictive). Hence, a low EPL would increase the overall value of the product of the three subindicators, while a high EPL would lower it. The unemployment rate is the period average for 2000-08.

The experience of OECD countries suggests that Estonia could improve the effectiveness of its ALMPs at a given level of expenditures by linking increases in unemployment benefits to participation in ALMP programmes and monitoring performance of the employment offices. Increases of unemployment benefits and their duration should be conditional on work availability and active job search and/or participation in job creating or training programmes (OECD, 2006). To raise ALMP's effectiveness, efficiency of employment services could also increase. Regarding benefit conditionality, Estonia could introduce practices of some of the OECD members:

• Required frequency of reporting of search activities could be raised from monthly to every two weeks, as is done, for example, in Australia, the Czech Republic, United Kingdom, and the United States. Personal visits seem most effective (OECD, 2007).

• Increases in benefit entitlements should be conditional on participation in ALMPs programmes, such as job creation (entrepreneurship) or training. Similar links have been established in Australia (Mutual obligation strategy); the UK (New Deal strategy) and other European countries [START_REF] Grubb | Activation policies in Ireland[END_REF].

Minimum wage, tax wedge and unemployment

A prevailing view in the economic profession is that a high tax wedge could lead to an insufficient creation of firms and jobs, and constitutes a particularly strong impediment for SMEs. Panel A of Figure 7 shows that a higher tax wedge goes hand in hand with higher unemployment rates in OECD countries. In the case of Estonia, surveys conducted by the Estonian Research Institute indicate that high taxes on labour are the main reason for undeclared work [START_REF] Leetmaa | Article on undeclared work from SYSDEM correspondent: Estonia[END_REF]. Against this backdrop, one of the proposals of the employers' representatives is to shift the burden of taxation from employers towards workers, by splitting the contribution between these two parties (Employers' Manifesto for 2007-2011).

High tax wedges are particularly detrimental to employment in countries with high minimum wages, because the tax burden cannot be passed on to workers [START_REF] Bassanini | Employment patterns in OECD countries: reassessing the role of policies and institutions, Social, Employment and Migration Working Papers[END_REF]. In fact, data shown in Panel A of Figure 7 that a higher tax wedge is associated with a higher unemployment rate in OECD countries over the period 2000 to 2008. In addition, a positive correlation exists between the product of the tax wedge and the minimum wage (as a share of average earnings), on the one hand, and the unemployment rate, on the other, implying that a higher tax wedge coupled with a higher minimum wage is linked to a higher unemployment rate in OECD countries.

In the Estonian context this provides additional reasons (besides macroeconomic and inflationary considerations) why minimum wage increases should be kept in line with productivity growth and at a level which does not reduce employment options of low-productivity workers. Estonia could include an independent committee of outside experts in negotiations, also to bring the macroeconomic perspective, as was done, for example, in Ireland, the United Kingdom, and Australia. In addition, the employers' social security contribution should be reduced, especially given the high tax wedge on low-income workers, as was recently done, for example in the Czech Republic in the context of the economic crisis.

More general policies may also influence labour market outcomes. A business-friendly environment that promotes the creation of firms and allows for more flexibility in adjusting to shocks is likely to reduce the unemployment rate. Panel B of Figure 7 shows a positive correlation between product market regulations (PMR) unemployment rate in OECD countries: a lower degree of regulation is associated with a lower unemployment rate. A better educated labour force is also essential to reduce frictions in matching job offers with job seekers. An increased ability to learn and think independently at the age of 15, captured by the PISA scores, tends to be associated with lower unemployment rates in OECD countries (Panel B of Figure 2). More broadly, and as shown in the above model, adult learning, in particular well targeted training programmes to close skill gaps in selected areas, can also help align workers' skills with demands of the labour market.

Conclusions

Following years of steady decline during 2001-2007, the unemployment rate in Estonia increased dramatically from 4.1 percent in December 2007 to 19.8 percent in June 2010 after the country entered a severe recession in 2008. While the rate was already down to 13.3 percent in September 2011, it remains high, especially among the less educated segments of the population. In this paper we examined labour market institutions and policies that may help Estonia reach better longer term labour market outcomes become.

While the Estonian labour market had been already flexible in many ways, the Employment Protection Legislation adopted in 2009 removed some of the remaining rigidities that hampered hiring of new workers, especially first entrants to the job market. It also eased transition from less to more productive activities, which is consistent with Estonia's objective to become a knowledge-based economy. The Estonian labour markets would also benefit from reduction of high tax wedge on wages as well as from keeping increases of the minimum wage in line with changes in labour productivity.

Results of a simulated search-matching model suggest that Estonia could adopt several measures to increase flexibility of its labour market and thus ease the recovery and improve medium term outcomes. These measures include strengthening incentives of the unemployed workers to search for jobs or participate in training and job search programmes and incentives for firms to create job creation such as:

(1) implementing fully the reduced lay-off notice periods and severance payments, as stipulated in the Employment Contract Act; (2) making increases in unemployment benefits conditional on active job search and retraining; and (3) reducing the tax wedge by cutting social security contributions of employers, especially on low-wage workers. The Estonian labour market would also benefit from improving employment incentives for low wage workers, such as reducing social security contributions of employers on low wage workers, as adopted, for example, in the Czech Republic as part of the anti-crisis package.

While not addressed in this paper, the experience of other countries shows that adequate social protection mechanisms would also improve longer term labour outcomes by allowing the unemployed to search for appropriate jobs or retrain for new jobs arising from structural changes in the economy. We leave this important topic for further research.

  2

Figure 1 .

 1 Figure 1. Labour market indicators, Estonia, 2000-2011

..

  Employed workers receive wage w. Firms post vacancies to fill jobs at cost c. Each filled job results in output y, with w y > . The key component of the model is of matches with respect to vacancies. The workers' search/training effort results in job offers, which arrive at rate of vacancy rate, v, to effective unemployment rate, xu, i.e. it describes the tightness of the labour market from firms' perspective.Conversely, firms fill their vacancies at rate 1 All job matches dissolve at rateδ , and firms pay to each laid-off worker a severance payment K. The employment rate, e , and unemployment rate, u , change according to:

  when the value of employment, E

  The search/training effort of the unemployed rises with effective job search and training programmes, lower search/training cost, improved matching efficiency, and reduced separation rate. The ALMPs can improve matching efficiency (by dissemination of information) as well as reduce search/training cost and separation rate.

Figure

  Figure 3. Impact of search cost cuts on search and unemployment

Figure

  Figure 4. Impact of minimum wage increase on search, unemployment and vacancies

  10

Figure

  Figure 5. Impact of social security tax on vacancies and unemployment

Figure 6 .

 6 Figure 6. The combination of ALMP, EPL and generous contributions and unemployment rate in OECD countries

Figure

  Figure 7. Policies and the unemployment rate in OECD countries Panel A. Tax wedge, minimum wages and the unemployment rate

Table 1 . Main characteristics of the Estonian labour market in an international comparison

 1

	Estonia	OECD
	year	AVERAGE MAX MIN

Source: OECD and Eurostat.

Table 2 . Comparative statics in the job search-matching model

 2

	Effect of an increase in:	On search effort of the unemployed x	On unemployment rate u
	Reduced utility from less leisure z Search cost reduction σ	+ +	--
	Matching efficiency A		+	-
	Minimum wage	w	y

Impact of mandatory participation in ALMPs on search and unemployment

											9
	0.09										0.9
	0.08										0.8
	0.07										0.7
	0.06										0.6
	0.05										0.5
	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1

below illustrate that participation in active labour market programmes, especially job search activation or training programmes, would increase workers search or training efforts through two channels: 1) by reducing the value of leisure and hence increasing relative payoffs from working; and 2) by increasing workers' chance of exiting unemployment. As a result of workers' increased search or training effort, unemployment would decline through both channels. Regarding effective application, programmes encouraging job search would help speed up recovery from cyclical unemployment where new jobs are created in the same sectors and hence workers can draw on existing skill. In contrast, training programmes would typically facilitate structural change, where new jobs are created in new sectors (for example in services rather than construction). 8 Figure 2.

The need for labour market flexibility is further underscored by the currency board arrangement.

In July 2009, the Employment Contracts Act became effective, which aimed at increasing the labor market flexibility by reducing costs of lay-offs and security through raising unemployment insurance. However, most of the measures aiming at raising security were postponed until 2013[START_REF] Leetmaa | EEO Review: Adapting unemployment benefit systems to the economic cycle, 2011 -Estonia[END_REF].

Overall though, the rate unionization and the use of collective bargaining coverage in the private sector of the Estonian economy are very low (12 and 9 percent, respectively). Collective bargaining is almost irrelevant for the wage setting process in the overall economy[START_REF] Dabusinskas | Survey evidence on wage and price setting in Estonia[END_REF].

A key factor behind the wage flexibility was a widespread use of performance-related bonuses. The 2007 survey of private firms in industry, constructions, services, and trade revealed that about two thirds of firms use bonuses, and their share in the wage bills ranged from 14% in industry to 23% in trade(Dabusinskas and Rõõm, 2008).

Yet, EPL regulations were not adhered to in practice[START_REF] Eamets | Paradox of the Baltic States: labour market flexibility but protected workers?[END_REF].

As a response to the global crisis, several OECD countries extending the coverage (Sweden) or duration of their unemployment benefits (Portugal, United States).

Training programs can also help the unemployed workers maintain or improve the existing skills.

All simulations (Figure2-5) focus on the impact of labour market policies on search effort, that is participation in job search programs. Results apply to participation in training programs as well.