Pierre-Guillaume Méon
email: pgmeon@ulb.ac.be

Friedrich Schneider
email: friedrich.schneider@jku.at

Laurent Weill
email: laurent.weill@iep.u-strasbg.fr

O11 -Macroeconomic Analyses of Economic Development <

Keywords: shadow economy, income, aggregate productivity, efficiency. JEL Classification: O11, O17, O47, O5 shadow economy, income, aggregate productivity, efficiency. JEL Classification: O11, O17, O47, O5

We analyze how adding the shadow economy to official output figures affects estimated technical efficiency at the country level. We find that this only slightly affects the ranking of efficiency scores, but increases average efficiency in a sample of 87 to 97 countries, both developed and developing. Our results are robust to the functional form of the production technology and the adjustment of labour to account for years of schooling.

Introduction

Most studies of economic development rest on official output figures. However, in so doing they neglect a sizeable part of economic activity, which takes place in the informal sector, and therefore goes unrecorded in official statistics. Nevertheless, as [START_REF] Tanzi | Uses and abuses of estimates of the underground economy[END_REF] remarks, though some of those activities may be illegal, others are legal and socially valuable.

They should therefore be taken into account when measuring a country's output. Moreover, the capacity of the informal sector to "provide goods and services for a large though often poor section of the population" (ILO, 1972) was recognized early, and repeatedly emphasized thereafter. [START_REF] Livingstone | A reassessment of Kenya's rural and urban informal sector[END_REF] for instance points out that the informal sector provides cheap and appropriate goods to markets quantitatively dominated by poor consumers.

Furthermore, those activities may also be important from a quantitative point of view.

Thus, according to [START_REF] Schneider | Shadow economies around the world: What do we really know?[END_REF], the "shadow economy", defined as currently unregistered economic activities that contribute to the officially calculated (or observed) Gross National Product, amounted to 16 percent of official output in OECD countries, 39 percent in developing countries, and up to 40 percent in transition countries, in 2002/2003.

Those daunting figures call into question the interpretation of the results of empirical studies that ignore this phenomenon, because poorer countries are also known to be less productive, as [START_REF] Hall | Why do some countries produce so much more output per worker than others?[END_REF] show, and to exhibit larger shadow economies, as most studies on the determinants of the shadow economy show, like Johnson et al. (1998a) or [START_REF] Schneider | Shadow economies: size, causes, and consequences[END_REF]. In particular, assessments of productivity at the aggregate 2 country level, like e.g. [START_REF] Collins | Economic growth in East Asia: Accumulation versus assimilation[END_REF], [START_REF] Klenow | The neoclassical revival in growth economics: Has it gone too far?[END_REF], [START_REF] Prescott | Needed: A theory of total factor productivity[END_REF], [START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF], or [START_REF] Kneller | The specification of the aggregate production function in the presence of inefficiency[END_REF], are likely to be affected when ignoring the shadow economy. This is particularly important for efficiency frontier methods such as stochastic frontier analysis (SFA), which estimates the world's production frontier and assesses countries' aggregate efficiency relative to that frontier (see e.g. Adkins et al., 2002, or Kneller and[START_REF] Kneller | The specification of the aggregate production function in the presence of inefficiency[END_REF]. Ignoring a substantial share of output is likely to result in biased estimates of the production frontier and a mismeasurement of inefficiencies. Most likely, efficiency is underestimated in countries with big shadow economies. The extent of the bias, however, is an empirical matter.

In what follows, we therefore check the robustness of the SFA to the inclusion of the shadow economy in official output figures. We first follow [START_REF] Kneller | The specification of the aggregate production function in the presence of inefficiency[END_REF] and estimate the world production frontier based on official output figures. We then add the shadow output to gauge the bias of existing studies. The rest of the paper is therefore organised as follows. Next section presents our empirical strategy. The following section displays and comments our results. The last section concludes.

Empirical strategy

In this section, we first present the various models that we estimated. We then describe the datasets on which they were estimated and how output figures were corrected.

The models

We apply the stochastic frontier approach to measure technical efficiency at the aggregate level. Technical efficiency measures how close a country's production is to what a country's optimal production would be for using the same bundle of inputs. [START_REF] Adkins | Institutions, freedom, and technical efficiency[END_REF] or Méon andWeill (2004, 2005), among others, adopted the same approach to evaluate the relationship of aggregate technical efficiency with institutional variables. 1 Its basic concept is illustrated in figure 1 below. A production frontier is estimated with the stochastic frontier approach, providing a benchmark for each country regardless of its inputs.

1 As an anonymous referee pointed out, by estimating and aggregate production frontier, we overlook the impact of countries' sectorial composition. However, in his survey, [START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF] shows that distinguishing sectors within countries does not improve our understanding of cross-country TFP differences. Moreover by considering countries' total outputs and factor endowments, our efficiency scores also measure the efficiency of those countries' specialisations. There are several reasons why macroeconomic performance is better measured using this approach than more usual performance indicators, like total factor productivity. First, it provides synthetic measures of performance. Namely, unlike productivity measures such as per capita income or output per worker, efficiency scores computed with the stochastic frontier approach allow to include several input dimensions in the evaluation of performances.

As a result, output can not only be compared to the labour stock, but also to the stocks of physical capital and human capital.

Second, technical efficiency provides relative measures of performance. Namely, once a production frontier is estimated, each country can be compared to the best-practice countries.

As a result, the efficiency score assesses how close each country's production is to what a hypothetical country's optimal production would be for using the same bundle of inputs. It thus directly provides a relative measure of performance.

Third, whereas total factor productivity measures assess performance by the whole residual from the production frontier for each country, stochastic frontier approach allows to disentangle the distance to the production frontier between an inefficiency term and a random error, taking exogenous events into account. In other words, it decomposes the residual into an efficiency component and a white noise component that may reflect bad luck or measurement errors.

In order to estimate the production frontier, we need to specify its functional form. For the sake of brevity, we consider the most common production functions analyzed in the development accounting literature, namely the Cobb-Douglas function. We complement it by the translog function. Those specifications respectively read:

ln(Y i ) = β 0 + β 1 ln(K i ) + β 2 ln(L i ) + v i -u i (1) ln(Y i ) = β 0 + β 1 ln(K i ) + β 2 ln(L i ) + β 3 ln(K i )² + β 4 ln(L i )² + β 5 ln(K i ) ln(L i )+ v i -u i (2)
where Y i measures country i's output, K i its capital stock, and L i its labour force. v i is the above-mentioned white noise component of the residual accounting for measurement errors or unpredictable events that make the frontier random. It is assumed to have a normal distribution with zero mean and variance σ v ². u i is the inefficiency term. It is a one-sided component with variance σ u ². As is common in the literature, we assume a half-normal distribution for the inefficiency term. We estimate the production frontier by maximum likelihood methods using the software program Frontier 4.1.

The Cobb-Douglas function is by far the most common in the development accounting and the aggregate efficiency literatures (see e.g. [START_REF] King | Capital fundamentalism, economic development, and economic growth[END_REF][START_REF] Klenow | The neoclassical revival in growth economics: Has it gone too far?[END_REF][START_REF] Hall | Why do some countries produce so much more output per worker than others?[END_REF][START_REF] Prescott | Needed: A theory of total factor productivity[END_REF], for the development accounting literature, and Adkins et al., 2002, or Méon and[START_REF] Méon | Does better governance foster efficiency? An aggregate frontier analysis[END_REF] for the aggregate efficiency literature) . However, estimating a translog function in addition to the standard Cobb-Douglas allows to statistically compare the performance of the two specifications.

Official data

We use [START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF] database, which provides the most comprehensive and up to date figures for development accounting. It provides data on official output, physical capital stocks, and human capital stocks. Capital stock figures are computed from the Penn World Tables mark 6.1, and are available for 1996. They are based on the perpetual inventory method. That method computes a period's capital stock according to the following equation:

K t = (1 -δ)K t -1 + I t (3) F o r P e e r R e v i e w 5
Where I t is investment and δ is the depreciation rate, which is assumed to be equal to 0.06. 2 The capital stock in the base year is computed as I 0 / (g + d), which is the steady state expression of the capital stock in the Solow growth model. I 0 is the first available value of investment, and g is the average geometric growth rate for the investment between the first year for which it is available and 1970. 3We use two different measures of the labour force. First, we define L i as the absolute number of workers. Second, following [START_REF] Kneller | The specification of the aggregate production function in the presence of inefficiency[END_REF] and [START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF], we replace it by a measure of human capital-adjusted labour supply

L i * = H i L i
, where H i is the mean years of schooling of the labour force.

Data on the shadow economy

The key element in the present paper is correcting output figures for the shadow economy. Data for the shadow economy are taken from [START_REF] Schneider | Shadow Economies of 145 countries all over the world: What do we know?[END_REF]. The MIMIC method is based on the statistical theory of unobserved variables, which considers multiple causes and multiple indicators of the phenomenon to be measured. For the estimation, a factor-analytic approach is used to measure the hidden economy as an unobserved variable over time. The unknown coefficients are estimated in a set of structural equations within which the "unobserved" variable cannot be measured directly. The MIMIC model here consists of two parts. The measurement model links the unobserved variables to observed indicators. 5 The structural equations model specifies causal relationships among the unobserved variables. In this case, there is one unobserved variable: the size of the shadow economy. The model for one latent variable (S) can be described as follows:

Structural equation model:

S = δ X + ν (4)
Measurement model:

Γ = λ S + ε (5)
where S is the unobservable scalar latent variable (the size of the informal economy),

Γ = (γ 1 …, γ p )' is a vector of indicators for S, X = (x 1 , … x q )
' is a vector of causes of S. λ and δ are the (p×1) and (q×1) vectors of parameters, and v and ε are respectively a scalar error and a (p×1) error.

Equation ( 5) links the informal economy to its indicators or symptoms, while equation (4) associates the informal economy with its causes. Assuming that errors are normally distributed and mutually uncorrelated, the model can be solved by combining equations ( 4) and ( 5):

Γ = π X + µ (6)
where π ≡ λ δ, and µ ≡ λ ν + ε.

Because Γ and X are observable data vectors, equation ( 6) can be estimated by maximum likelihood estimation using the restrictions implied in both the coefficient matrix π and the covariance matrix of the error µ.

Since the reduced form parameters of equation ( 6) remain unaltered when λ is multiplied by a scalar and Γ and σ v 2 are divided by the same scalar, the estimation of (4) and

(5) requires a normalization of the parameters in (4). A convenient way to achieve this is to constrain one element of λ to some pre-assigned value, usually 1.

5) One of the latest papers dealing extensively with the DYMIMIC approach, its development and its weaknesses is from Del'Anno (2003). One may also refer to the excellent study by Giles and Tedds (2002), as well as Breusch (2005aBreusch ( , 2005b)). Since the estimation of λ and δ is obtained by constraining one element of λ to some arbitrary value, it is useful to standardize the regression coefficients δ and λ as follows:

( )

Γ = σ σ δ δ Ŝ std (7a) ( ) S X std σ σ λ λ = (7b)
The standardized coefficient measures the expected change in the standard-deviation units of the dependent variable due to a one standard-deviation change of the given explanatory variable when the other variables are held constant.

Using the estimates of the std δ vector and setting the error term ν to its mean value of zero, the predicted ordinal values for the informal economy (S) can be estimated thanks to equation (4).

Then, by using information regarding the specific value of informal activity for some country (if it is a cross country study) or for some point in time (if it is a time series study), obtained from some other source, the within-sample predictions for S can be converted into absolute series.

There is a large body of literature on the possible causes and indicators of the shadow economy. 6 That literature distinguishes three broad types of causes of the shadow economy.

The first cause is the burden of direct and indirect taxation, both actual and perceived. A rising burden of taxation provides a strong incentive to work in the shadow economy to evade taxation. The second cause is the regulatory burden. The heavier it is, the larger the incentives to work in the shadow economy to avoid regulations. The last cause of the shadow economy hinges upon citizens' tax morale, which describes their attitude toward paying taxes. It determines the readiness of individuals to leave their official occupations and enter the shadow economy. It is assumed that a declining tax morale tends to increase the size of the shadow economy.

On the other hand, one may contend that the size of the shadow economy is reflected in three sets of indicators. The first is the development of monetary indicators. If activities in the shadow economy increase, additional monetary transactions are required. The second 6 Thomas (1992), Schneider (1994a[START_REF] Schneider | The shadow economies of Western Europe[END_REF][START_REF] Schneider | The shadow economy, in Encyclopedia of Public Choice[END_REF][START_REF] Schneider | Shadow economies around the world: What do we really know?[END_REF], Pozo (1996), Johnson, et al. (1998aJohnson, et al. ( , 1998b)), Giles (1997aGiles ( , 1997bGiles ( , 1999aGiles ( , 1999bGiles ( , 1999c)), Giles and Tedds (2002), Giles et al. (2002[START_REF] Del'anno | Estimating the shadow economy in Italy: A structural equation approach[END_REF], and Del'Anno and [START_REF] Schneider | The shadow economy, in Encyclopedia of Public Choice[END_REF]. The latest use of the model approach has been undertaken by Giles (1999aGiles ( , 1999bGiles ( , 1999c) ) and by Giles et al. (2002), Giles and Tedds (2002), [START_REF] Chatterjee | The Size and Development of the Indian Shadow Economy and a Comparison with other 18 Asian Countries: An Empirical Investigation[END_REF], and [START_REF] Bajada | The shadow economies of the Asia-Pacific[END_REF]. They basically estimate a comprehensive (sometime dynamic) MIMIC model to get a time series index of the hidden/measured output of New Zealand, Canada, India or Australia, and then estimate a separate "cash-demand model" to obtain a benchmark for converting this index into percentage units. Overall, this latest combination of the currency demand and DYMIMIC approach clearly shows that some progress in the estimation technique of the shadow economy has been achieved and a number of critical points have been overcome.

Admittedly the (DY)MIMIC method has its own drawbacks. It has for instance been criticized for the instability of estimated coefficients with respect to sample size changes and alternative specifications. The difficulty to obtain reliable data on cause variables other than tax variables has been pointed out, and the reliability of variables grouping into "causes" and "indicators" in explaining the variability of the shadow economy has sometimes been questioned. However, that method provides the largest available and consistent data set on the extent of the shadow economy. Since we need to merge that dataset with several datasets, we need to start with the largest possible sample, which Schneider (2006)'s dataset allows. 7

In our sample, the average size of the shadow economy is 34 percent.

Results

To assess the impact of adding the shadow economy to official figures on measured aggregate efficiency, we estimate each model twice: once with raw output figures, and once with output figures corrected for the shadow economy.

Estimations 1a, 2a, 3a, 4a use official output and estimations 1b, 2b, 3b, 4b add the shadow economy to these output figures. The first four estimations refer to the Cobb-Douglas specification, while the last four refer to the translog function. Finally, models 1 and 3 use raw labour figures, while models 2 and 4 use human capital-adjusted labour supply. We thus end up estimating eight specifications, the results of which are displayed in tables 2a and 2b.

F

σ = (σ u 2 + σ v 2 ) ½ . The gamma statistics is defined as γ = σ u 2 / (σ u 2 + σ v 2
). *, **, *** denote an estimate significantly different from 0 at the 10%, 5% or 1% level.

Not surprisingly, adding the shadow economy to official output produces different results across the two specifications of the production function. With the Cobb-Douglas specification, adding the shadow results in an increase of the production frontier's intercept.

As corrected output is by construction greater than official output, the production frontier shifts upwards. However, the other coefficients remain similar in magnitude.

The table also shows that -contrary to the results of [START_REF] Kneller | The specification of the aggregate production function in the presence of inefficiency[END_REF] -the translog specification does not outperform the Cobb-Douglas in our sample, as the loglikelihood ratios show. Moreover, the results obtained with the translog specification are less consistent. Namely, only the coefficient on labour is consistently significant, whereas other coefficients are insignificant, with the exception of the coefficient on physical capital in model 3, which turns significant when the shadow economy is added to official output. In addition, model 4 is the only specification whose goodness of fit deteriorates when the shadow economy is taken into account. What is more interesting though is the evolution of inefficiency scores when output is corrected for the shadow economy. Their summary statistics are displayed in table 3a and3b. It appears that correcting output figures for the shadow economy results in an increase of the average and median efficiency scores. Thus, average and median distance to the frontier diminishes. The decrease in the gamma statistics displayed in table 2a and2b 13 precisely, countries that were initially farther from the frontier benefited relatively more from the addition of unofficial production than the rest of the sample. Accordingly, minimum efficiency scores increase more than maximum scores, and the standard deviation of efficiency scores decreases. Thus, neglecting the size of the shadow economy results in overestimating inefficiencies in less efficient countries, and, in terms of traditional development accounting, this amounts to overestimating the residual. This is in line with our a priori expectations.

F

However, the last two lines of tables 3a and 3b also show that the ranking of countries in terms of efficiency is little affected when average efficiency rises. To be more specific, the coefficient of correlation between efficiency scores computed with or without the shadow economy is always greater than 95 percent and is significant at the one-percent level.

Similarly, the Spearman rank correlation coefficient (measuring the similarity in country rankings) exceeds 94 percent in all specifications and is also significant at the one percent level. One can therefore conclude that the ranking of countries in terms of efficiency does not dramatically depend on the inclusion of the shadow economy in output figures.

As a result of the strong rank correlation, the ranking of countries is little affected by the inclusion of the shadow economy in output figures. Nevertheless, the ranking of some countries can be markedly affected. With model 1, for instance, 10 countries experience a drop in their ranking by at least 10 positions. 9 At the same time, 12 countries improve their ranking by 10 positions or more. 10 Changes in rankings are similar with other models.

Concluding remarks

In this paper, we analyzed the impact of adding the shadow economy to official output figures on estimated production functions and technical efficiency across up to 97 countries.

Including the shadow economy hardly affects the ranking of countries in terms of efficiency.

However, it results in an increase of observed efficiency scores. Adding the shadow economy to official output figures thus allows a more precise estimate of countries' outputs.

Those results are important in several respects. First, they show that estimates of the production function based on total output differ from those based on official output figures.

Second, they therefore imply that ignoring the shadow economy leads to mistakes in measured efficiency.

9 Those countries are Australia, Austria, Indonesia, Iran, Jordan, the Netherlands, New Zealand, Singapore, Switzerland, and the United Kingdom. 10 These countries are Bolivia, Brazil, Honduras, Mexico, Nigeria, Panama, Peru, Philippines, Thailand, Turkey, Venezuela, and Zimbabwe.

  efficiency score is computed by comparing the optimal output per worker with the effective output per worker.

Figure

  Figure 1: The efficiency frontier Y/L Frontier y opt

Figure 2 :

 2 Figure 2: Development of the shadow economy.

  development of the labour market. Increasing participation of workers in the hidden sector results in a decrease in participation in the official economy. Similarly, increased activities in the hidden sector may be expected to be reflected in shorter working hours in the official economy. Third, the size of the shadow economy may also affect the development of the production market. An increase in the shadow economy means that inputs (especially labour) move out of the official economy. This displacement might reduce the growth rate of the official economy.

  results provide guidance to the empirical literature on economic output and productivity at large. Given that official output figures overlook a sizeable share of total activity, future research on the determinants and effects of a country's production should clearly start by a reflection on which definition of output, official or total, is relevant to the question at hand. Our results suggest that the answer to this question need not always be official output.

  Merging our data leaves us with 87 observations when human capital is taken into account and 97 otherwise. Those samples are large, by the standards of macroeconomics. They include both developed and developing countries. 8 Summary statistics are presented in table 1 above.

		Table 1: description of untransformed variables
	Variable	Definition	Mean	Std. deviation
	Y	Official output	331.93	939.63
		(billions of US$)
	K	Capital stock	721.77	2136.38
		(billions of US$)
	L	Number of workers	23349428.26	13.73
		(millions)
	H	Average years of	5.74	2.96
		schooling
	S	Shadow economy	33.65	8.60
		(percentage of Y)
	Finally, we corrected output figures for the shadow economy. To do so, we added the F shadow economy to official output figures. Corrected output figures are thus defined as the o r sum of official and shadow output such that Y i
		P
		e
		e r
		R
		e
		v i e
			w

7 Recall that

[START_REF] Schneider | Shadow Economies of 145 countries all over the world: What do we know?[END_REF]

dataset provides estimates of the shadow economy for 145 countries. By contrast,

[START_REF] Friedman | Dodging the grabbing hand: the determinants of unofficial activity in 69 countries[END_REF]

could only get estimates for 69 countries.

8

The sample of 97 countries includes 23 OECD countries and 74 non-OECD countries. It is described in the Appendix. * = (1+S i )Y i , where S i is the ratio of unofficial to official output in country i. As the oldest vintage of Schneider's estimates is 1999, we added that vintage to Caselli's dataset, which pertains to 1996. We accordingly worked with a crosssection of countries consisting of developed and developing countries for the late 1990s.

Table 2b :

 2b Stochastic frontier results: Translog

			Model 3	Model 4
			Official	Corrected	Official	Corrected
			output	output	output	output
			(3a)		(3b)	(4a)	(4b)
	Const.		2.266		0.322	6.112	5.398
			(0.54)		(0.08)	(1.44)	(1.20)
	K		0.511		0.720**	0.161	0.286
			(1.55)		(2.16)	(0.37)	(0.62)
	L		0.664*	0.645*	0.769*	0.727
			(1.94)		(1.88)	(1.73)	(1.53)
	K 2		0.012		-0.002	0.001	-0.016
			(1.06)		(0.18)	(0.05)	(0.67)
	L 2		0.008		-0.012	-0.024	-0.051
			(0.40)		(0.56)	(0.64)	(1.28)
	K×L σ	-0.025 o (0.95) r 0.132***	0.002 (0.09) 0.118***	0.019 (0.36) 0.194***	0.058 (1.03) 0.169***
	γ log-		(3.53) 0.640*** P (3.15) e 0.543* (3.10) (1.95) -13.55 -13.16	(3.54) 0.838*** (6.46) -16.89	(3.20) 0.711*** (3.56) -18.93
	likelihood LL ratio	1.68	e r 1.24	1.16	1.86
	N Absolute t-statistics in parentheses. The sigma statistics is defined as 97 97 87 87 R σ = (σ u 2 + σ v 2 ) ½ . The gamma statistics is defined as γ = σ u 2 / (σ u 2 + σ v 2 ). *, **, *** denote an estimate significantly different from 0 at the 10%, 5% or e e i v 1% level.
						w
					11

Table 3a :

 3a Descriptive statistics and correlation of raw and corrected efficiency scores:

			Cobb-Douglas
			Model 1	Model 2
			Official	Corrected	Official	Corrected
			output	output	output	output
			(1a)	(1b)	(2a)	(2b)
	Minimum		0.444	0.539	0.355	0.41
	Maximum		0.934	0.937	0.933	0.927
	Mean		0.808	0.828	0.748	0.774
	Median		0.826	0.835	0.787	0.800
	Std. deviation	0.0802	0.0655	0.131	0.103
	Pearson Spearman	F o r --	0.964 0.945	--	0.959 0.958
			P
			e
			e r
				R
				e
				v i e
					w
						, indicating a
	decreasing share of inefficiency in the estimations' total residuals, points to the same
	conclusion.
				12

All correlations are significant at the one percent level.

Table 3b :

 3b Descriptive statistics and correlation of raw and corrected efficiency scores:

	F o r
		P
		e
		Translog Model 3 e r	Model 4
	Minimum Maximum Mean Median Std. deviation	Official output (3a) 0.431 0.934 0.806 0.822 0.0828	Corrected output (3b) R 0.527 e 0.937 0.827 0.836 v Official output (4a) 0.351 0.936 0.748 0.786 i e 0.0663 0.132 w	Corrected output (4b) 0.407 0.93 0.776 0.797 0.102
	Pearson	-	0.974	-	0.965
	Spearman	-	0.955	-	0.963
	All correlations are significant at the one percent level.
	This result is not trivial since the efficiency frontier shifts upwards with the inclusion
	of the shadow economy. As efficiency is a relative measure, one could as well have witnessed

a decrease in efficiency. The observed evolution of efficiency scores therefore implies that the distribution of output figures changes due to the inclusion of the shadow economy. More

This value is the standard value in the literature. Moreover,[START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF] shows that the explanatory power of aggregate production functions is little affected when a different value is used.

A thorough discussion of those assumptions can be found in[START_REF] Caselli | Accounting for cross-country income differences, in Handbook of economic growth[END_REF]. He shows that the results of development accounting are robust to more refined assumptions.

A critical survey of existing methods to estimate the shadow economy can be found in[START_REF] Schneider | Shadow Economies of 145 countries all over the world: What do we know?[END_REF].γ 1 γ 2 ... γ p Causes X

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

< O -Economic Development, Technological Change, and Growth, O47 -Measurement of Economic Growth|Aggregate Productivity < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and Growth, O50 -General < O5 -Economywide Country Studies < O -Economic Development, Technological Change, and

Appendix:

Sample of countries: Algeria, Angola, Argentina, Australia, Austria, Bangladesh, Belgium, Benin, Bolivia, Botswana, Burkina Faso, Burundi, Brazil, Cameroon, Canada, Central African Republic, Chad, Chile, China, Colombia, Congo (Republic),Costa Rica, Côte d'Ivoire, Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Ethiopia, Fiji, Finland, France, Ghana, Greece, Guatemala, Guinea, Haiti, Honduras, Hong Kong, India, Indonesia, Iran, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea (Republic), Lesotho, Madagascar, Malawi, Malaysia, Mali, Mexico, Morocco, Mozambique, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Portugal, Romania, Rwanda, Senegal, Sierra Leone, Singapore, South Africa, Spain, Sri Lanka, Sweden, Switzerland, Syria, Taiwan, Tanzania, Thailand, Togo, Tunisia, Turkey, Uganda, United Kingdom, USA, Uruguay, Venezuela, Zaire, Zambia, Zimbabwe.


Ursula Jaenichen

Gesine Stephan
email: gesine.stephan@iab.de

The Effectiveness of Targeted Wage Subsidies for Hard-to-Place Workers

Keywords: J65 -Unemployment Insurance|Severance Pay|Plant Targeted wage subsidies, evaluation Targeted wage subsidies, evaluation of labour market programmes, propensity score matching JEL-Codes: J68, J64, J65

Targeted wage subsidies paid to employers are an important element of active labour market policies in Germany. This paper uses propensity score matching to investigate their effect on the employment and unemployment rates of subsidised hard-toplace workers. In a first scenario, we estimate the average treatment effect of a subsidy on previously unemployed individuals. A second scenario analyses the effects of a subsidy on employment probabilities conditional on taking-up employment. The third scenario investigates the additional effect of a subsidy on individuals, who have participated in a short-term training measure beforehand. Summing up and in line with the literature, the results show that subsidies have a favourable effect on the employment prospects of participants.

Introduction

Long-term unemployment is still a huge problem in Germany (e.g. OECD 2006). Policies aimed at increasing the chances of reintegration of long-term unemployed persons thus deserve special attention. In a recent meta-study, [START_REF] Kluve | The Effectiveness of European Active Labour Market Policy[END_REF] concludes that it is mostly the programme type that matters for effectiveness; in particular, wage subsidies, services and sanctions seem to work. However, there are considerable differences in the design of wage subsidies.

General wage subsidies are paid permanently for all low-wage earners in an economy, regardless of their employment history. Their obverse are negative payroll taxes for employees, which have been a major vehicle used by many governments to stimulate employment. Marginal wage subsidies concern only a firm's additional employment exceeding some reference level [START_REF] Knabe | Marginal Employment Subsidization: A New Concept and Reappraisal[END_REF]. Targeted wage subsidies -or hiring subsidies [START_REF] Orszag | Designing Employment Subsidies[END_REF] -are tailored to particular groups of unemployed and usually granted for a limited time period. In the following, wage subsidies are considered to be payments to employers [START_REF] Fay | Enhancing the Effectiveness of Active Labour Market Policies: Evidence from Programme Evaluations in OECD Countries[END_REF].

This paper analyses the effectiveness of a targeted wage subsidy programme, covering a share of labour costs and paid to employers for a fixed period of time. We ask if taking up a subsidized job during the second quarter of 2002 has improved the employment prospects of participating hard-to-place workers in Germany. The programme will be described in detail in Section 2, which also discusses recent results from the literature. Section 3 presents the evaluation strategy and describes data and variables. The empirical results are depicted in Section 4. In Section 5 we draw a summary of the results and discuss their implications. A main feature of our analysis is that we extend the usual approach of estimating the effect of taking up subsidized employment compared to remaining unemployed: We also estimate the effect of receiving a subsidy on employment and unemployment rates conditional on taking up a job and conditional on having participated in a short-term training measure beforehand.

Wage subsidies are a policy that tries to affect employment via the wage rate (Hamermesh 1993, Chapter 5): They obviously reduce labour costs of a given employee for a firm. The sub- sidy can compensate the firm for a gap between a worker's productivity and his minimum wage. A temporary subsidy might have long-run positive effects on individual labour market prospects if employees are able to close the gap over time by learning on-the-job. Also, a period of subsidization might be necessary to reduce an employer's uncertainty about the employability of job applicants and might thus serve as a screening advice.

But wage subsidies for the unemployed are also often criticized (Layard et al. 1991, Chapter 10): First, several of those subsidised would have been recruited anyway, thus a deadweight loss occurs (see also [START_REF] Welters | Employer Search and Employment Subsidies[END_REF]. Second, some of those recruited will merely replace others, thus the subsidy does only achieve preferential treatment for some and a substitution effect occurs. Third, if subsidies produce an increase in employment in some firms, this might be at the expense of jobs in other firms, thus the only effect is displacement. These effects cannot be identified by our research approach. A fourth argument against employer-based subsidies -in particular vouchers handed out to the unemployed -are potential stigma effects [START_REF] Burtless | Are Targeted Wage Subsidies Harmful? Evidence from a Wage Voucher Experiment[END_REF][START_REF] Bell | Getting the Unemployed Back to Work: The Role of Targeted Wage Subsidies[END_REF]. A counterargument in favour of wage subsides is made by [START_REF] Fay | Enhancing the Effectiveness of Active Labour Market Policies: Evidence from Programme Evaluations in OECD Countries[END_REF]. He makes the point that substitution effects may not be seen as detrimental from a policy perspective, since targeted subsidy schemes are intended to "shuffle the queue" of jobseekers. Thus, targeting should lead to preferential hiring of otherwise disadvantaged workers.

Programme features and empirical evidence 2.1 Characteristics and importance of the programme

Targeted wage subsidies to employers represent a standard instrument in the bundle of active labour market policies in Germany. For a long time, training programmes (see for instance The programme we are dealing with is one of three variants of a wage subsidy to employerscalled "Eingliederungszuschuss" (EGZ) -that were in place during the period 1998 to 2003.

We concentrate on the variant for hard-to-place workers ("EGZ bei erschwerter Vermittlung"), whose target group were unemployed with severe problems of reintegration, like e. The decision to support an unemployed with an EGZ has to be reasoned in each individual case. Case managers in local employment agencies have latitude in the allowance decision as well as in the fixing of the amount and duration of the subsidy. The EGZ for hard-to-place persons could regularly account for as much as 50 percent of the monthly wage or salary and continue for at most 12 months. These limits could be exceeded in exceptional cases. As a special feature of the EGZ, a follow-up period of further employment is obligatory after the expiration of the subsidy. If a person hired with an EGZ is dismissed within this period for reasons attributable to the employer, the employer can be asked to reimburse part of the subsidy.

Selected review of the literature

A number of studies have estimated the impact of targeted wage subsidies on participants. This requires knowledge of the potential labour market prospects participants would have had with- out the help of a subsidy. Several authors constructed comparison groups of similar, but nontreated individuals using statistical matching techniques and non-experimental data (see Section 3.1). For Germany, [START_REF] Jaenichen | Lohnkostenzuschüsse und individuelle Arbeitslosigkeit[END_REF][START_REF] Jaenichen | Lohnkostenzuschüsse und individuelle Beschäftigungschancen[END_REF] and [START_REF] Bernhard | Einarbeitungszuschüsse bei Einarbeitung und erschwerter Vermittlung: Matching-Analysen auf der Basis von Prozessdaten[END_REF] used this approach and showed that different kinds of targeted wage subsidies had a positive effect on the employment prospects of previously unemployed persons. [START_REF] Dorsett | The New Deal for Young People: Effect on the Labour Market Status of Young Men[END_REF] evaluated the British "New Deal" reform for young workers. A key option available to young workers of age 18 to 24, who had been claiming job seeker's allowance for six months or more, was a voucher for a subsidy to prospective employers. The voucher covered 60 pounds per week; this amount was paid for six months. Other options were full-time education, placement in a voluntary sector organization or environmental task force or staying in an "extended gateway". His result was that in the long run -after an initial lock-in effect -the subsidy dominated all other options in preventing unemployment.

Positive results on the effectiveness of targeted wage subsidies have also been obtained in a number of studies for Sweden. Sianesi (2002) ric survival function matching estimators to demonstrate the importance of the timing of programme entry. While the studies cited so far rely on the large number of observable characteristics available in their data sets to estimate treatment effects, [START_REF] Forslund | Employment Subsidies -A Fast Lane From Unemployment to Work?[END_REF] additionally used instrumental variable difference-in-difference techniques. Independently of the method used, the results suggested that wage subsidies had a positive effect on employment probabilities of the participants.

For the State of Wisconsin, [START_REF] Hamersma | The Effects of an Employer Subsidy on Employment Outcomes. A Study of the Work Opportunity and Welfare-to-work Tax Credits[END_REF] estimated the effects of eligibility compared to near eligibility on the labour market prospects of the eligible population. The programmes analysed are the "Work Opportunity Tax Credit" and the "Welfare-to-Work Tax Credit". For both programmes employers have to apply and -if granted -claim the subsidy on their federal tax return. The former programme is targeted at new hires from certain disadvantaged groups and covers up to 40 percent of the wage rate for the first year of employment. The latter programme aims at long-term welfare recipients and reimburses 35 percent of wages in the first year and 50 percent in the second year. Using matching techniques, Hamersma found limited effects on the labour market results of the eligible population. However, her information was restricted to a period of 18 months after the subsidy had started and the numbers of individuals participating in the programme were rather small.

Few studies are based on social experiments, where treatment is allocated randomly among the unemployed [START_REF] Burtless | Are Targeted Wage Subsidies Harmful? Evidence from a Wage Voucher Experiment[END_REF], or on natural experiments, which utilize changes in legislation and apply difference-in-differences estimators to the treated group and a similar group that is unaffected by the changes [START_REF] Boockmann | Do Hiring Subsidies Reduce Unemployment Among the Elderly? Evidence from Two Natural Experiments[END_REF]. [START_REF] Burtless | Are Targeted Wage Subsidies Harmful? Evidence from a Wage Voucher Experiment[END_REF] presented the results from an early social experiment of the effectiveness of targeted wage subsidies that was conducted in Ohio during the years 1980 to 1981. Some of the job seekers were given vouchers identifying them to employers as eligible for a tax credit or for a direct cash rebate. The subsidy amounted to 50 percent of wages during the first year and 25 percent of wages during the second year of employment, up to a threshold. Burtless showed that unemployed persons with a voucher were less likely to find employment than job-seekers without vouchers. He speculated that vouchers had a stigmatizing effect and were used by employers as a screening device.

For Germany, [START_REF] Boockmann | Do Hiring Subsidies Reduce Unemployment Among the Elderly? Evidence from Two Natural Experiments[END_REF] investigated changes in the legislation regarding the EGZ for workers of 50 or older. The regular subsidy used to amount to 50 percent of the wage rate, paid in monthly rates for up to two years. In exceptional cases, the subsidy could be granted at up to 70 percent for up to five years. Two changes took place in 2002 and 2004: In 2002, eligibility for the programme -which earlier had covered only the long-term unemployed -was extended to all workers of 50 or older. In 2004, under the new EGZ, eligibility was again confined to hard-to-place persons and the duration of the subsidy was cut down to a new maximum duration of three years. The authors used a difference-in-differences estimator to compare changes in transition probabilities between the treatment group (defined as all workers of 50)

and the comparison group (comprised of slightly younger workers). Significant effects of the changes in conditions were found only for the subgroup of female workers in East Germany.

The authors concluded that increases in subsidised employment for all other groups investigated are absorbed by deadweight losses. However, only a comparatively small percentage of individuals in the age groups investigated actually received the subsidy, and changes in legislation affected mainly the duration of the subsidy.

Finally, a comparison of subsidised and non-subsidised individuals taking-up a job has been conducted by [START_REF] Cockx | Active Labour Market Policies and Job Tenure[END_REF]. They analysed temporary wage subsidies that have been paid

to employers in Belgium during 1991 and 1992. The subsidy was granted for 12 to 24 months and covered 10 to 50 percent of the wage rate; it was often targeted at particular groups. The authors utilized data from firms on their last five recruitments and estimate a duration model.

They found positive, but insignificant effects of the subsidy on job tenure. In the already mentioned study for the State of Wisconsin, [START_REF] Hamersma | The Effects of an Employer Subsidy on Employment Outcomes. A Study of the Work Opportunity and Welfare-to-work Tax Credits[END_REF] also estimated the effect of a subsidy on wages and tenure of subsidized workers, using propensity score matching. She found significantly positive effects on wages in the subsidized job (around 40 percent of the tax credit were passed through to workers in the form of a wage premium), but insignificant effects on tenure.

Summing up, a number of studies based on non-experimental data obtain the result that targeted wage subsidies improve the labour market chances of the unemployed. The few findings from social and natural experiments are more ambiguous. Across countries, there are large differences in programme sizes as well as in the amount and duration of wage subsidies. Furthermore, the implementation of programmes differs across countries. Finally, the institutional framework -for instance replacement rates and the importance of activation strategies -will also have an impact on the success of a labour market programme.

3

Evaluation approach, data and variables

The estimands of interest

We are interested in the mean effect of taking up subsidized employment during the second quarter of 2002 on the consecutive unemployment and employment rates of participants. The fundamental evaluation problem is caused by the fact that participants in labour market programmes will sort themselves or will be sorted into programmes on the basis of their current as well as of their expected labour market prospects. In the absence of an experimental design, the challenge is to find a very similar group of non-participating individuals, whose outcomes can be interpreted as counterfactual outcomes of the group of participants. We estimate these counterfactual outcomes using statistical matching techniques. Appendix A gives a formal definition of the estimated parameter and explains the applied method.

An important topic is the choice of the classification window in time, which defines participation and non-participation in a labour market programme. Following [START_REF] Sianesi | An Evaluation of the Swedish System of Active Labour Market Programmes in the 1990s[END_REF][START_REF] Sianesi | Differential Effects of Active Labour Market Programs for the Unemployed[END_REF], our comparison state is either no participation at all or participation within a period of three years after the start of the subsidy. Consequently, our estimands display the effect of taking up a subsidized job during the second quarter of 2002, compared to no or latter participation in a labour A novel feature of our analysis is that we estimate three different counterfactuals for persons entering wage subsidy programmes:

1)

The effect of taking up a subsidised job versus remaining unemployed.

2)

The effect of taking up a subsidised job versus taking up non-subsidised employment.

3)

The effect of taking up a subsidised job after a short period of on-the-job training versus participation in on-the-job training only.

The first scenario assumes that -conditional on the observed characteristics of unemployed persons -access to the wage subsidy is random. However, to place an unemployed person on a subsidized job, an employer must agree to hire her or him. Accordingly, the fact that a person has been able to get a subsidised job may as such be a hint on unobserved individual heterogeneity. However, unobserved heterogeneity will be strongly correlated with the observed explaining variables; this should hold particularly for information on an individual's labour market history [START_REF] Heckman | The Economics and Econometrics of Active Labour Market Programs[END_REF]. As we have detailed information on previous employment histories, this should capture most of the effects of unobserved individual factors. Employer characteristics may be another source of unobserved heterogeneity. Previous studies for Germany indeed find that factors like firm size, industry, sales and previous experiences with wage subsidies have an influence on the probability that firms make use of wage subsidies [START_REF] Hartmann | Lohnkostenzuschüsse und Integration schwervermittelbarer Personen in den ersten Arbeitsmarkt[END_REF][START_REF] Jaenichen | Zur Inanspruchnahme von Beschäftigungshilfen der Bundesanstalt für Arbeit -Ergebnisse des IAB-Betriebspanels[END_REF]). More recently, there is some evidence that average wages and the size of firms may influence the success of wage subsidies [START_REF] Krug | The impact of firm characteristics on the success of employment subsidies[END_REF]). Unfortunately, our data are lacking information on employers. The third scenario is suggested by the observation that subsidized employment is often preceded by a short-term firm-related training measure ("betriebliche Trainingsmaßnahme"). The question we ask is, whether there is an additional advantage of an EGZ in this situation. On the one hand, if short-term training serves as a filter for employment, only workers showing a sufficiently high performance during their training period will be offered a subsidised job. On the other hand, employers who are informed about the "true" productivity after the training period may have better arguments to bargain for a further period of subsidised employment. In this case, workers with combined participation of training and EGZ would be those who really need an integration subsidy.

Data and variables

We utilize administrative data collected and provided by the German Federal Employment Our analysis distinguishes between several subgroups of participants. First, all analyses were conducted separately by gender and region (West vs. East Germany). Furthermore, we distinguish short-term subsidies with duration of four to six months from long-term subsidies lasting from seven to twelve months. Because of small case-loads for short-term subsidies, the impact of the EGZ in the third scenario is only estimated for long-term subsidies. Since own estimates [START_REF] Zew | Evaluation der Maßnahmen zur Umsetzung der Vorschläge der Hartz-Kommission. Arbeitspaket 1: Wirksamkeit der Instrumente, Modul 1d: Eingliederungszuschüsse und Entgeltsicherung[END_REF] showed no systematic differences across groups with different durations of unemployment, we do not present results for samples stratified by unemployment duration.

We consider two binary outcome variables to describe the labour market status. Our first outcome variable indicates whether an individual is in unsubsidised employment at the beginning Table B.1 in the Appendix shows variable means of selected explanatory variables for subsidised workers as well as for our samples of potential control persons (detailed information on the variable means before and after matching can be found in [START_REF] Zew | Evaluation der Maßnahmen zur Umsetzung der Vorschläge der Hartz-Kommission. Arbeitspaket 1: Wirksamkeit der Instrumente, Modul 1d: Eingliederungszuschüsse und Entgeltsicherung[END_REF]. Subsidised persons might be regarded to be a positive selection compared to all unemployed, but as a negative selection compared to those who have been hired into a regular unsubsidised job. The sample of individuals, who do not take up a subsidised job after having completed a training measure, might have some labour market advantages compared to those who receive a subsidy later.

Participants in East Germany have on average a better qualification than those in West Germany. This reflects mainly the fact that the average unemployed person in East Germany is much better qualified; and this is also the case for the population average (Autorengruppe Bildungsberichterstattung 2008, 236). Furthermore, participants in East Germany have less health problems and have more often participated in programmes during their employment history.

As we have already discussed in detail in Section 3.1, we are confident that unobserved individual heterogeneity should not be a major problem for our analysis.

Empirical results

Effect of a subsidy on the treated

In the first scenario, we estimate the average effect of the EGZ on the employment prospects of previously unemployed persons. The counterfactuals are employment and unemployment rates when participating never or only later in a labour market programme. Table 1 displays in Panel IV mean standardized biases before and after matching. The bias reduction obtained through the matching procedure is on average slightly less than 80 percent, while the absolute value of the mean standardized bias after matching never exceeds the value of 5. Due to these results the quality of the matching seems quite satisfactory.

Panel I and II of Table 1 summarize the results three years after programme start, documenting the share of treated and of matched control persons in regular unsubsidised employment, the share that is not unemployed (or in a labour market measure) as well as average treatment effects on the treated. The evolution of the estimated average treatment effects over time is displayed in Figure 1. Plots above the abscissa have to been interpreted as a "success" of the particular programme.

Figure 1 shows for the period of subsidization and for the compulsory period of further employment that treated individuals were less often in unsubsidised employment and have less often avoided unemployment. These locking-in effects are a necessary side-effect of the construction of the outcome variables. We find large and significant positive effects of the treatment on the treated immediately after the end of the support by the programme, which, however, decline slightly over time.

Three years after the start of subsidization, the share in "regular unsubsidised employment" is still 0.25 to 0.42 higher in the treated group than in the matched comparison group. In other words, we estimate that without treatment 25 to 42 percentage points of the treated would not have been regular employed. Turning to our second outcome variable, the difference in the shares "not unemployed and not in measure" varies between 0.14 and 0.28; thus 14 to 28 additional percentage points of the treated would have been unemployed without treatment.

The striking difference between both outcome variables results from a different share of individuals with an unknown state in the treated and the matched comparison group (Panel III of Table 1). This implies that a higher percentage of untreated individuals withdraw from the labour market as discouraged workers. Thus the subsidies help to activate hard-to-place individuals, who might otherwise have withdrawn from the labour market.

Comparisons of estimates of the treatment effect between the different groups investigated must be interpreted with caution, since characteristics of group members differ for each group (see Table 1). Nonetheless, some results should be mentioned:

• Across comparison groups, the average outcome "unsubsidised employment" (Panel I of Table 1) does not differ remarkably by gender or region, but is slightly smaller for the longterm subsidy. However, across treated groups the grant of an EGZ seems to have had a particularly large effect on employment opportunities of female workers, which was even stronger in East Germany. Accordingly, estimated treatment effects are much higher for female than for male workers.

• For the outcome "not unemployed and not in measure" (Panel II of Table 1), we observe a striking result for the matched control sample of females from West Germany -they are less often unemployed than females from East Germany or males. An obvious explanation is that housework has always been a rather accepted alternative for women in West Germany, which facilitates withdrawing from the labour market. In contrast, women in East Germany are much more attached to the labour market. This is partly a result of the ). Looking at the treatment groups, the outcome is again more advantageous for female workers. The net result is that the estimated treatment effect is highest for the group of females in East Germany and does not differ much among the other groups.

• Comparing the recipients of short-term and long-term EGZ, labour market outcomes are always more favourable for treated individuals who received a short EGZ as well as for their matched control persons. This is not surprising, since the duration of the subsidy should be a function of placement difficulties. However, estimated average treatment effects are rather similar for short-and long-term subsidies at each point of time after the employment promotion had expired (Figure 1).

A deadweight loss in a narrower sense only occurs when the same individual would have got the same job without the help of the EGZ. Data and technique applied do not provide a measure for this effect. Some studies for other labour market measures interpret the share of the matched comparison group that has successfully found an unsubsidised job as a measure of the deadweight loss in a wider sense (Winterhager et al. 2006, 513). In this sense, the deadweight accompanying EGZ would be around 20 percentage points (Panel I of Table 1).

Effect of a subsidy conditional on taking up a job

The previous estimates referred to the combined effect of receiving a subsidy and taking a job, while the second scenario investigates solely the effect of the subsidy, conditional on having found a -subsidised or unsubsidised -job. The results of the estimates can be found in Table 2 and Figure 2 (note that only significant effects are displayed in the figures). The information on the mean standardized bias in Panel IV of Table 2 indicates again a satisfactory matching quality, with a mean bias reduction of more than 80 percent through the matching procedure. Figure 2 shows clearly the initial lock-in effect of subsidization. However, after the subsidy and the obligation period have expired, the average treatment effect is rather small, follows no obvious trend and is very similar for short-term and long-term subsidies: Three years after the subsidy started, the effect is insignificant for all groups except for female workers in East Germany, which fare slightly better, if they have started in a subsidised employment relationship (Panel I and II of Table 2). Estimated treatment effects do not differ remarkably between both outcome variables; around 10 percentage points of the treatment group as well as of the matched control sample "vanish" into an unobserved labour market state.

In choosing the members of the matched comparison group, we focus on their labour market success -finding an unsubsidised job. We control for a number of observable characteristics of workers, which should also account at least partly for unobserved characteristics (see Section 3.2). However, the matched comparison group will differ from the treated group at least regarding some characteristics of the job. Jobs taken up by unsubsidised workers are probably -in terms of realised or perceived productivity -a positive selection compared to jobs taken up by subsidised workers. The results show, however, that employment prospects of individuals taking-up subsidised employment are -in the longer run -not worse than those of individuals, who entered an unsubsidised employment relationship.

Effect of a subsidy conditional on participation in a short training measure

In the last scenario, we estimate the average effect of the EGZ on supported individuals conditional on having participated in a firm-related short-term training measure beforehand. The analysis thus hinges on having gained at least some work experience within a firm during the last quarter. However, we cannot distinguish between situations, where employers have already Table 3 and Figure 3 display the main results. The mean standardized bias (Panel IV of Table 3) is reduced considerably through matching for three of four groups, while the bias reduction for female unemployed in West Germany is below 50 percent. The main conclusions are:

• Locking-in effects are rather large for the group of individuals, who take up a subsidised job after a short-term training measure (Figure 3): Matched control persons find regular employment rather quickly and/or avoid unemployment directly after their training measure.

• Labour market outcomes of unemployed, who participated in a short-term training measure and received a wage subsidy (Table 3, Panel I and II), are rather similar to the results of all subsidised individuals (Table 1, Panel I and II for the long-term subsidy). However, labour market outcomes of the matched control sample are much more favourable for previous participants in a short-term training measure. Accordingly, Panel I in Table 3 shows positive treatment effects -in the range of 14 to 31 percentage points -of a subsequent wage subsidy on the probability to be in regular (unsubsidised) employment three years after the start of the subsidy. But these effects are smaller than those found in Panel I of Table 1, which

were not conditional on the participation in a short-term training measure.

• Panel II in Table 3 implies that a subsequent wage subsidy increases the probability to avoid unemployment in East Germany. However, for West Germany the analysis finds no additional significant effect of a wage subsidy on the avoidance of unemployment, if a shortterm training measure has already taken place.

One explanation might be that (rather cheap) short-term training measures within firms already have a favourable effect on the labour market possibilities of participants; the effect may sometimes be of such a size that a subsequent EGZ does not exert any additional impact. On the other hand, particularly individuals who were found less productive during their training period may have received a subsequent subsidy. We apply matching methods to estimate the average effect of targeted wage subsidies for hardto-place workers in Germany. Our results show that wage subsidies may increase the employment prospects of supported workers, compared to being never in any programme or participating only later, to a considerable amount. For previously unemployed individuals, three years after the start of the programme, the share in regular employment is 25 to 42 percent higher in the treatment group than in the matched comparison group. A comparison between groups of unemployed persons taking subsidised employment with matched comparison groups of individuals moving directly into unsubsidised employment indicates that differences in the employment prospects are rather small after three years. Finally, participation in short-term training measures goes hand in hand with better labour market prospects compared to the entire sample of unemployed. This may result, however, from the previous training as well as from the selection into these measures. As a consequence, the effect of subsidization on participants in a previous short-term training measure is more modest: The share in regular employment increases by 14 to 31 percentage points, if a short-term training measure is followed by a wage subsidy.

However, some points deserve further discussion. Comparing the estimated impacts in the first two scenarios, one may be tempted to doubt the effectiveness of subsidies: The comparison group in the second scenario is characterised by a comparable distribution of characteristics, but its members entered unsubsidized employment directly. So, was it really necessary to support those who actually got the subsidy? A simple answer would be that a large part of the subsidized jobs are just deadweight effects. Another explanation is that heterogeneity in the matches for workers with the same characteristics is responsible for these results. Thus, the same worker, who needs a subsidy to get one job, will be fully productive in another job. A line for future research of course is to gather more information on jobs (while we analysed the workers' side of the match only). consuming decision for or against an EGZ may readily be postponed. There is some evidence from case studies in selected agencies that short training measures in firms and the EGZ were sometimes seen as substitutes, thus the choice between them was rather an incidental matter (ZEW et al. 2006, 61).

To conclude, our findings are in line with results from the literature; most studies that estimate effects of targeted wage subsidy programmes on the treated find positive effects on individual employment probabilities. For any assessment of the benefits of wage subsidies, it should be noted that the methods applied in this paper do not identify deadweight loss or potential displacement and substitution effects. In this sense [START_REF] Fay | Enhancing the Effectiveness of Active Labour Market Policies: Evidence from Programme Evaluations in OECD Countries[END_REF] emphasises that careful controls are an important part of designing wage subsidy programmes. Otherwise, there is a risk that firms use schemes as a permanent subsidy to their workforce. Note: All estimated treatment effects are significant at = 0.05. Short-term subsidies are paid for 4 to 6 months, while long-term subsidies are paid for 7 to 12 months. Small differences in the number of observations compared to Table B.1 result from the fact that each matched control person was assigned the date of the treatment start of his/her treated counterpart. If the matched control person was no longer unemployed on this date (which is the case for few observations, since we analyse only entries in a period of three months and also match on the duration of unemployment), the matched pair was dropped from further analysis. of the estimated propensity scores) can be observed for both participants and non-participants [START_REF] Heckman | The Economics and Econometrics of Active Labour Market Programs[END_REF].

F

In this paper, we use nearest-neighbour matching with replacement and apply the STATAmodule psmatch2 [START_REF] Leuven | psmatch2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing[END_REF]. The matching procedure chooses for each participant the non-participant with the most similar propensity score as a comparison person. Replacement implies that a non-participant can be used more than once in the matching procedure. Following

(2), the programme impact is estimated as the mean difference in the outcomes of both groups.

To obtain an estimate for the variance of the estimator a formula suggested by [START_REF] Lechner | Identification and Estimation of Causal Effects of Multiple Treatments under the Conditional Independence Assumption[END_REF] is used, which accounts for the possible variance-inflating effect of the multiple uses of nonparticipants. As an indicator for matching quality, we compute the mean standardized bias

Fitzenberger/

  [START_REF] Fitzenberger | Employment Effects of the Provision of Specific Professional Skills and Techniques in Germany[END_REF] and job creation in the public sector (see for instance[START_REF] Caliendo | Identifying Effect Heterogeneity to Improve the Efficiency of Job Creation Schemes in Germany[END_REF] used to be the largest programmes in Germany. Wage subsidies gained importance first in East Germany during the economic restructuring following the reunification and thereafter again in the late nineties.

  used matching techniques to compare the effects of participation in different labour market programmes in Sweden. She looked at individuals who became unemployed during 1994. Employers could claim subsidies for adults with unemployment duration of at least 6 months; the grant covered 50 percent of labour costs up to a fixed amount. According to her results, recruitment subsidies were the only scheme that improved the individual probability to get and keep a job. Carling/Richardson (2004) similarly compared the effectiveness of different programmes in reducing the unemployment duration of participants in Sweden, but estimated a hazard rate model instead. Their results were again in favour of subsidised work and training provided by firms, compared to classroom vocational training.[START_REF] Fredriksson | Dynamic Treatment Assignment -The Consequences for Evaluations Using Observational Data[END_REF] and[START_REF] Forslund | Employment Subsidies -A Fast Lane From Unemployment to Work?[END_REF] analysed the effectiveness of a targeted, time-limited wage subsidy scheme in Sweden. The scheme under consideration was implemented in 1998 and granted up to 50 percent of wages for a maximum of six months to firms who recruited long-term unemployed.[START_REF] Fredriksson | Dynamic Treatment Assignment -The Consequences for Evaluations Using Observational Data[END_REF] applied nonparamet-

  Sianesi and also[START_REF] Fredriksson | Dynamic Treatment Assignment -The Consequences for Evaluations Using Observational Data[END_REF] have pointed out, labour market programmes in Europe are ongoing and any unemployed is a potential participant. Individuals may decide against entering a programme because they expect to find a job soon. Thus selecting a comparison group consisting solely of individuals who never participated in any programme during the observational period implies to condition on their expected future outcomes (see Frederiksson/Johansson 2004, Proposition 4).

  has been presented less often in the literature: We compare participants supported with EGZ to persons who have left unemployment for regular employment at the same time. Again, individual heterogeneity could exist, since treated individuals have only been able to find a subsidised job. Here the arguments given above apply again: Information on the previous employment history should absorb most of individual heterogeneity. Still, employer heterogeneity may have a distortive effect on the results.

  Agency. The newly constructed research data set Integrated Employment Biographies (IEB) contains detailed information on socio-demographic characteristics, programme participation, employment and unemployment histories. Hummel et al. (2005) describe a sample of the database that is open for public use through the Research Data Center of the Federal EmploymentAgency. The combination of information on programme episodes and on employment episodes allows us to distinguish between times in subsidised employment (through a wage subsidy or in a public job creation measure) and regular employment. Since the data flows integrated in the IEB stem from different sources, we had to correct several inconsistencies.

  For our first and second scenario, the treatment sample consists of all individuals taking up subsidised employment during the second quarter of 2002, who have been unemployed beforehand (these were about 85 percent of all individuals receiving an EGZ during this period). Thus, our analysis avoids problems of dynamic programme entry by sampling only persons, who started their subsidised employment during a short interval of time. The analysis of the third scenario is based on a sample of all individuals that have participated in firm-related short-term training (with a maximum duration of three months) during the first half-year of 2002 and have taken up a subsidised job within three months after the training programme has ended. From those receiving an EGZ in the second quarter of 2002, about 20 percent had previously participated in short-term training; 64 percent of these measures had taken place within establishments. Special data sets were built up to get a pool of potential control persons for each scenario. For the first scenario, comparison groups were taken from monthly 2.5-percent-samples of entries into unemployment since 2000. For the second scenario, we utilize a 75-percent-sample of entries into employment from the first half-year of 2002. Finally, a sample of 310,000 exits from short-term training measures between October 2001 and June 2002 forms the basis for the construction of comparison groups for the third scenario.

  . The second outcome variable shows whether a person has successfully avoided unemployment at the beginning of a month (he/she is not registered as unemployed or as participating in a labour market programme). Beyond the period of subsidization itself, we interpret the follow-up period, during which the employer is obliged to sustain the employment relationship, as a further period of programme participation. If we observe differences in estimated treatment effects between the two outcome variables, than the share of individuals in the treated group and in the comparison group switching to an "unobserved" state differs, reflecting in most cases a withdrawal from the labour market for a period of time (examples are home-time or early retirement). To compute the outcomes of matched comparison persons, we assign to them the starting date of the treated counterparts in the first scenario. In the second scenario, outcomes of comparison persons are measured beginning with the month of entry into employment. In the third scenario, we assign a starting date to matched comparison persons by adding the time span between the participant's training programme exit and his entry into the EGZ to the control's end date of the training programme. The non-testable conditional independence assumption requires the observation of all explaining variables that determine selection into the programme as well as the outcome in the case of non-participation. The selection into the programme is the result of individual choice, of caseworkers' assessments and negotiation strategies as well as of firms' choices and behaviour. We model selection using the following observable information on individuals: a) Socio-demographic characteristics (nationality, age, education, health and -for female workers -information on the family status), b) Variables on the five-year-history prior to the respective unemployment spell (participation in measures and years in unsubsidised regular employment), c) The timing of entry into unemployment, d) Information on the regional labour market situation (performance cluster suggested by categorized as dummy variables and measured at the beginning of the subsidised employment spell. For members of the comparison groups, time-varying variables are measured in the midth of the first quarter 2002.

  filtered the more suited candidates for a subsidised job from training participants, and situations, where employers claim the subsidy because a worker's lower productivity has become visible during the training period.

  the third scenario -even if the estimated impact is positive -raise the question to what degree short training measures within firms might obtain results similar to an EGZ (at much lower costs). In addition to the previously raised argument of heterogeneity in the job matches, selectivity with respect to further EGZ support might occur, since employers learn about a participant's productivity during the training period. It is also plausible that case managers utilize short training measures in a kind of trial and error process. If a cheaper training measure suffices to integrate a previously unemployed person into a firm, than the more time-

  g. long-term unemployed or disabled persons. Of the other two variants, one was granted for special training requirements, while the other was targeted at workers of age 50 and older (in Germany unemployment rates are high and reemployment-chances are low for the over 50s). A legal reform of the EGZ was enacted in 2004, when the three former variants were collapsed into a single wage subsidy for hard-to-place workers.

The EGZ has been characterized by fairly high numbers of participants from 2001 to 2003, while other wage subsidy programmes phased out in this period. A peak was reached in 2002 with roughly 190,000 entries into one of the three variants of the EGZ and 80,000 entries into the EGZ for hard-to-place workers. As a consequence of the high stock of participants, total expenditure for the EGZ reached a maximum of 1.3 billion Euro in 2003. Entries dropped to 134,000 in 2005, but reached a new peak with nearly 250,000 entries in 2007.

  Common support (seeAppendix A) is achieved for all treated individuals in our sample. The validity of the stable unit treatment value assumption (see also Appendix A) depends mainly on the size of the programme. A large-scale programme can be expected to change the supply and demand conditions in some segment of the labour market or the labour market as a whole. While (especially in East Germany) the use of wage subsidies has been very intensive in some periods, the importance of subsidized employment compared to regular employment in the period of our study is fairly limited. As TableB.2 shows, the most frequent transition out of unemployment is still into regular employment. Transitions into (temporarily) subsidised employment like the EGZ accounted for only 2.6 percent of all unemployment exits in 2004.

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Table 1 :

 1 Individuals taking up a subsidised job (Treated) and matched unemployed persons (Controls): Labour market status, estimated average treatment effect on the treated (ATT), mean standardized bias before and after matching and bias reduction three years after programme start during the 2 nd quarter of 2002

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Table 2 :

 2 Individuals taking up a subsidised job (Treated) and matched persons taking up an unsubsidised job (Controls): Labour market status, estimated average treatment effect on the treated (ATT), mean standardized bias before and after matching and bias reduction three years after programme start during the 2 nd quarter of 2002

					Short-term subsidy		Long-term subsidy
				Male	Female	Male	Female	Male	Female	Male	Female
				West	West	East	East	West	West	East	East
	I.	Share in regular unsubsidised employment	Treated Controls	0.50 0.49	0.57 0.60	0.48 0.47	0.64 0.50	0.44 0.46	0.56 0.56	0.49 0.45	0.60 0.52
			ATT	n.s.	n.s.	n.s.	0.14	n.s.	n.s.	n.s.	0.08
		Share not unemployed	Treated	0.62	0.72	0.60	0.70	0.57	0.70	0.58	0.68
	II.	and not in labour market	Controls	0.61	0.74	0.59	0.62	0.59	0.71	0.55	0.64
		measure	ATT	n.s.	n.s.	n.s.	n.s.	n.s.	n.s.	n.s.	0.04
	III.	Share with unknown destination (Diff. II-I)	Treated Controls	0.12 0.12	0.15 0.15	0.11 0.12	0.06 0.12	0.13 0.14	0.14 0.15	0.09 0.10	0.09 0.12
			Before 15.85 13.00 16.45 14.66 20.75 15.41 19.94 14.38
	IV. Mean standardized bias	After	1.77	3.10	2.53	4.29	1.91	2.53	1.45	2.06
			Reduction	0.89	0.76	0.85	0.71	0.91	0.84	0.93	0.86
	V. Observations		1398	657	372	253 2044	1064 3580	3379
	Note: n.s. = not significant at = 0.05. Short-term subsidies are paid for 4 to 6 months, while long-term
	subsidies are paid for 7 to 12 months.

Table 3 :

 3 Individuals taking up a subsidised job following a short-term training measure (Treated) and matched persons that have participated solely in a shortterm training measure (Controls): Labour market status, estimated average treatment effect on the treated (ATT), mean standardized bias before and after matching and bias reduction three years after programme start during the 2 nd quarter of 2002

				Long-term subsidy
				Male	Female	Male	Female
				West	West	East	East
	I.	Share in regular unsubsidised employment	Treated Controls	0.48 0.34	0.59 0.38	0.52 0.29	0.65 0.34
			ATT	0.14	0.21	0.23	0.31
		Share not unemployed	Treated	0.58	0.67	0.59	0.69
	II.	and not in labour market	Controls	0.53	0.65	0.39	0.44
		measure	ATT	n.s.	n.s.	0.20	0.25
	III.	Share with unknown desti-nation (Diff. II-I)	Treated Controls	0.10 0.19	0.08 0.27	0.07 0.10	0.05 0.11
			Before 12.39 11.36 10.47 10.83
	IV. Mean standardized bias	After	3.14	6.06	1.29	2.06
			Reduction	0.75	0.47	0.88	0.81
	V. Observations		285	117	537	551
	Note: n.s. = not significant at = 0.05. Long-term subsidies are paid for 7 to 12 months.

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Table B .

 B Short-term subsidies are paid for 4 to 6 months, while long-term subsidies are paid for 7 to 12 months. 2: Transitions from unemployment during the year 2004: Employment states following unemployment exits in 2004 Source: Own calculations based on[START_REF] Rothe | Wege aus der Arbeitslosigkeit -Wege in die Beschäftigung. Eine Analyse anhand der Arbeitskräftegesamtrechnung[END_REF].

												Page
								Germany	West	East
		Transition to ...					in 1000		in %	in 1000	in %	in 1000	in %
	I.	Labour Market Programmes					1678		29 1000	25	678	39
		• Wage Subsidy						151		3	78	2	73	4
		• Self-Employment (with assistance)						272		5	186	5	87	5
	Male • Training Programme (short-and long-term measures) Variables (0 = no, 1 = yes) S L U E • Public Job Creation	LM	M	987 267	S	17 L 5	650 Female 16 U E 86 2	337 LM 181	19 M 10
	West Germany II. Employment Individual Characteristics Foreign nationality • Regular Employment Age 25 to 29 • Mini-Jobs (max. 360 €/month) 0.15 0.20	0.16 0.16	0.21 0.16	0.16 0.19	0.13 0.19	2105 0.12 0.07 1830 0.21 0.13 252	37 1517 0.10 0.16 32 1305 0.10 0.12 4 192	38 0.10 32 0.15 5	588 0.14 525 0.13 60	34 30 0.08 0.16 3
	Age 30 to 34 Age 35 to 39 • Self-Employment (without assistance) 0.19 0.19 0.23 0.21	0.17 0.17	0.21 0.20	0.16 0.20	0.21 0.21	0.16 0.26 23	0.20 0.23 0	0.15 0.17 20	0.18 0.20 0	0.24 0.21 4	0.20 0.23 0
	F o r P e e r R e v i e w 0.18 0.22 0.15 0.16 0.25 0.16 0.20 0.15 0.16 0.12 0.11 0.17 0.11 0.19 0.04 0.04 0.10 0.08 0.02 0.08 0.05 0.01 0.01 0.08 0.04 0.01 0.03 0.01 0.00 0.00 0.04 0.01 ---Lower secondary degree (9 years) or less, Age 40 to 44 Age 45 to 49 Age 50 to 54 Age 55 to 59 Age 60 to 64 no vocational training 0.37 0.36 0.38 0.30 0.34 0.28 0.24 Medium secondary degree (10 years), no vocational training 0.02 0.03 0.03 0.02 0.03 0.03 0.04 Vocational training 0.51 0.50 0.47 0.57 0.53 0.57 0.59 Highest secondary degree (12-13 years) 0.06 0.07 0.07 0.06 0.06 0.09 0.09 University degree 0.04 0.04 0.05 0.05 0.04 0.04 0.04 Health problems 0.18 0.19 0.21 0.10 0.21 0.16 0.15 Disabled at least 50% 0.01 0.02 0.04 0.02 0.04 0.08 0.02 Five-year-history Measure of active labour market policy 0.54 0.57 0.38 0.25 1.00 1.00 0.56 No unsubsidised regular employment 0.09 0.13 0.17 0.05 0.15 0.10 0.16 Up to 1 year in regular employment 0.16 0.21 0.15 0.07 0.25 0.15 0.16 1-2 years in regular employment 0.18 0.21 0.15 0.10 0.19 0.16 0.14 2-3 years in regular employment 0.20 0.19 0.16 0.14 0.19 0.16 0.19 3-4 years in regular employment 0.24 0.22 0.19 0.27 0.18 0.20 0.24 4-5 years in regular employment 0.13 0.05 0.18 0.36 0.05 0.22 0.11 Number of observations 1398 2044 69393 113584 285 10321 657 East Germany Individual Characteristics Foreign nationality 0.03 0.04 0.05 0.03 0.01 0.01 0.02 Age 25 to 29 0.16 0.17 0.13 0.14 0.20 0.17 0.11 Age 30 to 34 0.17 0.20 0.14 0.17 0.18 0.17 0.21 Age 35 to 39 0.23 0.21 0.16 0.19 0.20 0.19 0.25 Age 40 to 44 0.24 0.22 0.17 0.18 0.25 0.18 0.23 Age 45 to 49 0.20 0.19 0.15 0.16 0.16 0.15 0.18 Age 50 to 54 0.01 0.01 0.12 0.10 0.01 0.10 0.02 Age 55 to 59 -0.00 0.09 0.05 0.00 0.03 -Age 60 to 64 -0.00 0.04 0.01 ---Lower secondary degree (9 years) or less, no vocational training 0.08 0.10 0.14 0.07 0.07 0.07 0.04 Medium secondary degree (10 years), no vocational training 0.03 0.03 0.03 0.02 0.02 0.02 0.02 Vocational training 0.82 0.80 0.74 0.84 0.83 0.82 0.83 Highest secondary degree (12-13 years) 0.04 0.03 0.04 0.03 0.04 0.04 0.07 University degree 0.04 0.03 0.05 0.03 0.03 0.05 0.04 Health problems 0.10 0.11 0.16 0.07 0.11 0.09 0.11 Disabled at least 50% 0.01 0.00 0.02 0.01 0.00 0.03 0.01 Five-year-history Measure of active labour market policy 0.58 0.57 0.55 0.37 1.00 1.00 0.72 No unsubsidised regular employment 0.07 0.08 0.14 0.04 0.09 0.07 0.19 Up to 1 year in regular employment 0.16 0.15 0.20 0.08 0.14 0.16 0.31 1-2 years in regular employment 0.13 0.19 0.17 0.11 0.21 0.16 0.14 2-3 years in regular employment 0.22 0.23 0.16 0.15 0.20 0.17 0.13 3-4 years in regular employment 0.31 0.30 0.18 0.26 0.30 0.22 0.16 4-5 years in regular employment 0.11 0.06 0.16 0.37 0.06 0.22 0.07 Number of observations 372 3580 42832 58803 537 7900 253 o r P e e r R e v i e w III. Other (educational system, non-participation) 1972 Note: F IV. Number of Spells 5754	0.22 0.20 0.05 0.01 0.00 0.22 0.05 0.55 0.11 0.06 0.13 0.02 0.61 0.17 0.20 0.17 0.17 0.23 0.05 1064 0.02 0.10 0.22 0.24 0.23 0.20 0.01 0.00 -0.05 0.04 0.81 0.06 0.04 0.08 0.00 0.70 0.19 0.26 0.18 0.17 0.16 0.03 3379 34 1510 0.16 0.14 0.12 0.10 0.03 0.35 0.05 0.45 0.09 0.07 0.19 0.04 0.34 0.23 0.12 0.13 0.15 0.17 0.19 45610 0.04 0.09 0.14 0.16 0.17 0.16 0.15 0.12 0.02 0.14 0.04 0.72 0.05 0.05 0.15 0.02 0.64 0.27 0.26 0.15 0.12 0.11 0.09 31829 100 4026	0.18 0.14 0.09 0.04 0.01 0.25 0.04 0.52 0.11 0.07 0.10 0.02 0.31 0.10 0.09 0.13 0.15 0.21 0.32 58798 0.02 0.11 0.15 0.20 0.20 0.17 0.11 0.05 0.00 0.08 0.04 0.77 0.06 0.06 0.07 0.02 0.53 0.12 0.17 0.17 0.18 0.17 0.18 25958 37 100 1728 0.18 0.21 0.03 --0.21 0.03 0.62 0.08 0.07 0.14 0.03 1.00 0.17 0.22 0.15 0.14 0.26 0.06 117 0.01 0.08 0.21 0.29 0.23 0.18 0.01 --0.04 0.03 0.86 0.04 0.03 0.05 0.01 1.00 0.21 0.28 0.17 0.18 0.13 0.03 551 462	0.18 0.13 0.08 0.02 -0.20 0.05 0.54 0.14 0.07 0.14 0.08 1.00 0.16 0.15 0.15 0.15 0.18 0.22 5561 0.01 0.12 0.19 0.22 0.20 0.16 0.09 0.03 -0.06 0.03 0.80 0.06 0.05 0.08 0.04 1.00 0.18 0.26 0.18 0.13 0.12 0.12 4918 27 100
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(MSB, Rosenbaum/Rubin 1983)

between each treated group and its matched comparison group for each variable from X. The standardized bias of a covariate is defined as the difference of means in the treated and matched control sample, divided by the square root of the average sample variance. A lower value of the MSB indicates more similarity between both groups.

34 of 34 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The project has been part of the Module 1d of the evaluation of the Hartz reforms. We are grateful for financial support by the German Federal Ministry for Labour and Social Affairs (BMAS), to Sarah Bernhard and to Matthias Schäffer for valuable research assistance, to Katja Wolf and an anonymous referee for helpful hints, and to all our cooperating project partners from IAB, IAT and ZEW for helpful discus-

Appendix A: Method

The potential outcome approach [START_REF] Rubin | Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies[END_REF][START_REF] Lechner | Earnings and employment effects of continuous off-the-job training in East Germany after Unification[END_REF][START_REF] Heckman | The Economics and Econometrics of Active Labour Market Programs[END_REF]) assumes two hypothetical outcomes for every person. Y 1 is the potential outcome if a person participates in a programme, Y 0 is the potential outcome in the case of non-participation. The binary variable D t distinguishes participants (D t = 1) from non-participants (D t = 0). Participants have entered the EGZ programme during a month t of the second quarter of 2002. The stable unit treatment value assumption requires that no spillover effects take place [START_REF] Rosenbaum | The Central Role of the Propensity Score in Observational Studies for Causal Effects[END_REF].

The parameter we estimate is the mean effect of taking up subsidized employment during the analyzed quarter on the employment prospects of participants. It is given by the expected difference in an individual's two potential outcomes in t + h, where h = 0…36 is measured in months since entry into the subsidized job:

To estimate E[Y 0 t+h | (D t =1)] -the counterfactual average outcome of participants in the case of non-participation -matching methods choose a comparison group of non-participants under the assumption of unconfoundedness [START_REF] Rosenbaum | The Central Role of the Propensity Score in Observational Studies for Causal Effects[END_REF] or conditional independence [START_REF] Lechner | Earnings and employment effects of continuous off-the-job training in East Germany after Unification[END_REF]): Conditional on a vector X -containing all variables that jointly influence participation and outcomes -the outcome in the case of non-participation should not differ between participants and comparison persons. An estimator for (1) is then given by

Propensity score matching additionally uses the fundamental result from [START_REF] Rosenbaum | The Central Role of the Propensity Score in Observational Studies for Causal Effects[END_REF], and conditions simply on participation probabilities P(X) = P(D t = 1 | X): In a first step, propensity scores for participants and non-participants are estimated -for instance by a probit model -using the vector X as exogenous variables. The second step consists of a selection of a comparison group such that the distributions of the propensity scores are similar (balanced) for participants and controls. "Common support" requires that the realizations of X (and the values

Appendix B: Additional tables